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The role of mucus in the locomotion and adhesion of the pulmonate slug, Ariolimax Columbianus Denny, Mark William 1979

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THE ROLE OF MUCUS IN THE LOCOMOTION AND ADHESION OF THE PULMONATE SLUG, ARIOLIMAX  COLUMBIANUS.  by  MARK WILLIAM DENNY B.Sc.  Duke U n i v e r s i t y ,  1973  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ZOOLOGY  We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA June, 1979  O Mark W i l l i a m  Denny, 1979  In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e a t the U n i v e r s i t y of B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree that permission  f o r extensive copying of t h i s t h e s i s  f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by h i s r e p r e s e n t a t i v e s .  by the Head o f my Department o r  It i s understood that copying or p u b l i c a t i o n  o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my written  permission.  Department o f  P o t a t o  The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  ABSTRACT  Gastropod foot.  snails  move u s i n g a s i n g l e  F o r many g a s t r o p o d s  provided  by m u s c u l a r  of the f o o t , substratum  appendage - t h e  t h e power o f l o c o m o t i o n i s  waves moving a l o n g  the v e n t r a l  t h e f o r c e o f t h e s e waves b e i n g c o u p l e d  by a t h i n  g l u e which causes  layer  of mucus.  surface to the  T h i s mucus a c t s as a  the animal t o adhere  t o t h e s u r f a c e upon  which i t c r a w l s , b u t n o n e t h e l e s s a l l o w s f o r w a r d  movement o f  the animal.  In f u l f i l l i n g  some u n u s u a l  properties.  and  p r o p e r t i e s o f t h e p e d a l mucus o f t h e p u l m o n a t e  physical  slug the  T h i s study examines the c h e m i c a l  A r i o l i m a x columbianus role The  p e d a l mucus o f \A. c o l u m b i a n u s water r e s t r a i n e d  molecular  weight  accounts  influence  both  The measured short  nature o f the molecule  of low i o n i c  by d i s u l f i d e  b o n d s between p r o t e i n m o i e t i e s ,  (hydrophobic  interactions  and/or  molecules.  p r o p e r t i e s o f t h e p e d a l mucus were  i n shear.  time  This  The g e l network i s  bonds) between g l y c o p r o t e i n physical  strengths.  causing  f o r the glycoprotein's a b i l i t y t o  by "weak bonds"  hydrogen  of a high  The g l y c o p r o t e i n i s a  a l a r g e volume o f w a t e r .  stabilized and  t h e charged  to swell i n solutions  i s a gel consisting  by a network formed  glycoprotein.  polyelectrolyte;  swelling  , and r e l a t e s t h e s e . p r o p e r t i e s t o  o f mucus i n l o c o m o t i o n .  of 96-97%  it  t h i s f u n c t i o n t h e mucus must show  At shear r a t i o s  o f l e s s t h a n 5, and o v e r  p e r i o d s , t h e g e l shows t h e p r o p e r t i e s o f a  viscoelastic  solid.  G» i s 100 N/m  2  and t a n d i s 0.008; b o t h  are of  virtually time  constant  from  0.1  - 100 Hz.  the g e l s t r e s s r e l a x e s without  indicating  Over l o n g  periods  reaching e q u i l i b r i u m ,  t h a t t h e weak bonds o f t h e g e l network  allow the  network t o flow  under  stress.  At a s h e a r  ratio  o f about 5 t h e g e l n e t w o r k y i e l d s as  weak bonds a r e b r o k e n ,  and w i t h  mucus a c t s a s a v i s c o u s f l u i d poise.  I f this  fluid  g e l network w i l l  f u r t h e r deformation the  with  i s allowed  a viscosity  t o stand  process  result,  t h e mucus a g a i n a c t s a s a s o l i d .  begins  c a n be r e p e a t e d These p h y s i c a l  gastropod  form  i n much  numerous  has  " h e a l e d " and, as a s o l i d ,  parts of the foot  The mucus t h u s for effective  with for  of  recorder.  The t h i c k n e s s o f  These d a t a ,  p r o p e r t i e s of pedal  under a c r a w l i n g s l u g . these  columbianus  f r e e z i n g , and  crawling slugs.  physical  measuring  t h e mucus  locomotion.  t h e c o n s t r u c t i o n o f a model p r e d i c t i n g  actually  Under  a c t s as a m a t e r i a l r a t c h e t  adhesive  sectioning,  motion.  (the interwaves)  was measured by g u i c k l y  t h e measured  operating by  p o r t i o n s o f the f o o t  s e r v e s a s an e f f e c t i v e  using a video tape  t h e mucus l a y e r subsequently  "yield-heal"  suited to  forward  p r e c i s e movements o f t h e f o o t  were measured  This  and, a s a  times.  lubricating  stationary  The  a second  This  waves and t h e r i m ) t h e mucus i s p r e s e n t i n t h e .  the  allowing  than  Under t h e moving  of a viscous l i g u i d ,  adhesive.  less  properties are i d e a l l y  locomotion.  (the m u s c u l a r  unstressed, the  " h e a l " a s t h e weak b o n d s r e f o r m . .  healing  cycle  o f a b o u t 50  along  mucus, a l l o w  the f o r c e s  T h i s model h a s been t e s t e d  forces,  and h a s p r o v e n  accurate.  The  i n c r e a s e d oxygen c o n s u m p t i o n  locomotion  i n JU, c o l u m b i a n u s  crawling  speed  .  adhesive  locomotion  was measured  columbianus  of  t h e same w e i g h t .  have heen  i s about  calculated.  It  locomotion  made i n t h i s and as  as f o r a mouse  This high cost i s l a r g e l y While  of a running  likely  that  due t o t h e  the c o s t of  i s high, the e f f i c i e n c y  equal to that i s very  Movement o f  ten times as c o s t l y  c o s t o f p r o d u c i n g t h e p e d a l mucus.  roughly  as a f u n c t i o n o f  From t h e s e d a t a t h e c o s t and e f f i c i e n c y o f  &.  adhesive  a s s o c i a t e d with  of locomotion i s  man.  t h e measurements and p r e d i c t i o n s  study  will  apply t o a l l t e r r e s t r i a l  pulmonates;  i t i s possible  that  they w i l l  gastropods  well.  apply  to other  TABLE OF CONTENTS  Abstract Table  i  o f Contents  iv  L i s t of T a b l e s . . List  v  of F i g u r e s  i  i  i  ix  Acknowledgements  xiii  Chapter 1:  Introduction  1  Chapter 2:  S l u g Morphology  4  The Chapter 3:  Chapter 4:  Foot  • •••  1  0  Introduction  18  Ariolimax  19  columbianus Locomotory K i n e m a t i c s  Mechanism f o r S l u g K i n e m a t i c s  48  Physical Properties  54  Elasticity  54  Molecular  Basis f o r E l a s t i c i t y  58  Viscosity Molecular  63 Basis f o r Viscosity  and Flow  66  Viscoelastic Materials  67  Stress-Shear  70  Ratio Tests  Stress-Relaxation  Tests  71  Dynamic T e s t i n g  76  T e s t i n g Apparatus and P r o c e d u r e s  79  Dynamic t e s t i n g The  apparatus  cone and p l a t e a p p a r a t u s  Collection  o f p e d a l mucus  79 86 89  vi  Chapter 4:  Physical Properties (continued) Physical Properties of Ariolimax columbianus mucus  91  at Low Shear Ratios.  Chapter 5:  Stress-shear r a t i o tests  91  Stress-relaxation tests  94  Dynamic tests  99  Physical Properties of Ariolimax columbianus mucus at High Shear Ratios. Stress-shear r a t i o tests  102 102  Fiber Formation  120  Chemical Composition  126  What i s Mucus?  126  Mucus C o l l e c t i o n  127  Analysis  127  Water content  127  Protein  128  Polysaccharides  131  Uronic acids  131  Amino sugars  131  S i a l i c acid  133  Neutral sugars  133  Sulphate sugars Salts Comparison  *...134 134  to Other Mucins  Vertebrate mucins.. Invertebrate mucins...  138 138 .138  vii  Chapter 6:  Chapter 7:  Physical Chemistry  144  Polyelectrolytes  145  Tests....  149  Network swelling  149  S o l u b i l i t y tests  151  I n t r i n s i c v i s c o s i t y measurements  158  Molecular Weight Between Crosslinks  176  Gel F i l t r a t i o n .  178  Attachment of Carbohydrate to Protein  184  Summary  185  Comparison with Other Mucins  188  A Model for Slug Locomotion  193  The Model  197  Waves  198  Rims.....  201  Interwaves  .201  Waves  203  Rims  207  Interwaves  210  Force Plate.  215  Tests  221 Horizontal tests  221  V e r t i c a l tests  222  Pressures Beneath Pedal Waves Summary and Conclusions  ..230 235  v i i i  Chapter 8:  Chapter 9:  Cost of Locomotion  .242  Review of Terms  242  Apparatus and Experimental Protocol  245  Results  251  Adhesion  267  Theory A Test Chapter 10: Conclusions  .'  268 280 285  Direct Monotaxic Waves  286  Direct Ditaxic Waves  287  Retrograde Ditaxic Waves  290  Retrograde Monotaxic Waves  291  Summary  291  Literature Cited  293  ix  LIST OF TABLES  T a b l e 5.1:  Amino a c i d composition...  T a b l e 5.2:  Chemical  T a b l e 5.3:  Carbohydrate  .130  composition  ..135  composition  p r o t e o g l y c a n s and  of v a r i o u s  140  glycoproteins.  T a b l e 6.1:  H y d r a t i o n of p e d a l mucus  152  T a b l e 6.2:  Solubility  156  T a b l e 6.3:  Intrinsic viscosities  T a b l e 7.1:  P r e d i c t i o n s of the l o c o m o t i o n model  206  T a b l e 7.2:  Measured and p r e d i c t e d f o r c e s of A r i o l i m a x . . . columbianus l o c o m o t i o n .  223  of p e d a l mucus  of v a r i o u s macromolecules...171  X  LIST OF FIGURES  F i g u r e 2.1:  G e n e r a l i z e d g r o s s morphology o f the t e r r e s t r i a l  slug......6  F i g u r e 2.2:  Gross morphology o f A r i o l i m a x columbianus  F i g u r e 2.3:  Cross  F i g u r e 3.1:  Schematic r e p r e s e n t a t i o n o f the v e n t r a l s u r f a c e o f the f o o t of an A r i o l i m a x columbianus.  23  F i g u r e 3.2:  Diagrammatic e x p l a n a t i o n of the mechanism by which a wave of compression can r e s u l t i n movement.  25  F i g u r e 3.3:  Diagrammatic e x p l a n a t i o n of the mechanism by which s e v e r a l waves o f compression can e x i s t on one f o o t and r e s u l t i n movement.  30  F i g u r e 3.4:  R e l a t i o n between speed o f the p e d a l wave and o v e r a l l speed o f the s l u g .  33  F i g u r e 3.5:  V e l o c i t y and d i s t a n c e p r o f i l e s o f an average p e d a l wave..38  F i g u r e 3.6:  Forward movement of the rims and the a l t e r n a t e movement..41 and non-movement o f the c e n t e r of the f o o t r e s u l t i n the same average forward v e l o c i t y .  P l a t e 3.1:  M i c r o g r a p h o f the p e d a l e p i t h e l i u m o f a c r a w l i n g  F i g u r e 3.7:  Problems w i t h  l i f t e d p e d a l waves  46  F i g u r e 3.8:  Model f o r the movement o f the f o o t o f A r i o l i m a x  50  9  s e c t i o n of A r i o l i m a x columbianus  13  slug....43  columbianus. F i g u r e 4.1:  P r o p e r t i e s of e l a s t i c s o l i d s  56  F i g u r e 4.2:  Molecular  62  F i g u r e 4.3:  Properties of viscous l i q u i d s  65  F i g u r e 4.4:  Springs  69  F i g u r e 4.5:  P r o p e r t i e s of v i s c o e l a s t i c m a t e r i a l s  73  F i g u r e 4.6:  Representative  75  b a s i s o f rubber e l a s t i c i t y  and dashpots  s t r e s s r e l a x a t i o n curves  xi  F i g u r e 4.7:  C h a r a c t e r i s t i c s o f s i n u s o i d a l deformations  78  F i g u r e 4.8:  Diagram of the f o r c e d o s c i l l a t i o n dynamic t e s t i n g apparatus.  F i g u r e 4.9:  C o n s t r u c t i o n drawing o f the dynamic t e s t i n g apparatus.... 84  '82  F i g u r e 4.10: Cone and p l a t e apparatus F i g u r e 4.11: S t r e s s / s h e a r r a t i o curve at a low shear r a t i o . F i g u r e 4.12: S t r e s s / s h e a r  88 f o r A r i o l i m a x columbianus  93  r a t i o curve f o r A r i o l i m a x columbianus  96  a t a moderate shear  ratio.  F i g u r e 4.13: S t r e s s r e l a x a t i o n c h a r a c t e r i s t i c s o f p e d a l mucus  98  F i g u r e 4.14: Dynamic t e s t r e s u l t s  101  F i g u r e 4.15: C h a r a c t e r i s t i c s o f p e d a l mucus a t h i g h shear r a t i o s  105  F i g u r e 4.16: P l o t of y i e l d s t r e s s and flow s t r e s s v e r s u s r a t e f o r p e d a l mucus.  shear  F i g u r e 4.17: R a t i o o f y i e l d s t r e s s to f l o w s t r e s s  ......107 I l l  F i g u r e 4.18: I n i t i a l y i e l d s t r e s s a f t e r a sample has been l e f t u n s t r e s s e d f o r a p e r i o d o f time i s g r e a t e r than subsequent y i e l d s t r e s s e s a f t e r o n l y s h o r t time heal periods.  115  F i g u r e 4.19: T e s t i n g procedure used t o determine t h e e f f e c t on the r e c o v e r y o f s o l i d i t y .  115  F i g u r e 4.20: P l o t o f r e l a x a t i o n time v e r s u s h e a l time f o r p e d a l  117  mucus. F i g u r e 4.21: E f f e c t s o f v a r i o u s s a l t s on the i n c r e a s e i n shear modulus.  119  F i g u r e 6.1:  C h a r a c t e r i s t i c s of p o l y e l e c t r o l y t e s  147  F i g u r e 6.2:  Viscosity.....  160  F i g u r e 6.3:  I n t r i n s i c v i s c o s i t y of p e d a l mucus shows the c h a r a c t e r i s t i c s of a p o l y e l e c t r o l y t e .  167  F i g u r e 6.4:  Molecular  169  weight dependence on i n t r i n s i c v i s c o s i t y  F i g u r e 6.5:  S e p a r a t i o n of p e d a l mucus on Sepharose 4-BC1 r e s u l t s . . . . 181 i n two f r a c t i o n s .  F i g u r e 6.6:  Incompletely  d i s s o l v e d p e d a l mucus shows a t h i r d  183  f r a c t i o n when s e p a r a t e d .on Sepharose 4-BC1. F i g u r e 6.7:  Carbohydrate b o d i n g t o s e r i n e and/or t h r e o n i n e  187  F i g u r e 6.8:  Model f o r the s t r u c t u r e o f A r i o l i m a x columbianus p e d a l mucus.  191  F i g u r e 7.1:  P o s s i b l e f o r c e s a c t i n g on gastropod  195  Figure  Forces  7.2:  present  locomotion  under a moving s l u g  200  F i g u r e 7.3:  S t r e s s p r o f i l e beneath a p e d a l wave  F i g u r e 7.4:  P l o t o f y i e l d s t r e s s and flow s t r e s s v e r s u s f o r A r i o l i m a x columbianus p e d a l mucus.  F i g u r e 7.5:  I n t e r a c t i o n of g r a v i t y with  F i g u r e 7.6:  Apparatus f o r measuring the f o r c e s beneath a c r a w l i n g . . . 218 slug.  F i g u r e 7.7:  Record o f f o r c e s measured beneath a c r a w l i n g s l u g  F i g u r e 7.8:  P l o t o f weight p r e d i c t e d from the model v e r s u s weight f o r a l l v e r t i c a l c r a w l s .  Figure  F o r c e s measured beneath a s l u g when c r a w l i n g v e r t i c a l l y . 2 3 2 up, h o r i z o n t a l l y , and v e r t i c a l l y down.  7.9:  ....205 shear rate..209  the f o r c e s of l o c o m o t i o n . . . . 213  225  actual...228  F i g u r e 7.10: Apparatus f o r s i m u l t a n e o u s l y measuring a n t e r i o p o s t e r i o r f o r c e s and d o r s o - v e n t r a l f o r c e s beneath a crawling slug.  234  Figure  237  7.11: Simultaneous f o r c e and p r e s s u r e measurements  F i g u r e 7.12: Foot l o a d i n g of A r i o l i m a x columbianus i s c o n s t a n t above a weight o f 5 grams. F i g u r e 8.1:  Diagram o f the e l e c t r o l y t i c d i f f e r e n t i a l  F i g u r e 8.2:  Apparatus used t o measure the movement o f a s l u g i n the t e s t chamber.  241  respirometer...247 249  Figure 8.3:  Crawling v e l o c i t y and oxygen consumption f o r Ariolimax columbianus.  Figure 8.4:  Internal power of locomotion crawling speed.  as a function of  ....253 256  •  Figure 8.5:  Cost of locomotion  259  Figure 8.6: Figure 9.1:  Components of power i n the locomotion of Ariolimax 262 columbianus. Adhesive properties of a viscous l i q u i d . . . . ......270  Figure 9.2:  Stress concentrations  278  Figure 9.3:  Device f o r measuring the shear strength of pedal mucus under the slug.  283  Figure 10.1: Diagrammatic representation of the four regular forms...289 of pedal waves.  xiv  ACKNOWLEDGMENTS T h i s s t u d y was made p o s s i b l e b y t h e a d v i c e a n d s u p p o r t of  many p e o p l e .  I would  especially  like  t o thank  supervisor,  John G o s l i n e , f o r h i s encouragment,  and  o f thought.  to all  clarity  g e t me t h r o u g h  interest,  Susan K r e p p Denny p r o v i d e d t h e l o v e  the hard  t i m e s , and i n v a l u a b l e h e l p  a s p e c t s o f t h e work. . C o l i n  Parkinson  and F e r g u s  assisted  i n t h e c o n s t r u c t i o n o f t h e v a r i o u s weird  involved  in this  forebearance. occupants bad  study,  Finally  Aaron,  and Tony  Research Research Grant  O^ara  machines  I would l i k e  t o thank t h e o t h e r  i n good  experiments  humor t h r o u g h  my  - Bob Shadwick, Meyer  Harmon.  funds  f o rthis  C o u n c i l Grant  from  with  and I t h a n k them f o r t h e i r  o f t h e l a b who s u f f e r e d  j o k e s and c l u t t e r e d  my  study  were p r o v i d e d by N a t i o n a l  67-6934 and a P r e s i d e n t ' s Emergency  the University  o f B.C., b o t h  t o Dr.  Gosline.  1  CHAPTER  ONE  Introduction If  you  puttering likely  have e v e r  i n your garden, e a r l y  on  through  sunlight .  closely  you  winding  a c r o s s the  gliding  along.  hard  animal  will  I f you  see  bow  a trail  of  g r o u n d and  Watching  1.  a glimpse  a t i t s end  a snail  or slug kind  locomotion?  and  or  snail  move, i t i s a t  of l o c o m o t i o n . as  look  cellophane  a slug  i f slowly  However, a moment's o b s e r v a t i o n and  What i s t h e  of  to your c u r i o s i t y  a p p e a r s t o move e f f o r t l e s s l y ,  a number o f d i f f i c u l t  woods, o r  what l o o k s l i k e  to imagine a s i m p l e r  downhill.  the  a summer*s morning i t i s  t h a t y o u r e y e . h a s been c a u g h t by  reflected  first  been w a l k i n g  The  sliding  thought  raise  guestions: source  As e f f o r t l e s s  seems, some f o r c e must be  o f power f o r t h i s t y p e as a  slug  or s n a i l ' s  of  movement  o p e r a t i n g t o p r o p e l the  animal  forward. 2.  In  reach the to  climb  or s n a i l the  it  the  vertical  climb,  one  does n o t  snails food  are they  surfaces of plants.  i s immediately  to glide  upwards.  3.  crawls.  The  How  adhesion  of  can  we  s l u g s and  are o f t e n required Watching  a  slug  fact  that  to v e r t i c a l l y . , Obviously  account  To  movement when i t  must somehow manage t o a d h e r e t o t h e  the.animal  herbivores.  s t r u c k by t h e  change i t s mode o f  from c r a w l i n g h o r i z o n t a l l y  seems s i m p l y  foot  s l u g s and  l e a v e s t h a t are t h e i r  animal  switches  general  the  Instead  animal's  s u r f a c e upon which  for this  s n a i l s t o the  adhesion? substratum  2  immediately to  the  r a i s e s another  s u r f a c e upon w h i c h i t w a l k s ,  move a t a l l ? one  foot  In  o t h e r words, how  c o n t r i v e to  4.  These l a s t  walk on two  s l i m e t h a t s l u g s and important  to the  (1926a) h a s move n o r is  energy  Williamson  directed  this.mucus?  and  how  do  For  will  as  allow  known.  and  effort  While  well.  of t h e  the  the  slime i s Barr neither this  A n o t h e r measure o f  the  s n a i l s i s the large  snail  31%  and  36%  of  Cepea n e m o r a l i s  mucus.  the  was  What, t h e n , i s  glue that accounts  i t s p h y s i c a l and  chemical  for  properties  f o r movement?  z o o l o g i s t s have spent  running o f quadrupeds,and the  locomotion  only  mucus., P r e s u m a b l y  t h a t between  s t u d y i n g the f l i g h t  flamboyant  this  M i l a x s o w e r b i i can  t h e most p a r t t h e a n s w e r s t o t h e s e  not  less  That  on  be d e m o n s t r a t e d .  production of pedal  What a r e  with  expend i n p r o d u c i n g i t .  found  Is i t really  they  slug  t h i s pedal  expenditure  to the  adhession?  they  animal  glue?  s l i m e t o s l u g s and  (1975) has  energy  d o e s an  easily  gastropods  of t h i s  amount o f  can  i s stuck  does i t manage t o  questions focus attention  shown t h a t t h e  adhere without  importance  how  s n a i l s move o v e r .  animal  true of other  total  q u e s t i o n : I f the animal  birds,  swimming o f f i s h ;  have been  are  a great d e a l of  o f i n s e c t s and  forms of l o c o m o t i o n ,  of g a s t r o p o d s ,  questions  such  the  many o f  as the  largely  time  the  adhesive  ignored.  This  is  u n f o r t u n a t e , f o r I b e l i e v e t h e r e i s much i n f o r m a t i o n t o  be  gained  from  the  study  of slowly  be o f use  to a l l biologists.  study  undertaken  was  moving a n i m a l s  In l i g h t  of t h i s  t o p r o v i d e answers t o the  that  belief  will this  questions  3  posed  above. I  form  have approached  of adhesive  locomotion The  l o c o m o t i o n by e x a m i n i n g  i n d e t a i l the  the slug  aspects o f locomotion  aparatus,  locomotion.  The p h y s i c a l  with the chemical composition o f t h e p e d a l mucus. together  i n Chapter  were s t u d i e d s e p a r a t e l y :  of t h i s  model has b e e n t e s t e d  are also  Chapter  7 i s used  locomotion adhesion  in A  This  study  answering  p r o p e r t i e s of the pedal  4.  Chapters  5 and 6 d e a l  and m a c r o m o l e c u l a r  by c o m p a r i n g actually  i n Chapter  i n Chapter  validity  the p r e d i c t e d  measured, and t h e s e  7.  The model o f  9 e x a m i n e s t h e mechanism o f  columbianus. of the locomotion  many q u e s t i o n s about  q u e s t i o n s about  Chapter  10 d i s c u s s e s t h e s e  o f A. c o l u m b i a n u s  adhesive  gastropod  locomotion,  locomotion  locomotion  and t h e more f a m i l i a r  , while raises  i n general.  unanswered q u e s t i o n s and  p r o v i d e a p e r s p e c t i v e on t h e r e l a t i o n s h i p  movement.,  The  8 t o examine t h e e n e r g e t i c s o f  Chapter  further  adhesive  structure  are brought  o f JU c o l u m b i a n u s .  with those  presented  i n slugs.  structure  7 where a model i s c o n s t r u c t e d t o  f o r the locomotion  results  of the s l u g ' s  A l l of these r e s u l t s  account  forces of locomotion  this  columbianus.  and t h e movement o f t h i s  mucus a r e d e s c r i b e d i n C h a p t e r  to  Ariolimax  2 and 3 d e s c r i b e t h e s t r u c t u r e  locomotory during  of explaining  o f one a n i m a l ,  several  Chapters  t h e l a r g e problem  attempts  between  forms o f animal  4  CHAPTER  Slug Terrestrial of the closely  tied  which t h e y  are  m o r p h o l o g y may  terrestrial consist  The  s n a i l are  be  2.1  shows an The  portions world.  The  the  will  with be  snail  Peake,1973.  d e p i c t i o n of  The  a to  i n t e r n a l organs of  t o form  of the The  visceral  Head F o o t  .  in turn  the  the  provides  mass.  materials support  mass.  Extending  body t h a t  structure,  mantle s e c r e t e s  shell  the  a compact v i s c e r a l  within a bag-like  shell.  out  of  require contact  the with  shell the  are  the  outside  f o o t , a h y d r o s t a t i c a l l y supported,muscular  and  from t h e  extensions  snail  of  columella  the  foot  f o r locomotion.  foot,among o t h e r  allowing  of  and  body i s u s u a l l y c o n s i d e r e d  epithelium  movements n e c e s s a r y the  treatment  idealized  together  s t r u c t u r e , i s suspended Contractions  morphology of s n a i l s  V i s c e r a l Mass .  of the The  (Runham  from  parts:  p r o t e c t i o n f o r the 2-  garden s n a i l s  f o u n d i n F r e t t e r and  snail.  which form the and  gross  A more t h o r o u g h  grouped  The  familiar  morphology i s  a background f o r comparison  provide  mass i s e n c l o s e d  mantle.  such, t h e i r  To  o f two  1.  As  Pulmonata  t o have e v o l v e d  here.  Figure  .  subclass  considered  morphology, the  reviewed  This  molluscs  members o f t h e  to t h a t of the  Hunter,1970). slug  Morphology  slugs are  gastropod  TWO  to  things,functions remain anchored  The as  of the  provide  shell.  the  mucus s e c r e t e d an  t o the  onto  adhesive surface  upon  5  FIGURE 2.1.  A g e n e r a l i z e d g r o s s morphology t e r r e s t r i a l pulmonate s n a i l .  of t h e  F I G U R E  2.1 S H E L L  P O S T E R I O R T E N T A C L E S  A N T E R I O R F O O T  T E N T A C L E S  F R I N G E  M O U T H F O O T  P N E U M O S T O M E G E N I T A L  S O L E  P O R E  V I S C E R A L  M A S S  P N E U M O S T O M E M A N T L E  P O S T E R I O R T E N T A C L E S  A N T E R I O R T E N T A C L E S  P E D A L  M U C U S  M O U T H  G L A N D M U C U S C O L U M E L L A R  M U S C L E S  G L A N D  P O R E  7  which i t c r a w l s .  The f o o t  (or p e d a l )  mucus i s p r o d u c e d i n  the suprapedal gland contained within the foot extruded  through  a pore a t the a n t e r i o r  The  "head" o f t h e a n i m a l  and  a mouth.  eyes,  cavity the  radula.  pair  ( t h e pneumostome)  opening  t h e pneumostome.  contracted  and p u l l e d  The e n t i r e  back i n t o  being closed  the g e n i t a l  the s h e l l ,  by an  that  shell.  the d o r s a l  of the s n a i l  The v i s c e r a l  serves to protect  operculum. slugs  flap  shell,  morphology o f t h e s l u g At f i r s t maladapted is  highly  i s very  no l o n g e r p r e s e n t and  pneumostome.  In  beneath the  In other r e s p e c t s the similar  g l a n c e t h e morphology  to t e r r e s t r i a l  2.2)  to l i e along  is still  the heart, kidneys,and  of the mantle.  (Figure  by t h e l o s s o f t h e  t i m e s o f d a n g e r t h e head may a l s o be s h e l t e r e d anterior  c a n be  The m a n t l e , t h o u g h  c a p a b l e o f p r o d u c i n g an e x t e r n a l  which  the s h e l l  mass i s e x t e n d e d  surface o f the foot.  through  pore,  head-foot  g r o s s morphology o f t e r r e s t r i a l  external  also  and eggs a r e s h e d  opens near  d e r i v e d from  side of  f o r f a e c e s and n i t r o g e n o u s wastes. . S n a i l s  which can be e v e r t e d f r o m  is  hand  The pneumostome o p e n i n g  structures  The  gastropod  vascularized  on t h e r i g h t  a r e h e r m a p h r o d i t i c , and b o t h sperm  aperture then  t o serve as  Gas e x c h a n g e o c c u r s i n a  as an e x i t  supports the  The mouth h o u s e s a t y p i c a l  a n i m a l b e h i n d t h e head.  serves  of t e n t a c l e s  t e n t a c l e s a r e thought  chemosensory organs. rasping  end o f t h e f o o t .  c o n s i s t s o f two p a i r s o f t e n t a c l e s  The p o s t e r i o r  the a n t e r i o r  mass, and i s  to that  of a slug  existence.  of the s n a i l . seems  grossly  The s l u g * s e p i t h e l i u m  permeable t o water;and,unlike  the s n a i l ,  i t cannot  8  FIGURE 2.2.  The g r o s s Ariolimax  morphology o f t h e t e r r e s t r i a l columbianus .  slug  mantle  posterior tentacles [with eyes] anterior  tentacles  mouth  posterior tentacles  anterior tentacles pedal gland  mucus  10  retract lack  into  a shell  of a s h e l l  t o avoid d e s i c c a t i o n .  would  S i m i l a r l y , the  seem t o r e n d e r t h e s l u g  open t o  predation. These d i s a d v a n t a g e s apparently offset H u n t e r , 1970),. slug  of l i f e  by a number o f a d v a n t a g e s  Because i t i s n o t t i e d  can f i t p l a c e s t h a t  are adept ground  without a s h e l l are  a snail  t o a bulky s h e l l a  cannot.  For example,slugs  a t c r a w l i n g under l o g s a n d i n t o  where t h e h u m i d i t y  i s high.  damp s h e l t e r s  may t h u s o f f s e t  desiccation.  Slugs also  move w i t h o u t h a v i n g Finally,slugs  small holes i n the  The a v a i l a b i l i t y  the lack  have t h e a d v a n t a g e  from t h e n e c e s s i t y  of being able to shell. of i n g e s t i n g  l a r g e amounts o f c a l c i u m i n o r d e r t o p r o d u c e shell.  The v i a b i l i t y  the independent least  three different  worldwide  of these.advantages  evolution  and maintain a  i s evidenced  o f t h e s h e l l - l e s s body f o r m  families  present d i s t r i b u t i o n  o f pulmonates,and  by 1) i nat  2) t h e  of slugs.  S l u g s o c c u r i n a wide v a r i e t y  of sizes,from small  s p e c i e s where t h e a d u l t s weigh l e s s such  o f such  of protection against  t o drag a l o n g a heavy  are f r e e d  (Eunham and  as t h e A r i o l i m a x c o l u m b i a n u s  t h a n a gram, t o s p e c i e s  dealt  with i n t h i s  study  where a d u l t s may weigh 20-25 grams.  The  Foot The  foot  o f A r i o l i m a x columbianus  responsible f o r adhesion o f prime structure  importance  and l o c o m o t i o n  i n this  of the f o o t  study.  several  i s the organ and c o n s e q u e n t l y i s  To examine t h e f i n e  s m a l l A. c o l u m b i a n u s  were  11  prepared in  for histological  studies.  The  water c o n t a i n i n g a s m a l l amount o f MS222 .  were t h e n  fixed  in either  fixative,dehydrated,and 10 um)  and  wax  stained either  embedded.  with  alcian  the study  Mallory's t r i p l e  the f o o t 1  «  tubular  .  The  The  Suprapedal  organ  embedded  extending  i n t o t h e lumen.  pore  cilia  may  foot sole. similar 2  the  The  The  foot  two  thirds  cells  lumenal  structures:  suprapedal  the  of the  foot  length of the g l a n d and  movement o f t h e  Haemocoel And  gland  M u s c u l a t u r e -..  of a r e t i c u l u m o f c o n n e c t i v e  i n t e r s p e r s e d with  haemocoelic  slug..  and  mucus t o  Barr  the  second  slug.  The  circumferentially. of the  running  i s a band r u n n i n g  T h i s second  foot fringes  longitudinal  g l a n d and  (1926b). The  bulk  tissue  spaces.,  and  muscle band.  runs  the  of  and  There The  just  l e n g t h of  roughly  band s t a r t s  just  m e d i a l l y below  I t then  the  i s very  i s a l o n g i t u d i n a l m u s c l e band l y i n g suprapedal  the  onto  d i s c e r n a b l e l a r g e bands o f m u s c l e i n t h e f o o t .  of these  and  secreted  mucus i s e x t r u d e d  s t r u c t u r e of the suprapedal  i s formed  gland i s a  epithelium i s c i l i a t e d  i n the  v e n t r a l t o the  one  The  mouth where t h e  Pedal  muscle f i b e r s  first  shows t h e s t r u c t u r e  t o t h a t i n A r i o n a t e r d e s c r i b e d by  -  a r e two  .  the  were s t a i n e d  i n the d o r s a l s u r f a c e o f t h e  assist  beneath the  F i g u r e 2.3  Gland  i n the The  tissues  consists of three  approximately  Mucus i s p r o d u c e d  these  foot  (7-  Sections intended  connective  stain.  Bouins  b l u e / e o s i n o r by  for  o f muscle and  specimens  S e c t i o n s were c u t  method f o r t h e d e t e c t i o n o f mucus.  with  The  1% g l u t e r a l d e h y d e o r  PAS  of  s l u g s were r e l a x e d  proximal the  c o n t i n u e s around  the  to  12  FIGURE 2.3..  A c r o s s s e c t i o n of A r i o l i m a x c o l u m b i a n u s showing v a r i o u s s t r u c t u r e s of importance to t h i s study. T h i s s e c t i o n was made a t t h e p o s i t i o n i n d i c a t e d by t h e l i n e A-A i n F i g u r e 2. 2.  FIGURE 2.3  pedal haemocoel  14  dorsal  side  opposite  of  foot  bands a r e  the  slug  fringe.  circumferential earthworms  squeeze the lengthen.  At  first  of  the  of  slug  to  addition  coelomic to  these  haphazardly;  muscle  that  the  fluid  examination  to  run  directly dorso-ventrally  posterior ly. directions.  The  Fibers  f i b e r s run  obliguely  seem t o  laterally to t h a t Jones will  (1970).  discussed  The fibers  of  foot.  contrast  the  foot  to t h e  are  f i b e r s are  next  two  obliquely  oblique epithelium  posteriorly. Few  ?  or similar  described  by  t h i s f i b e r arrangement  chapter.  m u s c l e and  filled  seen  directly anterio-  pedal  as  foot.  some o r d e r .  s i t u a t i o n i s very  s i g n i f i c a n c e of i n the  of  to  arranged  same i n c r o s s - s e c t i o n  This  slug  dense  directly dorso-ventrally  s p a c e s between t h e the  or  i n Agriolimax rgtieulatum The  will  cause the  reveals few  i n one  a n t e r i o r l y or  either  a c r o s s the  found  be  run  foot  o r i g i n a t i n g on  s i t u a t i o n a p p e a r s much t h e  fibers  In  through the  Instead  become:wider.  throughout the be  and  longitudinal  m u s c l e bands a  section  run  and  muscle  of  m u s c l e band  a sagittal either  the  s h o r t e n and  In  either  of  shape  the  they  longitudinal  the  f i b e r s appear to  however c l o s e r  two  It is likely  muscle f i b e r s i s p r e s e n t  these  these  body  circumferential and  proximal to  changes i n  A contraction  cause the  viscera In  slugs.  that  m u s c l e s which c o n t r o l  will  A contraction  large  same manner as  (Gray,1968).  m u s c l e band  reticulum  f o r the  these  i n much the  back down t o end  I t seems l i k e l y  responsible  d i m e n s i o n s shown by function  and  with  the  s i t u a t i o n proposed  connective haemocoelic to exist in  tissue fluid. the  limpet  15  Patella  vulqata  microscopical confined  evidence  medially  along  of t h i s c a v i t y are i l l - d e f i n e d of contiguous  structured Again in  bounded l a t e r a l l y Two d i s t i n c t  densely  arrangement  .. The p e d a l  and v e n t r a l l y  areas  along will  The  haemocoel i s the foot. be  discussed  haemocoel i s  by t h e p e d a l  are discernable  in this  Sections  slugs  by c a r e f u l  The c i l i a  d i s s e c t i o n with  effective  stroke  i s found  propelled  posteriorly  producing  cells  i n the i n t a c t  present  on t h e f o o t f r i n g e s .  covered  by a s e c o n d but they  type  slug.  cells  The  live  cilia  mucus would be Scattered  mucus  of Arcadi,1963) a r e  The s o l e o f t h e f o o t i s  of e p i t h e l i u m  are shorter  from  4  d i s s e c t e d t i s s u e and t h e i r  t o be s u c h t h a t  (the " g r a n u l a r "  (about  c a n be o b t a i n e d a razor blade.  beat i n t h i s  The  groove are  here a r e quite long  of t h i s epithelium  to actively  epithelium.  epithelium.  o f t h e f o o t f r i n g e s and t h e p e d a l  um).  present,  together.  t h e movement o f f l u i d  Epithelium  ciliated.  continue  The w a l l s  chapter.  The P e d a l  epithelium  the entire foot.  and i t a p p e a r s t o be formed  the s i g n i f i c a n c e o f t h i s  3.  i s a sizable  c a v i t y suggests t h a t t h e pedal  to allow  t h e next  Indeed there  haemocoelic spaces strung  presence of t h i s  i s no  s p a c e s and t h e r e f o r e n o t f r e e t o  one s p a c e t o t h e n e x t .  extending  (1973) t h e r e  t o suggest that t h i s f l u i d i s  by t h e i n d i v i d u a l  move from cavity  by J o n e s and Trueman  (about  .  Cilia  2 um)  a r e again  and more s p a r s e l y  distributed.  I was n o t a b l e t o d e t e r m i n e t h e d i r e c t i o n o f  the  stroke  effective  found  that the pedal  f o r these cilia  cilia,  however B a r r  i n two o t h e r  (1926a, b)  species of slug  16  transported granular foot  mucus l a t e r a l l y  cells  sole.  are also present  pedal  i n other  epithelium  suprapedal  (distinct  the  JU  aluminum f o i l . strip  that  retract  using  o f t h e mucus l a y e r  were p l a c e d  When t h e s l u g s  were a c t i v e l y  f r o z e very  eye s t a l k s .  containing  differs  the  a r e moving o v e r a n o n - p o r o u s s u r f a c e  strip  Lissman  of f i l t e r After  sectioned  a piece  o f copper  t o one  (1973).  This  and J o n e s i n t h a t  screen  when t h e y a r e and J o n e s a  paper.  - 50% e t h a n o l  a t -20<>C) f o r one week.  specimens a r e dehydrated, a t 8-10 um a c c o r d i n g  t o standard  Sections  triple  f o r examining the general  stain  or alcian  mucus p r o d u c i n g  were s t a i n e d  blue/eosin cells  After  wax embedded, and  techniques.  foot,  could  f r e e z i n g , t h e specimens a r e f i x e d (1%  glutaraldehyde fixation  used  o f Lissman  they  i s similar  procedure  from those  liguid  r a p i d l y ; before  The p r o c e d u r e  Small  moving,the  by L i s s m a n , (1946) and used by J o n e s  frozen.  beneath  on a s t r i p o f  developed  slugs  by t h e  the f o l l o w i n g procedure:  columbianus  The s l u g s  their  produced  However I h a v e . n e v e r  was d r o p p e d i n t o a dewar f l a s k  nitrogen.  and J o n e s  columbianus .  was examined  cm l e n g t h )  (1926a,b)  o f w a t e r y mucous s e c r e t i o n s on t h e  The Mucus The t h i c k n e s s  foot  (3-4  from  gland) i s g u i t e watery.  of Ariolimax 4-  by B a r r  of the  s p e c i e s o f s l u g s t h e mucus p r o d u c e d by  observed t h e presence foot  Scattered  on t h e e p i t h e l i u m  I t h a s been r e p o r t e d  (1970) t h a t the  and p o s t e r i o r l y .  with  histological  either  Mallory's  s t r u c t u r e o f the  when t h e l o c a t i o n o f mucus and  were t o be e x a m i n e d .  Using  this  17  technique slugs.  saggital sections  were examined from  I n many c a s e s t h e mucus l a y e r  become d i s l o d g e d  during  beneath  the f o o t  had  the process of f i x a t i o n or  embedding, b u t i n t h o s e c a s e s where t h e apparently  several  i n t a c t i t was  found  t o be  mucus l a y e r  from  10 t o 20  was um  in  thickness. With locomotory of  t h i s b r i e f d e s c r i p t i o n of the a p p a r a t u s o f A.  this structure  may  now  columbianus be  examined.  morphology i n mind t h e  of the function  18  CHAPTER  THREE  Introduction K i n e m a t i c s i s t h e study o f motion t h e f o r c e s t h a t cause a p p r o p r i a t e term of  gastropods  specialized it  The broad  at a l l .  A closer  locomotory  parameters  (Elves,  form  species u t i l i z i n g  of t h e s e  the v e n t r a l  there are those  1961) t h a t  ciliary  fall  i n t o two  gastropods,  ciliary  I t has  locomotion i s L i s t s of  movement a r e p r o v i d e d by M i l l e r  (1971).  however move by means o f waves g e n e r a t e d on  surface o f the foot  These m u s c u l a r  pedal  by t h e c o n t r a c t i o n o f waves a r e b e s t o b s e r v e d  plate  and w a t c h i n g  t h e g l a s s a s t h e a n i m a l moves.  r e v e a l s a number o f a l t e r n a t i n g (corresponding  i s the  l o c o m o t i o n , and t h e v a r i o u s  p l a c i n g t h e a n i m a l on a g l a s s  animal  movements t h a t  o f movement f o r g a s t r o p o d s .  of t h e i r  Most g a s t r o p o d s  along  accompany l o c o m o t i o n , and  a q u a t i c , which move by means o f c i l i a .  primitive  which  appear t o g l i d e  movements o f g a s t r o p o d s First  been h y p o t h e s i z e d  through  movements  chapter.  catagories.  muscles.  i t i s a doubly  l o o k , however, r e v e a l s a  s e t o f movements t h a t  of this  primarily  regard f o r  f o r the study o f t h e locomotory  i s a precise description  objective  the  l o c o m o t i o n . , As s u c h  because these a n i m a l s  w i t h no e f f o r t  without  light  Close and dark  to extension o r compression  move p a r a l l e l crawls.  Presumably t h e s e  the foot  examination bands  of the foot)  t o the long a x i s of the f o o t  as t h e  The waves d i s a p p e a r when t h e a n i m a l p e d a l waves g e n e r a t e  by  the reactive  stops. forces  19  that  actually  propel  A variety and  o f wave p a t t e r n s a r e p r e s e n t i n g a s t r o p o d s ,  descriptions  studies 1970,  the a n i m a l .  o f t h e s e p e d a l waves a r e f o u n d i n s e v e r a l  (Miller,  Lissman,  1974a, J o n e s ,  1945a, and  Gainey,  o f p e d a l waves a r e c a t e g o r i z e d p r o p o s e d by V l e z Miller,  1974).  (1909)  direction  from  direct.  sides.  terms, though  A precise direct and  1945a,  i n the  A single  g e n e r a l agreement  wave  may  or  (ditaxic), by t h e s e move  and d i s a p p e a r moves by means o f  waves. o f t h e movements a s s o c i a t e d (1945a)  waves i n J o n e s and Columbianus  and  Trueman  Jones (1970).  observed i n t h i s  with these s t u d i e s .  A. c o l u m b i a n u s  locomotory kinematics.  A. c o l u m b i a n u s  Locomotory  Ariolimax columbianus of B r i t i s h  Kinematics  Areas of  (1970) The  disagreement of  (Methods)  were c o l l e c t e d Columbia..  with  study are i n  be n o t e d as t h e y a p p e a r i n t h e d e s c r i p t i o n  the U n i v e r s i t y  as the  (monotaxic)  be d e s c r i b e d  or appear  waves i s f o u n d i n L i s s m a n  for indirect  and  opposite  u n u s u a l s p e c i e s have waves t h a t  description  movements o f A..  will  t o a scheme  width of the f o o t  A r i o l i m a x columbianus  monotaxic  sorts  move i n t h e same d i r e c t i o n  Most s p e c i e s may  a few  Jones,  various  i n Lissman,  Waves moving  along the foot,  haphazardly. direct,  The  be o n l y h a l f t h e w i d t h o f t h e f o o t  alternating  diagonally  1976).  the a n i m a l a r e r e t r o g r a d e .  extend a c r o s s the e n t i r e waves may  Trueman and  according  (as c i t e d  Waves t h a t  a n i m a l a r e termed  1973,  i n t h e woods n e a r  S l u g s were k e p t a t  10  20  °C i n a c o n t r o l l e d  environment  chamber were c y c l e d , hours  of darkness.  12 h o u r s The s l u g s  chamber. of l i g h t  study  A l l tests  Slugs brought allowed  with  and  12  carrots.  slugs reported  o u t a t room t e m p e r a t u r e  into the laboratory  of the  be k e p t h e a l t h y f o r up t o  c o n d u c t e d on l i v e  were c a r r i e d  alternating  were f e d l e t t u c e  Under t h e s e c o n d i t i o n s s l u g s c o u l d a year.  The l i g h t s  from  t o come t o room t e m p e r a t u r e  in this  (21-23 ° G ) .  the cold  room  before tests  were  were  conducted. The observed  locomotory by a l l o w i n g  movements o f A., c o l u m b i a n u s a slug  Movements o f t h e v e n t r a l  t o c r a w l on a g l a s s  a t 60 f r a m e s / s e c o n d .  Taped  were p l a y e d h a c k o n t o a 25 i n c h ( d i a g o n a l )  television  screen.  f r a m e by f r a m e . slug  plate.  s u r f a c e o f t h e f o o t were r e c o r d e d  w i t h a Sony v i d e o t a p e r e c o r d e r records  were  When d e s i r e d , t h e t a p e c o u l d  A ruler  be a n a l y z e d  taped t o t h e g l a s s p l a t e  allowed f o r the size  calibration  near the  o f images on t h e  t e l e v i s i o n screen. A stationary The  foot  •the f o o t thin  slug  shows no e v i d e n c e o f p e d a l waves.  i s dark t a n , the c o l o r were t h e d a r k d i g e s t i v e  layer  d a r k e s t near the c e n t e r o f g l a n d shows t h r o u g h t h e  of pedal musculature.  As t h e s l u g  move, waves f i r s t  appear  from  end o f t h e f o o t .  the a n t e r i o r  epithelium  contraction  1/4 t o 1/3 o f t h e f o o t  and m u s c u l a t u r e  mask t h e dark  digestive  appears  begins to  lighter  back  When t h e p e d a l  are compressed  gland.  length  i n t h e wave t h e y  C o n s e q u e n t l y , a wave o f  than t h e r e s t i n g f o o t .  waves move f o r w a r d t h e a r e a o f wave f o r m a t i o n moves  As t h e s e  21  posteriorly  until  shown i n F i g u r e the  foot.  1/3  to  The  1/2  The  of  the  3.1.  Thirteen  pattern the  by  of  foot,  following  3.2a).  foot,  The  tail  length.  moves f o r w a r d  waveless areas forming  a  wave i n a  the  contraction  contraction  of  a bit. the  From v i d e o  foot,  i t i s possible  Such measurements were made on measured  measurements i t was  This foot  as  1.43  in  When t h e  muscles are and  no  within  t h i s chapter.  this  for  segment o f  the As the  the  A.  measure  average  three  to  four  these ratio  compression  along  and  anterior  end  longer a v a i l a b l e to  keep t h e  wave  length.  The  foot  and  will  a consequence foot,  the  provided  be  by  discussed  of the  anterior  end  of  the  energy  hydrostatic further  re-expansion of  the  muscles  wave r e a c h e s t h e  to i t s r e s t i n g  ratio  1.69.  of  forward  wave c o n t r a c t  the  columbianus .  a r e s u l t of  length),the  the  of  A columbianus the  i s presumably  of the  area of  to  slugs, As  w i t h an  the  i t returns  t h i s re-expansion  pressure  that  2.03  m u s c l e s ahead o f  compressed for  each s l u g .  found  to  three  wave o f c o m p r e s s i o n i s p a s s e d  behind r e l a x . foot,  on  length/compressed  , ranges from  a segment o f  recordings  t h i s compression i n a crawling  (extended  end  a conseguence o f t h i s c o n t r a c t i o n  extent  of  diagram  some f r a c t i o n o f i t s  a r e a s on  waves b e i n g  best  posterior  c a u s e s an to  on  central  schematic  near the  as  "rim".  locomotion are  pigmented of  present the  This  As  e n t i r e foot  waves a r e  to compress a n t e r i o - p o s t e r i o r l y  relaxed  the  waves o c c u p i e s o n l y  a single  p r e s u m a b l y by  along  17  to  wave i s f o r m e d  pedal musculature. foot  present  o v e r a l l movements d u r i n g  understood (Figure  waves a r e  the  foot  later of is  22  FIGURE 3 . 1 .  A schematic representation o f the v e n t r a l s u r f a c e o f the f o o t of a t y p i c a l A r i o l i m a x columbianus , showing t h e r e l a t i v e p o s i t i o n s , movements, and a r e a s o f t h e r i m s , waves, and interwaves.  23  24  FIGURE 3.2.  4 d i a g r a m m a t i c e x p l a n a t i o n o f t h e mechanism by w h i c h a wave o f c o m p r e s s i o n c a n r e s u l t i n movement,. A) As t h e wave moves f r o m l e f t t o r i g h t (shown by t h e s t i p p l e d l i n e ) t h e f o o t as a whole i s t r a n s p o r t e d t o the r i g h t . B) The movement o f t h e f o o t a t t h e same s p e e d as t h e wave r e s u l t s i n t h e c o l l a p s e of t h e foot.  25  26  moved f o r w a r d . distance  the t a i l  transferred expands  Thus,  .  each  i s pulled  t o t h e head  o f each  when t h e wave o f c o m p r e s s i o n r e -  3.2a t h a t  are not contained  point  Only  i  those p a r t s of the foot  when a p o r t i o n o f t h e f o o t i s i s i t moving.  must be e x p l a i n e d h e r e .  involves the d i f f e r e n c e travels  as a  1.0 t o 1.5 mm.  i n t h e wave o f c o m p r e s s i o n  One f u r t h e r  advances  i n a p e d a l wave a r e s t a t i o n a r y  t o t h e ground.  contained  Columbianus  wave i s a b o u t  Notice i n Fiqure  relative  f o r w a r d when t h e wave f o r m s i s  The d i s t a n c e i U  consequence  which  wave c o n s t i t u t e s one " s t e p " ; t h e  bjetween- t h e s p e e d  forward along the foot  This  a t which  and t h e s p e e d a t which t h e  segments o f t h e f o o t  move a s t h e y a r e m o m e n t a r i l y  in  known a s t h e segment s p e e d ) .  a wave  (hereafter  difference explained  i s somewhat c o n f u s i n g  the  the surf first  surfer  a group o f s u r f e r s along a l i n e  This  best  surfer  i s just  i s farthest  shoreward  tries  to catch  who have a r r a n g e d  perpendicular from  themselves  t o the beach.  surfer  As a wave comes i n t h e f i r s t  i t , i s accelerated  forwards a b i t , but  n e v e r g e t s up, t o s p e e d a n d t h e wave p a s s e s him by. second s u r f e r  does  wave moves i n t o surfer  arrives.  The  l i k e w i s e and so on down t h e g r o u p a s t h e  shore.  After  t h e wave h a s p a s s e d  w i l l h a v e moved s h o r e w a r d s  arrangement  Thus  the beach, t h e second  o f him, and s o o n , e a c h  w a i t i n g t o c a t c h a wave. surfer  and i s p e r h a p s  contained  by a n a l o g y .  Imagine in  a wave  and o r d e r w i l l  slightly  be t h e same.  This time t h e f i r s t  surfer  , each  but the l i n e a r  Now a s e c o n d  wave  " c a t c h e s " t h e wave.  27  ie.  he b e g i n s t o move a t t h e same s p e e d  wave and f i r s t  surfer  a s t h e wave.  advance on t h e s e c o n d  c a t c h e s t h e wave and s o on down t h e l i n e . reaches the l a s t forward all  surfer a l l the surfers  a t t h e same s p e e d  will  and s i n c e  surfer  will  be t r a v e l l i n g  This can only  I f each  collapses  a r e compelled  3.2b.  forward, speed  surfer  apply t h i s analogy  Imagine t h a t  compressed  to the schematic  of  As t h e wave a d v a n c e s ,  segments a r e added, f u r t h e r  t h e segments o f t h e f o o t the foot  two  methods:  with a speed foot to  that  compressing the  The f i n a l  outcome.is  This i s a  e q u a l t o t h e wave s p e e d  i n reality  d e c e l e r a t e by t h e p h y s i c a l  constraints  a r e compelled  compressibility  of  the foot.  by  t h e wave a f t e r i t h a s t r a v e l l e d f o r w a r d s a c e r t a i n  distance  each  move  of the foot  e x t e n s i b i l i t y and  As a c o n s e q u e n c e  never  by  o r 2) segments on t h e  move a t t h e wave s p e e d  i e . the f i n i t e  that  physical  e i t h e r t h e segments o f t h e f o o t  momentarily  structure,  more and more  T h i s s i t u a t i o n c a n be a v o i d e d  1)  moves  must a r r i v e a t t h e a n t e r i o r end  a t t h e same t i m e .  impossibility.  drawing of  segments b e g i n t o t r a v e l a t t h e same  segments a l r e a d y moving f o r w a r d . . all  i n line.  a s t h e wave o f c o m p r e s s i o n  t h e compressed  a s t h e wave.  i f the  t o d e c e l e r a t e and hop o f f t h e wave  b e f o r e they r e a c h t h e next Now  as  surfer catches the  wave t h e l i n e a r a r r a n g e m e n t c a n o n l y be m a i n t a i n e d surfers  also  a l l a r e on t h e same wave  r e a c h t h e s h o r e . a t t h e same t i m e .  wave t r a v e l s down t h e l i n e .  who  When t h e wave  happen i f t h e l i n e a r a r r a n g e m e n t o f t h e s u r f e r s the  The  segment i s l e f t  behind  and t h e l i n e a r a r r a n g e m e n t o f segments on t h e f o o t  28  is  maintained  (Figure  equal t o , but Figure a slug  i s usually  3.3  The the  g r e a t e r than, the  of m u l t i p l e  when c o m p r e s s e d  that  o f a moving s l u g . . part of the foot,  relative  diagrams exists How and  to the ground.  is  lifted greater  from  is  His feet  relative  the ground  foot  p l a n t e d and  turn  the l e n g t h of each  The.slug's  analogy "feet"  only  and  3.3  describe  slug  tied  to  foot this  e x p l a n a t i o n account f o r  e x p l a i n e d by  The  an torso  of  relative .  however a r e c o n s t a n t l y c h a n g i n g i s p l a n t e d on t h e . g r o u n d i t  t o the ground. i t travels  When t h e f o o t i s  forward  average number o f  with  This velocity  speed  a  velocity  eventually  a t which p o i n t  process i s repeated.  i s e q u a l to the  This  basic  movement o f a s l u g ?  ahead o f the t o r s o  t o r s o i s equal to the  that  ground.  a t a c o n s t a n t speed  of the t o r s o .  the  of  (the  mode o f l o c o m o t i o n : The  moves f o r w a r d  than that  c a r r i e s the  seen  p o r t i o n o f the  of the  does t h i s  O b v i o u s l y when a f o o t  stationary  t o the  t h e s e q u e s t i o n s c a n be  person  velocity.  be  moves f o r w a r d  o f F i g u r e s 3.2  i s the r e s t how  be  speed.  change t h e  i n the c e n t r a l  t o a more f a m i l i a r  a running  I t can  Again the f o o t  the a p p a r e n t l y continuous forward  analogy  segment  i n a wave; t h e a r e a between waves  schematic  answer t o b o t h  may  representation of the foot  waves does n o t  are s t a t i o n a r y  situation  wave speed  waves a r e p r e s e n t .  s e q u e n c e o f movements.  interwaves)  Thus t h e  i s a schematic  when s e v e r a l  the presence  3.2a).  The  speed  o f the f e e t .  steps taken  per  the  foot  of the This i n  second  times  step. can  be t r a n s f e r r e d  directly  a r e t h e s e r i e s o f waves and  t o the  slug.  interwaves.  A  29  FIGURE 3.3.  A d i a g r a m m a t i c e x p l a n a t i o n o f t h e mechanism by which s e v e r a l waves o f c o m p r e s s i o n c a n e x i s t on one f o o t and r e s u l t i n movement. As t h e waves move f r o m l e f t t o r i g h t t h e whole f o o t i s t r a n s p o r t e d t o the r i g h t .  30  31  segment o f  the  foot  interwave)  and  moving f o r w a r d  that  of  the  central  slug.  portion  of  i s alternately stationary  The  average  the  foot  constant  v e l o c i t y of  equal to  the  second  the  re-extension  function  (the  slug  constant  rate  directly  associated  the  (which do  foot  on  applies  time  22  video  that  points  foot  not  speed the  spent  the  of  foot  foot  the  is slug  fact  of  of  length,  there  waves  will  are  foot.  rate., the  a  that  the  by  This  slug  not  the  rims  of  waves). central portion  whole s l u g , t h e depend on  of  the  speed  of  the:relative  stationary.  Measurements  of c r a w l i n g ft. c o l u m b i a n u s show spend r o u g h l y e g u a l p e r i o d s o f  p e d a l waves.  Consequently the  average  time  speed  approximately twice that  of  slug.  Video recordings speed r e l a t i v e  from  the  the  of  waves, i n c l u d i n g  moving and  a segment i n a wave must be  a plot  The  a constant  will  of  is  (step  pedal  the  distance.gained  ensures that  the  and  whole  of  pedal  than  i n turn  front  wave  end  to  This  the  a l l portions  develop  recordings  on  whole.  anterior  in  the  out  each  average speed o f  moving s e g m e n t s o f  from  to  equal  times the  moves a t  with  must e q u a l t h e  periods of  the  r e a c h i n g the  Since the  a  compression r a t i o ) .  Consequently the  foot  rate)  v e l o c i t y of  t h u s be  waves r e a c h i n g  accompanying  13-^17 waves p r e s e n t be  as  an  a velocity greater  forward  will  slug  stepping  of t h e  constantly  the  number o f  per  with  (in  of  8 slugs.  to the  also allow f o r a speed o f  wave s p e e d The  ratio  and of  the  slug  measurement o f  whole s l u g . .  speed  for  wave s p e e d t o  18 slug  wave -  Figure  3.4  measurements speed  is  32  FIGURE 3.4.  The r e l a t i o n between t h e speed o f t h e p e d a l waves and t h e o v e r a l l s p e e d o f t h e s l u g . The waves move more t h a n t h r e e t i m e s a s f a s t as t h e slug.  33  Figure 3.4  2 Slug Speed  mm/sec  34  about  3.3. This  a check Since  knowledge o f wave s p e e d and  on  the  v a l u e of compression  wave s p e e d  i s 3.3  segment s p e e d  ratio  cited  t i m e s t h e whole s l u g  earlier.  speed,  advance  into  slug  speed.  Segments moving i n a wave, however, a r e travelling  speed r e l a t i v e  i n t e r w a v e a t 3.3  a wave  will  themselves  a stationary  provides  at 2 times the s l u g  t i m e s the  speed, o r at a  t o t h e wave o f 3-3/2=1.65 . . S i n c e t h e  segments i n a wave move s l o w e r r e l a t i v e  t o the  wave t h a n  segments i n an i n t e r w a v e , t h e a n t e r i o - p o s t e r i o r a wave segment ratio  must be l e s s t h a n an  which  The  calculated  information  further  use; h e l p i n g  control  t h e speed  be  individuals  The  could  slug 1.  i s thus  The  t h e y walk.  1mm/sec t o s l i g h t l y  could  may  W h i l e no  i t c a n be s e e n from  c o n t r o l i t s speed  slug  3.4  of  i n one  waves p r e s e n t on  1.69. be  put t o slugs could  Figure  3.4  of speeds  from  more t h a n 2 mm/sec. o f t h r e e ways:  v a r y t h e number o f waves p r e s e n t . number  i n c r e a s e the  slug's  I n t h e c o u r s e of m e a s u r i n g  t h e wave and  slug  3.4,  the c r a w l i n g  t h e number o f waves p r e s e n t on  slug  varied  the foot  the  would  Figure  present  1.65,  slug  other f a c t o r s remaining constant, i n c r e a s i n g  speed. for  ratio  and  t h e manner i n which  are c a p a b l e o f a range  more t h a n  of  to explain  a t which  slightly  Ml  compression  contained i n Figure  s a i d t o move v e r y f a s t ,  that  moving  compares c l o s e l y t o t h e measured a v e r a g e The  were c o u n t e d .  from  slug  of  i n t e r w a v e segment by a  1.6 5 i f e q u a l t i m e i s t o be s p e n t  stationary.  dimension  speeds  the f o o t  of  W h i l e t h e number o f waves  t o s l u g , t h e number o f waves  35  present  on t h e f o o t o f an i n d i v i d u a l  regardless 2. waves.  c f speed.  The s l u g  c o u l d vary the compression  I n c r e a s i n g the compression  s t e p l e n g t h and t h e r e b y other  d i d not vary,  wave f a c t o r .  the  wave s p e e d  3.4  shows  i n c r e a s e speed  If this  should  that t h i s  ratio  method  ratio  will  increase the  without  effecting  were p r e s e n t  be i n d e p e n d e n t o f s l u g  of the  any  i n reality,  speed.  Figure  i s n o t so, l e a d i n g t o t h e f i n a l  possibility. 3.  The s l u g  could vary  t h e wave s p e e d . . I n c r e a s i n g t h e  wave s p e e d , a l l o t h e r  factors  increase the stepping  r a t e and t h e r e b y  F i g u r e 3.4 that  shows, t h i s i s i n d e e d  t h e r a t e a t which  These o b s e r v a t i o n s a r e v e r y  and  (1924) who  than  found  Thus i t appears  o f i t s movement by  t o those  the foot.  o f C r o z i e r and  an i n c r e a s e i n s t e p l e n g t h effect  As  was  less  Crozier with  pronounced  t h e i n c r e a s e i n wave s p e e d .  accurate  during precise end  speed,  waves t r a v e l a l o n g  similar  speed, though t h i s  The o b s e r v a t i o n s an  the slug  will  were w o r k i n g w i t h L i m a x maximus .  Pilz,however,  increasing  constant,  the case..  c o l u m b i a n u s c o n t r o l s t h e speed  controlling  Pilz  remaining  d e s c r i p t i o n o f the gross  locomotion.  It will  Video  p o i n t s on t h e f o o t .  To  this  were made o f t h e f o o t o f a moving  slug  were c a r r i e d o u t .  tapes  while the t e l e v i s i o n microscope.  movements of t h e f o o t  be u s e f u l however t o know t h e  movement o f i n d i v i d u a l  two p r o c e d u r e s 1.  r e p o r t e d a b o v e f o r A. c o l u m b i a n u s a r e  camera was  mounted  M a g n i f i c a t i o n was s u c h  on a d i s s e c t i n g  t h a t a 4 mm  length of  36  foot  occupied  television blemishes the  foot  screen.  of  .  At t h i s  and t h e i r  movements c a n be r e c o r d e d .  jitter  possible.  a strict  screen.  that  T h u s , w h i l e a movement o f 20-30 um can be  between t h e s t a r t and f i n i s h this  actually  be s p e c i f i e d .  occurred  thus gained Figure  point can  point that  period  a s a wave o v e r t a k e s a p o i n t  i s gradually this  accelerated  velocity.  I t i s often  past  i n other  wave h a s p a s s e d .  words t h e r e  backslip  the time  greater  than  for a  short  back t o z e r o  deceleration  continues  i s some b a c k s l i p a f t e r t h e  This backslip i s small,  t o a b o u t 30 t o 50 um.  It  l e s s t h a n t h e wave  i s decelerated found t h a t  wave.  on t h e f o o t ,  peak v e l o c i t y i s c o n s i d e r a b l y  the point  fora  t o a peak v e l o c i t y .  The peak v e l o c i t y i s m a i n t a i n e d  before  zero;  Spatial resolution  the passage o f a pedal  average v e l o c i t y but i s s t i l l  velocity.  of  segment when t h e movement  3.5 shows an a v e r a g e v e l o c i t y p r o f i l e  on t h e f o o t d u r i n g  Notice the  cannot  o f a 5-10 f r a m e  a t t h e expense o f t e m p o r a l r e s o l u t i o n .  be s e e n t h a t  that  As a c o n s e q u e n c e o f  w i t h any c e r t a i n t y t h a t a  segment, t h e t i m e w i t h i n  is  i s a b o u t 20-  a number o f f r a m e s , 5 - 1 0 , be  i t c a n be s t a t e d  h a s moved.  detected  magnification  spatial  f r a m e by frame a n a l y s i s i s n o t  I t i s necessary  examined b e f o r e point  The  f a c t o r i s c o n t r o l l e d p r i m a r i l y by t h e " j i t t e r "  t h e image on t h e t e l e v i s i o n  this  individual  o f mucus g l a n d s a r e v i s i b l e on  o f the system a t t h i s  This  dimension of the  magnification  and c o n c e n t r a t i o n s  resolution 30 um  the e n t i r e v e r t i c a l  a m o u n t i n g a t most  As a c o n s e q u e n c e o f t h i s  small  course of b a c k s l i p i s uncertain,  amount as  37  FIGURE 3 . 5 .  The v e l o c i t y and d i s t a n c e p r o f i l e s o f an a v e r a g e p e d a l wave. The c u r v e s r e p r e s e n t v a l u e s a v e r a g e d from 22 s e p a r a t e c r a w l s by two Ariolima x columbianus .  F i g u r e 3.5  seconds  39  explained  above.  the  1/6  first By  of a s e c o n d a f t e r  television  to record the  movement o f  of t h e  f o o t and  simultaneously.  The  shown i n F i g u r e whole f o o t .  velocity point  rim  by  and  motion slug  rim  rim  i t gains  crawls.  t o the  They do  the  observations  are  on  i s just again  plane not,  slugs  the  the  the  wave .  foot  .  At  The  soon r e a c h i n g rim  speed.  point. The  sufficient  adjacent  are  made on  adjacent.  a  The  distance  so t h a t  the  a s a n o t h e r wave  of the  foot  shown i n p l a t e 3 - 1 . suggests t h a t the passage of a pedal  accurate  o f the  however, p r o v i d e to t h i s  plane.  In s a g g i t a l o r  the  pedal  The  evidence  the  pedal  be  the on  foot  during  sectioned  as  parasaggital  provided  wave when w a l k i n g  the.  To i n v e s t i g a t e  and  waves can  lift  which  information  movements o f t h e  s l u g does n o t  Instead,  measurements o f  g l a s s p l a t e on  were q u i c k l y f r o z e n  i n Chapter 2.  substratum.  the  provide  possible dorso-ventral  sections  s u c h measurement  moves a t a c o n s t a n t  recordings  parallel  described  rim  central point.  Video  locomotion  i n the c e n t r a l  i n the  points  a b o u t movements p e r p e n d i c u l a r the  i t is  one  ground  c e n t r a l point  the  2.  points  c e n t r a l p o r t i o n o f the  c e n t r a l p o i n t s are  overtakes  camera c o r r e c t l y  a c c e l e r a t e s r a p i d l y forward,  the  i s reached.  measurement i s s t a r t e d j u s t a s  such t h a t  i n the  gained  confirm  c e n t r a l and  point  velocity  points  r e s u l t s of  p o i n t i n the  time the  central  adjacent  3 . 6 and  The  reaches the this  zero  p o s i t i o n i n g the  possible area  I t i s c e r t a i n however t h a t i t h a p p e n s i n  clearly by  these  foot during a  seen  as  sections the  non-porous  wave c o n s i s t s e n t i r e l y  of  an  40  FIGURE 3.6.  The c o n t i n u o u s f o r w a r d movement o f t h e r i m s and t h e a l t e r n a t e movement and non^movement o f t h e c e n t e r o f t h e f o o t r e s u l t i n t h e same a v e r a g e forward v e l o c i t y .  Figure 3 . 6  0.5  1.0  seconds  42  PLATE 3.1.  a m i c r o g r a p h showing t h e p e d a l e p i t h e l i u m o f a crawling slug. A) A s a g g i t a l s e c t i o n showing t h e t r a n s i t i o n between a wave (W) and an i n t e r w a v e (I) . N o t i c e t h a t t h e f o o t i s n o t l i f t e d i n t h e wave. B) A h i g h e r m a g n i f i c a t i o n o f t h e e p i t h e l i u m u n d e r a wave. The e p i t h e l i a l c e l l s a r e compressed a n t e r i o - p o s t e r i o r l y . C) A h i g h e r m a g n i f i c a t i o n o f t h e e p i t h e l i u m u n d e r an i n t e r w a v e . The e p i t h e l i a l c e l l s a r e extended a n t e r i o - p o s t e r i o r l y .  44  anterio-posterior examining portion  compression.  t h e shape  of epithelial  o f the foot  and  short  the  compressed  the c e l l s  dorso-ventrally.  agreement  the is  foot  i s lifted  simply  that  from  anterio-posteriorly  The c o m p r e s s i o n  ratio  3.1 i s a b o u t  2, i n  by o t h e r methods.  those of Lissman  (1945a)  (1973) w o r k i n g  with  Both o f t h e s e a u t h o r s f o u n d  as i t i s compressed  this  In t h e extended  dimensions are reversed i n  a s p e r s a and J o n e s  reticulatus.  possible  These  with values c a l c u l a t e d  with Helix  Agriolimax  are long  shown i n P l a t e  These r e s u l t s d i f f e r working  cells.  areas o f the f o o t .  measured on t h e s e c t i o n rough  T h i s c a n be s e e n by  difference  r e f l e c t s a species  i n a p e d a l wave.  i n t h e shape  difference.  that It  o f p e d a l waves  Another  explanation,  however, a p p e a r s more p r o b a b l e .  Explanations o f gastropod  locomotion that  t o be l i f t e d  from  three  sandwiched 1. and J o n e s the  major  reguire  the foot  between t h e s l u g  I t h a s been  and s u b s t r a t u m  assumed  and Trueman,  mucus o r some f l u i d  observed. that  exudate.  this  when t h e f o o t  portion  travels This  (1973) s p e c u l a t e s ,  mucus o r f l u i d  is filled  i s lifted with  either  As t h e wave t r a v e l s f o r w a r d ,  i n f r o n t of the f o o t . Jones  (see F i g u r e 3 . 7 ) .  ( L i s s m a n , 1945a; J o n e s , 1973;  1970) t h a t  volume o f mucus o r f l u i d  deposited  suffered  p r o b l e m s , a l l r e l a t e d t o t h e mucus  space beneath t h e l i f t e d  this  have  i s somehow  w i t h i t and s h o u l d be p r o c e s s has never  been  but without evidence, reabsorbed i n t o the  foot. 2returned  Once t h e f o o t  i s lifted  i n a wave i t must be  t o t h e s u b s t r a t u m t o which  i t will  adhere  during  45  FIGURE  3.7.  P r o b l e m s w i t h l i f t e d p e d a l waves. A) A l i f t e d wave t r a n s p o r t s mucus o r f l u i d t o t h e a n t e r i o r end o f t h e f o o t . B) U n l e s s a p a r t i t i o n were t o s e p a r a t e t h e two h a l v e s o f t h e l i f t e d wave, t h e downward f o r c e o f t h e h y d r o s t a t i c p r e s s u r e would c o u n t e r a c t t h e upward f o r c e due t o m u s c u l a r c o n t r a c t i o n , l e a v i n g only a net forward f o r c e .  Figure  3.7  47  the  interwave.  Jones,  Mechanisms p r o p o s e d  1973; J o n e s and Trueman,  lifting  to occur  fluid  I t i s this  upwards on t h e mucus  o f low p r e s s u r e  p r e d i c t e d low p r e s s u r e  out o f t h e f o o t t o f i l l  2) i t t h e same t i m e  responsible for forcing  substratum)  i s pushing  partition  halves at  downwards of high  (as shown  none  will  within the foot  t h e f o o t back t o t h e  on t h e mucus b e n e a t h t h e  pressure.  However,  i n F i g u r e 3.7b)  unless a  separates  t h e two  o f t h e wave, t h e mucus b e n e a t h t h e wave must a l l be  t h e same p r e s s u r e .  (and  pull  t h e s p a c e b e n e a t h t h e wave.  (supposedly  rigid  (see F i g u r e  which w o u l d  the h y d r o s t a t i c pressure  wave c r e a t i n g an a r e a  f o r the  1) The c o n t r a c t i o n o f t h e  the f o o t p u l l s  b e n e a t h a wave, c r e a t i n g an a r e a 3.7b).  1945a;  o f t h e f o o t r e q u i r e two  simultaneously:  m u s c l e s which r a i s e  (Lissman,  1970) t o a c c o u n t  and s u b s e q u e n t l o w e r i n g  processes  t o date  In other  words i f no p a r t i t i o n  has been f o u n d ) t h e downwards  c a n c e l and t h e mucus w i l l  exists  and upwards f o r c e s  be a t ambient  pressure.  J o n e s and Trueman  (1970) however measure a  substantial  negative  ( ie,  under pedal  of  pressure  the limpet 3.  Patella  animal  fluid  first  must f l o w  surrounding occur  on  begins  t h e new  course  t h a t a very  large force  the f o o t from the substratum  t o move.  mucus o r from  i n the time  Such f l o w  to l i f t  into  waves  yulgata .  I t c a n a l s o be c a l c u l a t e d  would be n e c e s s a r y the  an upwards f o r c e )  F o r t h e f o o t t o be  volume c r e a t e d , e i t h e r  the t i s s u e s , of a s i n g l e  wave  would r e q u i r e t h e a p p l i c a t i o n  t h e f o o t on t h e o r d e r o f 10,000  and t h i s (about  flow  as  lifted from t h e must  1sec).  o f upwards s t r e s s e s  kg/cm . 2  This factor i s  48  fully  explained As  i n Chapter  a consequence  9.  of the problems d e s c r i b e d  mechanisms which r e q u i r e  lifting  here  these  of the foot are l e s s  than  convincing.  Mechanism The avoids  For Slug results  these  previous  of t h i s  suggest  proposed  a mechanism t h a t  the r e s u l t s  of the  a minor change i n t h e  by J o n e s  Simply  (1973).  a slug w i l l  i f i t i s crawling  not l i f t  stated,  i t s foot  on a n o n - p o r o u s  this during  inflexible  f  surface.  R a t h e r , t h e mucus l a y e r r e m a i n s c o n s t a n t i n  thickness  and t h e mucus i s s h e a r e d  and  t h e s t a t i o n a r y substratum  a porous s u r f a c e This  i t will  lift  assumption be  However, d u r i n g  i t s foot.  of l i f t i n g  substantiated  t i s s u e support  t h e f o o t from  concerning  the substratum.  the p r o p e r t i e s of the pedal  i n C h a p t e r 9.  Unable t o l i f t  thereby  narrowing t h e spaces o f the pedal to pull  a force pulling  This  upwards f o r c e  that the  of the foot are  muscles i n s t e a d a c t t o p u l l  force required  3.8.  on a n o n p o r o u s s u r f a c e t h e  oblique  by  movement on  o f t h e mucus b e n e a t h t h e f o o t a r e s u c h  m u s c l e s and c o n n e c t i v e incapable  .  between t h e moving f o o t  mechanism i s shown s c h e m a t i c a l l y i n F i g u r e  When t h e a n i m a l i s w a l k i n g properties  both  I t i s essentially  change r e g u i r e s t h a t locomotion  study  p r o b l e m s and e x p l a i n s  authors.  mechanism  Kinematics  This mucus  will  the f o o t , the  t h e body c a v i t y down hemocoel.  The  t h e body c a v i t y down i s c o u n t e r a c t e d  upwards on t h e mucus b e n e a t h t h e f o o t . will  appear  as a n e g a t i v e  pressure  i n the  49  FIGURE 3 . 8 . , a model f o r t h e movement o f t h e f o o t o f a r i o l i m a x c o l u m b i a n u s on a s o l i d s u b s t r a t u m (a) and a p o r o u s o r f l e x i b l e s u b s t r a t u m ( B ) . The f o r w a r d movement o f t h e wave and t h e d e c r e a s e d thickness of the foot r e s u l t i n a high h y d r o s t a t i c p r e s s u r e i n t h e h a e m o c o e l ahead o f t h e wave.  50  Figure 3.8  SOLID SURFACE epithelium  mucus layer  51  mucus t o  a s e n s o r on  however, t h i s directed  the  substratum  upwards f o r c e i s not  movement o f i n the  the  the  fluid  the  narrowed c h a n n e l s i n the  T h i s r a i s e s the the  wave.  the  of  radius,  that  the  v e n t r i c l e as  for  the  that  the  i s an  ahead  fourth  to create  of  fluid  necessary f o r the  power  spaces  of  a the  wave.  It  (rather than c o n t r a c t i o n  Jones of  through  contraction.,  to force  inverse  the  (1973) i s  peristaltic  This  pumping  of  hydrostatic  the  of  responsible  haemocoel.  f o r re-extending  be  the  muscles are  require  transported  i s never l i f t e d  i t b a c k down.  foot  there  I t also  slug i s walking  fluid pressure  at i t s  substratum  capable of  on  w i t h each  i s no  pedal  the  problem  a porous or  wave,  and  with  measurement  flexible  i n that  substratum  ability  fluid  waves.  either pulling  or deforming the  case of a porous s u r f a c e  mucus o r  accounts f o r the  s i t u a t i o n i s changed o n l y now  that  forward  pressures.under the  When t h e  the  muscular  It i s t h i s haemocoelic  foot  foot  negative  surface  to flow  haemocoelic f l u i d  mechanism  pressure  dorsally  wave moves f o r w a r d  h a e m o c o e l ahead o f  mechanism does n o t  beneath the  getting  i n the  by  end.  This  since  of  narrowed s l i g h t l y  s u g g e s t e d by  i s responsible  anterior  rate  i s analogous t o the  through a tube.  the  reguired  i t i s only  this  hydrostatic  situation  area  pressure  pressure  seems l i k e l y  As  of the  at a given  h a e m o c o e l t o be  substantial  of  the  .  Again,  accompanied  haemocoel i s f o r c e d  pressure  Since  through a tube function  pedal  foot  surface,,  the  the foot  itself.  to detach  the  oblique away f r o m In foot  the is a  52  consequence o f t h e p o r o s i t y o f t h e s u r f a c e which a l l o w s a i r to easily  r e p l a c e t h e d i s p l a c e d mucus.  for  a i r t o move i n t o  this  The  lowering o f the foot  space  than  I t i s much  easier  i t would be f o r mucus.  i s accomplished  by t h e h y d r o s t a t i c  pressure  i n t h e p e d a l h e m o c o e l , c r e a t e d a s e x p l a i n e d above.  In  f o r the foot  order  t o be f o r c e d down o n l y t h e a i r b e n e a t h  the  wave must be d i s p l a c e d , a p r o c e s s  the  p o r o s i t y of the s u r f a c e .  to  walk o v e r  In nature  s u r f a c e s o f many t y p e s .  are porous o r f l e x i b l e structures  again f a c i l i t a t e d  such  by  slugs are required  While  many o f t h e s e  there are smooth,nonporous,inflexible  as t h e bark  o f some t r e e s and s h r u b s , t h e  s t a l k s o f p l a n t s , a n d t h e s u r f a c e s o f r o c k s on which t h e slug  would n o t be a h l e t o l i f t At p r e s e n t t h i s  will  i t s foot.  mechanism i s p r i m a r i l y  require further experimentation  speculation.  It  b e f o r e i t c a n be  substantiated. One f u r t h e r slug  is lifted  will  attempt  the  foot  layer line  phenomenon may  o f f the substratum  to crawl.  Pedal  and, i f some c h a l k  can be s e e n  i n the c e n t r a l  across  mucus  the  e x t r e m e edges o f t h e f o o t  mucus i n t h e r i m s .  n  on  t h e mucus  If a straight i t c a n be seen  chalk that  p o r t i o n o f t h e f o o t and t h a t a l o n g move p o s t e r i o r l y  more l i k e l y  than  i s deformed  t o imagine  waves c a n a c c o u n t  I t seems much  faster  the chalk line  It is difficult  mechanism whereby t h e p e d a l o f mucus.  move a n t e r i o r l y  on t h e f o o t ,  the foot  Consequently  t h e shape o f an "M .  movement  waves w i l l  to move.posteriorly.  i s drawn l a t e r a l l y  If a  and h e l d i n m i d - a i r , i t  i s dusted  the  to  be m e n t i o n e d h e r e .  a  for this that the  53  movements o f c i l i a , responsible . the is  as d e s c r i b e d  However,  e f f e c t i v e n e s s with  Litt  a G' o f 1 N/m  ciliated  epithelium  observations  of a frog  a G' o f 100 N/m , 2  be e f f e c t i v e l y  transported.  this  :  modulus.  was t r a n s p o r t e d  2  mucus, w i t h  et a l *  (1976) have f o u n d  which mucus i s t r a n s p o r t e d  d e p e n d e n t on i t s s t o r a g e  with  i n C h a p t e r 2, a r e  by  They f o u n d t h a t most  palate.  effectively  that  cilia mucus by t h e  A. c o l u m b i a n u s p e d a l  w o u l d , by t h i s c r i t e r i o n , n o t Beyond  these  general  phenomenon h a s n o t been i n v e s t i g a t e d .  54  CHAPTER FOOfi Physical The  importance  adhesion period  o f p e d a l mucus i n t h e l o c o m o t i o n  of g a s t r o p o d s has  of time.  a supply  B a r r (1926a) r e p o r t s t h a t  neither  the  walk n o r a d h e r e .  p e d a l mucus t o l o c o m o t i o n .  authors,  n o r any  conducted It  other author  tests to ascertain  will  be  Later  will and  the  be u s e f u l testing  of the  the o b v i o u s  However none o f t o my  knowledge  physical  properties  to review  procedures  the b a s i c  used  importance  these ,have  t h e p r o p e r t i e s of  viscoelastic  pedal  authors  shown i n t h i s c h a p t e r t h a t  p e d a l mucus i s an u n u s u a l describing  slugs deprived of  cauterizing  ( L i s s m a n , 1 9 4 5 b ; J o n e s , 1 9 7 3 ) remark on of  and  been known f o r a c o n s i d e r a b l e  o f p e d a l mucus by  g l a n d can  Properties  p e d a l mucus. columbianus  material.  of t h i s  Before  slug's slime i t  concepts, terminology,  i n the study o f  viscoelastic  materials. The that and  term  viscoelastic  i s used  to d e s c r i b e a  s i m u l t a n e o u s l y shows p r o p e r t i e s t y p i c a l solids:  Elasticity  solids and  are e l a s t i c ,  viscosity  fluids  material  of both  fluids  are viscous.  are p r e c i s e l y  defined concepts.  Elasticity The pushed on term  primary c h a r a c t e r i s t i c they  push b a c k .  elasticity.  shown i n F i g .  of s o l i d s  T h i s concept  i s that  i s quantified  Take a s an example t h e cube o f  4.1a.  Imagine t h a t  one  g l u e d t o a non-moveable s t r u c t u r e and  when i n the  material  s i d e o f the  cube i s  the opposite side i s  55  FIGURE 4.1.  The p r o p e r t i e s o f e l a s t i c s o l i d s . An undeformed cube (A) i s d e f o r m e d (B) by t h e a p p l i c a t i o n o f a f o r c e . , F o r c e ( o r weight) can be p l o t t e d a g a i n s t d e f o r m a t i o n ( C ) . , N o r m a l i z i n g f o r c e and d e f o r m a t i o n t o t h e d i m e n s i o n s o f t h e sample a l l o w (C) t o be r e p l o t t e d (D) i n t e r m s o f s t r e s s ( f o r c e / a r e a ) and s h e a r r a t i o ( Y / X ) . The s l o p e o f t h e s t r e s s / s h e a r r a t i o l i n e i s t h e s h e a r modulus, G. The s t r e s s / s h e a r r a t i o c u r v e need n o t be l i n e a r , a s shown i n ( D ) , b u t G a t a p o i n t i s s t i l l the slope of the l i n e at that point.  56  Figure  4.1  P,shear  E  p.shear  ratio  ratio  57  glued t o a plate weights weight  applied  on which one c a n hang t h e cube w i l l  i s hung from  be u n d e f o r m e d .  t h e p l a t e t h e cube w i l l  d i s t a n c e a s shown i n F i g . . 4.1b. t h e cube w i l l  immediately  larger  applied  weight  distance,  shape.  as F i g .  4.1c c a n be drawn.  a larger  weights  a t each  of i n c r e a s i n g  weight  a curve  T h i s curve of weight  t o t h e p a r t i c u l a r cube, a p i e c e o f  t h e same m a t e r i a l o f d i f f e r e n t  shape o r s i z e  will  t o a c h i e v e t h e same d e f o r m a t i o n  require .  In  order t o d e s c r i b e t h e p r o p e r t i e s of t h e m a t e r i a l from a sample weights  and d e f o r m a t i o n s  i s distributed  This particular by t h e o t h e r (sigma).  be n o r m a l i z e d the is  are normalized.  A weight  hung on  i n F i g . , 4.1a p l a c e s a known f o r c e on t h e cube and  this force  stress  which  i s made r a t h e r t h a n t h e shajae o f t h e s a m p l e ,  the p l a t e  one  A  o f the weight, t h e  such  weights  i s removed  t h e cube t o d e f o r m  and r e c o r d i n g t h e d e f o r m a t i o n  different  a small  cause  size  refers  deform  t o i t s undeformed  will  no  When a s m a l l  I f t h e weight  d i s a p p e a r . . By a d d i n g  versus deformation  With  revert  and a g a i n upon r e m o v a l  deformation w i l l  weights-.  force  a c r o s s t h e a r e a o f t h e cube  and a r e a c a n be n o r m a l i z e d by  ( f o r c e / area) The d e f o r m a t i o n  t o the dimensions  sample s thickness. 1  known a s t h e s h e a r  to arrive incurred  by t h i s  o f t h e sample,  The r a t i o  ratio  a t a term  face.  dividing called  s t r e s s can  in this  case  (deformation/thickness)  symbolized  by r h o .  For small  deformations t h e shear r a t i o  i s approximately equal to the  shear  4.1b).  strain  the shear procedures  (tan a i n F i g .  strain used  cannot in this  For large  be m e a n i n g f u l l y a p p l i e d study.  Consequently  deformations t o the  shear  ratio i s  58  used.  The c u r v e  terms t o y i e l d m a t e r i a l from  4.1c c a n t h e n  4.1d.  immediately  T h i s graph  applied  4,1d  notice  that  r h o i s t h e same. the curve  i s a straight  linear  this  analysis".  value of rho the r a t i o  line  In  sigma  over  way o f s a y i n g  w i t h s l o p e sigma/rho  .  that  This  a l l the information contained i n the  sigma o v e r  A m a t e r i a l may be e l a s t i c  i s unambiguous y e t n o t l i n e a r . .  shear  modulus  rho curve i s s a i d b u t n o t have a  In t h i s case  no s i n g l e  d e f i n e t h e c u r v e , G must be computed f o r  point.  Molecular The has  from  s t r e s s - s h e a r r a t i o c u r v e ; f o r example t h e c u r v e o f  value of G w i l l each  t o be e l a s t i c .  A m a t e r i a l with a l i n e a r  be "Hookean".  4.1e  an unambiguous  and has been g i v e n a name , t h e e l a s t i c  o r G. to  increasing or  T h i s i s simply another  slope then conveys graph  magnitude o f d e f o r m a t i o n ,  f o r which such  c a n be g l e a n e d a t each  ratio  a t which t h e m a t e r i a l  whether t h e f o r c e . i s  Any m a t e r i a l  term  The r a t e  the f i n a l  c a n be drawn i s s a i d Another  s t r e s s t h e r e c o r r e s p o n d s one  returns to zero.  nor does i t matter  graph  The g r a p h i s  and when t h e s t r e s s i s removed t h e s h e a r  deforms does n o t e f f e c t  decreasing.  i n t h e s e new  describes a property of the  which t h e cube i s made.  unambiguous: f o r e a c h shear r a t i o ,  be r e p l o t t e d  Basis For E l a s t i c i t y molecular basis  forelastcity  been t h e s u b j e c t o f much s t u d y .  study i s the theory  of rubber  t o t h e t h e o r y may be f o u n d  i n " soft  The r e s u l t  elasticity  i n Aklonis,  .  " materials of this  An i n t r o d u c t i o n  M a c K n i g h t and Shen  59  (1967); o r a more t h o r o u g h  treatment  Ferry  t h e r m o d y n a m i c and  (1965).  The  precise  in Treloar  a r g u m e n t s o f t h e t h e o r y w i l l n o t be  reviewed  will  study.  be made o f them  assumptions  and  and  briefly  will  he  The account has  theory  a l l low  an  but  properties  been f o u n d  modulus  natural  heating.  (E o r G  collected  from  use  general  10  however,  proposed  of natural  6  N/m  to  rubber.. I t  f o r the  to 10  2  first  properties )  of  elastic  s e r v e s as the b e s t  the rubber  mixinq  the l a t e x  S t u d i e s o f the v u l c a n i z a t i o n t h e l a t e x i s formed  p o l y i s o b u t y l e n e c h a i n s , and  that  example  bridges.  the m a t e r i a l  Only  constant  and  the polymer  contort  t o each  be and  that  independent  other  .  The  c a n be  c h a i n s o f the  a t random and that  applied  thermal  the chains w i l l  shape o f any  moment i s t h u s a random e v e n t . probability  long,  when t h e s e c r o s s l i n k s  motion) e n s u r e s motion  with sulphur  are e x p l a i n e d i n the f o l l o w i n g  Before c r o s s l i n k i n g ,  (brownian  i t must  process reveal  from  latex  are  with by present  elastic.  These f a c t s  to t w i s t  rubber  during treatment  sulphur these c h a i n s are c r o s s l i n k e d disulfide  tree,  In o r d e r t o become " r u b b e r "  This involves  before treatment  free  was  to account  rubber s t i l l  a viscous l i q u i d .  vulcanized.  is  The  as no  e x p l a n a t i o n of the t h e o r y .  When f i r s t is  here  here.  of r u b b e r e l a s t i c i t y  f o r the p h y s i c a l  solids; for  reviewed  or  statistical  c o n c l u s i o n s of the t h e o r y are used,  subsequently  nearly  per se i n t h i s  (1975)  The  one  latex  group  are  agitation be i n  c h a i n a t any  statistics  to the e n t i r e  manner:  given  of of  chains  60  forming t h e latex configuration latex past  these each  to ascertain  of the chains.  kinetically  o t h e r , each  the m a t e r i a l w i l l Now t a k e  configuration crosslinked The  free chains w i l l  respond  to the  by s l i d i n g  flow.  still  .  i s applied  m a i n t a i n i n g a random c o n f i g u r a t i o n and  If crosslinks  chain w i l l  probable  I f a stress  an u n s t r e s s e d l a t e x  polymer c h a i n s . each  t h e most  fluid  and c r o s s l i n k t h e  are s u f f i c i e n t l y  f a r apart  be a b l e t o assume a random  I f , however, a s t r e s s  network o f c h a i n s , t h i s  i s applied  situation  c h a i n s a r e no l o n g e r f r e e t o s l i d e  t othe  i s changed.  past each  o t h e r . . As  a c o n s e q u e n c e , when t h e m a t e r i a l i s s t r e t c h e d , t h e ends o f the  c h a i n s a r e on t h e a v e r a g e  direction yields  of stretch  a certain  (see F i g .  average  pulled  farther apart i n the  4.2) .  S i n c e random  motion  end t o end d i s t a n c e , and t h i s  d i s t a n c e i s d i s t u r b e d upon s t r e t c h i n g ,  i t c a n be shown  that  t h e c o n f i g u r a t i o n s t h e c h a i n s assume when t h e m a t e r i a l i s stretched This  are l e s s situation  random. o f (undeformed-random)  random) c a n be r e s t a t e d entropy  i n terms o f the c o n f o r m a t i o n a l  o f the rubber  network.. The s t a t e  randomness i s a s t a t e  o f maximum e n t r o p y .  randomness c o n s t i t u t e s a d e c r e a s e deforming the.rubber  (deformed-less  a p i e c e o f rubber  o f maximum A decrease i n  i n entropy.  T h u s by  , one d e c r e a s e s t h e e n t r o p y o f  network, a process  which  under t h e l a w s o f  t h e r m o d y n a m i c s r e q u i r e s t h a t work be done on t h e r u b b e r . When t h e f o r c e to  of deformation  spontaneously  i s removed t h e n e t w o r k  maximize e n t r o p y ,  tends  which i s a c c o m p l i s h e d  by  61  FIGURE 4.2.  The m o l e c u l a r b a s i s o f r u b b e r e l a s t i c i t y . A) A l o n g c h a i n c o n s i s t i n g o f n l i n k s , e a c h o f l e n g t h , L, w i l l assume a c o n s t a n t l y c h a n g i n g random c o n f i g u r a t i o n . The most p r o b a b l e d i s t a n c e between t h e ends o f t h e c h a i n i s R = (2/3 n L ) x / 2 . B) A c r o s s l i n k e d , b u t u n s t r e s s e d network i s s t i l l randomly a r r a n g e d . However, when a c r o s s l i n k e d network i s s t r e s s e d (C) R i s s h i f t e d away from t h e a v e r a g e v a l u e , and t h e c h a i n s a r e c o n f i n e d t o fewer c o n f i g u r a t i o n s . As a c o n s e q u e n c e t h e e n t r o p y o f t h e s y s t e m i s decreased. 2  62  63  returning  to the  o r i g i n a l d i m e n s i o n s and  the  work  deformation  i s recovered.  Thus a c r o s s l i n k e d  kinetically  free  elastic.  This  principle applies  kinetically logically soft  free  valid  material  n e t w o r k , no proposed  chains i s  to  to  i n v e r t the  is elastic  between e l a s t i c i t y  crosslinked  structure  crosslinked  strong  evidence  This  of s o f t  a l l o w s one  network i s  of  say  that  to  a  crosslinked been  universal materials  use  f o r the  not  since  mechanism i s known o r has solids.  of  While i t i s  argument and  correlation  as  .  i t i s formed o f a  other e l a s t i c  network  s u c h network  random p o l y m e r c h a i n s  for soft elastic  elasticity  any  of  the  and  presence  f a c t that  of  a  present.  Viscosity The This  primary c h a r a c t e r i s t i c of  concept i s q u a n t i f i e d  i n the  term  s a k e o f t h i s example i m a g i n e t h a t tension  do  not  e x i s t so  as  shown i n F i g .  as  i n the  4.3b). will  a  t h i s case of  reach  an  cube o f  and  fluid  can  i s applied  As  sample w i l l  deform^ . I f a  stress i s applied  the  sample w i l l  deform  deformation. c u r v e can  be  By  stress, will  applying  drawn as  forces  in Fig.  be to  deform  the  the  For  not of  4.3c  the  formed the  plate,  (Fig._  c u b e , however, t h e  deformation.  flow..  surface  stress i s applied  upon r e m o v a l o f  they  viscosity.  sample w i l l  a liquid  equilibrium  i s that  gravity  • If a stress  p r e v i o u s example the  In  not  4.3a.  that  fluids  long  sample as  the  larger  f a s t e r , hut  again  recover i t s increasing showing the  magnitude  a  relationship  64  FIGURE 4.3.  The p r o p e r t i e s o f v i s c o u s l i q u i d s . . A g i v e n s t r e s s a p p l i e d t o a cube o f v i s c o u s l i q u i d (A) r e s u l t s (B) i n a s i n g l e s h e a r r a t e (shear ratio/second). The s h e a r r a t e i s p r o p o r t i o n a l t o t h e s t r e s s ( C ) . The s l o p e o f t h e s t r e s s / s h e a r rate curve i s the v i s c o s i t y . The s t r e s s / s h e a r r a t i o c u r v e need n o t be l i n e a r , as shown i n ( D ) , however t h e v i s c o s i t y a t a p o i n t i s s t i l l the slope of the l i n e at t h a t p o i n t .  Figure 4.3  shear  rate  shear  rate  66  between s t r e s s and symbolized  as  description there  rho  rate of dot.  This  of a p r o p e r t y  i s one  deformation. graph  of the  (shear  provides  fluid,  ratio)  an  unambiguous  f o r each  shear r a t e ; deformations of  the  stress  liquid  are  not  recovered. Again the single  linear  number - t h e  r e l a t i o n s h i p can  slope  of the  be  line.  characterized  This ratio  by  a  of  1 stress/shear  rate  i s the  stress/shear  rate  curve i s s a i d to  s h o w i n g a non  linear  characterized  by  Molecular The  Basis  one  to  fluid,  h e n c e , no would  be  zero.  that  the  That a l l r e a l  bound t o e a c h  The  can  i s at  one  be  for  independent  change shape  and  the have  that  were t o  e n e r g y , ,and  fluid's viscosity measurable  i n d i v i d u a l molecules are  t h e r e . i s some e n e r g e t i c a m o l e c u l e f r o m one  magnitude of the  energy c o s t  to  without  reguirement no  of  energetically  this criterion  require  fluids  while  other  of  If this  a fluid  a c c o m p a n i e s movement o f  another.  material  basis  to a s o l i d ,  that  flow  The.prime requirement  however, i t would  implies  be  certain fixed positions relative  f o r c e to deform  viscosities rigidly  met,  Fluids  r e l a t i o n s h i p must  v i s c o s i t y and  i t s i n t e r n a l energy.  strictly  linear  "Newtonian".  a m o l e c u l e i s not  I t i s on  in contrast  a  Flow  m o l e c u l e s of the  occupying  be  with  each s t r e s s .  complex .  i s , that  A fluid  rate  V i s c o s i t y And  and  the  molecules.  altering be  For  another, that  restrained  a  a viscosity at  simple  i s that  other  stress/shear  molecular basis of  time both flow  viscosity.  not  cost  point  determines  to the  67  viscosity  .  molecules  which a c c o u n t s f o r t h e  relative as  to  a fluid  benzene.  concept is  Thus i t i s t h e  constant  where no  breaking  and  v i s c o s i t y of  however, t o  precise fashion  assumed t h a t  high  between  h y d r o g e n bonds a r e  It is difficult,  i n any  usually  hydrogen bonding  flow  each  Viscoelastic No viscous the if  to macromolecular f l u i d s .  i n these f l u i d s i n v o l v e s  reforming  of  weak bonds ( i n d i v i d u a l  As  to  the  viscous  properties useful  elastic  the  contributions In  an  (synovial  these  separately  to the  equation  the  f o r the  fluid)..  materials In  a general  quantify  overall  of t h i s o b j e c t i v e i t aid  of  some  shown i n F i g u r e  spring  the  These  structures:  a model f o r a m a t e r i a l t h a t deform  show  proper  hypothetical  d a s h p o t as  a  which u n d e r  v i s c o e l a s t i c materials.  f r o m two  ideal  more you  Thus t h e  light  or  slightly  these t e s t s with the  i s used as  - the  of  solid  w i l l flow  deformation  properties  material.  constructed and  elastic  t e c h n i q u e s have been d e v i s e d .  to describe  spring,  spring  back.  the  liquids  from  m a t h e m a t i c a l models o f  models a r e  an  of these techniques i s to  and of  (bone) t o  recover  describe  standard  i s purely  between s o l i d s t h a t  enough t i m e  objective  elastic  molecules  a class , v i s c o e l a s t i c biomaterials  the  The  as  fluid.  order  ideal  the  material  given  It  Materials  e n t i r e spectrum  simple  simple  biological  number o f  is  this  such  other.  c i r c u m s t a n c e s may In  formed,  apply  h y d r o g e n b o n d s , h y d r o p h o b i c i n t e r a c t i o n s , etc) move p a s t  water  is  an  4.4. purely  harder i t p u l l s  force/deformation  curve  for  68  FIGURE 4.4.  S p r i n g s and d a s h p o t s . A s p r i n g (A) can be used t o model an i d e a l s o l i d where f o r c e , F, i s p r o p o r t i o n a l t o t h e d i s p l a c e m e n t , X. A dashpot (B) i s u s e d t o model an i d e a l v i s c o u s f l u i d where f o r c e i s p r o p o r t i o n a l t o t h e r a t e o f displacement. S p r i n g s and d a s h p o t s can be combined t o model v i s c o e l a s t i c m a t e r i a l s . A " M a x w e l l E l e m e n t " m o d e l s an u n c r o s s l i n k e d v i s c o e l a s t i c m a t e r i a l . . A "Maxwell Element" i n p a r a l l e l w i t h a s p r i n g (D) models a c r o s s l i n k e d viscoelastic material.  F i g u r e 4.4  D Maxwell Element  70  a spring i s :  f=kx  where f i s f o r c e , x i s d e f o r m a t i o n , a n d proportional immersed viscous  to  the  elastic  in a viscous materials.  viscosity  that  depends on  liquid,  force  fast  the  Springs  and  d a s h p o t s can  Ratio  an  4.1a  and  increasing  b.  be  The  purely  definition  t o deform a  piston  of  dashpot Thus  (dx/dt)  fluid  combined  i n the in  behaviour  testing  conducted  dashpot.  various of v i s c o e l a s t i c  conditions.  e s s e n t i a l l y as  A sample, s u i t a b l y h e l d ,  deformation  shear r a t i o .  the  a  Tests  These t e s t s a r e Fig.  n  to p r e d i c t the  under v a r i o u s  Stress-shear  dashpot,  dashpot i s deformed.  v i s c o s i t y of t h e  configurations materials  from  required  f=  where n i s t h e  The  constant  i s u s e d t o model  I t follows  the  how  modulus.  k is a  and  the  force  deformation  may  be  material  fails  ; o r a t some p o i n t  reversed  and  original  dimensions.  f o r c e measured as  d e f o r m e d may  be  viscoelastic  materials  The  varied.  rate  the at  the  in this  continued  at  until  i s returned  the  t e s t are  sample  behavior  to  each  d e f o r m a t i o n can  which t h e  in  i s subjected  measured  sample  Examples o f  depicted  the be to i t s  is of  shown i n F i g .  4.5a,  71  b,  and c.  as  h y s t e r e s i s , t h e l o s s o f energy accompanying  loading  Figures  4 . 5 b and c i l l u s t r a t e  o f a sample.  Hysteresis  nature of a v i s c o e l a s t i c  Stress-relaxation If the  required  a function  t o maintain  of time f o u r  force  solid  will  viscous  solid be  not vary  liguid  this  general  s h e a r r a t i o and  shear r a t i o  measured a s  types of curves could  4,.6. . I f t h e m a t e r i a l  with  there zero  and l i q u i d  modelled  Element")  will  .  time.  I f the material  be no f o r c e s i n c e  I f the m a t e r i a l  curves.  by s p r i n g s a spring  will  i s a pure  the r a t e of  i s viscoelastic i t  relaxation elasticity.  viscoelastic  materials  may  in series  (a " M a x w e l l  material.  an  initial  due t o t h e s t r e t c h i n g o f t h e s p r i n g . i n the dashpot flows the f o r c e  decay t o z e r o  force.  {37%) o f t h e i n i t i a l  time  between t h e  and d a s h p o t s e i t h e r i n s e r i e s o r  and d a s h p o t  However, as t h e f l u i d exponential  again,  model an u n c r o s s l i n k e d  force i s present  d e c a y t o 1/e  be  i s a pure  show a s t r e s s r e l a x a t i o n c u r v e i n t e r m e d i a t e  parallel.  an  of the viscous  ( m o d e l l e d b y a s p r i n g ) , by d e f i n i t i o n t h e  deformationis will  the c y c l i c  material,.  i s deformed t o a g i v e n  f o u n d a s shown i n F i g . elastic  i s a result  known  Tests  a material  force  the property  follows  The t i m e n e e d e d t o  force  i s known a s t h e  ,a measure o f t h e r a t i o  of viscosity to  a Maxwell Element  in parallel  models a c r o s s l i n k e d  viscoelastic  decays e x p o n e n t i a l l y  with time  with a  material.  t o a value  spring  Here, t h e f o r c e  above  zero.  72  FIGURE 4 , 5 .  P r o p e r t i e s of v i s c o e l a s t i c m a t e r i a l s . A) A s t r e s s / s h e a r r a t i o p l o t f o r a h y p o t h e t i c a l viscoelastic material. Each c u r v e r e p r e s e n t s one sample t e s t e d t o t h e p o i n t of f a i l u r e (o) . . Note t h a t t h e m a t e r i a l i s s e n s i t i v e t o t h e r a t e of shear; the s t i f f n e s s i n c r e a s i n g as the shear rate increases. B and C) E n e r g y i s l o s t due t o h y s t e r e s i s i n the deformation of v i s c o e l a s t i c m a t e r i a l s . The energy r e q u i r e d to deform the m a t e r i a l i s r e p r e s e n t e d by the v e r t i c a l l y h a t c h e d a r e a (force x distance = enerqy). The e n e r g y not r e c o v e r e d when t h e sample i s u n l o a d e d i s r e p r e s e n t e d by t h e h o r i z o n t a l l y h a t c h e d a r e a . H y s t e r e s i s e q u a l s t h e e n e r g y l o s t d i v i d e d by the t o t a l energy. In (B), a c r o s s l i n k e d m a t e r i a l , the h y s t e r e s i s i s p r e s e n t even though t h e sample r e t u r n s t o i t s o r i g i n a l d i m e n s i o n s . I n ( C ) , an u n c r o s s l i n k e d m a t e r i a l , t h e sample has been p e r m a n e n t l y d e f o r m e d by t h e l e n g t h , d.  )  73  74  FIGURE 4.6.  Representative s t r e s s r e l a x a t i o n curves. A) An i d e a l e l a s t i c s o l i d (a s p r i n g ) d o e s n o t relax,. B) . A croslinked v i s c o e l a s t i c material (Figure 4.4, model D) r e l a x e s t o an e q u i l i b r i u m modulus. C) An u n c r o s s l i n k e d v i s c o e l a s t i c m a t e r i a l ( F i g u r e 4.4, model C ) . D) An i d e a l v i s c o u s l i q u i d .  Time  76  Dynamic  Testing  As e x p l a i n e d proportional viscous  a b o v e , f o r an e l a s t i c  t o t h e amount o f d e f o r m a t i o n ,  fluid  force  deformation.  This  i s proportional fact  i s utilized  properties of a material.  achieve t h i s extent is  while f o r a  i n dynamic  of t e s t s to  and v i s c o s i t y  What i s r e g u i r e d  to the  to  end i s a r e g i m e n o f d e f o r m a t i o n where t h e  and r a t e  accomplished  that  force i s  to the rate  separate the c o n t r i b u t i o n of e l a s t i c i t y overall  solid  of deformation  are separated  by s i n u s o i d a l l y d e f o r m i n g  i n time.  This  the m a t e r i a l  such  the deformation  x=sin  Since  f o r a spring  w t  f=kx, t h e f o r c e  s i n u s o i d a l deformation  will  on t h e s p r i n g due t o t h e  be  f=k s i n wt,  and  the f o r c e  purely  viscous  will  material  f=n  so  that  force  by  90 d e g r e e s  elastic  f=n d x / d t .  (see F i g u r e  material  4.7) .  intermediate  material,  ie.  For a  Therefore  d ( s i n wt)/dt=n c o s  f o r a viscous  show a phase s h i f t purely  be i n phase w i t h t h e d e f o r m a t i o n .  wt.  will  lead  A viscoelatic between  deformation material  a purely  somewhere between  viscous 90 and 0  will or  F i g u r e 4.7:  C h a r a c t e r i s t i c s of s i n u s o i d a l d e f o r m a t i o n s . p=p sin(wt), therefore max o=a s i n ( w t ) f o r an e l a s t i c s o l i d max 0=0 d sin(wt)/dt=a cos(wt) f o r a v i s c o u s max max c o s ( w t ) l e a d s s i n ( w t ) b y 90°  liquid  78  79  degrees.  Thus by m e a s u r i n g  deformation elasticity ratio  and f o r c e  t h e phase s h i f t , d e l t a ,  a measure o f t h e r e l a t i v e  and v i s c o s i t y  can be found.  o f the force amplitude  amplitude modulus  will  yield  a stiffness,  ( t h e complex  contribution  divided  modulus)  by t h e d i s p l a c e m e n t  o r modulus.  i s denoted  the l o s s  The v i s c o u s c o n t r i b u t i o n  modulus .  The r a t i o  ( a t low values) t h a t  physical  knowledge to  properties  g a i n e d from  1) p r e d i c t  situation, structure  Testing  designed  the storage  stored  i n each  i s s i ndelta  c a n be r e l a t e d  to hysteresis.  the basis f o r this  of a material  and 2) p r o v i d e some c l u e  study o f  p e d a l mucus.  t h e t e s t s d e s c r i b e d here  t h e behaviour  G*=G" o r  o f G" o v e r G* i s t a n d e l t a , a  o f A. c o l u m b i a n u s  c a n be used  i n a given  t o t h e macromolecular  Apparatus  And P r o c e d u r e s m a c h i n e s were c o n s t r u c t e d t o  t h e t e s t s d e s c r i b e d above. to test  Both  machines  were  thin  l a y e r s o f mucus i n s h e a r ,  under  c o n d i t i o n s as c l o s e l y  as p o s s i b l e approximating  those  a moving  The  of the material.  Two t y p e s o f t e s t i n g perform  overall  The e l a s t i c  t o G* c o s d e l t a G* = G' i s c a l l e d  These t h r e e t e c h n i q u e s form the  G*.  This  O b v i o u s l y G'=G* when d e l t a = 0 ° a n d G'=0 when  delta=90°.  measure  values of  A t the.same t i m e t h e  modulus, as i t i s a measure o f t h e e n e r g y cycle.  between  under  slug.  Dynamic T e s t i n g A forced  Apparatus  oscillation  dynamic t e s t i n g  a p p a r a t u s was  80  constructed the sample  as shown i n F i g u r e 4.8 and 4.9. i s h e l d between two p a r a l l e l  t h i c k n e s s o f t h e sample b e i n g micrometer. observed  thicknesses visually  deforming  Typical  by t h e sample.  t h e sample.  One g l a s s p l a t e  the measuring  of displacements  output  sample measured  was l i n e a r  displacement  approximately  of t h i s g l a s s  to the vibrator  t r a n s d u c e r was c a l i b r a t e d by beam w i t h a m i c r o m e t e r .  used  i n this  Typical  were 20 um t o 50 um.  400 um c o u l d be used  Within the  study, the t r a n s d u c e r  with displacement.  dynamic t e s t s  i s coupled t o  and i s t h e i n s t r u m e n t f o r  The a c t u a l  This displacement  deflecting range  being  Sample a r e a s were  was measured by a t r a n s d u c e r c o n n e c t e d  shaft.  for  while  by e s t i m a t i n g t h e p r o p o r t i o n o f t h e 1 cm* g l a s s  electromagnetic vibrator  plate  glass plates, the  daily  microscope.  were 50um t o 150um.  plate occupied an  machine  measured and s e t by a  The p l a t e s were a l i g n e d  with a d i s s e c t i n g  In t h i s  displacements  Displacements  up t o  f o r stress/shear ratio  tests . The  second  transducer a test.  glass plate  which  senses  The f o r c e  accurately  i s supported  the f o r c e exerted  known w e i g h t s  from  is  The u n l o a d e d  approximately During  analyzer.  hanging  the center of the g l a s s p l a t e . 10 d y n e s c o u l d be measured  resonance  of the force  transducer  400 h z .  a dynamic  sinusoidal signal  beam  on a sample d u r i n g  t r a n s d u c e r was c a l i b r a t e d by  F o r c e s as s m a l l a s a p p r o x i m a t e l y accurately.  by a p a r a l l e l  test  generated  The a m p l i f i e d  the v i b r a t o r  was powered by a  by t h e t r a n s f e r  signals  from  function  t h e f o r c e and  81  FIGURE 4.8. ft s c h e m a t i c d i a g r a m o f t h e f o r c e d o s c i l l a t i o n dynamic t e s t i n g a p p a r a t u s used t o e x a m i n e t h e p h y s i c a l p r o p e r t i e s o f p e d a l mucus a t low s h e a r ratios. S= sample; F= f o r c e t r a n s d u c e r ; D= displacement transducer; &= matched c a r r i e r a m p l i f i e r s (SE L a b o r a t o r i e s t y p e 4 3 0 0 ) . The phase a n a l y z e r i s an SE L a b o r a t o r i e s t y p e SM 272DP t r a n s f e r f u n c t i o n a n a l y z e r . The v i b r a t o r i s a L i n g Dynamic S y s t e m s model 200.  CO N3  83  FIGURE 4.9.  A c o n s t r u c t i o n d r a w i n g o f t h e dynamic t e s t i n g aparatus. A= s t y r o f o a m insulation.„ B= c o i l e d c o p p e r t u b i n g c a r r y i n g w a t e r from a c o n t r o l l e d temperature bath. C= s h i e l d e d c a b l e f r o m t h e force transducer. D= b a s e p l a t e . E= s l i d i n g f o r c e t r a n s d u c e r assembly. F= s t a i n l e s s s t e e l beam (0.008" t h i c k ) w i t h mounted s e m i c o n d u c t o r s t r a i n g u a g e s (BLH t y p e SPB3-20-35). G= g l a s s s l i d i n g s u r f a c e . H= r o d c o n n e c t i n g t h e f o r c e t r a n s d u c e r t o the micrometer. 1= g u i d e b e a r i n g f o r the micrometer rod. J= m i c r o m e t e r , fixed t o the base p l a t e . K= t h e a l i g n m e n t s y s t e m f o r the displacement apparatus. L= s t a i n l e s s s t e e l beam (0.002" t h i c k ) s u p p o r t i n g t h e d i s p l a c e m e n t glass plate. M= r o d c o n n e c t i n g t h e displacement apparatus t o the displacement t r a n s d u c e r and v i b r a t o r . N= mucus sample s a n d w h i c h e d between t h e f o r c e and d i s p l a c e m e n t g l a s s plates,. 0= t h e f o r c e g l a s s p l a t e p= P l e x i g l a s c o n t a i n e r . Q= s t y r o f o a m i n s u l a t i n g c o v e r w i t h a gap f o r t h e d i s p l a c e m e n t r o d .  FIGURE 4.9  85  d i s p l a c e m e n t t r a n s d u c e r s were i n t u r n reference  signal.  t h e phase  shift  amplitude  of t h e t r a n s d u c e r s i g n a l .  phase s h i f t  F o r each  from  of the f o r c e  at  of amplitudes  resonances  this  to y i e l d  From t h e s e d a t a t o the  erratic  hz t o  semiconductor  readings.  strain  the  displacement  a value f o r d e l t a .  i s a measure o f G*. 0.2  the  Samples were  100  hz.  Below 0.2  guages of t h e f o r c e  The tested  Above 100  w i t h i n t h e frame s u p p o r t i n g the v i b r a t o r  s p u r i o u s and  allow  wave and  signal relative  f r e q u e n c i e s r a n g i n g from  to  s i g n a l the a n a l y z e r c a l c u l a t e s  the r e f e r e n c e s i n e  s i g n a l c o u l d be c a l c u l a t e d ratio  compared  hz d r i f t  hz  cause i n the  t r a n s d u c e r does n o t  f o r a c c u r a t e measurements. Stress-shear  vibrator force  ratio  tests  with a t r i a n g u l a r  and  were p e r f o r m e d  the  from  the  displacement transducer are then s u p p l i e d  to a  two  recorder.  the displacement  Both  c o u l d be  Amplified  powering  signals  channel chart  wave.  by  t h e f r e q u e n c y and  varied  within  amplitude  of  the l i m i t s described  above. The  testinq  temperature a bath  apparatus  controlled  t o immerse t h e  chamber t o m a i n t a i n All  tests  The two  this  that  100%  relative  1.  The  insulated,  c o u l d e i t h e r be  sample i n a t e s t  solution  testing  l e s s t h a n 0.1  strain  was  no  problem  for tests  closed test.  °C.  limited  gauges used  transducer are exceedingly temperature posed  as  temperature  apparatus  semiconductor  used  or a  humidity during a  a t 22-23 °C w i t h  usefulness of this  the force  e n c l o s e d i n an  during the course of a t e s t  respects.  While  chamber  were c o n d u c t e d  variations  was  in  in  sensitive.  of s h o r t d u r a t i o n such  86  as  dynamic o r  term be  stress/shear  stability  (such  performed.  2.  plates  parallel  ratios  that  In testing  The  physical  4.10 aluminum  and  revolution sample o f  of  the  of  diameter of  slime at large  relaxation  tests  sample  i s held  cone produced a uniform geometrical basis  configuration the  sandwiched  differential  transformer  channel chart  recorder.  cone i s s u p p o r t e d  t h i s bar  , a measure o f  +-2 by  4.10.  with  . to  core  on  a  of  The  LVDT was  core with a micrometer.  measured t o a p p r o x i m a t e l y  measured  (LVDT).  The  the  strain in  i n Figure  converted  recorded  an  shear r a t i o i n  sample was  which s u p p o r t s t h e  shear  One  f o r uniform  plate  a windlass  between  i s explained  was  the  Figure  angle P l e x i g l a s cone.  s i g n a l f r o m t h i s t r a n s f o r m e r was  of  measuring  i s shown i n  the  the  second  s h e a r r a t i o s and  rotation of  inserting  shear  .  area c a l c u l a t e d  variable  not  glass  l i m i t e d the  l i m i t a t i o n s the  the  measure by  The  apart  c a l i p e r s and  The  a two  maintaining, the  machine used f o r  a small  The  plate  could  obtained.  constructed  plate  and  249.  a c o n e and  vernier  distance  t h i s machine t h e  plate  of  tests)  long  Apparatus  for stress  In  necessity  overcome t h e s e  properties  and  relaxation  p r a c t i c a l l y be  Plate  cone  stress  a set  a p p a r a t u s was  The  The  could  Cone And  rates  The  and  order to  as  ratio tests, tests requiring  linear a  linearly  amplified  one  channel  calibrated  by  Rotations could  be  of  degrees. a t o r s i o n bar.  force,  The  r e s u l t s i n the  twisting deflection  87  FIGURE 4.10.  A combined s c h e m a t i c and c o n s t r u c t i o n d r a w i n g o f t h e c o n e and p l a t e a p p a r a t u s used t o examine t h e p h y s i c a l p r o p e r t i e s o f p e d a l mucus a t h i g h shear r a t i o s . The d i s t a n c e t h r o u g h which t h e sample i s deformed i s a f u n c t i o n o f r , t h e r a d i u s , and W, t h e a n g u l a r v e l o c i t y and i s e q u a l t o rW. The t h i c k n e s s o f t h e s a m p l e i s a g a i n a f u n c t i o n of t h e r a d i u s and i s e q u a l t o mr where m i s t h e s l o p e o f t h e c o n e . The s h e a r r a t i o t h u s e q u a l s Wr/mr = W/m and i s i n d e p e n d e n t o f t h e sample r a d i u s . The e f f e c t i v e sample r a d i u s i s t h e r a d i u s o f a c y l i n d e r c o a x i a l with the cone t h a t c o n t a i n s one h a l f o f t h e sample volume. It i s a p p r o x i m a t e l y e q u a l t o 0„79 R. The e l e c t r i c motor i s a C o l e - P a r m e r M a s t e r S e r v o d y n e , and t h e a m p l i f i e r s a r e SE L a b o r a t o r i e s t y p e 4300. A= a d j u s t a b l e m o u n t i n g p o s t f o r B, a S c h a e v i t z 050 MHR l i n e a r l y v a r i a b l e d i f f e r e n t i a l t r a n s f o r m e r (LVDT).. C= P l e x i g l a s cone s u p p o r t e d by an 18 guage h y p o d e r m i c n e e d l e . D= arm s u p p o r t i n g t h e LVDT c o r e . E= b a s e p l a t e b o l t e d t o the h o r i z o n t a l l y a d j u s t a b l e stage of a m i l l i n g machine. F= aluminum r o d w i t h a p o l i s h e d end a c t i n g a s t h e p l a t e . G= chuck a t t a c h e s t h e r o d t o t h e motor and a c t s as a capstan. H= S c h a e v i t z 100HR LVDT. L= d i s t a n c e from c o r e t o t h e c e n t e r o f t h e c o n e . P= m o i s t p a p e r t o slow e v a p o r a t i o n r a t e from t h e sample. S= sample. The e l e c t r i c motor i s mounted on the v e r t i c a l l y a d j u s t a b l e post of a m i l l i n g machine.  88  89  of  a rigid  The  signal  arm  which  from  s u p p o r t s the cone of a second  this  c h a n n e l o f the c h a r t calibrated  by  r e c o r d e d on  recorder .  force  turning  LVDT i s v e r t i c a l . from  t r a n s f o r m e r was  the c o r e .  t h e t r a n s d u c e r on  force  generated  assumed t o a c t a t a r a d i u s E a s t h e n compared  c e n t e r o f t h e cone t o t h e mechanical  advantage  F o r c e s as s m a l l a s  and  100  measured. was  The  unloaded  approximately The  ratios  electric  50  was the  were t h e n hung was  e x p l a i n e d i n F i g u r e 4,10..  t o t h e d i s t a n c e from  arrive  to c a l c u l a t e  at a f i n a l  (acting  sample r a d i u s o f a p p r o x i m a t e l y  second  transducer  during a test  LVDT c o r e  dynes  the  i t s side.so that  A c c u r a t e l y known w e i g h t s  The  T h i s r a d i u s was  The  LVDT.  5 mm)  resonance  c y c l e s per  the  the  calibration  at a t y p i c a l c o u l d be  .  effective  accurately  o f the f o r c e  transducer  second.  motor r o t a t i n g  the  plate  provided  shear  c o n t i n u o u s l y v a r i a b l e above s h e a r r a t e s of 5 per  second.  The  time  required  to reach f u l l  speed  was  about  20  (21-24  °C)  milliseconds. All with  no  sample  tests  were p e r f o r m e d  provision and  made t o r e g u l a t e t h e t e m p e r a t u r e  apparatus. than  placed  shown i n F i g u r e 4.10  relative  0.5  Temperature  were l e s s as  a t room t e m p e r a t u r e  °C.  A moist  humidity around  variations  ring  of the  during  of absorbent  tests  paper  serves to maintain a high  t h e sample and  thereby  minimize  evaporation.  Collection  Of  Ariolimax  Pedal  Mucus  columbianus  p e d a l mucus was  collected  by  90  allowing  t h e s l u g t o c r a w l on a g l a s s r o d .  attempted forcing  t o c r a w l a r o u n d t h e r o d t h e r o d was  the slug  footing. be  to c o n t i n u e c r a w l i n g  In t h i s  collected  sample from  manner 0.1  t o 0.3  from each s l u g .  any o f t h e t e s t s one  described individual.  a p p r o x i m a t e l y one testing  minute..  The  preponderance  though  was  ml o f p e d a l mucus c o u l d  collection  on a  single  procedure  lasted  i n the  collection.  precise  origin  No  collection  i t was  attempt  of the pedal  the  by t h e p e d a l g l a n d .  surface of a slug with chalk  was  sufficient for  Samples were p l a c e d  the d o r s a l  foot  i t lose i t s  i t i s probable that  produced  slug  rotated  above t o be p e r f o r m e d  apparatus immediately a f t e r  collected,  lest  T h i s amount was  has been made t o d e t e r m i n e t h e slime  As t h e  By  dusting  p r i o r t o p e d a l mucus  shown t h a t t h e mucus c o l l e c t e d  n o t c o n t a m i n a t e d by mucus from t h e  from  the  dorsal  epithelium. It  i s inevitable  p r o p e r t i e s of slime another s l u g , collected one  from  set of  from  or that one  18 s l i m e  that  one s l u g  slime  slug  v a r i a t i o n s be f o u n d i n t h e  properties  on d i f f e r e n t  of t h e mucus r a n g e d  wet  .  physical  variability  property  v a r y when  on a s i n g l e  day,  the  t o 4.46%  of the  In attempting to a c c u r a t e l y  describe  the  of slug  s l i m e an a c c o u n t o f  must be made when r e p o r t i n g  case of c e r t a i n t e s t s collected  will  of  2,85%  properties  from  to that  d a y s . . F o r example, i n  samples c o l l e c t e d  dry weight weight  compared  variation  results..  In the  i n the c o m p o s i t i o n of the  slime appears t o cause l i t t l e measured.  this  variation  In these cases information  i n the  about  91  individual  s a m p l e s i s not l o s t i n l o o k i n g  all  samples, c o n s e q u e n t l y  and  the confidence  tests  of for  by c o m p o s i t i o n a l  For these t e s t s  a l l tests  i t often  does not c l o s e l y  any i n d i v i d u a l  test  .  i n d i v i d u a l sample c l o s e s t a  "typical" test  be  of a l l tests  are averaged  l i m i t s a r o u n d t h e mean a r e n o t e d .  are a f f e c t e d  extent.  results  a t an a v e r a g e o f  variability  Other  t o a greater  happens t h a t  the average  r e s e m b l e t h e measured  value  In t h i s case t h e r e s u l t s t o he a v e r a g e  from t h e  w i l l be p r e s e n t e d  and t h e r a n g e o f v a l u e s f o r a l l t e s t s  as  will  noted.  Physical  Properties  Of A.  Columbianus  Mucus At Low  Shear  Ratios Three s o r t s properties ratios  of t e s t s  of Ariolimax  ( ie.  these t e s t s  for  tests  will  Stress-shear Ratio Figure  columbianus pedal  to ascertain  mucus a t low s h e a r  and 3) Dynamic t e s t s .  be d i s c u s s e d  The  with  4.11 shows a t y p i c a l s t r e s s -  shear  ratio  The s t r e s s / s h e a r  Under  a s an e l a s t i c  r a t i o curve i s e s s e n t i a l l y  an e l a s t i c modulus o f a p p r o x i m a t e l y  curve  apparatus to a  c o n d i t i o n s t h e s l i m e behaves p r i m a r i l y  200 N/m .  mucus i s e l a s t i c a t t h e s e s h e a r r a t i o s and s h e a r indicates  results  Tests  s h e a r r a t i o o f a few p e r c e n t a t a l o w s h e a r r a t e .  solid.  2)  i n turn.  mucus d e f o r m e d i n t h e dynamic t e s t i n g  these  the  l e s s t h a n 5) : 1) S t r e s s / s h e a r r a t i o t e s t s  Stress relaxation of  were c o n d u c t e d  t h e p r e s e n c e o f some network s t r u c t u r e  2  linear That t h e  rates within  the  92  FIGURE 4.11.  a stress/shear r a t i o curve f o r ariolimax c o l u m b i a n u s p e d a l mucus a t a low s h e a r r a t i o . S h e a r r a t e = 0.048/sec. and G = 210 N / m 2 . The h y s t e r e s i s i s 6.9%.  Figure 4.11  94  slime. slight  The  viscous  4.12  shows a t y p i c a l  mucus a t l a r g e r s h e a r  times that of  Figure  v i s c o e l a s t i c nature loading  the  unloading the  i t can  energy of  be  that the  that  elasticity the  Stress  course  2 to  the  material  seen t h a t  and  some o f  N/m  but  2  proportion  to i t s original  However  the  deformation  of  viscous The  fact  dimensions  for  or has  , the  upon  the rearranged  fact  that  shows t h a t  the some  present.  Tests shows t h e  averaged  t e s t s c a r r i e d out  i n the  r e s u l t s from cone and  No  d i f f e r e n c e i n the  of  shear r a t i o  was  characterized  by  times i n d i c a t i n g t h a t r e l a x a t i o n processes  time c o u r s e  noted.  The  10  shear r a t i o s of  are  occurring  relaxation  relaxation  a s i n g l e or s m a l l there  stress  plate  These t e s t s were done a t a r a n g e o f 5.  Upon  i s non-recoverable.  return  ten  the  gone t o d e f o r m i n g t h e  of d e f o r m a t i o n .  c u r v e c a n n o t be  different  i s evident.  a considerable  curve  r a t e over  w h a t e v e r network i s r e s p o n s i b l e  4. 13  a function  relaxation  at a shear  shows a G o f a b o u t 200  does not  Relaxation  apparatus.  This  and  e l a s t i c network i s s t i l l  relaxation  as  in  s t r e s s - shear r a t i o  i s e i t h e r b r o k e n down p a r t i a l l y  Figure  from  of the  material,  mucus d o e s r e c o v e r form of  shows o n l y  Under t h e s e c o n d i t i o n s  d e f o r m a t i o n has  material  indicates  ratio  4.11.  mucus a g a i n  component o f t h e  in  material  hysteresis.  Figure for  nature of the  number  a variety  i n the  of  material.  i s t y p i c a l for viscoelastic biomaterials.  Unfortunately  this  form of t e s t does not  give  any  clues  as  of  95  FIGURE 4 . 1 2  a stress/shear r a t i o curve f o r Ariolimax c o l u m b i a n u s p e d a l mucus a t a moderate s h e a r ratio. S h e a r r a t e = 0 . 5 6 / s e c . and G i s a p p r o x i m a t e l y 1 0 0 N/m . The h y s t e r e s i s i s 44.2%. Note t h a t t h e sample d o e s n o t r e t u r n i t s o r i g i n a l dimensions. 2  to  ON  97  FIGURE 4 . 1 3 .  The s t r e s s r e l a x a t i o n c h a r a c t e r i s t i c s o f ftriolimax c o l u m b i a n u s p e d a l mucus. The c u r v e i s t h e average o f 10 t e s t s ; the bars r e p r e s e n t 95% c o n f i d e n c e i n t e r v a l s .  Figure 4.13  500  1000  ,  1500  2000  Seconds  vo  Oo  99  to  the nature o f these r e l a x a t i o n  time  course of these  experiments  processes. (30 minutes)  s l i m e d o e s n o t r e a c h an e q u i l i b r i u m curve  g i v e any h i n t  relaxation In  that  the relaxing  s t r e s s , n o r do e s t h e  an e q u i l i b r i u m  f o r g r e a t e r p e r i o d s of time  this respect, i n that  Within the  would be r e a c h e d i f c o u l d be measured.  i t f l o w s , mucus b e h a v e s a s a f l u i d .  However, i t h a s been shown by s t r e s s - s h e a r r a t i o that  an e l a s t i c  network i s p r e s e n t d u r i n g d e f o r m a t i o n t o  these shear r a t i o s  f o r at least  s h o r t time  intervals.  t h e s e two f a c t s i t c a n be h y p o t h e s i z e d t h a t t h i s while  s t a b l e over r e l a t i v e l y  (minutes  From  network ,  short periods of time  (seconds), i s capable o f rearrangment time  tests  over  long p e r i o d s o f  to hours).  Dynamic T e s t s The  r e s u l t s o f t h e dynamic t e s t s  columbianus  p e d a l mucus a r e summarized  mentioned  earlier  extension  ratios  to  100 Hz.  on A r i o l i m a x  these t e s t s o f about  i n F i g u r e 4.14.  were c a r r i e d  o u t a t low  .2 t o .5 and f r e q u e n c i e s from  network on a t i m e  m i l l i s e c o n d s t o seconds.  Under t h e s e c o n d i t i o n s t h e  solid:  .2  These t e s t s a r e t h u s d e s i q n e d t o r e v e a l t h e  p r o p e r t i e s of the e l a s t i c  material  As  i s a g a i n shown t o behave p r i m a r i l y  scale of  as an  elastic  t h e s t o r a g e modulus i s t e n t i m e s t h e l o s s modulus and  the r a t i o  o f t h e two  over t h e range  ( t a n d e l t a ) does n o t vary  of f r e q u e n c i e s t e s t e d . .  t h e n e t w o r k o f t h e mucus i s k i n e t i c a l l y elastic)  on a t i m e  scale  significantly  This confirms free  o f 10 m i l l i s e c o n d s .  that  (and t h e r e b y This i s hardly  100  FIGURE 4.14.  Dynamic t e s t r e s u l t s . The c u r v e s a r e . a v e r a g e s f r o m 6 s a m p l e s t e s t e d i n a i r a t 100% r e l a t i v e humidity. The b a r s a r e 95% c o n f i d e n c e intervals.  102  suprising  s i n c e i n a network a s d i f f u s e  virtually  nothing  chains.  present to i n h i b i t  I t i s however f u r t h e r  hypothesis that the e l a s t i c Ariolimax  the freedom  evidence  network  a s mucus t h e r e i s o f network  supporting the  o f t h e p e d a l mucus o f  c o l u m b i a n u s c a n be t r e a t e d r e a l i s t i c a l l y  network c o n f o r m i n g  to the theory o f rubber  In summary, t h e t e s t s mucus a t low s h e a r viscoelastic,  ratios  a solid  network, t h e c r o s s l i n k s b e i n g m i l l i s e c o n d s t o seconds,  elasticity.  on A r i o l i m a x c o l u m b i a n u s indicate  i s primarily  as a  pedal  that the m a t e r i a l , while formed o f a c r o s s l i n k e d  stable  on a t i m e  scale of  but unstable a t longer periods o f  time.  Physical Shear  P r o p e r t i e s Of JU  Mucus At High  Ratios While  low  Columbianus Pedal  shear  problem  i t i s useful ratios,  of slug  t o know t h e p r o p e r t i e s o f mucus a t  the a p p l i c a b i l i t y  locomotion  of t h i s  i s restricted.  knowledge t o t h e For a slug  with  a  s t e p l e n g t h o f one m i l l i m e t e r and a mucus l a y e r  thickness of  10 m i c r o m e t e r s ,  t o a shear  ratio of  the pedal  on t h e o r d e r  mucus w i l l  o f 100 r a t h e r t h a n  t h e t e s t s d e s c r i b e d above.  properties of A ratios plate  a number o f t e s t s  t h e 0.1 t o 4.0  typical  In order t o i n v e s t i g a t e the  columbianus pedal  A  be e x p o s e d  mucus a t h i g h e r  were c a r r i e d  shear  o u t u s i n g t h e cone and  apparatus. .  Stress-shear Ratio The  results  Tests  o f s h e a r i n g p e d a l mucus t o h i g h e r  shear  103  ratios  a r e shown i n F i g u r e s 4.15 a n d 4.16.  even at a f i r s t different  from  glance t h a t these those  properties are quite  a t low s h e a r  ratios.  a r e b e s t e x p l a i n e d by f o l l o w i n g t h e t i m e shown i n F i g u r e 4.15. rotating through as  the p l a t e  about  falls.  sub  y) i s dependent  rate the l a r g e r strain  deformation.  rate;  stress.  rate f o r a typical beyond  This level  a ratio  and t h e s t r e s s the shear  ratio  t o an  Within the l i m i t s  shear  ratio  does n o t  r a t e i s one d i s t i n g u i s h i n g  A plot sample  of y i e l d  stress  i s shown i n 4.16.  i t s yield  p o i n t a new  remains constant  with  stress f o r a constant  characteristic  a p p e a r t h a t a s t h e mucus  (sigma  the higher t h e shear  As shown i n t h e i n t r o d u c t i o n t o t h i s  maintenance o f a c o n s t a n t  would t h u s  with  a t which t h e sample y i e l d s  on t h e s h e a r  As t h e mucus i s d e f o r m e d  the  ratio  r a t e a t which t h e sample i s d e f o r m e d .  the y i e l d  i s reached.  earlier.  can o n l y be d e t e r m i n e d  o f t h e machine t h e b r e a k i n g  the shear  as  when t h e motor  However , a t a s h e a r  2  contrast, the stress  level  shear  o f a b o u t p l u s o r minus 1.4 r h o .  with  versus  described  Due t o t h e d e s i g n o f t h e a p p a r a t u s  accuracy  of a test  t h e mucus sample i s d e f o r m e d  with  100-200 N/m .  w h i c h t h e mucus y i e l d s  vary In  linearly  course  differences  As t h e p l a t e r o t a t e s  5-6, t h e mucus a b r u p t l y y i e l d s  accuracy of  on.  few d e g r e e s  roughly  These  i s initiated  i n the s t r e s s - s h e a r r a t i o t e s t s  modulus o f a b o u t  at  i s switched  the i n i t i a l  Stress rises  of  The t e s t  I t i s evident  yields  stress  further chapter, shear  of a f l u i d .  It  i t s elastic  network s t r u c t u r e i s b r o k e n t o t h e p o i n t where t h e m a t e r i a l behaves a s a v i s c o u s l i q u i d .  If this  i s s o , two o t h e r  facts  104  FIGURE 4.15.  The c h a r a c t e r i s t i c s o f A r i o l i m a x c o l u m b i a n u s p e d a l mucus a t h i g h s h e a r r a t i o s . The mucus y i e l d s a t a shear r a t i o of approximately 5 to form a v i s c o u s l i q u i d , b u t w i l l " h e a l " i f allowed t o r e s t unstressed.  F i g u r e 4.15 p = 20  motor on  I  motor off  motor on  yield  motor off  motor on  106  FIGURE 4.16.  A representative p l o t o f y i e l d s t r e s s and f l o w s t r e s s versus shear r a t e f o r Ar iolimax c o l u m b i a n u s p e d a l mucus. Yield  stress  range:  low high flow  stress  y=0.024x + 0.83 y=0.117x + 1.92  range low high  y=0.010x + 0.070 y=0.053x + 0.53  108  should  be c o n s e q u e n t :  liquid  should  the  case.  Samples deformed  post-yield  A plot  of flow  stress  with  ie  5,000 t i m e s  of  sigma  that  the flow  versus shear  an i n c r e m e n t a l  of  (sigma  more v i s c o u s t h a n  r a t e s lower  line will  than  on t h e g r a p h . maintain  a liquid  i t has y i e l d e d  water.  Two  those  of about  First,  throughout  50 p o i s e  I t i s assumed  measured t h e f l u i d a s d e p i c t e d by t h e  2) When d e f o r m a t i o n  a positive  , behaves  value of s t r e s s ;  i s halted a i n the case  decay t o z e r o . mucus  again  As  behaves  .  physical  results.  sample  Note t h a t t h e l i n e  the s t r e s s w i l l immediately  as a l i q u i d  sub f) .  rate f o r a typical  shown i n F i g u r e 4.15 t h e h i g h l y d e f o r m e d  to  r a t e s show  stress  viscosity  mucus shows n o n - N e w t o n i a n b e h a v i o u r  solid  shear  sub f d o e s n o t e x t r a p o l a t e t o z e r o .  at shear  dotted  T h i s i s indeed  The s h a p e o f t h e r e l a t i o n s h i p i s  s h o w i n g t h a t mucus, a f t e r  as a l i q u i d  rate.  at higher  stresses,  shown i n F i g u r e 4.16,  linear.,  r e q u i r e d t o deform t h e  be d e p e n d e n t upon s h e a r  higher  is  1) The s t r e s s  i n t e r p r e t a t i o n s are c o n s i s t e n t with the e l a s t i c  the e n t i r e  n e t w o r k may b r e a k  these  down  sample a l l o w i n g t h e sample a s a whole  behave as a l i g u i d . . Second  i t i s possible t h a t only the  network i n t h e p o r t i o n o f t h e sample a d j a c e n t t o e i t h e r t h e cone o r p l a t e  i s destroyed, forming  s e p a r a t i n g the s t i l l In  this  second  of  this thin  case  layer  sample a s a w h o l e . thickness  solid  a thin  sample from  layer of l i q u i d  t h e cone o r p l a t e .  i t would e s s e n t i a l l y  be t h e p r o p e r t i e s  that are being t e s t e d r a t h e r than the If this  of t h e f l u i d  i s so , and d e p e n d i n g  layer,  the calculated  on t h e  v a l u e s of shear  109  rate  may be c o n s i d e r a b l y  the  tests  performed  distinguish one*. this not  i n error.  I t i s impossible  i n the course o f t h i s  guestion  , the f a c t  that  seems l i k e l y variation the  4.16 there  f o r breaking  samples t e s t e d .  these  mucus a s e x p l a i n e d  earlier  the r a t i o  4 . 1 7 shows a p l o t o f t h e y i e l d  /flow  stress equal  locomotion the  ability  This  of  solid  value  effectively  and s h e a r  rate.  Figure  s t r e s s values f o r  of yield  stress  be shown i n C h a p t e r 7 how  within  to a liguid  The i n v a r i a n t  ratio  h e r e means t h a t t h e  a wide r a n g e o f  rates.  Do t h e s e t e s t s t h e n  imply  i s i n t h e form  as t h e s l u g  stress  2.0 i s important f o r the  t o v i s c o s i t y described  mucus c a n f u n c t i o n  that  on s h e a r  f o r adhesive locomotion.  strength  This  between t h e two f o r any  o f t h e mucus t o change from a s o l i d  a necessity  moving s l u g  constant  t o about  present i n  s t r e s s and f l o w  stress/flow  of the animal.. I t w i l l  is  hydrations  was n o t t e s t e d i t  i n t h i s chapter.  sample n c r i s t h e r a t i o d e p e n d e n t  samples t e s t e d .  s t r e s s i n the  of glycoprotein  i n t h e magnitude o f y i e l d r  all  range i n  v a r i a t i o n s a r e due t o t h e n o r m a l  does not h o w e v e r , a f f e c t one  mucus.  i s considerable  s t r e s s and f l o w  i n the concentration  variation  o f s l u g pedal  Though t h e h y p o t h e s i s  that  does  o f the r e s u l t s o f these t e s t s i n  shown i n F i g u r e  values  to resolve  i t has not been r e s o l v e d  describing the e f f e c t i v e properties  the  i s the correct  be i n t e r e s t i n g t o be a b l e  a f f e c t the accuracy  As  study t o  which o f t h e s e two p o s s i b i l i t i e s  W h i l e i t would  from  that  t h e mucus b e n e a t h a  of a l i g u i d ?  One i s r e m i n d e d  moves t h e mucus i s d e f o r m e d t o a s h e a r  110  FIGURE 4.17.  The r a t i o o f y i e l d s t r e s s c o n s t a n t among s a m p l e s and rate.  t o flow s t r e s s i s r e g a r d l e s s of shear  F i g u r e 4.17  112  ratio  o f about This  100.  q u e s t i o n i s answered  testing.  Aqain r e f e r  the  i s stopped  is  plate  the interwave  I t i s found  a g a i n b e h a v e s as a s o l i d . At a shear r a t i o  y i e l d s a n d so f o r t h . deformation  that  of a l i q u i d , Stress rises  to the f i r s t  further  .  with  second  shear  again  period of  In f a c t  this before the  to recoveri t s  , reforms  quickly  broken .  p r o c e s s i s p r o v i d e d by two  tests.  a given shear  rate,  t h e sample  while the c o n t r o l s  d e f o r m a t i o n s a t a new initial  has " h e a l e d " and  20 t o 30 t i m e s  1 A f t e r a sample had been d e f o r m e d  seconds  than  n e t w o r k , w h i c h must be  t h e mucus t o a c t a s a l i q u i d of this  mucus  the p l a t e i s  e q u a l t o 5-6 t h e m a t e r i a l  Thus, t h e e l a s t i c  A d d i t i o n a l evidence  that  linearly  The r e c o r d o f t h i s  i s identical  This period  t h e mucus, r a t h e r  mucus b e g i n s t o show s i g n s o f f a i l i n g  for  , t h e sample  (and t h e r e f o r e n o t deformed)  " y i e l d - h e a l " c y c l e c a n be r e p e a t e d  solidity.  o f time  At t h e end o f t h i s t i m e  showing t h e c h a r a c t e r i s t i c s  ratio.  has decayed  u n s t r e s s e d f o r one s e c o n d . ,  u n d e r a moving s l u g . rotated.  further  After the rotation of  as e q u i v a l e n t t o t h e p e r i o d  would be b e n e a t h  again  t o F i g u r e 4.15. and t h e s t r e s s  a l l o w e d t o remain  was c h o s e n  i n the course.of  deformation  higher  yield  stress  values  of y i e l d  was a l l o w e d t o r e s t  f o r 10-12  were s e t f o r a n o t h e r s e t o f  shear r a t e .  i n t h i s new than  a number o f t i m e s a t  I t was noted  series  subsequent  that the  showed a c o n s i d e r a b l y  deformations.,  The  s t r e s s shown i n F i g u r e 4.16 a r e f o r  deformations subsequent  t o the i n i t i a l  deformation  as t h e s e  113  are  more c h a r a c t e r i s t i c  moving s l u g . comparing  function  F i g u r e 4.18 shows v a l u e s f r o m a t y p i c a l  initial  subsequent  o f t h e p r o p e r t i e s o f mucus u n d e r a  breaking stress  (sigma  sub y i ) and  (sigma sub y) v a l u e s f o r y i e l d  o f shear r a t e .  network formed  I t i s apparent  when t h e mucus r e s t s  stronger than t h a t  formed  when  rest  sample  s t r e s s as a  that the e l a s t i c  f o r 10-12 s e c o n d s i s i s a l l o w e d f o r o n l y one  second. The through  time  another  apparatus complete The  and  series of tests  of deformation  After  healing  I n t h e s e t e s t s one  was p e r f o r m e d  on t h e  a sub-yield a stress  required  level.  (sigma  typical  test  relaxation  time  (tau) measured. as the time  proved  However, t h e g e n e r a l t r e n d  As a m a t t e r o f  The r e s u l t s o f a  t o be q u i t e  of increasing  and i s t a k e n  sample becomes more s o l i d  Relaxation times variable.  t a u with  stopped decays  form.  the l o n g e r i t i s allowed t o h e a l .  When t h e r o t a t i o n  w h i l e t h e mucus i s i n i t s f l u i d quickly  to zero.  increasing  as e v i d e n c e t h a t t h e  T h i s p r o p e r t y o f t h e h e a l e d mucus c a n be compared mucus i n i t s f l u i d  halted  ( i n seconds)  a r e p r e s e n t e d i n F i g u r e 4.20.  i s apparent  but o n l y  t o 0.20 o f t h e i n i t i a l  sub z e r o i n F i g u r e 4 . 1 ) .  any g i v e n h e a l t i m e  h e a l time  lengths of  R o t a t i o n o f t h e p l a t e was t h e n  f o r the stress t o relax  stress  sample.  t h e sample was a g a i n s t r e s s e d ,  c o n v e n i e n c e , t a u was c h o s e n  for  u s i n g t h e cone and p l a t e  as shown i n F i g u r e 4.19. cycle  p r o c e s s was examined  sample was t h e n a l l o w e d t o " h e a l " f o r v a r y i n g  time. to  course o f the healing  The r e l a x a t i o n  to the  of the plate i s  form, t h e f o r c e time f o r t h i s  decay  1 14  FIGURE 4.18.  The i n i t i a l y i e l d s t r e s s a f t e r a sample has been l e f t u n s t r e s s e d f o r a p e r i o d o f t i m e i s g r e a t e r than subsequent y i e l d s t r e s s e s a f t e r o n l y s h o r t term " h e a l " p e r i o d s .  115  116  FIGURE 4 . 1 9 .  The t e s t i n g p r o c e d u r e used t o d e t e r m i n e t h e e f f e c t o f h e a l t i m e on t h e r e c o v e r y of solidity. R e l a x a t i o n t i m e , h e r e d e f i n e d as t h e time r e q u i r e d to r e l a x t o 0 . 2 0 of the i n i t i a l s t r e s s , i s used as a measure o f s o l i d i t y .  F i g u r e 4.19  118  FIGURE 4.20.  A r e p r e s e n t a t i v e p l o t o f r e l a x a t i o n time versus h e a l time f o r A r i o l i m a x columbianus p e d a l mucus. The r a n g e shown i n t h e s e t e s t s was: low high  y=0.11x + 0.41 rz=0.71 y=5.75x + 27.59 rz=0.51  120  is  t o o s h o r t t o be a c c u r a t e l y  procedure can  but  be s e e n  a period The can  be  that  of l e s s  At s h e a r  to  10 00  2) 5-6. 3)  as  4)  stress  shear  ratio  The  increasing  Fiber  ratio  with i n c r e a s i n g  a  yield  shear  rate.  point at a shear shear  ratio rate.  mucus b e h a v e s  o f 30-50 p o i s e . s t r e s s t o shear r a t e  mucus can  f o r any  one  recover i t s e l a s t i c i t y i f  amount o f s o l i d i t y  time. recovered i n c r e a s e s with  time.  properties  summarized  above were measured  t o s i m u l a t e those beneath  However, b e i n g  p e r i o d s o f time  lethargic  simply s i t t i n g  f o r k^_  walls.  The  columbianus  a  under  walking  b e a s t s , s l u g s spend i n one  t o house the s l u g s f o r t h i s  position glass  mucus b e h a v e s as  of g r e a t e r than 6 the  of y i e l d  c o n d i t i o n s designed  used  the  Formation The  slug.  5-6  2.0  fluid  The  in  modulus i s on t h e o r d e r o f  allowed to heal f o r a period o f 6)  Thus i t  p e d a l mucus  i n c r e a s e s with i n c r e a s i n g  with a v i s c o s i t y  sample i s a b o u t 5)  The  mucus shows a s h a r p  The  seconds.  second.  increasing  At a s h e a r  as a f l u i d  a  r a t i o s l e s s than  2  testing  follows:  solid.  Yield  0.1  p r o p e r t i e s o f A. c o l u m b i a n u s  N/m ,  The  l e s s than  this  mucus r e c o v e r s c o n s i d e r a b l e s o l i d i t y  than  physical  viscoelastic  of  the  summarized  1)  100  i s certainly  measured by  was  s l u g s commonly  study  spot. the  halfway spent  large  In t h e  cages  preferred  up t h e  resting  vertical  p e r i o d s of  12-24  121  hours  thus attached.  relaxation  tests  that  periods of time, gradually to t h i s  slide  why  do  q u e s t i o n may  If  a slug pried  behind.  has  long  p r o p e r t y of  layer  o f mucus w i l l  under a p o l a r i z i n g  to contain , i n addition  from  (up t o a b o u t  end  It is difficult  t o end b u t t h e y a p p e a r  .5mm).  F i b r e s a r e about  It pedal (at  If  was  found  100%  relative  a r e formed  , however t h e  fibers rapidly by  p o s s i b l e to induce  humidity)  either  t o o s l o w l y t o be sample i s immersed  form.  The  modulus was  shear r a t i o s 0.10/sec. tests;  a  quite  fibres  do  not  water.  a resting  The  slug  has  formation i n  apparatus.  Mucus a l o n e  does n o t form  F i g u r e 4.21  0.10  and  fibers  detected i n these in a salt  rates less  shows t h e r e s u l t s  the time c o u r s e of t h i s  ,  i s accompanied  modulus o f t h e  shear  or  tests.  solution  measured by s t r e s s - s h e a r r a t i o  l e s s than  following  fibre  f o r m a t i o n of f i b e r s  a dramatic i n c r e a s e i n the shear  This  debris,  to trace t o be  the  studied.  mucus i n t h e dynamic t e s t i n g  fibers  The  f o r m a t i o n beneath  microscope  in  i f t h e sample i s p l a c e d i n d i s t i l l e d of f i b e r  remain  um  dissolve  n o t been  a r e weakly b i r e f r i n g e n t .  wall i s  often  1.0  and  course  answer  pedal  to the.usual  diameter  time  The  been a t t a c h e d t o a v e r t i c a l  Upon e x a m i n a t i o n  fiber  w a l l s not  fibers.  a dense f e l t w o r k o f f i b r e s . single  flow over long  force of gravity?  l i e with another  o f f , a white  mucus i s f o u n d  stress  slugs attached to v e r t i c a l  t o form  that  been shown by  p e d a l mucus w i l l  down under t h e  mucus, i t s a b i l i t y  gently  Since i t has  o f one  sample.  tests  at  than series  of  i n c r e a s e i n modulus  122  FIGUEE 4.21.  The e f f e c t s o f v a r i o u s s a l t s on t h e r e l a t i v e i n c r e a s e (Gt/Go) i n s h e a r modulus due t o f i b e r formation i n ftriolimax c o l u m b i a n u s p e d a l mucus. A l l s a l t s were p r e s e n t a s 0.05 M a q u e o u s solutions.  Figure  4.21  124  for  various solutions.  performed found can  t o be  as b e i n g a r e s u l t o f t h e  be  concluded,  distilled  water) t h e  specific cation  cation  presence  distilled In  performed  i n shear  difficult  to design  been  possible  these  t o perform  function  (as would be and  of  necessary  construct.  may  the pedal  might  and  educated  assumed t h a t  Without  biological birefringent fliers that  and  to  f o r mucus) no  be are attempt  creep It  g u e s s a s t o what  when f i b e r s form not a l l , of  fibers.  o f the f i b e r s i n d i c a t e s .  stress  n o n - f i b r o u s p e d a l mucus.  c h a i n s a r e bound i n t o  i s ordered  h i g h e r than  "creep"  time.  Consequently  mucus u n d e r a s l u g some, b u t  birefringence  against  be.  r e a s o n a b l y be  glycoprotein  structure  of f i b r o u s  would  mucus under  allow f o r creep tests  however t o make an  properties It  of f i b r o u s  made i n t h i s s t u d y t o t e s t t h e  characteristics  they  sample i s s u b j e c t e d t o a c o n s t a n t  machines t h a t  a  removed.  the behavior  as a  It  the  exhaustively dialyzed  s a l t s thereby  measured  courses  formed i n  valence of either  i t would be n e c e s s a r y  where t h e  Unfortunately  is  the  were  d e p e n d e n t on e i t h e r  A g a i n , once f i b e r s were formed  w a t e r and  the deformation  has  or the  i f t h e s a m p l e was  slug  (no f i b e r s b e i n g  p r o c e s s i s not  order to p r e d i c t  a resting  tests  while f i b e r formation i s  of s a l t  or anion,  or a n i o n .  dissolve  number of  different salts applied.  however, t h a t  on t h e  tests  insufficient  able t o a t t r i b u t e the d i f f e r e n t time  dependent  not  An  that  in  the  The their  molecular  exception a l l other have a modulus c o n s i d e r a b l y  o f the randomly a r r a n g e d  mucus n e t w o r k .  125  No fibers  e v i d e n c e can are  be  connected.  s e e n under t h e  mucus c o n s i s t s o f  elastic  network) t h r o u g h  a very  similar  studied and  by  Koehl  fiber  rate of  follows:  fibers  deformation  fibers  viscous  of  serves  1.  increases  as  analogously  one to  slipping.  increases.  the  (19 71a  a  as  shear  2.  t h a n one the  t h u s be  c r e e p more s l o w l y  t o remain attached  to  these  i s not  explain  v e r t i c a l walls  the  given presence  on  the  reinforced. mucus  were t o  guessed t h a t  than the  i t could  a  as  reinforced  modulus o f f i b r o u s  I t can  so,  For  rate acting  material  b)  discontinuous  a whole.the  that  with been  and  mesoglea i n c r e a s e s  would e x p e c t i f t h e  I f t h i s i s indeed  slugs  materials  as a c o n s e q u e n c e a f i b e r  mesoglea.  mucus  higher  f i n d i n g s of  modulus o f  materials  been shown t h a t  f i b r o u s mucus w i l l slime.  to matrix of the  Gosline  relevant  The  c r e e p s more s l o w l y  I t has  of  The  to i n c r e a s e  component .  material  discontinuous  authors, notably b).  (the  the  this  anemone m e s o g l e a - has  r e i n f o r c e d c o m p o s i t e s u c h as  proportion  of  as  modulus m a t r i x  which r u n  s t r u c t u r e - sea  (1977a and  authors are  a low  another c l a s s of b i o l o g i c a l  several  that  Thus i t seems r e a s o n a b l e t h a t  fibrous  modulus f i b e r s .  microscope  behave the  nonfibrous the  ability  without  126  CHAPTER  Chemical  FIVE  Composition  As shown i n t h e p r e c e d i n g c h a p t e r mucus i s a v i s c o e l a s t i c properties. in  On  A. c o l u m b i a n u s  m a t e r i a l w i t h some  unusual  the b a s i s o f t h e s e p r o p e r t i e s the e x i s t e n c e  t h e mucus o f a network o f m a c r o m o l e c u l e s  hypothesized.  network i s c o n s t r u c t e d .  b l o c k s from  J u s t as the s i z e ,  of b r i c k s determines form  been examine  network i t i s n e c e s s a r y t o i d e n t i f y  chemical composition of the b u i l d i n g  overall  has  B e f o r e i t i s p o s s i b l e t o more c l o s e l y  the n a t u r e of t h i s  strength  pedal  which  shape,  the p o s s i b i l i t i e s  the this  and  f o r the  of a b u i l d i n g , the chemical p r o p e r t i e s  of  individual  monomers s e t t h e l i m i t s  f o r t h e form  of  networks.  the chemical a n a l y s i s  polymer  p e d a l mucus f o r m s  Consequently  the  subject  of t h i s  and  strength of  chapter.  What I s Mucus? The general, formed As  term any  extracellular  primarily  such, the term  secretions, feeding,  o f water  the f u n c t i o n s  1972)  .  and  been p r e c i s e l y  , viscoelastic is liable  o f which  t o be  defined.  animal  m u c i n s have a b a s i c a l l y  range  broad  to find  similar  that  In  secretion  lahelled  "mucus"..  of  from l o c o m o t i o n , t o  r e p r o d u c t i o n (Hunt,  Given t h i s  i s somewhat s u r p r i s i n g  there are  never  i s applied to a large variety  to protection  Gottschalk, it  "mucus" has  functional  1970; diversity  most, i f n o t  all,  chemical composition.  many v a r i a t i o n s on t h e theme, a l l mucins  While  studied  127  to  date c o n s i s t  polysaccharide  o f some s o r t o f complex and a p r o t e i n  dissolved  i n water.  fall  two g e n e r a l c a t e g o r i e s .  into  complex termed  i s dominated  dominates,  general,  protein  t h e complex  a r e not c o v a l e n t l y a r e (Hunt,  I f the composition of the  I f , on t h e o t h e r h a n d , t h e i s termed  a glycoprotein .  bound w h i l e i n a g l y c o p r o t e i n  1970).  i n C h a p t e r 3.  from h e a l t h y  divided  into  immediately sample slugs.  slugs  o f t h e whole  of d i s t i l l e d  lyophilized. dessicated  this  aliquot  was d i a l y z e d  against  water o v e r a p e r i o d  of the  s i x one of three  m o l e c u l a r weight molecules. was f r o z e n a t -80 <>C and  Both l y o p h i l i z e d  samples  a t room t e m p e r a t u r e s .  Analysis  Water C o n t e n t  t o provide a  mucus a s i t a p p e a r s on t h e f o o t  remove any unbound s m a l l dialysis  o f t h e s e was  a t -80 <>C and l y o p h i l i z e d  The s e c o n d a l i g u o t changes  t h e mucus  (about 5 ml) was p o o l e d and  two a l i q u o t s . , The f i r s t frozen  A. c o l u m b i a n u s a s  For chemical analysis  from a p p r o x i m a t e l y twenty  After  complexes  Collection  described  to  being  by t h e p o l y s a c c h a r i d e , t h e complex i s  Mucus was c o l l e c t e d  liter  this  i n a m u c o p o l y s a c c h a r i d e t h e p o l y s a c c h a r i d e and  they u s u a l l y  Mucus  1970);  polysaccharide-protein  a mucopolysaccharide .  protein In  These  (Hunt,  between a  were  stored  days  128  Mucus was weighed.  The  collected samples  from  were t h e n  f o u r h o u r s and  reweighed.  percent o f  wet  2.85  the  t o 4.46%.  eighteen  The  dried dry  s l u g s and at  105  weight  weight) averaged  3.44%  Thus p e d a l mucus i s a b o u t  immediately  °C f o r t w e n t y -  (expressed  as  and  from  ranged  95 t o 97%  a  water.  Protein The  protein  content  o f p e d a l mucus was  heated  biuret-folin  assay  (1977)  using bovine  serum a l b u m i n  T h i s assay  by  tested.  the  composition  are the  of  and  Boels  (1951) i n  t h a t i s not  protein the  p r o t e i n i n the  being  values  means. found  t o c o n t a i n 33.6%  protein  p r o t e i n / d r y w e i g h t o f mucus) w h i l e t h e  sample c o n t a i n e d  the  standard.  content  of the  were run i n t r i p l i c a t e  Whole p e d a l mucus was (weight  (Sigma) a s a  estimate of protein  amino a c i d  Assays  presented  o f D o r s e y , McDonald, and  i s p r e f e r r e d o v e r t h a t o f Lowry e t a l .  t h a t i t p r o v i d e s an biased  measured by  45.6%  protein.  dialyzed  of small, nonprotein  The . i n c r e a s e d p r o p o r t i o n o f  sample i s p r e s u m a b l y due  molecules  dialysed  (primarily  salts)  t o the  loss  during  dialysis. The was  amino a c i d  determined  composition  u s i n g a Beckman  119C  Samples were h y d r o l y z e d w i t h 6 at  100  °C.  Standards  and  Notes  N HC1  pedal  mucus  amino a c i d  protein  analyzer.  i n vacuo f o r 24  hours  s a m p l e s were c h r o m a t o g r a p h e d  a t h r e e hour sodium c i t r a t e Beckman O p e r a t i n g  of the  using  buffer cycle described i n  (119C  AN001, 1975).  c h r o m a t o g r a m s were t a b u l a t e d by  standard  The  procedures.  Three  129  s a m p l e s o f e a c h a l i q u o t were a n a l y z e d r e s u l t s are The  presented  i n Table  and  the  averaqed  5.2.  amino a c i d c o m p o s i t i o n  i s noteworthy i n  three  respects. 1„ acid  I f i t i s assumed t h a t  residues  present  of  the  measured r e p r e s e n t  i n the  glutamine)  protein  , the  total.  arginine)  the  only  17  t o 20%  The  Cysteine  disulfide chains  two  bonds a r e  and  crosslinks  thus are of  i n the  one  pedal  do  .  If  the  protein  will the  will  carboxyl behave  as  mucus  as  chapter. mucus p r o t e i n .  side chain  another c y s t e i n e  to  yielding a cysteine  can  form a  be  The oxidized  disulfide  molecule.  Such  a common method f o r c r o s s l i n k i n g p r o t e i n a likely  candidate  a polymer network.  indeed  of  this  dissociated  a c i d s and  i n the  cysteine  next chapter that d i s u l f i d e cysteine,  next  i s present  s u l f h y d r y l of  bond between t h e  glutamic  and  number  p o l y e l e c t r o l y t i c b e h a v i o r of  s u l f h y d r y l g r o u p of the  to the  proportion  (lysine  total  a t p h y s i o l o g i c a l pHs  a s p a r t i c and  a whole i s c o n f i r m e d  by  amino a c i d s  acids  and  form a l a r g e  a c i d i c s comprise  c h a r g e due  aspartic ,  aspartic  than a s p a r a g i n e  the  negative  2.  basic  and  and  of  have a n e t  a polyanion^  glutamic  a b o u t 4%  is valid,  the  qlutamic  amino a c i d s  Where t h e  assumption  group o f  (rather  acidic  comprise  amino a c i d s  the  f o r forming  It will  bridges,  be  the  shown i n  presumably formed  c r o s s l i n k the  n e t w o r k o f A.  threonine  present  the by  columbianus  mucus. 3.  Serine  and  ( 2 3 - 2 4 % ) . , T h e s e two  are  amino a c i d s  are  in large  likely  sites  amounts for  the  Table  5.1:  Amino A c i d  Composition  (residues/100  whole  Aspartic  dialyzed  9.8  9.0  Threonine  11.7  11.1  Serine  12.2  12.6  10.9  8.4  Glutamic  acid  acid  Proline  .8.0  8.6  Glycine  9.3  8.6  Alanine  7.4  7.4  Half  0.6  3.0  Valine  5.2  5.2  Methionine  trace  0.2  Isoleucine  4.5  4.5  Tyrosine  1.7  1.8  Phenylalanine  2.3  2.3  Lysine  1.1  0.9  Histidine  3.7  3.4  Arginine  3.0  3.9  Leucine  5.5  Acidics  20.7  17.4  4.1  4.8  Cystine  Basics  residues)  '  5.5  131  covalent  bonding  of p o l y s a c c h a r i d e  (Gottschalk,1972).  t o the protein  The e x i s t e n c e o f t h e s e  demonstrated i n t h e next  chain  bonds w i l l  be  chapter.  Polysaccharides No s i m p l e  assay  e x i s t s t h a t unambiguously  total  sugar content  pedal  mucus was a s s a y e d  and  sugar  Uronic  total  assay  dialyzed further  content  acid  whole p e d a l  (Sigma) a s a s t a n d a r d .  and v a l u e s  mucus, 7.7%  averaged. 6.8%  (wt/wt).  define the identity  dissociated  (1973)  using  using  A s s a y s were perfomed  The r e s u l t s  No a t t e m p t  show t h a t a c i d and  was made t o  of the u r o n i c  acids.  As w i t h  and a s p a r t i c a c i d s o f t h e p r o t e i n , t h e carboxyl  groups o f t h e u r o n i c a c i d s w i l l  mucus t o a c t as a p o l y a n i o n .  the  characteristics  of a polyanion  cause  The mucus d o e s i n d e e d as w i l l  show  be shown i n t h e  chapter.  Suqars The  assay  present.  (wt/wt) u r o n i c  the  Amino  suqars  o f u r o n i c a c i d s was measured  mucus c o n t a i n s  glutamic  next  t o be  o f B l u m e n k r a n t z and Osboe-Hansen  triplicate  the  f o r the various  d e r i v a t i v e s t h a t were l i k e l y  glucuronic in  separately  Consequently the  Acids  The the  of a polysaccharide,.  measures t h e  total  o f Boas  standard.  content  o f amino s u g a r s  (1953) u s i n g  galactosamine  Samples were h y d r o l y z e d  was measured  by t h e  (BDH) as a  i n 2N HC1 i n v a c u o f o r 20  132  hours  at  values was  100  °C.  averaged.  6.9%  and  amino s u g a r of  in triplicate  c o n t e n t of the  dialyzed  of the e l u a t e from  u s i n g a 450  galactosamine  show t h a t  (BDH)  (119C  1975).  t h e amino s u g a r s i n p e d a l mucus a r e  by a s m a l l amount o f g a l a c t o s a m i n e  mucus, 0.9%  dialysed  possibility  that  The  susceptible to acid  presence  Table  the a c e t y l fact that  hydrolysis  broken  5.3).  has One  suggestion that amino g r o u p s otherwise  i s a strong  being  as the  removed bond i s as  glycosidic  bonds for  t o assay f o r the Newberger,  a l l c a s e s i n which t h e p r e s e n c e  further  fact  they  have been f o u n d  lends support to  t h e amino s u g a r s a r e a c e t y l a t e d  will  be  These p o s i t i v e  charges  will  charges  uronic acids.  charged  1972). of  (see  : i f the (or  at physiological  tend to o f f s e t  the  as a c o n s e q u e n c e  c h a r a c t e r o f t h e mucus s h o u l d be  N-  the  amino s u g a r s a r e n o t a c e t y l a t e d  bound) t h e y  polyanionic  (0.8% whole  the acetamido  ( M a r s h a l l and  been t e s t e d  o f the  of the  groups  difficult  o f N - a c e t y l hexoses  groups  mucus wt/wt)  to r e l e a s e the monosaccharide  makes i t e x t r e m e l y  However, i n v i r t u a l l y acetyl  There  results  t h e s e amino s u g a r s a r e p r e s e n t i n t h e mucus  hydrolysis.  assaying)  dialyzed  mucus wt/wt) .  N - a c e t y l amino s u g a r s  must be  Glucosamine  primarily  accompanied  (which  the  acid  a s s t a n d a r d s . , The  (6.1% whole mucus, 6.9%  during  7.8%.  c i t r a t e cycle described  aN004,  were u s e d  amino  glucosamine  as  whole mucus  t h e Dowex 50 column o f  minute l i t h i u m  Beckman O p e r a t i n g N o t e s  and  s a m p l e s was  were c h r o m a t o g r a p h e d on a Beckman 119C  analyzer in  The  (wt/wt) w h i l e t h a t  aliquots assay  T e s t s were p e r f o r m e d  negative the  decreased.  pH's..  133  Since, as  as  w i l l tie shown i n t h e n e x t  a strong polyanion, i t i s l i k e l y  the  amino s u g a r s  able to ionize  Sialic  t h e r e f o r e probably  not  .  total  (1959).  s i a l i c acid the  Assays  detectable  s i a l i c acid  Neutral  was  measured  thiobarbituric acid  assay  (Sigma) was  were p e r f o r m e d present  acid  using  used  in triplicate.  i n pedal  the  o f Warren as a  T h e r e i s no  mucus..  Sugars  The  total  content  phenol-sulfuric glucose  acids  results the  from  (but n o t this  and  of n e u t r a l sugars  assay  o f Lo,  was  measured by  E u s s e l , and  as a s t a n d a r d .  While  measures n e u t r a l s u g a r s ,  Taylor  this  i t also  averaged.  results  (wt/wt) n e u t r a l s u g a r s ,  and  the  results  T e s t s were p e r f o r m e d  The  (1970)  measures  were c o r r e c t e d u s i n g t h e  assays.  the  assay  amino s u g a r s ) . . C o n s e q u e n t l y ,  assay  uronic acid  triplicate 7.2%  acid  (Sigma)  preferentially uronic  content  N-acetylneuraminic  standard.  from  t h a t t h e amino g r o u p s o f  a r e a c e t y l a t e d , and  H2S04 h y d r o l y s i s and  using  mucus a c t s  Acid  The  is  chapter, the  in  show t h a t whole mucus  dialyzed  mucus,  8.5%  wt/wt. The examined and  composition  of the n e u t r a l sugars  using a g a s / l i q u i d  dialized  chromatograph.  was  further  Samples o f  whole  mucus were h y d r o l y z e d , a c e t y l a t e d , and  chromatographed u s i n g the r e s u l t s show t h a t t h e  method o f C o u r t  n e u t r a l sugars  (1978).  o f p e d a l mucus  The consist  134  primarily 3.2%)  of fucose  (3,4  a c c o m p a n i e d by  (see T a b l e  Sulphated  t o 5.6%)  and  galactose  s m a l l amounts o f g l u c o s e  (Hunt,  1970)  sulphated  sugars  the t o t a l  sulphate content,  Price  .  The  (1962) and  either  8 M HC1  o r 25%  formic acid  assays  sulphate that  (6 h o u r s ,  as  a standard.  t h e r e i s no  100  C)  C)  results  these  sulphate using  Dietrich,  (Antonopoulos, using  1977) 1962).  potassium  of b o t h a s s a y s  show  mucus.  (1977) measures any was  any  were h y d r o l y z e d  in triplicate The  Both  liberate  (Nader and  100  In a d d i t i o n . t o s u l p h a t e the  phosphate  (1977).  Dodgson  detectable sulphate present i n  A. c o l u m b i a n u s p e d a l  Deitrich  To  of  measuring  methods of  Dietrich  sulphate.  (24 h o u r s ,  were p e r f o r m e d  examined by  using both  Nader and  measure o n l y f r e e  sulphated  p o s s i b l e presence  i n p e d a l mucus was  bound t o s u g a r s , the.mucus s a m p l e s  All  mannose  Sugars  polysaccharides  assays  and  to  5. 2) .  Many i n v e r t e b r a t e mucins c o n t a i n  and  (2.3  method  of  Nader  phosphate present.  and However,  no  detected.  Salts The was  composition  analyzed  using a Techtron  spectrophotometer. performed assays  of the c a t i o n s p r e s e n t i n pedal  using  absorption  A l l preparations f o r the assays  polypropylene  were c a r r i e d  AA20 a t o m i c  test  tubes  out i n g u i n t r i p l i c a t e  and and  mucus flame were  pipettes. the  All  results  135  Table  5.2'  Chemical  Composition  % whole  weight dialyzed  Glucosamine  6.1  6.9  Galactosamine  0.8  0.9  Neutral  7.2  8.5  fucose  3.4  5.6  galactose  3.2  2.3  mannose  0.4  0.4  glucose  0.2  0.3  Uronic Acid  6.8  7.7  Sialic  0.0  0.0  20.9  24.0  33.6  45.6  0.0  0.0  Total  Sugars  Acid  Carbohydrate  Protein  Salts S0,  =  i Na K  +  Mg Ca  ,.|..|  I. j.  (as the  chloride)  2.5  1.3  (as the  chloride)  9.2  1.9  (as the  chloride)  3.6  2.6  (as the  chloride)  0.6  0.6  15.9 70.4  6.4 76.0  Total Total  136  averaged.  Results  generated results  at the  are  were c a l c u l a t e d  same t i m e as as  the  the  c a t i o n , expressed  as  a percent  the  mucus.  as  follows:  weight  s p e c i f i c s f o r the  Sodium: Weighed s a m p l e s o f standards water.  were d i s s o l v e d  Sodium c h l o r i d e  of the assay  were d i s s o l v e d  containing Potassium  a swamp o f  used as  chloride  was  standards  1.5%  per a  The  chloride total  salt  weight  of  of each c a t i o n  glass  of  are  and  distilled  standard..  l y o p h i l i z e d mucus distilled  and  water  m i l l i o n sodium.  standard.  samples o f  were d i s s o l v e d  containing  parts  u s e d as  Magnesium: Weighed  a  i n deionized  500  curves  l y o p h i l i z e d mucus  P o t a s s i u m : Weighed s a m p l e s o f standards  of the  in deionized, was  standard  s a m p l e s were a s s a y e d .  presented  The  using  l y o p h i l i z e d mucus  i n deionized  distilled  EDTA . , Magnesium c h l o r i d e  was  and  water  used  as  a  standard. Calcium: standards Calcium  was  i n 0.1  used  as  r e s u l t s are  noteworthy 1.  nearly  a  containing  using  the  i n Table  ions  are  lost  h a l f r e m a i n s bound t o e i t h e r t h e  electrostatically  0.5%  LaCl3«  5.2.  wave l e n g t h s  and  manual.. These  results  respects:  While some o f t h e  c a r b o h y d r a t e of the  and  standard.  AA20 o p e r a t i n g  presented  i n two  l y o p h i l i z e d mucus M HC1  a s s a y s were c a r r i e d o u t  widths s p e c i f i e d i n the The  are  were d i s s o l v e d  chloride  All slit  Weighed s a m p l e s o f  mucus.  during protein  dialysis, or  Presumably these i o n s  bound t o t h e  dissociated carboxyl  are groups  137  of  the glutamic, a s p a r t i c 2.  Potassium  ions,and sodium for  magnesium t o c a l c i u m .  The  effect  acids.  ions are l o s t p r e f e r e n t i a l l y  and c a l c i u m b e i n g  this  and u r o n i c  t o sodium  P r e s u m a b l y t h i s i s due t o  preferentially  bound.  The b a s i s  i s n o t known.  anionic composition  o f p e d a l mucus was n o t  analyzed. The  chemical  exhaustive  and a c c o u n t s  glycoprotein. not  precisely  for  which t h i s  during  analysis  study  examination  lipids,  Unexpected l o s s e s  account  f o r some o f t h e  composition  mucin.  i s sufficient.  of t h i s study,  However,  this preliminary  I n summary, t h e s i g n i f i c a n t  composition  are as f o l l o w s :  The mucus i s 95 t o 97% water t h e r e m a i n d e r  being  p o l y s a c c h a r i d e complex.  Protein contributes the larger  protein-polysaccharide as  may be  be n e e d e d t o d e f i n e  of t h e p r e s e n t  and a p r o t e i n 2.  recovery i s  Much more work w i l l  aspects of the chemical 1.  incomplete  has not t e s t e d .  weight.  for the purposes  i s f a r from  Some o f t h e r e m a i n d e r  the p r e c i s e c h e m i c a l  salts  for this  v a r i o u s h y d r o l y s e s may a l s o  unrecovered  here  f o r o n l y 76% o f t h e w e i g h t o f t h e  The r e a s o n known.  presented  c o m p l e x ; a s such  p o r t i o n o f the t h e mucin i s c l a s s e d  a glycoprotein. 3.  likely 4.  Amino a c i d  a n a l y s i s r e v e a l s that the protein i s  t o be a p o l y a n i o n . The c a r b o h y d r a t e  polysaccharide  p o r t i o n o f the p r o t e i n  complex i s e v e n l y  s u g a r s , amino s u g a r s ,  and u r o n i c  divided acids.  among n e u t r a l  138  5-  No  sialic  6.  The  uronic  n a t u r e of the 7.  a c i d was  detected.  acids contribute  to the  polyelectrolytic  mucus.  Neither  sulphate  nor  phosphate  was  detected  in  the  mucin.  Comparison On  the  b a s i s of  composition and  o f JU  contrasted  Vertebrate  contain  In  sialic  an  and  respect  are  from  cervical  acid.  The  be  compared  to  a b s e n c e of s i a l i c n o t e d by  polysaccharide found  acid i s a disaccharide (through Pedal  n e u t r a l sugars.  monosaccharides of  Invertebrates  of  acid i n  Warren pedal  mucus  i n both acid.  The  basic  c o n s i s t i n g of  a  a B g l y c o s i d i c linkage) mucus d i f f e r s  from  However, s i n c e t h e pedal  mucus a r e  p r e c i s e . d i f f e r e n c e s between  unknown.  vertebrate  mucins) i n t h a t i t  c a t h o l i c as  the  most  invertebrates - hyaluronic  glucosamine.  which the  unknown t h e  mucin c a n  polysaccharide  a c i d coupled  N-acetyl  acid  to a  of h y a l u r o n i c  also containing in  chemical  mucins.  is virtually  this  vertebrates  glucuronic  other  t r a c h e a l and  bears s i m i l a r i t y  unit  f i n d i n g s , the  columbianus d i f f e r s  as  invertebrates (1963).  Mucins  Mucins  (such  does n o t  Other  columbianus pedal  with  Ariolimax mucins  these  To  i t and  this  to by  manner  linked i s hyaluronic  139  Ariolimax invertebrate sulphated from  c o l u m b i a n u s p e d a l mucus d i f f e r s  mucins i n g e n e r a l i n t h a t i t does n o t c o n t a i n  sugars.  In t h i s r e s p e c t i t s p e c i f i c a l l y  most g a s t r o p o d  most d e t a i l e d  African  Karnovsky,1971).  glucosamine acid.  study  Helix and  land s n a i l ,  They f o u n d  of u r o n i c a c i d  No n e u t r a l s u g a r s the  were d e t e c t e d .  of Suzuki  pedal  Otella  that this  laeda contained  content  composition  generally reviewed  mucus c o n t a i n e d  least  galactosamine  t h a t t h e p e d a l mucus o f (probably acetylated)  research  examined t h e amino  5.3. mucus s e c r e t i o n s have  1970).  polysaccharides.  mucins o f w h e l k s ( a s  The p r o t e i n  component  s e c r e t i o n s , t h a t o f Buceinium 1965) b e a r s  comparison  of pedal  a striking  various chemical  of at undulatum  similarity  to the  ( s e e T a b l e 5.3)-  mucus t o o t h e r m u c i n s i s o f  u s e f o r a number o f r e a s o n . has been c a r r i e d  been  These s e c r e t i o n s a l l c o n t a i n  o f _A- c o l u m b i a n u s p e d a l mucus  This  acids.  The c h e m i c a l  confined to the hypobranchial  (Hunt and J e v o n s ,  limited  nor Suzuki  s t u d i e s of gastropod  one o f t h e s e  protein  and i d u r o n i c  o f v a r i o u s mucins a r e compared t o A., c o l u m b i a n u s  by Hunt,  sulphated  (Pancake  T h i s i s i n c o n t r a s t with  o f t h e mucus s e c r e t i o n s .  p e d a l mucus i n T a b l e Other  mucus i s  lactea  g a l a c t o s e , but n e i t h e r s u l p h a t e nor u r o n i c  acid  The  t o hexosamine was 1.14 t o 1.  (1941) who f o u n d  N e i t h e r P a n c a k e and K a r n o v s k y  the  of gastropod  ( p r o b a b l y a c e t y l a t e d and s u l p h a t e d )  The r a t i o  differs  mucins which have b e e n s t u d i e d .  a n a l y s i s t o date  t h a t o f t h e North and  from  First,  out concerning  so  little  the d i s t r i b u t i o n of  components o f mucus t h a t i t i s  Table 5 . 3 :  The Carbohydrate  Polysaccharide  Composition o f Various Proteoglycans and G l y c o p r o t e i n s  Occurrence ( v e r t e b r a t e or invertebrate)  Components Repeating  Others  hyaluronic acid  both  D-glucosamine D-glucuronic a c i d  L-arabinose (?) D-galactose (?) D-glucose (?)  chondroitin  both  D-galactosamine D-glucuronic a c i d  D-xylose D-galactose  c h o n d r o i t i n 4 or 6 sulphate  both  D-galactosamine D-glucuronic a c i d  D-xylose D-galactose  dermatin  both  D-galactoamine L - i d u r o n i c or D-glucuronic a c i d  D-xylose D-galactose  heparin  both  D-glucoamine D-glucuronic or L-iduronic acid  D-xylose D-galactose  skeletal keratin sulphate  both  D-glucosamine D-galactose  D-galac tosamlne L-fucose S i a l i c acid D-mannose  glycan sulphate  both  glucose or fucose or galactose  sulphate  ovine or bovine submaxillary mucin glycoprotein p i g or human g a s t r i c mucin g l y c o p r o t e i n  vertebrate  vertebrate  N-acetyl  Sulphate  -(+)  galactosamlne s i a l i c acid D-galactose L-fucose glucosamine galactosamine galactose fucose s i a l i c acid  4> O  T a b l e 5.3:  (continued)  Polysaccharide  Occurrence (vertebrate or invertebrate)  Components Repeating  N-acetyl  Sulphate  +  Others  Otella lactea p e d a l mucus (a)  invertebrate  glucosamine hexuronic a c i d ( s )  +  H e l i x laeda p e d a l mucus (b)  invertebrate  glucosamine galactose  +  Buccinum undatum h y p o b r a n c h i a l mucus(c)  invertebrate  glucosamine galactosamine galactose mannose fucose glucose  +  Ariolimax  invertebrate  glucosamine galactosamine fucose galactose mannose glucose uronic acid(s)  +  (a) (b) (c)  columbianus  Pancake and K a r n o v s k y (1971) S u z u k i (1941) Hunt and J e v o n s (1965)  (?)  T a b l e 5.3:  ( c o n t i n u e d ) A c o m p a r i s o n of t h e amino a c i d c o m p o s i t i o n of s l u g p e d a l mucus and whelk h y p o b r a n c h i a l mucus.  Amino a c i d  A r i o l i m a x columbianus  aspartic  9.0  11.10  threonine  11.1  6.45  serine  12.6  6.27  8.4  11.34  proline  8.6  5.19  glycine  8.6  5.19  alanine  7.4  7.67  cystine  3.0  1.73  valine  5.2  6.91  methionine  0.2  0.31  isoleucine  4.5  4.20  leucine  5.5  8.16  tyrosine  1.8  2.85  phenylalanine  2.3  3.66  lysine  0.9  7.29  histidine  3.4  2.45  arginine  3.9  5.54  glutamic  acid  acid  Buccinum undatum (c)  143  impossible  to  "typical".  say  w i t h any  While  A.  in significant  likely  that  the  secretions  slug  what i s and  columbianus pedal  differ  this  certainty  a s p e c t s from  reflects  studied,  a bias  rather  i n the  to  m u c i n s , i t seems historical  choice  some u n i q u e q u i r k  of  of  biochemistry. S e c o n d , w h i l e mucous s e c r e t i o n s a s  received  scant  have r e c e i v e d of  not  mucus a p p e a r s  other  than  is  the  histochemical  recognized  epithelial  even l e s s a t t e n t i o n . . The  present  distribution  attention, invertebrate  a whole h a v e  preponderance  knowledge of t h e s e mucins i s b a s e d studies.  and  and  vast  Hopefully  importance of  this  situation  i n the  future  invertebrate rectified.  mucins  solely  the  on  broad  mucins w i l l  be  144  CHAPTER  Physical  Chemistry  Armed w i t h t h e knowledge p e d a l mucus, i t i s now  i t will  of t h e c h e m i c a l c o m p o s i t i o n o f  p o s s i b l e t o examine t h e e l a s t i c  n e t w o r k o f .A. c o l u m b i a n u s Specifically  mucus i n more  be u s e f u l  questions concerning  SIX  detail.  t o examine t h e f o l l o w i n g  t h e network a n d t h e m o l e c u l e s  from  which i t i s c o n s t r u c t e d . 1.  How  large  a r e the molecules  that  make up t h e  network? 2.  I s t h e n e t w o r k c o n s t r u c t e d from  molecule, 3. of  or a r e d i f f e r e n t How  form  joined  does t h e g l y c o p r o t e i n ,  the hydrated 4.  types  How  one t y p e o f together?  which f o r m s o n l y 3 t o 4%  mucus, i n f l u e n c e t h e water around i t ?  are the individual  molecules  crosslinked to  a network? 5.  during  And f i n a l l y ,  once t h i s  network i s b r o k e n  apart  l o c o m o t i o n , how d o e s i t manage t o r e c o n s t r u c t i t s e l f ?  With t h e s e performed. several  q u e s t i o n s i n mind, a number o f t e s t s  Each t e s t  provides information concerning  o f these guestions.  Taken  together, these  p r o v i d e enough i n f o r m a t i o n t o answer some o f t h e s e and  thereby  c o n s t r u c t a reasonable  macromolecular A complete until  picture  c o n s t r u c t i o n o f A. c o l u m b i a n u s  tests  are carried out.  tests questions  of t h e pedal  answer t o t h e s e q u e s t i o n s must, however,  further  were  mucus.. wait  145  Before it  will  be  d e s c r i b i n g the  testing  u s e f u l to explain the  when d e a l i n g w i t h t h e  procedures of  c o n c e p t s and  physical chemistry  this  terms  study  used  of  polyelectrolytes.  Polyelectrolytes As  explained  solution  will  the  be  used t o  this  force  supplying  randomly c o n f i g u r e d  crosslinking subsequent  of the  chain  on  the  Another  Every  pol/ymeric  its  the  order  One  mechanism i s the  third  g r o u p and  link  of  s u c h mechanism,  chains,  and  interaction  such as t h a t  this chain  macromolecule c o n t a i n i n g  distance. links  In  As  are  neighbors  configuration.  w h i c h may  on  the  the already  affect of  the  charges  t h i s case the  , thereby If this  charge.  Any  force of r e p u l s i o n neqative  Each c h a r g e  were t h e  c h a r g e r e p u l s i o n would c a u s e t h e  Figure  a dissociated  i t i s a polyanion.  maintaining  in  such  many c h a r g e d g r o u p s i s a  a consequence the  forced apart.  depicted  contains  therefore a negative  c h a r g e s r e p e l each o t h e r ,  chain  A l l of  the  to other  polymer c h a i n  polyelectrolyte.  with  of  a c t i o n o f a f o r c e on e n e r g y t o impose  in  chain.  Imagine a  carboxyl  A number  this configuration.  chains.  shape o f a p o l y m e r c h a i n present  polymer c h a i n  a p p l i c a t i o n o f an e x t e r n a l f o r c e , h a s  been d e s c r i b e d .  6.1a.  alter  mechanisms i n v o l v e t h e  chains;  a flexible  assume a random c o n f i g u r a t i o n .  mechanisms may these  i n C h a p t e r 4,  decreasing  c h a r g e s on  the  moves away from  a minimum  only  Negative  energy  f a c t o r operating,  polymer c h a i n  to  extend  this  146  FIGURE  6.1..  The c h a r a c t e r i s t i c s o f p o l y e l e c t r o l y t e s . A) I f t h e c h a r g e d c h a i n were r a n d o m l y c o n f i g u r e d ( h i g h e n t r o p y ) many o f t h e c h a r g e s would be c l o s e t o g e t h e r . B) The c h a r g e s a r e a maximum d i s t a n c e a p a r t when t h e c h a i n i s f u l l y e x t e n d e d . However, t h e entropy i s low. C) A r e a l p o l y e l e c t r o l y t e c h a i n r e p r e s e n t s a compromise between A. And B. D) The p r e s e n c e o f c o u n t e r i o n s c a n mask c h a r g e s from e a c h o t h e r , a l l o w i n g t h e c h a i n t o assume a more c o m p a c t and random c o n f i g u r a t i o n .  147  FIGURE  6.1  Polyelectroly tes  C  Compromise  o -  positive charge  148  into a long 6.1b). will the  As  with  cause the chain  expected coil  be  f o r minimum e l e c t r o s t a t i c  this  network t o  agitation  were n o t  water.  if  (eg.  a salt  salt  will  charges around  be  p o l y a n i o n , and  will  each  and  will  molecules  on  will  network w i l l  T h i s i s the  will  charge,  the  the  be  on i t s  chain.  than  situation  that  however,  t o the  negative  of c a t i o n s w i l l  negative charges  i s then  response  assume a more k i n k e d  s h r i n k somewhat.  volume  the  shown i n F i g u r e 6.Id.  energy In  the  cause  changed,  f o r c e o f r e p u l s i o n between Less  own,  water, the d i s s o l v e d  a cluster as  rod  i s dissolved in  attracted  s e r v e t o mask t h e  decrease.  impose o r d e r  present.  NaCl) i s added t o t h e  counterions  links  existing  expand t o a l a r g e r  This situation  each n e g a t i v e  other,  and  of  6.1c),  c h a i n s t o form a network,  electrostatically  of the  shape  the:random  (see F i g u r e  i f a c r o s s l i n k e d polyanion  distilled  agitation  extended  i n t e r a c t i o n s d e s c r i b e d above w i l l  the charges  Figure  final  e n e r g y and  polymer c h a i n , r a t h e r than  repel itself  occur  The  a compromise between t h e  crosslinked tc similar  should  c o n f i g u r a t i o n (see  polymer c h a i n t o c o n t o r t .  will  electrostatic  if  ordered  a n e u t r a l polymer,however,thermal  f a v o r e d by t h e r m a l If  is  rod, a very  from  to  individual  c o n f i g u r a t i o n and  While the  These  neighboring  available  the  form  presence  the  of  c o u n t e r i o n s causes the f o r c e o f r e p u l s i o n t o decrease i t does not  a b o l i s h the  network,in  the  presence  above i t s u n c h a r g e d Precise  repulsion altogether._ of c o u n t e r i o n s ,  Consequently  is still  the  expanded  level.  e x p l a n a t i o n s f o r the  e f f e c t s of charge density  149  and  counterion  be  found  or  Tanford  d e n s i t y on t h e s h a p e s o f m a c r o m o l e c u l e s may  i n t h e r e v i e w s by K a t c h a l s k y  (1964), V e i s  (1970),  (1961).  Tests  Network  Swelling  As  shown i n t h e p r e c e d i n g  chemical  charged  a t p h y s i o l o g i c a l pH's.  components a r e l i n k e d t o g e t h e r  T h i s c a n be d e t e c t e d  mucus i s c o l l e c t e d compact b l o b . solution natural  (roughly  mucus) i t w i l l  mucus i s p l a c e d  counterions slowly  blob  equivalent  shape f o r s e v e r a l d a y s . of  diffuse  i n Chapter  i s placed  to the s a l t  remain r o u g h l y  below t h e l e v e l glycoprotein  I f a sample o f 4 i t forms a NaCl  concentration of  t h e same s i z e and  I f however a sample  (0.1 t o 0.3 ml)  water t h e  o u t o f t h e mucus and t h e b l o b  majority  by l o w e r i n g  groups are h a l f d i s s o c i a t e d pH i s l o w e r e d below  will  size .  o f t h e c h a r g e s c a n be  t h e pH o f t h e mucus  where t h e c a r b o x y l  are disscociated.  they  as d e s c r i b e d  i n a 0.1W  i n 10 ml o f d i s t i l l e d  the vast  removed a l t o g e t h e r  be  simply.  expand t o s e v e r a l t i m e s i t s i n i t i a l  Alternatively,  the  quite  be  I f these  of a polyanion  as described  If this  mucus s h o u l d  i n t o polymer c h a i n s ,  show t h e c h a r a c t e r i s t i c s  above.  s e v e r a l of the  components o f JU c o l u m b i a n u s p e d a l  negatively  should  chapter,  blob  groups o f t h e  The pH a t which t h e c a r b o x y l  ( t h e pK) i s a b o u t 4.  4 most o f t h e c a r b o x y l  Thus when  groups  u n d i s s o c i a t e d and t h e mucus n e t w o r k , no l o n g e r  held  will  150  expanded indeed  by  the case.  solution by  the negative charges,  of  pH  interstices water.  As t h e  water out  of the  water c o n t a i n e d milliliters network  s h r i n k i n g e f f e c t s can  placed or  the c o n t r a c t i o n of the  interstices.  (expressed  values  were measured  the  amount o f  as h y d r a t i o n ,  t o pH  water,0.1  2.1  with  i n 25 ml o f t h e t e s t s o l u t i o n  complete  reached.  w i t h i n two  hours,  however t h e  hours t o ensure  After equilibration  the  remove t h e  was  weight i s the  The  t o expand temperature  was  mucous b l o b was  with  was  visually  network  left  water  value  in  was  qrasped  immediately  N a C l were t h e n  A l l s a m p l e s were t h e n  reweighed.  procedure  that equilibrium  changes of d i s t i l l e d  salt.  18 h o u r s and  weight)/dry  a t room  the solvent,and  Samples e q u i l i b r a t e d  against repeated  The  allowed  Change i n volume o f t h e b l o b  a f o r c e p s , removed f r o m  weighed.  HCl.  and  pedal  M NaCl,1.0 M  (0.05-0.15 ml)  A l l t e s t s were c o n d u c t e d  t h e s o l v e n t f o r 6-7  for  up  f o r A., c o l u m b i a n u s  f o l l o w s : A s m a l l b l o b o f mucus  (21-23 ° C ) .  to  soaks  the  network f o r c e s  Conseguently  i n t h e network  water a d j u s t e d  contract.  with  easily  expansion.  and  as  be  c h a i n s much a s a sponge  mucus i n f o u r s o l v e n t s : d i s t i l l e d  was  2.1  o f H20/gram o f g l y c o p r o t e i n ) i s a measure o f  Hydration  NaCl,  been a d j u s t e d t o  network e x p a n d s water i s drawn i n t o  between t h e  Conversely,  o f which has  HC1.  These s w e l l i n g and quantified.  This i s  A b l o b o f mucus s h r i n k s when p l a c e d i n a  o f water t h e  the a d d i t i o n  should contract.  dialyzed  (24 h r . , 22 dried  (wet  h y d r a t i o n expressed  a t 105  °C) °C  weight-dry a s grams of  151  water  p e r gram d r y w e i g h t .  quintriplicate. in  Table  above. the  6.1.  A l l t e s t s were p e r f o r m e d i n  The r e s u l t s f r o m These t e s t s c o n f i r m  The mucus i s h i g h l y  solvent,  being  nearly  configuration  nearly  20 t i m e s as expanded  a liter  those  mucus  solvent.  to  mucus  expanded  Under  of i t s f u l l y  hydration  of the slug  in distilled  value  conditions  expanded  measured to that that  here f o r of f r e s h l y  mucus as i t  i s not a t e q u i l i b r i u m  P r e s u m a b l y t h e mucus i s s e c r e t e d gland  i n the  (0.1 M NaCl) t h e  (21-34 g/g) i t i s e v i d e n t  lumen o f t h e s u p r a p e d a l  made  i s contained  (206 g/g) i s compared  a p p e a r s on t h e f o o t  time spent  fully  o f water  t o one f i f t h  If the equilibrium  mucus i n 0.1 M NaCl  its  In t h i s  i n natural  network i s c o n t r a c t e d  collected  the p r e d i c t i o n s  o f one gram o f mucus n e t w o r k .  approximating  size.  t e s t s are presented  s e n s i t i v e t o the compostion of  water a s compared t o pH 2.1.  interstices  these  i n a dehydrated  on t h e f o o t i s i n s u f f i c i e n t  with  into the state  t o allow  and t h e  equilibrium  be r e a c h e d .  Solubility  Tests  Anyone who h a n d l e s a s l u g mucus i s v e r y  difficult  attaches i t s e l f  i s again  crosslinked As elastic  discovers  to dissolve.  that  tied  will  make i t go away.  t o the presence  pedal  Once a b i t o f  t o y o u r f i n g e r s , i t seems t h a t  w a s h i n g and s c r u b b i n g fact  soon  slime  no amount o f  This  simple  i n t h e mucus o f a  network.  explained  i n C h a p t e r 4, an e l a s t i c  network i s  as a r e s u l t of i t s being c r o s s l i n k e d .  Further,  a  Table  6.1:  Hydration  Solvent  of Pedal  Mucus  Equilibrium hydration ( m l H „ 0 gm d r y m u c u s )  Estimate hydrodynamic h y d r a t i o n (ml H „ 0 / g m )  954.7 ± 432.3  2430  0.1 M N a C l  206.1 ± 38.7  276  1.0 M N a C l  138.8 ± 24.4  197  distilled  water  (pH=6.0)  pH 2.1  Mucus  59.7 ±  as c o l l e c t e d  21.4  12.6  34.1  28  153  considerable  deformation  network b e f o r e  the c r o s s l i n k s break  network c a n be p u l l e d situation  and s t r e s s must be imposed  away f r o m  and t h e m o l e c u l e s o f t h e  each other.  A similar  a r i s e s when t h e mucus network i s p l a c e d  volume o f f l u i d .  on t h e  in a  large  The p r o c e s s o f d i f f u s i o n i s s u c h t h a t t h e  m o l e c u l e s o f t h e network a r e e n e r g e t i c a l l y c o m p e l l e d t o a r r a n g e t h e m s e l v e s randomly t h r o u g h o u t This  1.  Protein  requirinq  hiqh  possible  or polysaccharide  bound t o e a c h o t h e r .  types:  c h a i n s c a n be  T h e s e bonds a r e q u i t e  temperatures,large  forces,or  covalently  stable, chemical  action  be b r o k e n . 2.  Protein  or polysaccharide  e a c h o t h e r by "weak" bonds such hydrophobic i n t e r a c t i o n s . conditions covalent half  mild  Further,  t h e s e bonds w i l l  bonds can g r a d u a l l y force.  ensures that 3.  a s h y d r o g e n bonds o r  with  those  be c o n s t a n t l y  likely  agitation.  that  short.  rearranqing.  chains crosslinked  apart  half l i f e  by weak  under t h e i n f l u e n c e  o f a weak bond  protein  by p h y s i c a l  or polysaccharide  entanqlements.  t o become e n t w i n e d  As a  As a  of a  also  i f a bond i s b r o k e n i t c a n be r e f o r m e d  Finally,  crosslinked  t o break  a t p h y s i o l o g i c a l temperatures the  be p u l l e d  The s h o r t  under  required  o f an i s o l a t e d weak bond may be q u i t e  consequence i t i s p o s s i b l e  small  c h a i n s c a n be bound t o  These bonds a r e l a b i l e  i n comparison  bonds.  life  result  are  volume.  p r o c e s s i s r e s i s t e d by t h e c r o s s l i n k s o f t h e n e t w o r k .  These c r o s s l i n k s a r e o f t h r e e  to  the f l u i d  quickly.  c h a i n s c a n be  Lonq p o l y m e r  chains  a s t h e y a r e j o s t l e d by t h e r m a l  I f two c h a i n s s o l i n k e d  are pulled  upon i t w i l l  154  t a k e some p e r i o d this  period  o f t i m e f o r them t o d i s e n t a n g l e . .  (while t h e c h a i n s a r e s t i l l  entanglements  will  act as c r o s s l i n k s .  periods,however,entanglements c a n n o t a c t as permanent As l o n g  will  the  Over  Only  which  and t h u s  of c r o s s l i n k i s  be m a i n t a i n e d and t h e mucus  when t h e c r o s s l i n k s a r e b r o k e n  mucus be a b l e t o d i s s o l v e .  c o n d i t i o n s under  longer  become.unraveled  a s any one o f t h e s e f o r m s  not d i s s o l v e .  the  crosslinks.  p r e s e n t t h e mucous network w i l l will  entwined)  During  will  Thus by e x a m i n i n g t h e  t h e mucus d i s s o l v e s , i n f o r m a t i o n  be g a i n e d c o n c e r n i n g t h e t y p e ( s ) o f c r o s s l i n k  may  present i n  p e d a l mucus . Before d e s c r i b i n g the experiments i t i s necessary to d e f i n e t h e term there e x i s t s  "soluble".  a continuous spectrum  end o f t h e s p e c t r u m solution means  This i s d i f f i c u l t  because  of s o l u b i l i t i e s .  a r e s m a l l m o l e c u l e s which  c a n n o t be e a s i l y  t o do  s e p a r a t e d back  (filtration,centrifugation).  A t one  once i n  o u t by  "normal"  At t h e o t h e r end o f t h e  sectrum a r e t h e macromolecules  that  be s e p a r a t e d by n o r m a l  As w i t h any c o n t i n u o u s  spectrum, or l e s s  solubility  arbitrary  means.  c a n be d e f i n e d  cut-off  point.  present study such a p o i n t defined 1,  um pore  and c a n  o n l y by c h o o s i n g a more  For the purposes of the  i s chosen  and a m o l e c u l e i s  t o be s o l u b l e i n a l i q u i d i f : I t c a n n o t be s e d i m e n t e d  (12,100 g f o r 30 m i n u t e s ) 2.  are " c o l l o i d a l "  centrifugation  and  I t i s not r e t a i n e d size.  by low speed  by a N u c l e o p o r e f i l t e r  with a 1  155  Utilizing conducted  this  t o determine  would d i s s o l v e . Samples small  operational under  The t e s t  tests  what c o n d i t i o n s  procedure  were c o l l e c t e d  volume o f mucus  definition,  pedal  as f o rthe p h y s i c a l t e s t s .  (0.1 t o 0.3 ml) was combined  i n a Potter  Teflon  o f t h e g r i n d e r was t h e n r o t a t e d  and  slowly inserted  This s t i r r i n g a result  Elvehyjem  tissue  and withdrawn f r o m  t h e mucus was d i s p e r s e d  The s a m p l e s  minutes.  Formation  show t h a t  t h e mucus h a d n o t d i s s o l v e d .  form  of a gelatinous  t h e sample was t h e n f i l t e r e d  Nucleopore  filters  series  a pore  completely  size  all  the f i l t e r .  was u s u a l l y  larger  retained  I f a pellet  pore  with ease,  by t h e f i n a l  pore s i z e .  through  A number  (5.0um, 1.0um, i n this would  c o u l d be  that t h i s  cut-off  a sample p a s s i n g t h r o u g h before being completely  a 0.1 um f i l t e r  Some s a m p l e s and t h i s  passed  was n o t e d . .  o f compounds known t o be u s e f u l i n d i s s o l v i n g  macromolecules  were t r i e d  6.2.  sizes  The p o r e  d i d not  a series of  t h e sample  I t was f o u n d  sizes  completely  was s u f f i c i e n t t o  A t some p o i n t  a t which  quite d i s t i n c t ,  samples  25* 40, o r 55  o c c l u d e t h e p o r e s a n d no more f l u i d  forced through point  pellet  o f descending pore s i z e  was r e a c h e d  10 ml sample  a t 12,100 g f o r 30  through  0.8um, 0.6um, 0.4um, 0.2um, 0.1um).  and a s  stirring  at either  were t h e n c e n t r i f u g e d  tube.  minutes  and t h e e n t i r e  were a l l o w e d t o s t a n d f o r 24 h o u r s  The  a t 1740 rpm  the grinder  After  A  with t e n  grinder.  p r o c e s s was c o n t i n u e d f o r f i v e  became a t r a n s p a r e n t v i s c o u s l i g u i d .  oc.  mucus  was a s f o l l o w s :  ml o f s o l v e n t pestle  were  and t h e r e s u l t s  are.shown i n T a b l e  shown a r e t h e s m a l l e s t t h r o u g h  which  156  Table  6.2:  Solubility  Solvent  distilled 1%  water  mercaptoethanol  8 M guanidine 8 M  HC1  urea  o f A. c o l u m b i a n u s  p e d a l mucus  25 C  40 C  55 C  pellet  pellet  pellet  pellet  0.1  0.1  pellet  pellet  0. 1 ym  NF  5 ym  0.1  5 ym  pellet  ym  pm  formamide  5  2 M  pellet  pellet  pellet  pellet  pellet  pellet  pellet  pellet  pellet  KC1  0.5% T r i t o n 0.2% Tween  sizes  noted  X100 20  um  ym  are the smallest  NF=nonfilterable  filter  size  the s o l u t i o n  will  go  through.  157  t h e sample would  pass.  I t i s apparent solubilized  i s raised  p e d a l mucus  mercaptoethanol already  a t 25 °C none o f t h e t r e a t m e n t s  t h e mucus i n a p e r i o d  the temperature dissolved  that  o f 24 h o u r s .  t o 40 °C one compound  , 1% 2 - m e r c a p t o e t h a n o l .  contains a sulfhydral  existing  disulfide  with the s u l f h y d r y l  However when  group  effectively 2-  which  reduces  bonds by f o r m i n g a d i s u l f i d e  of the cysteine  bond  molecules present i n t h e .  mucus p r o t e i n .  Thus 2 - m e r c a p t o e t h a n o l  protein-protein  crosslinks.  a c t s by b r e a k i n g  Subsequent  tests  showed t h a t i t  was n o t n e c e s s a r y t o d i s p e r s e t h e mucus i n o r d e r f o r 2mercaptoethanol  t o show t h i s  solubilizing  effect.  p e d a l mucus p l a c e d i n a 1% m e r c a p t o e t h a n o l will,over  t h e c o u r s e o f 24 h o u r s  solubilizing  effect  A blob of  solution  a t 40 °C, d i s s o l v e .  of 2-mercaptoethanol  and s i m i l a r  The thiol  r e d u c i n g compounds ( N - a c e t y l c y s t i n e , d i t h i o t h r e i t o l )  has  been n o t e d  types  of  i n studies dealing  mucin s u c h  bronchial  mucins  are c a r r i e d the to  as p i g g a s t r i c  mucus  slug  human c e r v i c a l and 1978).  o u t a t 55 °C a number o f compounds  Thus, a second  t o S-S bonds) e x i s t s  Unfortunately determined  tests  solubilize  bonds o r h y d r o p h o b i c  catagory of c r o s s l i n k ( i n i n t h e mucus.  p e d a l mucus i s a g a i n s i m i l a r t o s u c h  as p i g g a s t r i c  When  A l l o f t h e s e compounds a r e known  weak b o n d s such as h y d r o g e n  interactions. addition  mucin,and  (see r e v i e w by C r e e t h ,  (see T a b l e 6 . 2 ) .  disrupt  with s e v e r a l d i f f e r e n t  mucus and human  cervical  In t h i s  respect  v e r t e b r a t e mucins  mucus.  t h e p r e c i s e n a t u r e o f t h e weak bonds c a n n o t  from  these  tests.  be  158  Intrinsic As  Viscosity  explained  fluid's  held  plate  directly the  rate  plates.  One  established  As  the  i n the  fluid  as  faster  next l a y e r  than the  the  next  the  formation maintain  of  6.2b.. A number o f  rigid  within  (the  shown i n t h e  of  the  slightly  slower  The  i s changed.  the  Each  rigid  same s p e e d  rigid  disrupting  particles will orderly of  an  flow.  Figure  "tie" fluid This  new  additional force  before  same.  of  pattern  hence  plate  deformation  particle fluid as t h e  layers  the  However,  between t h e  pattern  e a c h p a r t i c l e must move a t t h e  input  internal  consider  volume c o n t a i n e d  Since the  the  the  p a r t i c l e s have been added t o  non-deformable)  fluid  opposes needed  measure o f Now  than  force  sample i s t h e  several  fluid  slightly  the  fluid  The  moving  of d e f o r m a t i o n o f  ( ie.  is  of  same v e l o c i t y a s  the  the  slip  between l a y e r s  fluid.  is  fluid  figure.  layers.  the  "no  a stack  i s thus a  for  and  a v e l o c i t y gradient  below i t and  a  moves a t e s s e n t i a l l y  the  the  straddle  plates  The  p l a t e moves a t  because a f r a c t i o n of rigid  velocity.  t h i s v e l o c i t y gradient.  (= v i s c o s i t y , n )  rate  i s stationary  "Friction"  t h i s gradient  The  6.2a.  l a y e r s ; each l a y e r  l a y e r above i t .  friction  is  A fluid  c o n s i s t i n g of  thick  the  i n Figure  itself  a conseguence  thought of as  fluid.  Take  plate  plate  measure o f  of deformation.  a constant  infinitesimally  to  viscosity is a  a d j a c e n t t o each of the  same v e l o c i t y a s  be  the  moves a t  condition").  may  to  s i t u a t i o n depicted  between two  second  i n C h a p t e r 4,  resistance  example t h e  Measurements  will  adjacent  to  particle  together, of f l o w  i f i t i s t o be  requires  maintained.  159  FIGURE 6.2.  Viscosity A) F l u i d s a n d w h i c h e d between a moving p l a t e and a s t a t i o n a r y p l a t e w i l l e s t a b l i s h an o r d e r l y velocity gradient. The f o r c e , F1, n e c e s s a r y t o move t h e p l a t e i s F = An(dx/dy)/dt B) The p r e s e n c e o f r i g i d p a r t i c l e s i n t h e f l u i d d i s r u p t s the o r d e r l y v e l o c i t y gradient. As a c o n s e q u e n c e F2>F1 e v e n t h o u g h t h e v e l o c i t y o f t h e p l a t e and t h e v i s c o s i t y o f t h e f l u i d a r e not a l t e r e d .  160  Figure  F, ^  6.2  moving plate , area = A  v  e  |  o  c  j  t  y  S fluid , v i s c o s i t y = q  F > F, 2  161  Thus t h e  internal  particles  friction  i s higher  apparent  viscosity,  particles  i s higher  increase  i n apparent  of t h e  fluid  n',  containing  o f the  viscosity  particles,  concentration  of  particles  describes  c  the  account  rigid by  particles'  concentrations.  transformed  Each  k graph can  to a s p e c i f i c  viscosity)  of these certain the it can  t h e n be  value  be  thought  particle  on  an  complications The function  of.both  hydrodynamic  The  the higher  the  number t h a t  fluid.  viscosity  This i s  a t a number  i s then  nsp:  nsp.  the  value  concentration. zero  viscosity. £ n ] , and  nsp/c  The  extrapolation  concentration This  (the  value  gives  zero concentration  the  intrinsic  a measure o f t h e volume o f  inter  molecular  viscosity  the  volume.  as  Since viscosity  a  single  I t thus avoids  any  interaction.  of a r i g i d  shape o f t h e The  i n f l u e n c e of  fluid.  a  i s known  u n i t s ml/g.  to  the  apparent  the  infinite  intrinsic  rigid  has  of a s  due  =  the  concentration  on  apparent  points to  viscosity  i s measured a t  effect  and  The  at a s i n g l e  viscosity,  against  of reduced  intrinsic  this  drawn p l o t t i n g  experimental  the  rigid  alone.  apparent v i s c o s i t y  (n'-n)/n  reduced  higher  arrive  measuring the  fluid  ( i n grams/ml).  the  and  itself  i s a f u n c t i o n of  I t i s p o s s i b l e t o take  accomplished of  fluid  than that of the  of  dependence i n t o  containing  than that of the  concentration  viscosity.  fluid  particle  p a r t i c l e and  more a p a r t i c l e  is a  i t s effective  deviates  from  a  162  spherical be,  shape, the g r e a t e r i t s i n t r i n s i c  For r i g i d  the e q u a t i o n  Equation  particles  these  viscosity  two f a c t o r s  are r e l a t e d  6.1  , . . [ n ] = s ( v + hvo)  volume o f t h e a n h y d r o u s p a r t i c l e Snary,Allen,and  Pain  ( c a l c u l a t e d t o be 0.65 by  ml H20/gm) and vo i s t h e p a r t i a l  1.0),  c o n t a i n a term  f o r the molecular  molecules. molecular  Equation  Note t h a t t h i s  weight,  For a f l e x i b l e weight such  specific  with t h e p a r t i c l e  (approximately  4.n ,3 and m o l e c u l a r  a s i t moves  equation  weight.  M, h o l d s  only  for rigid  molecule I n i ] w i l l  Alpha  by p r o c e d u r e s  point f o r further  i s usually  i s some  hydrodynamic p a r t i c l e s  molecular  with  I t will  value  determined  n o t a p p l i c a b l e t o mucus. discussion i t will  t h a t t h e d i s p e r s e d mucus i s a s o l u t i o n  applicable.  vary  [ n i j = KM  between 0.5 and 0.8.  here  does n o t  The i n d e p e n d e n c e  where K i s an e m p i r i c a l c o n s t a n t a n d *  starting  volume o f t h e  that  6.2  empirically  specific  ( 1 9 7 0 ) ) , h i s a measure o f h y d r a t i o n  water w h i c h i s c a r r i e d  of  by  ( T a n f o r d , 1961) :  where s i s a measure o f s h a p e , v i s t h e p a r t i a l  (in  will  and t h a t e q u a t i o n  of  As a  be assumed rigid  6.1 i s t h e r e f o r e  be k e p t i n mind however t h a t a  w e i g h t d e p e n d e n c e may c a u s e t h e s e  v a l u e s t o d e v i a t e from  reality..  Eguation  calculated  6.1 w i l l  be  used  163  to  provide  a means by which t h e g e n e r a l  h y d r o d y n a m i c volume o f m o l e c u l e s equation minimum  shape and  may be examined.  i s a p p l i e d a s f o l l o w s : The v a l u e (s=2.5) when t h e m o l e c u l e  J.n-3 =  2.5  value  Thus  t o the d e n s i t y of bulk  water  f o r t h e h y d r a t i o n r e p r e s e n t s t h e maximum  value f o r hydration. hydration  i s a sphere.  U n 3/2. 5  where vo i s assumed t o be e q u a l This  of s i s at a  (0.65 + h vo) o r  h = 1. 625  (=1.0).  The  Conversely,  i s a t a minimum  In  j}  i t c o u l d be assumed  that  (h=0) so t h a t  = 0.65 s o r  s = l.n!j/0.65  This w i l l This  g i v e a maximum v a l u e  p a r a m e t e r c a n be r e l a t e d  f o r t h e shape parameter. to the r e l a t i v e  a spheroid  (Simha,1940).  and  l i e somewhere between t h e maximum and minimum  s will  values  calculated  The the  present  intrinsic  In r e a l i t y  dimensions of  here. study  makes u s e o f t h i s t h e o r y  viscosity  of p a r t i c l e s  f r a g m e n t s o f t h e mucus network shearing  in distilled  reasonable  the true values f o r h  formed f r o m  by e x a m i n i n g small  when mucus i s d i s p e r s e d by  water a s d e s c r i b e d above.  t o assume t h a t p a r t i c l e s  I t seems  of t h e mucus n e t w o r k ,  164  created  when mucus i s d i s p e r s e d  random d i s t r i b u t i o n forming any  of shapes.  t h e network o f e a c h  expansion  particles  seems u n l i k e l y t h a t will  shape  shape under  I f these  allow  f o r estimation  network.  value  f o r hydration  measured 1. an  This  The h y d r a t i o n  effective  sheared  different  estimated  different  may  will  differ  from  be a  from  intrinsic  constant of the  that  a network f r a g m e n t a s t h e f r a g m e n t T h i s amount o f w a t e r may be within the  o f t h e network i n an e q u i l i b r i u m  The h y d r a t i o n  of small  from t h e network i n sample  that t h i s  viscosity i s  I t represents the  from t h e amount o f w a t e r h e l d  extensively possible  reasonably  of the h y d r a t i o n  hydrodynamie h y d r a t i o n .  i n the viscometer.  interstices 2.  normal  by e q u i l i b r i u m s w e l l i n g i n two r e s p e c t s :  water w h i c h t r a v e l s w i t h is  network  assumptions a r e v a l i d  f a c t o r s o f t h e above e g u a t i o n  2.5 and s h o u l d  Thus, i t  of the e l a s t i c  a v e r a g e s h a p e may be  approximated as s p h e r i c a l .  arranged change t h e  i t s shape.  formed  some  chains  a r e randomly  not a l t e r  assume a h i g h l y a s s y m m e t r i c their  have  I f the i n d i v i d u a l  particle  particles  c o n d i t i o n s and t h a t  the  will  o r c o n t r a c t i o n o f t h e network w i l l  volume b u t w i l l  1  by s t i r r i n g ,  situation.  network f r a q m e n t s may be  as a whole.  preparation  The mucus i s s h e a r e d  ( s e e below) and i t i s  d i s r u p t i o n c h a n g e s t h e network  properties. In l i g h t by  intrinsic  equilibrium it  of these viscosity  f a c t o r s the hydration may  provide  a better estimate  swelling o f the hydration  i s sheared  during  a pedal  wave.  value  estimated than  s t a t e o f t h e mucus a s  165  Tests standard  were c a r r i e d  curve  concentration  distilled  tests.  (g/ml) was  1 ml  their  A280 were t h e n This  a l i q u o t s of  curve  particulate  matter.  serially  t i m e was for  I t was  and  one  sample  the  using  time  measured  but  with  until  the  and  at  +-  6.4  .  Averaqed  dispersed  Samples were  i n the  than  values  of  For  in then large  particles  1um..  S a m p l e s were  viscosity  meausured f o r  watch.  The  t e s t s are  to  solubility  viscometer  Tests  were  t i m e was  viscometer  was  Transit repeated  measured r i n s e d with  A l l t e s t s were c a r r i e d  i n a c o n t r o l l e d temperature bath..  of these  ml  the  Ostwald c a p i l l a r y  d r i e d between s a m p l e s .  results  ml  serially  manner c o n s i s t s o f  same t r a n s i t  N HC1  the  and  shown t h a t  a stop  10  weighed  o f 80-100 s e c o n d s f o r w a t e r .  times c o n s e c u t i v e l y .  0.1°C  h o u r s and  above.  specific  three  25  resulting  i n subsequent t e s t s .  greater  an  i n 10  solubility  u s e d t o measure  in this  in size  diluted  a transit  dispersed  12,100 g f o r 5 m i n u t e s t o remove any  each c o n c e n t r a t i o n with  was  Two  concentration, _  were c o l l e c t e d  mucus d i s p e r s e d 5um  follows.  and  A  mucus  O t h e r a l i q u o t s were  water as d e s c r i b e d at  l e s s than  as  of the  °C f o r 24  o f mucus p r e s e n t  centrifuqed  tests  105  versus  above f o r t h e each  plotted against  t e s t s samples  distilled  nm  a b s o r b a n c e measured,  standard  concentration these  280  constructed  concentration.  and  f o l l o w i n g procedures..  mucus were c o l l e c t e d  s a m p l e s were d r i e d a t  diluted  the  water as d e s c r i b e d  Three  determine  by  cf absorbance at  samples o f p e d a l of  out  presented  out  Some o f  in Figures  6.3  1  and  166  FIGURE 6.3-  The i n t r i n s i c v i s c o s i t y o f t h e d i s r u p t e d f r a g m e n t s o f A r i o l i m a x c o l u m b i a n u s p e d a l mucus shows t h e c h a r a c t e r i s t i c s o f a p o l y e l e c t r o l y t e . The i n t r i n s i c v i s c o s i t y d e c r e a s e s a s e i t h e r t h e n e g a t i v e c h a r g e s a r e masked by sodium i o n s , o r t h e pH i s l o w e r e d t o r e a s s o c i a t e t h e c a r b o x y l groups. The two c u r v e s f o r d i s t i l l e d w a t e r r e p r e s e n t t h e e x t r e m e s i n t h e range o f samples tested.  FIGURE 6.3  ON  168  FIGURE 6-4.  M o l e c u l a r weight dependence o f i n t r i n s i c viscosity. D i s s o l v i n g A r i o l i m a x -columbianus p e d a l mucus w i t h 1% 2 - m e r c a p t o e t h a n o l l o w e r s t h e i n t r i n s i c v i s c o s i t y o b s e r v e d i n 0.1 M NaCl t o l e s s t h a n o r e g u a l t o t h a t o b s e r v e d i n 1.0 M N a C l , p r e s u m a b l y as a r e s u l t o f t h e ; d i s r u p t i o n o f t h e mucus n e t w o r k .  Figure  6.4  170  The  specific  dispersed  viscosities  in distilled  were h i g h l y v a r i a b l e . 11,300. to  that tests  form  by  by t h e n o n l i n e a r i t y  average in  of these  t o e x t r a p o l a t e the  concentratons  t o or g r e a t e r than  large  and h i g h l y a s s y m m e t r i c a l  of i n t r i n s i c  Regardless  those  molecule.  The  are r i g i d  h y d r a t i o n s c a n be c a l c u l a t e d .  hydration average  i s t h e same as b u l k  intrinsic  hydration  viscosity  intrinsic  6.2. t h a t t h e mucus  and r o u g h l y The p a r t i a l  volume o f t h e mucus c o n t r i b u t e s n e g l i g i b l y , specific  a very  macromolecules a r e  mucus i n T a b l e  being t e s t e d here  assumed t h a t t h e p a r t i a l  of the v a r i a t i o n  F o r example t h e y a r e  As e x p l a i n e d a b o v e , i f i t i s assumed  their  ( w i t h an  r e p o r t e d f o r DNA,  of several biological  to that of pedal  particles  to  t e s t s a l l o f the values of i n t r i n s i c  equal  compared  formed  i s extended  4,000 t o 11,500  obtained are quite large.  viscosities  tests  are further  c o n c e n t r a t i o n . . I f , however, t h e l i n e  o f 6,100) a r e o b t a i n e d .  viscosity  attributed  o f t h e nsp/c v e r s u s c p l o t s .  makes i t d i f f i c u l t  v a l u e s r a n g i n g from  the results  be  2,500 t o  o f the range o f  These r e s u l t s  and assumed t o p r o v i d e an e s t i m a t e  viscosity,  from  results  p r o c e d u r e . . The two  boundaries  a r e shown i n F i g u r e 6.3*  t o zero  The  could not d e f i n i t e l y  t h e two p o i n t s o f l o w e s t  zero  o f nsp ranged  i n the experimental  This nonlinearity curve  Values  t h e u p p e r and l o w e r  complicated  s a m p l e s o f mucus  w a t e r were measured.  This v a r i a b i l i t y  any f a c t o r  of nine  spherical specific  and i t i s  volume o f t h e w a t e r o f  water  ( =1).  Therefore the  o f 6,100 c o r r e s p o n d s  o f 2430 ml o f w a t e r p e r gram o f mucus.  to a Even  171  Table  6.3:  I n t r i n s i c V i s c o s i t i e s of V a r i o u s  Molecule  Molecular weight  Macromolecules  Intrinsic viscosity  ribonuclease (globular protein)  13,683  3.3  hemoglobin  68,000  3.6  10,700,000  3.4  39,000,000  36.7  bushy s t u n t (spherical)  virus  tobacco, mosaic (cylindrical)  virus  myosin  493,000  217  collagen  345,000  1150  6,000,000  5000  DNA  172  considering the f a c t be  that these  estimates  of h y d r a t i o n  h i g h due t o i n a c c u r a c i e s i n t h e a s s u m p t i o n s  computations,  i t i s e v i d e n t t h a t t h e mucus  considerably The  slope  of t h e s e  curves  testing.  I f the r i g i d  interact,  the slope  (Tanford,  1961).  particles  I t i s u s u a l l y found,  higher concentrations.  decreased to  curve  polyelectrolyte counteracted  lower  with  are d i l u t e d .  a positive  processes  of c o u n t e r  network.  goes through  of  curve pedal  decreases. versus  a minimum  water t h i s  will  be leads  trend i s  ions i n the i s d i l u t e d the  and t h e more t h e  T h i s expansion  of the  molecular  and n s p / c i n c r e a s e s a s t h e  As a c o n e g u e n c e o f t h e s e c plots  (Tanford,  i s f u r t h e r evidence mucus.  of n s p / c  For a  The more t h e sample  (Tanford,1961) .  t h e nsp/c  g r e a t e r at  This process  slope.  dissolved i n d i s t i l l e d  volume/molecular weight r a t i o concentration  being  a high value  network l e a d s t o an i n c r e a s e i n t h e  the  however, t h a t a t  the concentrations of counterions  network expands  be z e r o  c o n c e n t r a t i o n s and n s p / c w i l l  by d i l u t i o n  polyelectrolyte  do n o t  i s a f u n c t i o n of  Therefore  as t h e m o l e c u l e s  an n s p / c / c  should  t h e amount o f i n t e r a c t i o n  at high  i n the course of  m a c r o m o l e c u l a r s o l u t e s do i n t e r a c t .  amount o f t h i s i n t e r a c t i o n  measured  of  dissolved i n a f l u i d  of the nsp/c curve  concentrations  concentration,  be  network  i s also indicative  o c c u r r i n g a s t h e mucus i s d i l u t e d  The  made i n t h e  i n f l u e n c e s the water i n i t s v i c i n i t y .  processes  finite  may  for a  1961).  two  polyelectrolyte Thus t h e shape o f  of the p o l y e l e c t r o l y t e  nature  173  Two f u r t h e r v i s c o s i t y whole mucus. of  Two  0.1 M N a C l .  equivalent  The  results  Dispersing intrinsic  This i s a salt  were t h e n  of these  viscosity  o u t on t h e  were d i s p e r s e d i n 10 ml  concentration  roughly  c o n c e n t r a t i o n s i n whole mucus.  t e s t e d i n t h e Ostwald  tests  the pedal  value obtained  were c a r r i e d  s a m p l e s o f mucus  to physiological  These samples  tests  are plotted  mucus i n t h i s by a f a c t o r  in distilled  i n Figure  salt  solution  of roughly  water.  viscometer.  still For  viscosity  The p r e s e n c e  quite large f o r a biological  comparison  Allen,Pain,and  320 ml/g f o r p i g g a s t r i c for of  slug  pedal  mucus)  M NaCl.  T h i s sample  corresponds  Neither o f these  o f Na+  more  water.  (690) i s  a value o f  T h i s J.niJ (690,  t o a h y d r a t i o n o f 276 ml  lower  was d i s p e r s e d i n 1.0 intrinsic  viscosity  t o a h y d r a t i o n o f 197 ml H20/g.  s a m p l e s shows t h e n o n - l i n e a r p l o t  mucus i n d i s t i l l e d  compact.  (see T a b l e 6 . 2 ) .  (1976) f o u n d  One sample  showed s t i l l  ml/g) c o r r e s p o n d i n g  molecule  Snary  the lowest  i t s value  mucus i n 0.2 M KC1.  water p e r gram o f mucus.  (495  i s lower,  lowers the  5 from  c o u n t e r i o n s c a u s e s t h e mucus n e t w o r k t o become Though t h e i n t r i n s i c  6.3.  The p r e s e n c e  seen f o r  o f c o u n t e r i o n s , by  d e c r e a s i n g t h e n e t w o r k volume and masking c h a r g e s ,  should  decrease  Further  the  the l e v e l  presence  ensures  of i n t e r m o l e c u l a r i n t e r a c t i o n .  o f a l a r g e amount o f c o u n t e r i o n s  a constant  level  of c o u n t e r i o n s  Thus b o t h  processes  minimized  and t h e p l o t becomes l i n e a r  i n the solvent  i n t h e network.  l e a d i n g to a n o n - l i n e a r p l o t are with a very  small  slope. Two s a m p l e s  were d i s p e r s e d i n d i s t i l l e d  water as f o r  174  previous tests to  and  then the  pH  2.1  u s i n g HCl.  tests  are  also  plotted  below t h e  pK  of the  intrinsic  viscosity  counterions.  The  pH  of the  samples was  experimental  adjusted  p o i n t s from  i n F i g u r e 6.3.  Lowering  these  the  pH  network's c a r b o x y l groups lowers even f u r t h e r  than  d o e s the  Presumably i n i t s non-charged  well  the  presence  state  of  the  p o l y m e r n e t w o r k o f t h e mucus assumes a random c o n f i g u r a t i o n and  the  charged  volume o f t h i s c o n f i g u r a t i o n i s l e s s t h a n network c o n t a i n i n g c o u n t e r i o n s .  viscosity  of mucus p a r t i c l e s under t h e s e  70  ml/g,  corresponding  In  Table  6.1  intrinsic obtained the  two  from  swelling.  match f a i r l y  changed f r o m  2.50  an  particle  ellipsoid  between 2.7  and  For the  closely.  with  The  two  o f 3.47  (depending  on  solutions  v a l u e s may  whether the e l l i p s o i d Thus t h e s e  t h a t the  elongated,hydrodynamically  be  is  axis ratio  data  network rigid  to of  is  are fragments  particles in  extremes of the s w e l l i n g range the e s t i m a t e s  hydrodynamic h y d r a t i o n d i v e r g e c o n s i d e r a b l y from  2.1.  values  solutions.  At t h e  hydration,  from  corresponds  a major a x i s / m i n o r  with t h e : p o s s i b i l i t y  salt  The  NaCl  to  H20/g. ,  s, o f e q u a t i o n 6.1  value  or o b l a t e , r e s p e c t i v e l y ) .  are s l i g h t l y these  t o 3.47.  3.0  here  ml  measurements a r e compared t o t h e  eguilibrium  figures  consistent  c o n d i t i o n s i s 60  the h y d r a t i o n values estimated  viscosity  intrinsic  t o a h y d r a t i o n o f 24 t o 28  matched e x a c t l y i f t h e s h a p e f a c t o r ,  prolate  The  t h a t of a  being l a r g e r  I t may  be  in distilled  s p e c u l a t e d t h a t the  number o f c h a r g e s  in distilled  w a t e r and presence  water and  the  of  equilibrium  smaller at  pH  of a l a r g e near  total  lack  175  of  charges  a t pH  bound t o t h e  moving  discrepancy. immediately study.  2.1  somehow a f f e c t s t h e amount o f particle.  T h i s c o u l d account  for this  However a mechanism f o r t h i s e f f e c t e v i d e n t and  Regardless  with e g u i l i b r i u m  the matter  will  t h a t t h e mucous n e t w o r k i n f l u e n c e s  i s not  reguire further  of the p r e c i s e comparison  h y d r a t i o n these t e s t s  water  of  hydrodynamic  r e c o n f i r m the  very  fact  l a r g e amounts o f  water. All  o f t h e above t e s t s were made on  prepared. to  either  Ccnseguently  mucus i s d i s s o l v e d  mercaptoethanol and  should  be  by  than t h a t  o f t h e network f r a g m e n t s  be  glycoprotein crosslinked  trapped i n the  "released" ( i e ,  not  together  In  other  like  should  the  f o r 24 h o u r s  intrinsic  <>C w i t h  t e s t s were p e r f o r m e d viscosity  dissolves  decrease.  shows t h e r e s u l t s  a t 40  are  a sponge)  Thus,as mercaptoethanol  F i g u r e 6.4  Both  words,  more water when t h e y  viscosity  much o f  hydrodynamically  o f u n t r e a t e d mucus i n 0, 1 !3 N a C l  mercaptoethanol. predicted  intrinsic  the case.  been t r e a t e d  of  i n t e r s t i c e s of a g e l  (by e n c l o s i n g s p a c e s  separately.  the network the  has  affect  are  particles  I t seems r e a s o n a b l e t o assume t h a t  c h a i n s can  can  2-  o f t h e network  of the r e s u l t a n t  bound) when t h e n e t w o r k i s d i s s o l v e d .  comparison  with  less  network w i l l  indeed  hoth.  weight  which would be  is  attributable  molecular  the  they  similarly  the  mucus.  than  are  treatment  many of t h e c r o s s l i n k s  untreated water  i n J_ n  a change i n h y d r a t i o n , s h a p e , o r  If,however,the  broken  differences  mucus  from  This a  w i t h mucus t h a t 2a t 25  of the d i s s o l v e d  <>C.  As  mucus i s  176  considerably  lowered,  mercaptoethanol  f u r t h e r confirming the f a c t  effectively  I n summary, t h e s e viscosity 1.  of pedal  t h a t 2-  d i s s o l v e s the.mucous n e t w o r k .  measurements o f t h e i n t r i n s i c  mucus show t h a t :  Even u n d e r n o n - e q u i l i b r i u m  c o n d i t i o n s t h e mucous  n e t w o r k i n f l u e n c e s l a r g e volumes o f w a t e r . 2.  The f a c t  i s reconfirmed  t h a t t h e mucous network  expands a n d c o n t r a c t s d e p e n d i n g on t h e n a t u r e solvent;  evidence  o f the p o l y a n i o n i c nature  of the  of the  glycoprotein. 3. weight  2 - m e r c a p t o e t h a n o l i s shown t o r e d u c e t h e o f t h e mucous p a r t i c l e s  Molecular One  of t h e p r e d i c t i o n s o f t h e theory  present,  randomly  stiffness the less  deformed  of chain  molecules  few c r o s s l i n k s a r e  i n t h e .network w i l l  will  be l o w .  freedom c h a i n s  The more will  there are i n a given  will  be f r e e  as t h e n e t w o r k i s s t r e s s e d and t h e  shorter the lengths of chain length  I f very  crosslinks  have when t h e network  and t h e s t i f f e r t h e network w i l l  more c r o s s l i n k s  elastic  t o t h e number o f c r o s s l i n k s  the majority of chains  rearrange  network's  is  be r e l a t e d  p e r volume o f m a t e r i a l .  present,  of rubber  i s t h a t t h e modulus o f an e n t r o p y  m a t e r i a l should  to  i n solution.  Weight Between C r o s s l i n k s  elasticity  present  molecular  between c r o s s l i n k s .  w e i g h t between c r o s s l i n k s  should  Now t h e  v o l u m e . o f network t h e  contain a certain  a relationship  be.  exist  (and t h e r e b y  Since  each  weight o f polymer between  the:molecular  c h a i n l e n g t h and  177  number o f c r o s s l i n k s )  and  Theory s t a t e s t h a t t h i s  t h e modulus o f t h e m a t e r i a l .  relationship  i s of the  form:  G = pBT/M  where p i s t h e d e n s i t y o f p o l y m e r c h a i n s i n t h e n e t w o r k ( i n g/ml  of g e l ) , E i s the  mole),  T i s absolute  value.  t r u e , the  eguation  test  value  must be  time.  equation  In t h i s  However o v e r  (Chapter  sense  s h o r t p e r i o d s of t i m e ,  modulus, presumably a s the Thus, i f t h i s  result  instantaneous  equation  the  (1965) and tests  Ferry  of C h a p t e r  measurements were c o n d u c t e d figure  including g/ml.  be  the  Using  used  these  100  at about  i s t h a t o f the  water w i t h  The  mucus d o e s have a  which  values the  crosslinks..  the  molecular  estimated.  The  suggested  by  value f o r G i s taken  t o 200 20  therefore  be a p p l i e d .  modulus i s u s e d ,  4 t o be  this  modulus and  o f temporary  (1970).  on  show t h a t  can  the  between  i s a p p l i e d i n t h e f o l l o w i n g manner as  Alexander  density  manner  cannot  be  stress  tests  pedal  w e i g h t between t e m p o r a r y c r o s s l i n k s  to  weight  equilibrium  a  weight  4)  equilibrium  in i t s strictest  the  from  Stress relaxation  m a t e r i a l d o e s n o t h a v e an  from  eguation  i s a measure o f t h e m o l e c u l a r  mucus  ergs/degree  M i s molecular  of G obtained  at i n f i n i t e  columbianus pedal  this  and  v a l u e o f G used  permanent c r o s s l i n k s . A.  (8,300  In order f o r t h i s  T h i s i s the  relaxation  constant  temperature,  between c r o s s l i n k s . strictly  gas  °C  N/m .  (293  These  2  °K).  mucous network  The  (not  i t i s mixed) o r a b o u t f i g u r e s f o r molecular  0.03 weight  178  between c r o s s l i n k s c a n be c a l c u l a t e d T h i s r e p r e s e n t s the glycoprotein  present  i n mucus.  on e a c h  Gel  w i l l be  agarose Large  elastic  crosslink i s  molecule, the molecular some m u l t i p l e  of t h i s  weight weight  composition of s o l u b i l i z e d  mucus was  T h i s t e c h n i g u e uses the  p r o p e r t i e s of  g e l t o s e p a r a t e m o l e c u l e s on t h e b a s i s  molecules applied  t o such  examined  of  "excluded").  These  t h e g e l b e a d s and column, as used molecular  are r a p i d l y  in this  weight  large  size.  a g e l column a r e t o o bulky  excluded Pain  eluted.  o f g r e a t e r t h a n 20  at a lower  (1970) f o u n d  million  between  molecules with  million  m o l e c u l a r weight.  o f 5.5  a r e washed  (they  For a Sepharose  glycoprotein  that pig gastric  a m o l e c u l a r weight Sepharose  molecules  s t u d y , compact  However, t h e more e x p a n d e d  by an  f i t i n t o t h e i n t e r s t i c e s o f the column's g e l beads  are  IE-  a  are excluded..  molecules Snary,  are  Mien,  and  mucus g l y c o p r o t e i n s  with  o r l a r g e r were e x c l u d e d  on  4B.  A column o f S e p h a r o s e the separation.  The  solvent  o f 0.1M  samples  were c o l l e c t e d  and  s  that  form the  I f more t h a n one  10 .  Filtration  gel f i l r a t i o n .  for  still  x  crosslinks.  The  to  be and  glycoprotein  o f t h e whole m o l e c u l e between  t o 7.5  minimum m o l e c u l a r w e i g h t  chains could  network f o u n d  a s 8.8  4B  (CL)  column was  NaCl c o n t a i n i n q and  allowed to s o l u b i l i z e  (100cm by 2 cm)  i n 1%  °C f o r 24  used  to a  1% 2 - m e r c a p t o e t h a n o l .  dispersed a t 40  equilibrated  was  Mucus  2-mercaptoethanol hours.  Samples  179  were t h e n c e n t r i f u g e d particulate sample was 1%  matter.  ft  l o a d e d on  2-mercaptoethanol  All  tests  Ten  ml  and  protein.  Lo,  10  ml a l i q u o t  of t h i s  solubilized  a t a flow  of about  12  ml/hour.  a t room t e m p e r a t u r e  21  t o 23  rate  were c o l l e c t e d  Taylor  and  a t 280  concentration.  The  nm  (1970) was  similar  The  w i t h 0.1M  assayed was  phenol  carbohydrate concentrations. s e v e r a l times with  12,100 g t o remove  eluted  Absorbance  B u s s e l , and  at  t h e column and  were c o n d u c t e d  fractions  protein  f o r 5 minutes  used  to  t o measure  chromatogram o f t h r e e o f t h e s e t e s t s  The  acid  assay o f  measure  procedure  results.  °C.  f o r carbohydrate  - sulfuric used  NaCl,  was  repeated  composite  i s presented i n Figure  6. 5. This of  test  indicates  molecules are released  t h e mucus a r e b r o k e n 1. probably 2.  A larger  by  protein  assumed t h a t  tests a third  (peak  protein  networks.  shown i n F i g u r e  peak  see F i g u r e 6.5)  2)  of  and  was  protein. found  and  eluting main  was  s m a l l e r .. I t i s  profile  i s accounted f o r  of t h e . c r o s s l i n k e d  sample o f b o t h  l a r g e complexes of  An example o f one 6.6.  crosslinks  peak.. I n t h e s e c a s e s t h e  solubilization  (peak  fractions  carbohydrate  containing only  t o t h e p r e s e n c e i n the  protein chains protein  2;  major  protein,  t h i s type of e l u t i o n  the incomplete  leading  containing  A s m a l l e r molecule  peak  two  2-mercaptoethanol.  molecule  before the carbohydrate  at l e a s t  when t h e d i s u l f i d e  a s m a l l amount o f  In two  by  that  network  uncrosslinked crosslinked  s u c h chromatogram i s  180  FIGORE 6.5,.  S e p a r a t i o n o f p e d a l mucus on S e p h a r o s e . 4 - B CL r e s u l t s i n t h e e l u t i o n o f two major f r a c t i o n s : 1) a h i g h m o l e c u l a r w e i g h t f r a c t i o n c o n t a i n i n g b o t h p r o t e i n and c a r b o h y d r a t e , and 2) a l o w e r m o l e c u l a r weight f r a c t i o n c o n t a i n i n g p r o t e i n alone.  P R O T E I N  C A R B O H Y D R A T E  <  M O L E C U L A R  S I Z E  182  FIGURE 6.6.  I n c o m p l e t e l y d i s s o l v e d p e d a l mucus shows a t h i r d f r a c t i o n when s e p a r a t e d on S e p h a r o s e 4-B CL. T h i s i s p r e s u m a b l y due t o a g g r e g a t e s o f t h e p r o t e i n o f f r a c t i o n 2.  184  A t t a c h m e n t Of C a r b o h y d r a t e To P r o t e i n It  h a s been  shown  (Gottschalk,1972;Hunt,1970)  many g l y c o p r o t e i n s t h e p o l y s a c c h a r i d e the  p r o t e i n through  threonine. detected  (Carubelli e t a l .  bonds may be e a s i l y  ,1965).  The O - g l y c o s i d i c bond  of a hexose t o a s e r i n e o r t h r e o n i n e solutions,and  as  B-elimination.  is  converted  not  Normal g l y c o s i d i c  i s cleaved  with  a process  known  t h e amino a c i d  s t r o n g l y i n the  bonds and p e p t i d e mild  labile i n  alkali.  bonds a r e  Thus, t h e  between a d i l u t e s o l u t i o n o f NaOH and a  glycoprotein an  i s broken through  When t h e bond  a f f e c t e d by t r e a t m e n t  reaction  i s unusually  t o a compound t h a t a b s o r b s  ultraviolet.  a r e bound t o  O - g l y c o s i d i c bonds t o e i t h e r s e r i n e o r  The p r e s e n c e o f s u c h  weak a l k a l i  chains  that f o r  increase  may be c a r r i e d i n absorption  o u t i n a s p e c t r o p h o t o m e t e r and  a t 241 nm i s i n d i c a t i v e  of the  p r e s e n c e o f O - g l y c o s i d i c bonds between hexose and s e r i n e and/or  threonine.  A. c o l u m b i a n u s in  distilled  above. one  pedal  water as f o r t h e s o l u b i l i t y  One m i l l i l i t e r  ml o f d i s t i l l e d Another  thoroughly  mixed w i t h  (at  milliliter  tests  1750 d u a l  were r e c o r d e d  described  mucus s o l u t i o n was mixed  with  a s an a b s o r b a n c e  o f mucus s o l u t i o n was  relative  The a b s o r b a n c e o f t h i s t o t h e standard  beam u l t r a v i o l e t  were c o n d u c t e d  tests  and d i s p e r s e d  1 ml o f 1 N NaOH f o r a f i n a l  o f 0.5 N NaOH.  241 nm) was r e a d  Onicam  of this  water and s e r v e d  standard.  concentration  mucus was c o l l e c t e d  i n a Pye  spectrophotometer.  a t room t e m p e r a t u r e .  f o r 15-20 m i n u t e s a f t e r  sample  Absorbance  the i n i t i a l  The values  mixing.  185  The  experiment  concentration an  was r e p e a t e d  with  o f 0.25 N NaOH.  were p e r f o r m e d  presented  i n triplicate  a b s o r b a n c e a t 241 nm. after  computed  the  value  almost  f o r the i n i t i a l  obtained  and t h e r e s u l t s a r e  with  g l y c o p r o t e i n i n 0.50 N NaOH i s with  0.25 NAOH.. The  d i d n o t change w i t h  a r e very  (1965) and a r e t a k e n  I f the rate of increase  t e n minutes o f the experiment  e x a c t l y twice that obtained  similar  as evidence  t o those (though  time. of C a r u b e l l i et  not c o n c l u s i v e )  t h e p o l y s a c c h a r i d e component o f A. c o l u m b i a n u s  mucus i s a t l e a s t by  as a c o n t r o l . A l l  NaOH show an i n c r e a s i n g  about t e n minutes.  These r e s u l t s  that  i n part connected  t o the protein  O - g l y c o s i d i c bonds t o s e r i n e and/or t h r e o n i n e . .  treatment  with  The r a t e o f i n c r e a s e o f a b s o r b a n c e  absorbance o f the c o n t r o l  al  served  mixed  i n F i g u r e 6.7.  Mucus s a m p l e s t r e a t e d w i t h  decreases  sample  A mucous s o l u t i o n  e q u a l volume o f d i s t i l l e d w a t e r  tests  is  a final  of the a l k a l i  t r e a t e d mucus a n d amino  analysis of the r e s u l t i n g a d d i t i o n a l evidence  compounds s h o u l d  concerning  this  pedal component Further  acid  provide  point.  Summary In  summary, t h e r e s u l t s o f t h e s e  1. is  formed 2.  large  The e l a s t i c from  that:  network o f A, c o l u m b i a n u s - p e d a l  mucus  a polyanion..  The m o l e c u l a r  (greater than 3.  tests indicate  At l e a s t  weight o f t h i s  polyanion i s quite  7.5 x 1 0 ) . s  two s o r t s o f m o l e c u l e s  contribute tothe  186  FIGURE 6.7.  C a r b o h y d r a t e bonding t o s e r i n e and/or threonine. The i n c r e a s e i n a b s o r b a n c e a t 241 nm. o f mucus i n weak NaOH s o l u t i o n s i n d i c a t e s t h a t p o l y s a c c h a r i d e i s c o v a l e n t l y bound t o p r o t e i n i n A r i o l i m a x c o l u m b i a n u s p e d a l mucus.  F i g u r e 6.7  5  10  minutes  15  188  mucus n e t w o r k , a l a r g e polysaccharides 4.  and a s m a l l e r  site(s)  covalently  being  5.  serine  of p r o t e i n .  i f the glycoprotein i s  bonded t o t h e p r o t e i n , t h e a t t a c h m e n t and/or  threonine.  The mucus n e t w o r k i s c r o s s l i n k e d  bridges  p r i m a r i l y of  m o l e c u l e composed  The c a r b o h y d r a t e p o r t i o n  apparently  either  molecule c o n s i s t i n g  between p r o t e i n the carbohydrate  molecules, portion,  both  by  disulfide  and weak b o n d s between  the protein  portion,or  both. 6.  The c r o s s l i n k e d ,  influences  large  physical chemistry  only  a very cursory  study o f the  o f A. c o l u m b i a n u s p e d a l mucus.  With O t h e r  A considerable physical chemistry  Many  Mucins  amount o f s t u d y  h a s been d i r e c t e d a t t h e  of mucous s e c r e t i o n s .  on mucins t h e s e s t u d i e s  to the study  of vertebrate  other  been  limited  ( p r i m a r i l y mammalian)  and m u c o p o l y s a c c h a r i d e s .  these studies  are reviewed  and p a r k e  As w i t h  have g e n e r a l l y  glycoproteins  ,Elstein  mucous network  r e m a i n t o be a n s w e r e d .  Comparison  studies  expanded  amounts o f w a t e r . ,  These t e s t s f o r m  questions  highly  i n Gottschalk  The f i n d i n g s o f ( 1 9 7 2 ) , Hunt  ( 1 9 7 6 ) , and t h e B r i t i s h  Medical  (1970)  Journal  (1978). Recently  a number o f a u t h o r s have made  progress i n examining  the p h y s i c a l  sufficient  chemistry of a variety of  mucins t o be a b l e  t o p r o p o s e models f o r mucus  structure  ( A l l e n and Snary,  1971; A l l e n ,  1978; Rao and  1978; R o b e r t s ,  189  Massen,  1977).  similar  features.  1.  A l l of  t h e s e models i n c o r p o r a t e  Subunits c o n s i s t i n g of  carbohydrate 2.  side  3.  be  formed  number o f  the  the  crosslinked  molecules.  model i s v a l i d  are  for a large  as  iU c o l u m b i a n u s  pedal  There appears t o  contain  a large  a model as  protein  are  these small  JU  of the  an  only  one  of  are  by  in this  may  6,8.  mucin  i s not  (such  with  easily  be  are  this  the  to  incorporated  bonds.  In  this  covalently  of  Some o f protein manner  constructed  weak b o n d s  o v e r a l l mucus n e t w o r k . of  It  in  study  l i n k e d t o the  chain..  foot  of  mucins.  Small lengths  molecules then i n t e r a c t through  under t h e  sort  mucus a p p e a r s  that  of g l y c o p r o t e i n  the  basic  form  compare.  disulfide  in turn  protein/poly saccharide  mucus i s s h e a r e d  a  form  i n t e r a c t to  m i n o r problem  This fact  bound t o g e t h e r  entanglements t o form  other  to  invertebrate  protein  shown i n F i g u r e  composite molecules large  how  (S-S)  vertebrate  columbianus pedal  portion  proteins  this  data presented  bound t o c a r b o h y d r a t e . into  that  mucus) m i g h t  be  scant  in turn  number o f  speculate  model.  or  m o l e c u l e s formed of  crosslinked  These m o l e c u l e s  i n t e r e s t i n g to  vertebrate  disulfide  subunits,  I t seems l i k e l y  the  where  subunits.  is  reconciling  core  between l a r g e c o m p o s i t e  mucus g e l .  with  i n t e r a c t i o n (hydrophobic  Thus s e v e r a l s u b u n i t s larger  protein  between two  Some form o f  "weak" bonds)  a p r o t e i n core  chains,  " n a k e d " a r e a s on  bonds can  three  s l u g , the  core  large .  These  and When  the  weak bonds  190  FIGURE 6 , 8 .  A model f o r t h e s t r u c t u r e o f A r i o l i m a x c o l u m b i a n u s p e d a l mucus. The two f r a c t i o n s o b s e r v e d i n F i g u r e 6 , 5 a r e c r o s s l i n k e d by d i s u l f i d e bonds t o form l a r g e c o m p o s i t e molecules. These c o m p o s i t e s s u b s e q u e n t l y i n t e r a c t by "weak b o n d s " t o f o r m t h e o v e r a l l mucus network,.  191  FIGURE Building  6.8  Blocks  large fraction  H  H  :  :  i  j  j  j  j  j  small fraction 1  g  B  1  sulfhydryl g r o u p - s i l o of disulfide  Composite  Molecule  small fraction  crossl inking polysaccharide protein  C  Overall  chain  chain  Network targe fraction  largo and small  Y W  i\  © ~ "weak" bond composit e mo I ecu Ie  crosslinked  with  fractions are disulfide  bonds  192  between l a r g e c o m p o s i t e  molecules  are ruptured  and t h e mucus  flows.  When s h e a r i n g i s t e r m i n a t e d  t h e weak b o n d s  reform,  a n d t h e mucous network  allowed  f o r h e a l i n g , t h e more weak bonds and e n t a n g l e m e n t s  "heals".  rapidly  The l o n g e r t h e t i m e  a r e f o r m e d and t h e h i g h e r t h e modulus o f t h e n e t w o r k ; At p r e s e n t t h i s structure  model f o r A. c o l u m b i a n u s p e d a l  i s pure s p e c u l a t i o n .  work must y e t be p e r f o r m e d substantiated follow  model i s i n d e e d  before t h i s  model c a n be be i n t e r e s t i n g t o  o f f u t u r e r e s e a r c h t o see i f t h i s type o f  a p p l i c a b l e to slug  mucus i n g e n e r a l . for  A c o n s i d e r a b l e amount o f  or discounted., I t w i l l  the course  The p r e s e n c e  mucus and t o i n v e r t e b r a t e  of a simple,general  mucus s t r u c t u r e would be e x t r e m e l y  further  mucus  research into  model  u s e f u l as a b a s i s f o r  t h e s t r u c t u r e and f u n c t i o n o f mucous  secretions. At p r e s e n t fiber  formation  further  I c a n p r o p o s e no model f o r t h e mechanism o f i n A., c o l u m b i a n u s p e d a l  research i s required.  mucus.  Again,  193  CHAPTER  SEVEN  A Model F o r Slug  Locomotion  Complex b i o l o g i c a l p r o b l e m s , locomotion, model. used  are often  b e s t examined  A model i n t h i s s e n s e  to r e l a t e i s o l a t e d facts  thereby basis  such  provide predictions  as  gastropod  through  t h e use  i s a hypothetical known a b o u t  about  that  corresponding The  structure  t o the  of the  actual  process.  mechanism  been  locomotion.  the k i n e m a t i c s of s n a i l s of the As t h e  locomotory  t h o s e o f Au  model s h o u l d be  and  tested  This  of  by  as  Lissman the  model i s b a s e d  genus H e l i x  (described  applicable  the  thought  model t o e x a m i n e  movements o f H e l i x  columbianus  I f on  structure.  , to date, the only  of q a s t r o p o d  and  predictions,  model can be  q u a l i t a t i v e model p r o p o s e d  (1945b) h a s  structure  a process  o f known f a c t s a model p r o v i d e s c o r r e c t  the h y p o t h e t i c a l  of a  (Lissman,  are very  i n Chapter  on  1945a)  s i m i l a r to  3),  Lissman's  t o the problem  of  slug  the  o f s n a i l s (or  locomotion. Lissman slugs)  can  possibly 1.  be  types  f o r by  of f o r c e s  Forces acting pressure)  locomotion the  i n t e r a c t i o n of f o u r  as shown i n F i g u r e  t o extend  the f o o t  (most  and  7.1:  probably  ;  Forces acting  contraction) 3.  that  accounted  five,  hydrostatic 2.  proposes  t o compress the f o o t  (muscular  ;  A frictional  segments o f t h e f o o t  drag that  between t h e s u b s t r a t u m a r e moving f o r w a r d s  and  the  (a f u n c t i o n  of  194  FIGURE 7.1.. The p o s s i b l e f o r c e s a c t i n g d u r i n g g a s t r o p o d l o c o m o t i o n ( a f t e r L i s s m a n , 1945b). 1) An i n t e r n a l f o r c e o f e x p a n s i o n c a u s e s t h e foot to elongate. 2) An i n t e r n a l f o r c e o f c o m p r e s s i o n c a u s e s t h e f o o t t o become s h o r t e r . . 3) and 4) An e l o n g a t i n g f o o t segment i n c o n t a c t with the ground w i l l r e s u l t i n a f r i c t i o n a l r e s i s t a n c e t o movement, F, and a r e a c t i v e f o r c e r e s i s t i n g t h i s movement, R. 5a and b) Compression o r e l o n g a t i o n o f the c e n t r a l o f t h r e e segments w i l l r e s u l t i n a f r i c t i o n a l resistive force.  195  Figure  7.1  196  the  properties 4.  This of  also acts  foot  5.  opposing the  these  measuring the  five  This  of  forces exerted  Helix  4, on  mucus, p r e d i c t i o n s o f d r a g and  Without  resistive  L i s s m a n ' s model i s i n  be  compared t o  Second, t h e  force  mounted on the  l a r g e r the  1.0  seconds.  accurately  the  the  by  a  by  movinq  and  in  the  The  If this  was  his the  i t is  the:properties the  impossible.  qualitatively evaluate  d i r e c t i o n and  u s e d by  While  acccurate, such a  magnitude  Lissman  more f o r c e  apparatus are Lissman of the  i s so,  may  apparatus c o n s i s t s of  displacement of the  the  period  First  magnitude of  forces  transducer  d i a g r a m s shown i n G r a y and that  quantified  problems:  knowledge o f  a pendulum, t h e  p r e c i s e dimensions of  estimated  be  of  reality.  h a v e been i n a p p r o p r i a t e .  platform,  stationary  substratum  to c r i t i c a l l y  model t h a n a model where b o t h  platform  5 can  the  most r e s p e c t s  i s much more d i f f i c u l t  can  ;  .  of  forces  segments  p r o d u c e a q u a l i t a t i v e model f o r  qualitative.  it  and  model s u f f e r s f r o m s e v e r a l  frictional  interwave)  t o measure t h e s e f o r c e s  strictly pedal  (the  o r t h r u s t s between  f o r c e s , 3,  r e l a t e s them t o  locomotion  drag.  foot.  Lissman attempted  analysis  frictional  mucus under t h o s e  stationary  Possibly tensions  Of  ;  through the  which a r e  segments o f t h e  slug.  mucus)  a reactive force  force  the  of pedal  not  (1938)  well a  placed  on  pendulum. given,  i t can  the The  but  from  0.5  to  be  pendulum i s a b o u t  the  device  i s incapable  measuring o s c i l l a t i n g  forces  with a  period  of of  197  a r o u n d one fall  second or  less.  squarely  into this  In  tc explain  order  The  f o r c e s measured  invoking  o f the lead the  tensions  foot  him  what a r e  probably  from r e g i o n s  suspiciously bootstraps,  like and  interpreting  avoids  regions  whereas t h e lying  the  of the  many o f  the  operating  present  foot  end  lift  f r o n t end  of  lying  i s being  aided  ".  sounds  This  himself  confusion  up  by  by  his  in  the  differ  surface. the  Thus, as  will  this  present  this  but model,  predictions.  from  on  slug  form  model's major  Lissman's.  to predict  the;forces  a smooth  Under t h e s e  s l u g does not  the  of  which  p r e c i s e c a l c u l a t i o n s which  model i s d e s i g n e d  shown i n C h a p t e r 3,  1-6  constructed  u s e f u l to o u t l i n e the  these  nonporous,inflexible  i n Chapters  Model  under a s l u g c r a w l i n g  locomotion.  model  forces  f e a t u r e s o f L i s s m a n ' s model  t e s t s of these  be  show how  be  This chapter  examining  model, i t w i l l  The  to  f a c t s presented  p r e d i c t i o n s , and  p o i n t s and  hind  These  of the  of the  causes considerable  The  the  .  more a n t e r i o r l y  someone t r y i n g  problems.  Before  7.1)  propulsion  a q u a n t i t a t i v e model c a n  incorporates  simple  force  L i s s m a n ' s model.  In l i g h t thesis,  a basically  (type 5 f o r c e o f F i g u r e  to i t s e l f ,  inaccurate  t h r u s t s between s t a t i o n a r y segments  a n i m a l i s e f f e c t e d by  a pull  its  and  to argue t h a t "the  posterior  Lissman  category.  measurements, L i s s m a n c o m p l i c a t e s by  by  lift  moves a l o n g  conditions, the  foot  as  during  i t passes over  a  198  layer  o f mucus of a c o n s t a n t t h i c k n e s s . . V a r i o u s s t r e s s e s  are imposed  on t h i s  magnitude o f t h e s e  mucus l a y e r  by t h e moving f o o t .  s t r e s s e s c a n be e s t i m a t e d  knowledge o f t h e movements o f t h e f o o t  from  The  a  and t h e p h y s i c a l  p r o p e r t i e s o f t h e p e d a l mucus. As shown e a r l i e r f u n c t i o n a l areas: The  may be d i v i d e d  t h e waves, t h e i n t e r w a v e s ,  s t r e s s e s a s s o c i a t e d with each area  turn.  r e l a t e s these  will  into  three  and t h e r i m s . be examined i n  i n F i g u r e 7.2.  The s t r e s s e s a r e diagrammed  model c a l c u l a t e s  The  the foot  This  t h e s t r e s s a s s o c i a t e d w i t h e a c h a r e a and  s t r e s s e s t o account  f o r locomotion.  Hayes As a segment o f t h e f o o t  i s overtaken  by a  compressional  pedal  wave, i t b e g i n s  movement  shear  t h e mucus b e n e a t h t h a t segment.  shear  will  ratio,rho,  distance  be e q u a l  moved by t h e f o o t  thickness  Subsequently,  viscosity  be moving o v e r  of t h e f l u i d  moving segment experienced  p o i n t and i t w i l l  mucus  will  determine  by t h e moving  shear  a viscous f l u i d . .  and the shear  Fw=  r a t e imposed  i s moving The by t h e  Fw, t h e r e s i s t e n c e t o movement  wave:  stress,  will  flow.  a s l o n g a s t h e segment o f t h e f o o t  i t will  The . ; >  layer  A t some p o i n t t h i s  beyond i t s y i e l d  This  t o x/y where x i s t h e  and y i s t h e mucus  (see F i g u r e 7.2).  be s h e a r e d  forward  will  t o move f o r w a r d .  2 gma = n  sigma  Aw  dp/dt  199  FIGURE 7.2.  The f o r c e s  p r e s e n t under a moving  slug.  A) Waves. The s t r e s s a t any p o i n t i s e g u a l t o the shear r a t e times the v i s c o s i t y a t that shear r a t e . The sum o f a l l s t r e s s e s u n d e r a wave i s t h e wave s t r e s s . . The wave s t r e s s t i m e s t h e wave a r e a e q u a l s t h e wave f o r c e , Fw. B) Rim. The r i m s t r e s s i s e q u a l t o t h e s h e a r r a t e under t h e r i m t i m e s t h e v i s c o s i t y a t t h a t shear r a t e . The r i m s t r e s s t i m e s t h e r i m a r e a equals the rim f o r c e , F r . C) I n t e r w a v e s . In o r d e r f o r l o c o m o t i o n t o occur Fi  = - ( F r + Fw)  where F i i s t h e i n t e r w a v e f o r c e . Thus t h e i n t e r w a v e s t r e s s e q u a l s F i d i v i d e d by t h e interwave area.  c.  o o  201  where n i s t h e v a l u e the  area  of the foot contained  7.1 t h i s  Figure  of v i s c o s i t y  resistance  f o r c e on t h e s t a t i o n a r y  from  7.4,  Figure  i n t h e waves.  will  place  portions  and Aw i s  As shown i n  an e q u a l  and  opposite  of the foot - the  interwaves.  The  Rims The  rims  of the foot  speed as t h e s l u g its  yield  point  beneath these long  itself,  move f o r w a r d  a t t h e same  Conseguently,  constant  once s h e a r e d  beyond  when t h e s l u g b e g i n s t o move t h e mucus  rims w i l l  as t h e s l u g  always remain  c o n t i n u e s t o move.  form a s  Again the r a t e of  movement o f t h e r i m and t h e v i s c o s i t y determine F r , the r e s i s t a n c e  in i t s fluid  of the f l u i d  will  t o movement.  Sigma = n d p / d t  F r = s i g m a Ar  where Ar i s t h e a r e a move t h e r i m s f o r w a r d  o f the rims. will  place  The f o r c e  required  to  an a d d i t i o n a l s t r e s s on t h e  mucus b e n e a t h t h e i n t e r w a v e s .  The  Interwaves As  a wave l e a v e s  segment w i l l the  a segment o f t h e f o o t b e h i n d , t h e  decelerate  until  segment i s s t a t i o n a r y  heal,  becoming  heals  quickly  more s o l i d  i t i s stationary..  As soon as  t h e mucus b e n e a t h i t w i l l as time passes.  enough most o f t h e s t a t i o n a r y  begin to  I f t h e mucus segment  will  202  rest the  on mucus i n i t s s o l i d interwave  stationary  solid  is  strong  will  This  model d o e s n o t a l l o w  thrusts  between i n t e r w a v e s  This  i s simply  a n o t h e r way  which t h e f o o t c o n t r a c t s simultaneously wave. ,it  This  will  offset  this  be a b l e  and  rates  o f t h e - waves and  ( F r + Fw)  as t h e s o l i d  to  (type  5 force  of s a y i n g  that  on e n t e r i n g  by t h e f o o t  a pedal  equivalent  of the foot that  segment  on l e a v i n g a t h e model and  i t s accuracy.  i n t o account f o r c e s  present .should  tend  to cancel.  due  o f segments o f t h e f o o t .  by t h e f a c t t h a t  t h e masses Further,  i s accelerating there  decelerating  by  wave i s  simplifies from  tensions  the length  of a c c e l e r a t i o n are n e g l i g i b l y small.  f o r each p a r t  mucus  of Lissman).  re-extending  model d o e s n o t t a k e  i s justified  /  crawl.  f o r the presence o f  ,does n o t d e t r a c t  simplification  hold  t h e s t r e s s i m p o s e d by t h e  to the a c c e l e r a t i o n or d e c e l e r a t i o n This  mucus w i l l  motion  As l o n g  assumption c o n s i d e r a b l y  be shown  Similarly  of forward  to r e s i s t  r i m s and waves, t h e s l u g  or  the force  of the interwaves..  sufficiently  solid  The m a g n i t u d e o f t h e s t r e s s on  mucus i s t h e f o r c e  (Ai) t h e a r e a  This  against  i n t e r w a v e s moving f o r w a r d . this  form.  so t h a t  the small  Finally,  account f o r the a c t i o n of those c i l i a  this  present  i s an  forces  model does n o t on t h e  pedal  epithelium. With t h i s  general  be e x a m i n e d : T h i s determined  scheme  i n mind a s p e c i f i c  example makes use o f an " a v e r a g e " s l u g  by t h e k i n e m a t i c s t u d i e s  o f C h a p t e r 3.  average s l u g weighs a p p r o x i m a t e l y f i f t e e n total  f o o t area  example  o f 15 cm . 2  Slightly  may as  An  grams and has a  more t h a n  a third  (5.5  203  cm )  i s contained  2  6,0 cm  i s i n the interwaves,  2  Now  let this  resembling here  from  rims)  i n the rims.  slug  average  speed  the  wave w i l l  only  thickness effect  time  by t h e p e d a l  (reproduced  o f 0.85 mm/sec. the time  move a t an  o f a segment i n The  interwaves  foot speeds the shear  mucus w i l l  The  o r 1.7 mm/second ,  v a r y a s shown i n F i g u r e 7.3 .  o f mucus l a y e r  rate  be d e t e r m i n e d  In order  thickness, stress  by t h e  t o examine t h e values  will  be  f o r two t h i c k n e s s e s , 10 um and 20 um,  corresponding thicknesses  t o the approximate l i m i t s  observed  convenience,  i n histological  i n Table  7,1,  Given  dimensions  o f t h e mucus l a y e r  the  under e a c h  stress  be f o u n d these  o f the range o f  sections.  o n l y t h e 10 um example w i l l  however, a l l v a l u e s w i l l  presented  i n waves,.  the p r e c i s e speed  For these  2  (and c o n s e q u e n t l y t h e  move f o r h a l f  o f t h e mucus l a y e r .  calculated  text,  speed  cm ,  w i t h p e d a l waves  twice t h a t o f the s l u g ,  are s t a t i o n a r y . experienced  The s l u g  a constant  However a t any g i v e n  2  9-5  wave shown i n F i g u r e 7.3  F i g u r e 3.4) .  waves, b e c a u s e t h e y  and 3,5 c m  move f o r w a r d  t h e average  moves w i t h  Of t h e r e m a i n i n g  As a  be d i s c u s s e d i n t h e i n t h e summary  specific  values f o r the  and t h e movement o f t h e f o o t ,  of t h e s e c t i o n s o f the f o o t  c a n be  calculated.  Waves Under a wave t h e mucus i s f i r s t point,  and t h e n  thickness.  flows.  stressed to i t s yield  Take f o r example a 10 um mucus  This layer w i l l  yield  when t h e s h e a r  layer  ratio i s  204  FIGURE 7-3-  The s t r e s s p r o f i l e b e n e a t h a p e d a l wave. The s t r e s s h a s been c a l c u l a t e d f o r t h e v e l o c i t y p r o f i l e o f F i g u r e 3.4 f o r mucus l a y e r t h i c k n e s s e s o f 10 and 20 um.  F i g u r e 7.3  T a b l e 7.1:  P r e d i c t i o n s of t h e Locomotion Slug:  weight foot area  15 gm rims waves interwaves  mucus t h i c k n e s s 10 shear r a t e  (rims)  shear s t r e s s  (rims)  m  0.85 mm/sec. m 20  395  (waves)  (waves) (waves+rims)  542  N/m  297  2  N/m  365  2  o v e r a l l s t r e s s amplitude (waves+interwaves) (horizontal)  1232  o v e r a l l stress amplitude ( v e r t i c a l up)  1482  o v e r a l l s t r e s s amplitude ( v e r t i c a l down)  970  N/m  659  2  N/m  1059  2  m  100/sec  N/m  429  2  0.363 N  N/m  2  0.236 N  N/m  2  0.371 N  0.290 N  N/m  2.00 mm/sec. m 20  200/sec  0.127 N  0.410 N 682  10  0.163 N  0.193 N  shear s t r e s s ( i n t e r w a v e s ) (horizontal)  m  42.5/sec  0.217 N  average shear s t r e s s t o t a l force  ^ 5.5 x 10_^ ml 3.5 x 10_^ l 6.0 x 10 m'  85/sec  force (rims) force  Model  610  N/m  2  0.213 N  0.724 N  0.449 N  485  N/m  1222  N/m  749  N/m  2  850  N/m  2281  N/m  1359  N/m  N/m  2  1100  2531  N/m  2  1609  N/m  2031  N/m  2  1109  N/m  2  N/m  2  2  2  N/m  2  2 600  N/m  2  2  N/m  2  2  2  2  o  207  5,5;  i e at a foot  displcement  o f 55 um.  Noting  i n Figure  7,3 t h e p o i n t  on t h e d i s t a n c e c u r v e  e g u a l t o 55 um t h e  corresponding  point  curve  This i s egual  t o 0.54  on t h e v e l o c i t y  (see F i g u r e 7,4)?  second  (reproduced  from  N/m )  .  2  also  be d e t e r m i n e d ;  rate  equal  calculated force as  a t a shear  f o r every  stress  profile  layer,  layer  involved  This stress  By i n t e g r a t i n g dividing  by t i m e  this thicker  be m u l t i p l i e d  t o move f o o t  profile  o f a 10  S i m i l a r l y the mucus  Since a  shear  rate,  layer  are s m a l l e r .  by t h e t o t a l  segments f o r w a r d  i s 0.19 N f o r a 10 um mucus  this  average  For the case  shown i n F i g u r e 7.3.  2  value  the  f o r a 20 um t h i c k  r e s u l t i n a lower  can then  velocity  This  t h e a r e a under  (3.5.10~*m ) t o a r r i v e a t a f i g u r e  necessary This  t o the average  2  i n moving o v e r  continues to  under t h e moving segment.  c a n be c a l c u l a t e d  will  at shear  c a n be s i m i l a r l y  t h i s v a l u e i s 550 N/m .  and t h i s i s a l s o  thicker  waves  wave t h e s t r e s s  part  and t h e n  mucus l a y e r  determined  stress  As t h e f o o t  under a wave c a n be c a l c u l a t e d .  um t h i c k force  a t which a t y p i c a l  f o r flow  2  corresponds  curve  7,4  o f 54 c a n be  o r 323 N/m .  shown i n F i g u r e 7.3,  force/time  o f 53/  t o w h i c h t h i s sample y i e l d s c a n  i n the pedal  profile,  rate  i t i s the value  t o 54/sec,  rate  found.  By r e f e r r i n g t o F i g u r e  The s t r e s s  move f o r w a r d  or a shear  F i g u r e 4,16) t h e s t r e s s  mucus sample y i e l d s (685  mm/second  c a n be  the forces  area of the  f o r the t o t a l with pedal  force  waves.  layer.  Bims The  rim force  i s more s i m p l y c a l c u l a t e d  ._ S i n c e t h e  208  FIGURE 7.4.  A r e p r e s e n t a t i v e p l o t o f y i e l d s t r e s s and f l o w s t r e s s v e r s u s shear r a t e f o r A r i o l i m a x c o l u m b i a n u s p e d a l mucus.  y = 0.069X + 3.13 r2= 0.0973  O",f  y=»0.023x + 1.99 r = 0.943  0  100 °  150  200  -1  P , sec  O  210  r i m s move a t a c o n s t a n t  0-85 mm/second, t h e s h e a r  b e n e a t h them i s 8 5 / s e c o n d The  flow  stress f o r this  reference stress  to Figure  value  7.4  f o r a 10 um l a y e r shear  rate  (395 N/m  rate  (Figure  i s determined  7.2) .  by  f o r a 10 um l a y e r )  2  m u l t i p l i e d by t h e t o t a l  r i m area  f o r c e needed t o move t h e r i m s a t t h i s  .  This  y i e l d s the  speed. . T h i s  value i s  0.22 N f o r a 10 um mucus l a y e r .  The  I n t e r waves The  due  force  t o t h e waves and t h e r i m s  case o f a force, the  divided  by t h e a r e a  stress experienced  calculation  this  solid  The  i s 680 N/m  2  f o r c e forms t h e f i r s t  T h i s i s the s t r e s s t h a t  ability this  of the s o l i d  2  The  t e s t of t h i s  model  must b e . r e s i s t e d by Is this  a  mucus b e n e a t h an i n t e r w a v e t o  tape records  moves b a c k w a r d s o n l y i t i s only  o c c u r s i n l e s s than  on t h e s h e a r r a t e  As shown i n C h a p t e r 3 t h i s  t o measure f r o m v i d e o  the foot  foot  _  t o t h e r e s u l t s of the  s t r e s s i s dependent  s t r e s s causes.  recordings  the  (6.0 10 *m ) i s  tests?  difficult on  This  f o r a 10 um l a y e r .  mucus b e n e a t h t h e i n t e r w a v e s .  withstand this  Thus i n t h e  of the interwaves  r e a s o n a b l e f i g u r e when compared physical  7.2)  by t h e mucus under t h e i n t e r w a v e s .  value  of this  locomotion.  the  (Figure  10 um l a y e r i t i s (0.22 + 0.19) = 0.41N.  Consequently  of  imposed on t h e i n t e r w a v e s i s t h e sum o f t h a t  possible  very  briefly  t o say t h a t  0.08 s e c o n d s .  value i s  since .  that  a point  From  video  t h e movement  The d i s t a n c e  moves b a c k w a r d s c a n be more a c c u r a t e l y  a point  on  measured,  211  however, and i s e q u a l  t o about 30 um o r l e s s .  case corresponds to a shear r a t i o is  necessary  at  least  that t h i s  f o r t h e mucus o f 3.0.  s h e a r h a v e been a p p l i e d  60/sec i n order  become a f l u i d .  At a s h e a r r a t e  It  too short  with these  under t h e i n t e r w a v e s i s s h e a r e d to  withstand  initial  o f 60/sec the backwards  period  of time  f o r which a p o i n t  a b o u t one s e c o n d .  creep  data t o creep data.  provide  relax  it  may be e s t i m a t e d  I t takes  to h a l f of i t s i n i t i a l that  to creep t o twice  After  hiqh this  occur f o r the  under t h e . f o o t valid  i s stressed;  t o equate  stress  However, s t r e s s r e l a x a t i o n  solid  mucus a b o u t  s t r e s s value.  mucus would r e q u i r e i t s length,  t o be d e t e c t e d  100 s e c o n d s  Consequently a b o u t t h e same  o r a c r e e p o f 0.1  um/sec f o r a 10 um t h i c k mucus l a y e r . f a r too small  t h e mucus  an e d u c a t e d g u e s s as t o how f a r mucus would  to  is  that  sufficiently  however c a n o n l y  I t i s not s t r i c t l y  i n one s e c o n d .  period  technique.  t h e mucus under t h e i n t e r w a v e s  This  creep  milliseconds,  2  creep.  may  observations at a rate  should  data  50  t h e c a l c u l a t e d s t r e s s o f 680 N/m .  application of force  relaxation  at a r a t e o f  t o have been measured by t h i s  i s thus consistent  It  f o r t h e mucus t o n o t y i e l d and  movement o f t h e f o o t would have l a s t e d o n l y a period  30 um i n t h i s  T h i s amount o f c r e e p  by t h e v i d e o  tests  conducted  here. These p r e d i c t i o n s f o r the s t r e s s e s moving s l u g  apply  If  i s crawling  the slug  will  apply  a force  to a slug  beneath t h e interwaves  moving on a h o r i z o n t a l  vertically  which  operating  under a surface.  up o r down, i t s weight  must be r e s i s t e d by t h e s o l i d  (Figure  7.5) .  If i n this  mucus  example a  212  FIGURE 7.5.  The i n t e r a c t i o n o f g r a v i t y w i t h t h e f o r c e s o f locomotion. A) C r a w l i n g h o r i z o n t a l l y ; g r a v i t y n e i t h e r a i d s n o r h i n d e r s movement. B) C r a w l i n g v e r t i c a l l y upwards; t h e w e i g h t o f t h e s l u g adds t o t h e f o r c e a c t i n g on t h e interwaves. C) C r a w l i n g v e r t i c a l l y downwards; t h e w e i g h t o f t h e s l u g s u b t r a c t s from t h e f o r c e a c t i n g on t h e interwaves.  214  slug  i s crawling v e r t i c a l l y  (0.15  N)  will  up,  stress  2  stress  due  and  will  For  a slug  caused  by  subtract  summarized The  0.85  o f the range  to a slug slow  2,00  of speeds  slug,  some v a l u e s a r e q u i t e  shear  rates  (120/sec).  l a r g e r than those  by t h e  caused  solid  by t h e s e  t h e s e s h e a r r a t e s was shear  In answering taken i n t o based  on  estimated  example  As  upper  columbianus. might  be  moving s l u g  expected are  u n d e r a s l o w l y moving  high.. I f these s t r e s s e s  are the  high  t h e a c c u r a t e measurement Is i t possible to  stresses are compatible  with t h i s  q u e s t i o n a number o f f a c t o r s  The  by  rapid  i s near t h e  s t r e s s e s must be v e r y  calculations  a number o f e s t i m a t e s , relative  f o r the  speed, even f o r a  i n .A.  not p o s s i b l e .  this  account.  interwaves  mucus under t h e i n t e r w a v e s ,  As e x p l a i n e d e a r l i e r  whether t h e s e  on t h e  segments  moving a t a c o n s t a n t  which  observed  t o be  be r e s i s t e d  o p p o s i t e to  moving a t a more  mm/second  predicted  to  this  v a r i o u s s t r e s s e s c a n be c a l c u l a t e d  s t r e s s e s p r e s e n t under a r a p i d l y  and  the  7.1.  These v a l u e s a r e shown i n T a b l e 7.1. the  (6.0 on  2  down ,  values calculated  above f o r a s l u g  f o r example  N/m  in a direction  This i s a f a i r l y  Values f o r the  speed, end  A l l the  example a b o v e r e f e r s  t h e method used  o f 250  vertically  be  t o i t s weight  interwaves  t h e s t r e s s imposed  i n Table  mm/second.  slug.  will  due  t h e f o r w a r d movement o f f o o t  from  (see F i g u r e 7 . 5 ) . are  walking  to i t s weight  the stress  force  a c t over the area of the  10-*m ) t o p l a c e an a d d i t i o n a l interwaves.  the  presented  here  of  say model?  must  be  are  A s m a l l change i n t h e  proportions of the d i f f e r e n t  areas of  the  215  foot  will  values.  have a l a r g e  will  a f f e c t the c a l c u l a t i o n , as w i l l  the i n vivo  properties  measurements. propulsion  remarkable that correlate  v a l u e s somewhat. i t i s somewhat  interwave stress  these  than  do.  they  and even l i k e l y  interwave  a clue  stress  The f a s t e r a s l u g  accurate,  do n o t t r a v e l any f a s t e r walks, t h e l a r g e r the  A t some s p e e d t h i s s t r e s s  t o crawl.  I f the interwave stress  will  values  no l o n g e r be calculated  h e r e f o r an a n i m a l moving a t 2.0 mm/sec seem l a r g e ,  is  be a r e f l e c t i o n o f t h e f a c t t h a t  walking  nearly  A second model.  f o r m o f t e s t may be a p p l i e d  to this  allow, locomotion  above t h i s model makes s p e c i f i c  predictions  moving s l u g  and t h e s e  appropriate  apparatus.  about t h e s t r e s s e s  forces  Force The  t h i s may  a t 2.0 mm/sec a s l u g  a s f a s t a s i t s p e d a l mucus w i l l  As e x p l a i n e d  quantitative  will  enough t o c a u s e t h e mucus b e n e a t h t h e  i n t e r w a v e s t o become a f l u i d a n d t h e s l u g  simply  rates  under t h e f o o t ,  values a r e indeed  a s t o why s l u g s  on i t s i n t e r w a v e s .  become g r e a t  able  values  a s c l o s e l y a s t h e y do t o t h e r a n g e o f s h e a r  they give  stress  difference  t o the force of  sources of e r r o r  the calculated  i s possible If  by c i l i a  would c h a n g e t h e c a l c u l a t e d possible  a  of  a s compared t o t h e i n v i t r o  A contribution  With a l l these  that  stress  Use o f a d i f f e r e n t c u r v e f o r t h e e s t i m a t i o n  viscosity in  e f f e c t on t h e c a l c u l a t e d  present  c a n be measured u s i n g  under a an  Plate  a p p a r a t u s used t o measure t h e l o c o m o t o r y  forces of  216  slugs  i s shown i n F i g u r e  plate  p r o t r u d e s t h r o u g h a 1.5 mm  surface. beam.  This  force-plate  A force  beam t h e f o r c e - p l a t e  that  During  the shorter  direction  (0.5 x 1.0 mm)  hole i n a l a r g e  i s supported  the f o r c e , the  i s sensitive to force  i n only  a t e s t , the f o r c e - p l a t e  dimension  (0.5 mm)  lies  one  i s oriented  in line  transformer.  transducer  side  (so t h a t  accurately  and r e c o r d e d  encountered  accurate  Forces as small  plexiglass  force-plate)  surface a slug  along  to force.  direction  as  measured and w i t h i n t h e  during  t e s t i n g the transducer  The u n l o a d e d  resonant high t o  locomotion.  i s performed  then allowing  this  and h a n g i n g  measurement of t h e 1 hz o s c i l l a t o r y f o r c e s  with s l u g  A test  sensitive  recorder.  o f t h e a p p a r a t u s i s 100 h z ; s u f f i c i e n t l y  associated  the  force.  this  t h e a p p a r a t u s on i t s  known w e i g h t s from t h e p l a t e . .  output i s l i n e a r with  allow  from  t h e m e a s u r i n g beam i s h o r i z o n t a l )  range o f f o r c e s  The linearly  on a c h a r t  i s c a l i b r a t e d by t u r n i n g  a b o u t 5 d y n e s c a n be a c c u r a t e l y  frequency  The o u t p u t  so  with t h e  i n which t h e beam i s s e n s i t i v e t o f o r c e .  differential  will  Due t o t h e shape o f t h e s u p p o r t i n g  transformer i s amplified The  steel  surface  amount o f d e f l e c t i o n o f t h e beam i s measured by a variable  force-  plexiglass  by a d o u b l e  t o move, t h e l a r g e r  the deflection.  direction.  A small  i n the plane of the p l e x i g l a s s  cause the f o r c e - p l a t e larger  7.6.  by o r i e n t i n g t h e a p p a r a t u s s o t h a t  i s either horizontal  o r v e r t i c a l , and  t o crawl across the surface  (and t h e  t h e d i r e c t i o n i n which t h e f o r c e - p l a t e i s The d i m e n s i o n s o f t h e f o r c e - p l a t e i n  (0.5 mm)  i s l e s s than the s h o r t e s t  length  of  217  FIGURE 7.6.  An a p p a r a t u s f o r m e a s u r i n g t h e f o r c e s b e n e a t h a crawling slug. A) S c h e m a t i c r e p r e s e n t a t i o n o f t h e a p p a r a t u s . B and C) The d i m e n s i o n s o f t h e f o r c e p l a t e a r e s m a l l e r t h a n e i t h e r a wave o r an i n t e r w a v e .  219  a compressed  wave.  plate  b e n e a t h waves and  be  forces  measured  slug  the  force  measured. measured for  (see  Thus,as a  Figure  forces  comparison  can  be  amply shown by  Lissman  This  ventral  surface  1.  was  of  was  tested  Because the  as  means t h a t  measure f o r c e  slug  the  plate.  Thus as  the  surface  only  the  foot  the  force-plate  i s not  can long  the  as  anteriorly by  be  the  plate  above t h e  150  um).  This  the  force-plate  can  lift  This  m a i n t a i n s the at  The  i t s foot  i n the  the  the.force  respects:  presence of as  able  to  hole  is flush  interwaves  forces  Apparently, of  while the  unless  raising  (50  between t h e  with  w i l l not  by  slightly  over  (where  Further,  i s remedied  surface  a  a  a wave p a s s e s  measured.  general region  i t sufficiently  directed  must be  force-plate  contact  a l l times.  a  i t must p r o t r u d e t h r o u g h  problem  plexiglass  been  observing  i d e a l i n two  b e n e a t h the  will  A l l tests  .  i t s foot the  stress,  passage o f  i s p r e c i s e l y f l u s h , these  measured a c c u r a t e l y .  cannot l i f t  lift  forces  lifted)  the  measuring p l a t e  plexiglass surface. the  model.  i t passed over  further  force  the  ie  the  (21-23 ° C ) . , I t has  t o an  apparatus i s l e s s than  hole i n the  of  the  be  i s known  force/area,  corroborated  foot  alternately  also  force-plate  (1945b) t h a t  the  not  move i n o r d e r t o  r i m s may  room t e m p e r a t u r e  observation  force-  correctly positioning  prediction  wave c o r r e s p o n d s  force.  This  By  e x p r e s s e d as  with the at  and  interwaves w i l l  area of the  were p e r f o r m e d  plate,  7.6).  passes over the  present beneath the  Since the  compressional  slug  um  to  foot the  hole,  i n the:localized region  and slug i t  of  the  be  220  force-plate  to break c o n t a c t with the  force-plate  i s raised  the  foot  the d i s t a n c e that  50-150 um)  does not  The.correlation amplitude far  has  from  The  again  between f o r c e - p l a t e  a  second  passed slug  direction at  While of  I t i s noted measured by  reaches  the  as the  i n the  gap  t h i s zero s h i f t  stresses  relative  encountered  plate  overall  i s raised i s  that the  i n a large  plate  plate..  slug  The  m a g n i t u d e and  over  the  a f f e c t the  and  before  the  the  Apparently solid  the  overall  mucus  plate. amplitude  that  stress  i s s h i f t e d by  level  amplitude  category Tests  are  the  directed  posteriorly.  The  level.  has  m e a s u r e d , i t makes i t i m p o s s i b l e t o measure  categories.  one  slug  even  plate,  e i t h e r i n f r o n t or behind does not  percentage  measured  i s unpredictable.  passes  apparatus  a f t e r the  As a c o n s e q u e n c e , t e s t r e s u l t s a r e d i v i d e d  force  force  o f a hole i n the  amounts o f t h i s o v e r a l l a m p l i t u d e  anteriorly  measured.  with t h i s  the z e r o s t r e s s  of t h i s zero s h i f t  up  with  the l i m i t s  stresses  d i s t a n c e the  problem  stress  some p o i n t  builds  The  i s d i f f e r e n t than  first  (within  h e i g h t and  a t t r i b u t a b l e to the presence  t e s t s the  contact  the  micrometer.  plexiglass surface. of  i t i s raised  Once  a c o r r e l a t i o n c o e f f i c i e n t of 0.059, which i s  with  2.  to maintain  appear to e f f e c t the  significant .  measured  is  sufficiently  force-plate.  and  s m a l l percentage  during the stresses  of tests  l e s s than  10%  where t h e  of the  passage of a s l u g a r e are  into  two zero  overall placed i n  measured r e l a t i v e t o t h e  where t h e z e r o l e v e l  amount a r e p l a c e d i n t h e s e c o n d  i s s h i f t e d by  category.  a  In t h i s  zero  larger category  221  the  o v e r a l l amplitude  (as  shown i n F i g u r e  this  overall  stress  of t h e  stress  7.7)  but  no  into  anteriorly  oscillation  attempt and  is  measured  i s made t o  subdivide  posteriorly  directed  stress.  Tests Two  sorts  plexiglass  of  tests  surface  horizontal  waves, i n t e r w a v e s and plexiglass  surface  i n t e r w a v e s was up  or  tests  were n o t  involving  the  of  in a  the  may  not  plate.  To  area of  the  actually  an  and  the  was  be  3.3.  beneath  due  to  slugs. the  stops of  measure t h e  the the  with  waves  and  vertically during  practical  The  slug  is  capable  anterior  half  of  the  posterior  i t moves o v e r  either the  speed  the  head  speed a t of  the  half.  the or  the  slug  Without a t r a n s p a r e n t  tail force-  in  force  is similar t h e s e two  the  to  I t i s assumed t h a t  r e s u l t s from turn.  the  problems  i t would have been n e c e s s a r y  impossible.  the  The  as  measure o f  discussed i n  Tests  Second  speed than the  speed  t h i s area,. proved  beneath  s l u g s walked  walking speeds i n these t e s t s  will  Horizontal  starts  force-plate  shown i n F i g u r e tests  different  with  walking e i t h e r  which t h e This  accurate  transducer t h i s range of  a  accurately  film  stresses  stress  manner such t h a t  measuring  give  the  perverse nature of  slug  force-plate  vertical  speeds a t  at  First  r i m s were measured.  measured,.  body i s moving Thus, as  the  measured f o r s l u g s  down.. The  moving  were p e r f o r m e d .  to  the  those  types  of  222  The o v e r a l l  amplitude  of the s t r e s s  measured under t h e  c e n t r a l p o r t i o n o f t h e f o o t f o r 34 t e s t s slugs  was  1493 N/m  with  2  a range from  on 19  different  780 t o 2820  N/m . 2  :  T h i s compares q u i t e f a v o r a b l y w i t h t h e p r e d i c t e d v a l u e s f o r overall A list 7.2.  stress  amplitude  o f p r e d i c t e d and measured v a l u e s  and r a n g e from  very  similar  2  overall  N/m . 2  i s shown i n T a b l e  shifts  posteriorly  three  directed  2  N/m  2  stresses?  The small  of a n t e r i o r l y  Anteriorly  r a n g i n g from  s t r e s s e s averaged  Again  measurement  and  The r e c o r d o f one o f t h e s e  i n F i g u r e 7.7.  these  p r e d i c t e d by t h e model  directed  290 t o 390 660  N/m  N/m . 2  ranging  2  from  values are quite c l o s e to (see T a b l e 7.2).  Tests  Seventeen stress  vertically amplitude  values are  s l u g s had s u f f i c i e n t l y  stress.  340  directed  590 t o 740 N/m .  Vertical  directed  t o a l l o w f o r t h e measurement  averaged  Posteriorly  those  from  i s reproduced  stresses  these  t h e model's p r e d i c t i o n s a r e q u i t e  and a n t e r i o r l y  records obtained  tests  Again  2  Does t h e a c c u r a c y a l s o h o l d f o r the  of p o s t e r i o r l y  zero  200 t o 510 N/m .  350  t o t h e p r e d i c t e d v a l u e s . . T h u s , on t h e b a s i s o f  amplitude  accurate.  t e s t s on 9 s l u g s were c o n d u c t e d  t o compare  v a l u e s between c r a w l i n g h o r i z o n t a l l y up.  The a v e r a g e  i s significantly  t h e mean o f t h e o v e r a l l  and  value f o r the o v e r a l l  while c r a w l i n g v e r t i c a l l y  This value than  830 t o 2280  The v a l u e s o f 5 measurements o f r i m s t r e s s a v e r a g e  N/m  the  which r a n g e f r o m  up was  greater  1991  (p l e s s  s t r e s s amplitude  stress  +- 354 than  N/m  0.01)  f o r the  2  Figure  7.2:  The measured and p r e d i c t e d f o r c e s o f A r i o l i m a x columbianus l o c o m o t i o n .  STRESS (N/m ) predicted measured 2  rims  297-659  201-512  waves  365-1059  336-526  interwaves  485-1222  591-1171  overall  850-2281  780-2280  x=1493  224  FIGURE 7.7.  An example of t h e r e c o r d o f f o r c e s measured b e n e a t h a c r a w l i n g s l u g , w i t h terms d e f i n e d . A m p l i t u d e s a r e measured f o r e a c h wave and a r e averaged f o r each s l u g .  FIGURE 7.7  Anterior  Poster ior  1 second  T - total  amplitude  A - amplitude ~  P-  »  of a n t e r i o r l y »  .  •  .  posteriorly  directed  force  "  "  226  horizontal  t e s t s w h i c h were c o n d u c t e d c o n c u r r e n t l y (see  below) when compared by a one way a n a l y s i s o f v a r i a n c e . Each o f t h e s e the  plexiglass surface  allowing  so t h a t  the slug t o crawl  mean o f t h e s e the  17 v e r t i c a l  foot  over the f o r c e  measured  and e a c h s l u g was weighed.  the  d i f f e r e n c e i n s t r e s s value  and  h o r i z o n t a l l y should  weight  plate.again.  of the slug  using  the video  As e x p l a i n e d  between  The  The a r e a o f  2  was t h e n  by t u r n i n g  i t was h o r i z o n t a l and  h o r i z o n t a l t e s t s was 1383 N/m .  o f each s l u g  recorder  t e s t s was f o l l o w e d  walking  earlier  vertically  be e g u a l t o t h e f o r c e due t o t h e  divided  by t h e a r e a  of the interwaves.  H a v i n g measured t h e d i f f e r e n c e i n s t r e s s , t h e i n t e r w a v e area, can  and t h e s l u g w e i g h t  be compared.  This  the p r e d i c t e d  i s accomplished  predicted  weight  In  the r e s u l t should  theory  origin  with  predicted, predicted  versus the a c t u a l  a slope  I t c a n be s e e n  as the s l u g ' s  However, t h e change i n s t r e s s a m p l i t u d e greater  (p< 0.05) t h a n t h a t  words., some f a c t o r o t h e r increasing The  basis  the force forthis  several possibilities 1-  than  that,as  (and t h e r e f o r e t h e weight  increases.  i s significantly  by t h e o r y .  t o move t h e s l u g  i s not a t p r e s e n t  In other  weight i s vertically.  known, t h o u g h  exist:  i ti s possible that  a response t o being  through the  j u s t the s l u g ' s  A*, c o l u m b i a n u s i s s t r o n g l y  Consequently as  predicted  required  fact  (see F i g u r e 7 . 8 ) .  passing  t h e change i n s t r e s s a m p l i t u d e weight) i n c r e a s e s  values  by p l o t t i n g t h e  weight  be a l i n e  o f one.  and a c t u a l  tilted  negatively  the slug  geotactic.  would c r a w l  to a vertical  position.  faster While  227  FIGURE 7.8.  A p l o t o f w e i g h t as p r e d i c t e d f r o m t h e model v e r s u s a c t u a l weight f o r a l l v e r t i c a l c r a w l s . While p r e d i c t e d weight i s p r o p o r t i o n a l t o a c t u a l weight the s l o p e o f the r e l a t i o n s h i p i s greater than expected.  F i g u r e 7.8  a c t u a l weight  (grams)  229  the  speed  of the slug  (as e x p l a i n e d definitely for  slugs 2.  was n o t measured d u r i n g  above), so t h a t t h i s  tests  f a c t o r c a n n o t be  r u l e d o u t , no v i s i b l e i n c r e a s e crawling  these  i n speed  was n o t e d  vertically.  I t i s p o s s i b l e that t h e s l u g a l t e r s t h e area  of the  rims i n response t o t h e angle  of the substratum  the  h o r i z o n t a l l y a r e o f t e n seen t o  vertical.  have p a r t  Slugs  of the rims l i f t e d  when c r a w l i n g applied area  vertically  would i n c r e a s e  from t h e substratum.  This increase  the stress  thickness  amplitude.  vertically.  o f t h e mucus l a y e r would  once t h e s l u g s t o p s  surface.  Perhaps t h i s  offsets the increase expenditure.  vertically the In the  slugs  necessary  i n locomotory  t h i s case the o v e r a l l  weight.  strength  i s t o crawl  t o walk  t o conduct as  up a v e r t i c a l  s t r e s s amplitude  study.  walking  up, t h e s l u g was i n d u c e d  should  face.  be l e s s f o r  down c r a w l i n g t h a n t h e h o r i z o n t a l c r a w l  amount r e l a t e d t o t h e s l u g ' s w e i g h t . qualitatively  down t h e  warrants f u r t h e r  These t e s t s a r e d i f f i c u l t  likely  energy  i n addition to the slug's  normal behavior  vertically  slide  advantage o f e x t r a adhesive  and v e r t i c a l l y  down.  the  a l s o make i t l e s s  i t will  T h i s matter c e r t a i n l y  two t e s t s ,  horizontally  crawling  Decreasing  thickness  i n c r e a s e t h e f o r c e needed  t o move t h e s l u g upwards, b u t would  In  i n e f f e c t i v e rim  I t i s a l s o p o s s i b l e t h a t t h e mucus l a y e r  a l t e r e d when c r a w l i n g  that  However,  the r i m s a r e i n v a r i a b l y c l o s e l y  t o the substratum.  3. is  crawling  realtive to  Again  while  c o r r e c t , t h e model o v e r e s t i m a t e s  The s t r e s s r e c o r d s  from one s u c h  by an  the animal's  s e r i e s of t e s t s  230  a r e shown i n F i g u r e 7 . 9 .  Pressures The  model p r e s e n t e d  A. c o l u m b i a n u s dorsally  cannot  be p r e d i c t e d .  detect  this force,  Figure  from by  used  7. 10.  replacing  tubing  ventrally  o f the role  I t s h o u l d , however, be p o s s i b l e t o  i f i t i s indeed  will  tube  with  t h i s new  plate  was m o d i f i e d  end t h e  a s shown i n  with a hollow T h i s tube  degassed  water.  force plate,  tube c u t  i s connected  to a pressure transducer.  All  Thus, as t h e s l u g  any f o r c e d i r e c t e d  the detection of pressure  dorso-  transducer.  by t h i s  transducer  by m e a s u r i n g t h e movement o f a d i a p h r a g m .  t h e r e i s some volume change i n t h e s y s t e m  accompanying a p r e s s u r e change. would accompany a s l u g  wave a r e l i k e l y  S i n c e t h e volume  lifting  t o be q u i t e s m a l l  whole wave, c o n s i d e r a b l y l e s s  is  p r e s e n t . . To t h i s  be d e t e c t e d by t h e p r e s s u r e  accomplished  over  Without  p l a y e d by m u s c l e s i n t h e  i n t h e above t e s t s  plastic  Consequently  wave  waves, t h e m a g n i t u d e o f t h i s f o r c e  t h e f o r c e measuring  Unfortunately  that  t h a t t h e r e s h o u l d be a  The e s s e n t i a l m o d i f i c a t i o n c o n s i s t s o f  is filled  walks o v e r  is  predicts  a 20 guage h y p o d e r m i c n e e d l e .  a rigid  3 f o r the kinematics o f  i s c r a w l i n g on a n o n - p o r o u s s u r f a c e .  of pedal  plate  Waves  f o r c e on t h e mucus b e n e a t h a p e d a l  a better understanding propagation  Pedal  i n Chapter  locomotion  directed  when t h e s l u g  force  Beneath  changes  i t s foot during (about  ,1 t o . 5  a pedal  u l f o r one  f o r t h e s m a l l p a r t o f a wave  t h e t u b e ) t h e volume change due t o p r e s s u r e d e t e c t i o n  likely  to substantially  affect  the pressures  being  231  FIGURE 7-9.  A r e p r e s e n t a t i v e r e c o r d o f t h e f o r c e s measured b e n e a t h a s l u g when c r a w l i n g v e r t i c a l l y up, h o r i z o n t a l l y , and v e r t i c a l l y down. The s l u g weighed 16.24 gm and t h e v e r t i c a l l y up and own r e c o r d s p r e d i c t a w e i g h t o f 34.0 and 54.4 gm respectively.  232  233  FIGORE 7.10.  A schematic drawing of the a p p a r a t u s f o r s i m u l t a n e o u s l y measuring a n t e r i o - p o s t e r i o r f o r c e s and d o r s o - v e n t r a l f o r c e s b e n e a t h a crawling slug. The s y r i n g e and v a l v e a r e used to a d j u s t the l e v e l o f t h e degassed water i n the system.  Figure  7.10  CO  235  measured.  T h u s , t h e magnitud e o f p r e s s u r e  apparatus  a r e p r o b a b l y much t o o s m a l l  however, a c c u r a t e l y pressure.  measure.the presence  In a d d i t i o n  apparatus  can s t i l l  .  t o these  pressure  measured by t h e  The a p p a r a t u s  does  and d i r e c t i o n o f measurements t h e  measure a n t e r i o - p o s t e r i o r l y  directed  forces. A s e r i e s o f s i x t e s t s on t h r e e there  i s a dorsally directed  wave.  The r e c o r d  force  slugs  confirms  acting  that  under a p e d a l  f r o m one s u c h t e s t i s r e p r o d u c e d  i n Figure  7,11.  C o n c l u s i o n s And On t h e b a s i s physical  moving s l u g . and  of the kinematics o f locomotion  properties  quantitatively  and t h e  o f p e d a l mucus a model c a n be drawn  predicts  the stresses  These s t r e s s e s  t h e measured  Discussion  stresses  operating  c a n be measured  that  under a experimentally  compare c l o s e l y t o t h e p r e d i c t e d  stresses. These r e s u l t s l e a d 1.  conclusions:  The model p r e s e n t e d h e r e i s i n g e n e r a l a n a c c u r a t e  description A,  t o two  o f t h e p r o c e s s of l o c o m o t i o n i n t h e s l u g  columbianus  .  simplifications  I t appears t h a t  t h e a s s u m p t i o n s and  made i n c o n s t r u c t i n g  t h e model a r e  justified.  More s t u d y i s needed,however, t o a c c o u n t  discrepancy  encountered  2.  I f the properties  from t h e f o o t the  when s l u g s  properties  of the slug of this  of pedal  crawl  f o r the  vertically.  mucus measured  separate  p r o v i d e an a c c u r a t e d e s c r i p t i o n o f  mucus when a c t u a l l y  used i n  236  FIGURE 7 . 1 1 .  An example o f s i m u l t a n e o u s f o r c e and p r e s s u r e measurements. The d o r s a l l y d i r e c t e d f o r c e p e a k s a t t h e same t i m e a s t h e a n t e r i o r l y directed force. The o v e r a l l s l o p e o f t h e p r e s s u r e t r a c e i s due t o t e m p e r a t u r e d r i f t i n the t r a n s d u c e r .  Figure  7.11  2  S E C  238  locomotion mechanism  then  whereby t h e  by  the  is  reasonably  not  during  a c c u r a t e as  wish t o i m p l y t h a t  aspect and  of  which a slug  noted slug  this  In  vertical  suspended  these  times,  phenomenon.  c o n c e r n s the  application  retograde  the  model drawn h e r e and  with a f o o t  scaled are  to  thereby the  all  slugs  to  will  the  do  Chapter  present  not  been study  some d e r i v a t i v e  i n animals i n Chapter  of  weighing  10.  must t h i s model  How  2  different sizes? 1)  The  foot  area  mucus o v e r w h i c h t h e resistance  same shape,  to  foot  area  length  of  square of  the  slug  determine the  will  external  work, and  Two  slug  15  the  be  grams be  will must move, Thus, i f  expected  slug,  volume of  for a slug  The  factors  movement. may  of  using  of  cm .  the  transport  slug  15  on  explain  for future  discussed  one  mucus  t h i s has  t h i s model o r  be  for  explain,  t h i s mucus  area  do  least  in  o f t h i s model c a n  but  I  for a "typical"  slugs  of  described  that  model  model  there i s at  of l o c o m o t i o n  frictional  have t h e  mass o f t h e  available  area  area  and  as  of  i n t h i s problem:  determine the  The  was  apply to  involved  increase  This  this  discrepancy  waves a r e  Another l a r g e  problem  waves.  While  transport  While  action,  shown.  model t o  As  can  aspect  conclusively  controlled  been t e s t e d ,  to the  study.  I t seems l i k e l y  ciliary  mucus a r e  which t h i s model c a n n o t  foot. no  elaborate  a l l encompassing  crawling  i n midair  along the  the  i t has  addition  locomotion  a r e s u l t of  this  f a r as  deserves f u r t h e r  posteriorly f o o t at  for  of  p r o p o s e any  locomotion.  i t i s an  locomotion.  previously  is  properties  pedal epithelium  gastropod  3,  i t i s unnecessary t o  L . 2  2)  muscle  crawling  to  239  vertically, required related  a l s o a f f e c t the  t o move. t o the  standard the  will  The  volume of  s h a p e , may  length  of  the  (mass/foot area proportion  be  be  the  slug, L „  length  necessary  will thus,  to i n c r e a s e  be  of t h e  expected  slug.  force  directly  f o r a slug of as  the  t h i s b a s i s , the  would be  2  slug  s l u g , and  On  3  3  the  expected  or L / L )  to the  c a s e i t may  mass o f  amount o f e x t e r n a l  cube  foot  of  loading  to increase  If this  a  in  i s indeed  to b u i l d a s c a l i n g f a c t o r i n t o  the the  model. Foot variety be  loading  of  s i z e s and  seen t h a t  the  are  were measured presented  slugs  at a value  Thus, t h e  movement may  be  ratio  of  expected  w h i l e c a l c u l a t e d f o r a 15 to  any  being  A.  i n Figure  columbianus  required.  of  a b o u t 0.95  must c h a n g e shape as  which m a i n t a i n s a c o n s t a n t area.  for slugs  of  7. 12.  ratio  g/cm . 2  of g r e a t e r  means  t h e y grow i n a manner  frictional  to remain constant, gram s l u g ,  can  loading  This  between w e i g h t and  muscle to  a It  f o r s l u g s above a b o u t 5 grams t h e : f o o t  remains constant that  values  may  be  foot  resistance  and  the  directly  t h a n 5 grams, no  of  model, applied  scaling  240  FIGURE 7.12.  The f o o t l o a d i n g ( w e i g h t / f o o t area) o f A r i o l i m a x c o l u m b i a n u s i s c o n s t a n t above a w e i g h t o f a b o u t 5 grams.  7.12  FIGURE  2  4  6  8  10  SLUG  12  WEIGHT  14  (GRAMS)  16  18  20  22  242  CHAPTER 8  Cost  The  preceeding  mechanism  p r o v i d e s a model f o r t h e  of l o c o m o t i o n i n A, c o l u m b i a n u s  this  question:  how  a fish,  it  for a slug  examining  i n movement.  knowledge o f how  to  review  Locomotion  chapter  the f o r c e s i n v o l v e d extend  Of  costly  a bird,  an e s t i m a t e  of  I t would be  interesting  to  t h e a n i m a l c r a w l s , and  i s t h i s form  a reptile,  of locomotion?  o r a mammal, how  t o move i t s e l f f r o m  this  and  dealing  the  Compared  expensive i s  place to place?  guestion i n d e t a i l i t w i l l  some b a s i c c o n c e p t s  ask  Before  be u s e f u l  with the c o s t  to  of  locomot i o n .  Review Of  Terms  As shown i n C h a p t e r anteriorly  directed  the v i s c o e l a s t i c crawls.  The  s l u g through distance Joules  by  a moving s l u g  p r o p e r t i e s of t h e  result  of t h i s  a certain  Energy  must e x e r t an  f o r c e i n o r d e r t o overcome g r a v i t y mucus o v e r  f o r c e i s the  distance.  i s work o r e n e r g y  (J).  expressed  7,  and  The  i s expressed  e x p e n d i t u r e per  as J / s e c o n d  o r Watts  (W).  unit  distance/time comparing  of f o r c e  times as  i s power ,  Thus t h e f o r c e of  exerted  movement  i s e q u a l t o t h e power e x p e n d i t u r e  = w o r k / t i m e = power)..  the  i n SI u n i t s  time  an a n i m a l a s i t moves, t i m e s t h e v e l o c i t y  (distance/time)  which i t  movement o f  product  and  I t i s useful  (force  x  when  c o s t s between a n i m a l s t o n o r m a l i z e t h e c o s t t o  the  243  weight given  of t h e a n i m a l . velocity  The  will  Thus t h e power r e g u i r e d  be e x p r e s s e d as  power n e c e s s a r y  two c a t e g o r i e s . by  t h e model i n C h a p t e r 7 .  is  exerted  the  This  i t i s exerted,  expended  i s t h e power  The f o r c e p r e d i c t e d  f o r c e , t i m e s the s l u g provides  internal  power  (Pe) .  slug's  body t o c a u s e  The  internal  slug's  there  to occur.  parts.  o f muscular  The p r o d u c t i o n  i s f a r from being  First,  t o t h e muscles  o f ATP f r o m t h e  more e n e r g y  process. i n providing  ATP t o t h e m u s c l e s t h a n w i l l a p p e a r a s e x t e r n a l Further  a l l work o f c o n t r a c t i o n  applied  t o locomotion.  muscles o f the foot the  pedal  them) i n c r e a s e  Finally,  energy  glycoprotein  skeleton  during  Again these f a c t o r s  t h e amount  expended t o r e s u l t  of muscles i s not d i r e c t l y  expend e n e r g y a s t h e y  haemocoel.  work.  F o r e x a m p l e , m u s c l e s must  maintain the h y d r o s t a t i c  of i n t e r n a l  i n a given  the  contraction.,  a 100% e f f i c i e n t  C o n s e q u e n t l y t h e a n i m a l must s p e n d  to  i s the  must be e x p e n d e d i n s i d e  of s e v e r a l  of locomotion are a r e s u l t  food  v e l o c i t y at  work t o be done on t h e e n v i r o n m e n t .  power i s t h e sum  contraction  by t h e model  t o t h e s l u g and i s  E n e r g y , i n t h e form o f ATP, must be p r o v i d e d for  predicted  , t h e mucus and  In contrast  power. P i , t h e power t h a t  the  into  a measure o f t h e . p o w e r  i n overcoming f a c t o r s e x t e r n a l  termed t h e e x t e r n a l  forces  of t h e s e  c a n be d i v i d e d  by t h e a n i m a l on i t s s u r r o u n d i n g s  substratum.  which  W/kg.  f o r locomotion  The f i r s t  t o move a t a  amount  contract  movement, and  move.the f l u i d o f (and o t h e r s  energy that of external  like  must be work.  must be e x p e n d e d i n c o n s t r u c t i n g t h e  o f t h e mucus, an i n t e r n a l  expenditure  that  does  244  not r e s u l t these the  i n any  factors  external force.  the t o t a l  e x t e r n a l power.  measure o f t h e  internal  The  ratio  efficiency  As  a result  power w i l l  o f t h e two,  of the  of a l l of  be  greater  Pe/Pi, i s  locomotory  than  one  process.  As m e n t i o n e d a b o v e t h e e x t e r n a l power r e q u i r e d f o r s l u g locomotion the  can  be  accurately estimated  model of C h a p t e r  7.  The  calculated.  The  expenditures  of locomotion  oxidaton  i n the  glycogen,  energy  slug  lipids,  and  D e p e n d i n g on  g i v e n amount o f  C02  p r o d u c t i o n and  conversion internal large  factors  energy  the  related  i n the  02  the  animal.  total  i s estimated  production  and  associated  with  energy  designed  a  will  and  the  oxidized a  these  the  total  one  time.  be  i s not  directly power o f C02  levels that i s  calculating animal  the  (see  1972). t e r m s and  concepts  to simultaneously  i n mind, an  measure 02  A  used  increase i n  by t h e  total  proper  internal  above r e s t i n q from  consumption  measuring  a t any  by m e a s u r i n q t h e  movement, and  the  compounds;  using the  supply  Consequently  consumption  by  02 consumed, f o r  Thus by  animal  number of J o u l e s expended  with these  and  and  animal  maintenance o f t h e  Schmidt-Nielsen,  storage  i t i s possible to estimate  locomotion  was  produced,  by t h e  directly  external characteristics  c o n s u m p t i o n and  to locomotion.  increased  be  expended  02  provided  p r e c i s e compound b e i n g  will  p o r t i o n of t h i s  simply  i s ultimately  The  using  internal  a p r o d u c t i o n o f C02  e a c h J o u l e expended by C02  r e q u i r e d f o r the  protein..  speed  power i s l e s s  of v a r i o u s e n e r g y  of t h i s o x i d a t i o n are o f 02.  internal  f o r any  experiment  consumption,  245  distance  crawled,  From t h e s e  data  and r a t e o f c r a w l i n g  i n A. c o l u m b i a n u s -.  and t h e model o f C h a p t e r 7 t h r e e  factors  were c a l c u l a t e d . 1) The c o s t  of moving a c e r t a i n d i s t a n c e  (expressed  as  J o u l e s / k g m). 2) t h e power move a t a g i v e n 3)  (both  velocity,  the efficiency  Apparatus  And  internal  expended t o  and  of  locomotion.  Experimental  A differential  and e x t e r n a l )  Protocol  electrolytic  respirometer  was  constructed  t o measure t h e 02 c o n s u m p t i o n and C02  of crawling  A._ c o l u m b i a n u s  respirometer that in  was  of Close,  a 1.9 l i t e r  (concentrated  airtight KOH).  reference the  test  equal  chamber.  by a t h i n  diaphragm  i s a small  in  i n the t e s t  ).. as  absorbant  metabolizes,  02 i s  As t h e C02 i s a b s o r b e d t h e  chamber d e c r e a s e s r e l a t i v e The r e f e r e n c e  The t e s t  chamber  to a  i s i d e n t i c a l to  and r e f e r e n c e  rubber diaphragm mirror  This  The a n i m a l i s h o u s e d  chamber e x c e p t t h a t t h e s l u g i s r e p l a c e d  separated  and  As t h e a n i m a l  volume o f w a t e r .  pressure  (1978).  box c o n t a i n i n g a C02  produced.  i n the t e s t  8.1 and 8.2  on t h e same b a s i c p r i n c i p l e  Dnwin and Brown  consumed and C02 pressure  designed  (see F i g u r e s  production  .  of s i l v e r e d  by an  chambers a r e  Mounted on t h e mylar.  As t h e  chamber d e c r e a s e s t h e d i a p h r a g m i s b e n t  the o r i e n t a t i o n of the mirror i s a l t e r e d . orientation deflects a light  beam.  beam o f f o f an e l e c t r o n i c p h o t o d e t e c t o r  T h i s change  The movement o f t h e causes a r e l a y to  246  FIGURE 8 - 1 . .  A schematic diagram o f the e l e c t r o l y t i c d i f f e r e n t i a l r e s p i r o m e t e r used t o measure t h e metabolic rate of slugs. The t e s t and r e f e r e n c e chambers a r e submerged i n a c o n s t a n t temperature bath..  FIGURE 8.1  reference  chamber  248  FIGURE 8.2.  A s c h e m a t i c diagram o f t h e apparatus used t o measure t h e movement o f a s l u g i n t h e t e s t chamber. The chamber i s s u p p o r t e d by a compound beam c o n s i s t i n g o f two o r t h o g o n a l l y a r r a n g e d beams. E a c h o f t h e s e s i n g l e beams i s d e s i g n e d t o bend i n one d i r e c t i o n o n l y . The f a r t h e r t h e s l u g i s from t h e c e n t e r o f t h e chamber a l o n g t h e b e n d i n g a x i s o f a beam, t h e more t h a t beam i s b e n t . T h u s , s t r a i n guages r e s p o n d i n g t o t h e degree o f bending i n each beam p r o v i d e a measure o f t h e s l u g ' s c e n t e r o f mass.  FIGURE 8.2  amplifier chart  recorder  250  c l o s e and c u r r e n t  t o be p a s s e d  t h r o u g h an e l e c t r o l y s i s  in  the t e s t  chamber.  in  the c e l l  r e l e a s e s 02 i n t o t h e t e s t  has  replaced  returned fall.on  cell  a timer  will such  discreet pulses  and t h e c u r r e n t  be c u t o f f . that current  and t h e r e b y  submerged  i n a constant  0.01  The t e s t the  bending along strain  recorder,  records  From t h i s ,  circuit  t o the c e l l recorder  t h e amperage o f of  a time  record of  a n i m a l c a n be  chambers a r e .01  C.  a consumption  detected.  i s supported  about  by a c e n t r a l beam and a s  i n t h e chamber i t s w e i g h t c a u s e s t h e  S t r a i n guages g l u e d orthogonal  axes.  guages i s r e c o r d e d and p r o v i d e s  of the slug's center distance  i s supplied  o f the apparatus i s such t h a t  chamber  slug crawls  beam t o bend.  the  to the  t e m p e r a t u r e b a t h a t 19.5 +-  ml of 02 c a n be  again  The e l e c t r o l y s i s  Both t h e t e s t and r e f e r e n c e  The s e n s i t i v i t y of  beam w i l l  o f 02 consumed by t h e e x p e r i m e n t a l  calculated.  02  have  i s a measure o f t h e number  coulombs d e l i v e r e d t o the c e l l . amount  When t h i s  o f a known d u r a t i o n . ft c h a r t  to the e l e c t r o l y s i s c i r c u i t  each p u l s e  the  chamber.  t h e 02 consumed t h e d i a p h r a g m w i l l  the photodetector  contains  coupled  o f t h e CuS04 s o l u t i o n  t o i t s unbent p o s i t i o n , t h e l i g h t  electrolysis  in  The e l e c t r o l y s i s  cell  The a m p l i f i e d  moved by t h e c e n t e r  movement c a n be c a l c u l a t e d .  output  on a two c h a n n e l  a continuous  o f mass.  t o t h e beam measure  From  record  this  from  chart  of the l o c a t i o n  t h i s record  the t o t a l  o f mass and t h e v e l o c i t y o f Movement o f t h e s l u g  the  side  walls  o f t h e chamber a r e n o t r e c o r d e d ,  the  flat  shape o f t h e chamber, v e r t i c a l  up o r down  b u t due t o  movements a r e l i k e l y  251  to  be  small  compared t o h o r i z o n t a l movements.  A.  columbianus  i n t h i s a p p a r a t u s showed a d i s t i n c t  r h y t h m i n movement, r e m a i n i n g and  moving f o r  continuously 24  4 hours i n the  recording  hour p e r i o d  t h u s be  3 to  the  Crawling  c o n d i t i o n s were q u i t e one  respiration  r e s t i n g and  determined.  m/sec, r o u g h l y  s t a t i o n a r y during  the  middle of the r a t e and  slow, a v e r a g i n g  tenth the s l u g * s  maximum  , By  movement o v e r rates  under  about  day  night.  a c t i v e metabolic velocities  diurnal  a  could  these  2.2  x  10-*  crawling  velocity. The  r e s p i r a t o r y quotient  measured by for  comparing  a slug in a test  to  the  RQ  t h u s measured  using with  the  apparent  chamber  0.92,  an  p r i m a r i l y carbohydrates this  RQ  calculating  rate  power  of 02  C02  with  C02  as  o f 20,9  (Prosser  and  compared  absorbant.  t h a t the  i t s fuel,.  was  consumption  absorbant  indication  measurement a v a l u e internal  f o r A., c o l u m b i a n u s  chamber w i t h o u t  same s l u g i n a t e s t was  (RQ)  In  J/ml  The  slug i s  accordance 02  Brown,  was  used i n  1961).  Results A typical is  example o f a r e s p i r a t i o n  shown i n F i g u r e  First,  the  by  .  peak i n 02  approximately  one  inefficiency  o f the  hour.  due  to  circulatory  (as compared f o r example  l a g s the  This delay three and  movement  worth  move a t a c o n s t a n t  consumption  consumption i s probably  slug  Three f a c t s are  s l u g does n o t  Second, t h e rate  8,3  and  record  noting.  velocity. peak i n  crawling  i n observed  f a c t o r s : 1)  Given  02 the  r e s p i r a t o r y systems i n  t o a mammal) i t seems  likely  252  FIGURE 8.3.  A representative record of crawling v e l o c i t y and oxygen c o n s u m p t i o n f o r A r i o l i m a x c o l u m b i a n u s . Note t h a t t h e s l u g does n o t c r a w l a t a u n i f o r m s p e e d , and t h a t t h e oxygen c o n s u m p t i o n l a g s t h e peak i n r a t e o f movement and c o n t i n u e s f o r s e v e r a l h o u r s a f t e r movement ceases.  C R A W L I N G  V E L O C I T Y  ( M / S E C  X  IO~  4  )  254  that  an e n e r g y  result to  i n an oxygen d e b t  be r e a l i z e d  switching cost  expenditure i n the locomotory musculature  as C02  third  fact  respiration  all  by  the  precisely  t o n o t e from  rate  due  correlate  The  rate  This  may  i s that  the  w e l l be due  The  increased  a r e a under  02  i t is difficult  the i n t e r n a l  distance velocity  t h e peak i n i n c r e a s e d 8.3)  was  t a k e n as a that and  t h e t i m e o f movement  t o move a t t h a t  energy,  wii:h  t h e s e d a t a were a n a l y z e d  i s a measure o f t h e t o t a l i n t e r n a l  power i n W/kg  to  respiration  (converted t o energy  by  or  of the  consumed i n moving t h r o u g h  when d i v i d e d  hours  t o any  initiation  peak i n i n c r e a s e d  (as shown i n F i g u r e  a s J/kg)  the i n t e r n a l  8.3  of these f a c t s  T h i s 02 c o n s u m p t i o n  e x p e n d i t u r e , and  distance  The  n o t be i n s t a n t a n e o u s .  b o u t o f movement t h e t o t a l  measure o f t h e t o t a l distance.  3)  t i m e o f movement, and t h e a v e r a g e  were d e t e r m i n e d . respiration  Figure  Conseguently  f o r each  moved, t h e t o t a l  bath w i l l  above f o r t h e  each  velocity.  as f o l l o w s :  Similarly  time  2)  t o movement c o n t i n u e s f o r s e v e r a l  As a r e s u l t  a specific  average  J/kg, d i v i d e d  moved, i n m e t e r s , g i v e s t h e c o s t  by  the  energy yields  velocity. total  o f movement i n  m. The  a r e shown 8.1  KOH  of the f a c t o r s c i t e d  time l a g .  J/kg  l a g the onset of c r a w l i n g .  movement has c e a s e d .  expressed  take a c o n s i d e r a b l e  e x c r e t e d i n t o t h e atmosphere.  o f p r o d u c t i o n , may  after  will  on o f mucus p r o d u c t i o n , and t h e r e b y t h e m e t a b o l i c  a b s o r p t i o n o f C02 The  which  may  results  from  i n Figure  t o 23-3  grams.  9 measurements on  8.4  .  These  I t c a n be  7 different  s l u g s ranged  seen  that  slugs  i n weight  from  t h e power n e c e s s a r y  255  FIGURE 8.4.  The i n t e r n a l power o f l o c o m o t i o n as a f u n c t i o n of c r a w l i n g speed f o r A r i o l o j m a x columbianus . The s l o p e o f t h e l i n e i s t h e a v e r a g e c o s t o f l o c o m o t i o n (952.5 J / k g m).  FIGURE 8.4 .30  .26  .22  .18  O \  i  .14§-  .10  .06  .02  .2  1.0  1.8  M  2.2  2.6  SEC"' X IO"  4  3.0  3.4  257  for  movements i n c r e a s e s w i t h i n c r e a s i n g  divided these  Since  by m/sec e q u a l s J / k g m t h e s l o p e o f t h e l i n e  p o i n t s e g u a l s t h e average  952.5 +The used  speed.  cost of locomotion  through  which i s  130.6 J / k g m. method o f c a l c u l a t i n g  here  differs  Goldspink  from  that  and A l e x a n d e r ,  cost of locomotion  used  and power  by o t h e r a u t h o r s ( s e e  1977).  The t y p i c a l p r o c e d u r e  i n d u c e an a n i m a l t o move a t a c o n s t a n t r a t e and t h e n the steady  state  experiment  c o u l d n o t be p e r s u a d e d  rate,  s t a t e 02 c o n s u m p t i o n v a l u e s used locomotion  was n o t  here, i n has ceased,  t o be somewhat h i g h e r t h a n i f s t e a d y  be measured.  measure  t o walk a t a c o n s t a n t  i n c l u d e 02 consumed a f t e r  are l i k e l y  i sto  Since the slugs i n t h i s  The t o t a l 02 c o n s u m p t i o n  they  could  02 c o n s u m p t i o n .  t h e measurement o f s t e a d y  possible. that  W/kg  state  values  They a r e however an a c c u r a t e measure o f  the c o s t o f l o c o m o t i o n . Keeping of  locomotion  comparison by  Tucker  i n mind  i s facilitated  review  Alexander,  fact  i n slugs to that  (1971),  excellent  of  this  1977).  locomotion  of other animals.  by t h e g e n e r a l i z a t i o n s  and S c h m i d t - N i e l s e n of this  literature  These a u t h o r s  (1972)  The most s t r i k i n g  plotted  which move i n a s i m i l a r  i s that  manner f a l l  presented  ( f o r an  the l o g of the cost  simple r e l a t i o n s h i p s of these  This  s e e G o l d s p i n k and  a g a i n s t t h e l o g o f body w e i g h t  number o f s u r p r i s i n g l y ).  we c a n now compare t h e c o s t  and f o u n d  ( s e e F i g u r e 8.5  a l l those  on a s i n g l e  animals line.  the data  p o i n t s f o r a l l swimming a n i m a l s  may be l i n k e d  straight  line,  that f l y ,  and s i m i l a r l y  f o r animals  a  and  Thus by a  258  FIGOBE 8.5-  The c o s t o f l o c o m o t i o n (redrawn from G o l d s p i n k , 1977, a f t e r S c h m i d t - N i e l s e n , 1972), F o r any g i v e n w e i g h t i t i s more c o s t l y t o f l y t h a n t o swim; and r u n t h a n f l y . The c o s t o f l o c o m o t i o n measured f o r a s l u g i s c o n s i d e r a b l y g r e a t e r t h a n any v a l u e p r e v i o u s l y measured.  F I G U R E  8.5  260  animals t h a t are s i z a b l e  pertinent  fact  i s that  1 kg o f t h a t  animal  1 meter i s l e a s t  and g r e a t e s t i f i t w a l k s .  regardless of the f i n e  there  between t h e t y p e s o f  F o r an a n i m a l o f a g i v e n w e i g h t ,  more i f i t f l i e s , that  The s e c o n d  differences i n cost  locomotion. moving  run.  details  about  the cost of  i f i t swims, This  implies  how a n a n i m a l  moves, i t s b a s i c and most g e n e r a l p a t t e r n o f movement it,  i n a metabolic sense, t o other animals t h a t  basically  similar  patterns.  examine t h e open c i r c l e cost  way t o move. of cost  difference will  cost  distance Why it  I t i s immediately  of adhesive  nearly  that the estimate  and t o t a l  02 c o n s u m p t i o n , i t  t e n t i m e s a s much t o move a g i v e n  animal o f equal  i s this  Using s e v e r a l  i s possible  costly  h i g h due t o t h e  as a running so?  apparent  locomotion i s a very  may be s l i g h t l y  between s t e a d y s t a t e a slug  we c a n  on F i g u r e 8.5 w h i c h r e p r e s e n t s t h e  Even a l l o w i n g f o r t h e f a c t  f o r a slug  show  I n t h i s context then  of locomotion i n the s l u g .  t h a t t h e s l u g ' s form  ties  size.  means o f a p p r o x i m a t i o n  t o examine t h e v a r i o u s components o f t h e  energy  expenditures of the slug  and t h e r e b y a r r i v e  better  i d e a o f what i t i s a b o u t  adhesive  at a  locomotion  that  makes i t s o c o s t l y . U s i n g t h e l o c o m o t i o n model o f C h a p t e r power o f movement on l e v e l several velocities are p l o t t e d  ground  c a n be c a l c u l a t e d f o r  and f o r a mucus l a y e r  i n F i g u r e 8.6 .  7, t h e e x t e r n a l  10 um t h i c k .  The s l o p e o f t h i s  curve  (W/kg/m/sec = J / k g m)  (the cost  increasing  T h i s i s a s one would e x p e c t  velocity.  These  o f movement) i n c r e a s e s w i t h from  261  FIGURE  8,6..  The components o f power i n t h e l o c o m o t i o n o f A r i o l i m a x c o l u m b i a n u s . The e s t i m a t e d e x t e r n a l power, Pe, f o r m s o n l y 1.7% t o 5.2% o f t h e i n t e r n a l power. P i , measured f r o m r e s p i r a t i o n studies. The e s t i m a t e d power o f mucus production i s s e v e r a l times l a r g e r than the e x t e r n a l power.  FIGURE 8.6  263  trying  to  move o v e r  movement, t h e cost.  a viscous l i q u i d ;  g r e a t e r the  These c a l c u l a t e d  compared  for efficiency. walked  i n the  At  _  respirometer)  of  1.7%.  J/kg  the  I f the c o s t of  10-  3  at the  m/sec w i l l  are i n r e a l i t y ground. ground  yielding  (Tucker,  be  show an  locomotion  invertebrate  shown t o be reach t h i s  alone.  differ  of v a r i o u s 20  t o 25%  efficiency  Still,  5.2% be  .  there How  question  t o 25%  is still  t o the  c a n n o t be  the  low  and  on  level  and  3.2%  of likely  be  efficiency a l a r g e gap inefficiency  production  answered w i t h  under  be t h e  To  lower.  maximum  of a walking  t o 1.7 slug  At p r e s e n t  certainty,  an  other  when compared  o f mucus? any  1977).  considerably may  been  contracting at  optimum l o a d , and will  they  maximum  Alexander,  m u s c l e must be  the  i s t h a t of  efficiency  from  for  level  been measured, i t i s  (Goldspink  much o f t h e  attributed  sound g u i t e  running  the  of a b o u t 2 x  f o r movement on  substantially  the e f f i c i e n c y  e v e n i f 20  expected  velocities,  o f between 2.0%  While  the  slugs  efficiency  v e r t e b r a t e m u s c l e s which has  optimum r a t e a g a i n s t an circumstances  values  not  value  measured h e r e  higher  a human b e i n g  m u s c l e s has  i t does not  efficiency  to  While these  efficiency  be  at a  energy  Perhaps a b e t t e r comparison  muscle e f f i c i e n c y  that  5.2%.  reasonable  1973).  an  of  the  (the r a t e a t which  l a r g e s l u g s maximum v e l o c i t y  For comparison, will  the g r e a t e r  power n e e d e d t o overcome  s l o w s p e e d s i s assumed t o a p p l y efficiency  the r a t e  power t o a r r i v e  m/sec  m,  faster  f o r e x t e r n a l power can  internal  2 x 10 *  mucus r e s i s t a n c e i s 16 value  r e s i s t a n c e and  values  t o t h e measured  the  but  to can  this  264  r e a s o n a b l e assumptions can A 15  gm  thick it  slug  w i t h a one  mucus l a y e r w i l l  crawls.  If this  the  amount o f  can  be  carbohydrate). metabolic  centimeter expend  and  (1.0  The  cost  made t o a r r i v e a t an  0.1  wide f o o t , ml  of  and  a  be  3%  c a r b o h y d r a t e expended p e r  x 10~  gm  s  protein,  problem i s then t o  of producing t h i s  6.3  x 10  estimate  amount o f  expended i n p r o d u c i n g t h e  pyruvate.  This  3099.3 J/gm. can  be  cost  to  estimated  313  as  independent the  at a  of  J/kg  If  to the  m for a  may  muscle the  calculated five.  Atkinson  producing  i n a slug  producing  cost as  of  the  simply Thus t h e  by  this  represents  dominant  intrinsic  leading  to  multiplying  of  cost  during  locomotion  be  is  about  32.5%  T h u s , when  maximum  external the  the  cost  of  factor.  i s s i m i l a r to that  minimum i n t e r n a l c o s t  muscular c o n t r a c t i o n  Atkinson,  s l u g c r a w l s can  gram s l u g , and  value  at  protein  the  minimum o v e r a l l i n t e r n a l c o s t directly  the  (from  the  the  from  (1977)  work of l o c o m o t i o n , t h e  w e l l be  the  glycogen  expenditure of crawling.  external  and  2704.1 J/gm  15  This  i t i s assumed t h a t  contraction  by  of  from of  that l o s t  velocity.  mucus p r o d u c t i o n  (20%)  cost  value  replace  o v e r a l l energy  compared  of the  i s estimated  gm  - 6  polysaccharides  producing  From t h e s e e s t i m a t i o n s  glycoprotein  of  of  S i m i l a r l y the  estimated  1977).  cost  meter  meter  protein  maximum e n e r g y  s i m i l a r to the  um  the  I t seems r e a s o n a b l e t o assume t h a t  be  10  glycoprotein,  carbohydrate.  will  estimate.  mucus f o r e a c h  mucus i s assumed t o  protein  calculated  be  in  efficiency  vertebrates  muscular  work c a n  be  of e x t e r n a l  work  of e f f e c t i v e  v a r i e s from  8,5%  of  265  the at  o v e r a l l cost  at a crawling  t h e maximum c r a w l i n g  added t o t h a t  rate  of 2 x 10~  rate of 2 x 1 0  o f mucus p r o d u c t i o n  m/sec t o 26%  4  m/sec.  - 3  The c o s t ,  a c c o u n t s f o r an e s t i m a t e d  41.-0% t o 58.5% o f t h e o v e r a l l i n t e r n a l c o s t  of locomotion.  Where d o e s t h e r e s t o t t h e i n t e r n a l e n e r g y go? mentioned  above t h e r e  which r e q u i r e forces. not of  energy  As  a r e a number o f i n t e r n a l mechanisms b u t do n o t d i r e c t l y  result i n external  As shown i n C h a p t e r 2 t h e m u s c l e s o f t h e f o o t do  contract force  i n the plane of the f o o t . .  Thus f o r each  which i s d i r e c t e d a n t e r i o r l y a s a muscle will  contracts  a roughly  egual force  effective  external  necessary  t o overcome t h e r e s i s t a n c e o f t h e mucus, t h e p e d a l  work.  m u s c l e s must a l s o e x e r t  be d i r e c t e d  unit  Further,  d o r s a l l y , d o i n g no  i n addition  to the force  a f o r c e t o overcome t h e i n t e r n a l  v i s c o s i t i e s o f t h e f o o t , f o r example, t h e v i s c o u s of  pumping h a e m o c o e l i c f l u i d  Muscular energy  will during  a l s o be expended  slug's  posture  strong  probability that  working a t t h e i r  as described  locomotion. the slug's  i n C h a p t e r 3.  i n maintaining  Finally  there  muscles w i l l  and l o a d  contracting  will  vary  against  which each pedal  a s waves p a s s a l o n g  A l l of these  account f o r the remaining conclusion  t h i s chapter: is:  very  muscle i s  t h e f o o t , and  f a c t o r s and o t h e r s  contracting  like  them,  will  expenditures o f i n t e r n a l energy.  we r e t u r n t o t h e o r i g i n a l  how c o s t l y i s a d h e s i v e  costly.  i s the n o t a l l be  c o n s e q u e n t l y e a c h m u s c l e c a n n o t be c o n t i n u o u s l y  In  the  maximum e f f i c i e n c y . , The speed o f  contraction  optimally.  resistance  The e s t i m a t e d  cost  guestion of  locomotion? to a slug  The answer  of p r o d u c i n g  266  mucus a l o n e i s g r e a t e r mammal o r r e p t i l e t h i s high  cost  than the t o t a l  o f s i m i l a r weight.  o f movement  these animals,  will  high  evolutionary being  able  Finally quite  of t r a n s p o r t  sense,  while the cost  need  animal  o f movement  person.  over  which i t w a l k s .  f o r ft. c o l u m b i a n u s i s  Instead,  s l u g i s no l e s s  the high  cost  the v i s c o e l a s t i c r e s i s t a n c e  studies  grade.  This  increased  of  efficient transport  part,  o f moving u p h i l l  1973).  a large portion indeed  of t h e i r  ground t o r u n n i n g  i t s natural  habitat.  up a  that the  itself  against  be i n t e r e s t i n g t o see  i n slugs,  locomotion  lower than  as t h e  i s l e s s than the i n c r e a s e i n  the case, the e f f i c i e n c y  be c o n s i d e r a b l y  increases  to the f a c t  I t will  t h e same phenomenon! o c c u r s  mucus.  F o r example, i n  work p e r f o r m e d a s t h e a n i m a l l i f t s (see Tucker,  of t h a t  of locomotion i n t h i s  o f movement  moving on l e v e l  i s due, i n l a r g e  cost  external gravity  of the energetics  animals the e f f i c i e n c y  animal s w i t c h e s from  in  t h e advantages t o a s l u g of  would be u s e f u l and i n f o r m a t i v e .  running  may  However,  t o c o n t i n u a l l y p r o d u c e mucus, and t h e n e c e s s i t y o f  Further  is  of food.  d i c t a t e d by t h e r e q u i r e m e n t s o f t h e l o c o m o t o r y mechanism:  workinq a g a i n s t  if  over  must be w e i g h e d , i n an  Certainly a crawling  than a running  the  that  i t i s n o t b e c a u s e t h e mechanism o f l o c o m o t i o n i s  inefficient.  is  against  in a  style" of  the distance  i n search  t o adhere t o the s u r f a c e  high,  I t seems l i k e l y  f o r example, by l i m i t i n g  cost  o f movement  e f f e c t the " l i f e  which i t i s p r o f i t a b l e t o c r a w l this  cost  a n i m a l s which  time c r a w l i n g . ,  If this  figures calculated  those relevant  spend  here  t o t h e animal  267  CHAPTES NINE  Adhesion The ability  locomotion  of gastropods i s c h a r a c t e r i z e d  t o move w h i l e a d h e r i n g t o t h e  preceding  chapters i n t h i s  substratum.  study have d e a l t  mechanisms o f movement o f A., c o l u m b i a n u s been s a i d this A,  What a r e t h e a d h e s i v e  columbianus The  , and  body f o r m  how  exert  a force  slug,  t h e r e i s no  exert  a force  adhesive  on t h e a d h e s i v e solid  on t h e  apparatus.  structure  animal.  mucus c o a t e d d o r s a l e p i t h e l i u m , and s u t u r e s cannot  Given  these  be  used  l i m i t a t i o n s one  general g u a l i t a t i v e  accurate  However, w i t h a  will  grasped  not s t i c k  t h e body w a l l  to a t t a c h weights i s f o r the  slugs'  to  t o the i s so weak  t o the  most p a r t  o b s e r v a t i o n s of the  In  must be a b l e t o  which c a n be  Glues  of  difficult.  one  has  for?  r e n d e r s an  capabilities  little  operating i n  accounted  of j\. columbianus  order to determine  the  capabilities  c a n t h e y be  the  The  but very  measurement o f a d h e s i v e s t r e n g t h e x t r e m e l y  that  with  c o n c e r n i n g t h e mechanism o f a d h e s i o n  animal.  by  slug.  confined to  ability  to  adhere. If  a slug  i s p l a c e d on a s h e e t  smooth s u r f a c e , a l l o w e d t o a d h e r e , made t o d e t a c h t h e s l u g become  the  and  an  or a  similar  attempt  i s then  substratum  three facts  soon  apparent:  1. direction 2.  from  of glass  I t i s very d i f f i c u l t p e r p e n d i c u l a r t o the On  to p u l l  the animal i n a  surface.  t h e o t h e r hand i t i s r e l a t i v e l y  easy  to  slide  268  the  slug 3.  the  along  the surface.  I f , by u s i n g a f i n g e r n a i l  or s l i d i n g  the s l u g t o  e d g e . o f t h e g l a s s , one s m a l l p o r t i o n o f t h e f o o t  lifted  from  t h e s u r f a c e , t h e whole a n i m a l  can then  peeled  o f f , much a s one would p e e l o f f a p i e c e . o f  These o b s e r v a t i o n s may be a d e g u a t e l y existing  c a n be  be e a s i l y tape.  e x p l a i n e d by  t h e o r i e s o f adhesion,  THEOBY Adhesion  i s the a b i l i t y  a t t a c h e d t o each  other.  o f two o b j e c t s t o r e m a i n  T a k e , f o r example t h e s i t u a t i o n  depicted  i n F i g u r e .9.1.  Two d i s c s ,  arranged  co-axially  a gap s e p a r a t i n g them.  with  (of t h i c k n e s s y) i s t o be f i l l e d strength o f the adhesive  each  with  1 cm i n r a d i u s , a r e  an a d h e s i v e ;  may t h e n be measured by  t h e f o r c e r e q u i r e d t o s e p a r a t e t h e two d i s c s . separation 1.  o f t h e d i s c s may o c c u r  The d i s c s  9,1b),  In this  may s l i d e  case  T h i s gap  i n either  determining  The  of two ways:  past each other  (as i n F i g u r e  t h e t h i c k n e s s o f t h e a d h e s i v e , y,  remains c o n s t a n t but the x c o o r d i n a t e o f t h e d i s c s with  9.1c.  The d i s c s In t h i s case  may be p u l l e d  apart a x i a l l y  As a f i r s t fluid  disc  vary  with  as i n F i g u r e  the x coordinate of the discs  c o n s t a n t but t h e t h i c k n e s s changes  the  will  time. 2,  in  The  example, i m a g i n e  a known v i s c o s i t y ,  gap and a c t a s an a d h e s i v e .  with  remains  time.  that the discs  a r e immersed  n.  will  This fluid  In t h e case  past t h e other t h e f o r c e o f adhesion  fill  of sliding  one  c a n be c a l c u l a t e d  269  FIGURE 9.1.  The a d h e s i v e p r o p e r t i e s o f a v i s c o u s l i q u i d . A) The d i m e n s i o n s o f two d i s k s immersed i n a viscous l i q u i d . B) The f o r c e r e q u i r e d t o s l i d e t h e d i s k s r e l a t i v e t o each o t h e r i s p r o p o r t i o n a l to the a r e a and t h e s h e a r r a t e . C) The f o r c e r e q u i r e d t o s e p a r a t e t h e d i s k s a x i a l l y i s p r o p o r t i o n a l to the s e p a r a t i o n r a t e , t h e s q u a r e o f t h e a r e a , and i n v e r s e l y p r o p o r t i o n a l t o the i n i t i a l s e p a r a t i o n c u b e d .  270  F i g u r e 9.1  A  • d i s k of ra&ius R "*  0  adhesive-filled gap (viscosity = fj)  dX B F=7rR  Y"  shear rate = " [  d X  /dt]/  Y  271  quite  simply  presented  by a p p l y i n g  i n Chapter  the d e f i n i t i o n of v i s c o s i t y  4:  F = A r (dx/dt)  y-i = pi R  where F i s t h e s h e a r f o r c e at  the v e l o c i t y  the  radius.  (dx/dt),  reguired  (dx/dt) y - i  2  to s l i d e the discs  A i s the area  By d i v i d i n g t h e f o r c e  s t r e s s n e c e s s a r y t o move t h e d i s c s  of the d i s c s ,  apart  and R  by t h e d i s c a r e a t h e at a given rate  can be  calculated:  shear The  stress  stress = n  required  The  on t h e t h i c k n e s s force  required  been c a l c u l a t e d  of the adhesive  tensile  stress)  1.5 p i R* n  function a  viscous  layer.  the d i s c s a x i a l l y  has  (1973).  (dy/dt) y - 3  and x, y and R a r e a s b e f o r e . (in this  case  by d i v i d i n g by t h e a r e a .  s t r e s s = 1.5  stress reguired of the rate fluid.  thus  a r e s e p a r a t e d and  c a n be e x p r e s s e d a s a s t r e s s ,  Tensile The  apart  (1874) a s c i t e d i n C r i s p  where F i s t h e a x i a l f o r c e , Again t h i s f o r c e  a t which t h e y  to separate  by S t e f a n  F =  y~1  to s l i d e the plates  depends d i r e c t l y on t h e r a t e inversely  (dx/dt)  S  2  n  (dy/dt)  y~  to separate the plates  of separation  3  axially  as one might e x p e c t  However, t h e t e n s i l e s t r e s s i s a l s o  i s a from  highly  272  sensitive  t o t h e dimensions o f the system, i n c r e a s i n g as t h e  s q u a r e o f r a d i u s and i n v e r s e c u b e o f a d h e s i v e  thickness.  T h i s dependence on t h e d i m e n s i o n s o f t h e s y s t e m i s due t o the  geometry  discs  slide  involved i n pulling past  each other  between t h e p l a t e s .  move a p a r t .  volume o f f l u i d and  must be i n t r o d u c e d  must f l o w  i n t o t h e widening  which  fluid  must move i n f o r a g i v e n  separation,  adhesive  value  ability  may be u s e d t o p r o v i d e  separation  s t a t e o f 40 p o i s e  tensile i s evident  discs apart a x i a l values here  than to p u l l  them  apart  c a n be q u i t e l a r q e . be l i m i t e d  (Hammel a n d S c h o l l a n d e r ,  2  s  N/m  2  axially  In f a c t  t h e two  and t h a t t h e  the a x i a l  by t h e t e n s i l e  value  strength of  a t 0.2 - 1.0 x 1 0  1976) t h i s  basis the f i r s t that  N/m  s t r e s s = 6 x 10  w a t e r , w h i c h h a s been e s t i m a t e d  columbianus,  and a s s u m i n g  t h a t i t i s much e a s i e r t o s l i d e  would i n r e a l i t y  qualitative  an a v e r a g e  r a t e o f 1 mm/sec.  S h e a r s t r e s s = 400  It  an e s t i m a t e o f  o f k c o l u m b i a n u s by u s i n g  f o r mucus i n i t s f l u i d  arbitrary  through  must be t r a n s p o r t e d .  These e g u a t i o n s the  gap a s t h e  The l a r g e r t h e r a d i u s t h e g r e a t e r t h e  the t h i n n e r the l a y e r the smaller t h e "pipe"  which t h i s  an  no new f l u i d  When two  F o r t h e movement t o o c c u r  axially,however,fluid discs  the d i s c s apart.  8  N/m  explains at least  two o b s e r v a t i o n s  2  on a  made on A.  i t a d h e r e s s t r o n g l y t o g l a s s , and e x p l a i n s  why t h e f o o t o f a s l u g i s n o t l i f t e d  when t h e a n i m a l i s  273  crawling  on a n o n - p o r o u s s u r f a c e ( C h a p t e r 3 ) .  The large.  value f o r t e n s i l e I f this  application slug.  reason  the v i s c o s i t y  ability.  i s pulled  away from  The d e g r e e  fluid  understanding  the slug's foot away from  by  t o be  the substratum i s  1 x 10-s t h a t o f to adhesion.  estimates a slug* s adhesive  of o v e r e s t i m a t i o n cannot  beneath  o f the flow  when a f o r c e  t h e substratum.  be  determined  patterns of f l u i d s  i s attempting Data  concerning  to pull these  patterns are not yet a v a i l a b l e . 2.  Any f l a w s  (such a s a i r b u b b l e s  the g l a s s surface) i n t h e adhesive  concentrations strength  which w i l l  o f such  theory capable  reality lower  anchored  therefore contribute negligibly  a clear  in  f o r discs  For a slug  o f which i s r o u g h l y  without  the.foot  The  Thus when t h e d i s c s a r e  i s drawn i n .  Thus t h e S t e f a n e q u a t i o n o v e r  on  too large.  mucus t o a g l a s s p l a t e t h e most l i k e l y  drawn i n a s t h e s l u g  flow  i n tension, this  discrepancy i s two-fold:  more f l u i d  mucus and w i l l  a 20 gram  i s available f o r the  v a l u e i s o b v i o u s l y many t i m e s  i n a viscous f l u i d .  separated  i s very  kg t o d e t a c h  s  The S t e f a n e q u a t i o n i s c a l c u l a t e d  immersed  here  i t would r e q u i r e t h e  o f 1.5 x 1 0  no a c c u r a t e f i g u r e  for this  1.  air,  i s correct  strength of the slug's f o o t  calculated  fluid  o f a weight  While  adhesive  estimate  stress calculated  a fluid  layer  system.  Thus,  of unavoidable  on a d h e s i v e  will  the e f f e c t i v e  o f tremendous a d h e s i v e  t h e presence  limit  lower  i n t h e mucus o r d u s t  strength;  form  stress  adhesive  w h i l e t h e system i s strength, i n  flaws w i l l  impose  -  a much  The t h e o r y o f s t r e s s  274  concentrations  will  be d i s c u s s e d  more f u l l y  later  in this  chapter. Until the of  t h e e f f e c t s o f t h e s e two f a c t o r s a r e q u a n t i f i e d  Stefan  equation  can only  the adhesive a b i l i t y  provide  high  fluid  beneath  adhesive  be  to the Stefan  t h e high  to the r e l a t i v e l y  mucus i n i t s o l i d 8 . 1c.  form?  by a s o l i d  strain  3  N/m  2  .  solid  mucus  here, i t w i l l  i s attributable  (coupled  with t h e  The l o w e r t h e r a t e o f Thus a s m a l l  of time  will  fact  How  stress  result i n a large  leads  t o another  aspect  Return  for -  t o t h e s i t u a t i o n shown i n  c a s e , h o w e v e r , t h e two d i s c s a r e h e l d  mucus l a y e r  10 um t h i c k and a f o r c e  t h e d i s c s a t 1 mm/second  r a t e o f 100/sec) .  3 times that strain  (an i n i t i a l  At t h i s r a t e the y i e l d mucus i n s h e a r i s a b o u t 1 x  The s t i f f n e s s o f a m a t e r i a l  (at t h i s  the presence o f  does t h e s i t u a t i o n d i f f e r  columbianus pedal  approximately  cited  of s e p a r a t i o n  This  form.  In t h i s  s t r e s s o f A. 10  and remembering t h e  d i s c u s s i o n h a s assumed  applied t o separate tensile  the p o t e n t i a l f o r a  system o f s l u g s .  mucus i n i t s f l u i d  together  period  o f the d i s c s .  f a r this  Figure  rate  the lower the s t r e s s .  the adhesive So  presence o f a  s t r e s s f i g u r e obtained  high  over a long  separation of  equation  t h i n l a y e r o f mucus).  separation applied  provides  used t o c a l c u l a t e t h e v a l u e s  seen t h a t  extremely  the f o o t  the simple  I ti s  strength.  Returning assumptions  rough i n d i c a t i o n  o f the s l u g ' s f o o t .  r e a s o n a b l y c l e a r , however, t h a t viscous  a very  i n tension i s  i n shear so the y i e l d rate)  i s about  strength of  3 x 10  3  N/m  2  ; a  275  value  much l o w e r t h a n t h a t c a l c u l a t e d by t h e S t e f a n  eguation.  However t h i s i s o n l y  change t h e s o l i d as  a fluid  Stefan solid in  apply.  Once t h e mucus b e h a v e s  resisting  of i t s u l t i m a t e a d h e s i v e  r a p i d deformation  o f the adhesive solidity  resisting  the  Thus i f t h e s l u g i s a d h e r i n g  mucus, t h e p r o b l e m  The in  mucus i n t o a f l u i d .  t h e a r g u m e n t s o u t l i n e d above c o n c e r n i n g  equation  question  the s t r e s s r e q u i r e d to  returns  strength  i n t h e end t o t h e  strength of a viscous  fluid.  o f mucus i s , however, an i m p o r t a n t  smaller  f o r c e s on t h e t i m e s c a l e  1 second)  imposed d u r i n g  locomotion  discussed  i n Chapter  The s o l i d i t y  7.  with  factor  (approximately  a s has been  thoroughly  o f mucus w i l l  also  allow  i t t o f u n c t i o n as an e f f e c t i v e a d h e s i v e  force  o f g r a v i t y on t h e t i m e s c a l e o f m i n u t e s and h o u r s .  this  time  scale a f l u i d  properties adhesive  adhesive  a g a i n s t the  would be i n e f f e c t i v e .  o f mucus and t h e mucus  On The  e f f e c t i v e n e s s a s an  1  a t l a r g e t i m e s have a l r e a d y  been d i s c u s s e d (see  Chapter 4 ) . In l i g h t  of this  assume t h a t p e d a l this all  d i s c u s s i o n i t seems r e a s o n a b l e  mucus f o r m s an e f f e c t i v e  i s s o how d o e s . t h e s l u g e v e r o f i t s f o o t from  in  order  strong  to reach  adhesive  from a p i e c e The  manage t o d e t a c h  the substratum?  are o f t e n seen t o l i f t  the a n t e r i o r  a leaf.  adhesive.  When f e e d i n g ,  to If  part or slugs  1/4 t o 1/3 o f t h e body  Also, i f pedal  mucus i s s u c h a  how i s i t p o s s i b l e t o s o e a s i l y  peel a slug  of glass?  answer t o t h e s e  stress concentrations  questions  i n t h e mucus.  lies  i n the formation  of  Take f o r example t h e  276  situation placed  d e p i c t e d i n F i g u r e 9.2.  on a b l o c k  of material.  can be t r a c e d , m o l e c u l e  m a t e r i a l t o an a r e a distribution  stress i s  I t c a n be i m a g i n e d  f o r c e a c t i n g on one i n f i n i t e s i m a l block  A tensile  area  on t h e t o p o f t h e  t o molecule,  through  on t h e b o t t o m o f t h e b l o c k .  force i s evenly  distributed  surfaces  of the block  parallel  and e v e n l y  uniformly  throughout  introduced changed. can  into  over  spaced  and t h e f o r c e w i l l  the m a t e r i a l .  Now  be p a s s e d  directly  all  t h e f o r c e t h a t would the crack  and i n d o i n g normally  i s concentrated  i f a crack i s  i s expressed  (1 +  must c u r v e  (21/w) )  adhesive  the area  t i p c a n be q u i t e l a r g e  (Wainright  e t a l , 1976; G o r d o n , 1972)  t i p , S i s the overall  and 1 and w a r e t h e d i m e n s i o n s o f t h e c r a c k 9.2b.  Thus  by  where S t i s t h e s t r e s s a t t h e c r a c k  Figure  around  i n the area a t the crack t i p .  and  slug's  spread  be a p p l i e d a r o u n d  increase i n s t r e s s a t the crack  in  be  be  so squeeze t o g e t h e r .  The  stress,  will  t o t h e m a t e r i a l below t h e  Instead the stress t r a j e c t o r i e s  = S  If  one edge o f t h e m a t e r i a l t h e s i t u a t i o n i s  end o f t h e c r a c k  St  9.2a.  t h e t o p and bottom  the s t r e s s t r a j e c t o r i e s  the  of  Thus t h e  The f o r c e a c t i n g on t h e m a t e r i a l above t h e c r a c k  no l o n g e r  crack.  the  o f f o r c e s w i t h i n t h e b l o c k c a n b e . v i s u a l i z e d as  a s e t o f s t r e s s t r a j e c t o r i e s a s shown i n F i g u r e the  that the  This equation  s t r u c t u r e of a s l u g  foot provides  a ready  as shown  c a n be a p p l i e d d i r e c t l y t o  (Figure 9.2c). made c r a c k ,.  The edge o f t h e As a  reasonable  277  FIGOBE 9.2..  Stress concentrations. A) I n a u n i f o r m l y l o a d e d sample t h e . s t r e s s t r a j e c t o r i e s a r e u n i f o r m l y spaced.„ B) A c r a c k c a u s e s t h e t r a j e c t o r e i e s t o converge, forming a s t r e s s c o n c e n t r a t i o n . C) The edge o f a s l u g ' s f o o t w i l l a c t a s a crack, causing a stress concentration.  fttttttfftt NOI1VH1N30NO0 . SS3UJLS  n u u i i i i !  a  ttttttttttt  S3IU0103rVbl  SS3H1S  UUUUHl 2*6  9Jn5ij  279  example s e t c a n n o t be and  the  any  l a r g e r t h a n the  i s likely  t o be  conservatively  Any  stress  at  be  will  be  In  this  manner t h e  force  at  S/St  =  easier  to  the  to  i t s foot  thickness  foot 41  The of  width  mucus  concentration  edge by  the  the  contraction  crack t i p . w i l l grow  applying  edge, can  the  larger  a relatively  detach i t s foot  of  As  detach a d d i t i o n a l areas of the by  w  41  concentrations  slug,  layer  f o r example s e t  stress  times at  crack  the  smaller,  (1 + 200/5) =  stress  it  100um.  Thus t h e  magnified  extends the  at  considerably  5 um.  applied  muscle w i l l crack  "crack length"  and  foot. small  from  the  substratum. In  order  edge o f t h e edges.  p u l l s the  and of  foot  the  the  and  slug  little  the  take  slug  pull  force  foot  the  i s easily  presence  of  third  crack present at  the  muscles a t t a c h e d to  the  zoologist  piece  center  of  directly  propagated.  up  and  pulled  can  be  stress concentration noted  at  he  the at  the  to  usually  foot  case  fringes  I f however an  upon a  applied  p e e l e d o f f as  observation  glass  to the  not  force  attempts  o f i t s back i n w h i c h  are  i s pried  a large  slug  inquisitive  i s applied  edge c r a c k s  the  contracts  i t off a  from the  created,  the  advantage of  However when an  grasp a slug  very  to  large  to that crack  crack  crack  edge is  area  propagates.  crack t i p s beginning of  can  and This  explain  this  chapter. As  already  mentioned the  existence  of  other cracks  in  280  the  mucus l a y e r ,  such  as a i r b u b b l e s t r a p p e d a s t h e s l u g  moves, c a v i t i e s i n t h e s u b s t r a t u m , o r d i r t form  stress concentrations.  particles will  The p r e s e n c e o f a number o f  t h e s e s t r e s s c o n c e n t r a t i o n s would l o w e r t h e a d h e s i v e strength  o f t h e mucus l a y e r  theoretical  t o a v a l u e w e l l below i t s  maximum.  A TEST As  m e n t i o n e d above t h e s t r u c t u r e  not  lend  one  case,  itself  of a slug's  t o t h e measurement o f a d h e s i v e  however, i t proved p o s s i b l e  adhesive strength  of  body  does  strength.  In  t o measure t h e  slugs.  I f a mass i s swung a t t h e end o f a s t r i n g t h e p a t h t a k e n by t h e mass i s t h e r e s u l t o f two f a c t o r s : 1. the  The mass i s t r a v e l l i n g a t a c e r t a i n v e l o c i t y .  s t r i n g were n o t p r e s e n t  straight 2.  t h e mass would  If  travel i n a  line. I n o r d e r f o r t h e mass t o t r a v e l i n a c i r c u l a r p a t h  a constant r a d i a l acceleration  must be a p p l i e d  This  to the " c e n t r i f i g a l  radial acceleration  leads  t o t h e mass. force",  F.  F = ma  where m i s mass and a i s a c c e l e r a t i o n . calculated  as  a =  w r z  The a c c e l e r a t i o n i s  281  where w i s t h e its  circular  angular v e l o c i t y of  p a t h and  r i s the  the  radius  mass as of the  i t travels in  circle.  Thus  F = mw r 2  If the  a slug  disk  exerted  on  i s then r o t a t e d , on  relative  the  slug.  to the  by  the  is  rotated  solid  foot  area,  disk  and  disk  the  allowed to  a c e n t r i f u g a l force as t h e  slug  adhere, will  remains  and  be stationary  t h i s c e n t r i f u g a l f o r c e must be r e s i s t e d mucus b e n e a t h t h e  disk.  speed, the  Thus i f the  radius  angular  the  a disk,  long  sufficient  the  the  known  As  adhesive  at  o u t w a r d s on  all  i s placed  at  slug.  When t h e  slug w i l l  be  mass o f t h e  which t h e  slug  velocity reguired  adhesive shear strength  forced  s l u g and  i s placed to  disk  on  its  the  move;the s l u g  of the  mucus can  are be  calculated. This  experiment  shown i n F i g u r e  9.3  columbianus  (0.18  then  on  placed  adhere.,  The  Servodyne  was  c a r r i e d out  . . The  - 0.26  the  disk  grams)  disk was  motor, and  foot area  at  of  by  rotation  was  increased  the  was  spun o u t w a r d s t o t h e then  stress calculated. each of f i v e was  780  (+-  slugs 335)  until  read  the  slug's  o f f the  Three t o f i v e and  N/m  2  the .  and  The  not  yield  slug  allowed  to  matched  rate.of  adhesive yielded  stroboscope trials  the  Master  retaining wall.  average  i t was  A.  of r e v o l u t i o n  with a c a l i b r a t e d stroboscope.  o f r o t a t i o n was  a small  a Cole-Parmer  frequency  apparatus  measured and  manually  slug  the  a measured r a d i u s  rotated the  was  using  and  The the  and  rate yield  were c a r r i e d out stress calculated  possible  with  this  on  282  FIGURE 9,3.  A device f o r measuring the shear s t r e n g t h of A r i o l i m a x c o l u m b i a n u s p e d a l mucus u n d e r t h e slug. The e l e c t r i c motor s p i n s t h e d i s k a t an a n g u l a r v e l o c i t y , W, t h a t i s measured w i t h t h e stroboscope. The f o r c e a c t i n g t o s l i d e t h e s l u g r a d i a l l y o u t w a r d s i s MW R, where w i s t h e s l u g ' s mass, and R i s t h e r a d i u s . . I n t h i s manner t h e f o r c e (and t h e s t r e s s ) a t w h i c h t h e mucus y i e l d s and t h e s l u g b e g i n s t o s l i d e , can be measured. 2  283  Figure  9.3  k STROBE Slug M a s s = M Foot Area = A  FORCE = MW R = F STRESS = F/A  RETAINING WALL  SLUG  j^Z  / R  DISK  ^f;w~™>:^ji~i^aKi.,"r,!rf,itiwit^ ,  ELECTRIC MOTOR  SPEED CONTROL  /  284  apparatus  t o measure t h e s h e a r  rate:incurred  centrifugation.  However,  increased  the c e n t r i f u g a l f o r c e  slowly  number o f s e c o n d s . quite  low.  s i n c e the rate  Consequently  In Chapter  by  of r o t a t i o n  was a p p l i e d  was  over a  t h e s h e a r r a t e s h o u l d be  4 the y i e l d  s t r e s s of A  columbianus  p e d a l mucus a t a s h e a r r a t e o f a p p r o x i m a t e l y 5 / s e c o n d ( t h e l o w e s t measured) of  was 320  t h i s experiment  quite closely..  N/m  2  .  the predicted  Thus q i v e n t h e c r u d e  nature  and measured v a l u e s match  285  CHAPTER TEN•  i  Conclusions This  s t u d y has  examined i n c o n s i d e r a b l e d e t a i l  mechanism o f a d h e s i v e slug, here  A r i o l i m a x columbianus unique  account  t o t h i s one  useful  to r e v i e w  locomotion.  Any  have two  movement: that  .  the  gastropod  types  friction  with t h i s  fundamental  utilizing  The  in resisted  The  interaction  of the s t a t i o n a r y  substratum  beneath  stationary  portions of the  than the  them.  i s brought  Thus, i f the foot  I f the  about  of forward  i n any  resistance  slide  which  about  by  and  are -  with  the  of the  backwards i s  p o r t i o n s of  will  this  an  resistance  moving  must  the  be a b l e t o  backwards  resistances  o f t h r e e ways: t o movement p e r u n i t  same f o r a l l p a r t s o f t h e f o o t , s m a l l e r a r e a be  areas  t o overcome  t o b e i n g moved  t o b e i n g moved f o r w a r d s t h e a n i m a l  be b r o u g h t  2.  p o r t i o n s o f the f o o t  r e s i s t a n c e o f the  This inequality  sole during  as t h e y  by t h e a r e a s o f t h e f o o t  This resistance  1.  p e d a l waves  the f o o t  reguired  be  f o r adhesive  muscular  friction  force  stationary.  can  question i t w i l l  moving segments of t h e f o o t  some amount o f s l i d i n g  to  gastropods?  requirements  o f a r e a s p r e s e n t on  a c r o s s t h e substratum..  crawl.  i t be g e n e r a l i z e d  1. a r e a s t h a t a r e moving f o r w a r d , and  encounter  foot  s p e c i e s of  I s the mechainism d e s c r i b e d  s p e c i e s o r can  directly  are s t a t i o n a r y .  greater  i n one  f o r the locomotion of other types of  Before dealing  will  locomotion found  the  moved f o r w a r d s  area i s the  i t i s necessary that than  remains  a  stationary.  286  2. from  The r e s i s t a n c e t o movement  one p o r t i o n  per u n i t area can vary  of t h e f o o t t o the next  moving a r e a s o f t h e f o o t ,  taken  r e s i s t a n c e than the s t a t i o n a r y  such t h a t t h e  a s a whole, show portions.  In t h i s  moving segments o f t h e f o o t c o u l d have a l a r g e r the s t a t i o n a r y movement  was s u f f i c i e n t l y  3.  1.  Both  It  segments p r o v i d e d t h a t  and 2.  than  t h e r e s i s t a n c e to  study t h a t  of t h i s t h i r d c a s e .  A. c o l u m b i a n u s  ) start  are thus n e c e s s a r i l y  area  areas.  c o u l d be a c t i n g s i m u l t a n e o u s l y .  a good example  the f o o t .  case the  s m a l l e r under t h e moving  h a s been shown i n t h i s  compressing  less  A., c o l u m b i a n u s i s  Direct  waves ( a s used  a t the p o s t e r i o r  end o f t h e a n i m a l by  Areas o f forward  movement  ( t h e waves)  smaller than the s t a t i o n a r y areas.  addition,  t h e p h y s i c a l p r o p e r t i e s o f t h e p e d a l mucus a r e  such t h a t  the forward  smaller than effective question  sliding  resistance  t h e backwards r e s i s t a n c e .  locomotory  system.  i s considerably The r e s u l t  or a  mechanism, be o p e r a t i n g i n o t h e r g a s t r o p o d  locomotory  Direct  types  Monotaxic  The  to  similar species?  The  be d i s c u s s e d a c c o r d i n g t o t h e i r  Waves  prominent  members o f t h i s  group  are the t e r r e s t r i a l  As r e g a r d s t h e mechanism o f l o c o m o t i o n  vast m a j o r i t y of these are very s i m i l a r A columbianus.  model p r o p o s e d  i s an  (as d e f i n e d i n C h a p t e r 3 ) .  s l u g s and s n a i l s . the  In  We now r e t u r n t o t h e o r i g i n a l  of t h i s chapter; could t h i s ,  various species w i l l  bu  here  Consequently,  i n a l l respects  I s e e no r e a s o n why t h e  f o r A_. c o l u m b i a n u s  cannot  be  applied  287  directly  Direct  t o these other  Ditaxic  Direct  species.  Waves  ditaxic  waves  (see F i g u r e 10.1b) a r e f o u n d i n  relatively  few s p e c i e s o f g a s t r o p o d s s u c h  Haliotidae  and some s p e c i e s of T h a i s .  of d i t a x i c  direct  tuberculata,  and t h i s  for  discussion.  As w i t h d i r c t  areas o f forward  motion  to the stationary without  The b e s t  waves i s t h a t o f L i s s m a n  Haliotis this  as t h e a b a l o n e s  (1945a) u s i n g  s t u d y i s used a s t h e b a s i s  i n Haliotis  a r e a s so t h a t  a variation  descrption  monotaxic  waves, t h e  a r e compressed  locomotion could  in frictional  a r e a s o f t h e f o o t , , The a b a l o n e  resistance  does,  relative  occur  under  clearly  be s e e n t o l i f t  process i s f a c i l i t a t e d foot.  the foot along  d u r i n g the passage  t h e edges o f t h e f o o t  under  and a r e t h u s d i r e c t l y  stationary  portions  I t seems l i k e l y  the l i f t e d  less resistance  portion  columbianus  .  specialized  moves i n contact  that  t h e water  of the f o o t  will  t o movement t h a n t h e mucus u n d e r t h e  of the foot.  of the abalone, animals u t i l i z i n g employ a d i f f e r e n t  This  o f t h e waves on t h e  and e n c l o s e d by a r i m , t h e a b a l o n e ' s wave  being sheared  for  o f a wave.  where t h e waves a r e i n t h e c e n t e r o f  with the surrounding f l u i d .  offer  under t h e  I n these animals t h e f o o t can  by t h e p o s i t i o n  U n l i k e the s l u g ,  different  however, e x h i b i t a  mechanism f o r l o w e r i n g t h e r e s i s t a n c e t o movement moving segments o f t h e f o o t .  even  Thus, a t l e a s t  i n the case  direct  waves  mechanism t h a n t h a t  The end r e s u l t  ditaxic  proposed  f o rA  i s s i m i l a r but the requirement  mucus p r o p e r t i e s i s a b s e n t .  288  FIGURE  10.1.  A diagrammatic r e p r e s e n t a t i o n of t h e f o u r r e g u l a r f o r m s o f p e d a l waves. The s t i p p l e d a r e a s r e p r e s e n t t h o s e a r e a s on t h e f o o t which a r e moving, and t h e a r r o w s i n d i c a t e t h e d i r e c t i o n o f movement.  289  D.  RETROGRADE  RETROGRADE  DITAXIC  MONOTAXIC  Patella vulgata  Neritina recli vata  290  Retrograde  Ditaxic  Retrograde  ditaxic  most common f o r m gastropods  Waves waves  (see F i g u r e 10.1c) a r e t h e  o f p e d a l wave f o u n d  (Miller,  1974b).  Jones  among  prosobranch  and Truman  (1970) have  s t u d i e d t h e l o c o m o t i o n of the l i m p e t P a t e l l a their  study  Retrograde at  will  waves, i n c o n t r a s t  to direct  one t h i r d  larger  that  length or greater  t h e a r e a of t h e s e  .  is  d u r i n g movement and t h a t  as  and Trueman  as w i t h a b a l o n e s .  Trueman  o f the f o o t  lifiting  their  situation inflexible  surface.  3 that  a mechanism  that  to the  the foot  the space f i l l e d  apparent.  with  J o n e s and  plate..  I t has  measurements o f f o o t  n o t conform  i s c r a w l i n g over  I t i s highly  (and p r e s u m a b l y  foot  p o r t i o n s of the  c o n c l u s i o n s on measurements made  manner may  when an a n i m a l  a  to the solid,  probable, then,  other prosobranchs)  that  do n o t  lift  d u r i n g l o c o m o t i o n and must t h e r e f o r e . r e l y  properties of their  It  waves o f e x t e n s i o n  over a h o l e i n a g l a s s  made i n t h i s  1974a).  O n l i k e a b a l o n e s , however, t h e  been p o i n t e d o u t i n C h a p t e r  their  large  (1970) p r o p o s e  i s not v i s u a l l y  (1970) b a s e d  a limpet crawled  limpets  (Miller,  resistance relative  backwards lifted  Jones  sliding  posteriorly  wave i s t y p i c a l l y  t h e s e a n i m a l s must p o s s e s s  lowering the forward  lifting  passed  than t h e area o f the s t a t i o n a r y  Consequently  water,  waves, a r e i n i t i a t e d  as the f o o t i s extended  The l e n g t h o f a s i n g l e  of the foot  seems l i k e l y  foot.  discussion.  The wave o f e x t e n s i o n i s t h e n  along the f o o t .  for  the basis of t h i s  t h e a n t e r i o r end o f t h e f o o t  forwards.  is  form  v u l g a t a , and  p e d a l mucus t o a f f e c t  movement.  on t h e The  291  resolution  of t h i s  question awaits  Retrograde  Monotaxic  Waves  While r e t r o g r a d e gastropods little  (Miller,  attention.  of Gainey ditaxic  typically  waves a r e  1974a). foot. the  one  As  have r e c e i v e d  most e x t e n s i v e  (see F i g u r e of the  present  on  reclivata  f o o t i s l e s s than  Neratina  o n l y one  area of  t h a t of the  s t a t i o n a r y area  mucus.  concerning  To  this  my  time  the  movinq  one  on  the  segment  o f t h i s type  advantageous.  As  r e s i s t a n c e c o u l d be of the  f o o t or the  knowledge no  problem.  of  with  no  need  other  brought  the  wave  about  p r o p e r t i e s of  measurements have  Thus, u n t i l  It  o f wave.  moving a r e a ,  moving a r e a  the  been made  more d a t a h a v e been  p o s s i b l e existence i n these  or  (Miller,  the  mechanism  s i m i l a r t o t h a t i n A., c o l u m b i a n u s c a n n o t  Summary  are  and  gathered,  determined.  with  A reduction i n r e s i s t a n c e beneath  waves would however be forms, a lowering of  one  exceeds the  i n r e s i s t a n c e beneath the  necessarily exist.  pedal  As  s t a t i o n a r y segments.  indeed  a lifting  i s that  .  wave i s p r e s e n t  If  by  to date  E a c h wave i s  t h e f o o t a t any  n o t known whether t h i s i s t y p i c a l  either  relatively  reclivata  10.Id).  is  reduction  study  common i n  f o o t l e n g t h or g r e a t e r  a consequence the  the  fairly  waves, m o n o t a x i c r e t r o g r a d e . w a v e s  third  I n N.  waves a r e  1974b) t h e y  (1976) d e a l i n g w i t h  waves o f e x t e n s i o n  two  monotaxic  The  retrograde  f u r t h e r study.  animals  of be  a  292  In proposed  summary, t h e mechanism in this  of adhesive.locomotion  study i s l i k e l y t o apply t o t e r r e s t r i a l  s l u g s and s n a i l s .  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