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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 Un 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 i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ZOOLOGY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1979 O Mark William 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 degree a t the U n i v e r s i t y o f 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 a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r 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 w r i t t e n p e r m i s s i o n . 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 s n a i l s move using a s i n g l e appendage - the f o o t . For many gastropods the power of locomotion i s provided by muscular waves moving along the v e n t r a l s u r f a c e of the f o o t , the f o r c e of these waves being coupled to the substratum by a t h i n l a y e r of mucus. T h i s mucus a c t s as a glue which causes the animal t o adhere t o the s u r f a c e upon which i t c r a w l s , but nonetheless a l l o w s forward movement of the animal. In f u l f i l l i n g t h i s f u n c t i o n the mucus must show some unusual p r o p e r t i e s . This study examines the chemical and p h y s i c a l p r o p e r t i e s of the pedal mucus of the pulmonate s l u g A r i o l i m a x columbianus , and r e l a t e s t h e s e . p r o p e r t i e s to the r o l e of mucus i n locomotion. The pedal mucus of \A. columbianus i s a g e l c o n s i s t i n g of 96-97% water r e s t r a i n e d by a network formed of a high molecular weight g l y c o p r o t e i n . The g l y c o p r o t e i n i s a p o l y e l e c t r o l y t e ; the charged nature of the molecule causing i t to s w e l l i n s o l u t i o n s of low i o n i c s t r e n g t h s . T h i s s w e l l i n g accounts f o r the g l y c o p r o t e i n ' s a b i l i t y t o i n f l u e n c e a l a r g e volume of water. The g e l network i s s t a b i l i z e d both by d i s u l f i d e bonds between p r o t e i n m o i e t i e s , and by "weak bonds" (hydrophobic i n t e r a c t i o n s and/or hydrogen bonds) between g l y c o p r o t e i n molecules. The p h y s i c a l p r o p e r t i e s of the pedal mucus were measured i n shear. At shear r a t i o s of l e s s than 5, and over short time p e r i o d s , the g e l shows the p r o p e r t i e s of a v i s c o e l a s t i c s o l i d . G» i s 100 N/m2 and tan d i s 0.008; both are v i r t u a l l y constant from 0.1 - 100 Hz. Over long p e r i o d s of time the g e l s t r e s s r e l a x e s without r e a c h i n g e q u i l i b r i u m , i n d i c a t i n g t h a t the weak bonds of the g e l network allow the network t o flow under s t r e s s . At a shear r a t i o of about 5 the g e l network y i e l d s as weak bonds are broken, and with f u r t h e r deformation the mucus a c t s as a v i s c o u s f l u i d with a v i s c o s i t y of about 50 po i s e . I f t h i s f l u i d i s allowed to stand unstressed, the gel network w i l l " h e a l " as the weak bonds reform.. T h i s h e a l i n g process begins i n much l e s s than a second and, as a r e s u l t , the mucus again a c t s as a s o l i d . T h i s " y i e l d - h e a l " c y c l e can be repeated numerous times. These p h y s i c a l p r o p e r t i e s are i d e a l l y s u i t e d t o gastropod locomotion. Under the moving p o r t i o n s of the f o o t (the muscular waves and the rim) the mucus i s present i n the. form of a v i s c o u s l i g u i d , l u b r i c a t i n g forward motion. Under the s t a t i o n a r y p a r t s of the f o o t (the interwaves) the mucus has "healed" and, as a s o l i d , s e r v e s as an e f f e c t i v e adhesive. The mucus thus a c t s as a m a t e r i a l r a t c h e t a l l o w i n g f o r e f f e c t i v e adhesive locomotion. The p r e c i s e movements of the f o o t of columbianus were measured using a video tape r e c o r d e r . The t h i c k n e s s of the mucus l a y e r was measured by g u i c k l y f r e e z i n g , and subsequently s e c t i o n i n g , c r a w l i n g s l u g s . These d a t a , along with the measured p h y s i c a l p r o p e r t i e s of pedal mucus, allow f o r the c o n s t r u c t i o n of a model p r e d i c t i n g the f o r c e s o p e r a t i n g under a c r a w l i n g s l u g . T h i s model has been t e s t e d by a c t u a l l y measuring these f o r c e s , and has proven a c c u r a t e . The i n c r e a s e d oxygen consumption a s s o c i a t e d with locomotion i n JU, columbianus was measured as a f u n c t i o n of c r a w l i n g speed . From these data the c o s t and e f f i c i e n c y of adhesive locomotion have heen c a l c u l a t e d . Movement of &. columbianus i s about ten times as c o s t l y as f o r a mouse of the same weight. T h i s high c o s t i s l a r g e l y due to the c o s t of producing the pedal mucus. While the c o s t of adhesive locomotion i s high, the e f f i c i e n c y of locomotion i s roughly e q u a l t o t h a t of a running man. I t i s very l i k e l y t h a t the measurements and p r e d i c t i o n s made i n t h i s study w i l l apply t o a l l t e r r e s t r i a l pulmonates; and i t i s p o s s i b l e t h a t they w i l l apply to other gastropods as w e l l . TABLE OF CONTENTS Abstract i Table of Contents i v L i s t of Tables.. v i i i L i s t of Figures i x Acknowledgements x i i i Chapter 1: Introduction 1 Chapter 2: Slug Morphology 4 The Foot • • • • 1 0 Chapter 3: Introduction 18 Ariolimax columbianus Locomotory Kinematics 19 Mechanism f or Slug Kinematics 48 Chapter 4: Ph y s i c a l Properties 54 E l a s t i c i t y 54 Molecular Basis f o r E l a s t i c i t y 58 V i s c o s i t y 63 Molecular Basis f o r V i s c o s i t y and Flow 66 V i s c o e l a s t i c Materials 67 Stress-Shear Ratio Tests 70 Stress-Relaxation Tests 71 Dynamic Testing 76 Testing Apparatus and Procedures 79 Dynamic te s t i n g apparatus 79 The cone and p l a t e apparatus 86 C o l l e c t i o n of pedal mucus 89 v i Chapter 4: Physical Properties (continued) Physical Properties of Ariolimax columbianus mucus 91 at Low Shear Ratios. Stress-shear ratio tests 91 Stress-relaxation tests 94 Dynamic tests 99 Physical Properties of Ariolimax columbianus mucus 102 at High Shear Ratios. Stress-shear ratio tests 102 Fiber Formation 120 Chapter 5: Chemical Composition 126 What is Mucus? 126 Mucus Collection 127 Analysis 127 Water content 127 Protein 128 Polysaccharides 131 Uronic acids 131 Amino sugars 131 Si a l i c acid 133 Neutral sugars 133 Sulphate sugars *...134 Salts 134 Comparison to Other Mucins 138 Vertebrate mucins.. 138 Invertebrate mucins... .138 v i i Chapter 6: Physical Chemistry 144 Polyelectrolytes 145 Tests.... 149 Network swelling 149 Solubility tests 151 Intrinsic viscosity 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 Chapter 7: 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 Vertical tests 222 Pressures Beneath Pedal Waves ..230 Summary and Conclusions 235 v i i i Chapter 8: Cost of Locomotion .242 Review of Terms 242 Apparatus and Experimental Protocol 245 Results 251 Chapter 9: Adhesion 267 Theory .' 268 A Test 280 Chapter 10: Conclusions 285 Direct Monotaxic Waves 286 Direct Ditaxic Waves 287 Retrograde Ditaxic Waves 290 Retrograde Monotaxic Waves 291 Summary 291 Literature Cited 293 i x LIST OF TABLES Table 5.1: Amino acid composition... .130 Table 5.2: Chemical composition ..135 Table 5.3: Carbohydrate composition of various 140 proteoglycans and glycoproteins. Table 6.1: Hydration of pedal mucus 152 Table 6.2: S o l u b i l i t y of pedal mucus 156 Table 6.3: I n t r i n s i c v i s c o s i t i e s of various macromolecules...171 Table 7.1: Predictions of the locomotion model 206 Table 7.2: Measured and predicted forces of Ariolimax... 223 columbianus locomotion. X LIST OF FIGURES Figure 2.1: Generalized gross morphology of the t e r r e s t r i a l slug......6 Figure 2.2: Gross morphology of Ariolimax columbianus 9 Figure 2.3: Cross section of Ariolimax columbianus 13 Figure 3.1: Schematic representation of the v e n t r a l surface of 23 the foot of an Ariolimax columbianus. Figure 3.2: Diagrammatic explanation of the mechanism by which a 25 wave of compression can r e s u l t i n movement. Figure 3.3: Diagrammatic explanation of the mechanism by which 30 several waves of compression can e x i s t on one foot and r e s u l t i n movement. Figure 3.4: Relation between speed of the pedal wave and o v e r a l l 33 speed of the slug. Figure 3.5: V e l o c i t y and distance p r o f i l e s of an average pedal wave..38 Figure 3.6: Forward movement of the rims and the alternate movement..41 and non-movement of the center of the foot r e s u l t i n the same average forward v e l o c i t y . Plate 3.1: Micrograph of the pedal epithelium of a crawling slug....43 Figure 3.7: Problems with l i f t e d pedal waves 46 Figure 3.8: Model f or the movement of the foot of Ariolimax 50 columbianus. Figure 4.1: Properties of e l a s t i c s o l i d s 56 Figure 4.2: Molecular basis of rubber e l a s t i c i t y 62 Figure 4.3: Properties of viscous l i q u i d s 65 Figure 4.4: Springs and dashpots 69 Figure 4.5: Properties of v i s c o e l a s t i c materials 73 Figure 4.6: Representative stress r e l a x a t i o n curves 75 x i Figure 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 deformations 78 Figure 4.8: Diagram of the forced o s c i l l a t i o n dynamic t e s t i n g '82 apparatus. Figure 4.9: Construction drawing of the dynamic t e s t i n g apparatus.... 84 Figure 4.10: Cone and plate apparatus 88 Figure 4.11: Stress/shear r a t i o curve f o r Ariolimax columbianus 93 at a low shear r a t i o . Figure 4.12: Stress/shear r a t i o curve f o r Ariolimax columbianus 96 at a moderate shear r a t i o . Figure 4.13: Stress 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 of pedal mucus 98 Figure 4.14: Dynamic test r e s u l t s 101 Figure 4.15: C h a r a c t e r i s t i c s of pedal mucus at high shear r a t i o s 105 Figure 4.16: Plot of y i e l d stress and flow stress versus shear ......107 rate f o r pedal mucus. Figure 4.17: Ratio of y i e l d stress to flow stress I l l Figure 4.18: I n i t i a l y i e l d stress a f t e r a sample has been l e f t 115 unstressed f o r a period of time i s greater than subsequent y i e l d stresses a f t e r only short time heal periods. Figure 4.19: Testing procedure used to determine the e f f e c t on 115 the recovery of s o l i d i t y . Figure 4.20: Plot of r e l a x a t i o n time versus heal time f o r pedal 117 mucus. Figure 4.21: E f f e c t s of various s a l t s on the increase i n shear 119 modulus. Figure 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 Figure 6.2: V i s c o s i t y . . . . . 160 Figure 6.3: I n t r i n s i c v i s c o s i t y of pedal mucus shows the 167 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 . Figure 6.4: Molecular weight dependence on i n t r i n s i c v i s c o s i t y 169 Figure 6.5: Separation of pedal 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 . Figure 6.6: Incompletely dissolved pedal mucus shows a t h i r d 183 f r a c t i o n when separated .on Sepharose 4-BC1. Figure 6.7: Carbohydrate boding to serine and/or threonine 187 Figure 6.8: Model for the structure of Ariolimax columbianus 191 pedal mucus. Figure 7.1: Possible forces acting on gastropod locomotion 195 Figure 7.2: Forces present under a moving slug 200 Figure 7.3: Stress p r o f i l e beneath a pedal wave ....205 Figure 7.4: P l o t of y i e l d stress and flow stress versus shear rate..209 for Ariolimax columbianus pedal mucus. Figure 7.5: Interaction of gravity with the forces of locomotion.... 213 Figure 7.6: Apparatus f o r measuring the forces beneath a crawling... 218 slug. Figure 7.7: Record of forces measured beneath a crawling slug 225 Figure 7.8: P l o t of weight predicted from the model versus actual...228 weight for a l l v e r t i c a l crawls. Figure 7.9: Forces measured beneath a slug when crawling 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. Figure 7.10: Apparatus f o r simultaneously measuring an t e r i o - 234 post e r i o r forces and dorso-ventral forces beneath a crawling slug. Figure 7.11: Simultaneous force and pressure measurements 237 Figure 7.12: Foot loading of Ariolimax columbianus i s constant 241 above a weight of 5 grams. Figure 8.1: Diagram of 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 respirometer...247 Figure 8.2: Apparatus used to measure the movement of a slug i n 249 the test chamber. Figure 8.3: Crawling velocity and oxygen consumption for ....253 Ariolimax columbianus. Figure 8.4: Internal power of locomotion as a function of 256 crawling speed. • Figure 8.5: Cost of locomotion 259 Figure 8.6: Components of power in the locomotion of Ariolimax 262 columbianus. Figure 9.1: Adhesive properties of a viscous liquid.... ......270 Figure 9.2: Stress concentrations 278 Figure 9.3: Device for measuring the shear strength of pedal 283 mucus under the slug. Figure 10.1: Diagrammatic representation of the four regular forms...289 of pedal waves. x i v ACKNOWLEDGMENTS Th i s study was made p o s s i b l e by the advice and support of many people. I would e s p e c i a l l y l i k e t o thank my s u p e r v i s o r , John G o s l i n e , f o r h i s encouragment, i n t e r e s t , and c l a r i t y o f thought. Susan Krepp Denny provided the l o v e t o get me through the hard times, and i n v a l u a b l e help with a l l a s p e c t s of the work. . C o l i n Parkinson and Fergus O ^ a r a a s s i s t e d i n the c o n s t r u c t i o n o f the v a r i o u s weird machines i n v o l v e d i n t h i s study, and I thank them f o r t h e i r f orebearance. F i n a l l y I would l i k e t o thank the other occupants of the lab who s u f f e r e d i n good humor through my bad jokes and c l u t t e r e d experiments - Bob Shadwick, Meyer Aaron, and Tony Harmon. Research funds f o r t h i s study were provided by N a t i o n a l Research C o u n c i l Grant 67-6934 and a P r e s i d e n t ' s Emergency Grant from the U n i v e r s i t y of B.C., both to Dr. G o s l i n e . 1 CHAPTER ONE I n t r o d u c t i o n I f you have ever been walking through the woods, or p u t t e r i n g i n your garden, e a r l y on a summer*s morning i t i s l i k e l y t h a t your eye.has been caught by a glimpse of r e f l e c t e d s u n l i g h t . I f you bow to your c u r i o s i t y and look c l o s e l y you w i l l see a t r a i l of what l o o k s l i k e c e l l o p h a n e winding a c r o s s the ground and a t i t s end a s l u g or s n a i l g l i d i n g a l o n g . Watching a s n a i l or s l u g move, i t i s at f i r s t hard to imagine a s i m p l e r kind of locomotion. The animal appears t o move e f f o r t l e s s l y , as i f slowly s l i d i n g d o w n h i l l . However, a moment's o b s e r v a t i o n and thought r a i s e a number of d i f f i c u l t g u e s t i o n s : 1. What i s the source of power f o r t h i s type of locomotion? As e f f o r t l e s s as a s l u g or s n a i l ' s movement seems, some f o r c e must be o p e r a t i n g to p r o p e l the animal forward. 2. In general s l u g s and s n a i l s are h e r b i v o r e s . To reach the l e a v e s t h a t are t h e i r food they are o f t e n r e q u i r e d t o climb the v e r t i c a l s u r f a c e s of p l a n t s . Watching a s l u g or s n a i l c l i m b , one i s immediately s t r u c k by the f a c t t h a t the animal does not change i t s mode of movement when i t switches from c r a w l i n g h o r i z o n t a l l y t o v e r t i c a l l y . , Instead i t seems simply t o g l i d e upwards. Obviously the animal's f o o t must somehow manage to adhere t o the s u r f a c e upon which the.animal c r a w l s . How can we account f o r t h i s adhesion? 3. The adhesion of slugs and s n a i l s t o the substratum 2 immediately r a i s e s another q u e s t i o n : I f the animal i s stuck to the s u r f a c e upon which i t walks, how does i t manage to move at a l l ? In other words, how does an animal with only one f o o t c o n t r i v e to walk on glue? 4. These l a s t two questions focus a t t e n t i o n on the slime t h a t s l u g s and s n a i l s move over. That t h i s slime i s important to the animal can e a s i l y be demonstrated. Barr (1926a) has shown t h a t the s l u g Milax s o w e r b i i can n e i t h e r move nor adhere without t h i s pedal mucus., Presumably t h i s i s t r ue o f other gastropods as w e l l . Another measure o f the importance of t h i s slime to s l u g s and s n a i l s i s the l a r g e amount of energy they w i l l expend i n producing i t . Williamson (1975) has found t h a t between 31% and 36% of the t o t a l energy expenditure of the s n a i l Cepea nemoralis was d i r e c t e d to the p r o d u c t i o n of pedal mucus. What, then, i s this.mucus? I s i t r e a l l y the glue t h a t accounts f o r adhession? What are i t s p h y s i c a l and chemical p r o p e r t i e s and how do they allow f o r movement? For the most p a r t the answers to these q u e s t i o n s are not known. While z o o l o g i s t s have spent a great d e a l of time and e f f o r t s t u d y i n g the f l i g h t of i n s e c t s and b i r d s , the running o f quadrupeds,and the swimming of f i s h ; many of the l e s s flamboyant forms of locomotion, such as the adhesive locomotion of gastropods, have been l a r g e l y i g n o r e d . This i s u n f o r t u n a t e , f o r I b e l i e v e there i s much i n f o r m a t i o n to be gained from the study of s l o w l y moving animals t h a t w i l l be of use t o a l l b i o l o g i s t s . In l i g h t of t h i s b e l i e f t h i s study was undertaken t o provide answers to the q u e s t i o n s 3 posed above. I have approached the l a r g e problem o f e x p l a i n i n g t h i s form of adhesive locomotion by examining i n d e t a i l the locomotion of one animal, the s l u g A r i o l i m a x columbianus. The s e v e r a l aspects o f locomotion were s t u d i e d s e p a r a t e l y : Chapters 2 and 3 d e s c r i b e the s t r u c t u r e of the s l u g ' s locomotory aparatus, and the movement of t h i s s t r u c t u r e d u r i n g l o c o m o t i o n . The p h y s i c a l p r o p e r t i e s of the pedal mucus are des c r i b e d i n Chapter 4. Chapters 5 and 6 deal with the chemical composition and macromolecular s t r u c t u r e of the pedal mucus. A l l of these r e s u l t s are brought together i n Chapter 7 where a model i s c o n s t r u c t e d to account f o r the locomotion of JU columbianus. The v a l i d i t y o f t h i s model has been t e s t e d by comparing the p r e d i c t e d f o r c e s of locomotion with those a c t u a l l y measured, and these r e s u l t s are a l s o presented i n Chapter 7. The model of Chapter 7 i s used i n Chapter 8 to examine the e n e r g e t i c s of locomotion i n s l u g s . Chapter 9 examines the mechanism of adhesion i n A columbianus. This study of the locomotion of A. columbianus , while answering many q u e s t i o n s about adhesive locomotion, r a i s e s f u r t h e r q u e s t i o n s about gastropod locomotion i n g e n e r a l . Chapter 10 d i s c u s s e s these unanswered questions and attempts to provide a p e r s p e c t i v e on the r e l a t i o n s h i p between adhesive locomotion and the more f a m i l i a r forms of animal movement., 4 CHAPTER TWO Slug Morphology T e r r e s t r i a l s l u g s are members of the s u b c l a s s Pulmonata of the gastropod molluscs . As such, t h e i r morphology i s c l o s e l y t i e d to t h a t of the f a m i l i a r garden s n a i l s from which they are c o n s i d e r e d to have evolved (Runham and Hunter,1970). To provide a background f o r comparison with s l u g morphology, the gross morphology of s n a i l s w i l l be reviewed here. A more thorough treatment of s n a i l morphology may be found i n F r e t t e r and Peake,1973. F i g u r e 2.1 shows an i d e a l i z e d d e p i c t i o n of a t e r r e s t r i a l s n a i l . The body i s u s u a l l y c o n s i d e r e d to c o n s i s t o f two p a r t s : 1. The V i s c e r a l Mass . The i n t e r n a l organs of the s n a i l are grouped to g e t h e r to form a compact v i s c e r a l mass. This mass i s enclosed w i t h i n a b a g - l i k e s t r u c t u r e , the mantle. The e p i t h e l i u m of the mantle s e c r e t e s the m a t e r i a l s which form the s h e l l . The s h e l l i n t u r n provides support and p r o t e c t i o n f o r the v i s c e r a l mass. 2- The Head Foot . Extending out of the s h e l l are the p o r t i o n s of the body t h a t r e q u i r e c o n t a c t with the o u t s i d e world. The f o o t , a h y d r o s t a t i c a l l y supported,muscular s t r u c t u r e , i s suspended from the c o l u m e l l a of the s h e l l . C o n t r a c t i o n s and extensions of the f o o t provide the movements necessary f o r locomotion. The mucus s e c r e t e d onto the foot,among other t h i n g s , f u n c t i o n s as an adhesive a l l o w i n g the s n a i l t o remain anchored t o the s u r f a c e upon 5 FIGURE 2.1. A g e n e r a l i z e d gross morphology of the t e r r e s t r i a l pulmonate s n a i l . F I G U R E 2.1 S H E L L F O O T F R I N G E P N E U M O S T O M 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 M O U T H F O O T S O L E G E N I T A L 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 G L A N D C O L U M E L L A R M U S C L E S M O U T H M U C U S G L A N D P O R E 7 which i t crawls. The f o o t (or pedal) mucus i s produced i n the suprapedal gland contained w i t h i n the f o o t mass, and i s extruded through a pore a t the a n t e r i o r end of the f o o t . The "head" of the animal c o n s i s t s o f two p a i r s of t e n t a c l e s and a mouth. The p o s t e r i o r p a i r of t e n t a c l e s supports the eyes, the a n t e r i o r t e n t a c l e s a re thought t o serve as chemosensory organs. The mouth houses a t y p i c a l gastropod r a s p i n g r a d u l a . Gas exchange occurs i n a v a s c u l a r i z e d c a v i t y (the pneumostome) opening on the r i g h t hand s i d e of the animal behind the head. The pneumostome opening a l s o serves as an e x i t f o r faeces and nitrogenous wastes. . S n a i l s are h e r m a p h r o d i t i c , and both sperm and eggs are shed through s t r u c t u r e s which can be everted from the g e n i t a l pore, which opens near the pneumostome. The e n t i r e head-foot can be c o n t r a c t e d and p u l l e d back i n t o the s h e l l , the s h e l l a p e r t u r e then being c l o s e d by an operculum. The gross morphology of t e r r e s t r i a l s l u g s (Figure 2.2) i s d e r i v e d from t h a t of the s n a i l by the l o s s of the e x t e r n a l s h e l l . The v i s c e r a l mass i s extended to l i e along the d o r s a l s u r f a c e o f the f o o t . The mantle,though no l o n g e r capable of producing an e x t e r n a l s h e l l , i s s t i l l p resent and se r v e s t o p r o t e c t the h e a r t , kidneys,and pneumostome. In times of danger the head may a l s o be s h e l t e r e d beneath the a n t e r i o r f l a p of the mantle. In other r e s p e c t s the morphology of the s l u g i s very s i m i l a r to t h a t of the s n a i l . At f i r s t glance the morphology of a s l u g seems g r o s s l y maladapted t o t e r r e s t r i a l e x i s t e n c e . The s l u g * s e p i t h e l i u m i s h i g h l y permeable t o water;and,unlike the s n a i l , i t cannot 8 FIGURE 2.2. The gross morphology of the t e r r e s t r i a l s l u g A r i o l i m a x columbianus . mantle pedal gland m u c u s posterior tentacles [with eyes] anterior tentacles mouth posterior tentacles anterior tentacles 10 r e t r a c t i n t o a s h e l l t o avoid d e s i c c a t i o n . S i m i l a r l y , the l a c k of a s h e l l would seem to render the s l u g open to p r e d a t i o n . These disadvantages of l i f e without a s h e l l are a p p a r e n t l y o f f s e t by a number o f advantages (Eunham and Hunter, 1970),. Because i t i s not t i e d t o a bulky s h e l l a s l u g can f i t p l a c e s t h a t a s n a i l cannot. For example,slugs are adept at c r a w l i n g under l o g s and i n t o s m a l l h o l e s i n the ground where the humidity i s hi g h . The a v a i l a b i l i t y of such damp s h e l t e r s may thus o f f s e t the l a c k of p r o t e c t i o n a g a i n s t d e s i c c a t i o n . Slugs a l s o have the advantage of being able to move without having t o drag along a heavy s h e l l . F i n a l l y , s l u g s are f r e e d from the n e c e s s i t y of i n g e s t i n g l a r g e amounts of calcium i n order t o produce and maintain a s h e l l . The v i a b i l i t y of these.advantages i s evidenced by 1) the independent e v o l u t i o n o f the s h e l l - l e s s body form i n a t l e a s t t h r e e d i f f e r e n t f a m i l i e s of pulmonates,and 2) the worldwide present d i s t r i b u t i o n of s l u g s . Slugs occur i n a wide v a r i e t y of s i z e s , f r o m small s p e c i e s where the a d u l t s weigh l e s s than a gram, t o s p e c i e s such as t h e A r i o l i m a x columbianus d e a l t with i n t h i s study where a d u l t s may weigh 20-25 grams. The Foot The f o o t of A r i o l i m a x columbianus i s the organ r e s p o n s i b l e f o r adhesion and locomotion and consequently i s of prime importance i n t h i s study. To examine the f i n e s t r u c t u r e of the f o o t s e v e r a l s m a l l A. columbianus were 11 prepared f o r h i s t o l o g i c a l s t u d i e s . The s l u g s were r e l a x e d i n water c o n t a i n i n g a s m a l l amount of MS222 . The specimens were then f i x e d i n e i t h e r 1% g l u t e r a l d e h y d e or Bouins f i x a t i v e , d e h y d r a t e d , a n d wax embedded. Sect i o n s were cut (7-10 um) and s t a i n e d e i t h e r with a l c i a n b l u e / e o s i n or by the PAS method f o r the d e t e c t i o n o f mucus. S e c t i o n s intended f o r the study of muscle and connective t i s s u e s were s t a i n e d with M a l l o r y ' s t r i p l e s t a i n . F i g u r e 2.3 shows the s t r u c t u r e of the f o o t . The f o o t c o n s i s t s of three s t r u c t u r e s : 1« The Suprapedal Gland . The suprapedal gland i s a t u b u l a r organ embedded i n the d o r s a l s u r f a c e of the f o o t and extending approximately two t h i r d s the length of the s l u g . . Mucus i s produced i n the c e l l s of the gland and s e c r e t e d i n t o the lumen. The lumenal e p i t h e l i u m i s c i l i a t e d and these c i l i a may a s s i s t i n the movement of the mucus to the pore beneath the mouth where the mucus i s extruded onto the f o o t s o l e . The s t r u c t u r e of the suprapedal gland i s very s i m i l a r 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 Barr (1926b). 2 - The Pedal Haemocoel And Musculature -.. The bulk of the f o o t i s formed of a r e t i c u l u m of connective t i s s u e and muscle f i b e r s i n t e r s p e r s e d with haemocoelic spaces., There are two d i s c e r n a b l e l a r g e bands of muscle i n the f o o t . The f i r s t of these i s a l o n g i t u d i n a l muscle band l y i n g j u s t v e n t r a l t o the suprapedal gland and running the l e n g t h of the s l u g . The second i s a band running roughly c i r c u m f e r e n t i a l l y . T h i s second band s t a r t s j u s t proximal to one of the f o o t f r i n g e s and runs m e d i a l l y below the l o n g i t u d i n a l muscle band. I t then c o n t i n u e s around the 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 columbianus 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 at the p o s i t i o n i n d i c a t e d by the l i n e A-A i n Fi g u r e 2. 2. FIGURE 2.3 pedal haemocoel 14 d o r s a l s i d e of the s l u g and back down to end proximal to the o p p o s i t e f o o t f r i n g e . I t seems l i k e l y t h a t these two muscle bands are r e s p o n s i b l e f o r the l a r g e changes i n body dimensions shown by these s l u g s . I t i s l i k e l y t h a t they f u n c t i o n i n much the same manner as the l o n g i t u d i n a l and c i r c u m f e r e n t i a l muscles which c o n t r o l the shape of earthworms (Gray,1968). A c o n t r a c t i o n of the l o n g i t u d i n a l muscle band w i l l cause the s l u g to shorten and become:wider. A c o n t r a c t i o n of the c i r c u m f e r e n t i a l muscle band w i l l squeeze the v i s c e r a and coelomic f l u i d and cause the s l u g t o lengthen. In a d d i t i o n to these muscle bands a dense r e t i c u l u m of muscle f i b e r s i s present throughout the f o o t . At f i r s t these muscle f i b e r s appear to be arranged haphazardly; however c l o s e r examination r e v e a l s some order. In a s a g i t t a l s e c t i o n through the f o o t few f i b e r s are seen to run e i t h e r d i r e c t l y d o r s o - v e n t r a l l y or d i r e c t l y a n t e r i o -p o s t e r i o r l y . Instead f i b e r s run i n one of two o b l i q u e d i r e c t i o n s . F i b e r s o r i g i n a t i n g on the pedal e p i t h e l i u m e i t h e r run o b l i g u e l y a n t e r i o r l y or o b l i q u e l y p o s t e r i o r l y . The s i t u a t i o n appears much the same i n c r o s s - s e c t i o n ? Few f i b e r s seem to run e i t h e r d i r e c t l y d o r s o - v e n t r a l l y or l a t e r a l l y a c r o s s the f o o t . T h i s s i t u a t i o n i s very s i m i l a r to t h a t found i n Agriolimax r g t i e u l a t u m as d e s c r i b e d by Jones (1970). The s i g n i f i c a n c e o f t h i s f i b e r arrangement w i l l be d i s c u s s e d i n the next chapter. The spaces between the muscle and connective t i s s u e f i b e r s of the f o o t are f i l l e d with the haemocoelic f l u i d . In c o n t r a s t to the s i t u a t i o n proposed t o e x i s t i n the l i m p e t 15 P a t e l l a v u l q a t a by Jones and Trueman (1973) there i s no m i c r o s c o p i c a l evidence t o suggest t h a t t h i s f l u i d i s c o n f i n e d by the i n d i v i d u a l spaces and t h e r e f o r e not f r e e t o move from one space to the next. Indeed there i s a s i z a b l e c a v i t y extending m e d i a l l y along the e n t i r e f o o t . The w a l l s of t h i s c a v i t y are i l l - d e f i n e d and i t appears t o be formed of contiguous haemocoelic spaces strung together. The presence of t h i s c a v i t y suggests t h a t the pedal haemocoel i s s t r u c t u r e d to allow the movement of f l u i d along the f o o t . Again the s i g n i f i c a n c e o f t h i s arrangement w i l l be discu s s e d i n the next chapter. 3. The Pedal E p i t h e l i u m .. The pedal haemocoel i s bounded l a t e r a l l y and v e n t r a l l y by the pedal e p i t h e l i u m . Two d i s t i n c t areas are d i s c e r n a b l e i n t h i s e p i t h e l i u m . The e p i t h e l i u m of the f o o t f r i n g e s and the pedal groove are densely c i l i a t e d . The c i l i a here are q u i t e long (about 4 um). S e c t i o n s of t h i s e p i t h e l i u m can be obtained from l i v e s l u g s by c a r e f u l d i s s e c t i o n with a r a z o r blade. The c i l i a c ontinue to a c t i v e l y beat i n t h i s d i s s e c t e d t i s s u e and t h e i r e f f e c t i v e s t r o k e i s found t o be such t h a t mucus would be p r o p e l l e d p o s t e r i o r l y i n the i n t a c t s l u g . S c a t t e r e d mucus producing c e l l s (the " g r a n u l a r " c e l l s of Arcadi,1963) are present on the f o o t f r i n g e s . The s o l e of the f o o t i s covered by a second type of e p i t h e l i u m . C i l i a are again present, but they are s h o r t e r (about 2 um) and more s p a r s e l y d i s t r i b u t e d . I was not ab l e t o determine the d i r e c t i o n of the e f f e c t i v e s t r o k e f o r these c i l i a , however Barr (1926a, b) found t h a t the pedal c i l i a i n two other s p e c i e s of sl u g 16 t r a n s p o r t e d mucus l a t e r a l l y and p o s t e r i o r l y . S c a t t e r e d g r a n u l a r c e l l s are a l s o present on the e p i t h e l i u m of the f o o t s o l e . I t has been repo r t e d by Barr (1926a,b) and Jones (1970) t h a t i n other s p e c i e s of s l u g s the mucus produced by the pedal e p i t h e l i u m ( d i s t i n c t from that produced by the suprapedal gland) i s g u i t e watery. However I have.never observed the presence of watery mucous s e c r e t i o n s on the f o o t of A r i o l i m a x columbianus . 4- The Mucus The t h i c k n e s s of the mucus l a y e r beneath the f o o t was examined using the f o l l o w i n g procedure: Small (3-4 cm length) J U columbianus were placed on a s t r i p of aluminum f o i l . When the sl u g s were a c t i v e l y moving,the s t r i p was dropped i n t o a dewar f l a s k c o n t a i n i n g l i g u i d n i t r o g e n . The s l u g s f r o z e very r a p i d l y ; before they could r e t r a c t t h e i r eye s t a l k s . The procedure i s s i m i l a r to one developed by Lissman, (1946) and used by Jones (1973). T h i s procedure d i f f e r s from those o f Lissman and Jones i n t h a t the s l u g s are moving over a non-porous s u r f a c e when they are f r o z e n . Lissman used a pie c e of copper screen and Jones a s t r i p of f i l t e r paper. A f t e r f r e e z i n g , the specimens are f i x e d (1% glu t a r a l d e h y d e - 50% eth a n o l a t -20<>C) f o r one week. A f t e r f i x a t i o n specimens are dehydrated, wax embedded, and se c t i o n e d at 8-10 um according t o standard h i s t o l o g i c a l techniques. S e c t i o n s were s t a i n e d with e i t h e r M a l l o r y ' s t r i p l e s t a i n f o r examining the g e n e r a l s t r u c t u r e of the f o o t , or a l c i a n b l u e / e o s i n when the l o c a t i o n of mucus and mucus producing c e l l s were t o be examined. Using t h i s 17 technique s a g g i t a l s e c t i o n s were examined from s e v e r a l s l u g s . I n many cases the mucus l a y e r beneath the f o o t had become d i s l o d g e d d u r i n g the process of f i x a t i o n or embedding, but i n those cases where the mucus l a y e r was a p p a r e n t l y i n t a c t i t was found t o be from 10 t o 20 um i n t h i c k n e s s . With t h i s b r i e f d e s c r i p t i o n of the morphology of the locomotory apparatus of A. columbianus i n mind the f u n c t i o n of t h i s s t r u c t u r e may now be examined. 18 CHAPTER THREE I n t r o d u c t i o n Kinematics i s the study of motion without regard f o r the f o r c e s t h a t cause locomotion. , As such i t i s a doubly a p p r o p r i a t e term f o r the study o f the locomotory movements of gastropods because these animals appear to g l i d e along with no e f f o r t at a l l . A c l o s e r look, however, r e v e a l s a s p e c i a l i z e d s e t of movements t h a t accompany locomotion, and i t i s a p r e c i s e d e s c r i p t i o n of these movements t h a t i s the o b j e c t i v e of t h i s chapter. The locomotory movements of gastropods f a l l i n t o two broad c a t a g o r i e s . F i r s t there are those gastropods, p r i m a r i l y a q u a t i c , which move by means of c i l i a . I t has been hypothesized ( E l v e s , 1961) t h a t c i l i a r y locomotion i s the p r i m i t i v e form of movement f o r gastropods. L i s t s of s p e c i e s u t i l i z i n g c i l i a r y locomotion, and the v a r i o u s parameters of t h e i r movement are provided by M i l l e r (1971). Most gastropods however move by means of waves generated on the v e n t r a l s u r f a c e o f the f o o t by the c o n t r a c t i o n of muscles. These muscular pedal waves are best observed by p l a c i n g the animal on a g l a s s p l a t e and watching the f o o t through the g l a s s as the animal moves. Close examination r e v e a l s a number of a l t e r n a t i n g l i g h t and dark bands (corresponding to ext e n s i o n or compression of the foot) which move p a r a l l e l t o the long a x i s of the f o o t as the animal crawls. The waves disappear when the animal stops. Presumably these pedal waves generate the r e a c t i v e f o r c e s 19 t h a t a c t u a l l y p r o p e l the animal. A v a r i e t y of wave p a t t e r n s are present i n gastropods, and d e s c r i p t i o n s of these pedal waves are found i n s e v e r a l s t u d i e s ( M i l l e r , 1974a, Jones, 1973, Trueman and Jones, 1970, Lissman, 1945a, and Gainey, 1976). The v a r i o u s s o r t s of pedal waves are c a t e g o r i z e d a c c o r d i n g t o a scheme proposed by V l e z (1909) (as c i t e d i n Lissman, 1945a, and M i l l e r , 1974). Waves t h a t move i n the same d i r e c t i o n as the animal are termed d i r e c t . Waves moving i n the opposite d i r e c t i o n from the animal are r e t r o g r a d e . A s i n g l e wave may extend a c r o s s the e n t i r e width of the f o o t (monotaxic) or waves may be o n l y h a l f the width of the f o o t ( d i t a x i c ) , a l t e r n a t i n g s i d e s . Most s p e c i e s may be d e s c r i b e d by these terms, though a few unusual s p e c i e s have waves t h a t move d i a g o n a l l y along the f o o t , or appear and disappear haphazardly. A r i o l i m a x columbianus moves by means of d i r e c t , monotaxic waves. A p r e c i s e d e s c r i p t i o n of the movements a s s o c i a t e d with d i r e c t waves i s found i n Lissman (1945a) and Jones (1970) and f o r i n d i r e c t waves i n Jones and Trueman (1970). The movements of A.. Columbianus observed i n t h i s study are i n g e n e r a l agreement with these s t u d i e s . Areas of disagreement w i l l be noted as they appear i n the d e s c r i p t i o n of A. columbianus locomotory kinematics. A. columbianus Locomotory Kinematics (Methods) A r i o l i m a x columbianus were c o l l e c t e d i n the woods near the U n i v e r s i t y of B r i t i s h Columbia.. Slugs were kept at 10 20 °C i n a c o n t r o l l e d environment chamber. The l i g h t s of the chamber were c y c l e d , 12 hours of l i g h t a l t e r n a t i n g with 12 hours of darkness. The s l u g s were fed l e t t u c e and c a r r o t s . Under these c o n d i t i o n s s l u g s c o u l d be kept healthy f o r up to a year. A l l t e s t s conducted on l i v e s l u g s r e p o r t e d i n t h i s study were c a r r i e d out at room temperature (21-23 °G). Slugs brought i n t o the l a b o r a t o r y from the c o l d room were allowed t o come t o room temperature before t e s t s were conducted. The locomotory movements of A., columbianus were observed by a l l o w i n g a s l u g t o crawl on a g l a s s p l a t e . Movements of the v e n t r a l s u r f a c e of the f o o t were recorded with a Sony video tape r e c o r d e r at 60 frames/second. Taped records were played hack onto a 25 i n c h (diagonal) t e l e v i s i o n s creen. When d e s i r e d , the tape could be analyzed frame by frame. A r u l e r taped t o the g l a s s p l a t e near the s l u g allowed f o r the s i z e c a l i b r a t i o n of images on the t e l e v i s i o n s c r e e n . A s t a t i o n a r y s l u g shows no evidence of pedal waves. The f o o t i s dark t a n , the c o l o r darkest near the center of •the f o o t were the dark d i g e s t i v e gland shows through the t h i n l a y e r of pedal musculature. As the s l u g begins to move, waves f i r s t appear 1/4 t o 1/3 of the f o o t l e n g t h back from the a n t e r i o r end of the f o o t . When the pedal e p i t h e l i u m and musculature are compressed i n the wave they mask the dark d i g e s t i v e gland. Consequently, a wave of c o n t r a c t i o n appears l i g h t e r than the r e s t i n g f o o t . As these waves move forward the area of wave formation moves 2 1 p o s t e r i o r l y u n t i l waves are present along the e n t i r e f o o t as shown i n F i g u r e 3 .1. T h i r t e e n to 17 waves are present on the f o o t . The p a t t e r n of waves occupies only the c e n t r a l 1/3 t o 1/2 of the f o o t , waveless areas forming a "rim". The o v e r a l l movements during locomotion are best understood by f o l l o w i n g a s i n g l e wave i n a schematic diagram (Figure 3.2a). The wave i s formed near the p o s t e r i o r end of the f o o t , presumably by the c o n t r a c t i o n of a segment of the pedal musculature. T h i s c o n t r a c t i o n causes an area of the f o o t to compress a n t e r i o - p o s t e r i o r l y to some f r a c t i o n of i t s r e l a x e d l e n g t h . As a conseguence of t h i s c o n t r a c t i o n the t a i l moves forward a b i t . From video r e c o r d i n g s of pigmented areas on the f o o t , i t i s p o s s i b l e to measure the extent of t h i s compression i n a c r a w l i n g A. columbianus . Such measurements were made on three s l u g s , three t o f o u r waves being measured on each s l u g . As a r e s u l t of these measurements i t was found that f o r A columbianus the r a t i o of (extended length/compressed l e n g t h ) , t h e compression r a t i o , ranges from 1.43 to 2.03 with an average of 1.69. This wave of compression i s passed forward along the f o o t as muscles ahead of the wave c o n t r a c t and muscles behind r e l a x . When the wave reaches the a n t e r i o r end of the f o o t , muscles are no longer a v a i l a b l e to keep the wave compressed and i t r e t u r n s to i t s r e s t i n g l e n g t h . The energy f o r t h i s re-expansion i s presumably provided by h y d r o s t a t i c p r e ssure w i t h i n the f o o t and w i l l be d i s c u s s e d f u r t h e r l a t e r i n t h i s c h a p t e r . As a consequence of the re-expansion of t h i s segment of the f o o t , the a n t e r i o r end of the f o o t i s 22 FIGURE 3. 1 . A 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 of 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 the r e l a t i v e p o s i t i o n s , movements, and areas of the r i m s , waves, and interwaves. 23 24 FIGURE 3.2. 4 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,. A) As the wave moves from l e f t t o r i g h t (shown by the s t i p p l e d l i n e ) the 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 of the f o o t a t the same speed as the wave r e s u l t s i n the c o l l a p s e of the f o o t . 25 26 moved forward. Thus, each wave c o n s t i t u t e s one "s t e p " ; the d i s t a n c e the t a i l i s p u l l e d forward when the wave forms i s t r a n s f e r r e d t o the head when the wave of compression r e -expands . The d i s t a n c e iU Columbianus advances as a consequence of each wave i s about 1.0 to 1.5 mm. i Notice i n Fiqu r e 3.2a t h a t those p a r t s of the f o o t which are not contained i n a pedal wave are s t a t i o n a r y r e l a t i v e to the ground. Only when a p o r t i o n of the f o o t i s contained i n the wave of compression i s i t moving. One f u r t h e r p o i n t must be e x p l a i n e d here. T h i s i n v o l v e s the d i f f e r e n c e bjetween- the speed a t which a wave t r a v e l s forward along the f o o t and the speed at which the segments of the f o o t move as they are momentarily contained i n a wave ( h e r e a f t e r known as the segment speed). This d i f f e r e n c e i s somewhat c o n f u s i n g and i s perhaps best e x p l a i n e d by analogy. Imagine a group of s u r f e r s who have arranged themselves i n the s u r f along a l i n e p e r p e n d i c u l a r t o the beach. Thus the f i r s t s u r f e r i s f a r t h e s t from the beach, the second s u r f e r i s j u s t shoreward of him, and so on, each s u r f e r w a i t i n g t o c a t c h a wave. As a wave comes i n the f i r s t s u r f e r t r i e s t o c a t c h i t , i s a c c e l e r a t e d forwards a b i t , but never gets up, to speed and the wave passes him by. The second s u r f e r does l i k e w i s e and so on down the group as the wave moves i n t o shore. A f t e r the wave has passed , each s u r f e r w i l l have moved shorewards s l i g h t l y but the l i n e a r arrangement and order w i l l be the same. Now a second wave a r r i v e s . This time the f i r s t s u r f e r "catches" the wave. 27 i e . he begins t o move at the same speed as the wave. The wave and f i r s t s u r f e r advance on the second s u r f e r who a l s o catches the wave and so on down the l i n e . When the wave reaches the l a s t s u r f e r a l l the s u r f e r s w i l l be t r a v e l l i n g forward a t the same speed and s i n c e a l l are on the same wave a l l w i l l reach the shore.at the same time. T h i s can only happen i f the l i n e a r arrangement of the s u r f e r s c o l l a p s e s as the wave t r a v e l s down the l i n e . I f each s u r f e r c a t c h e s the wave the l i n e a r arrangement can only be maintained i f the s u r f e r s are compelled to d e c e l e r a t e and hop o f f the wave before they reach the next s u r f e r i n l i n e . Now apply t h i s analogy to the schematic drawing of 3.2b. Imagine t h a t as the wave of compression moves forward, the compressed segments begin t o t r a v e l at the same speed as the wave. As the wave advances, more and more compressed segments are added, f u r t h e r compressing the segments a l r e a d y moving forward.. The f i n a l outcome.is t h a t a l l the segments of the f o o t must a r r i v e a t the a n t e r i o r end of the foot at the same time. T h i s i s a p h y s i c a l i m p o s s i b i l i t y . T h i s s i t u a t i o n can be avoided i n r e a l i t y by two methods: 1) e i t h e r t h e segments of the f o o t never move with a speed e q u a l t o the wave speed or 2) segments on the f o o t t h a t momentarily move at the wave speed are compelled to d e c e l e r a t e by the p h y s i c a l c o n s t r a i n t s of the f o o t s t r u c t u r e , i e . the f i n i t e e x t e n s i b i l i t y and c o m p r e s s i b i l i t y of the f o o t . As a consequence each segment i s l e f t behind by the wave a f t e r i t has t r a v e l l e d forwards a c e r t a i n d i s t a n c e and the l i n e a r arrangement of segments on the f o o t 28 i s maintained (Figure 3.2a). Thus the wave speed may be equal t o , but i s u s u a l l y g r e a t e r than, the segment speed. F i g u r e 3.3 i s a schematic r e p r e s e n t a t i o n of the f o o t of a s l u g when s e v e r a l waves are present. I t can be seen t h a t the presence of m u l t i p l e waves does not change the b a s i c sequence of movements. Again the f o o t moves forward only when compressed i n a wave; the area between waves (the interwaves) are s t a t i o n a r y r e l a t i v e t o the ground. The schematic diagrams of F i g u r e s 3.2 and 3.3 d e s c r i b e the s i t u a t i o n t h a t e x i s t s i n the c e n t r a l p o r t i o n of the f o o t of a moving s l u g . . How i s the r e s t of the s l u g t i e d to t h i s p a r t of the f o o t , and how does t h i s e x p l a n a t i o n account f o r the a p p a r e n t l y continuous forward movement of a s l u g ? The answer to both these questions can be e x p l a i n e d by an analogy to a more f a m i l i a r mode of locomotion: The t o r s o of a running person moves forward a t a c o n s t a n t speed r e l a t i v e . to the ground. His f e e t however are c o n s t a n t l y changing v e l o c i t y . Obviously when a f o o t i s planted on the.ground i t i s s t a t i o n a r y r e l a t i v e to the ground. When the f o o t i s l i f t e d from the ground i t t r a v e l s forward with a v e l o c i t y g r e a t e r than t h a t of the t o r s o . T h i s v e l o c i t y e v e n t u a l l y c a r r i e s the f o o t ahead of the t o r s o at which p o i n t the f o o t i s p l a n t e d and the process i s repeated. The speed of the t o r s o i s equal to the average speed of the f e e t . T h i s i n t u r n i s equal to the number of steps taken per second times the l e n g t h of each s t e p . This analogy can be t r a n s f e r r e d d i r e c t l y t o the s l u g . The.slug's " f e e t " are the s e r i e s of waves and interwaves. A 29 FIGURE 3.3. A 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 of compression can e x i s t on one f o o t and r e s u l t i n movement. As the waves move from l e f t t o r i g h t the 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 f o o t i s a l t e r n a t e l y s t a t i o n a r y ( i n an interwave) and moving forward with a v e l o c i t y g r e a t e r than t h a t of the s l u g . The average forward v e l o c i t y of the c e n t r a l p o r t i o n of the f o o t w i l l thus be equal to the c onstant v e l o c i t y o f the s l u g as a whole. T h i s i n turn i s equal t o the number of waves r e a c h i n g the f r o n t of the s l u g per second (the s t e p p i n g rate) times the d i s t a n c e . g a i n e d by the r e - e x t e n s i o n accompanying each wave (step l e n g t h , a f u n c t i o n of the compression r a t i o ) . The f a c t t h a t there are 13-^17 waves present on the f o o t ensures t h a t waves w i l l c o n s t a n t l y be r e a c h i n g the a n t e r i o r end of the f o o t . Consequently the s l u g moves at a c o n s t a n t r a t e . , T h i s constant r a t e a p p l i e s t o a l l p o r t i o n s o f the s l u g not d i r e c t l y a s s o c i a t e d with pedal waves, i n c l u d i n g the rims of the f o o t (which do not develop pedal waves). Since the average speed of the c e n t r a l p o r t i o n of the f o o t must equal the speed of the whole s l u g , the speed of moving segments of the f o o t w i l l depend on t h e : r e l a t i v e p e r i o d s of time spent moving and s t a t i o n a r y . Measurements from 22 video r e c o r d i n g s of c r a w l i n g ft. columbianus show t h a t p o i n t s on the f o o t spend roughly e g u a l p e r i o d s of time i n and out of pedal waves. Consequently the average speed of a segment i n a wave must be approximately twice t h a t of the whole s l u g . Video r e c o r d i n g s a l s o allow f o r a measurement of wave -speed r e l a t i v e t o the speed of the whole s l u g . . F i g u r e 3.4 i s a p l o t of wave speed and s l u g speed f o r 18 measurements from 8 s l u g s . The r a t i o of wave speed to s l u g speed i s 32 FIGURE 3.4. The r e l a t i o n between the speed of the pedal waves and the o v e r a l l speed of the s l u g . The waves move more than three times as f a s t as the s l u g . 33 Figure 3.4 2 Slug Speed mm/sec 34 about 3.3. This knowledge of wave speed and segment speed provides a check on the value of compression r a t i o c i t e d e a r l i e r . Since wave speed i s 3.3 times the whole s l u g speed, a wave w i l l advance i n t o a s t a t i o n a r y interwave a t 3.3 times the s l u g speed. Segments moving i n a wave, however, are themselves t r a v e l l i n g at 2 times the s l u g speed, or at a speed r e l a t i v e t o the wave of 3-3/2=1.65 . . Since the segments i n a wave move slower r e l a t i v e t o the wave than segments i n an interwave, the a n t e r i o - p o s t e r i o r dimension of a wave segment must be l e s s than an interwave segment by a r a t i o 1.6 5 i f equal time i s to be spent moving and s t a t i o n a r y . The c a l c u l a t e d compression r a t i o i s thus 1.65, which compares c l o s e l y t o the measured average of 1.69. The i n f o r m a t i o n contained i n F i g u r e 3.4 may be put to f u r t h e r use; h e l p i n g t o e x p l a i n the manner i n which sl u g s c o n t r o l the speed a t which they walk. While no s l u g could be s a i d t o move very f a s t , i t can be seen from F i g u r e 3 .4 t h a t i n d i v i d u a l s are capable of a range of speeds from s l i g h t l y more than 1mm/sec to s l i g h t l y more than 2 mm/sec. The s l u g could c o n t r o l i t s speed i n one of t h r e e ways: 1. The s l u g c o u l d vary the number o f waves present. M l other f a c t o r s remaining c o n s t a n t , i n c r e a s i n g the number of waves present on the f o o t would i n c r e a s e the s l u g ' s speed. In the course of measuring the wave and s l u g speeds f o r F i g u r e 3.4, the number of waves present on the f o o t of the c r a w l i n g s l u g were counted. While the number of waves present v a r i e d from s l u g to s l u g , the number of waves 35 present on the f o o t of an i n d i v i d u a l d i d not vary, r e g a r d l e s s cf speed. 2. The s l u g c o u l d vary the compression r a t i o of the waves. I n c r e a s i n g the compression r a t i o w i l l i n c r e a s e the step l e n g t h and thereby i n c r e a s e speed without e f f e c t i n g any other wave f a c t o r . I f t h i s method were present i n r e a l i t y , the wave speed should be independent of s l u g speed. F i g u r e 3.4 shows that t h i s i s not so, l e a d i n g to the f i n a l p o s s i b i l i t y . 3. The s l u g c o u l d vary the wave speed.. I n c r e a s i n g the wave speed, a l l other f a c t o r s remaining constant, w i l l i n c r e a s e the st e p p i n g r a t e and thereby the sl u g speed, As F i g u r e 3 .4 shows, t h i s i s indeed the case.. Thus i t appears t h a t columbianus c o n t r o l s the speed of i t s movement by c o n t r o l l i n g the r a t e at which waves t r a v e l along the f o o t . These o b s e r v a t i o n s are very s i m i l a r to those of C r o z i e r and P i l z (1924) who were working with Limax maximus . C r o z i e r and Pilz,however, found an i n c r e a s e i n st e p l e n g t h with i n c r e a s i n g speed, though t h i s e f f e c t was l e s s pronounced than the i n c r e a s e i n wave speed. The o b s e r v a t i o n s reported above f o r A. columbianus are an accurate d e s c r i p t i o n o f the gross movements of the f o o t d u r i n g locomotion. I t w i l l be u s e f u l however t o know the p r e c i s e movement of i n d i v i d u a l p o i n t s on the f o o t . To t h i s end two procedures were c a r r i e d out. 1. Video tapes were made of the f o o t of a moving s l u g while the t e l e v i s i o n camera was mounted on a d i s s e c t i n g microscope. M a g n i f i c a t i o n was such t h a t a 4 mm l e n g t h of 36 f o o t occupied the e n t i r e v e r t i c a l dimension of the t e l e v i s i o n screen. At t h i s m a g n i f i c a t i o n i n d i v i d u a l blemishes and c o n c e n t r a t i o n s o f mucus glands are v i s i b l e on the f o o t and t h e i r movements can be recorded. The s p a t i a l r e s o l u t i o n o f the system at t h i s m a g n i f i c a t i o n i s about 20-30 um . This 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 the " j i t t e r " of the image on the t e l e v i s i o n screen. As a consequence of t h i s j i t t e r a s t r i c t frame by frame a n a l y s i s i s not p o s s i b l e . I t i s necessary t h a t a number of frames,5-10, be examined b e f o r e i t can be s t a t e d with any c e r t a i n t y t h a t a po i n t has moved. Thus, while a movement of 20-30 um can be detected between the s t a r t and f i n i s h of a 5-10 frame segment, the time w i t h i n t h i s segment when the movement a c t u a l l y o c c u r r e d cannot be s p e c i f i e d . S p a t i a l r e s o l u t i o n i s thus gained at the expense of temporal r e s o l u t i o n . F i g u r e 3.5 shows an average v e l o c i t y p r o f i l e f o r a p o i n t on the f o o t d u r i n g the passage of a pedal wave. I t can be seen t h a t as a wave overtakes a p o i n t on the f o o t , t h a t p o i n t i s g r a d u a l l y a c c e l e r a t e d to a peak v e l o c i t y . Notice t h a t t h i s peak v e l o c i t y i s c o n s i d e r a b l y g r e a t e r than the average v e l o c i t y but i s s t i l l l e s s than the wave v e l o c i t y . The peak v e l o c i t y i s maintained f o r a s h o r t p e r i o d before the p o i n t i s d e c e l e r a t e d back t o zero v e l o c i t y . I t i s o f t e n found t h a t d e c e l e r a t i o n c o n t i n u e s past zero; i n other words there i s some b a c k s l i p a f t e r the wave has passed. T h i s b a c k s l i p i s s m a l l , amounting a t most to about 30 to 50 um. As a consequence of t h i s s m a l l amount of b a c k s l i p the time course of b a c k s l i p i s u n c e r t a i n , 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 of an average pedal wave. The curves r e p r e s e n t values averaged from 22 separate crawls by two Ar i o l i m a x columbianus . F igu re 3.5 seconds 3 9 e x p l a i n e d above. I t i s c e r t a i n however t h a t i t happens i n the f i r s t 1/6 of a second a f t e r zero v e l o c i t y i s reached. By p o s i t i o n i n g the t e l e v i s i o n camera c o r r e c t l y i t i s p o s s i b l e t o r e c o r d the movement of p o i n t s i n the c e n t r a l area of the f o o t and adjacent p o i n t s i n the rim s i m u l t a n e o u s l y . The r e s u l t s o f one such measurement are shown i n F i g u r e 3.6 and confirm the o b s e r v a t i o n s made on the whole f o o t . The measurement i s s t a r t e d j u s t as the wave . reaches the p o i n t i n the c e n t r a l p o r t i o n o f the f o o t . At t h i s time the c e n t r a l and rim p o i n t s are adjacent. The c e n t r a l p o i n t a c c e l e r a t e s r a p i d l y forward, soon reaching a v e l o c i t y such that i t gains ground on the rim p o i n t . The p o i n t i n the rim moves at a c o n s t a n t speed. The d i s t a n c e gained by the c e n t r a l p o i n t i s j u s t s u f f i c i e n t so t h a t the rim and c e n t r a l p o i n t s are again adjacent as another wave overtakes the c e n t r a l p o i n t . 2. Video r e c o r d i n g s provide accurate measurements of motion p a r a l l e l t o the plane o f the g l a s s p l a t e on which the. s l u g crawls. They do not, however, provide i n f o r m a t i o n about movements p e r p e n d i c u l a r to t h i s plane. To i n v e s t i g a t e the p o s s i b l e d o r s o - v e n t r a l movements of the f o o t d u r i n g locomotion the s l u g s were q u i c k l y f r o z e n and s e c t i o n e d as d e s c r i b e d i n Chapter 2. In s a g g i t a l or p a r a s a g g i t a l s e c t i o n s of the f o o t the pedal waves can be c l e a r l y seen as shown i n p l a t e 3-1. The evidence provided by these s e c t i o n s suggests t h a t the s l u g does not l i f t the f o o t d u r i n g the passage of a pedal wave when walking on a non-porous substratum. I n s t e a d , the pedal wave c o n s i s t s e n t i r e l y of an 40 FIGURE 3.6. The continuous forward movement of the rims and the a l t e r n a t e movement and non^movement of the center 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 . Figure 3 . 6 0.5 1 . 0 s e c o n d s 4 2 PLATE 3.1. a micrograph showing the pedal e p i t h e l i u m of a c r a w l i n g s l u g . A) A s a g g i t a l s e c t i o n showing the t r a n s i t i o n between a wave (W) and an interwave (I) . No t i c e t h a t t h e f o o t i s not l i f t e d i n the wave. B) A h i g h e r m a g n i f i c a t i o n of the e p i t h e l i u m under a wave. The e p i t h e l i a l c e l l s are compressed a n t e r i o - p o s t e r i o r l y . C) A high e r m a g n i f i c a t i o n o f the e p i t h e l i u m under an interwave. The e p i t h e l i a l c e l l s are extended a n t e r i o - p o s t e r i o r l y . 44 a n t e r i o - p o s t e r i o r compression. T h i s can be seen by examining the shape o f e p i t h e l i a l c e l l s . In the extended p o r t i o n o f the f o o t the c e l l s are l o n g a n t e r i o - p o s t e r i o r l y and short d o r s o - v e n t r a l l y . These dimensions are reversed i n the compressed areas of the f o o t . The compression r a t i o measured on the s e c t i o n shown i n P l a t e 3.1 i s about 2, i n rough agreement with values c a l c u l a t e d by other methods. These r e s u l t s d i f f e r from those of Lissman (1945a) working with H e l i x aspersa and Jones (1973) working with Ag r i o l i m a x r e t i c u l a t u s . Both of these authors found t h a t the f o o t i s l i f t e d as i t i s compressed i n a pedal wave. I t i s p o s s i b l e t h a t t h i s d i f f e r e n c e i n the shape of pedal waves simply r e f l e c t s a s p e c i e s d i f f e r e n c e . Another e x p l a n a t i o n , however, appears more probable. E x p l a n a t i o n s of gastropod locomotion t h a t r e g u i r e the f o o t to be l i f t e d have s u f f e r e d from three major problems, a l l r e l a t e d t o the mucus sandwiched between the s l u g and substratum (see F i g u r e 3.7). 1. I t has been assumed (Lissman, 1945a; Jones, 1973; and Jones and Trueman, 1970) t h a t when the f o o t i s l i f t e d the space beneath the l i f t e d p o r t i o n i s f i l l e d with e i t h e r mucus or some f l u i d exudate. As the wave t r a v e l s forward, t h i s volume of mucus or f l u i d t r a v e l s with i t and should be dep o s i t e d i n f r o n t of the f o o t . T h i s process has never been observed. Jones (1973) s p e c u l a t e s , but without evidence, t h a t t h i s mucus or f l u i d i s somehow reabsorbed i n t o the f o o t . 2- Once the f o o t i s l i f t e d i n a wave i t must be retu r n e d t o the substratum to which i t w i l l adhere during 4 5 FIGURE 3 . 7 . Problems with l i f t e d pedal 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 to the a n t e r i o r end of the f o o t . B) Unless a p a r t i t i o n were to separate the two halves o f the l i f t e d wave, the downward f o r c e of the h y d r o s t a t i c pressure would c o u n t e r a c t the upward f o r c e due to muscular 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 . F i g u r e 3.7 47 the interwave. Mechanisms proposed t o date (Lissman, 1945a; Jones, 1973; Jones and Trueman, 1970) t o account f o r the l i f t i n g and subsequent lowering of the f o o t r e q u i r e two processes t o occur s i m u l t a n e o u s l y : 1) The c o n t r a c t i o n of the muscles which r a i s e the f o o t p u l l s upwards on the mucus beneath a wave, c r e a t i n g an area of low pressure (see F i g u r e 3.7b). I t i s t h i s p r e d i c t e d low pressure which would p u l l f l u i d out of the f o o t to f i l l t he space beneath the wave. 2) i t the same time the h y d r o s t a t i c pressure w i t h i n the f o o t (supposedly r e s p o n s i b l e f o r f o r c i n g the f o o t back to the substratum) i s pushing downwards on the mucus beneath the wave c r e a t i n g an area of high pressure. However, unless a r i g i d p a r t i t i o n (as shown i n F i g u r e 3.7b) separates the two halves of the wave, the mucus beneath the wave must a l l be at the same pr e s s u r e . In other words i f no p a r t i t i o n e x i s t s (and none has been found) the downwards and upwards f o r c e s w i l l c a n c e l and the mucus w i l l be at ambient p r e s s u r e . Jones and Trueman (1970) however measure a s u b s t a n t i a l negative pressure ( i e , an upwards force) under pedal waves of the limpet P a t e l l a yulgata . 3. I t can a l s o be c a l c u l a t e d t h a t a very l a r g e f o r c e would be necessary t o l i f t the foot from the substratum as the animal f i r s t begins t o move. For the f o o t to be l i f t e d f l u i d must flow i n t o the new volume c r e a t e d , e i t h e r from the surrounding mucus or from the t i s s u e s , and t h i s flow must occur i n the time course of a s i n g l e wave (about 1 s e c ) . Such flow would r e q u i r e the a p p l i c a t i o n of upwards s t r e s s e s on the f o o t on the order of 10,000 kg/cm 2. T h i s f a c t o r i s 48 f u l l y e x p l a i n e d i n Chapter 9. As a consequence of the problems d e s c r i b e d here these mechanisms which r e q u i r e l i f t i n g of the f o o t are l e s s than c o n v i n c i n g . Mechanism For Slug Kinematics The r e s u l t s of t h i s study suggest a mechanism that both avoids these problems and e x p l a i n s the r e s u l t s of the previous authors. I t i s e s s e n t i a l l y a minor change i n the mechanism proposed by Jones (1973). Simply s t a t e d , t h i s change r e g u i r e s t h a t a s l u g w i l l not l i f t i t s f o o t during locomotion i f i t i s c r a w l i n g on a non-porous f i n f l e x i b l e s u r f a c e . Rather, the mucus l a y e r remains constant i n t h i c k n e s s and the mucus i s sheared between the moving f o o t and the s t a t i o n a r y substratum . However, during movement on a porous s u r f a c e i t w i l l l i f t i t s f o o t . T h i s 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 3.8. When the animal i s walking on a nonporous s u r f a c e the p r o p e r t i e s of the mucus beneath the f o o t are such that the muscles and c o n n e c t i v e t i s s u e support of the f o o t are in c a p a b l e of l i f t i n g the f o o t from the substratum. T h i s assumption concerning the p r o p e r t i e s of the pedal mucus w i l l be s u b s t a n t i a t e d i n Chapter 9. Unable to l i f t the f o o t , the obl i q u e muscles i n s t e a d a c t to p u l l the body c a v i t y down thereby narrowing the spaces o f the pedal hemocoel. The f o r c e r e q u i r e d t o p u l l the body c a v i t y down i s counteracted by a f o r c e p u l l i n g upwards on the mucus beneath the f o o t . T h i s upwards f o r c e w i l l appear as a negative pressure i n the 49 FIGURE 3 . 8 . , a model f o r the movement of the f o o t of a r i o l i m a x columbianus on a s o l i d substratum (a) and a porous or f l e x i b l e substratum (B). The forward movement of the wave and the decreased t h i c k n e s s of the f o o t r e s u l t i n a high h y d r o s t a t i c pressure i n the haemocoel ahead of the wave. 50 Figure 3.8 SOLID SURFACE mucus epithel ium layer 51 mucus to a sensor on the substratum s u r f a c e , , Again, however, t h i s upwards f o r c e i s not accompanied by d o r s a l l y d i r e c t e d movement of the f o o t . As the wave moves forward the f l u i d i n the pedal haemocoel i s f o r c e d to flow through the narrowed channels i n the area of muscular c o n t r a c t i o n . , T h i s r a i s e s the pressure of the haemocoelic f l u i d ahead of the wave. Since the pressure r e g u i r e d to f o r c e f l u i d through a tube at a given r a t e i s an i n v e r s e f o u r t h power f u n c t i o n of r a d i u s , i t i s only necessary f o r the spaces of the haemocoel to be narrowed s l i g h t l y t o c r e a t e a s u b s t a n t i a l pressure i n the haemocoel ahead of the wave. I t seems l i k e l y t h a t t h i s mechanism ( r a t h e r than c o n t r a c t i o n of the v e n t r i c l e as suggested by Jones (1973) i s r e s p o n s i b l e f o r the h y d r o s t a t i c pressure of the haemocoel. T h i s s i t u a t i o n i s analogous t o the p e r i s t a l t i c pumping of f l u i d through a tube. I t i s t h i s haemocoelic h y d r o s t a t i c pressure t h a t i s r e s p o n s i b l e f o r re-extending the f o o t a t i t s a n t e r i o r end. This mechanism does not r e q u i r e t h a t mucus or f l u i d beneath the f o o t be t r a n s p o r t e d forward with each wave, and s i n c e the f o o t i s never l i f t e d there i s no problem with g e t t i n g i t back down. I t a l s o accounts f o r the measurement of negative pressures.under the pedal waves. When the s l u g i s walking on a porous or f l e x i b l e s u r f a c e the s i t u a t i o n i s changed only i n t h a t the oblique muscles are now capable of e i t h e r p u l l i n g the f o o t away from the substratum or deforming the substratum i t s e l f . In the case of a porous s u r f a c e the a b i l i t y t o detach the f o o t i s a 52 consequence of the p o r o s i t y of the s u r f a c e which allows a i r t o e a s i l y r e p l a c e the d i s p l a c e d mucus. I t i s much e a s i e r f o r a i r to move i n t o t h i s space than i t would be f o r mucus. The lowering o f the f o o t i s accomplished by the h y d r o s t a t i c pressure i n the pedal hemocoel, c r e a t e d as e x p l a i n e d above. In order f o r the f o o t to be f o r c e d down only the a i r beneath the wave must be d i s p l a c e d , a process again f a c i l i t a t e d by the p o r o s i t y of the s u r f a c e . In nature s l u g s are r e q u i r e d to walk over s u r f a c e s of many types. While many of these are porous or f l e x i b l e t h e r e are smo o t h , n o n p o r o u s , i n f l e x i b l e s t r u c t u r e s such as the bark of some t r e e s and shrubs, the s t a l k s of p l a n t s , and the s u r f a c e s of rocks on which the s l u g would not be a h l e t o l i f t i t s f o o t . At present t h i s mechanism i s p r i m a r i l y s p e c u l a t i o n . I t w i l l r e q u i r e f u r t h e r experimentation before i t can be s u b s t a n t i a t e d . One f u r t h e r phenomenon may be mentioned here. I f a s l u g i s l i f t e d o f f the substratum and held i n m i d - a i r , i t w i l l attempt t o c r a w l . Pedal waves w i l l move a n t e r i o r l y on the f o o t and, i f some chalk i s dusted on the f o o t , the mucus l a y e r can be seen t o move . p o s t e r i o r l y . I f a s t r a i g h t chalk l i n e i s drawn l a t e r a l l y across the f o o t i t can be seen t h a t the mucus i n the c e n t r a l p o r t i o n of the f o o t and t h a t along the extreme edges o f the f o o t move p o s t e r i o r l y f a s t e r than mucus i n the rim s . Consequently the c h a l k l i n e i s deformed to the shape of an "Mn. I t i s d i f f i c u l t t o imagine a mechanism whereby the pedal waves can account f o r t h i s movement of mucus. I t seems much more l i k e l y t h a t the 53 movements of c i l i a , as d e s c r i b e d i n Chapter 2, are r e s p o n s i b l e . However, L i t t e t a l * : (1976) have found t h a t the e f f e c t i v e n e s s with which mucus i s t r a n s p o r t e d by c i l i a i s dependent on i t s storage modulus. They found t h a t mucus with a G' of 1 N/m2 was t r a n s p o r t e d most e f f e c t i v e l y by the c i l i a t e d e p i t h e l i u m of a f r o g p a l a t e . A. columbianus pedal mucus, with a G' of 100 N/m2, would, by t h i s c r i t e r i o n , not be e f f e c t i v e l y t r a n s p o r t e d . Beyond these general o b s e r v a t i o n s t h i s phenomenon has not been i n v e s t i g a t e d . 5 4 CHAPTER FOOfi P h y s i c a l P r o p e r t i e s The importance of pedal mucus i n the locomotion and adhesion of gastropods has been known f o r a c o n s i d e r a b l e p e r i o d of time. Barr (1926a) r e p o r t s t h a t s l u g s deprived of a supply of pedal mucus by the c a u t e r i z i n g of the pedal gland can n e i t h e r walk nor adhere. Later authors (Lissman,1945b;Jones,1973) remark on the obvious importance of pedal mucus t o locomotion. However none of these authors, nor any other author t o my knowledge ,have conducted t e s t s t o a s c e r t a i n the p r o p e r t i e s of pedal mucus. I t w i l l be shown i n t h i s chapter t h a t columbianus pedal mucus i s an unusual v i s c o e l a s t i c m a t e r i a l . Before d e s c r i b i n g the p h y s i c a l p r o p e r t i e s of t h i s s l u g ' s slime i t w i l l be u s e f u l to review the b a s i c concepts, terminology, and t e s t i n g procedures used i n the study of v i s c o e l a s t i c m a t e r i a l s . The term v i s c o e l a s t i c i s used to d e s c r i b e a m a t e r i a l t h a t s i m u ltaneously shows p r o p e r t i e s t y p i c a l of both f l u i d s and s o l i d s : s o l i d s are e l a s t i c , f l u i d s are v i s c o u s . E l a s t i c i t y and v i s c o s i t y are p r e c i s e l y d e f i n e d concepts. E l a s t i c i t y The primary c h a r a c t e r i s t i c of s o l i d s i s t h a t when pushed on they push back. T h i s concept i s q u a n t i f i e d i n the term e l a s t i c i t y . Take as an example the cube of m a t e r i a l shown i n F i g . 4.1a. Imagine t h a t one s i d e of the cube i s glued t o a non-moveable s t r u c t u r e and the opposite si d e i s 55 FIGURE 4.1. The p r o p e r t i e s of e l a s t i c s o l i d s . An undeformed cube (A) i s deformed (B) by the a p p l i c a t i o n of a f o r c e . , Force (or weight) can be p l o t t e d a g a i n s t deformation (C). , Nor m a l i z i n g f o r c e and deformation t o the dimensions of the sample allow (C) t o be r e p l o t t e d (D) i n terms o f s t r e s s (force/area) and shear r a t i o (Y/X). The slope of the s t r e s s / s h e a r r a t i o l i n e i s the shear modulus, G. The s t r e s s / s h e a r r a t i o curve need not be l i n e a r , as shown i n (D), but G at a p o i n t i s s t i l l the s l o p e of the l i n e a t t h a t p o i n t . 56 Figure 4.1 P , s h e a r ratio E p . shear ra t io 5 7 glued t o a p l a t e on which one can hang weights-. With no weights a p p l i e d the cube w i l l be undeformed. When a small weight i s hung from the p l a t e the cube w i l l deform a small d i s t a n c e as shown i n F i g . . 4.1b. I f the weight i s removed the cube w i l l immediately r e v e r t to i t s undeformed shape. A l a r g e r weight a p p l i e d w i l l cause the cube t o deform a l a r g e r d i s t a n c e , and again upon removal of the weight, the deformation w i l l d i sappear.. By adding weights of i n c r e a s i n g s i z e and r e c o r d i n g the deformation at each weight a curve such as F i g . 4.1c can be drawn. T h i s curve of weight versus deformation r e f e r s t o the p a r t i c u l a r cube, a piece of the same m a t e r i a l o f d i f f e r e n t shape or s i z e w i l l r e q u i r e d i f f e r e n t weights t o achieve the same deformation . In order to d e s c r i b e the p r o p e r t i e s of the m a t e r i a l from which a sample i s made r a t h e r than the shajae of the sample, weights and deformations are normali z e d . A weight hung on the p l a t e i n F i g . , 4.1a places a known f o r c e on the cube and t h i s f o r c e i s d i s t r i b u t e d a c r o s s the area of the cube f a c e . T h i s p a r t i c u l a r f o r c e and area can be normalized by d i v i d i n g one by the other (force / area) to a r r i v e at a term c a l l e d s t r e s s (sigma). The deformation i n c u r r e d by t h i s s t r e s s can be normalized t o the dimensions o f the sample, i n t h i s case the sample 1s t h i c k n e s s . The r a t i o (deformation/thickness) i s known as the shear r a t i o symbolized by rho. For small deformations the shear r a t i o i s approximately e q u a l to the shear s t r a i n (tan a i n F i g . 4.1b). For l a r g e deformations the shear s t r a i n cannot be meaningfully a p p l i e d t o the procedures used i n t h i s study. Consequently shear r a t i o i s 5 8 used. The curve 4.1c can then be r e p l o t t e d i n these new terms to y i e l d 4.1d. T h i s graph d e s c r i b e s a property of the m a t e r i a l from which the cube i s made. The graph i s unambiguous: f o r each a p p l i e d s t r e s s t h e r e corresponds one shear r a t i o , and when the s t r e s s i s removed the shear r a t i o immediately r e t u r n s t o zero. The r a t e at which the m a t e r i a l deforms does not e f f e c t the f i n a l magnitude of deformation, nor does i t matter whether the f o r c e . i s i n c r e a s i n g or de c r e a s i n g . Any m a t e r i a l f o r which such an unambiguous graph can be drawn i s s a i d to be e l a s t i c . Another term can be gleaned from t h i s analysis". In 4,1d n o t i c e t h a t at each value of rho the r a t i o sigma over rho i s the same. T h i s i s simply another way of s a y i n g t h a t the curve i s a s t r a i g h t l i n e with slope sigma/rho . This slope then conveys a l l the i n f o r m a t i o n c o n t a i n e d i n the graph and has been given a name , the e l a s t i c shear modulus or G. A m a t e r i a l with a l i n e a r sigma over rho curve i s s a i d t o be "Hookean". A m a t e r i a l may be e l a s t i c but not have a l i n e a r 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 the curve of 4.1e i s unambiguous yet not l i n e a r . . In t h i s case no s i n g l e value of G w i l l d e f i n e the curve, G must be computed f o r each p o i n t . Molecular B a s i s For E l a s t i c i t y The molecular b a s i s f o r e l a s t c i t y i n " s o f t " m a t e r i a l s has been the s u b j e c t of much study. The r e s u l t of t h i s study i s the theory of rubber e l a s t i c i t y . An i n t r o d u c t i o n to the theory may be found i n A k l o n i s , MacKnight and Shen 59 (1967); o r a more thorough treatment i n T r e l o a r (1975) or F e r r y (1965). The p r e c i s e thermodynamic and s t a t i s t i c a l arguments of the theory w i l l not be reviewed here as no use w i l l be made of them per se i n t h i s study. The g e n e r a l assumptions and c o n c l u s i o n s of the theory are used, however, and w i l l he b r i e f l y reviewed here. The theory of rubber e l a s t i c i t y was f i r s t proposed to account f o r the p h y s i c a l p r o p e r t i e s of n a t u r a l rubber.. I t has subsequently been found to account f o r the p r o p e r t i e s of n e a r l y a l l low modulus (E or G 10 2 to 10 6 N/m ) e l a s t i c s o l i d s ; but n a t u r a l rubber s t i l l s e r v e s as the best example f o r an e x p l a n a t i o n of the theory. When f i r s t c o l l e c t e d from the rubber t r e e , rubber l a t e x i s a v i s c o u s l i q u i d . In order to become "rubber" i t must be v u l c a n i z e d . T h i s i n v o l v e s mixinq the l a t e x with sulphur and h e a t i n g . S t u d i e s o f the v u l c a n i z a t i o n process r e v e a l t h a t before treatment the l a t e x i s formed from long, independent p o l y i s o b u t y l e n e c h a i n s , and t h a t d u r i n g treatment with sulphur these c h a i n s are c r o s s l i n k e d to each other by d i s u l f i d e b r i d g e s . Only when these c r o s s l i n k s are present i s the m a t e r i a l e l a s t i c . These f a c t s are explained i n the f o l l o w i n g manner: Before c r o s s l i n k i n g , the polymer c h a i n s of the l a t e x are f r e e to t w i s t and c o n t o r t at random and thermal a g i t a t i o n (brownian motion) ensures that the chains w i l l be i n constant motion . The shape of any one chain a t any given moment i s thus a random event. The s t a t i s t i c s of p r o b a b i l i t y can be a p p l i e d to the e n t i r e group of c h a i n s 60 forming the l a t e x t o a s c e r t a i n the most probable c o n f i g u r a t i o n o f the c h a i n s . I f a s t r e s s i s a p p l i e d t o the l a t e x these k i n e t i c a l l y f r e e c h a i n s w i l l respond by s l i d i n g past each other, each maintaining a random c o n f i g u r a t i o n and the m a t e r i a l w i l l f l o w . Now take an unstressed l a t e x f l u i d and c r o s s l i n k the polymer c h a i n s . I f c r o s s l i n k s are s u f f i c i e n t l y f a r apart each c h a i n w i l l s t i l l be able t o assume a random c o n f i g u r a t i o n . I f , however, a s t r e s s i s a p p l i e d t o the c r o s s l i n k e d network of c h a i n s , t h i s s i t u a t i o n i s changed. The c h a i n s are no l o n g e r f r e e t o s l i d e past each other.. As a consequence, when the m a t e r i a l i s s t r e t c h e d , the ends of the c h a i n s are on the average p u l l e d f a r t h e r apart i n the d i r e c t i o n of s t r e t c h (see F i g . 4.2) . Since random motion y i e l d s a c e r t a i n average 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 can be shown t h a t the c o n f i g u r a t i o n s the chains assume when the m a t e r i a l i s s t r e t c h e d are l e s s random. This s i t u a t i o n of (undeformed-random) (deformed-less random) can be r e s t a t e d i n terms of the co n f o r m a t i o n a l entropy o f the rubber network.. The s t a t e of maximum randomness i s a s t a t e of maximum entropy. A decrease i n randomness c o n s t i t u t e s a decrease i n entropy. Thus by deforming a pie c e o f rubber , one decreases the entropy of the.rubber network, a process which under the laws of thermodynamics r e q u i r e s t h a t work be done on the rubber. When the f o r c e of deformation i s removed the network tends t o spontaneously maximize entropy, which i s accomplished by 61 FIGURE 4.2. The molecular b a s i s of rubber e l a s t i c i t y . A) A long c h a i n c o n s i s t i n g of n l i n k s , each of l e n g t h , L, w i l l assume a c o n s t a n t l y changing random c o n f i g u r a t i o n . The most probable d i s t a n c e between the ends of the chain i s R = (2/3 n L 2) x / 2 . B) A c r o s s l i n k e d , but unstressed network i s s t i l l randomly arranged. 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 average value, and the c h a i n s are confi n e d t o fewer c o n f i g u r a t i o n s . As a consequence the entropy of the system i s decreased. 62 63 r e t u r n i n g to the o r i g i n a l dimensions and the work of deformation i s recovered. Thus a c r o s s l i n k e d network of k i n e t i c a l l y f r e e c h a i n s i s e l a s t i c . T h i s p r i n c i p l e a p p l i e s to any such network of k i n e t i c a l l y f r e e random polymer c h a i n s . While i t i s not l o g i c a l l y v a l i d t o i n v e r t the argument and say t h a t s i n c e a s o f t m a t e r i a l i s e l a s t i c i t i s formed o f a c r o s s l i n k e d network, no other e l a s t i c mechanism i s known or has been proposed f o r s o f t e l a s t i c s o l i d s . T h i s u n i v e r s a l c o r r e l a t i o n between e l a s t i c i t y of s o f t m a t e r i a l s and c r o s s l i n k e d s t r u c t u r e allows one to use the presence of e l a s t i c i t y as strong evidence f o r the f a c t t h a t a c r o s s l i n k e d network i s present. V i s c o s i t y The primary c h a r a c t e r i s t i c of f l u i d s i s t h a t they flow.. T h i s concept i s q u a n t i f i e d i n the term v i s c o s i t y . For the sake of t h i s example imagine t h a t g r a v i t y and s u r f a c e t e n s i o n do not e x i s t so t h a t a cube of f l u i d can be formed as shown i n F i g . 4.3a. • I f a s t r e s s i s a p p l i e d t o the p l a t e , as i n the p r e v i o u s example the sample w i l l deform (Fig._ 4.3b). In t h i s case of a l i q u i d cube, however, the sample w i l l not reach an e q u i l i b r i u m deformation. As long as the s t r e s s i s a p p l i e d the sample w i l l deform^ . I f a l a r g e r s t r e s s i s a p p l i e d the sample w i l l deform f a s t e r , hut again upon removal of the s t r e s s , w i l l not r e c o v e r i t s deformation. By a p p l y i n g f o r c e s of i n c r e a s i n g magnitude a curve can be drawn as i n F i g . 4.3c showing the r e l a t i o n s h i p 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 gi v e n s t r e s s a p p l i e d t o a cube of 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 shear r a t e (shear r a t i o / s e c o n d ) . The shear r a t e i s p r o p o r t i o n a l to the s t r e s s (C). The s l o p e of the s t r e s s / s h e a r r a t e 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 curve need not be l i n e a r , as shown i n (D), however the v i s c o s i t y at 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 6 6 between s t r e s s and r a t e of deformation. (shear r a t i o ) symbolized as rho dot. T h i s graph pro v i d e s an unambiguous d e s c r i p t i o n of a property of the f l u i d , f o r each s t r e s s there i s one shear r a t e ; deformations of the l i q u i d are not recovered. Again the l i n e a r r e l a t i o n s h i p can be c h a r a c t e r i z e d by a s i n g l e number - the slope of the l i n e . T h i s r a t i o of 1 s t r e s s / s h e a r r a t e i s the v i s c o s i t y . A f l u i d with a l i n e a r s t r e s s / s h e a r r a t e curve i s s a i d to be "Newtonian". F l u i d s showing a non l i n e a r s t r e s s / s h e a r r a t e r e l a t i o n s h i p must be c h a r a c t e r i z e d by a v i s c o s i t y a t each s t r e s s . Molecular B a s i s For V i s c o s i t y And Flow The molecular b a s i s of v i s c o s i t y and flow i s at one time both simple and complex . The.prime requirement f o r flow i s t h a t the molecules of the m a t e r i a l be independent of one another, t h a t i s , t h a t a molecule i s not e n e r g e t i c a l l y r e s t r a i n e d to occupying c e r t a i n f i x e d p o s i t i o n s r e l a t i v e to other molecules. I t i s on the b a s i s of t h i s c r i t e r i o n t h a t a f l u i d , i n c o n t r a s t to a s o l i d , can change shape without a l t e r i n g i t s i n t e r n a l energy. I f t h i s reguirement were to be s t r i c t l y met, however, i t would r e q u i r e no energy, ,and hence, no f o r c e to deform a f l u i d and the f l u i d ' s v i s c o s i t y would be zero. That a l l r e a l f l u i d s have measurable v i s c o s i t i e s i m p l i e s t h a t while i n d i v i d u a l molecules are not r i g i d l y bound t o each other t h e r e . i s some e n e r g e t i c c o s t t h a t accompanies movement of a molecule from one p o i n t to another. The magnitude of the energy c o s t determines the 67 v i s c o s i t y . Thus i t i s the hydrogen bonding between molecules which accounts f o r the high v i s c o s i t y of water r e l a t i v e to a f l u i d where no hydrogen bonds are formed, such as benzene. I t i s d i f f i c u l t , however, to apply t h i s simple concept i n any p r e c i s e f a s h i o n to macromolecular f l u i d s . I t i s u s u a l l y assumed t h a t flow i n these f l u i d s i n v o l v e s the constant breaking and reforming of weak bonds ( i n d i v i d u a l hydrogen bonds, hydrophobic i n t e r a c t i o n s , etc) as molecules move past each other. V i s c o e l a s t i c M a t e r i a l s No b i o l o g i c a l m a t e r i a l i s purely an e l a s t i c s o l i d or a v i s c o u s f l u i d . As a c l a s s , v i s c o e l a s t i c b i o m a t e r i a l s show the e n t i r e spectrum between s o l i d s t h a t w i l l flow s l i g h t l y i f given enough time (bone) to l i q u i d s which under proper circumstances may recover from deformation ( s y n o v i a l f l u i d ) . . In order to d e s c r i b e the p r o p e r t i e s o f these m a t e r i a l s a number of standard techniques have been de v i s e d . In g e n e r a l the o b j e c t i v e of these techniques i s t o s e p a r a t e l y q u a n t i f y the v i s c o u s and e l a s t i c c o n t r i b u t i o n s to the o v e r a l l p r o p e r t i e s of the m a t e r i a l . In l i g h t of t h i s o b j e c t i v e i t i s u s e f u l to d e s c r i b e these t e s t s with the a i d of some simple mathematical models of v i s c o e l a s t i c m a t e r i a l s . These models are c o n s t r u c t e d from two h y p o t h e t i c a l s t r u c t u r e s : an i d e a l s p r i n g , and an i d e a l dashpot as shown i n F i g u r e 4.4. The s p r i n g i s used as a model f o r a m a t e r i a l t h a t i s purely e l a s t i c - the more you deform the s p r i n g the harder i t p u l l s back. Thus the equation f o r the f o r c e / d e f o r m a t i o n curve f o r 68 FIGURE 4.4. Springs and dashpots. 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 the displacement, X. A dashpot (B) i s used to 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 to the r a t e of displacement. Springs and dashpots can be combined to model v i s c o e l a s t i c m a t e r i a l s . A "Maxwell Element" models 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 with a s p r i n g (D) models a 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 . Figure 4.4 M a x w e l l Element D 70 a s p r i n g i s : f=kx where f i s f o r c e , x i s deformation,and k i s a constant p r o p o r t i o n a l to the e l a s t i c modulus. The dashpot, a p i s t o n immersed i n a v i s c o u s l i q u i d , i s used to model purely v i s c o u s m a t e r i a l s . I t f o l l o w s from the d e f i n i t i o n of v i s c o s i t y t h a t the f o r c e r e q u i r e d to deform a dashpot depends on how f a s t the dashpot i s deformed. Thus f= n (dx/dt) where n i s the v i s c o s i t y of the f l u i d i n the dashpot. Springs and dashpots can be combined i n v a r i o u s c o n f i g u r a t i o n s to p r e d i c t the behaviour of v i s c o e l a s t i c m a t e r i a l s under v a r i o u s t e s t i n g c o n d i t i o n s . S t r e s s - s h e a r R a t i o Tests These t e s t s are conducted e s s e n t i a l l y as d e p i c t e d i n F i g . 4.1a and b. A sample, s u i t a b l y h e l d , i s s u b j e c t e d to an i n c r e a s i n g deformation and the f o r c e measured at each shear r a t i o . The deformation may be continued u n t i l the m a t e r i a l f a i l s ; or a t some p o i n t the deformation can be r e v e r s e d and f o r c e measured as the sample i s r e t u r n e d to i t s o r i g i n a l dimensions. The rate a t which the sample i s deformed may be v a r i e d . Examples of the behavior of v i s c o e l a s t i c m a t e r i a l s i n t h i s t e s t are shown i n F i g . 4.5a, 71 b, and c. F i g u r e s 4.5b and c i l l u s t r a t e the pr o p e r t y known as h y s t e r e s i s , the l o s s of energy accompanying the c y c l i c l o a d i n g of a sample. H y s t e r e s i s i s a r e s u l t of the v i s c o u s nature of a v i s c o e l a s t i c m a t e r i a l , . S t r e s s - r e l a x a t i o n T e s t s I f a m a t e r i a l i s deformed t o a given shear r a t i o and the f o r c e r e q u i r e d t o maintain t h i s shear r a t i o measured as a f u n c t i o n of time f o u r g e n e r a l types of curves c o u l d be found as shown i n F i g . 4,.6. . I f the m a t e r i a l i s a pure e l a s t i c s o l i d (modelled by a s p r i n g ) , by d e f i n i t i o n the f o r c e w i l l not vary with time. I f the m a t e r i a l i s a pure v i s c o u s l i g u i d t h e r e w i l l be no f o r c e s i n c e the r a t e of de f o r m a t i o n i s zero . I f the m a t e r i a l i s v i s c o e l a s t i c i t w i l l show a s t r e s s r e l a x a t i o n curve i n t e r m e d i a t e between the s o l i d and l i q u i d curves. a g a i n , v i s c o e l a s t i c m a t e r i a l s may be modelled by s p r i n g s and dashpots e i t h e r i n s e r i e s or p a r a l l e l . a s p r i n g and dashpot i n s e r i e s (a "Maxwell Element") w i l l model an u n c r o s s l i n k e d m a t e r i a l . an i n i t i a l f o r c e i s present due to the s t r e t c h i n g of the s p r i n g . However, as the f l u i d i n the dashpot flows the f o r c e f o l l o w s an e x p o n e n t i a l decay t o zero f o r c e . The time needed to decay to 1/e {37%) of the i n i t i a l f o r c e i s known as the r e l a x a t i o n time ,a measure of the r a t i o of v i s c o s i t y to e l a s t i c i t y . a Maxwell Element i n p a r a l l e l with a s p r i n g models a 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 . Here, the f o r c e decays e x p o n e n t i a l l y with time to a value 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 v i s c o e l a s t i c m a t e r i a l . Each curve r e p r e s e n t s one sample t e s t e d to the p o i n t of f a i l u r e (o) . . Note t h a t the m a t e r i a l i s s e n s i t i v e to the 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 r a t e i n c r e a s e s . B and C) Energy 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 hatched area ( f o r c e x d i s t a n c e = enerqy). The energy not recovered when the sample i s unloaded i s represented by the h o r i z o n t a l l y hatched area. H y s t e r e s i s equals the energy 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 present even though the sample r e t u r n s to i t s o r i g i n a l dimensions. In (C), an u n c r o s s l i n k e d m a t e r i a l , the sample has been permanently deformed by the l e n g t h , d. ) 73 74 FIGURE 4.6. R e p r e s e n t a t i v e 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 spring) does not relax,. B) . A c r o 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 (Figure 4.4, model D) r e l a x e s to 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 (Figure 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 T e s t i n g As e x p l a i n e d above, f o r an e l a s t i c s o l i d f o r c e i s p r o p o r t i o n a l t o the amount of deformation, while f o r a v i s c o u s f l u i d f o r c e i s p r o p o r t i o n a l t o the r a t e of deformation. T h i s f a c t i s u t i l i z e d i n dynamic t e s t s to sep a r a t e the c o n t r i b u t i o n of e l a s t i c i t y and v i s c o s i t y t o the o v e r a l l p r o p e r t i e s of a m a t e r i a l . What i s r e g u i r e d to achieve t h i s end i s a regimen o f deformation where the extent and r a t e of deformation are separated i n time. T h i s i s accomplished by s i n u s o i d a l l y deforming the m a t e r i a l such t h a t the deformation Since f o r a s p r i n g f=kx, the f o r c e on the s p r i n g due to the s i n u s o i d a l deformation w i l l be and the f o r c e w i l l be i n phase with the deformation. For a p u r e l y v i s c o u s m a t e r i a l f=n dx/dt. Therefore so t h a t f o r c e f o r a v i s c o u s m a t e r i a l w i l l lead deformation by 90 degrees (see F i g u r e 4.7) . A v i s c o e l a t i c m a t e r i a l w i l l show a phase s h i f t i n t e r m e d i a t e between a purely v i s c o u s or p u r e l y e l a s t i c m a t e r i a l , i e . somewhere between 90 and 0 x=sin w t f=k s i n wt, f=n d ( s i n wt)/dt=n cos wt. Figure 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 deformations. p=p s i n ( w t ) , t h e r e f o r e max o=a sin(wt) 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 l i q u i d max max cos(wt) leads sin(wt)by 90° 78 79 degrees. Thus by measuring the phase s h i f t , d e l t a , between deformation and f o r c e a measure of the r e l a t i v e values of e l a s t i c i t y and v i s c o s i t y can be found. At the.same time the r a t i o o f the f o r c e amplitude d i v i d e d by the displacement amplitude w i l l y i e l d a s t i f f n e s s , or modulus. T h i s o v e r a l l modulus (the complex modulus) i s denoted G*. The e l a s t i c c o n t r i b u t i o n t o G* cos d e l t a G* = G' i s c a l l e d the storage modulus, as i t i s a measure of the energy s t o r e d i n each c y c l e . O b v i o u s l y G'=G* when delta=0° and G'=0 when delta=90°. The v i s c o u s c o n t r i b u t i o n i s s i n d e l t a G*=G" or the l o s s modulus . The r a t i o of G" over G* i s tan d e l t a , a measure (at low values) t h a t can be r e l a t e d to h y s t e r e s i s . These t h r e e techniques form the b a s i s f o r t h i s study of the p h y s i c a l p r o p e r t i e s of A. columbianus pedal mucus. The knowledge gained from the t e s t s d e s c r i b e d here can be used to 1) p r e d i c t the behaviour of a m a t e r i a l i n a given s i t u a t i o n , and 2) provide some c l u e to the macromolecular s t r u c t u r e of the m a t e r i a l . T e s t i n g Apparatus And Procedures Two types of t e s t i n g machines were c o n s t r u c t e d to perform the t e s t s d e s c r i b e d above. Both machines were designed t o t e s t t h i n l a y e r s of mucus i n shear, 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 under a moving s l u g . Dynamic T e s t i n g Apparatus A 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 was 80 c o n s t r u c t e d as shown i n F i g u r e 4.8 and 4.9. In t h i s machine the sample i s he l d between two p a r a l l e l g l a s s p l a t e s , the t h i c k n e s s of the sample being measured and set by a micrometer. The p l a t e s were a l i g n e d d a i l y while being observed with a d i s s e c t i n g microscope. T y p i c a l sample t h i c k n e s s e s were 50um to 150um. Sample areas were measured v i s u a l l y by e s t i m a t i n g the p r o p o r t i o n of the 1 cm* g l a s s p l a t e occupied by the sample. One g l a s s p l a t e i s coupled to an e l e c t r o m a g n e t i c v i b r a t o r and i s the instrument f o r deforming the sample. The a c t u a l displacement of t h i s g l a s s p l a t e was measured by a tra n s d u c e r connected t o the v i b r a t o r s h a f t . T h i s displacement t r a n s d u c e r was c a l i b r a t e d by d e f l e c t i n g the measuring beam with a micrometer. Within the range of displacements used i n t h i s study, the tra n s d u c e r output was l i n e a r with displacement. T y p i c a l displacements f o r dynamic t e s t s were 20 um to 50 um. Displacements up to approximately 400 um co u l d be used f o r s t r e s s / s h e a r r a t i o t e s t s . The second g l a s s p l a t e i s supported by a p a r a l l e l beam tra n s d u c e r which senses the f o r c e exerted on a sample dur i n g a t e s t . The f o r c e t ransducer was c a l i b r a t e d by hanging a c c u r a t e l y known weights from the cente r of the g l a s s p l a t e . Forces as s m a l l as approximately 10 dynes could be measured a c c u r a t e l y . The unloaded resonance o f the f o r c e t r a n s d u c e r i s approximately 400 hz. During a dynamic t e s t the v i b r a t o r was powered by a s i n u s o i d a l s i g n a l generated by the 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 a m p l i f i e d s i g n a l s from the f o r c e and 81 FIGURE 4.8. ft schematic 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 used t o examine the p h y s i c a l p r o p e r t i e s o f pedal mucus a t low shear r a t i o s . 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 type 4300). 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 type 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 Systems model 200. CO N3 83 FIGURE 4.9. A c o n s t r u c t i o n drawing o f the dynamic t e s t i n g aparatus. A= styrofoam insulation.„ B= c o i l e d copper t u b i n g c a r r y i n g water 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 from the f o r c e t r a n s d u c e r . D= base p l a t e . E= s l i d i n g f o r c e transducer assembly. F= s t a i n l e s s s t e e l beam (0.008" t h i c k ) with mounted semiconductor s t r a i n guages (BLH type SPB3-20-35). G= g l a s s s l i d i n g s u r f a c e . H= rod connecting the f o r c e t r a n s d u c e r to the micrometer. 1= guide bearing f o r the micrometer rod. J= micrometer, f i x e d t o the base p l a t e . K= the alignment system f o r the displacement apparatus. L= s t a i n l e s s s t e e l beam (0.002" thick) s u p p o r t i n g the displacement g l a s s p l a t e . M= rod connecting the 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 sandwhiched between the f o r c e and displacement g l a s s plates,. 0= the 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= styrofoam i n s u l a t i n g cover with a gap f o r the displacement r o d . FIGURE 4.9 85 displacement t r a n s d u c e r s were i n t u r n compared to t h i s r e f e r e n c e s i g n a l . For each 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 phase s h i f t from the r e f e r e n c e s i n e wave and the amplitude of the transducer s i g n a l . From these d a t a the phase s h i f t of the f o r c e s i g n a l r e l a t i v e t o the displacement s i g n a l c o u l d be c a l c u l a t e d to y i e l d a value f o r d e l t a . The r a t i o of amplitudes i s a measure of G*. Samples were t e s t e d at f r e q u e n c i e s r a n g i n g from 0.2 hz to 100 hz. Above 100 hz resonances wi t h i n the frame s u p p o r t i n g the v i b r a t o r cause s p u r i o u s and e r r a t i c readings. Below 0.2 hz d r i f t i n the semiconductor s t r a i n guages of the f o r c e transducer does not allow f o r a c c u r a t e measurements. S t r e s s - s h e a r r a t i o t e s t s were performed by powering the v i b r a t o r with a t r i a n g u l a r wave. A m p l i f i e d s i g n a l s from the f o r c e and displacement t r a n s d u c e r are then s u p p l i e d to a two channel c h a r t r e c o r d e r . Both the frequency and amplitude of the displacement c o u l d be v a r i e d w i t h i n the l i m i t s d e s c r i b e d above. The t e s t i n q apparatus was enclosed i n an i n s u l a t e d , temperature c o n t r o l l e d chamber t h a t c o u l d e i t h e r be used as a bath to immerse the sample i n a t e s t s o l u t i o n or a c l o s e d chamber t o maintain 100% r e l a t i v e humidity during a t e s t . A l l t e s t s were conducted at 22-23 °C with temperature v a r i a t i o n s d u r i n g the course of a t e s t l e s s than 0.1 °C. The u s e f u l n e s s o f t h i s t e s t i n g apparatus was l i m i t e d i n two r e s p e c t s . 1. The semiconductor s t r a i n gauges used i n the f o r c e t ransducer are e x c e e d i n g l y temperature s e n s i t i v e . While t h i s posed no problem f o r t e s t s of s h o r t d u r a t i o n such 86 as dynamic or s t r e s s / s h e a r r a t i o t e s t s , t e s t s r e q u i r i n g l o n g term s t a b i l i t y (such as s t r e s s r e l a x a t i o n t e s t s ) c o u l d not be performed. 2. The n e c e s s i t y of maintaining, the g l a s s p l a t e s p a r a l l e l and a s e t d i s t a n c e apart l i m i t e d the shear r a t i o s t h a t c o u l d p r a c t i c a l l y be o b t a i n e d . In order to overcome these l i m i t a t i o n s the second t e s t i n g apparatus was c o n s t r u c t e d . The Cone And P l a t e Apparatus The cone and p l a t e machine used f o r measuring the p h y s i c a l p r o p e r t i e s of slime a t l a r g e shear r a t i o s and shear r a t e s and f o r s t r e s s r e l a x a t i o n t e s t s i s shown i n F i g u r e 4.10 In t h i s machine the sample i s held between an aluminum p l a t e and a s m a l l angle P l e x i g l a s cone. One r e v o l u t i o n of the cone produced a uniform shear r a t i o i n the sample of 249. The g e o m e t r i c a l b a s i s f o r uniform s t r a i n i n a cone and p l a t e c o n f i g u r a t i o n i s e x p l a i n e d i n F i g u r e 4.10. The diameter of the sandwiched sample was measured with v e r n i e r c a l i p e r s and the area c a l c u l a t e d . The r o t a t i o n o f the p l a t e was converted to a l i n e a r measure by a windlass which supports the core of a 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 transformer (LVDT). The a m p l i f i e d s i g n a l from t h i s t r a n s f o r m e r was recorded on one channel o f a two channel c h a r t r e c o r d e r . The LVDT was c a l i b r a t e d by i n s e r t i n g the core with a micrometer. R o t a t i o n s could be measured to approximately +-2 degrees. The cone i s supported by a t o r s i o n bar. The t w i s t i n g of t h i s bar , a measure of f o r c e , r e s u l t s i n the d e f l e c t i o n 87 FIGURE 4.10. A combined schematic and c o n s t r u c t i o n drawing of the cone and p l a t e apparatus used t o examine the p h y s i c a l p r o p e r t i e s of pedal mucus at high shear r a t i o s . The d i s t a n c e through which the sample i s deformed i s a f u n c t i o n of r, the r a d i u s , and W, the angular v e l o c i t y and i s equal to rW. The t h i c k n e s s o f the sample i s a gain a f u n c t i o n of the r a d i u s and i s equal to mr where m i s the s l o p e of the cone. The shear r a t i o thus equals Wr/mr = W/m and i s independent of the 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 the r a d i u s of 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 of the sample volume. I t i s approximately equal to 0„79 R. The e l e c t r i c motor i s a Cole-Parmer Master Servodyne, and the a m p l i f i e r s are SE L a b o r a t o r i e s type 4300. A= a d j u s t a b l e mounting post 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 supported by an 18 guage hypodermic needle. D= arm s u p p o r t i n g the LVDT co r e . E= base 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 rod with a p o l i s h e d end a c t i n g as the p l a t e . G= chuck attaches the rod to the 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 core to the c e n t e r of the cone. P= moist paper to slow e v a p o r a t i o n r a t e from the 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 r i g i d arm which supports the cone of a second LVDT. The s i g n a l from t h i s transformer was recorded on the second channel of the c h a r t r ecorder . The f o r c e t r a n s d u c e r was c a l i b r a t e d by t u r n i n g the t r a n s d u c e r on i t s s i d e . s o that the LVDT i s v e r t i c a l . A c c u r a t e l y known weights were then hung from the c o r e . The f o r c e generated d u r i n g a t e s t was assumed t o act at a r a d i u s E as e x p l a i n e d i n F i g u r e 4,10.. T h i s r a d i u s was then compared to the d i s t a n c e from the c e n t e r of the cone to the LVDT core to c a l c u l a t e the mechanical advantage and a r r i v e at a f i n a l c a l i b r a t i o n . Forces as s m a l l as 100 dynes ( a c t i n g at a t y p i c a l e f f e c t i v e sample r a d i u s of approximately 5 mm) c o u l d be a c c u r a t e l y measured. The unloaded resonance o f the f o r c e transducer was approximately 50 c y c l e s per second. The e l e c t r i c motor r o t a t i n g the p l a t e provided shear r a t i o s c o n t i n u o u s l y v a r i a b l e above shear r a t e s of 5 per second. The time r e q u i r e d to reach f u l l speed was about 20 m i l l i s e c o n d s . A l l t e s t s were performed at room temperature (21-24 °C) with no p r o v i s i o n made to r e g u l a t e the temperature of the sample and apparatus. Temperature v a r i a t i o n s d u r i n g t e s t s were l e s s than 0.5 °C. A moist r i n g of absorbent paper placed as shown i n Figure 4.10 serves to maintain a high r e l a t i v e humidity around the sample and thereby minimize e v a p o r a t i o n . C o l l e c t i o n Of Pedal Mucus A r i o l i m a x columbianus pedal mucus was c o l l e c t e d by 90 a l l o w i n g the s l u g t o crawl on a g l a s s rod. As the s l u g attempted to crawl around the rod the rod was r o t a t e d f o r c i n g the s l u g to continue c r a w l i n g l e s t i t l o s e i t s f o o t i n g . In t h i s manner 0.1 t o 0.3 ml of pedal mucus c o u l d be c o l l e c t e d from each s l u g . T h i s amount was s u f f i c i e n t f o r any o f the t e s t s d e s c r i b e d above to be performed on a s i n g l e sample from one i n d i v i d u a l . The c o l l e c t i o n procedure l a s t e d approximately one minute.. Samples were placed i n the t e s t i n g apparatus immediately a f t e r c o l l e c t i o n . No attempt has been made to determine the p r e c i s e o r i g i n of the pedal slime c o l l e c t e d , though i t i s probable t h a t the preponderance was produced by the pedal gland. By d u s t i n g the d o r s a l s u r f a c e of a s l u g with c h a l k p r i o r t o pedal mucus c o l l e c t i o n i t was shown t h a t t h e mucus c o l l e c t e d from the f o o t was not contaminated by mucus from the d o r s a l e p i t h e l i u m . I t i s i n e v i t a b l e t h a t v a r i a t i o n s be found i n the p r o p e r t i e s of slime from one s l u g compared to t h a t of another s l u g , or t h a t slime p r o p e r t i e s w i l l vary when c o l l e c t e d from one s l u g on d i f f e r e n t days.. For example, i n one s e t of 18 slime samples c o l l e c t e d on a s i n g l e day, the dry weight of the mucus ranged from 2,85% to 4.46% of the wet weight . In attempting to a c c u r a t e l y d e s c r i b e the p h y s i c a l p r o p e r t i e s of s l u g slime an account of t h i s v a r i a b i l i t y must be made when r e p o r t i n g r e s u l t s . . In the case of c e r t a i n t e s t s v a r i a t i o n i n the composition of the c o l l e c t e d slime appears t o cause l i t t l e v a r i a t i o n i n the property measured. In these cases i n f o r m a t i o n about 91 i n d i v i d u a l samples i s not l o s t i n l o o k i n g at an average of a l l samples, consequently r e s u l t s o f a l l t e s t s are averaged and the co n f i d e n c e l i m i t s around the mean are noted. Other t e s t s are a f f e c t e d by c o m p o s i t i o n a l v a r i a b i l i t y t o a g r e a t e r extent. For these t e s t s i t o f t e n happens that the average of a l l t e s t s does not c l o s e l y resemble the measured value f o r any i n d i v i d u a l t e s t . In t h i s case the r e s u l t s from the i n d i v i d u a l sample c l o s e s t t o he average w i l l be presented as a " t y p i c a l " t e s t and the range o f valu e s f o r a l l t e s t s w i l l be noted. P h y s i c a l P r o p e r t i e s Of A. Columbianus Mucus At Low Shear R a t i o s Three s o r t s of t e s t s were conducted t o a s c e r t a i n the p r o p e r t i e s of A r i o l i m a x columbianus pedal mucus a t low shear r a t i o s ( i e . l e s s than 5) : 1) S t r e s s / s h e a r r a t i o t e s t s 2) S t r e s s r e l a x a t i o n t e s t s and 3) Dynamic t e s t s . The r e s u l t s of these t e s t s w i l l be d i s c u s s e d i n t u r n . S t r e s s - s h e a r R a t i o Tests F i g u r e 4.11 shows a t y p i c a l s t r e s s - shear r a t i o curve f o r mucus deformed i n the dynamic t e s t i n g apparatus to a shear r a t i o of a few percent a t a low shear r a t e . Under these c o n d i t i o n s the s l i m e behaves p r i m a r i l y as an e l a s t i c s o l i d . The s t r e s s / s h e a r r a t i o curve i s e s s e n t i a l l y l i n e a r with an e l a s t i c modulus of approximately 200 N/m2. That the mucus i s e l a s t i c at these shear r a t i o s and shear r a t e s i n d i c a t e s the presence of some network s t r u c t u r e w i t h i n the 92 FIGURE 4.11. a s t r e s s / s h e a r r a t i o curve f o r a r i o l i m a x columbianus pedal mucus at a low shear r a t i o . Shear 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 s l i m e . The v i s c o u s nature of the m a t e r i a l shows only i n the s l i g h t h y s t e r e s i s . F i g u r e 4.12 shows a t y p i c a l s t r e s s - shear r a t i o curve f o r mucus at l a r g e r shear r a t i o and at a shear r a t e over ten times t h a t of F i g u r e 4.11. Under these c o n d i t i o n s the v i s c o e l a s t i c nature of the m a t e r i a l i s e v i d e n t . Upon l o a d i n g the mucus again shows a G of about 200 N/m2 but upon unloading i t can be seen that a c o n s i d e r a b l e p r o p o r t i o n of the energy of deformation has gone to deforming the v i s c o u s component of the m a t e r i a l , and i s non-recoverable. The f a c t t h a t the m a t e r i a l does not r e t u r n t o i t s o r i g i n a l dimensions i n d i c a t e s t h a t whatever network i s r e s p o n s i b l e f o r the e l a s t i c i t y i s e i t h e r broken down p a r t i a l l y or has rearranged i n the course of deformation. However , the f a c t t h a t the mucus does re c o v e r some of the deformation shows t h a t some form of e l a s t i c network i s s t i l l p r esent. S t r e s s R e l a x a t i o n T e s t s F i g u r e 4. 13 shows the averaged r e s u l t s from 10 s t r e s s r e l a x a t i o n t e s t s c a r r i e d out i n the cone and p l a t e apparatus. These t e s t s were done at a range of shear r a t i o s from 2 to 5. No d i f f e r e n c e i n the time course of r e l a x a t i o n as a f u n c t i o n of shear r a t i o was noted. The r e l a x a t i o n curve cannot be c h a r a c t e r i z e d by a s i n g l e or s m a l l number of r e l a x a t i o n times i n d i c a t i n g t h a t t h e r e are a v a r i e t y of d i f f e r e n t r e l a x a t i o n processes o c c u r r i n g i n the m a t e r i a l . T h i s i s t y p i c a l f o r v i s c o e l a s t i c b i o m a t e r i a l s . U n f o r t u n a t e l y t h i s form of t e s t does not g i v e any c l u e s as 95 FIGURE 4 . 1 2 a s t r e s s / s h e a r r a t i o curve f o r A r i o l i m a x columbianus pedal mucus at a moderate shear r a t i o . Shear r a t e = 0.56/sec. and G i s approximately 1 0 0 N/m2. The h y s t e r e s i s i s 4 4 . 2 % . Note that the sample does not r e t u r n to i t s o r i g i n a l dimensions. O N 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 of ftriolimax columbianus pedal mucus. The curve i s the average of 1 0 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 5 0 0 1 0 0 0 , 1500 2 0 0 0 S e c o n d s vo Oo 99 to the nature o f these r e l a x a t i o n p r o c e s s e s . Within the time course of these experiments (30 minutes) the r e l a x i n g slime does not reach an e q u i l i b r i u m s t r e s s , nor do es the curve give any h i n t t h a t an e q u i l i b r i u m would be reached i f r e l a x a t i o n f o r g r e a t e r p e r i o d s of time c o u l d be measured. In t h i s r e s p e c t , i n t h a t i t flows, mucus behaves as a f l u i d . However, i t has been shown by s t r e s s - shear r a t i o t e s t s t h a t an e l a s t i c network i s present during deformation t o these shear r a t i o s f o r a t l e a s t s h o r t time i n t e r v a l s . From these two f a c t s i t can be hypothesized t h a t t h i s network , while s t a b l e over r e l a t i v e l y s h o r t p e r i o d s of time (seconds), i s capable of rearrangment over long p e r i o d s of time (minutes to hou r s ) . Dynamic Te s t s The r e s u l t s of the dynamic t e s t s on Ariolimax columbianus pedal mucus are summarized i n F i g u r e 4.14. As mentioned e a r l i e r these t e s t s were c a r r i e d out at low extension r a t i o s of about .2 t o .5 and f r e q u e n c i e s from .2 to 100 Hz. These t e s t s are thus desiqned t o r e v e a l the p r o p e r t i e s of the e l a s t i c network on a time s c a l e of m i l l i s e c o n d s t o seconds. Under these c o n d i t i o n s the m a t e r i a l i s again shown to behave p r i m a r i l y as an e l a s t i c s o l i d : the storage modulus i s ten times the l o s s modulus and the r a t i o of the two (tan delta) does not vary s i g n i f i c a n t l y over the range of f r e q u e n c i e s t e s t e d . . T h i s c o n f i r m s t h a t the network of the mucus i s k i n e t i c a l l y f r e e (and thereby e l a s t i c ) on a time s c a l e of 10 m i l l i s e c o n d s . T h i s i s h a r d l y 100 FIGURE 4.14. Dynamic t e s t r e s u l t s . The curves are.averages from 6 samples t e s t e d i n a i r a t 100% r e l a t i v e humidity. The bars are 95% confidence i n t e r v a l s . 102 s u p r i s i n g s i n c e i n a network as d i f f u s e as mucus there i s v i r t u a l l y nothing present to i n h i b i t the freedom of network c h a i n s . I t i s however f u r t h e r evidence s u p p o r t i n g the hy p o t h e s i s t h a t the e l a s t i c network of the pedal mucus of Ariolimax columbianus can be t r e a t e d r e a l i s t i c a l l y as a network conforming to the theory of rubber e l a s t i c i t y . In summary, the t e s t s on A r i o l i m a x columbianus pedal mucus a t low shear r a t i o s i n d i c a t e t h a t the m a t e r i a l , while v i s c o e l a s t i c , i s p r i m a r i l y a s o l i d formed of a c r o s s l i n k e d network, the c r o s s l i n k s being s t a b l e on a time s c a l e of m i l l i s e c o n d s t o seconds, but u n s t a b l e a t longer p e r i o d s o f time. P h y s i c a l P r o p e r t i e s Of JU Columbianus Pedal Mucus At High Shear R a t i o s While i t i s u s e f u l t o know the p r o p e r t i e s of mucus at low shear r a t i o s , the a p p l i c a b i l i t y of t h i s knowledge to the problem of s l u g locomotion i s r e s t r i c t e d . For a s l u g with a step l e n g t h of one m i l l i m e t e r and a mucus l a y e r t h i c k n e s s of 10 micrometers, the pedal mucus w i l l be exposed t o a shear r a t i o on the order of 100 r a t h e r than the 0.1 t o 4.0 t y p i c a l o f the t e s t s d e s c r i b e d above. In order t o i n v e s t i g a t e the p r o p e r t i e s of A A columbianus pedal mucus a t h i g h e r shear r a t i o s a number of t e s t s were c a r r i e d out using the cone and p l a t e apparatus. . S t r e s s - s h e a r R a t i o Tests The r e s u l t s of sh e a r i n g pedal mucus t o high e r shear 103 r a t i o s are shown i n F i g u r e s 4.15 and 4.16. I t i s evident even at a f i r s t glance t h a t these p r o p e r t i e s are q u i t e d i f f e r e n t from those a t low shear r a t i o s . These d i f f e r e n c e s are best e x p l a i n e d by f o l l o w i n g the time course of a t e s t as shown i n F i g u r e 4.15. The t e s t i s i n i t i a t e d when the motor r o t a t i n g the p l a t e i s switched on. As the p l a t e r o t a t e s through the i n i t i a l few degrees the mucus sample i s deformed as i n the s t r e s s - s h e a r r a t i o t e s t s d e s c r i b e d e a r l i e r . S t r e s s r i s e s roughly l i n e a r l y with shear r a t i o with a modulus o f about 100-200 N/m2. However , at a shear r a t i o of about 5-6, the mucus a b r u p t l y y i e l d s and the s t r e s s f a l l s . Due to the design of the apparatus the shear r a t i o at which the mucus y i e l d s can onl y be determined t o an accuracy o f about p l u s or minus 1.4 rho. Within the l i m i t s of accuracy of the machine the breaking shear r a t i o does not vary with the shear r a t e at which the sample i s deformed. In c o n t r a s t , the s t r e s s a t which the sample y i e l d s (sigma sub y) i s dependent on the shear r a t e ; the higher the shear r a t e the l a r g e r the y i e l d s t r e s s . A p l o t of y i e l d s t r e s s versus s t r a i n r a t e f o r a t y p i c a l sample i s shown i n 4.16. As the mucus i s deformed beyond i t s y i e l d p o i n t a new s t r e s s l e v e l i s reached. T h i s l e v e l remains constant with f u r t h e r deformation. As shown i n the i n t r o d u c t i o n t o t h i s chapter, the maintenance of a con s t a n t s t r e s s f o r a constant shear r a t e i s one d i s t i n g u i s h i n g c h a r a c t e r i s t i c of a f l u i d . I t would thus appear t h a t as the mucus y i e l d s i t s e l a s t i c network s t r u c t u r e i s broken to the p o i n t where the m a t e r i a l behaves as a v i s c o u s l i q u i d . I f t h i s i s so, two other f a c t s 104 FIGURE 4.15. The c h a r a c t e r i s t i c s of A r i o l i m a x columbianus pedal mucus at high shear 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 , but w i l l " h e a l " i f allowed t o r e s t unstressed. Figure 4.15 p = 20 I y i e l d motor on motor off motor on motor off motor on 106 FIGURE 4.16. A r e p r e s e n t a t i v e p l o t of y i e l d s t r e s s and flow s t r e s s versus shear r a t e f o r Ar i o l i m a x columbianus pedal mucus. Y i e l d s t r e s s range: low y=0.024x + 0.83 high y=0.117x + 1.92 flow s t r e s s range low y=0.010x + 0.070 high y=0.053x + 0.53 108 should be consequent: 1) The s t r e s s r e q u i r e d t o deform the l i q u i d should be dependent upon shear r a t e . T h i s i s indeed the case. Samples deformed at higher shear r a t e s show higher p o s t - y i e l d s t r e s s e s , the flow s t r e s s (sigma sub f) . A p l o t of flow s t r e s s versus shear r a t e f o r a t y p i c a l sample i s shown i n F i g u r e 4.16, The shape of the r e l a t i o n s h i p i s l i n e a r . , showing t h a t mucus, a f t e r i t has y i e l d e d , behaves as a l i q u i d with an inc r e m e n t a l v i s c o s i t y of about 50 p o i s e i e 5,000 times more v i s c o u s than water. Note t h a t the l i n e of sigma sub f does not e x t r a p o l a t e t o zero. I t i s assumed t h a t at shear r a t e s lower than those measured the f l u i d mucus shows non-Newtonian behaviour as depicted by the dotted l i n e on the graph. 2) When deformation i s h a l t e d a s o l i d w i l l maintain a p o s i t i v e value of s t r e s s ; i n the case of a l i q u i d the s t r e s s w i l l immediately decay t o zero. As shown i n F i g u r e 4.15 the h i g h l y deformed mucus again behaves as a l i q u i d . Two p h y s i c a l 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 these r e s u l t s . F i r s t , the e l a s t i c network may break down throughout the e n t i r e sample a l l o w i n g the sample as a whole to behave as a l i g u i d . . Second i t i s p o s s i b l e t h a t only the network i n the p o r t i o n of the sample adjacent t o e i t h e r the cone or p l a t e i s destroyed, forming a t h i n l a y e r of l i q u i d s e p a r a t i n g the s t i l l s o l i d sample from the cone or p l a t e . In t h i s second case i t would e s s e n t i a l l y be the p r o p e r t i e s of t h i s t h i n l a y e r t h a t are being t e s t e d r a t h e r than the sample as a whole. I f t h i s i s so , and depending on the t h i c k n e s s of the f l u i d l a y e r , the c a l c u l a t e d values of shear 1 0 9 r a t e may be c o n s i d e r a b l y i n e r r o r . I t i s im p o s s i b l e from the t e s t s performed i n the course of t h i s study t o d i s t i n g u i s h which o f these two p o s s i b i l i t i e s i s the c o r r e c t one*. While i t would be i n t e r e s t i n g t o be able to r e s o l v e t h i s guestion , the f a c t t h at i t has not been r e s o l v e d does not a f f e c t the accuracy of the r e s u l t s of these t e s t s i n d e s c r i b i n g the e f f e c t i v e p r o p e r t i e s of s l u g pedal mucus. As shown i n F i g u r e 4 . 1 6 t h e r e i s c o n s i d e r a b l e range i n the va l u e s f o r breaking s t r e s s and flow s t r e s s i n the samples t e s t e d . Though the h y p o t h e s i s was not t e s t e d i t seems l i k e l y t h a t these v a r i a t i o n s are due to the normal v a r i a t i o n i n the c o n c e n t r a t i o n o f g l y c o p r o t e i n present i n the mucus as e x p l a i n e d e a r l i e r i n t h i s c h a pter. T h i s v a r i a t i o n i n the magnitude of y i e l d s t r e s s and flow s t r e s s does not r h o w e v e r , a f f e c t the r a t i o between the two f o r any one sample ncr i s the r a t i o dependent on shear r a t e . F i g u r e 4 . 1 7 shows a p l o t o f the y i e l d s t r e s s / f l o w s t r e s s values f o r a l l samples t e s t e d . T h i s constant value of y i e l d s t r e s s /flow s t r e s s e q u a l to about 2.0 i s important f o r the locomotion of the animal.. I t w i l l be shown i n Chapter 7 how the a b i l i t y of the mucus to change from a s o l i d t o a l i g u i d i s a n e c e s s i t y f o r adhesive locomotion. The i n v a r i a n t r a t i o of s o l i d s t r e n g t h t o v i s c o s i t y d e s c r i b e d here means t h a t the mucus can f u n c t i o n e f f e c t i v e l y w i t h i n a wide range of hyd r a t i o n s and shear r a t e s . Do these t e s t s then imply t h a t the mucus beneath a moving s l u g i s i n the form of a l i g u i d ? One i s reminded t h a t as the s l u g moves the mucus i s deformed t o a shear 110 FIGURE 4.17. The r a t i o of y i e l d s t r e s s t o flow s t r e s s i s constant among samples and r e g a r d l e s s of shear r a t e . F i g u r e 4.17 112 r a t i o of about 100. This question i s answered i n the course.of f u r t h e r t e s t i n g . Aqain r e f e r to F i g u r e 4.15. A f t e r the r o t a t i o n of the p l a t e i s stopped and the s t r e s s has decayed , the sample i s allowed t o remain unstressed f o r one second., T h i s p e r i o d was chosen as e q u i v a l e n t to the p e r i o d o f time t h a t mucus would be beneath the interwave (and t h e r e f o r e not deformed) under a moving s l u g . At the end of t h i s time the p l a t e i s again r o t a t e d . I t i s found t h a t the mucus, r a t h e r than showing the c h a r a c t e r i s t i c s of a l i q u i d , has "healed" and again behaves as a s o l i d . S t r e s s r i s e s l i n e a r l y with shear r a t i o . At a shear r a t i o equal to 5-6 the m a t e r i a l again y i e l d s and so f o r t h . The record of t h i s second p e r i o d of deformation i s i d e n t i c a l to the f i r s t . In f a c t t h i s " y i e l d - h e a l " c y c l e can be repeated 20 t o 30 times before the mucus begins t o show s i g n s of f a i l i n g t o recover i t s s o l i d i t y . Thus, the e l a s t i c network, which must be broken f o r the mucus to a c t as a l i q u i d , reforms q u i c k l y . A d d i t i o n a l evidence of t h i s process i s provided by two f u r t h e r t e s t s . 1 A f t e r a sample had been deformed a number of times at a given shear r a t e , the sample was allowed to r e s t f o r 10-12 seconds while the c o n t r o l s were set f o r another s e t of deformations a t a new shear r a t e . I t was noted t h a t the i n i t i a l deformation i n t h i s new s e r i e s showed a c o n s i d e r a b l y hi g h e r y i e l d s t r e s s than subsequent deformations., The values of y i e l d s t r e s s shown i n F i g u r e 4.16 are f o r deformations subsequent t o the i n i t i a l deformation as these 113 are more c h a r a c t e r i s t i c o f the p r o p e r t i e s of mucus under a moving s l u g . F i g u r e 4.18 shows values from a t y p i c a l sample comparing i n i t i a l breaking s t r e s s (sigma sub y i ) and subsequent (sigma sub y) values f o r y i e l d s t r e s s as a f u n c t i o n of shear r a t e . I t i s apparent t h a t the e l a s t i c network formed when the mucus r e s t s f o r 10-12 seconds i s st r o n g e r than t h a t formed when r e s t i s allowed f o r only one second. The time course of the h e a l i n g process was examined through another s e r i e s of t e s t s using the cone and p l a t e apparatus as shown i n F i g u r e 4.19. In these t e s t s one complete c y c l e of deformation was performed on the sample. The sample was then allowed to " h e a l " f o r varying l e n g t h s of time. A f t e r h e a l i n g the sample was again s t r e s s e d , but only to a s u b - y i e l d l e v e l . R o t a t i o n of the p l a t e was then h a l t e d and a s t r e s s r e l a x a t i o n time (tau) measured. As a matter of convenience, t au was chosen as the time ( i n seconds) r e q u i r e d f o r the s t r e s s t o r e l a x to 0.20 of the i n i t i a l s t r e s s (sigma sub zero i n F i g u r e 4.1). The r e s u l t s of a t y p i c a l t e s t are presented i n F i g u r e 4.20. R e l a x a t i o n times f o r any given h e a l time proved to be q u i t e v a r i a b l e . However, the g e n e r a l trend of i n c r e a s i n g tau with i n c r e a s i n g h e a l time i s apparent and i s taken as evidence t h a t the sample becomes more s o l i d the l o n g e r i t i s allowed t o h e a l . T h i s property of the healed mucus can be compared to the mucus i n i t s f l u i d form. When the r o t a t i o n of the p l a t e i s stopped while the mucus i s i n i t s f l u i d form, the f o r c e decays q u i c k l y to zero . The r e l a x a t i o n 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 of 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 only s h o r t term " h e a l " p e r i o d s . 115 1 1 6 FIGURE 4 . 1 9 . The t e s t i n g procedure used t o determine the e f f e c t o f heal time on the recovery of s o l i d i t y . R e l a x a t i o n time, here d e f i n e d as the 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 of s o l i d i t y . F igu re 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 of 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 pedal mucus. The range shown i n these t e s t s was: low y=0.11x + 0.41 rz=0.71 high y=5.75x + 27.59 rz=0.51 120 i s too s h o r t to be a c c u r a t e l y measured by t h i s t e s t i n g procedure but i s c e r t a i n l y l e s s than 0.1 seconds. Thus i t can be seen t h a t the mucus recovers c o n s i d e r a b l e s o l i d i t y i n a p e r i o d of l e s s than a second. The p h y s i c a l p r o p e r t i e s of A. columbianus pedal mucus can be summarized as f o l l o w s : 1) At shear r a t i o s l e s s than 5-6 the mucus behaves as a v i s c o e l a s t i c s o l i d . The shear modulus i s on the order of 100 t o 10 00 N/m2, i n c r e a s i n g with i n c r e a s i n g shear r a t e . 2) The mucus shows a sharp y i e l d p o i n t at a shear r a t i o of 5-6. Y i e l d s t r e s s i n c r e a s e s with i n c r e a s i n g shear r a t e . 3) At a shear r a t i o of g r e a t e r than 6 the mucus behaves as a f l u i d with a v i s c o s i t y of 30-50 p o i s e . 4) The r a t i o of y i e l d s t r e s s t o shear r a t e f o r any one sample i s about 2.0 5) The f l u i d mucus can recover i t s e l a s t i c i t y i f allowed t o h e a l f o r a p e r i o d o f time. 6) The amount of s o l i d i t y recovered i n c r e a s e s with i n c r e a s i n g time. F i b e r Formation The p r o p e r t i e s summarized above were measured under c o n d i t i o n s designed t o simulate those beneath a walking s l u g . However, being l e t h a r g i c beasts, s l u g s spend l a r g e p e r i o d s of time simply s i t t i n g i n one spot. In the cages used to house the s l u g s f o r t h i s study the p r e f e r r e d r e s t i n g p o s i t i o n f o r k^_ columbianus was halfway up the v e r t i c a l g l a s s w a l l s . The s l u g s commonly spent p e r i o d s of 12-24 1 2 1 hours thus a t t a c h e d . Since i t has been shown by s t r e s s r e l a x a t i o n t e s t s t h a t pedal mucus w i l l flow over long p e r i o d s of time, why do s l u g s attached t o v e r t i c a l w a l l s not g r a d u a l l y s l i d e down under the f o r c e of g r a v i t y ? The answer to t h i s q u e s t i o n may l i e with another property of pedal mucus, i t s a b i l i t y t o form f i b e r s . I f a s l u g t hat has been attached t o a v e r t i c a l wall i s g e n t l y p r i e d o f f , a white l a y e r of mucus w i l l o f t e n remain behind. Upon examination under a p o l a r i z i n g microscope the mucus i s found t o c o n t a i n , i n a d d i t i o n t o t h e . u s u a l d e b r i s , a dense f e l t w o r k of f i b r e s . I t i s d i f f i c u l t t o t r a c e a s i n g l e f i b e r from end to end but they appear t o be q u i t e l o n g (up to about .5mm). F i b r e s are about 1.0 um i n diameter and are weakly b i r e f r i n g e n t . The f i b r e s do not d i s s o l v e i f the sample i s p l a c e d i n d i s t i l l e d water. The time course of f i b e r formation beneath a r e s t i n g s l u g has not been s t u d i e d . I t was found p o s s i b l e t o induce f i b r e f ormation i n pedal mucus i n the dynamic t e s t i n g apparatus. Mucus alone (at 100% r e l a t i v e humidity) e i t h e r does not form f i b e r s or f i b e r s are formed too slowly t o be d e t e c t e d i n these t e s t s . I f , however the sample i s immersed i n a s a l t s o l u t i o n , f i b e r s r a p i d l y form. The formation of f i b e r s i s accompanied by a dramatic i n c r e a s e i n the shear modulus of the sample. T h i s modulus was measured by s t r e s s - s h e a r r a t i o t e s t s at shear r a t i o s l e s s than 0.10 and shear r a t e s l e s s than 0.10/sec. F i g u r e 4.21 shows the r e s u l t s of one s e r i e s of t e s t s ; f o l l o w i n g the time course of t h i s i n c r e a s e i n modulus 122 FIGUEE 4.21. The e f f e c t s of v a r i o u s s a l t s on the r e l a t i v e i n c r e a s e (Gt/Go) i n shear modulus due t o f i b e r f ormation i n ftriolimax columbianus pedal mucus. A l l s a l t s were present as 0.05 M aqueous s o l u t i o n s . F i g u r e 4 . 2 1 124 f o r v a r i o u s s o l u t i o n s . An i n s u f f i c i e n t number of t e s t s were performed t o be able to a t t r i b u t e the d i f f e r e n t time courses found as being a r e s u l t of the d i f f e r e n t s a l t s a p p l i e d . I t can be concluded, however, t h a t while f i b e r f o r m a t i o n i s dependent on the presence of s a l t (no f i b e r s being formed i n d i s t i l l e d water) the process i s not dependent on e i t h e r a s p e c i f i c c a t i o n or anion, or the valence of e i t h e r the c a t i o n or anion . Again, once f i b e r s were formed they would not d i s s o l v e i f the sample was e x h a u s t i v e l y d i a l y z e d a g a i n s t d i s t i l l e d water and the s a l t s thereby removed. In o r d e r to p r e d i c t the behavior of f i b r o u s mucus under a r e s t i n g s l u g i t would be necessary t o perform "creep" t e s t s where the sample i s subjected to a constant s t r e s s and the deformation measured as a f u n c t i o n of time. U n f o r t u n a t e l y machines t h a t allow f o r creep t e s t s t o be performed i n shear (as would be necessary f o r mucus) are d i f f i c u l t to design and c o n s t r u c t . Consequently no attempt has been made i n t h i s study to t e s t the creep c h a r a c t e r i s t i c s of f i b r o u s and n o n - f i b r o u s pedal mucus. I t i s p o s s i b l e however t o make an educated guess as to what these p r o p e r t i e s might be. I t may reasonably be assumed t h a t when f i b e r s form i n the pedal mucus under a s l u g some, but not a l l , of the g l y c o p r o t e i n c h a i n s are bound i n t o f i b e r s . The b i r e f r i n g e n c e of the f i b e r s i n d i c a t e s t h a t t h e i r molecular s t r u c t u r e i s ordered . Without e x c e p t i o n a l l other b i o l o g i c a l b i r e f r i n g e n t f l i e r s have a modulus c o n s i d e r a b l y higher than t h a t of the randomly arranged mucus network. 125 No evidence can be seen under the microscope that the f i b e r s are connected. Thus i t seems reasonable t h a t t h i s f i b r o u s mucus c o n s i s t s of a low modulus matrix (the mucus e l a s t i c network) through which run d i s c o n t i n u o u s higher modulus f i b e r s . another c l a s s of b i o l o g i c a l m a t e r i a l s with a very s i m i l a r s t r u c t u r e - sea anemone mesoglea - has been s t u d i e d by s e v e r a l authors, n o t a b l y G o s l i n e (19 71a and b) and Koehl (1977a and b). The r e l e v a n t f i n d i n g s of these authors are as f o l l o w s : 1. The modulus of a d i s c o n t i n u o u s f i b e r r e i n f o r c e d composite such as mesoglea i n c r e a s e s as the p r o p o r t i o n of f i b e r s t o matrix i n c r e a s e s . 2. For a given r a t e o f deformation of the m a t e r i a l s as a whole.the presence of f i b e r s s e r v e s to i n c r e a s e the shear r a t e a c t i n g on the v i s c o u s component . as a consequence a f i b e r r e i n f o r c e d m a t e r i a l creeps more slowly than one that i s not r e i n f o r c e d . I t has been shown t h a t the modulus of f i b r o u s mucus i n c r e a s e s as one would expect i f the m a t e r i a l were to behave analogously to mesoglea. I t can thus be guessed t h a t the f i b r o u s mucus w i l l creep more slo w l y than the n o n f i b r o u s s l i m e . I f t h i s i s indeed so, i t could e x p l a i n the a b i l i t y o f s l u g s t o remain attached to v e r t i c a l w a l l s without s l i p p i n g . 126 CHAPTER FIVE Chemical Composition As shown i n the preceding chapter A. columbianus pedal mucus i s a v i s c o e l a s t i c m a t e r i a l with some unusual p r o p e r t i e s . On the b a s i s o f these p r o p e r t i e s the e x i s t e n c e i n the mucus of a network of macromolecules has been hypo t h e s i z e d . Before i t i s p o s s i b l e t o more c l o s e l y examine the nature of t h i s network i t i s necessary to i d e n t i f y the chemical composition of the b u i l d i n g b l o c k s from which t h i s network i s c o n s t r u c t e d . Just as the s i z e , shape, and s t r e n g t h of b r i c k s determines the p o s s i b i l i t i e s f o r the o v e r a l l form of a b u i l d i n g , the c h e m i c a l p r o p e r t i e s of i n d i v i d u a l monomers s e t the l i m i t s f o r the form and s t r e n g t h of polymer networks. Consequently the chemical a n a l y s i s of pedal mucus forms the s u b j e c t of t h i s chapter. What Is Mucus? The term "mucus" has never been p r e c i s e l y d e f i n e d . In g e n e r a l , any e x t r a c e l l u l a r , v i s c o e l a s t i c animal s e c r e t i o n formed p r i m a r i l y of water i s l i a b l e to be l a h e l l e d "mucus".. As such, the term i s a p p l i e d t o a l a r g e v a r i e t y of s e c r e t i o n s , the f u n c t i o n s of which range from locomotion, to f e e d i n g , t o p r o t e c t i o n and r e p r o d u c t i o n (Hunt, 1970; G o t t s c h a l k , 1972) . Given t h i s broad f u n c t i o n a l d i v e r s i t y i t i s somewhat s u r p r i s i n g t o f i n d t h a t most, i f not a l l , mucins have a b a s i c a l l y s i m i l a r chemical composition. While t h e r e are many v a r i a t i o n s on the theme, a l l mucins s t u d i e d 127 to date c o n s i s t of some s o r t o f complex between a p o l y s a c c h a r i d e and a p r o t e i n (Hunt, 1970); t h i s being d i s s o l v e d i n water. These p o l y s a c c h a r i d e - p r o t e i n complexes f a l l i n t o two g e n e r a l c a t e g o r i e s . I f the composition of the complex i s dominated by the p o l y s a c c h a r i d e , the complex i s termed a mucopolysaccharide . I f , on the other hand, the p r o t e i n dominates, the complex i s termed a g l y c o p r o t e i n . In g e n e r a l , i n a mucopolysaccharide the p o l y s a c c h a r i d e and p r o t e i n a re not c o v a l e n t l y bound while i n a g l y c o p r o t e i n they u s u a l l y are (Hunt, 1970). Mucus C o l l e c t i o n Mucus was c o l l e c t e d from h e a l t h y A. columbianus as de s c r i b e d i n Chapter 3. For chemi c a l a n a l y s i s the mucus from approximately twenty s l u g s (about 5 ml) was pooled and d i v i d e d i n t o two a l i q u o t s . , The f i r s t o f these was immediately f r o z e n at -80 <>C and l y o p h i l i z e d t o provide a sample of the whole mucus as i t appears on the f o o t of the s l u g s . The second a l i g u o t was d i a l y z e d a g a i n s t s i x one l i t e r changes of d i s t i l l e d water over a pe r i o d of th r e e days to remove any unbound small molecular weight molecules. A f t e r d i a l y s i s t h i s a l i q u o t was f r o z e n a t -80 <>C and l y o p h i l i z e d . Both l y o p h i l i z e d samples were s t o r e d d e s s i c a t e d at room temperatures. A n a l y s i s Water Content 128 Mucus was c o l l e c t e d from eighteen s l u g s and immediately weighed. The samples were then d r i e d a t 105 °C f o r twenty-f o u r hours and reweighed. The dry weight (expressed as a percent o f the wet weight) averaged 3.44% and ranged from 2.85 to 4.46%. Thus pedal mucus i s about 95 t o 97% water. P r o t e i n The p r o t e i n content of pedal mucus was measured by the heated b i u r e t - f o l i n assay o f Dorsey, McDonald, and Boels (1977) using bovine serum albumin (Sigma) as a standard. T h i s assay i s p r e f e r r e d over t h a t of Lowry e t a l . (1951) i n t h a t i t p r o v i d e s an estimate of p r o t e i n content t h a t i s not b i a s e d by the amino a c i d composition of the p r o t e i n being t e s t e d . Assays were run i n t r i p l i c a t e and the values presented are the means. Whole pedal mucus was found to c o n t a i n 33.6% p r o t e i n (weight of p r o t e i n / d r y weight of mucus) while the d i a l y s e d sample c o n t a i n e d 45.6% p r o t e i n . The .increased p r o p o r t i o n of p r o t e i n i n the d i a l y z e d sample i s presumably due to the l o s s of s m a l l , nonprotein molecules ( p r i m a r i l y s a l t s ) during d i a l y s i s . The amino a c i d composition of the pedal mucus p r o t e i n was determined using a Beckman 119C amino a c i d a n a l y z e r . Samples were hyd r o l y z e d with 6 N HC1 i n vacuo f o r 24 hours at 100 °C. Standards and samples were chromatographed using a t h r e e hour sodium c i t r a t e b u f f e r c y c l e d e s c r i b e d i n Beckman Op e r a t i n g Notes (119C AN001, 1975). The chromatograms were t a b u l a t e d by standard procedures. Three 129 samples of each a l i q u o t were analyzed and the averaqed r e s u l t s are presented i n Table 5.2. The amino a c i d composition i s noteworthy i n t h r e e r e s p e c t s . 1„ I f i t i s assumed that the qlutamic and a s p a r t i c , a c i d r e s i d u e s measured r e p r e s e n t glutamic and a s p a r t i c a c i d s present i n the p r o t e i n ( r a t h e r than asparagine and glutamine) , the a c i d i c amino a c i d s form a l a r g e p r o p o r t i o n of the t o t a l . Where the b a s i c amino a c i d s ( l y s i n e and a r g i n i n e ) comprise only about 4% of the t o t a l number of amino a c i d s the a c i d i c s comprise 17 to 20% . I f t h i s assumption i s v a l i d , a t p h y s i o l o g i c a l pHs the p r o t e i n w i l l have a net negative charge due to the d i s s o c i a t e d c a r b o x y l group of the a s p a r t i c and glutamic a c i d s and w i l l behave as a polyanion^ The p o l y e l e c t r o l y t i c behavior of the mucus as a whole i s confirmed i n the next chapter. 2. C y s t e i n e i s present i n the mucus p r o t e i n . The s u l f h y d r y l group of one c y s t e i n e s i d e c h a i n can be o x i d i z e d by the s u l f h y d r y l o f another c y s t e i n e t o form a d i s u l f i d e bond between the two y i e l d i n g a c y s t e i n e molecule. Such d i s u l f i d e bonds are 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 c h a i n s and thus are a l i k e l y c a n d i d a t e f o r forming the c r o s s l i n k s of a polymer network. I t w i l l be shown i n the next chapter t h a t d i s u l f i d e b r i d g e s , presumably formed by c y s t e i n e , do indeed c r o s s l i n k the network of A. columbianus pedal mucus. 3. Serine and t h r e o n i n e are present i n l a r g e amounts (23-24%)., These two amino a c i d s are l i k e l y s i t e s f o r the T a b l e 5.1: Amino A c i d C o m p o s i t i o n ( r e s i d u e s / 1 0 0 r e s i d u e s ) whole d i a l y z e d A s p a r t i c a c i d 9.8 9.0 T h r e o n i n e 11.7 11.1 S e r i n e 12.2 12.6 G l u t a m i c a c i d 10.9 8.4 P r o l i n e . 8 . 0 8.6 G l y c i n e 9.3 8.6 A l a n i n e 7.4 7.4 H a l f C y s t i n e 0.6 3.0 V a l i n e 5.2 5.2 M e t h i o n i n e t r a c e 0.2 I s o l e u c i n e 4.5 4.5 T y r o s i n e 1.7 1.8 P h e n y l a l a n i n e 2.3 2.3 L y s i n e 1.1 0.9 H i s t i d i n e 3.7 3.4 A r g i n i n e 3.0 3.9 L e u c i n e 5.5 ' 5.5 A c i d i c s 20.7 17.4 B a s i c s 4.1 4.8 131 c o v a l e n t bonding of p o l y s a c c h a r i d e t o the p r o t e i n chain (Gottschalk,1972). The e x i s t e n c e o f these bonds w i l l be demonstrated i n the next chapter. P o l y s a c c h a r i d e s No simple assay e x i s t s t h a t unambiguously measures the t o t a l sugar content of a polysaccharide,. Consequently the pedal mucus was assayed s e p a r a t e l y f o r the v a r i o u s suqars and sugar d e r i v a t i v e s t h a t were l i k e l y t o be present. Uronic Acids The t o t a l content of u r o n i c a c i d s was measured using the assay of Blumenkrantz and Osboe-Hansen (1973) using g l u c u r o n i c a c i d (Sigma) as a standard. Assays were perfomed i n t r i p l i c a t e and values averaged. The r e s u l t s show t h a t whole pedal mucus c o n t a i n s 6.8% (wt/wt) uro n i c a c i d and d i a l y z e d mucus, 7.7% (wt/wt). No attempt was made to f u r t h e r d e f i n e the i d e n t i t y of the uro n i c a c i d s . As with the glutamic and a s p a r t i c a c i d s of the p r o t e i n , the d i s s o c i a t e d c a r b o x y l groups of the u r o n i c a c i d s w i l l cause the mucus to a c t as a polyanion. The mucus does indeed show the c h a r a c t e r i s t i c s o f a polyanion as w i l l be shown i n the next chapter. Amino Suqars The t o t a l content of amino sugars was measured by the assay o f Boas (1953) u s i n g galactosamine (BDH) as a standard. Samples were hydrolyzed i n 2N HC1 i n vacuo f o r 20 132 hours a t 100 °C. T e s t s were performed i n t r i p l i c a t e and values averaged. The amino sugar content of the whole mucus was 6.9% (wt/wt) while t h a t of d i a l y z e d samples was 7.8%. a l i q u o t s of the e l u a t e from the Dowex 50 column of the assay were chromatographed on a Beckman 119C amino a c i d a n a l y z e r using a 450 minute l i t h i u m c i t r a t e c y c l e d e s c r i b e d i n Beckman Operating Notes (119C aN004, 1975). Glucosamine and galactosamine (BDH) were used as standards., The r e s u l t s show that the amino sugars i n pedal mucus are p r i m a r i l y glucosamine (6.1% whole mucus, 6.9% d i a l y z e d mucus wt/wt) accompanied by a s m a l l amount of galactosamine (0.8% whole mucus, 0.9% d i a l y s e d mucus wt/wt) . There i s a s t r o n g p o s s i b i l i t y t h a t these amino sugars are present i n the mucus as N - a c e t y l amino sugars the a c e t y l groups being removed du r i n g h y d r o l y s i s . The f a c t t h a t the acetamido bond i s as s u s c e p t i b l e t o a c i d h y d r o l y s i s as the g l y c o s i d i c bonds (which must be broken to r e l e a s e the monosaccharide f o r assaying) makes i t extremely d i f f i c u l t t o assay f o r the presence of N - a c e t y l hexoses ( M a r s h a l l and Newberger, 1972). However, i n v i r t u a l l y a l l cases i n which the presence of N-a c e t y l groups has been t e s t e d they have been found (see Table 5.3). One f u r t h e r f a c t lends support to the s u g g e s t i o n t h a t the amino sugars are a c e t y l a t e d : i f the amino groups of the amino sugars are not a c e t y l a t e d (or otherwise bound) they w i l l be charged a t p h y s i o l o g i c a l pH's.. These p o s i t i v e charges w i l l tend to o f f s e t the negative charges of the u r o n i c a c i d s . as a consequence the p o l y a n i o n i c c h a r a c t e r of the mucus should be decreased. 133 Since, as w i l l tie shown i n the next c h a p t e r , the mucus ac t s as a s t r o n g p o l y a n i o n , i t i s l i k e l y t h a t the amino groups of the amino sugars are a c e t y l a t e d , and t h e r e f o r e probably not a b l e t o i o n i z e . S i a l i c Acid The t o t a l s i a l i c a c i d content was measured using the H2S04 h y d r o l y s i s and the t h i o b a r b i t u r i c a c i d assay of Warren (1959). N-acetylneuraminic a c i d (Sigma) was used as a standard. Assays were performed i n t r i p l i c a t e . There i s no d e t e c t a b l e s i a l i c a c i d present i n pedal mucus.. Ne u t r a l Sugars The t o t a l content of n e u t r a l sugars was measured by the p h e n o l - s u l f u r i c a c i d assay of Lo, E u s s e l , and T a y l o r (1970) using glucose (Sigma) as a standard. While t h i s assay p r e f e r e n t i a l l y measures n e u t r a l sugars, i t a l s o measures u r o n i c a c i d s (but not amino s u g a r s ) . . Consequently, the r e s u l t s from t h i s assay were c o r r e c t e d u s i n g the r e s u l t s from the u r o n i c a c i d assays. Tests were performed i n t r i p l i c a t e and averaged. The r e s u l t s show t h a t whole mucus i s 7.2% (wt/wt) n e u t r a l sugars, and d i a l y z e d mucus, 8.5% wt/wt. The composition of the n e u t r a l sugars was f u r t h e r examined using a g a s / l i q u i d chromatograph. Samples of whole and d i a l i z e d mucus were hydrolyzed, a c e t y l a t e d , and chromatographed using the method of Court (1978). The r e s u l t s show t h a t the n e u t r a l sugars of pedal mucus c o n s i s t 134 p r i m a r i l y of fucose (3,4 to 5.6%) and g a l a c t o s e (2.3 to 3.2%) accompanied by s m a l l amounts of glucose and mannose (see Table 5. 2) . Sulphated Sugars Many i n v e r t e b r a t e mucins c o n t a i n sulphated p o l y s a c c h a r i d e s (Hunt, 1970) . The p o s s i b l e presence of sulphated sugars i n pedal mucus was examined by measuring the t o t a l s u l phate content, using both methods of Dodgson and P r i c e (1962) and Nader and D i e t r i c h (1977). Both these assays measure only f r e e s u l p h a t e . To l i b e r a t e any sulphate bound to sugars, the.mucus samples were hydrolyzed using e i t h e r 8 M HC1 (6 hours, 100 C) (Nader and D i e t r i c h , 1977) or 25% f o r m i c a c i d (24 hours, 100 C) (Antonopoulos, 1962). A l l assays were performed i n t r i p l i c a t e using potassium sulphate as a standard. The r e s u l t s of both assays show t h a t t h e r e i s no d e t e c t a b l e s u l p h a t e present i n A. columbianus pedal mucus. In a d d i t i o n . t o sulphate the method of Nader and D e i t r i c h (1977) measures any phosphate present. However, no phosphate was d e t e c t e d . S a l t s The composition of the c a t i o n s present i n pedal mucus was analyzed u s i n g a Techtron AA20 atomic a b s o r p t i o n flame spectrophotometer. A l l p r e p a r a t i o n s f o r the assays were performed using polypropylene t e s t tubes and p i p e t t e s . A l l assays were c a r r i e d out i n g u i n t r i p l i c a t e and the r e s u l t s 135 T a b l e 5.2' Chemical C o m p o s i t i o n % weight whole d i a l y z e d Glucosamine 6.1 6.9 G a l a c t o s a m i n e 0.8 0.9 N e u t r a l Sugars 7.2 8.5 f u c o s e 3.4 5.6 g a l a c t o s e 3.2 2.3 mannose 0.4 0.4 g l u c o s e 0.2 0.3 U r o n i c A c i d 6.8 7.7 S i a l i c A c i d 0.0 0.0 T o t a l C a r b o h y d r a t e 20.9 24.0 P r o t e i n 33.6 45.6 S a l t s S 0 , = 0.0 0.0 i Na (as the c h l o r i d e ) 2.5 1.3 K + (as the c h l o r i d e ) 9.2 1.9 ,.|..| Mg (as the c h l o r i d e ) 3.6 2.6 I. j . Ca (as the c h l o r i d e ) 0.6 0.6 T o t a l 15.9 6.4 T o t a l 70.4 76.0 136 averaged. R e s u l t s were c a l c u l a t e d using standard curves generated at the same time as samples were assayed. The r e s u l t s are presented as the weight of the c h l o r i d e s a l t of the c a t i o n , expressed as a percent of the t o t a l weight of the mucus. The s p e c i f i c s f o r the assay of each c a t i o n are as f o l l o w s : Sodium: Weighed samples o f l y o p h i l i z e d mucus and standards were d i s s o l v e d i n d e i o n i z e d , g l a s s d i s t i l l e d water. Sodium c h l o r i d e was used as a standard.. Potassium: Weighed samples of l y o p h i l i z e d mucus and standards were d i s s o l v e d i n d e i o n i z e d d i s t i l l e d water c o n t a i n i n g a swamp of 500 p a r t s per m i l l i o n sodium. Potassium c h l o r i d e was used as a standard. Magnesium: Weighed samples of l y o p h i l i z e d mucus and standards were d i s s o l v e d i n d e i o n i z e d d i s t i l l e d water c o n t a i n i n g 1.5% EDTA . , Magnesium c h l o r i d e was used as a standard. Calcium: Weighed samples of l y o p h i l i z e d mucus and standards were d i s s o l v e d i n 0.1 M HC1 c o n t a i n i n g 0.5% LaCl3« Calcium c h l o r i d e was used as a standard. A l l assays were c a r r i e d out using the wave l e n g t h s and s l i t widths s p e c i f i e d i n the AA20 o p e r a t i n g manual.. The r e s u l t s are presented i n Table 5.2. These r e s u l t s are noteworthy i n two r e s p e c t s : 1. While some of the i o n s are l o s t during d i a l y s i s , n e a r l y h a l f remains bound to e i t h e r the p r o t e i n or carbohydrate of the mucus. Presumably these i o n s are e l e c t r o s t a t i c a l l y bound t o the d i s s o c i a t e d c a r b o x y l groups 137 of the g l u t a m i c , a s p a r t i c and u r o n i c a c i d s . 2. Potassium i o n s are l o s t p r e f e r e n t i a l l y t o sodium ions,and magnesium t o calcium. Presumably t h i s i s due to sodium and calcium being p r e f e r e n t i a l l y bound. The b a s i s f o r t h i s e f f e c t i s not known. The a n i o n i c composition o f pedal mucus was not analyzed. The chemical a n a l y s i s presented here i s f a r from exhaustive and accounts f o r only 76% of the weight of the g l y c o p r o t e i n . The reason f o r t h i s incomplete recovery i s not p r e c i s e l y known. Some of the remainder may be l i p i d s , f o r which t h i s study has not t e s t e d . Unexpected l o s s e s du r i n g v a r i o u s h y d r o l y s e s may a l s o account f o r some of the unrecovered weight. Much more work w i l l be needed t o d e f i n e the p r e c i s e chemical composition of t h i s mucin. However, f o r the purposes of the present study, t h i s p r e l i m i n a r y examination i s s u f f i c i e n t . In summary, the s i g n i f i c a n t a s p e c t s o f the chemical composition are as f o l l o w s : 1. The mucus i s 95 to 97% water the remainder being s a l t s and a p r o t e i n - p o l y s a c c h a r i d e complex. 2. P r o t e i n c o n t r i b u t e s the l a r g e r p o r t i o n of the p r o t e i n - p o l y s a c c h a r i d e complex; as such the mucin i s c l a s s e d as a g l y c o p r o t e i n . 3. Amino a c i d a n a l y s i s r e v e a l s t h a t the p r o t e i n i s l i k e l y t o be a p o l y a n i o n . 4. The carbohydrate p o r t i o n o f the p r o t e i n p o l y s a c c h a r i d e complex i s evenly d i v i d e d among n e u t r a l sugars, amino sugars, and u r o n i c a c i d s . 1 3 8 5- No s i a l i c a c i d was detected. 6. The u r o n i c a c i d s c o n t r i b u t e to the p o l y e l e c t r o l y t i c nature of the mucus. 7. Neither sulphate nor phosphate was d e t e c t e d i n the mucin. Comparison To Other Mucins On the b a s i s of these f i n d i n g s , the chemical composition of JU columbianus pedal mucin can be compared to and c o n t r a s t e d with other mucins. V e r t e b r a t e Mucins Ar i o l i m a x columbianus d i f f e r s from most v e r t e b r a t e mucins (such as t r a c h e a l and c e r v i c a l mucins) i n t h a t i t does not c o n t a i n s i a l i c a c i d . The absence of s i a l i c a c i d i n i n v e r t e b r a t e s i s v i r t u a l l y c a t h o l i c as noted by Warren (1963). In t h i s r e s p e c t the p o l y s a c c h a r i d e of pedal mucus bears s i m i l a r i t y t o a p o l y s a c c h a r i d e found i n both v e r t e b r a t e s and i n v e r t e b r a t e s - h y a l u r o n i c a c i d . The b a s i c u n i t of h y a l u r o n i c a c i d i s a d i s a c c h a r i d e c o n s i s t i n g of a g l u c u r o n i c a c i d coupled (through a B g l y c o s i d i c linkage) to an N - a c e t y l glucosamine. Pedal mucus d i f f e r s from t h i s by a l s o c o n t a i n i n g n e u t r a l sugars. However, s i n c e the manner i n which the monosaccharides of pedal mucus are l i n k e d i s unknown the p r e c i s e . d i f f e r e n c e s between i t and h y a l u r o n i c a c i d are unknown. I n v e r t e b r a t e s 139 A r i o l i m a x columbianus pedal mucus d i f f e r s from i n v e r t e b r a t e mucins i n g e n e r a l i n t h a t i t does not c o n t a i n sulphated 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 d i f f e r s from most gastropod mucins which have been s t u d i e d . The most d e t a i l e d a n a l y s i s t o date of gastropod pedal mucus i s t h a t of the North A f r i c a n l a n d s n a i l , O t e l l a l a c t e a (Pancake and Karnovsky,1971). They found t h a t t h i s mucus contained glucosamine (probably a c e t y l a t e d and sulphated) and i d u r o n i c a c i d . The r a t i o of u r o n i c a c i d to hexosamine was 1.14 to 1. No n e u t r a l sugars were det e c t e d . T h i s i s i n c o n t r a s t with the study of Suzuki (1941) who found t h a t the pedal mucus of H e l i x l a e d a contained galactosamine (probably a c e t y l a t e d ) and 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 a c i d s . N either Pancake and Karnovsky nor Suzuki examined the amino a c i d content of the mucus s e c r e t i o n s . The chemical composition of v a r i o u s mucins are compared to A., columbianus pedal mucus i n Table 5.3. Other s t u d i e s of gastropod mucus s e c r e t i o n s have been g e n e r a l l y c o n f i n e d t o the hypobranchial mucins of whelks (as reviewed by Hunt, 1970). These s e c r e t i o n s a l l c o n t a i n sulphated p o l y s a c c h a r i d e s . The p r o t e i n component of at l e a s t one o f these s e c r e t i o n s , t h a t o f Buceinium undulatum (Hunt and Jevons, 1965) bears a s t r i k i n g s i m i l a r i t y to the p r o t e i n of _A- columbianus pedal mucus (see Table 5.3)-This comparison of pedal mucus to other mucins i s of l i m i t e d use f o r a number of reason. F i r s t , so l i t t l e r e s e a r c h has been c a r r i e d out concerning the d i s t r i b u t i o n of the v a r i o u s chemical components of mucus t h a t i t i s Table 5 . 3 : The Carbohydrate Composition of Various Proteoglycans and Glycoproteins Polysaccharide hyaluronic acid chondroitin chondroitin 4 or 6 sulphate dermatin sulphate heparin ske l e t a l keratin sulphate glycan sulphate ovine or bovine submaxillary mucin glycoprotein pig or human gastr i c mucin glycoprotein Occurrence (vertebrate or invertebrate) Components Repeating Others N-acetyl Sulphate both both both both both both both vertebrate vertebrate D-glucosamine D-glucuronic acid D-galactosamine D-glucuronic acid D-galactosamine D-glucuronic acid D-galactoamine L-iduronic or D-glucuronic acid D-glucoamine D-glucuronic or L-iduronic acid D-glucosamine D-galactose glucose or fucose or galactose L-arabinose (?) D-galactose (?) D-glucose (?) D-xylose D-galactose D-xylose D-galactose D-xylose D-galactose D-xylose D-galactose D-galac tosamlne L-fucose S i a l i c acid D-mannose 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 Table 5.3: (continued) P o l y s a c c h a r i d e Occurrence Components N-acetyl Sulphate ( v e r t e b r a t e or Repeating Others i n v e r t e b r a t e ) O t e l l a l a c t e a pedal mucus (a) H e l i x laeda pedal mucus (b) Buccinum undatum hypobranchial mucus(c) i n v e r t e b r a t e i n v e r t e b r a t e i n v e r t e b r a t e A r i o l i m a x columbianus i n v e r t e b r a t e glucosamine hexuronic a c i d ( s ) glucosamine galactose glucosamine galactosamine galactose mannose fucose glucose glucosamine galactosamine fucose galactose mannose glucose u r o n i c a c i d ( s ) + + + + + ( ? ) (a) Pancake and Karnovsky (1971) (b) Suzuki (1941) (c) Hunt and Jevons (1965) Table 5.3: (continued) A comparison of the amino a c i d composition of s l u g pedal mucus and whelk hypobranchial mucus. Amino a c i d A r i o l i m a x columbianus Buccinum undatum (c) a s p a r t i c a c i d 9.0 11.10 threonine 11.1 6.45 s e r i n e 12.6 6.27 glutamic a c i d 8.4 11.34 p r o l i n e 8.6 5.19 g l y c i n e 8.6 5.19 a l a n i n e 7.4 7.67 c y s t i n e 3.0 1.73 v a l i n e 5.2 6.91 methionine 0.2 0.31 i s o l e u c i n e 4.5 4.20 l e u c i n e 5.5 8.16 t y r o s i n e 1.8 2.85 ph e n y l a l a n i n e 2.3 3.66 l y s i n e 0.9 7.29 h i s t i d i n e 3.4 2.45 a r g i n i n e 3.9 5.54 143 i m p o s s i b l e t o say with any c e r t a i n t y what i s and i s not " t y p i c a l " . While A. columbianus pedal mucus appears to d i f f e r i n s i g n i f i c a n t aspects from other mucins, i t seems l i k e l y t h a t t h i s r e f l e c t s a b i a s i n the h i s t o r i c a l c h o ice of the s e c r e t i o n s s t u d i e d , r a t h e r than some unique q u i r k of s l u g b i o c h e m i s t r y . Second, while mucous s e c r e t i o n s as a whole have r e c e i v e d scant a t t e n t i o n , i n v e r t e b r a t e e p i t h e l i a l mucins have r e c e i v e d even l e s s a t t e n t i o n . . The vast preponderance of the present knowledge of these mucins i s based s o l e l y on h i s t o c h e m i c a l s t u d i e s . H o p e f u l l y i n the f u t u r e the broad d i s t r i b u t i o n and importance of i n v e r t e b r a t e mucins w i l l be r e c o g n i z e d and t h i s s i t u a t i o n r e c t i f i e d . 144 CHAPTER SIX P h y s i c a l Chemistry Armed with the knowledge of the chemical composition of pedal mucus, i t i s now p o s s i b l e to examine the e l a s t i c network of .A. columbianus mucus i n more d e t a i l . S p e c i f i c a l l y i t w i l l be u s e f u l to examine the f o l l o w i n g q u e s t i o n s concerning the network and the molecules from which i t i s c o n s t r u c t e d . 1. How l a r g e are the molecules t h a t make up the network? 2. I s the network c o n s t r u c t e d from one type of molecule, or are d i f f e r e n t types j o i n e d together? 3. How does the g l y c o p r o t e i n , which forms only 3 to 4% of the hydrated mucus, i n f l u e n c e the water around i t ? 4. How are the i n d i v i d u a l molecules c r o s s l i n k e d to form a network? 5. And f i n a l l y , once t h i s network i s broken apart during locomotion, how does i t manage to r e c o n s t r u c t i t s e l f ? With these q u e s t i o n s i n mind, a number of t e s t s were performed. Each t e s t provides i n f o r m a t i o n concerning s e v e r a l o f these g u e s t i o n s . Taken to g e t h e r , these t e s t s provide enough i n f o r m a t i o n to answer some of these q u e s t i o n s and thereby c o n s t r u c t a reasonable p i c t u r e of the macromolecular c o n s t r u c t i o n of A. columbianus pedal mucus.. A complete answer to these q u e s t i o n s must, however, wait u n t i l f u r t h e r t e s t s are c a r r i e d out. 145 Before d e s c r i b i n g the t e s t i n g procedures of t h i s study i t w i l l be u s e f u l t o e x p l a i n the concepts and terms used when d e a l i n g with the p h y s i c a l chemistry of p o l y e l e c t r o l y t e s . P o l y e l e c t r o l y t e s As e x p l a i n e d i n Chapter 4, a f l e x i b l e polymer chain i n s o l u t i o n w i l l assume a random c o n f i g u r a t i o n . A number of mechanisms may be used to a l t e r t h i s c o n f i g u r a t i o n . A l l of these mechanisms i n v o l v e the a c t i o n of a f o r c e on the chains; t h i s f o r c e s u p p l y i n g the energy t o impose order on the randomly c o n f i g u r e d c h a i n s . One such mechanism, the c r o s s l i n k i n g of the c h a i n to other c h a i n s , and the subsequent a p p l i c a t i o n of an e x t e r n a l f o r c e , has a l r e a d y been d e s c r i b e d . Another mechanism which may a f f e c t the shape of a polymer c h a i n i s the i n t e r a c t i o n of charges present on the c h a i n . Imagine a polymer c h a i n such as t h a t d e p i c t e d i n F i g u r e 6.1a. Every t h i r d l i n k of t h i s c h a i n c o n t a i n s a d i s s o c i a t e d c a r b o x y l group and t h e r e f o r e a negative charge. Any such pol/ymeric macromolecule c o n t a i n i n g many charged groups i s a p o l y e l e c t r o l y t e . In t h i s case i t i s a p o l y a n i o n . Negative charges r e p e l each other, the f o r c e of r e p u l s i o n d e c r e a s i n g with d i s t a n c e . As a consequence the neqative charges on the c h a i n l i n k s are f o r c e d apart. Each charge moves away from i t s neighbors , thereby maintaining a minimum energy c o n f i g u r a t i o n . I f t h i s were the only f a c t o r o p e r a t i n g , t h i s charge r e p u l s i o n would cause the polymer c h a i n to extend 1 4 6 FIGURE 6 . 1 . . The 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 . A) I f the charged c h a i n were randomly c o n f i g u r e d (high entropy) many of the charges would be c l o s e t o g e t h e r . B) The charges are a maximum d i s t a n c e a p a r t when the c h a i n i s f u l l y extended. However, the 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 chain r e p r e s e n t s a compromise between A. And B. D) The presence of c o u n t e r i o n s can mask charges from each other, a l l o w i n g the c h a i n to assume a more compact and random c o n f i g u r a t i o n . 147 FIGURE 6.1 P o l y e l e c t r o l y t e s C Compromise o - p o s i t i v e c h a r g e 148 i n t o a l ong rod, a very ordered c o n f i g u r a t i o n (see F i g u r e 6.1b). As with a n e u t r a l polymer,however,thermal a g i t a t i o n w i l l cause the polymer c h a i n t o c o n t o r t . The f i n a l shape of the chain w i l l be a compromise between the extended rod expected f o r minimum e l e c t r o s t a t i c energy and the:random c o i l f avored by thermal a g i t a t i o n (see F i g u r e 6.1c), I f t h i s polymer c h a i n , r a t h e r than e x i s t i n g on i t s own, i s c r o s s l i n k e d t c s i m i l a r c h a i n s to form a network, the e l e c t r o s t a t i c 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 cause the network t o r e p e l i t s e l f and expand to a l a r g e r volume than i f the charges were not present. T h i s i s the s i t u a t i o n t h a t should occur i f a c r o s s l i n k e d polyanion i s d i s s o l v e d i n d i s t i l l e d water. T h i s s i t u a t i o n w i l l be changed, however, i f a s a l t (eg. NaCl) i s added to the water, the d i s s o l v e d s a l t w i l l be e l e c t r o s t a t i c a l l y a t t r a c t e d t o the negative charges of the p o l y a n i o n , and a c l u s t e r of c a t i o n s w i l l form around each negative charge, as shown i n Figure 6.Id. These c o u n t e r i o n s w i l l serve to mask the n e g a t i v e charges from each other, and the f o r c e of r e p u l s i o n between neighboring l i n k s w i l l decrease. Less energy i s then a v a i l a b l e to impose order on the c h a i n . In response the i n d i v i d u a l molecules w i l l assume a more kinked c o n f i g u r a t i o n and the network w i l l s h r i n k somewhat. While the presence of c o u n t e r i o n s causes the f o r c e of r e p u l s i o n to decrease i t does not a b o l i s h the r e p u l s i o n a l t o g e t h e r . _ Consequently the network,in the presence of c o u n t e r i o n s , i s s t i l l expanded above i t s uncharged l e v e l . P r e c i s e 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 d e n s i t y 149 and c o u n t e r i o n d e n s i t y on the shapes of macromolecules may be found i n the reviews by Katchalsky (1964), V e i s (1970), or Tanford (1961). Tests Network S w e l l i n g As shown i n the preceding chapter, s e v e r a l of the chemical components of JU columbianus pedal mucus should be n e g a t i v e l y charged at p h y s i o l o g i c a l pH's. I f these components are l i n k e d together i n t o polymer c h a i n s , they should show the c h a r a c t e r i s t i c s of a polyanion as d e s c r i b e d above. T h i s can be detected q u i t e simply. I f a sample of mucus i s c o l l e c t e d as d e s c r i b e d i n Chapter 4 i t forms a compact b l o b . I f t h i s blob i s placed i n a 0.1W NaCl s o l u t i o n (roughly e q u i v a l e n t t o the s a l t c o n c e n t r a t i o n of n a t u r a l mucus) i t w i l l remain roughly the same s i z e and shape f o r s e v e r a l days. I f however a sample (0.1 t o 0.3 ml) of mucus i s placed i n 10 ml of d i s t i l l e d water the co u n t e r i o n s d i f f u s e out of the mucus and the blob w i l l s l o w l y expand t o s e v e r a l times i t s i n i t i a l s i z e . A l t e r n a t i v e l y , the vast m a j o r i t y of the charges can be removed a l t o g e t h e r by lowering the pH of the mucus blob below the l e v e l where the c a r b o x y l groups of the g l y c o p r o t e i n are d i s s c o c i a t e d . The pH at which the c a r b o x y l groups are h a l f d i s s o c i a t e d (the pK) i s about 4. Thus when the pH i s lowered below 4 most of the c a r b o x y l groups w i l l be u n d i s s o c i a t e d and the mucus network, no lon g e r held 150 expanded by the negative charges, should c o n t r a c t . T h i s i s indeed the case. A blob of mucus s h r i n k s when placed i n a s o l u t i o n of water the pH of which has been adju s t e d to 2.1 by the a d d i t i o n of HC1. These s w e l l i n g and s h r i n k i n g e f f e c t s can be e a s i l y q u a n t i f i e d . As the network expands water i s drawn i n t o the i n t e r s t i c e s between the chains much as a sponge soaks up water. C o n v e r s e l y , the c o n t r a c t i o n of the network f o r c e s water out of the i n t e r s t i c e s . Conseguently the amount of water contained i n the network (expressed as h y d r a t i o n , m i l l i l i t e r s of H20/gram of g l y c o p r o t e i n ) i s a measure of network expansion. Hydration values were measured f o r A., columbianus pedal mucus i n f o u r s o l v e n t s : d i s t i l l e d water,0.1 M NaCl,1.0 M NaCl, and water a d j u s t e d to pH 2.1 with HCl. The procedure was as f o l l o w s : A s m a l l blob of mucus (0.05-0.15 ml) was placed i n 25 ml o f the t e s t s o l u t i o n and allowed t o expand or c o n t r a c t . A l l t e s t s were conducted at room temperature (21-23 ° C ) . Change i n volume of the blob was v i s u a l l y complete w i t h i n two hours, however the network was l e f t i n the s o l v e n t f o r 6-7 hours t o ensure t h a t e q u i l i b r i u m was reached. A f t e r e q u i l i b r a t i o n the mucous blob was qrasped with a f o r c e p s , removed from the solvent,and immediately weighed. Samples e q u i l i b r a t e d with NaCl were then d i a l y z e d a g a i n s t repeated changes of d i s t i l l e d water (24 hr., 22 °C) t o remove the s a l t . A l l samples were then d r i e d a t 105 °C f o r 18 hours and reweighed. The value (wet weight-dry weight)/dry weight i s the h y d r a t i o n expressed as grams of 151 water per gram dry weight. A l l t e s t s were performed i n q u i n t r i p l i c a t e . The r e s u l t s from these t e s t s are presented i n Table 6.1. These t e s t s confirm the p r e d i c t i o n s made above. The mucus i s h i g h l y s e n s i t i v e t o the compostion of the s o l v e n t , being n e a r l y 20 times as expanded i n d i s t i l l e d water as compared t o pH 2.1. In t h i s f u l l y expanded c o n f i g u r a t i o n n e a r l y a l i t e r o f water i s con t a i n e d i n the i n t e r s t i c e s of one gram of mucus network. Under c o n d i t i o n s approximating those i n n a t u r a l mucus (0.1 M NaCl) the network i s c o n t r a c t e d to one f i f t h of i t s f u l l y expanded s i z e . I f the e q u i l i b r i u m h y d r a t i o n value measured here f o r mucus i n 0.1 M NaCl (206 g/g) i s compared to t h a t of f r e s h l y c o l l e c t e d mucus (21-34 g/g) i t i s e v i d e n t that mucus as i t appears on the f o o t of the s l u g i s not a t e q u i l i b r i u m with i t s s o l v e n t . Presumably the mucus i s sec r e t e d i n t o the lumen of the suprapedal gland i n a dehydrated s t a t e and the time spent on the f o o t i s i n s u f f i c i e n t t o allow e q u i l i b r i u m to be reached. S o l u b i l i t y T e s t s Anyone who handles a s l u g soon d i s c o v e r s t h a t pedal mucus i s very d i f f i c u l t t o d i s s o l v e . Once a b i t of slime a t t a c h e s i t s e l f t o your f i n g e r s , i t seems th a t no amount of washing and scrubbing w i l l make i t go away. T h i s simple f a c t i s again t i e d t o the presence i n the mucus of a c r o s s l i n k e d network. As e x p l a i n e d i n Chapter 4, an e l a s t i c network i s e l a s t i c 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 T a b l e 6.1: H y d r a t i o n of P e d a l Mucus S o l v e n t E q u i l i b r i u m h y d r a t i o n E s t i m a t e hydrodynamic (ml H„0 gm d r y mucus) h y d r a t i o n (ml H„0/gm) d i s t i l l e d water 954.7 ± 432.3 2430 (pH=6.0) 0.1 M NaCl 206.1 ± 38.7 276 1.0 M N a C l 138.8 ± 24.4 197 pH 2.1 59.7 ± 12.6 28 Mucus as c o l l e c t e d 21.4 34.1 153 c o n s i d e r a b l e deformation and s t r e s s must be imposed on the network before the c r o s s l i n k s break and the molecules of the network can be p u l l e d away from each other. A s i m i l a r s i t u a t i o n a r i s e s when the mucus network i s placed i n a l a r g e volume of f l u i d . The process of d i f f u s i o n i s such that the molecules of the network are e n e r g e t i c a l l y compelled to arrange themselves randomly throughout the f l u i d volume. T h i s process i s r e s i s t e d by the c r o s s l i n k s of the network. These c r o s s l i n k s are of three p o s s i b l e types: 1. P r o t e i n or p o l y s a c c h a r i d e chains can be c o v a l e n t l y bound to each other. These bonds are q u i t e s t a b l e , r e q u i r i n q hiqh temperatures,large f o r c e s , o r chemical a c t i o n to be broken. 2. P r o t e i n or p o l y s a c c h a r i d e c h a i n s can be bound to each other by "weak" bonds such as hydrogen bonds or hydrophobic i n t e r a c t i o n s . These bonds are l a b i l e under c o n d i t i o n s mild i n comparison with those r e q u i r e d to break c o v a l e n t bonds. F u r t h e r , at p h y s i o l o g i c a l temperatures the h a l f l i f e of an i s o l a t e d weak bond may be q u i t e s h o r t . As a r e s u l t these bonds w i l l be c o n s t a n t l y r e a r r a n q i n g . As a consequence i t i s p o s s i b l e t h a t c h a i n s c r o s s l i n k e d by weak bonds can g r a d u a l l y be p u l l e d apart under the i n f l u e n c e of a small f o r c e . The s h o r t h a l f l i f e o f a weak bond a l s o ensures t h a t i f a bond i s broken i t can be reformed q u i c k l y . 3. F i n a l l y , p r o t e i n or p o l y s a c c h a r i d e c h a i n s can be c r o s s l i n k e d by p h y s i c a l entanqlements. Lonq polymer chains are l i k e l y t o become entwined as they are j o s t l e d by thermal a g i t a t i o n . I f two c h a i n s so l i n k e d are p u l l e d upon i t w i l l 154 take some p e r i o d of time f o r them t o d i s e n t a n g l e . . During t h i s p e r i o d (while the ch a i n s are s t i l l entwined) the entanglements w i l l a c t as c r o s s l i n k s . Over longer periods,however,entanglements w i l l become.unraveled and thus cannot act as permanent c r o s s l i n k s . As l o n g as any one of these forms of c r o s s l i n k i s present the mucous network w i l l be maintained and the mucus w i l l not d i s s o l v e . Only when the c r o s s l i n k s are broken w i l l the mucus be able t o d i s s o l v e . Thus by examining the c o n d i t i o n s under which the mucus d i s s o l v e s , i n f o r m a t i o n may be gained concerning the type(s) of c r o s s l i n k present i n pedal 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 the term " s o l u b l e " . T h i s i s d i f f i c u l t t o do because there e x i s t s a continuous spectrum of s o l u b i l i t i e s . At one end of the spectrum are s m a l l molecules which once i n s o l u t i o n cannot be e a s i l y separated back out by "normal" means ( f i l t r a t i o n , c e n t r i f u g a t i o n ) . At the other end of the sectrum are the macromolecules t h a t are " c o l l o i d a l " and can be separated by normal means. As with any continuous spectrum, s o l u b i l i t y can be d e f i n e d only by choosing a more or l e s s a r b i t r a r y c u t - o f f p o i n t . For the purposes of the present study such a p o i n t i s chosen and a molecule i s de f i n e d t o be s o l u b l e i n a l i q u i d i f : 1, I t cannot be sedimented by low speed c e n t r i f u g a t i o n (12,100 g f o r 30 minutes) and 2. I t i s not r e t a i n e d by a Nucleopore f i l t e r with a 1 um pore s i z e . 155 U t i l i z i n g t h i s o p e r a t i o n a l d e f i n i t i o n , t e s t s were conducted t o determine under what c o n d i t i o n s pedal mucus would d i s s o l v e . The t e s t procedure was as f o l l o w s : Samples were c o l l e c t e d as f o r the p h y s i c a l t e s t s . A sm a l l volume of mucus (0.1 to 0.3 ml) was combined with ten ml of s o l v e n t i n a P o t t e r Elvehyjem t i s s u e g r i n d e r . The T e f l o n p e s t l e of the g r i n d e r was then r o t a t e d at 1740 rpm and s l o w l y i n s e r t e d and withdrawn from the g r i n d e r tube. T h i s s t i r r i n g process was continued f o r f i v e minutes and as a r e s u l t the mucus was d i s p e r s e d and the e n t i r e 10 ml sample 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 . A f t e r s t i r r i n g samples were allowed t o stand f o r 24 hours at e i t h e r 25* 40, or 55 oc. The samples were then c e n t r i f u g e d a t 12,100 g f o r 30 minutes. Formation o f a g e l a t i n o u s p e l l e t was s u f f i c i e n t t o show that the mucus had not d i s s o l v e d . I f a p e l l e t d i d not form the sample was then f i l t e r e d through a s e r i e s of Nucleopore f i l t e r s of descending pore s i z e (5.0um, 1.0um, 0.8um, 0.6um, 0.4um, 0.2um, 0.1um). At some p o i n t i n t h i s s e r i e s a pore s i z e was reached a t which the sample would completely o cclude the pores and no more f l u i d c o u l d be f o r c e d through the f i l t e r . I t was found t h a t t h i s c u t - o f f p o i n t was u s u a l l y q u i t e d i s t i n c t , a sample passing through a l l l a r g e r pore s i z e s with ease, before being completely r e t a i n e d by the f i n a l pore s i z e . Some samples passed completely through a 0.1 um f i l t e r and t h i s was noted.. A number of compounds known to 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 and the r e s u l t s are.shown i n Table 6.2. The pore s i z e s shown are the s m a l l e s t through which 156 T a b l e 6.2: S o l u b i l i t y of A. columbianus p e d a l mucus S o l v e n t 25 C 40 C 55 C d i s t i l l e d water p e l l e t p e l l e t p e l l e t 1% m e r c a p t o e t h a n o l p e l l e t 0.1 ym 0.1 ym 8 M g u a n i d i n e HC1 p e l l e t p e l l e t 0. 1 ym 8 M ure a NF 5 ym 0.1 pm formamide 5 um 5 ym p e l l e t 2 M KC1 p e l l e t p e l l e t p e l l e t 0.5% T r i t o n X100 p e l l e t p e l l e t p e l l e t 0.2% Tween 20 p e l l e t p e l l e t p e l l e t s i z e s n o t e d a r e the s m a l l e s t f i l t e r s i z e the s o l u t i o n w i l l go through. N F = n o n f i l t e r a b l e 157 the sample would pass. I t i s apparent t h a t at 25 °C none of the treatments s o l u b i l i z e d the mucus i n a period o f 24 hours. However when the temperature i s r a i s e d t o 40 °C one compound e f f e c t i v e l y d i s s o l v e d pedal mucus , 1% 2-mercaptoethanol. 2-mercaptoethanol c o n t a i n s a s u l f h y d r a l group which reduces already e x i s t i n g d i s u l f i d e bonds by forming a d i s u l f i d e bond with the s u l f h y d r y l of the c y s t e i n e molecules present i n the. mucus p r o t e i n . Thus 2-mercaptoethanol a c t s by breaking p r o t e i n - p r o t e i n c r o s s l i n k s . Subsequent t e s t s showed t h a t i t was not necessary t o d i s p e r s e the mucus i n order f o r 2-mercaptoethanol t o show t h i s s o l u b i l i z i n g e f f e c t . A blob of pedal mucus placed i n a 1% mercaptoethanol s o l u t i o n w i l l , o v e r the course of 24 hours at 40 °C, d i s s o l v e . The s o l u b i l i z i n g e f f e c t of 2-mercaptoethanol and s i m i l a r t h i o l r e d u c i n g compounds (N-acetyl c y s t i n e , d i t h i o t h r e i t o l ) has been noted i n s t u d i e s d e a l i n g with s e v e r a l d i f f e r e n t types of mucin such as p i g g a s t r i c mucin,and human c e r v i c a l and b r o n c h i a l mucins (see review by Creeth, 1978). When t e s t s are c a r r i e d out a t 55 °C a number of compounds s o l u b i l i z e the mucus (see Table 6.2). A l l of these compounds are known to d i s r u p t weak bonds such as hydrogen bonds or hydrophobic i n t e r a c t i o n s . Thus, a second catagory of c r o s s l i n k ( i n a d d i t i o n t o S-S bonds) e x i s t s i n t h e mucus. In t h i s r e s p e c t s l u g pedal mucus i s again s i m i l a r t o such v e r t e b r a t e mucins as p i g g a s t r i c mucus and human c e r v i c a l mucus. U n f o r t u n a t e l y the p r e c i s e nature of the weak bonds cannot be determined from these t e s t s . 158 I n t r i n s i c V i s c o s i t y Measurements As e x p l a i n e d i n Chapter 4, v i s c o s i t y i s a measure of a f l u i d ' s r e s i s t a n c e to the r a t e of deformation. Take f o r example the s i t u a t i o n depicted i n F i g u r e 6.2a. A f l u i d i s h e l d between two p l a t e s . One p l a t e i s s t a t i o n a r y and the second p l a t e moves at a constant v e l o c i t y . The f l u i d d i r e c t l y adjacent t o each of the p l a t e s moves a t e s s e n t i a l l y the same v e l o c i t y as the p l a t e i t s e l f (the "no s l i p c o n d i t i o n " ) . As a conseguence a v e l o c i t y g r a d i e n t i s e s t a b l i s h e d i n the f l u i d as shown i n the f i g u r e . The f l u i d may be thought of as c o n s i s t i n g of a stack of i n f i n i t e s i m a l l y t h i c k l a y e r s ; each l a y e r moving s l i g h t l y f a s t e r than the next l a y e r below i t and s l i g h t l y slower than the next l a y e r above i t . " F r i c t i o n " between l a y e r s opposes the formation of t h i s v e l o c i t y g r a d i e n t . The f o r c e needed to maintain t h i s g r a d i e n t i s thus a measure of the i n t e r n a l f r i c t i o n (= v i s c o s i t y , n ) of the f l u i d . Now c o n s i d e r F i g u r e 6.2b.. A number of r i g i d p a r t i c l e s have been added t o the f l u i d . The p l a t e moves at the same v e l o c i t y as before hence the r a t e of deformation of the sample i s the same. However, because a f r a c t i o n of the volume con t a i n e d between the p l a t e i s r i g i d ( i e . non-deformable) the p a t t e r n of deformation w i t h i n the f l u i d i s changed. Each r i g i d p a r t i c l e w i l l s t r a d d l e s e v e r a l f l u i d l a y e r s . Since the f l u i d adjacent to each p a r t i c l e must move at the same speed as the p a r t i c l e the r i g i d p a r t i c l e s w i l l " t i e " f l u i d l a y e r s t o g e t h e r , d i s r u p t i n g o r d e r l y flow. This new p a t t e r n of flow r e q u i r e s the i n p u t of an a d d i t i o n a l f o r c e i f i t i s to be maintained. 159 FIGURE 6.2. V i s c o s i t y A) F l u i d sandwhiched 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 v e l o c i t y g r a d i e n t . The f o r c e , F1, necessary t o move the p l a t e i s F = An(dx/dy)/dt B) The presence of r i g i d p a r t i c l e s i n the 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 g r a d i e n t . As a consequence F2>F1 even though the v e l o c i t y of the p l a t e and the v i s c o s i t y of the f l u i d are not a l t e r e d . 160 F i g u r e 6.2 F, ^ moving plate , area = A v e | o c j t y S fluid , v i s c o s i t y = q F 2 > F, 161 Thus the i n t e r n a l f r i c t i o n of the f l u i d c o n t a i n i n g r i g i d p a r t i c l e s i s higher than that o f the f l u i d i t s e l f and the apparent v i s c o s i t y , n', of the f l u i d c o n t a i n i n g r i g i d p a r t i c l e s i s higher than that of the f l u i d alone. The i n c r e a s e i n apparent v i s c o s i t y i s a f u n c t i o n of the c o n c e n t r a t i o n of p a r t i c l e s , c ( i n grams/ml). The higher the c o n c e n t r a t i o n of p a r t i c l e s the higher the apparent v i s c o s i t y . I t i s p o s s i b l e to take t h i s c o n c e n t r a t i o n dependence i n t o account and a r r i v e at a s i n g l e number t h a t d e s c r i b e s the r i g i d p a r t i c l e s ' e f f e c t on the f l u i d . T h i s i s accomplished by measuring the apparent v i s c o s i t y a t a number of c o n c e n t r a t i o n s . Each apparent v i s c o s i t y i s then transformed t o a s p e c i f i c v i s c o s i t y , nsp: (n'-n)/n = nsp. k graph can then be drawn p l o t t i n g the value nsp/c (the reduced v i s c o s i t y ) a g a i n s t c o n c e n t r a t i o n . The e x t r a p o l a t i o n of these experimental p o i n t s t o zero c o n c e n t r a t i o n g i v e s a c e r t a i n v alue of reduced v i s c o s i t y . T h i s value i s known as the i n t r i n s i c v i s c o s i t y £ n ] , and has the u n i t s ml/g. Since i t i s measured at zero c o n c e n t r a t i o n the i n t r i n s i c v i s c o s i t y can be thought of as a measure of the i n f l u e n c e of a s i n g l e p a r t i c l e on an i n f i n i t e volume o f f l u i d . I t thus avoids any c o m p l i c a t i o n s due t o i n t e r molecular i n t e r a c t i o n . The i n t r i n s i c v i s c o s i t y of a r i g i d p a r t i c l e i s a f u n c t i o n o f . b o t h the shape of the p a r t i c l e and i t s e f f e c t i v e hydrodynamic volume. The more a p a r t i c l e d e v i a t e s from a 162 s p h e r i c a l shape, the g r e a t e r i t s i n t r i n s i c v i s c o s i t y w i l l be, For r i g i d p a r t i c l e s these two f a c t o r s are r e l a t e d by the equation (Tanford, 1961) : Equation 6.1 ,.. [ n ] = s ( v + hvo) where s i s a measure of shape, v i s the p a r t i a l s p e c i f i c volume of the anhydrous p a r t i c l e ( c a l c u l a t e d t o be 0.65 by Snary,Allen,and P a i n (1970)), h i s a measure of h y d r a t i o n ( i n ml H20/gm) and vo i s the p a r t i a l s p e c i f i c volume of the water which i s c a r r i e d with the p a r t i c l e as i t moves (approximately 1.0), Note t h a t t h i s equation does not c o n t a i n a term f o r the molecular weight. The independence of 4.n ,3 and molecular weight, M, holds only f o r r i g i d molecules. For a f l e x i b l e molecule I n i ] w i l l vary with molecular weight such t h a t Equation 6.2 [nij = KM where K i s an e m p i r i c a l constant and * i s some value between 0.5 and 0.8. Alpha i s u s u a l l y determined e m p i r i c a l l y by procedures not a p p l i c a b l e to mucus. As a s t a r t i n g p o i n t f o r f u r t h e r d i s c u s s i o n i t w i l l be assumed here that the d i s p e r s e d mucus i s a s o l u t i o n of r i g i d hydrodynamic p a r t i c l e s and t h a t equation 6.1 i s t h e r e f o r e a p p l i c a b l e . I t w i l l be kept i n mind however t h a t a molecular weight dependence may cause these c a l c u l a t e d values to d e v i a t e from r e a l i t y . . Eguation 6.1 w i l l be used 163 t o provide a means by which the g e n e r a l shape and hydrodynamic volume of molecules may be examined. The equa t i o n i s a p p l i e d as f o l l o w s : The value o f s i s a t a minimum (s=2.5) when the molecule i s a sphere. Thus J.n-3 = 2.5 (0.65 + h vo) or h = 1. 625 U n 3/2. 5 where vo i s assumed t o be equal to the d e n s i t y of bulk water (=1.0). T h i s value f o r the h y d r a t i o n r e p r e s e n t s the maximum value f o r h y d r a t i o n . Conversely, i t co u l d be assumed t h a t h y d r a t i o n i s at a minimum (h=0) so t h a t I n j} = 0.65 s or s = l.n!j/0.65 T h i s w i l l give a maximum value f o r the shape parameter. T h i s parameter can be r e l a t e d t o the r e l a t i v e dimensions of a spheroid (Simha,1940). In r e a l i t y the t r u e v a l u e s f o r h and s w i l l l i e somewhere between the maximum and minimum value s c a l c u l a t e d here. The present study makes use of t h i s theory by examining the i n t r i n s i c v i s c o s i t y of p a r t i c l e s formed from small fragments of the mucus network when mucus i s d i s p e r s e d by sh e a r i n g i n d i s t i l l e d water as d e s c r i b e d above. I t seems reasonable t o assume t h a t p a r t i c l e s of the mucus network, 1 6 4 c r e a t e d when mucus i s d i s p e r s e d by s t i r r i n g , w i l l have some random d i s t r i b u t i o n of shapes. I f the i n d i v i d u a l chains forming the network of each p a r t i c l e are randomly arranged any expansion or c o n t r a c t i o n o f the network w i l l change the p a r t i c l e s 1 volume but w i l l not a l t e r i t s shape. Thus, i t seems u n l i k e l y t h a t p a r t i c l e s formed of the e l a s t i c network w i l l assume a h i g h l y assymmetric shape under normal c o n d i t i o n s and t h a t t h e i r average shape may be reasonably approximated as s p h e r i c a l . I f these assumptions are v a l i d the shape f a c t o r s of the above eguation w i l l be a constant 2.5 and should allow f o r e s t i m a t i o n of the h y d r a t i o n of the network. This value f o r hy d r a t i o n may d i f f e r from that measured 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 : 1. The h y d r a t i o n estimated from i n t r i n s i c v i s c o s i t y i s an e f f e c t i v e hydrodynamie h y d r a t i o n . I t r e p r e s e n t s the water which t r a v e l s with a network fragment as the fragment i s sheared i n the viscometer. T h i s amount of water may be d i f f e r e n t from the amount of water held w i t h i n the i n t e r s t i c e s of the network i n an e q u i l i b r i u m s i t u a t i o n . 2. The h y d r a t i o n o f s m a l l network fraqments may be d i f f e r e n t from the network as a whole. The mucus i s sheared e x t e n s i v e l y i n sample p r e p a r a t i o n (see below) and i t i s p o s s i b l e t hat t h i s d i s r u p t i o n changes the network p r o p e r t i e s . In l i g h t of these f a c t o r s the h y d r a t i o n value estimated by i n t r i n s i c v i s c o s i t y may provide a b e t t e r estimate than e q u i l i b r i u m s w e l l i n g o f the h y d r a t i o n s t a t e of the mucus as i t i s sheared d u r i n g a pedal wave. 165 Tests were c a r r i e d out by the f o l l o w i n g procedures.. A standard curve cf absorbance at 280 nm versus mucus c o n c e n t r a t i o n (g/ml) was c o n s t r u c t e d as f o l l o w s . Two samples of pedal mucus were c o l l e c t e d and d i s p e r s e d i n 10 ml of d i s t i l l e d water as d e s c r i b e d above f o r the s o l u b i l i t y t e s t s . Three 1 ml a l i q u o t s of each of the r e s u l t i n g 10 ml samples were d r i e d at 105 °C f o r 24 hours and weighed to determine c o n c e n t r a t i o n . Other a l i q u o t s were s e r i a l l y d i l u t e d and t h e i r absorbance measured, Averaqed values of A280 were then p l o t t e d against c o n c e n t r a t i o n , _ This standard curve was used t o measure the c o n c e n t r a t i o n of mucus present i n subsequent t e s t s . For these t e s t s samples were c o l l e c t e d and d i s p e r s e d i n d i s t i l l e d water as d e s c r i b e d above. Samples were then c e n t r i f u q e d at 12,100 g f o r 5 minutes to remove any l a r g e p a r t i c u l a t e matter. I t was shown t h a t i n the s o l u b i l i t y t e s t s mucus d i s p e r s e d i n t h i s manner c o n s i s t s of p a r t i c l e s l e s s than 5um i n s i z e but g r e a t e r than 1um.. Samples were s e r i a l l y d i l u t e d and the s p e c i f i c v i s c o s i t y meausured f o r each c o n c e n t r a t i o n using an Ostwald c a p i l l a r y viscometer with a t r a n s i t time of 80-100 seconds f o r water. T r a n s i t time was measured with a stop watch. Te s t s were repeated f o r one sample u n t i l the same t r a n s i t time was measured three times c o n s e c u t i v e l y . The viscometer was r i n s e d with 1 N HC1 and d r i e d between samples. A l l t e s t s were c a r r i e d out a t 25 +- 0.1°C i n a c o n t r o l l e d temperature bath.. Some of the r e s u l t s of these t e s t s are presented i n F i g u r e s 6.3 and 6.4 . 166 FIGURE 6.3- The i n t r i n s i c v i s c o s i t y of the d i s r u p t e d fragments of A r i o l i m a x columbianus pedal 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 . The i n t r i n s i c v i s c o s i t y decreases as e i t h e r the negative charges are masked by sodium i o n s , or the pH i s lowered t o r e a s s o c i a t e the c a r b o x y l groups. The two curves f o r d i s t i l l e d water rep r e s e n t the extremes i n the range of samples t e s t e d . FIGURE 6.3 O N 168 FIGURE 6-4. Mo l e c u l a r weight dependence of i n t r i n s i c v i s c o s i t y . D i s s o l v i n g A r i o l i m a x -columbianus pedal mucus with 1% 2-mercaptoethanol lowers the i n t r i n s i c v i s c o s i t y observed i n 0.1 M NaCl to l e s s than or egua l to t h a t observed i n 1.0 M NaCl, presumably as a r e s u l t of t h e ; d i s r u p t i o n of the mucus network. F i g u r e 6 . 4 170 The s p e c i f i c v i s c o s i t i e s of nine samples of mucus d i s p e r s e d i n d i s t i l l e d water were measured. The r e s u l t s were h i g h l y v a r i a b l e . Values of nsp ranged from 2,500 to 11,300. This v a r i a b i l i t y could not d e f i n i t e l y be a t t r i b u t e d t o any f a c t o r i n the experimental procedure. . The two t e s t s t h a t form the upper and lower boundaries o f the range of t e s t s are shown i n F i g u r e 6.3* These r e s u l t s are f u r t h e r c omplicated by the n o n l i n e a r i t y o f the nsp/c versus c p l o t s . T h i s n o n l i n e a r i t y makes i t d i f f i c u l t t o e x t r a p o l a t e the curve t o zero c o n c e n t r a t i o n . . I f , however, the l i n e formed by the two p o i n t s of lowest concentratons i s extended to zero and assumed t o provide an estimate of i n t r i n s i c v i s c o s i t y , values ranging from 4,000 to 11,500 (with an average of 6,100) are obt a i n e d . Regardless of the v a r i a t i o n i n the r e s u l t s of these t e s t s a l l o f the values of i n t r i n s i c v i s c o s i t y o b tained a r e q u i t e l a r g e . For example they are equal t o or g r e a t e r than those reported f o r DNA, a very l a r g e and h i g h l y assymmetrical molecule. The i n t r i n s i c v i s c o s i t i e s o f s e v e r a l b i o l o g i c a l macromolecules are compared to t h a t of pedal mucus i n Table 6.2. As e x p l a i n e d above, i f i t i s assumed that the mucus p a r t i c l e s being t e s t e d here are r i g i d and roughly s p h e r i c a l t h e i r h y d r a t i o n s can be c a l c u l a t e d . The p a r t i a l s p e c i f i c volume of the mucus c o n t r i b u t e s n e g l i g i b l y , and i t i s assumed t h a t the p a r t i a l s p e c i f i c volume of the water of h y d r a t i o n i s the same as bulk water ( =1). Th e r e f o r e the average i n t r i n s i c v i s c o s i t y of 6,100 corresponds t o a hy d r a t i o n o f 2430 ml of water per gram of mucus. Even 1 7 1 T a b l e 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 Macromolecules M o l e c u l e M o l e c u l a r weight I n t r i n s i c v i s c o s i t y r i b o n u c l e a s e 13,683 3.3 ( g l o b u l a r p r o t e i n ) hemoglobin 68,000 3.6 bushy s t u n t v i r u s 10,700,000 3.4 ( s p h e r i c a l ) tobacco, mosaic v i r u s 39,000,000 36.7 ( c y l i n d r i c a l ) myosin 493,000 217 c o l l a g e n 345,000 1150 DNA 6,000,000 5000 172 c o n s i d e r i n g the f a c t t h a t these estimates of h y d r a t i o n may be high due t o i n a c c u r a c i e s i n the assumptions made i n the computations, i t i s e v i d e n t t h a t the mucus network c o n s i d e r a b l y 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 . The slope of these curves i s a l s o i n d i c a t i v e of processes o c c u r r i n g as the mucus i s d i l u t e d i n the course of t e s t i n g . I f the r i g i d p a r t i c l e s d i s s o l v e d i n a f l u i d do not i n t e r a c t , the slope of the nsp/c curve should be zero (Tanford, 1961). I t i s u s u a l l y found, however, t h a t at f i n i t e c o n c e n t r a t i o n s macromolecular s o l u t e s do i n t e r a c t . The amount of t h i s i n t e r a c t i o n i s a f u n c t i o n of c o n c e n t r a t i o n , the amount of i n t e r a c t i o n being g r e a t e r at higher c o n c e n t r a t i o n s . T h e r e f o r e a high value of nsp/c w i l l be measured at high c o n c e n t r a t i o n s and nsp/c w i l l be decreased as the molecules are d i l u t e d . T h i s process l e a d s to an nsp/c/c curve with a p o s i t i v e s l o p e . For a p o l y e l e c t r o l y t e d i s s o l v e d i n d i s t i l l e d water t h i s trend i s cou n t e r a c t e d by d i l u t i o n of counter i o n s i n the p o l y e l e c t r o l y t e network. The more the sample i s d i l u t e d the lower the c o n c e n t r a t i o n s of c o u n t e r i o n s and the more the network expands (Tanford,1961) . T h i s expansion o f the network l e a d s to an i n c r e a s e i n the molecular volume/molecular weight r a t i o and nsp/c i n c r e a s e s as the c o n c e n t r a t i o n decreases. As a coneguence of these two processes the nsp/c versus c p l o t s f o r a p o l y e l e c t r o l y t e goes through a minimum (Tanford, 1961). Thus the shape of the curve i s f u r t h e r evidence of the p o l y e l e c t r o l y t e nature of pedal mucus. 173 Two f u r t h e r v i s c o s i t y t e s t s were c a r r i e d out on the whole mucus. Two samples of mucus were di s p e r s e d i n 10 ml of 0.1 M NaCl. T h i s i s a s a l t c o n c e n t r a t i o n roughly e q u i v a l e n t to p h y s i o l o g i c a l c o n c e n t r a t i o n s i n whole mucus. These samples were then t e s t e d i n the Ostwald viscometer. The r e s u l t s of these t e s t s are p l o t t e d i n Fig u r e 6.3. D i s p e r s i n g the pedal mucus i n t h i s s a l t s o l u t i o n lowers the i n t r i n s i c v i s c o s i t y by a f a c t o r of roughly 5 from the lowest value obtained i n d i s t i l l e d water. The presence of Na+ c o u n t e r i o n s causes the mucus network to become more compact. Though the i n t r i n s i c v i s c o s i t y i s lower, i t s value (690) i s s t i l l q u i t e l a r g e f o r a b i o l o g i c a l molecule (see Table 6.2). For comparison A l l e n , P a i n , a n d Snary (1976) found a value o f 320 ml/g f o r pig g a s t r i c mucus i n 0.2 M KC1. T h i s J.niJ (690, f o r s l u g pedal mucus) corresponds t o a h y d r a t i o n of 276 ml of water per gram of mucus. One sample was d i s p e r s e d i n 1.0 M NaCl. T h i s sample showed s t i l l lower i n t r i n s i c v i s c o s i t y (495 ml/g) corresponding to a h y d r a t i o n of 197 ml H20/g. Neither o f these samples shows the n o n - l i n e a r p l o t seen f o r mucus i n d i s t i l l e d water. The presence o f c o u n t e r i o n s , by dec r e a s i n g the network volume and masking charges, should decrease the l e v e l 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 . Further the presence of a l a r g e amount of c o u n t e r i o n s i n the s o l v e n t ensures a constant l e v e l of c o u n t e r i o n s i n the network. Thus both processes l e a d i n g to a n o n - l i n e a r p l o t are minimized and the p l o t becomes l i n e a r with a very s m a l l s l o p e . Two samples 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 p r e v i o u s t e s t s and then the pH of the samples was adjusted to pH 2.1 u s i n g HCl. The experimental p o i n t s from these t e s t s are a l s o p l o t t e d i n F i g u r e 6.3. Lowering the pH w e l l below the pK of the network's c a r b o x y l groups lowers the i n t r i n s i c v i s c o s i t y even f u r t h e r than does the presence of c o u n t e r i o n s . Presumably i n i t s non-charged s t a t e the polymer network of the mucus assumes a random c o n f i g u r a t i o n and the volume of t h i s c o n f i g u r a t i o n i s l e s s than t h a t of a charged network c o n t a i n i n g c o u n t e r i o n s . The i n t r i n s i c v i s c o s i t y of mucus p a r t i c l e s under these c o n d i t i o n s i s 60 to 70 ml/g, corresponding t o a h y d r a t i o n of 24 t o 28 ml H20/g. , In Table 6.1 the h y d r a t i o n v a l u e s estimated here from i n t r i n s i c v i s c o s i t y measurements are compared t o the values obtained from e g u i l i b r i u m s w e l l i n g . For the NaCl s o l u t i o n s the two f i g u r e s match f a i r l y c l o s e l y . The two values may be matched e x a c t l y i f the shape f a c t o r , s, of equation 6.1 i s changed from 2.50 t o 3.47. The value of 3.47 corresponds to an e l l i p s o i d p a r t i c l e with a major axis/minor a x i s r a t i o of between 2.7 and 3.0 (depending on whether the e l l i p s o i d i s p r o l a t e or o b l a t e , r e s p e c t i v e l y ) . Thus these data are c o n s i s t e n t with t h e : p o s s i b i l i t y t h a t the network fragments are s l i g h t l y elongated,hydrodynamically r i g i d p a r t i c l e s i n these s a l t s o l u t i o n s . At the extremes of the s w e l l i n g range the e s t i m a t e s of hydrodynamic h y d r a t i o n diverge c o n s i d e r a b l y from e q u i l i b r i u m h y d r a t i o n , being l a r g e r i n d i s t i l l e d water and s m a l l e r a t pH 2.1. I t may be s p e c u l a t e d t h a t the presence of a l a r g e number of charges i n d i s t i l l e d water and the near t o t a l l a c k 175 of charges at pH 2.1 somehow a f f e c t s the amount of water bound t o the moving p a r t i c l e . T h i s c o u l d account f o r t h i s d i s c r e p a n c y . However a mechanism f o r t h i s e f f e c t i s not immediately evident and the matter w i l l r e g u i r e f u r t h e r study. Regardless of the p r e c i s e comparison of hydrodynamic with e g u i l i b r i u m h y d r a t i o n these t e s t s r e c o n f i r m the f a c t t h a t the mucous network i n f l u e n c e s very l a r g e amounts of water. A l l of the above t e s t s were made on mucus s i m i l a r l y prepared. Ccnseguently d i f f e r e n c e s i n J_ n are a t t r i b u t a b l e to e i t h e r a change i n hydration,shape,or hoth. If,however,the mucus i s d i s s o l v e d by treatment with 2-mercaptoethanol many of the c r o s s l i n k s of the network are broken and the molecular weight of the r e s u l t a n t p a r t i c l e s should be l e s s than t h a t of the network fragments of untreated mucus. I t seems reasonable t o assume t h a t much o f the water which would be trapped i n the i n t e r s t i c e s of a g e l network w i l l be " r e l e a s e d " ( i e , not hydrodynamically bound) when the network i s d i s s o l v e d . In other words, g l y c o p r o t e i n c h a i n s can a f f e c t more water when they are c r o s s l i n k e d together (by e n c l o s i n g spaces l i k e a sponge) than they can s e p a r a t e l y . Thus,as mercaptoethanol d i s s o l v e s the network the i n t r i n s i c v i s c o s i t y should decrease. T h i s i s indeed the case. F i g u r e 6.4 shows the r e s u l t s from a comparison of untreated mucus i n 0, 1 !3 NaCl with mucus t h a t has been t r e a t e d f o r 24 hours a t 40 <>C with 2-mercaptoethanol. Both t e s t s were performed at 25 <>C. As p r e d i c t e d the i n t r i n s i c v i s c o s i t y of the d i s s o l v e d mucus i s 1 7 6 c o n s i d e r a b l y lowered, f u r t h e r c o n f i r m i n g the f a c t t h a t 2-mercaptoethanol e f f e c t i v e l y d i s s o l v e s the.mucous network. In summary, these measurements of the i n t r i n s i c v i s c o s i t y of pedal mucus show t h a t : 1 . Even under n o n - e q u i l i b r i u m c o n d i t i o n s the mucous network i n f l u e n c e s l a r g e volumes of water. 2. The f a c t i s reconfirmed t h a t the mucous network expands and c o n t r a c t s depending on the nature of the s o l v e n t ; evidence o f the p o l y a n i o n i c nature of the g l y c o p r o t e i n . 3. 2-mercaptoethanol i s shown to reduce the molecular weight of the mucous p a r t i c l e s i n s o l u t i o n . Molecular Weight Between C r o s s l i n k s One of the p r e d i c t i o n s of the theory of rubber e l a s t i c i t y i s t h a t the modulus of an entropy e l a s t i c m a t e r i a l should be r e l a t e d to the number of c r o s s l i n k s present per volume of m a t e r i a l . I f very few c r o s s l i n k s are present, the major i t y of chains i n the .network w i l l be f r e e to rearrange randomly as the network i s s t r e s s e d and the network's s t i f f n e s s w i l l be low. The more c r o s s l i n k s present, the l e s s freedom c h a i n s w i l l have when the network i s deformed and the s t i f f e r the network w i l l be. Now the more c r o s s l i n k s there are i n a given volume.of network the s h o r t e r the le n g t h s of chain between c r o s s l i n k s . Since each l e n g t h of ch a i n w i l l c o n t a i n a c e r t a i n weight of polymer molecules a r e l a t i o n s h i p should e x i s t between the:molecular weight between c r o s s l i n k s (and thereby c h a i n l e n g t h and 177 number of c r o s s l i n k s ) and the modulus of the m a t e r i a l . Theory s t a t e s t h a t t h i s r e l a t i o n s h i p i s of the form: G = pBT/M where p i s the d e n s i t y of polymer c h a i n s i n the network ( i n g/ml of g e l ) , E i s the gas constant (8,300 ergs/degree mole), T i s a b s o l u t e temperature, and M i s molecular weight between c r o s s l i n k s . In order f o r t h i s eguation t o be s t r i c t l y t r u e , the value of G used must be the e q u i l i b r i u m v a l u e . T h i s i s the value of G obtained from a s t r e s s r e l a x a t i o n t e s t a t i n f i n i t e time. In t h i s manner the eguation i s a measure of the molecular weight between permanent c r o s s l i n k s . S t r e s s r e l a x a t i o n t e s t s on A. columbianus pedal mucus (Chapter 4) show t h a t t h i s m a t e r i a l does not have an e q u i l i b r i u m modulus and t h e r e f o r e t h i s equation i n i t s s t r i c t e s t sense cannot be a p p l i e d . However over s h o r t p e r i o d s of time, pedal mucus does have a modulus, presumably as the r e s u l t of temporary c r o s s l i n k s . . Thus, i f t h i s i nstantaneous modulus i s used, the molecular weight between temporary c r o s s l i n k s can be estimated. The equation i s a p p l i e d i n the f o l l o w i n g manner as suggested by Alexander (1965) and F e r r y (1970). The value f o r G i s taken from the t e s t s of Chapter 4 to be 100 t o 200 N/m2. These measurements were conducted at about 20 °C (293 ° K ) . The d e n s i t y f i g u r e used i s t h a t of the mucous network (not i n c l u d i n g the water with which i t i s mixed) or about 0.03 g/ml. Using these values the f i g u r e s f o r molecular weight 178 between c r o s s l i n k s can be c a l c u l a t e d as 8.8 to 7.5 x 10 s. T h i s r e p r e s e n t s the minimum molecular weight t h a t g l y c o p r o t e i n chains could be and s t i l l form the e l a s t i c network found i n mucus. I f more than one c r o s s l i n k i s present on each g l y c o p r o t e i n molecule, the molecular weight of the whole molecule w i l l be some m u l t i p l e of t h i s weight between c r o s s l i n k s . Gel F i l t r a t i o n The composition of s o l u b i l i z e d mucus was examined by g e l f i l r a t i o n . T h i s technigue uses the p r o p e r t i e s of an agarose g e l t o separate molecules on the b a s i s of s i z e . Large molecules a p p l i e d t o such a g e l column are too bulky to f i t i n t o the i n t e r s t i c e s of the column's g e l beads (they are " e x c l u d e d " ) . These l a r g e molecules are washed between the g e l beads and are r a p i d l y e l u t e d . For a Sepharose IE-column, as used i n t h i s study, compact molecules with a molecular weight of g r e a t e r than 20 m i l l i o n are excluded.. However, the more expanded g l y c o p r o t e i n molecules are excluded at a lower molecular weight. Snary, M i e n , and Pain (1970) found t h a t p i g g a s t r i c mucus g l y c o p r o t e i n s with a molecular weight of 5.5 m i l l i o n o r l a r g e r were excluded on Sepharose 4B. A column of Sepharose 4B (CL) (100cm by 2 cm) was used f o r the s e p a r a t i o n . The column was e q u i l i b r a t e d t o a s o l v e n t of 0.1M NaCl c o n t a i n i n q 1% 2-mercaptoethanol. Mucus samples were c o l l e c t e d and d i s p e r s e d i n 1% 2-mercaptoethanol and allowed to s o l u b i l i z e a t 40 °C f o r 24 hours. Samples 179 were then c e n t r i f u g e d f o r 5 minutes a t 12,100 g t o remove p a r t i c u l a t e matter. ft 10 ml a l i q u o t of t h i s s o l u b i l i z e d sample was loaded on the column and e l u t e d with 0.1M NaCl, 1% 2-mercaptoethanol a t a flow r a t e of about 12 ml/hour. A l l t e s t s were conducted at room temperature 21 to 23 °C. Ten ml f r a c t i o n s were c o l l e c t e d and assayed f o r carbohydrate and p r o t e i n . Absorbance at 280 nm was used to measure p r o t e i n c o n c e n t r a t i o n . The phenol - s u l f u r i c a c i d assay of Lo, B u s s e l , and T a y l o r (1970) was used to measure carbohydrate c o n c e n t r a t i o n s . The procedure was repeated s e v e r a l times with s i m i l a r r e s u l t s . The composite chromatogram o f t h r e e of these t e s t s i s presented i n F i g u r e 6. 5. This t e s t i n d i c a t e s t h a t at l e a s t two major f r a c t i o n s of molecules are r e l e a s e d when the d i s u l f i d e c r o s s l i n k s of the mucus are broken by 2-mercaptoethanol. 1. A l a r g e r molecule c o n t a i n i n g carbohydrate and probably a s m a l l amount of p r o t e i n , 2. A s m a l l e r molecule c o n t a i n i n g o n l y p r o t e i n . In two t e s t s a t h i r d p r o t e i n peak was found e l u t i n g before the carbohydrate peak.. In these cases the main p r o t e i n peak (peak 2; see F i g u r e 6.5) was s m a l l e r .. I t i s assumed t h a t t h i s type of e l u t i o n p r o f i l e i s accounted f o r by the incomplete s o l u b i l i z a t i o n of t h e . c r o s s l i n k e d network l e a d i n g t o the presence i n the sample of both u n c r o s s l i n k e d p r o t e i n c h a i n s (peak 2) and l a r g e complexes of c r o s s l i n k e d p r o t e i n networks. An example of one such chromatogram i s shown i n F i g u r e 6.6. 180 FIGORE 6.5,. Separation of pedal mucus on Sepharose.4-B CL r e s u l t s i n the e l u t i o n o f two major f r a c t i o n s : 1) a high molecular weight f r a c t i o n c o n t a i n i n g both p r o t e i n and carbohydrate, and 2) a lower molecular 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. < M O L E C U L A R S I Z E P R O T E I N C A R B O H Y D R A T E 182 FIGURE 6.6. Incompletely d i s s o l v e d p edal mucus shows a t h i r d f r a c t i o n when separated on Sepharose 4-B CL. T h i s i s presumably due to aggregates of the p r o t e i n of f r a c t i o n 2. 184 Attachment Of Carbohydrate To P r o t e i n I t has been shown (Gottschalk,1972;Hunt,1970) t h a t f o r many g l y c o p r o t e i n s the p o l y s a c c h a r i d e c h a i n s are bound to the p r o t e i n through 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 or th r e o n i n e . The presence of such bonds may be e a s i l y d e t e c t e d ( C a r u b e l l i e t a l . ,1965). The O - g l y c o s i d i c bond of a hexose to a s e r i n e or threonine i s unusually l a b i l e i n weak a l k a l i s o l u t i o n s , a n d i s broken through a process known as B - e l i m i n a t i o n . When the bond i s cl e a v e d the amino a c i d i s converted t o a compound t h a t absorbs s t r o n g l y i n the u l t r a v i o l e t . Normal g l y c o s i d i c bonds and peptide bonds are not a f f e c t e d by treatment with mild a l k a l i . Thus, the r e a c t i o n between a d i l u t e s o l u t i o n of NaOH and a g l y c o p r o t e i n may be c a r r i e d out i n a spectrophotometer and an i n c r e a s e i n a b s o r p t i o n a t 241 nm i s i n d i c a t i v e of the presence 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 t h r e o n i n e . A. columbianus pedal mucus was c o l l e c t e d and 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 the s o l u b i l i t y t e s t s d e s c r i b e d above. One m i l l i l i t e r of t h i s mucus s o l u t i o n was mixed with one ml of d i s t i l l e d water and served as an absorbance standard. Another m i l l i l i t e r o f mucus s o l u t i o n was thoroughly mixed with 1 ml of 1 N NaOH f o r a f i n a l c o n c e n t r a t i o n of 0.5 N NaOH. The absorbance of t h i s sample (at 241 nm) was read r e l a t i v e t o the standard i n a Pye Onicam 1750 dua l beam u l t r a v i o l e t spectrophotometer. The t e s t s were conducted at room temperature. Absorbance values were recorded f o r 15-20 minutes a f t e r the i n i t i a l mixing. 1 8 5 The experiment was repeated with a f i n a l sample c o n c e n t r a t i o n of 0.25 N NaOH. A mucous s o l u t i o n mixed with an equal volume of d i s t i l l e d water served as a c o n t r o l . A l l t e s t s were performed i n t r i p l i c a t e and the r e s u l t s are presented i n Fig u r e 6.7. Mucus samples t r e a t e d with NaOH show an i n c r e a s i n g absorbance at 241 nm. The r a t e of i n c r e a s e of absorbance decreases a f t e r about t en minutes. I f the rate of i n c r e a s e i s computed f o r the i n i t i a l ten minutes of the experiment the value obtained with g l y c o p r o t e i n i n 0.50 N NaOH i s almost e x a c t l y twice t h a t obtained with 0.25 NAOH.. The absorbance of the c o n t r o l d i d not change with time. These r e s u l t s are very s i m i l a r t o those of C a r u b e l l i et a l (1965) and are taken as evidence (though not c o n c l u s i v e ) t h a t the p o l y s a c c h a r i d e component of A. columbianus pedal mucus i s at l e a s t i n part connected t o the p r o t e i n component by O - g l y c o s i d i c bonds to s e r i n e and/or t h r e o n i n e . . Further treatment of the a l k a l i t r e a t e d mucus and amino a c i d a n a l y s i s of the r e s u l t i n g compounds should provide a d d i t i o n a l evidence concerning t h i s p o i n t . Summary In summary, the r e s u l t s o f these t e s t s i n d i c a t e t h a t : 1. The e l a s t i c network of A, columbianus- pedal mucus i s formed from a pol y a n i o n . . 2. The molecular weight o f t h i s polyanion i s q u i t e l a r g e (greater than 7.5 x 1 0 s ) . 3. At l e a s t two s o r t s of molecules c o n t r i b u t e to the 186 FIGURE 6.7. Carbohydrate bonding t o s e r i n e and/or t h r e o n i n e . The i n c r e a s e i n absorbance at 241 nm. of 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 to p r o t e i n i n Ari o l i m a x columbianus pedal mucus. Figure 6.7 5 10 15 m i n u t e s 188 mucus network, a l a r g e molecule c o n s i s t i n g p r i m a r i l y of p o l y s a c c h a r i d e s and a s m a l l e r molecule composed of p r o t e i n . 4. The carbohydrate p o r t i o n i f the g l y c o p r o t e i n i s ap p a r e n t l y c o v a l e n t l y bonded t o the p r o t e i n , the attachment s i t e ( s ) being s e r i n e and/or t h r e o n i n e . 5. The mucus network i s c r o s s l i n k e d both by d i s u l f i d e b r idges between p r o t e i n molecules, and weak bonds between e i t h e r the carbohydrate p o r t i o n , the p r o t e i n p o r t i o n , o r both. 6. The c r o s s l i n k e d , h i g h l y expanded mucous network i n f l u e n c e s l a r g e amounts of water., These t e s t s form only a very c u r s o r y study o f the p h y s i c a l chemistry of A. columbianus pedal mucus. Many questions remain to be answered. Comparison With Other Mucins A c o n s i d e r a b l e amount of study has been d i r e c t e d a t the p h y s i c a l chemistry of mucous s e c r e t i o n s . As with other s t u d i e s on mucins these s t u d i e s have g e n e r a l l y been l i m i t e d t o the study of v e r t e b r a t e ( p r i m a r i l y mammalian) g l y c o p r o t e i n s and mucopolysaccharides. The f i n d i n g s of these s t u d i e s are reviewed i n G o t t s c h a l k (1972), Hunt (1970) , E l s t e i n and parke (1976), and the B r i t i s h Medical J o u r n a l (1978). Recently a number of authors have made s u f f i c i e n t progress i n examining the p h y s i c a l chemistry of a v a r i e t y of mucins to be able t o propose models f o r mucus s t r u c t u r e ( A l l e n and Snary, 1971; A l l e n , 1978; Roberts, 1978; Rao and 189 Massen, 1977). A l l of these models i n c o r p o r a t e t h r e e s i m i l a r f e a t u r e s . 1. Subunits c o n s i s t i n g o f a p r o t e i n core with carbohydrate s i d e c h a i n s , 2. "naked" areas on the p r o t e i n core where d i s u l f i d e bonds can be formed between two subunits, 3. Some form o f i n t e r a c t i o n (hydrophobic or other "weak" bonds) between l a r g e composite molecules formed of a number of c r o s s l i n k e d s u b u n i t s . Thus s e v e r a l s u b u n i t s are c r o s s l i n k e d (S-S) t o form l a r g e r molecules. These molecules i n t u r n i n t e r a c t to form the mucus g e l . I t seems l i k e l y t h a t t h i s b a s i c s o r t of model i s v a l i d f o r a l a r g e number of v e r t e b r a t e mucins. I t i s i n t e r e s t i n g to s p e c u l a t e how an i n v e r t e b r a t e mucin (such as iU columbianus pedal mucus) might compare. There appears t o be only one minor problem i n r e c o n c i l i n g the scant data presented i n t h i s study with t h i s v e r t e b r a t e model. JU columbianus pedal mucus appears t o c o n t a i n a l a r g e p o r t i o n of p r o t e i n t h a t i s not c o v a l e n t l y bound to carbohydrate. T h i s f a c t may e a s i l y be i n c o r p o r a t e d i n t o a model as shown i n F i g u r e 6,8. Small l e n g t h s of p r o t e i n are bound t o g e t h e r by d i s u l f i d e bonds. Some of these s m a l l p r o t e i n s are i n t u r n l i n k e d t o the p r o t e i n core of the p r o t e i n / p o l y s a c c h a r i d e chain.. In t h i s manner l a r g e composite molecules of g l y c o p r o t e i n are c o n s t r u c t e d . These l a r g e molecules then i n t e r a c t through weak bonds and entanglements t o form the o v e r a l l mucus network. When the mucus i s sheared under the f o o t of the s l u g , the weak bonds 1 9 0 FIGURE 6,8. A model f o r t h e s t r u c t u r e of Ariolimax columbianus pedal mucus. The two f r a c t i o n s observed i n F i g u r e 6,5 are 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 composite molecules. These composites subsequently i n t e r a c t by "weak bonds" t o form the o v e r a l l mucus network,. 1 9 1 Building Blocks large fraction H H : : i j j j j j small fraction g 1 1 sulfhydryl g r o u p-silo of disulfide crossl inking polysaccharide chain protein chain FIGURE 6.8 C Overall Network Y W i\ © ~ "weak" bond composit e mo I ecu Ie B Compos i te Molecule small fraction targe fraction largo and small fractions are crosslinked with disulfide bonds 1 9 2 between l a r g e composite molecules are ruptured and the mucus f l o w s . When s h e a r i n g i s terminated the weak bonds r a p i d l y reform, and the mucous network " h e a l s " . The l o n g e r the time allowed f o r h e a l i n g , the more weak bonds and entanglements are formed and the higher the modulus of the network; At present t h i s model f o r A. columbianus pedal mucus s t r u c t u r e i s pure s p e c u l a t i o n . A c o n s i d e r a b l e amount of work must yet be performed b e f o r e t h i s model can be s u b s t a n t i a t e d or discounted., I t w i l l be i n t e r e s t i n g t o f o l l o w the course of f u t u r e r e s e a r c h to see i f t h i s type o f model i s indeed a p p l i c a b l e to s l u g mucus and t o i n v e r t e b r a t e mucus i n g e n e r a l . The presence of a s i m p l e , g e n e r a l model f o r mucus s t r u c t u r e would be extremely u s e f u l as a b a s i s f o r f u r t h e r r e s e a r c h i n t o the s t r u c t u r e and f u n c t i o n of mucous s e c r e t i o n s . At p r e s e n t I can propose no model f o r the mechanism of f i b e r f ormation i n A., columbianus pedal mucus. Again, f u r t h e r r e s e a r c h i s r e q u i r e d . 193 CHAPTER SEVEN A Model For Slug Locomotion Complex b i o l o g i c a l problems, such as gastropod locomotion, are o f t e n best examined through the use of a model. A model i n t h i s sense i s a h y p o t h e t i c a l s t r u c t u r e used to r e l a t e i s o l a t e d f a c t s known about a process and thereby provide p r e d i c t i o n s about t h a t process. I f on the b a s i s of known f a c t s a model p r o v i d e s c o r r e c t p r e d i c t i o n s , the h y p o t h e t i c a l s t r u c t u r e of the model can be thought of as corresponding t o the a c t u a l s t r u c t u r e . The q u a l i t a t i v e model proposed and t e s t e d by Lissman (1945b) has been , to date, the only model to examine the mechanism of qastropod locomotion. T h i s model i s based on the k i n e m a t i c s of s n a i l s of the genus H e l i x (Lissman, 1945a) As the locomotory movements o f H e l i x are very s i m i l a r to those of Au columbianus (described i n Chapter 3), Lissman's model should be a p p l i c a b l e to the problem of s l u g locomotion. Lissman proposes t h a t the locomotion of s n a i l s (or slugs) can be accounted f o r by the i n t e r a c t i o n of f o u r and p o s s i b l y f i v e , types of f o r c e s as shown i n F i g u r e 7.1: 1. Forces a c t i n g t o extend the f o o t (most probably h y d r o s t a t i c pressure) ; 2. Forces a c t i n g t o compress the f o o t (muscular c o n t r a c t i o n ) ; 3. A f r i c t i o n a l drag between the substratum and the segments of the f o o t that are moving forwards (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 gastropod locomotion ( a f t e r Lissman, 1945b). 1) An i n t e r n a l f o r c e of expansion causes the f o o t t o e l o n g a t e . 2) An i n t e r n a l f o r c e of compression causes the f o o t to 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 contact 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 to 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 or e l o n g a t i o n of the c e n t r a l of 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 r e s i s t i v e f o r c e . 195 F i g u r e 7.1 196 the p r o p e r t i e s of pedal mucus) ; 4. a r e a c t i v e f o r c e opposing the f r i c t i o n a l drag. T h i s f o r c e a l s o a c t s through the mucus under those segments of the f o o t which are s t a t i o n a r y (the interwave) ; 5. P o s s i b l y t e n s i o n s or t h r u s t s between s t a t i o n a r y segments of the f o o t . Of these f i v e f o r c e s , 3, 4, and 5 can be q u a n t i f i e d by measuring the f o r c e s exerted on the substratum by a movinq s l u g . Lissman attempted t o measure these f o r c e s and i n h i s a n a l y s i s r e l a t e s them to produce a q u a l i t a t i v e model f o r the locomotion of H e l i x . This model s u f f e r s from s e v e r a l problems: F i r s t i t i s s t r i c t l y q u a l i t a t i v e . Without knowledge of t h e : p r o p e r t i e s of pedal mucus, p r e d i c t i o n s of the magnitude of the f r i c t i o n a l drag and r e s i s t i v e f o r c e s was i m p o s s i b l e . While Lissman's model i s i n most r e s p e c t s q u a l i t a t i v e l y a c c c u r a t e , i t i s much more d i f f i c u l t t o c r i t i c a l l y evaluate such a model than a model where both the d i r e c t i o n and magnitude of f o r c e s can be compared to r e a l i t y . Second, the f o r c e transducer used by Lissman may w e l l have been i n a p p r o p r i a t e . The apparatus c o n s i s t s of a p l a t f o r m mounted on a pendulum, the more f o r c e placed on the p l a t f o r m , the l a r g e r the displacement of the pendulum. The p r e c i s e dimensions of the apparatus are not g i v e n , but from diagrams shown i n Gray and Lissman (1938) i t can be estimated t h a t the p e r i o d of the pendulum i s about 0.5 to 1.0 seconds. I f t h i s i s so, the device i s i n c a p a b l e of a c c u r a t e l y measuring o s c i l l a t i n g f o r c e s with a p e r i o d of 197 around one second or l e s s . The f o r c e s measured by Lissman f a l l s q u a r e l y i n t o t h i s category. In order t c e x p l a i n what are probably i n a c c u r a t e f o r c e measurements, Lissman complicates a b a s i c a l l y simple model by i n v o k i n g t e n s i o n s and t h r u s t s between s t a t i o n a r y segments o f the f o o t (type 5 f o r c e of F i g u r e 7.1) . These f o r c e s l e a d him to argue t h a t "the p r o p u l s i o n of the f r o n t end of the animal i s e f f e c t e d by r e g i o n s of the f o o t l y i n g p o s t e r i o r t o i t s e l f , whereas the hind end i s being aided by a p u l l from r e g i o n s l y i n g more a n t e r i o r l y ". T h i s sounds s u s p i c i o u s l y l i k e someone t r y i n g to l i f t h i m s e l f up by h i s b o o t s t r a p s , and causes c o n s i d e r a b l e c o n f u s i o n i n i n t e r p r e t i n g Lissman's model. In l i g h t of the f a c t s presented i n Chapters 1-6 of t h i s t h e s i s , a q u a n t i t a t i v e model can be c o n s t r u c t e d which i n c o r p o r a t e s many o f the f e a t u r e s o f Lissman's model but avoids the problems. T h i s chapter w i l l present t h i s model, i t s p r e d i c t i o n s , and t e s t s of these p r e d i c t i o n s . The Model Before examining the p r e c i s e c a l c u l a t i o n s which form the model, i t w i l l be u s e f u l to o u t l i n e the model's major p o i n t s and show how these d i f f e r from Lissman's. The present model i s designed t o p r e d i c t t h e ; f o r c e s o p e r a t i n g under a s l u g c r a w l i n g on a smooth n o n p o r o u s , i n f l e x i b l e s u r f a c e . Under these c o n d i t i o n s , as shown i n Chapter 3, the s l u g does not l i f t the f o o t during locomotion. Thus, as the s l u g moves along i t passes over a 1 9 8 l a y e r of mucus of a constant t h i c k n e s s . . Various s t r e s s e s are imposed on t h i s mucus l a y e r by the moving f o o t . The magnitude of these s t r e s s e s can be estimated from a knowledge of the movements of the f o o t and the p h y s i c a l p r o p e r t i e s of the pedal mucus. As shown e a r l i e r the f o o t may be d i v i d e d i n t o three f u n c t i o n a l areas: the waves, the interwaves, and the rims. The s t r e s s e s a s s o c i a t e d with each area w i l l be examined i n t u r n . The s t r e s s e s are diagrammed i n F i g u r e 7.2. T h i s model c a l c u l a t e s the s t r e s s a s s o c i a t e d with each area and r e l a t e s these s t r e s s e s to account f o r locomotion. The Hayes As a segment of the f o o t i s overtaken by a compressional pedal wave, i t begins t o move forward. T h i s movement w i l l shear the mucus beneath t h a t segment. The .;> shear r a t i o , r h o , w i l l be equal t o x/y where x i s the d i s t a n c e moved by the f o o t and y i s the mucus l a y e r t h i c k n e s s (see F i g u r e 7.2). At some p o i n t t h i s mucus w i l l be sheared beyond i t s y i e l d p o i n t and i t w i l l f l ow. Subsequently, as long as the segment of the f o o t i s moving forward i t w i l l be moving over a v i s c o u s f l u i d . . The v i s c o s i t y of the f l u i d and the shear r a t e imposed by the moving segment w i l l determine Fw, the r e s i s t e n c e t o movement experienced by the moving wave: shear s t r e s s , 2 gma = n dp/dt Fw= sigma Aw 199 FIGURE 7.2. The f o r c e s present under a moving s l u g . A) Waves. The s t r e s s at any p o i n t i s egual to the shear r a t e times the v i s c o s i t y a t t h a t shear r a t e . The sum of a l l s t r e s s e s under a wave i s the wave s t r e s s . . The wave s t r e s s times the wave area equals the wave f o r c e , Fw. B) Rim. The rim s t r e s s i s equal to the shear r a t e under the rim times the v i s c o s i t y at t h a t shear r a t e . The r i m s t r e s s times the rim area equals the rim f o r c e , F r . C) Interwaves. In order f o r locomotion to occur F i = - (Fr + Fw) where F i i s the interwave f o r c e . Thus the interwave s t r e s s equals F i d i v i d e d by the interwave area. c. o o 201 where n i s the value of v i s c o s i t y from F i g u r e 7 . 4 , and Aw i s the area of the f o o t contained i n the waves. As shown i n F i g u r e 7 .1 t h i s r e s i s t a n c e w i l l p l a c e an equal and opposite f o r c e on the s t a t i o n a r y p o r t i o n s of the f o o t - the interwaves. The Rims The rims of the f o o t move forward at the same constant speed as the s l u g i t s e l f , Conseguently, once sheared beyond i t s y i e l d p o i n t when the slug begins t o move the mucus beneath these rims w i l l always remain i n i t s f l u i d form as long as the s l u g continues t o move. Again the r a t e of movement of the rim and the v i s c o s i t y of the f l u i d w i l l determine F r , the r e s i s t a n c e to movement. Sigma = n dp/dt Fr=sigma Ar where Ar i s the area of the rims. The f o r c e r e q u i r e d t o move the rims forward w i l l p l a c e an a d d i t i o n a l s t r e s s on the mucus beneath the interwaves. The Interwaves As a wave l e a v e s a segment of the f o o t behind, the segment w i l l d e c e l e r a t e u n t i l i t i s s t a t i o n a r y . . As soon as the segment i s s t a t i o n a r y the mucus beneath i t w i l l begin to h e a l , becoming more s o l i d as time passes. I f the mucus h e a l s q u i c k l y enough most of the s t a t i o n a r y segment w i l l 202 r e s t on mucus i n i t s s o l i d form. T h i s s o l i d mucus w i l l hold the interwave s t a t i o n a r y a g a i n s t the f o r c e of the - waves and interwaves moving forward. The magnitude of the s t r e s s on t h i s s o l i d mucus i s the f o r c e of forward motion (Fr + Fw) / (Ai) the area of the interwaves.. As long as the s o l i d mucus i s s u f f i c i e n t l y s t r o n g to r e s i s t the s t r e s s imposed by the rims and waves, the s l u g w i l l be ab l e to c r a w l . T h i s model does not allow f o r the presence of t e n s i o n s or t h r u s t s between interwaves (type 5 f o r c e of Lissman). This i s simply another way of s a y i n g t h a t the l e n g t h by which the f o o t c o n t r a c t s on e n t e r i n g a pedal wave i s sim u l t a n e o u s l y o f f s e t by the f o o t re-extending on l e a v i n g a wave. T h i s assumption c o n s i d e r a b l y s i m p l i f i e s the model and , i t w i l l be shown ,does not d e t r a c t from i t s accuracy. S i m i l a r l y t h i s model does not take i n t o account f o r c e s due 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 of segments of the f o o t . T h i s s i m p l i f i c a t i o n i s j u s t i f i e d by the f a c t t h a t the masses and r a t e s of a c c e l e r a t i o n are n e g l i g i b l y s m a l l . F u r t h e r , f o r each p a r t of the f o o t t h a t i s a c c e l e r a t i n g t h e r e i s an e q u i v a l e n t segment d e c e l e r a t i n g so t h a t the s m a l l f o r c e s present .should tend to c a n c e l . F i n a l l y , t h i s model does not account f o r the a c t i o n of those c i l i a present on the pedal e p i t h e l i u m . With t h i s g e n e r a l scheme i n mind a s p e c i f i c example may be examined: T h i s example makes use of an "average" s l u g as determined by the kinematic s t u d i e s of Chapter 3. An average s l u g weighs approximately f i f t e e n grams and has a t o t a l f o o t area of 15 cm 2. S l i g h t l y more than a t h i r d (5.5 203 cm 2) i s contained i n the rims. Of the remaining 9-5 cm 2, 6,0 cm 2 i s i n the interwaves, and 3,5 cm 2 i n waves,. Now l e t t h i s s l u g move forward with pedal waves resembling the average wave shown i n F i g u r e 7.3 (reproduced here from Figure 3.4) . The s l u g (and consequently the rims) moves with a constant speed o f 0.85 mm/sec. The waves, because they only move f o r h a l f the time move at an average speed twice t h a t of the s l u g , or 1.7 mm/second , However a t any given time the p r e c i s e speed of a segment i n the wave w i l l vary as shown i n F i g u r e 7.3 . The interwaves are s t a t i o n a r y . For these f o o t speeds the shear r a t e experienced by the pedal mucus w i l l be determined by the t h i c k n e s s of the mucus l a y e r . In order to examine the e f f e c t of mucus l a y e r t h i c k n e s s , s t r e s s values w i l l be c a l c u l a t e d f o r two t h i c k n e s s e s , 10 um and 20 um, corresponding to the approximate l i m i t s of the range of t h i c k n e s s e s observed i n h i s t o l o g i c a l s e c t i o n s . As a convenience, only the 10 um example w i l l be d i s c u s s e d i n the t e x t , however, a l l values w i l l be found i n the summary presented i n Table 7,1, Given these s p e c i f i c v a l u e s f o r the dimensions of the mucus l a y e r and the movement of the f o o t , the s t r e s s under each of the s e c t i o n s of the f o o t can be c a l c u l a t e d . Waves Under a wave the mucus i s f i r s t s t r e s s e d t o i t s y i e l d p o i n t , and then f l o w s . Take f o r example a 10 um mucus l a y e r t h i c k n e s s . T h i s l a y e r w i l l y i e l d when the shear r a t i o i s 204 FIGURE 7-3- The s t r e s s p r o f i l e beneath a pedal wave. The s t r e s s has been c a l c u l a t e d f o r the v e l o c i t y p r o f i l e of Figure 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. Figure 7.3 Table 7.1: P r e d i c t i o n s of the Locomotion Model Slug: weight 15 gm ^ fo o t area rims 5.5 x 10_^ ml waves 3.5 x 10_^ m l interwaves 6.0 x 10 m' mucus t h i c k n e s s 0.85 mm/sec. 2.00 mm/sec. 10 m 20 m 10 m 20 m shear r a t e (rims) 85/sec shear s t r e s s (rims) 395 N/m2 f o r c e (rims) 0.217 N average shear s t r e s s (waves) 542 N/m2 f o r c e (waves) 0.193 N t o t a l f o r c e (waves+rims) 0.410 N shear s t r e s s (interwaves) 682 N/m2 ( h o r i z o n t a l ) o v e r a l l s t r e s s amplitude 1232 N/m2 (waves+interwaves) ( h o r i z o n t a l ) o v e r a l l s t r e s s amplitude 1482 N/m2 ( v e r t i c a l up) o v e r a l l s t r e s s amplitude 970 N/m2 ( v e r t i c a l down) 42.5/sec 200/sec 100/sec 297 N/m2 659 N/m2 429 N/m2 0.163 N 0.363 N 0.236 N 365 N/m2 1059 N/m2 610 N/m2 0.127 N 0.371 N 0.213 N 0.290 N 0.724 N 0.449 N 485 N/m2 1222 N/m2 749 N/m2 850 N/m2 2281 N/m2 1359 N/m2 1100 N/m2 2531 N/m2 1609 N/m2 2 600 N/m 2031 N/m2 1109 N/m2 o 207 5,5; i e a t a f o o t displcement of 55 um. Noting i n Fig u r e 7,3 the p o i n t on the d i s t a n c e curve e g u a l t o 55 um the corresponding poin t on the v e l o c i t y curve can be found. T h i s i s egual t o 0.54 mm/second or a shear r a t e of 53/ second (see F i g u r e 7 ,4)? By r e f e r r i n g t o Figure 7,4 (reproduced from F i g u r e 4,16) the s t r e s s a t which a t y p i c a l mucus sample y i e l d s a t a shear r a t e o f 54 can be determined (685 N/m2) . The s t r e s s to which t h i s sample y i e l d s can a l s o be determined; i t i s the value f o r flow s t r e s s at shear r a t e equal to 54/sec, or 323 N/m2. As the f o o t c o n t i n u e s to move forward i n the pedal wave the s t r e s s can be s i m i l a r l y c a l c u l a t e d f o r every part under the moving segment. T h i s f o r c e p r o f i l e , corresponds to the average v e l o c i t y p r o f i l e as shown i n F i g u r e 7.3, By i n t e g r a t i n g the area under t h i s f o r c e / t i m e curve and then d i v i d i n g by time the average  s t r e s s under a wave can be c a l c u l a t e d . For the case of a 10 um t h i c k mucus l a y e r t h i s value i s 550 N/m2. S i m i l a r l y the f o r c e p r o f i l e can be c a l c u l a t e d f o r a 20 um t h i c k mucus l a y e r , and t h i s i s a l s o shown i n F i g u r e 7.3. Since a t h i c k e r l a y e r w i l l r e s u l t i n a lower shear r a t e , the f o r c e s i n v o l v e d i n moving over t h i s t h i c k e r l a y e r are s m a l l e r . T h i s s t r e s s can then be m u l t i p l i e d by the t o t a l area of the waves (3.5.10~*m2) to a r r i v e a t a f i g u r e f o r the t o t a l f o r c e necessary t o move f o o t segments forward with pedal waves. Th i s value i s 0.19 N f o r a 10 um mucus l a y e r . Bims The rim f o r c e i s more simply c a l c u l a t e d ._ Since the 208 FIGURE 7.4. A r e p r e s e n t a t i v e p l o t of y i e l d s t r e s s and flow s t r e s s versus shear r a t e f o r Ariolimax  columbianus pedal mucus. 0 y = 0.069X + 3.13 r2= 0.0973 O", f y=»0.023x + 1.99 r = 0.943 100 150 200 ° -1 P , sec O 210 rims move at a constant 0-85 mm/second, the shear r a t e beneath them i s 85/second f o r a 10 um l a y e r (Figure 7.2) . The flow s t r e s s f o r t h i s shear r a t e i s determined by re f e r e n c e to Fig u r e 7.4 (395 N/m2 f o r a 10 um l a y e r ) . T h i s s t r e s s value m u l t i p l i e d by the t o t a l rim area y i e l d s the f o r c e needed t o move the rims a t t h i s 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 f o r c e imposed on the interwaves i s the sum of t h a t due t o the waves and the rims (Figure 7.2) Thus i n the case of a 10 um l a y e r i t i s (0.22 + 0.19) = 0.41N. T h i s f o r c e , d i v i d e d by the area of the interwaves (6.0 10 _*m 2) i s the s t r e s s experienced by the mucus under the interwaves. Consequently t h i s value i s 680 N/m2 f o r a 10 um l a y e r . The c a l c u l a t i o n o f t h i s f o r c e forms the f i r s t t e s t of t h i s model of locomotion. T h i s i s the s t r e s s t h a t must b e . r e s i s t e d by the s o l i d mucus beneath the interwaves . I s t h i s a reasonable f i g u r e when compared to the r e s u l t s of the p h y s i c a l t e s t s ? The a b i l i t y of the s o l i d mucus beneath an interwave t o withstand t h i s s t r e s s i s dependent on the shear r a t e t h a t t h i s s t r e s s causes. As shown i n Chapter 3 t h i s value i s d i f f i c u l t t o measure from video tape records s i n c e a p o i n t on the f o o t moves backwards only very b r i e f l y . From video r e c o r d i n g s i t i s only p o s s i b l e t o say t h a t the movement occurs i n l e s s than 0.08 seconds. The d i s t a n c e a point on the f o o t moves backwards can be more a c c u r a t e l y measured, 211 however, and i s equal to about 30 um or l e s s . 30 um i n t h i s case corresponds to a shear r a t i o f o r the mucus of 3.0. I t i s necessary t h a t t h i s shear have been a p p l i e d at a r a t e of at l e a s t 60/sec i n order f o r the mucus to not y i e l d and become a f l u i d . At a shear r a t e of 60/sec the backwards movement of the f o o t would have l a s t e d only 50 m i l l i s e c o n d s , a p e r i o d too sh o r t to have been measured by t h i s technique. I t i s thus c o n s i s t e n t with these o b s e r v a t i o n s t h a t the mucus under the interwaves i s sheared at a r a t e s u f f i c i e n t l y hiqh to withstand the c a l c u l a t e d s t r e s s of 680 N/m2. A f t e r t h i s i n i t i a l a p p l i c a t i o n of f o r c e the mucus under the interwaves should creep. This creep however can only occur f o r the p e r i o d of time f o r which a point under t h e . f o o t i s s t r e s s e d ; about one second. I t i s not s t r i c t l y v a l i d to equate s t r e s s r e l a x a t i o n data to creep data. However, s t r e s s r e l a x a t i o n data may provide an educated guess as t o how f a r mucus would creep i n one second. I t takes s o l i d mucus about 100 seconds t o r e l a x to h a l f of i t s i n i t i a l s t r e s s value. Consequently i t may be estimated t h a t mucus would r e q u i r e about the same p e r i o d to creep t o twice i t s l e n g t h , or a creep of 0.1 um/sec f o r a 10 um t h i c k mucus l a y e r . T h i s amount of creep i s f a r too s m a l l to be detected by the video t e s t s 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 o p e r a t i n g under a moving s l u g apply t o a s l u g moving on a h o r i z o n t a l s u r f a c e . I f the s l u g i s c r a w l i n g v e r t i c a l l y up or down, i t s weight w i l l apply a f o r c e which must be r e s i s t e d by the s o l i d mucus beneath the interwaves (Figure 7.5) . I f i n t h i s example a 2 1 2 FIGURE 7.5. The i n t e r a c t i o n of g r a v i t y with the f o r c e s of locomotion. A) Crawling 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 aids nor h i n d e r s movement. B) Crawling v e r t i c a l l y upwards; the weight of the slug adds to the f o r c e a c t i n g on the interwaves. C) Crawling v e r t i c a l l y downwards; the weight of the s l u g s u b t r a c t s from the f o r c e a c t i n g on the interwaves. 214 s l u g i s c r a w l i n g v e r t i c a l l y up, the f o r c e due t o i t s weight (0.15 N) w i l l a ct over the area of the interwaves (6.0 10-*m2) t o place an a d d i t i o n a l s t r e s s of 250 N/m2 on the interwaves. For a s l u g walking v e r t i c a l l y down , t h i s s t r e s s due to i t s weight w i l l be i n a d i r e c t i o n o p p o s i t e to the s t r e s s caused by the forward movement of f o o t segments and w i l l s u b t r a c t from the s t r e s s imposed on the interwaves (see F i g u r e 7.5). A l l the values c a l c u l a t e d f o r the example are summarized i n Table 7.1. The example above r e f e r s t o a s l u g moving at a constant 0.85 mm/second. T h i s i s a f a i r l y slow speed, even f o r a s l u g . Values f o r the v a r i o u s s t r e s s e s can be c a l c u l a t e d by the method used above f o r a s l u g moving at a more r a p i d speed, f o r example 2,00 mm/second which i s near the upper end of the range of speeds observed i n .A. columbianus. These values are shown i n Table 7.1. As might be expected the s t r e s s e s present under a r a p i d l y moving s l u g are p r e d i c t e d t o be l a r g e r than those under a slowly moving s l u g , and some values are q u i t e high.. I f these s t r e s s e s are to be r e s i s t e d by the s o l i d mucus under the interwaves, the shear r a t e s caused by these s t r e s s e s must be very high (120/sec). As e x p l a i n e d e a r l i e r the accurate measurement of these shear r a t e s was not p o s s i b l e . I s i t p o s s i b l e t o say whether these shear s t r e s s e s are compatible with t h i s model? In answering t h i s q u e s t i o n a number of f a c t o r s must be taken i n t o account. The c a l c u l a t i o n s presented here are based on a number o f estimates, A s m a l l change i n the estimated r e l a t i v e p r o p o r t i o n s of the d i f f e r e n t areas of the 215 f o o t w i l l have a l a r g e e f f e c t on the c a l c u l a t e d s t r e s s v a l u e s . Use o f a d i f f e r e n t curve f o r the e s t i m a t i o n of v i s c o s i t y w i l l a f f e c t the c a l c u l a t i o n , as w i l l a d i f f e r e n c e i n the i n v i v o p r o p e r t i e s as compared t o the i n v i t r o measurements. A c o n t r i b u t i o n by c i l i a t o the f o r c e of p r o p u l s i o n would change the c a l c u l a t e d values somewhat. With a l l these p o s s i b l e sources of e r r o r i t i s somewhat remarkable t h a t the c a l c u l a t e d interwave s t r e s s v a l u e s c o r r e l a t e as c l o s e l y as they do to the range of shear r a t e s t h a t i s p o s s i b l e and even l i k e l y under the f o o t , I f these interwave s t r e s s values are indeed a c c u r a t e , they give a c l u e as t o why s l u g s do not t r a v e l any f a s t e r than they do. The f a s t e r a s l u g walks, the l a r g e r the s t r e s s on i t s interwaves. At some speed t h i s s t r e s s w i l l become great enough t o cause the mucus beneath the interwaves to become a f l u i d and the s l u g w i l l no longer be able t o c r a w l . I f the interwave s t r e s s values c a l c u l a t e d here f o r an animal moving at 2.0 mm/sec seem l a r g e , t h i s may simply be a r e f l e c t i o n of the f a c t t h a t a t 2.0 mm/sec a s l u g i s walking n e a r l y as f a s t as i t s pedal mucus w i l l allow, A second form of t e s t may be a p p l i e d to t h i s locomotion model. As ex p l a i n e d above t h i s model makes s p e c i f i c q u a n t i t a t i v e p r e d i c t i o n s about the s t r e s s e s present under a moving s l u g and these f o r c e s can be measured using an ap p r o p r i a t e apparatus. Force P l a t e The apparatus used to measure the locomotory f o r c e s of 216 s l u g s i s shown i n F i g u r e 7.6. A s m a l l (0.5 x 1.0 mm) f o r c e -p l a t e protrudes through a 1.5 mm hole i n a l a r g e p l e x i g l a s s s u r f a c e . T h i s f o r c e - p l a t e i s supported by a double s t e e l beam. A f o r c e i n the plane of the p l e x i g l a s s s u r f a c e w i l l cause the f o r c e - p l a t e to move, the l a r g e r the f o r c e , the l a r g e r the d e f l e c t i o n . Due to the shape of the s u p p o r t i n g beam the f o r c e - p l a t e i s s e n s i t i v e t o f o r c e i n only one d i r e c t i o n . During a t e s t , the f o r c e - p l a t e i s o r i e n t e d so t h a t the s h o r t e r dimension (0.5 mm) l i e s i n l i n e with the d i r e c t i o n i n which the beam i s s e n s i t i v e t o f o r c e . The amount of d e f l e c t i o n of the beam i s measured by a 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 transformer. The output from t h i s transformer i s a m p l i f i e d and recorded on a c h a r t r e c o r d e r . The transducer i s c a l i b r a t e d by t u r n i n g the apparatus on i t s s i d e (so t h a t the measuring beam i s h o r i z o n t a l ) and hanging a c c u r a t e l y known weights from the p l a t e . . Forces as small as about 5 dynes can be a c c u r a t e l y measured and w i t h i n the range of f o r c e s encountered during t e s t i n g the transducer output i s l i n e a r with f o r c e . The unloaded resonant frequency of the apparatus i s 100 hz; s u f f i c i e n t l y high t o allow accurate measurement of the 1 hz o s c i l l a t o r y f o r c e s a s s o c i a t e d with s l u g locomotion. A t e s t i s performed by o r i e n t i n g the apparatus so t h a t the p l e x i g l a s s s u r f a c e i s e i t h e r h o r i z o n t a l or v e r t i c a l , and then a l l o w i n g a s l u g t o crawl a c r o s s the s u r f a c e (and the f o r c e - p l a t e ) along the d i r e c t i o n i n which the f o r c e - p l a t e i s s e n s i t i v e t o f o r c e . The dimensions of the f o r c e - p l a t e i n t h i s d i r e c t i o n (0.5 mm) i s l e s s than the s h o r t e s t l e n g t h o f 217 FIGURE 7.6. An apparatus f o r measuring the f o r c e s beneath a c r a w l i n g s l u g . A) Schematic r e p r e s e n t a t i o n of the apparatus. B and C) The dimensions of the f o r c e p l a t e are s m a l l e r than e i t h e r a wave or an interwave. 219 a compressed wave. Thus,as a s l u g passes over the f o r c e -p l a t e f o r c e s beneath waves and interwaves w i l l a l t e r n a t e l y be measured (see F i g u r e 7.6). By c o r r e c t l y p o s i t i o n i n g the s l u g the f o r c e present beneath the rims may a l s o be measured. Since the area of the f o r c e - p l a t e i s known the measured f o r c e s can be expressed as f o r c e / a r e a , i e s t r e s s , f o r comparison with the p r e d i c t i o n of the model. A l l t e s t s were performed at room temperature (21-23 °C ) . , I t has been amply shown by Lissman (1945b) that the passage of a compressional wave corresponds to an a n t e r i o r l y d i r e c t e d f o r c e . T h i s o b s e r v a t i o n was c o r r o b o r a t e d by observing the v e n t r a l s u r f a c e of the f o o t as i t passed over t h e . f o r c e p l a t e , and was not t e s t e d f u r t h e r . This apparatus i s l e s s than i d e a l i n two r e s p e c t s : 1. Because the f o r c e measuring p l a t e must be able to move i n order t o measure f o r c e i t must protrude through a hole i n the p l e x i g l a s s s u r f a c e . The presence of a hole means t h a t the slug can l i f t i t s f o o t as a wave passes over the p l a t e . Thus as long as the f o r c e - p l a t e i s f l u s h with the s u r f a c e o n l y the f o r c e s beneath the interwaves (where the f o o t i s not l i f t e d ) w i l l be measured. F u r t h e r , unless the f o r c e - p l a t e i s p r e c i s e l y f l u s h , these f o r c e s w i l l not be measured a c c u r a t e l y . T h i s problem i s remedied by r a i s i n g the p l a t e above the p l e x i g l a s s s u r f a c e s l i g h t l y (50 um to 150 um). This maintains the c o n t a c t between the f o o t and the f o r c e - p l a t e at a l l times. Apparently, while the s l u g can l i f t i t s f o o t i n the g e n e r a l r e g i o n of the h o l e , i t cannot l i f t i t s u f f i c i e n t l y i n t h e : l o c a l i z e d r e g i o n of the 220 f o r c e - p l a t e to break c o n t a c t with the f o r c e - p l a t e . Once the f o r c e - p l a t e i s r a i s e d s u f f i c i e n t l y to maintain c o n t a c t with the f o o t the d i s t a n c e t h a t i t i s r a i s e d (within the l i m i t s 50-150 um) does not appear to e f f e c t the s t r e s s e s measured. T h e . c o r r e l a t i o n between f o r c e - p l a t e height and o v e r a l l f o r c e amplitude has 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 f a r from s i g n i f i c a n t . The d i s t a n c e the p l a t e i s r a i s e d i s measured with a micrometer. 2. The second problem encountered with t h i s apparatus i s again a t t r i b u t a b l e t o the presence of a hole i n the p l e x i g l a s s s u r f a c e . I t i s noted t h a t i n a l a r g e percentage of t e s t s the s t r e s s measured by the p l a t e a f t e r the s l u g has passed i s d i f f e r e n t than the zero s t r e s s measured before the s l u g f i r s t reaches the p l a t e . . The magnitude and even the d i r e c t i o n of t h i s zero s h i f t i s u n p r e d i c t a b l e . Apparently at some p o i n t as the slug passes over the p l a t e , s o l i d mucus b u i l d s up i n the gap e i t h e r i n f r o n t or behind the p l a t e . While t h i s zero s h i f t does not a f f e c t the o v e r a l l amplitude of s t r e s s e s measured, i t makes i t i m p o s s i b l e t o measure the r e l a t i v e amounts of t h i s o v e r a l l amplitude t h a t are d i r e c t e d a n t e r i o r l y and p o s t e r i o r l y . As a consequence, t e s t r e s u l t s are d i v i d e d i n t o two c a t e g o r i e s . The s m a l l percentage o f t e s t s where the zero s t r e s s l e v e l i s s h i f t e d by l e s s than 10% of the o v e r a l l f o r c e amplitude d u r i n g the passage of a s l u g are placed i n one category and s t r e s s e s are measured r e l a t i v e t o the zero l e v e l . T e s t s where the zero l e v e l i s s h i f t e d by a l a r g e r amount are placed i n the second category. In t h i s category 2 2 1 the o v e r a l l amplitude of the s t r e s s o s c i l l a t i o n i s measured (as shown i n F i g u r e 7.7) but no attempt i s made t o s u b d i v i d e t h i s o v e r a l l s t r e s s i n t o a n t e r i o r l y and p o s t e r i o r l y d i r e c t e d s t r e s s . Tests Two s o r t s of t e s t s were performed. F i r s t with the p l e x i g l a s s s u r f a c e h o r i z o n t a l the s t r e s s e s beneath the waves, interwaves and rims were measured. Second with the p l e x i g l a s s s u r f a c e v e r t i c a l the s t r e s s beneath waves and interwaves was measured f o r s l u g s walking e i t h e r v e r t i c a l l y up or down.. The speeds a t which the s l u g s walked during the t e s t s were not measured,. This was due to p r a c t i c a l problems i n v o l v i n g the perverse nature o f s l u g s . The s l u g i s capable of moving i n a manner such t h a t the a n t e r i o r h a l f of the body i s moving at a d i f f e r e n t speed than the p o s t e r i o r h a l f . Thus, as the s l u g s t a r t s and stops as i t moves over the f o r c e - p l a t e measuring the speed of e i t h e r the head or t a i l may not g i v e an a c c u r a t e measure of the speed at the f o r c e -p l a t e . To a c c u r a t e l y measure the speed of the s l u g i n the area of the f o r c e - p l a t e i t would have been necessary to a c t u a l l y f i l m t h i s area,. Without a t r a n s p a r e n t f o r c e t r a n s d u c e r t h i s proved i m p o s s i b l e . I t i s assumed t h a t the range of walking speeds i n these t e s t s i s s i m i l a r to those shown i n F i g u r e 3.3. The r e s u l t s from these two types of t e s t s w i l l be d i s c u s s e d i n t u r n . H o r i z o n t a l T e s t s 222 The o v e r a l l amplitude of the s t r e s s measured under the c e n t r a l p o r t i o n of the f o o t f o r 34 t e s t s on 19 d i f f e r e n t s l u g s was 1493 N/m2 with a range from 780 t o : 2820 N/m2. T h i s compares q u i t e f a v o r a b l y with the p r e d i c t e d values f o r o v e r a l l s t r e s s amplitude which range from 830 t o 2280 N/m2. A l i s t of p r e d i c t e d and measured valu e s i s shown i n Table 7.2. The values of 5 measurements of rim s t r e s s average 350 N/m2 and range from 200 to 510 N/m2. Again these values are very s i m i l a r t o the p r e d i c t e d v a l u e s . . Thus, on the b a s i s of o v e r a l l amplitude the model's p r e d i c t i o n s are q u i t e a c c u r a t e . Does the accuracy a l s o hold f o r the measurement of p o s t e r i o r l y and a n t e r i o r l y d i r e c t e d s t r e s s e s ? The re c o r d s obtained from three s l u g s had s u f f i c i e n t l y small zero s h i f t s t o allow f o r the measurement of a n t e r i o r l y and p o s t e r i o r l y d i r e c t e d s t r e s s . The r e c o r d of one of these t e s t s i s reproduced i n F i g u r e 7.7. A n t e r i o r l y d i r e c t e d s t r e s s e s averaged 340 N/m2 ranging from 290 to 390 N/m2. P o s t e r i o r l y d i r e c t e d s t r e s s e s averaged 660 N/m2 ranging from 590 t o 740 N/m2. Again these v a l u e s are q u i t e c l o s e to those p r e d i c t e d by the model (see Table 7.2). V e r t i c a l Tests Seventeen t e s t s on 9 slu g s were conducted to compare the s t r e s s values between c r a w l i n g h o r i z o n t a l l y and v e r t i c a l l y up. The average value f o r the o v e r a l l s t r e s s amplitude while c r a w l i n g v e r t i c a l l y up was 1991 +- 354 N/m2 This value i s s i g n i f i c a n t l y g r e a t e r (p l e s s than 0.01) than the mean of the o v e r a l l s t r e s s amplitude f o r the Figure 7.2: The measured and p r e d i c t e d columbianus locomotion. f o r c e s of A r i o l i m a x STRESS (N/m2) pr e d i c t e d measured rims 297-659 201-512 waves 365-1059 336-526 interwaves 485-1222 591-1171 o v e r a l l 850-2281 780-2280 x=1493 224 FIGURE 7.7. An example of the r e c o r d of f o r c e s measured beneath a c r a w l i n g s l u g , with terms d e f i n e d . Amplitudes are measured f o r each wave and are averaged f o r each s l u g . FIGURE 7.7 Anterior Poster ior 1 second T - to ta l ampl i tude A - amplitude of anter ior ly d i r e c t e d fo rce ~ » » . • . " " P - posteriorly 226 h o r i z o n t a l t e s t s which were conducted 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 of v a r i a n c e . Each of these 17 v e r t i c a l t e s t s was followed by t u r n i n g the p l e x i g l a s s s u r f a c e so that i t was h o r i z o n t a l and al l o w i n g the s l u g t o crawl over the f o r c e p l a t e . a g a i n . The mean of these h o r i z o n t a l t e s t s was 1383 N/m2. The area of the f o o t of each s l u g was then measured using the video r e c o r d e r and each s l u g was weighed. As e x p l a i n e d e a r l i e r the d i f f e r e n c e i n s t r e s s value between walking v e r t i c a l l y and h o r i z o n t a l l y should be egual t o the f o r c e due to the weight of the s l u g d i v i d e d by the area of the interwaves. Having measured the d i f f e r e n c e i n s t r e s s , the interwave area, and the s l u g weight the p r e d i c t e d and a c t u a l values can be compared. T h i s i s accomplished by p l o t t i n g the p r e d i c t e d weight versus the a c t u a l weight (see F i g u r e 7.8). In theory the r e s u l t should be a l i n e p a s s i n g through the o r i g i n with a slope of one. I t can be seen t h a t , a s p r e d i c t e d , the change i n s t r e s s amplitude (and t h e r e f o r e the p r e d i c t e d weight) i n c r e a s e s as the s l u g ' s weight i n c r e a s e s . However, the change i n s t r e s s amplitude i s s i g n i f i c a n t l y g r e a t e r (p< 0.05) than t h a t p r e d i c t e d by theory. In other words., some f a c t o r other than j u s t the s l u g ' s weight i s i n c r e a s i n g the f o r c e r e q u i r e d to move the s l u g v e r t i c a l l y . The b a s i s f o r t h i s f a c t i s not a t present known, though s e v e r a l p o s s i b i l i t i e s e x i s t : 1- A*, columbianus i s s t r o n g l y n e g a t i v e l y g e o t a c t i c . Consequently i t i s p o s s i b l e t h a t the s l u g would c r a w l f a s t e r as a response t o being t i l t e d to a v e r t i c a l p o s i t i o n . While 227 FIGURE 7.8. A p l o t of weight as p r e d i c t e d from the model versus a c t u a l weight f o r a l l v e r t i c a l crawls. 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 to a c t u a l weight the slope of the r e l a t i o n s h i p i s g r e a t e r than expected. F igu re 7.8 actual weight (grams) 229 the speed of the s l u g was not measured during these t e s t s (as e x p l a i n e d above), so t h a t t h i s f a c t o r cannot be d e f i n i t e l y r u l e d out, no v i s i b l e i n c r e a s e i n speed was noted f o r slugs c r a w l i n g v e r t i c a l l y . 2. I t i s p o s s i b l e t h a t the s l u g a l t e r s the area of the rims i n response to the angle of the substratum r e a l t i v e t o the v e r t i c a l . Slugs c r a w l i n g h o r i z o n t a l l y are o f t e n seen to have part of the rims l i f t e d from the substratum. However, when c r a w l i n g v e r t i c a l l y the rims are i n v a r i a b l y c l o s e l y a p p l i e d t o the substratum. T h i s i n c r e a s e i n e f f e c t i v e rim area would i n c r e a s e the s t r e s s amplitude. 3. I t i s a l s o p o s s i b l e t h a t the mucus l a y e r t h i c k n e s s i s a l t e r e d when c r a w l i n g v e r t i c a l l y . Decreasing the t h i c k n e s s of the mucus l a y e r would i n c r e a s e the f o r c e needed to move the s l u g upwards, but would a l s o make i t l e s s l i k e l y t h a t once the s l u g stops c r a w l i n g i t w i l l s l i d e down the s u r f a c e . Perhaps t h i s advantage of e x t r a adhesive s t r e n g t h o f f s e t s the i n c r e a s e necessary i n locomotory energy expenditure. T h i s matter c e r t a i n l y warrants f u r t h e r study. In two t e s t s , i n a d d i t i o n to the s l u g ' s walking h o r i z o n t a l l y and v e r t i c a l l y up, the s l u g was induced to walk v e r t i c a l l y down. These t e s t s are d i f f i c u l t t o conduct as the s l u g s normal behavior i s t o crawl up a v e r t i c a l f a c e . In t h i s case the o v e r a l l s t r e s s amplitude should be l e s s f o r the v e r t i c a l l y down c r a w l i n g than the h o r i z o n t a l crawl by an amount r e l a t e d to the s l u g ' s weight. Again while q u a l i t a t i v e l y c o r r e c t , the model overestimates the animal's weight. The s t r e s s records from one such s e r i e s of t e s t s 230 are shown i n Figure 7.9. Pressures Beneath Pedal Waves The model presented i n Chapter 3 f o r the kinematics o f A. columbianus locomotion p r e d i c t s t h a t there should be a d o r s a l l y d i r e c t e d f o r c e on the mucus beneath a pedal wave when the s l u g i s c r a w l i n g on a non-porous s u r f a c e . Without a b e t t e r understanding o f the r o l e played by muscles i n the propagation of pedal waves, the magnitude of t h i s f o r c e cannot be p r e d i c t e d . I t should, however, be p o s s i b l e to det e c t t h i s f o r c e , i f i t i s indeed present.. To t h i s end the f o r c e p l a t e used i n the above t e s t s was modified as shown i n F i g u r e 7. 10. 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 of r e p l a c i n g the f o r c e measuring p l a t e with a hollow tube cut from a 20 guage hypodermic needle. T h i s tube i s connected by a r i g i d p l a s t i c tube to a pressure t r a n s d u c e r . A l l tu b i n g i s f i l l e d with degassed water. Thus, as the s l u g walks over t h i s new f o r c e p l a t e , any f o r c e d i r e c t e d dorso-v e n t r a l l y w i l l be d e t e c t e d by the pressure t r a n s d u c e r . U n f o r t u n a t e l y the d e t e c t i o n of pressure by t h i s transducer i s accomplished by measuring the movement of a diaphragm. Consequently there i s some volume change i n the system accompanying a pressure change. Since the volume changes t h a t would accompany a s l u g l i f t i n g i t s f o o t d u r i n g a pedal wave are l i k e l y t o be q u i t e s m a l l (about ,1 t o . 5 u l f o r one whole wave, c o n s i d e r a b l y l e s s f o r the s m a l l p a r t of a wave over the tube) the volume change due t o pressure d e t e c t i o n i s l i k e l y t o s u b s t a n t i a l l y a f f e c t 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 of the 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 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 slug weighed 16.24 gm and the v e r t i c a l l y up and own records p r e d i c t a weight of 34.0 and 54.4 gm r e s p e c t i v e l y . 232 233 FIGORE 7.10. A schematic drawing of the apparatus f o r si 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 c r a w l i n g s l u g . The s y r i n g e and valve are used to a d j u s t the l e v e l of the degassed water i n the system. F i g u r e 7 . 1 0 CO 235 measured. Thus, the magnitude of pressure measured by the apparatus are probably much too s m a l l . The apparatus does however, a c c u r a t e l y measure.the presence and d i r e c t i o n of pressure. In a d d i t i o n t o these pressure measurements the apparatus can s t i l l measure a n t e r i o - p o s t e r i o r l y d i r e c t e d f o r c e s . A s e r i e s of s i x t e s t s on three s l u g s confirms that t h e r e i s a d o r s a l l y d i r e c t e d f o r c e a c t i n g under a pedal wave. The r e c o r d from one such t e s t i s reproduced i n F i g u r e 7 , 1 1 . C o n c l u s i o n s And D i s c u s s i o n On the b a s i s of the kinematics of locomotion and the p h y s i c a l p r o p e r t i e s o f pedal mucus a model can be drawn t h a t q u a n t i t a t i v e l y p r e d i c t s the s t r e s s e s o p e r a t i n g under a moving s l u g . These s t r e s s e s can be measured e x p e r i m e n t a l l y and the measured s t r e s s e s compare c l o s e l y to the p r e d i c t e d s t r e s s e s . These r e s u l t s l e a d to two c o n c l u s i o n s : 1. The model presented here i s i n general an accurate d e s c r i p t i o n of the process of locomotion i n the s l u g A, columbianus . I t appears t h a t the assumptions and s i m p l i f i c a t i o n s made i n c o n s t r u c t i n g the model are j u s t i f i e d . More study i s needed,however, to account f o r the dis c r e p a n c y encountered when s l u g s crawl v e r t i c a l l y . 2. I f the p r o p e r t i e s of pedal mucus measured separate from the f o o t of the slu g provide an accurate d e s c r i p t i o n of the p r o p e r t i e s of t h i s mucus when a c t u a l l y used i n 2 3 6 FIGURE 7 . 1 1 . An example of simultaneous f o r c e and pressure measurements. The d o r s a l l y d i r e c t e d f o r c e peaks at the same time as the a n t e r i o r l y d i r e c t e d f o r c e . The o v e r a l l slope of the pressure t r a c e i s due to temperature 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 then i t i s unnecessary t o propose any e l a b o r a t e mechanism whereby the p r o p e r t i e s of the mucus are c o n t r o l l e d by the pedal e p i t h e l i u m during locomotion. While t h i s model i s reasonably a c c u r a t e as f a r as i t has been t e s t e d , I do not wish to imply t h a t i t i s an a l l encompassing model f o r gastropod locomotion. In a d d i t i o n to the d i s c r e p a n c y p r e v i o u s l y noted f o r v e r t i c a l c r a w l i n g there i s a t l e a s t one aspect of s l u g locomotion which t h i s model cannot e x p l a i n , and which deserves f u r t h e r study. As d e s c r i b e d i n Chapter 3, a s l u g suspended i n midair can t r a n s p o r t mucus p o s t e r i o r l y along the f o o t . While waves are present on the f o o t a t these times, no aspect of t h i s model can e x p l a i n t h i s phenomenon. I t seems l i k e l y t h a t t h i s mucus t r a n s p o r t i s a r e s u l t of c i l i a r y a c t i o n , but t h i s has not been c o n c l u s i v e l y shown. Another l a r g e area f o r f u t u r e study concerns the a p p l i c a t i o n of t h i s model or some d e r i v a t i v e of t h i s model t o the problem of locomotion i n animals using retograde waves. T h i s w i l l be d i s c u s s e d i n Chapter 10. The model drawn here was f o r a " t y p i c a l " s l u g weighing 15 grams and with a f o o t area of 15 cm 2. How must t h i s model be s c a l e d to apply t o s l u g s of d i f f e r e n t s i z e s ? Two f a c t o r s are i n v o l v e d i n t h i s problem: 1) The f o o t area w i l l determine the area of mucus over which the slug must move, and thereby the f r i c t i o n a l r e s i s t a n c e t o movement. Thus, i f a l l s l u g s have the same shape, f o o t area may be expected to i n c r e a s e as the square of the l e n g t h of the s l u g , L 2 . 2) The mass of the s l u g w i l l determine the volume of muscle a v a i l a b l e to do e x t e r n a l work, and f o r a s l u g c r a w l i n g 239 v e r t i c a l l y , w i l l a l s o a f f e c t the amount of e x t e r n a l f o r c e r e q u i r e d to move. The mass of the s l u g w i l l be d i r e c t l y r e l a t e d t o the volume of the s l u g , and thus, f o r a slug of a standard shape, may be expected to i n c r e a s e as the cube of the l e n g t h of the s l u g , L 3„ On t h i s b a s i s , the f o o t l o a d i n g (mass/foot area or L 3 / L 2 ) would be expected t o i n c r e a s e i n p r o p o r t i o n to the l e n g t h of the s l u g . I f t h i s i s indeed the case i t may be necessary 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 model. Foot l o a d i n g values were measured f o r s l u g s of a v a r i e t y of s i z e s and are presented i n F i g u r e 7. 12. I t can be seen t h a t f o r s l u g s above about 5 grams t h e : f o o t l o a d i n g remains con s t a n t at a value of about 0.95 g/cm 2. T h i s means t h a t the s l u g s must change shape as they grow i n a manner which maintains a constant r a t i o between weight and f o o t area. Thus, the r a t i o of muscle to f r i c t i o n a l r e s i s t a n c e of movement may be expected to remain c o n s t a n t , and the model, while c a l c u l a t e d f o r a 15 gram s l u g , may be d i r e c t l y a p p l i e d t o any A. columbianus of g r e a t e r than 5 grams, no s c a l i n g being r e q u i r e d . 240 FIGURE 7.12. The f o o t l o a d i n g (weight/foot area) of A r i o l i m a x columbianus i s constant above a weight of about 5 grams. F I G U R E 7.12 2 4 6 8 10 12 14 16 18 20 22 S L U G W E I G H T ( G R A M S ) 2 4 2 CHAPTER 8 Cost Of Locomotion The preceeding chapter p r o v i d e s a model f o r the mechanism of locomotion i n A, columbianus and an estimate of the f o r c e s i n v o l v e d i n movement. I t would be i n t e r e s t i n g to extend t h i s knowledge of how the animal crawls, and ask the q u e s t i o n : how c o s t l y i s t h i s form of locomotion? Compared to a f i s h , a b i r d , a r e p t i l e , or a mammal, how expensive i s i t f o r a s l u g t o move i t s e l f from p l a c e to place? Before examining t h i s g uestion i n d e t a i l i t w i l l be u s e f u l t o review some b a s i c concepts d e a l i n g with the c o s t of locomot i o n . Review Of Terms As shown i n Chapter 7 , a moving s l u g must e x e r t an a n t e r i o r l y d i r e c t e d f o r c e i n order to overcome g r a v i t y and the v i s c o e l a s t i c p r o p e r t i e s of the mucus over which i t crawl s . The r e s u l t of t h i s f o r c e i s the movement of the s l u g through a c e r t a i n d i s t a n c e . The product of f o r c e times d i s t a n c e i s work or energy and i s expressed i n SI u n i t s as J o u l e s ( J ) . Energy expenditure per u n i t time i s power , expressed as J/second or Watts (W). Thus the f o r c e exerted by an animal as i t moves, times the v e l o c i t y of movement (distance/time) i s equal to the power expenditure (force x d i s t a n c e / t i m e = work/time = power).. I t i s u s e f u l when comparing c o s t s between animals t o normalize the c o s t to the 2 4 3 weight of the animal. Thus the power r e g u i r e d to move at a given v e l o c i t y w i l l be expressed as W/kg. The power necessary f o r locomotion can be d i v i d e d i n t o two c a t e g o r i e s . The f i r s t of these i s the power p r e d i c t e d by the model i n Chapter 7 . The f o r c e p r e d i c t e d by the model i s exerted by the animal on i t s surroundings , the mucus and the substratum. T h i s f o r c e , times the s l u g v e l o c i t y at which i t i s e x e r t e d , provides a measure of the.power expended i n overcoming f a c t o r s e x t e r n a l to the s l u g and i s termed the e x t e r n a l power (Pe) . In c o n t r a s t t h e r e i s the i n t e r n a l power. P i , the power t h a t must be expended i n s i d e the s l u g ' s body to cause work to be done on the environment. The i n t e r n a l power i s the sum of s e v e r a l p a r t s . F i r s t , the f o r c e s of locomotion are a r e s u l t o f muscular c o n t r a c t i o n . , Energy, i n the form of ATP, must be provided t o the muscles f o r c o n t r a c t i o n to occur. The pro d u c t i o n of ATP from the s l u g ' s food i s f a r from being a 1 0 0 % e f f i c i e n t process. Consequently the animal must spend more energy i n p r o v i d i n g ATP to the muscles than w i l l appear as e x t e r n a l work. Fu r t h e r a l l work of c o n t r a c t i o n of muscles i s not d i r e c t l y a p p l i e d t o locomotion. For example, muscles must c o n t r a c t to maintain the h y d r o s t a t i c s k e l e t o n d u r i n g movement, and muscles o f the foot expend energy as they move.the f l u i d of the pedal haemocoel. Again these f a c t o r s (and others l i k e them) i n c r e a s e the amount of i n t e r n a l energy that must be expended t o r e s u l t i n a given amount of e x t e r n a l work. F i n a l l y , energy must be expended i n c o n s t r u c t i n g the g l y c o p r o t e i n o f the mucus, an i n t e r n a l expenditure that does 244 not r e s u l t i n any e x t e r n a l f o r c e . As a r e s u l t of a l l of these f a c t o r s the t o t a l i n t e r n a l power w i l l be g r e a t e r than the e x t e r n a l power. The r a t i o o f the two, Pe/Pi, i s one measure of the e f f i c i e n c y of the locomotory p r o c e s s . As mentioned above the 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 can be a c c u r a t e l y estimated f o r any speed using the model of Chapter 7. The i n t e r n a l power i s l e s s d i r e c t l y c a l c u l a t e d . The energy r e q u i r e d f o r the i n t e r n a l expenditures of locomotion i s u l t i m a t e l y provided by the oxidaton i n the s l u g of v a r i o u s energy storage compounds; glycogen, l i p i d s , and p r o t e i n . . The e x t e r n a l c h a r a c t e r i s t i c s of t h i s o x i d a t i o n are a production of C02 and a consumption of 02. Depending on the p r e c i s e compound being o x i d i z e d a given amount of C02 w i l l be produced, and 02 consumed, f o r each J o u l e expended by the animal. Thus by measuring t o t a l C02 p r o d u c t i o n and 02 consumption and using the proper co n v e r s i o n f a c t o r s i t i s p o s s i b l e t o estimate the t o t a l i n t e r n a l energy expended by the animal at any one time. A l a r g e p o r t i o n of t h i s t o t a l energy supply w i l l be used simply i n the maintenance of the animal and i s not d i r e c t l y r e l a t e d t o locomotion. Consequently the i n t e r n a l power of locomotion i s estimated by measurinq the i n c r e a s e i n C02 p r o d u c t i o n and 02 consumption above r e s t i n q l e v e l s t h a t i s a s s o c i a t e d with movement, and from these c a l c u l a t i n g the i n c r e a s e d number of J o u l e s expended by the animal (see Schmidt-Nielsen, 1972). with these terms and concepts i n mind, an experiment was designed t o simultaneously measure 02 consumption, 245 d i s t a n c e crawled, and r a t e of c r a w l i n g i n A. columbianus -. From these data and the model of Chapter 7 th r e e f a c t o r s 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 /kg m). 2) the power (both i n t e r n a l and ex t e r n a l ) expended to move at a given v e l o c i t y , and 3) the e f f i c i e n c y of locomotion. Apparatus And Experimental P r o t o c o l A d i f f e r e n t i a l e l e c t r o l y t i c r e s p i r o m e t e r was c o n s t r u c t e d to measure the 02 consumption and C02 production of c r a w l i n g A._ columbianus (see F i g u r e s 8.1 and 8.2 ).. This r e s p i r o m e t e r was designed on the same b a s i c p r i n c i p l e as t h a t of C l o s e , Dnwin and Brown (1978). The animal i s housed i n a 1.9 l i t e r a i r t i g h t box c o n t a i n i n g a C02 absorbant (concentrated KOH). As the animal metabolizes, 02 i s consumed and C02 produced. As the C02 i s absorbed the pressure i n the t e s t chamber decreases r e l a t i v e t o a r e f e r e n c e chamber. The r e f e r e n c e chamber i s i d e n t i c a l to the t e s t chamber except t h a t the s l u g i s r e p l a c e d by an equal volume of water. The t e s t and r e f e r e n c e chambers are separated by a t h i n rubber diaphragm . Mounted on the diaphragm i s a s m a l l mirror of s i l v e r e d mylar. As the pressure i n the t e s t chamber decreases the diaphragm i s bent and the o r i e n t a t i o n of the m i r r o r i s a l t e r e d . T h i s change i n o r i e n t a t i o n d e f l e c t s a l i g h t beam. The movement of the beam o f f of an e l e c t r o n i c photodetector causes a r e l a y to 246 FIGURE 8- 1 .. A schematic diagram of 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 to measure the metabolic r a t e of s l u g s . The t e s t and r e f e r e n c e chambers are submerged i n a constant temperature bath.. FIGURE 8.1 reference chamber 248 FIGURE 8.2. A schematic diagram of the apparatus used to measure the movement of a s l u g i n the t e s t chamber. The chamber i s supported by a compound beam c o n s i s t i n g of two o r t h o g o n a l l y arranged beams. Each of these s i n g l e beams i s designed 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 the s l u g i s from the cente r of the chamber along the bending a x i s of a beam, the more t h a t beam i s bent. Thus, s t r a i n guages responding to the degree of bending i n each beam provide a measure of the slu g ' s c e n t e r of mass. FIGURE 8.2 amplifier chart recorder 250 c l o s e and c u r r e n t t o be passed through an e l e c t r o l y s i s c e l l i n the t e s t chamber. The e l e c t r o l y s i s of the CuS04 s o l u t i o n i n the c e l l r e l e a s e s 02 i n t o the t e s t chamber. When t h i s 02 has r e p l a c e d the 02 consumed the diaphragm w i l l have returned t o i t s unbent p o s i t i o n , the l i g h t beam w i l l again f a l l . o n the photodetector and the c u r r e n t t o the e l e c t r o l y s i s c e l l w i l l be cut o f f . The e l e c t r o l y s i s c i r c u i t c o n t a i n s a t i m e r such t h a t c u r r e n t i s s u p p l i e d to the c e l l i n d i s c r e e t p u l s es of a known d u r a t i o n . ft c h a r t r e c o r d e r coupled to the e l e c t r o l y s i s c i r c u i t r e c o r ds the amperage o f each pulse and thereby i s a measure of the number of coulombs d e l i v e r e d t o the c e l l . From t h i s , a time record of the amount of 02 consumed by the experimental animal can be c a l c u l a t e d . Both the t e s t and r e f e r e n c e chambers are submerged i n a constant temperature bath at 19.5 +- .01 C. The s e n s i t i v i t y of the apparatus i s such t h a t a consumption o f 0.01 ml of 02 can be detected. The t e s t chamber i s supported by a c e n t r a l beam and as the s l u g crawls about i n the chamber i t s weight causes the beam to bend. S t r a i n guages glued t o the beam measure t h i s bending along orthogonal axes. The a m p l i f i e d output from the s t r a i n guages i s recorded on a two channel c h a r t r e c o r d e r , and p r o v i d e s a continuous r e c o r d of the l o c a t i o n of the s l u g ' s c e n t e r of mass. From t h i s r e c o r d the t o t a l d i s t a n c e moved by the c e n t e r of mass and the v e l o c i t y of movement can be c a l c u l a t e d . Movement of the s l u g up or down the s i d e w a l l s of the chamber are not recorded, but due to the f l a t shape of the chamber, v e r t i c a l movements are l i k e l y 251 to be s m a l l compared t o h o r i z o n t a l movements. A. columbianus i n t h i s apparatus showed a d i s t i n c t d i u r n a l rhythm i n movement, remaining s t a t i o n a r y during the day , and moving f o r 3 to 4 hours i n the middle of the night. By c o n t i n u o u s l y r e c o r d i n g r e s p i r a t i o n r a t e and movement over a 24 hour p e r i o d the r e s t i n g and a c t i v e metabolic r a t e s c o u l d thus be determined. Crawling v e l o c i t i e s under these c o n d i t i o n s were q u i t e slow, averaging about 2.2 x 10-* m/sec, roughly one t e n t h the s l u g * s maximum c r a w l i n g v e l o c i t y . The r e s p i r a t o r y q u o t i e n t (RQ) f o r A., columbianus was measured by comparing the apparent r a t e of 02 consumption f o r a s l u g i n a t e s t chamber without C02 absorbant compared to the same s l u g i n a t e s t chamber with C02 absorbant. The RQ thus measured was 0.92, an i n d i c a t i o n t h a t the s l u g i s using p r i m a r i l y carbohydrates as i t s f u e l , . In accordance with t h i s RQ measurement a value of 20,9 J/ml 02 was used i n c a l c u l a t i n g i n t e r n a l power (Prosser and Brown, 1961). Re s u l t s A t y p i c a l example of a r e s p i r a t i o n and movement record i s shown i n F i g u r e 8,3 . Three f a c t s are worth n o t i n g . F i r s t , the s l u g does not move at a c o n s t a n t v e l o c i t y . Second, the peak i n 02 consumption l a g s the peak i n c r a w l i n g r a t e by approximately one hour. T h i s delay i n observed 02 consumption i s probably due to t h r e e f a c t o r s : 1) Given the i n e f f i c i e n c y of the c i r c u l a t o r y and r e s p i r a t o r y systems i n s l u g (as compared f o r example to a mammal) i t seems l i k e l y 2 5 2 FIGURE 8.3. A r e p r e s e n t a t i v e record of c r a w l i n g v e l o c i t y and oxygen consumption f o r A r i o l i m a x columbianus . Note that the s l u g does not cr a w l a t a uniform speed, and t h a t the oxygen consumption l a g s the peak i n r a t e of movement and continues f o r s e v e r a l hours 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 I O ~ 4 ) 254 t h a t an energy expenditure i n the locomotory musculature may r e s u l t i n an oxygen debt which w i l l take a c o n s i d e r a b l e time to be r e a l i z e d as C02 excreted i n t o the atmosphere. 2) The s w i t c h i n g on of mucus production, and thereby the metabolic c o s t of p r o d u c t i o n , may l a g the onset of c r a w l i n g . 3) The a b s o r p t i o n of C02 by the KOH bath w i l l not be i n s t a n t a n e o u s . The t h i r d f a c t to note from F i g u r e 8.3 i s that the i n c r e a s e d r e s p i r a t i o n r a t e due t o movement c o n t i n u e s f o r s e v e r a l hours a f t e r movement has ceased. T h i s may w e l l be due t o any or a l l of the f a c t o r s c i t e d above f o r the i n i t i a t i o n of the time l a g . As a r e s u l t of these f a c t s i t i s d i f f i c u l t t o p r e c i s e l y c o r r e l a t e each peak i n i n c r e a s e d r e s p i r a t i o n wii:h a s p e c i f i c v e l o c i t y . Conseguently these data were analyzed as f o l l o w s : f o r each bout of movement the t o t a l d i s t a n c e moved, the t o t a l time of movement, and the average v e l o c i t y were determined. The area under the peak i n i n c r e a s e d r e s p i r a t i o n r a t e (as shown i n F i g u r e 8.3) was taken as a measure of the t o t a l 02 consumed i n moving through that d i s t a n c e . T h i s 02 consumption (converted to energy and expressed as J/kg) i s a measure of the t o t a l i n t e r n a l energy expenditure, and when d i v i d e d by the time of movement y i e l d s the i n t e r n a l power i n W/kg to move at t h a t average v e l o c i t y . S i m i l a r l y the i n t e r n a l energy, J/kg, d i v i d e d by the t o t a l d i s t a n c e moved, i n meters, g i v e s the c o s t of movement i n J/kg m. The r e s u l t s from 9 measurements on 7 d i f f e r e n t s l u g s are shown i n Fi g u r e 8.4 . These s l u g s ranged i n weight from 8.1 t o 23-3 grams. I t can be seen t h a t the power necessary 255 FIGURE 8.4. The i n t e r n a l power of locomotion as a f u n c t i o n of c r a w l i n g speed f o r Ariolojmax columbianus . The slope of the l i n e i s the average c o s t of locomotion (952.5 J/kg m). FIGURE 8.4 .30 .26 .22 .18 O \ i . 1 4 § -.10 .06 .02 .2 1.0 1.8 2.2 2.6 3.0 3.4 M SEC"' X IO"4 257 f o r movements i n c r e a s e s with i n c r e a s i n g speed. Since W/kg d i v i d e d by m/sec equals J/kg m the slope of the l i n e through these p o i n t s eguals the average c o s t of locomotion which i s 952.5 +- 130.6 J/kg m. The method of c a l c u l a t i n g c o s t of locomotion and power used here d i f f e r s from t h a t used by other authors (see Goldspink and Alexander, 1977). The t y p i c a l procedure i s to induce an animal t o move at a constant r a t e and then measure the steady s t a t e 02 consumption. Since the s l u g s i n t h i s experiment c o u l d not be persuaded t o walk at a constant r a t e , the measurement of steady s t a t e 02 consumption was not p o s s i b l e . The t o t a l 02 consumption values used here, i n t h a t they i n c l u d e 02 consumed a f t e r locomotion has ceased, are l i k e l y to be somewhat higher than i f steady s t a t e values could be measured. They are however an accurate measure of the c o s t of locomotion. Keeping t h i s f a c t i n mind we can now compare the co s t of locomotion i n s l u g s to th a t of other animals. T h i s comparison i s f a c i l i t a t e d by the g e n e r a l i z a t i o n s presented by Tucker (1971), and Schmidt-Nielsen (1972) ( f o r an e x c e l l e n t review of t h i s l i t e r a t u r e see Goldspink and Alexander, 1977). These authors p l o t t e d the l o g of the c o s t of locomotion a g a i n s t the l o g of body weight and found a number of s u r p r i s i n g l y simple r e l a t i o n s h i p s (see F i g u r e 8.5 ). The most s t r i k i n g of these i s t h a t a l l those animals which move i n a s i m i l a r manner f a l l on a s i n g l e l i n e . Thus the data p o i n t s f o r a l l swimming animals may be l i n k e d by a s t r a i g h t l i n e , and s i m i l a r l y f o r animals t h a t f l y , and 258 FIGOBE 8.5- The cost of locomotion (redrawn from Goldspink, 1977, a f t e r Schmidt-Nielsen, 1972), For any given weight i t i s more c o s t l y t o f l y than to swim; and run than f l y . The c o s t of locomotion 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 than any value 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 run. The second p e r t i n e n t f a c t i s t h a t there are s i z a b l e d i f f e r e n c e s i n c o s t between the types of locomotion. For an animal of a given weight, the c o s t of moving 1 kg of that animal 1 meter i s l e a s t i f i t swims, more i f i t f l i e s , and g r e a t e s t i f i t walks. T h i s i m p l i e s t h a t r e g a r d l e s s of the f i n e d e t a i l s about how an animal 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 of movement t i e s i t , i n a metabolic sense, t o other animals t h a t show b a s i c a l l y s i m i l a r p a t t e r n s . In t h i s context then we can examine the open c i r c l e on F i g u r e 8.5 which r e p r e s e n t s the c o s t of locomotion i n the s l u g . I t i s immediately apparent t h a t the s l u g ' s form of adhesive locomotion i s a very c o s t l y way t o move. Even a l l o w i n g f o r the f a c t t h a t the estimate of c o s t f o r a s l u g may be s l i g h t l y high due to the d i f f e r e n c e between steady s t a t e and t o t a l 02 consumption, i t w i l l c ost a s l u g n e a r l y ten times as much to move a given d i s t a n c e as a running animal o f equal s i z e . Why i s t h i s so? Using s e v e r a l means of approximation i t i s p o s s i b l e t o examine the v a r i o u s components of the energy expenditures of the s l u g and thereby a r r i v e at a b e t t e r i d e a of what i t i s about adhesive locomotion t h a t makes i t so c o s t l y . Using the locomotion model of Chapter 7, the e x t e r n a l power of movement on l e v e l ground can be c a l c u l a t e d f o r s e v e r a l v e l o c i t i e s and f o r a mucus l a y e r 10 um t h i c k . These are p l o t t e d i n F i g u r e 8.6 . The s l o p e of t h i s curve (W/kg/m/sec = J/kg m) (the cost of movement) i n c r e a s e s with i n c r e a s i n g v e l o c i t y . T h i s i s as one would expect from 261 FIGURE 8,6.. The components of power i n the locomotion of A r i o l i m a x columbianus . The estimated e x t e r n a l power, Pe, forms only 1.7% to 5.2% of the i n t e r n a l power. P i , measured from r e s p i r a t i o n s t u d i e s . The estimated power of 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 2 6 3 t r y i n g to move over a v i s c o u s l i q u i d ; the f a s t e r the r a t e of movement, the g r e a t e r the r e s i s t a n c e and the g r e a t e r the c o s t . These c a l c u l a t e d values f o r e x t e r n a l power can be compared to the measured i n t e r n a l power to a r r i v e at a value f o r e f f i c i e n c y . At 2 x 10 _* m/sec (the r a t e at which s l u g s walked i n the respirometer) the power needed to overcome the mucus r e s i s t a n c e i s 16 J/kg m, y i e l d i n g an energy e f f i c i e n c y value of 1.7%. I f the c o s t of locomotion measured here f o r slow speeds i s assumed to apply to higher v e l o c i t i e s , the e f f i c i e n c y at the l a r g e s l u g s maximum v e l o c i t y of about 2 x 10- 3 m/sec w i l l be 5.2%. While these sound g u i t e low they are i n r e a l i t y reasonable v a l u e s f o r movement on l e v e l ground. For comparison, a human being running on l e v e l ground w i l l show an e f f i c i e n c y of between 2.0% and 3.2% (Tucker, 1973). Perhaps a b e t t e r comparison i s t h a t of muscle e f f i c i e n c y a l o n e . While the e f f i c i e n c y of i n v e r t e b r a t e muscles has not been measured, i t i s l i k e l y t h a t i t does not d i f f e r s u b s t a n t i a l l y from maximum e f f i c i e n c y of v a r i o u s v e r t e b r a t e muscles which has been shown to be 20 to 25% (Goldspink and Alexander, 1977). To reach t h i s e f f i c i e n c y the muscle must be c o n t r a c t i n g a t an optimum r a t e a g a i n s t an optimum l o a d , and under other circumstances the e f f i c i e n c y w i l l be c o n s i d e r a b l y lower. S t i l l , even i f 20 t o 25% e f f i c i e n c y may be the maximum expected t h e r e i s s t i l l a l a r g e gap when compared to 1.7 t o 5.2% . How much of the i n e f f i c i e n c y of a walking s l u g can be a t t r i b u t e d to the production of mucus? At present t h i s q u e s t i o n cannot be answered with any c e r t a i n t y , but 264 reasonable assumptions can be made to a r r i v e a t an estimate. A 15 gm s l u g with a one centimeter wide f o o t , and a 10 um t h i c k mucus l a y e r w i l l expend 0.1 ml of mucus f o r each meter i t c r a w l s . I f t h i s mucus i s assumed to be 3% g l y c o p r o t e i n , the amount of p r o t e i n and carbohydrate expended per meter can be c a l c u l a t e d (1.0 x 10~ s gm p r o t e i n , 6.3 x 1 0 - 6 gm c a r b o h y d r a t e ) . The problem i s then to estimate the metabolic c o s t of producing t h i s amount of p r o t e i n and carbohydrate. I t seems reasonable to assume t h a t the maximum energy expended i n producing the p o l y s a c c h a r i d e s w i l l be s i m i l a r to the c o s t of producing glycogen from pyruvate. T h i s c o s t i s estimated from Atkinson (1977) at 3099.3 J/gm. S i m i l a r l y the c o s t of producing the p r o t e i n can be estimated at a value of 2704.1 J/gm (from Atkinson, 1977). From these e s t i m a t i o n s the c o s t of producing the g l y c o p r o t e i n to r e p l a c e t h a t l o s t as the s l u g c r a w l s can be estimated as 313 J/kg m f o r a 15 gram s l u g , and t h i s i s independent of v e l o c i t y . T h i s value r e p r e s e n t s about 32.5% of the o v e r a l l energy expenditure of c r a w l i n g . Thus, when compared to the e x t e r n a l work of locomotion, the c o s t of mucus p r o d u c t i o n may w e l l be the dominant f a c t o r . I f i t i s assumed t h a t the i n t r i n s i c maximum e f f i c i e n c y of the muscle i n a s l u g i s s i m i l a r to t h a t i n v e r t e b r a t e s (20%) the minimum o v e r a l l i n t e r n a l c o s t of muscular c o n t r a c t i o n d i r e c t l y l e a d i n g t o e x t e r n a l work can be c a l c u l a t e d simply by m u l t i p l y i n g the c o s t of e x t e r n a l work by f i v e . Thus the minimum i n t e r n a l c o s t of e f f e c t i v e muscular c o n t r a c t i o n during locomotion v a r i e s from 8,5% of 265 the o v e r a l l c o s t at a c r a w l i n g r a t e of 2 x 10~ 4 m/sec to 26% at the maximum c r a w l i n g r a t e o f 2 x 1 0 - 3 m/sec. The c o s t , added to t h a t of mucus production accounts f o r an estimated 41.-0% to 58.5% of the o v e r a l l i n t e r n a l c o s t of locomotion. Where does the r e s t ot the i n t e r n a l energy go? As mentioned above there are a number of i n t e r n a l mechanisms which r e q u i r e energy but do not d i r e c t l y r e s u l t i n e x t e r n a l f o r c e s . As shown i n Chapter 2 the muscles of the f o o t do not c o n t r a c t i n the plane of the f o o t . . Thus f o r each u n i t of f o r c e which i s d i r e c t e d a n t e r i o r l y as a muscle c o n t r a c t s a roughly egual f o r c e w i l l be d i r e c t e d d o r s a l l y , doing no e f f e c t i v e e x t e r n a l work. F u r t h e r , i n a d d i t i o n to the f o r c e necessary to overcome the r e s i s t a n c e of the mucus, the pedal muscles must a l s o e x e r t a f o r c e to overcome the i n t e r n a l v i s c o s i t i e s of the f o o t , f o r example, the vi s c o u s r e s i s t a n c e of pumping haemocoelic f l u i d as d e s c r i b e d i n Chapter 3. Muscular energy w i l l a l s o be expended i n maint a i n i n g the s l u g ' s posture during locomotion. F i n a l l y there i s the stron g p r o b a b i l i t y t h a t the s l u g ' s muscles w i l l not a l l be working a t t h e i r maximum e f f i c i e n c y . , The speed of c o n t r a c t i o n and loa d a g a i n s t which each pedal muscle i s c o n t r a c t i n g w i l l vary as waves pass along the f o o t , and consequently each muscle cannot be c o n t i n u o u s l y c o n t r a c t i n g o p t i m a l l y . A l l of these f a c t o r s and others l i k e them, w i l l account f o r the remaining expenditures of i n t e r n a l energy. In c o n c l u s i o n we r e t u r n t o the o r i g i n a l guestion of t h i s c h a p t e r : how c o s t l y i s adhesive locomotion? The answer i s : very c o s t l y . The estimated c o s t to a slu g of producing 266 mucus alone i s g r e a t e r than the t o t a l c o s t of movement i n a mammal or r e p t i l e of s i m i l a r weight. I t seems l i k e l y t h a t t h i s high c o s t of movement w i l l e f f e c t the " l i f e s t y l e " of these animals, f o r example, by l i m i t i n g the d i s t a n c e over which i t i s p r o f i t a b l e t o crawl i n search of food. However, t h i s high c o s t of t r a n s p o r t must be weighed, i n an e v o l u t i o n a r y sense, a g a i n s t the advantages t o a s l u g of being a b l e to adhere t o the surface over which i t walks. F i n a l l y while the c o s t of movement f o r ft. columbianus i s q u i t e h i g h , i t i s not because the mechanism of locomotion i s i n e f f i c i e n t . C e r t a i n l y a c r a w l i n g s l u g i s no l e s s e f f i c i e n t than a running person. I n s t e a d , the high c o s t of t r a n s p o r t i s d i c t a t e d by the requirements of the locomotory mechanism: the need to c o n t i n u a l l y produce mucus, and the n e c e s s i t y o f workinq a g a i n s t the v i s c o e l a s t i c r e s i s t a n c e of t h a t mucus. F u r t h e r s t u d i e s of the e n e r g e t i c s of locomotion i n t h i s animal would be u s e f u l and i n f o r m a t i v e . For example, i n running animals the e f f i c i e n c y of movement i n c r e a s e s as the animal switches from moving on l e v e l ground to running up a grade. T h i s i s due, i n l a r g e p a r t , to the f a c t t h a t the i n c r e a s e d c o s t of moving u p h i l l i s l e s s than the i n c r e a s e i n e x t e r n a l work performed as the animal l i f t s i t s e l f a g ainst g r a v i t y (see Tucker, 1973). I t w i l l be i n t e r e s t i n g t o see i f the same phenomenon! occurs i n s l u g s , animals which spend a l a r g e p o r t i o n of t h e i r locomotion time c r a w l i n g . , I f t h i s i s indeed the case, the e f f i c i e n c y f i g u r e s c a l c u l a t e d here may be c o n s i d e r a b l y lower than those r e l e v a n t t o the animal i n i t s n a t u r a l h a b i t a t . 267 CHAPTES NINE Adhesion The locomotion of gastropods i s c h a r a c t e r i z e d by the a b i l i t y t o move while adhering to the substratum. The preceding chapters i n t h i s study have d e a l t with the mechanisms of movement of A., columbianus but very l i t t l e has been s a i d concerning the mechanism of adhesion o p e r a t i n g i n t h i s animal. What are the adhesive c a p a b i l i t i e s of A, columbianus , and how can they be accounted f o r ? The body form of j \ . columbianus renders an accurate measurement of adhesive s t r e n g t h extremely d i f f i c u l t . In order to determine adhesive c a p a b i l i t i e s one must be able to e x e r t a f o r c e on the adhesive apparatus. However, with a s l u g , t h e r e i s no s o l i d s t r u c t u r e which can be grasped to exert a f o r c e on the animal. Glues w i l l not s t i c k t o the mucus coated d o r s a l e p i t h e l i u m , and the body w a l l i s so weak th a t s u t u r e s cannot be used to a t t a c h weights t o the s l u g . Given these l i m i t a t i o n s one i s f o r the most p a r t c o n f i n e d to g e n e r a l g u a l i t a t i v e o b s e r v a t i o n s of the s l u g s ' a b i l i t y to adhere. I f a s l u g i s placed on a sheet of g l a s s or a s i m i l a r smooth s u r f a c e , allowed to adhere, and an attempt i s then made to detach the s l u g from the substratum three f a c t s soon become apparent: 1 . I t i s very d i f f i c u l t t o p u l l the animal i n a d i r e c t i o n p e r p e n d i c u l a r to the s u r f a c e . 2. On the other hand i t i s r e l a t i v e l y easy t o s l i d e 268 the s l u g along the s u r f a c e . 3. I f , by using a f i n g e r n a i l or s l i d i n g the s l u g to the edge.of the g l a s s , one s m a l l p o r t i o n of the f o o t can be l i f t e d from the s u r f a c e , the whole animal can then be e a s i l y peeled o f f , much as one would pee l o f f a p i e c e . o f tape. These o b s e r v a t i o n s may be adeguately e x p l a i n e d by e x i s t i n g t h e o r i e s o f adhesion, THEOBY Adhesion i s the a b i l i t y o f two o b j e c t s to remain attached t o each other. Take, f o r example the s i t u a t i o n d e p i c t e d i n F i g u r e .9.1. Two d i s c s , each 1 cm i n r a d i u s , are arranged c o - a x i a l l y with a gap s e p a r a t i n g them. T h i s gap (of t h i c k n e s s y) i s t o be f i l l e d with an adhesive; The s t r e n g t h o f the adhesive may then be measured by determining the f o r c e r e q u i r e d t o separate the two d i s c s . The s e p a r a t i o n of the d i s c s may occur i n e i t h e r of two ways: 1. The d i s c s may s l i d e p a s t each other (as i n Fig u r e 9,1b), In t h i s case the t h i c k n e s s of the adhesive, y, remains c o n s t a n t but the x c o o r d i n a t e of the d i s c s w i l l vary with time. 2, The d i s c s may be p u l l e d a p a r t a x i a l l y as i n F i g u r e 9.1c. In t h i s case the x c o o r d i n a t e of the d i s c s remains constant but the t h i c k n e s s changes with time. As a f i r s t example, imagine t h a t the d i s c s are immersed i n f l u i d with a known v i s c o s i t y , n. T h i s f l u i d w i l l f i l l the gap and a c t as an adhesive. In the case of s l i d i n g one d i s c past the other the f o r c e of adhesion can be c a l c u l a t e d 269 FIGURE 9.1. The adhesive p r o p e r t i e s of a v i s c o u s l i q u i d . A) The dimensions of two d i s k s immersed i n a v i s c o u s l i q u i d . B) The f o r c e r e q u i r e d to s l i d e the d i s k s r e l a t i v e t o each other i s p r o p o r t i o n a l to the area and the shear r a t e . C) The f o r c e r e q u i r e d to separate the 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 , the square of the area, and i n v e r s e l y p r o p o r t i o n a l to the i n i t i a l s e p a r a t i o n cubed. 270 Figure 9.1 A • d isk of ra&ius R " * 0 adhesive-f i l led gap (viscosity = fj) dX B F=7rR Y " shear rate = " [ d X / d t ] / Y 271 q u i t e simply by a p p l y i n g the d e f i n i t i o n of v i s c o s i t y presented i n Chapter 4: F = A r (dx/dt) y - i = p i R 2 (dx/dt) y - i where F i s the shear f o r c e r e g u i r e d to s l i d e the d i s c s apart a t the v e l o c i t y (dx/dt), A i s the area of the d i s c s , and R the r a d i u s . By d i v i d i n g the f o r c e by the d i s c area the s t r e s s necessary to move the d i s c s a t a given r a t e can be c a l c u l a t e d : shear s t r e s s = n (dx/dt) y~1 The s t r e s s r e q u i r e d to s l i d e the p l a t e s apart thus depends d i r e c t l y on the r a t e a t which they are separated and i n v e r s e l y on the t h i c k n e s s of the adhesive l a y e r . The f o r c e r e q u i r e d to separate the d i s c s a x i a l l y has been c a l c u l a t e d by Stefan (1874) as c i t e d i n C r i s p (1973). F = 1.5 p i R* n (dy/dt) y-3 where F i s the a x i a l f o r c e , and x, y and R are as befo r e . Again t h i s f o r c e can be expressed as a s t r e s s , ( i n t h i s case t e n s i l e s t r e s s ) by d i v i d i n g by the area. T e n s i l e s t r e s s = 1.5 S 2 n (dy/dt) y ~ 3 The s t r e s s r e g u i r e d to sep a r a t e the p l a t e s a x i a l l y i s a f u n c t i o n of the r a t e of s e p a r a t i o n as one might expect from a v i s c o u s f l u i d . However, the t e n s i l e s t r e s s i s a l s o h i g h l y 272 s e n s i t i v e t o the dimensions of the system, i n c r e a s i n g as the square of r a d i u s and i n v e r s e cube o f adhesive t h i c k n e s s . T h i s dependence on the dimensions of the system i s due to the geometry i n v o l v e d i n p u l l i n g the d i s c s apart. When two d i s c s s l i d e past each other no new f l u i d must be i n t r o d u c e d between the p l a t e s . For the movement to occur a x i a l l y , h o w e v e r , f l u i d must flow i n t o the widening gap as the d i s c s move apart. The l a r g e r the r a d i u s the g r e a t e r the volume of f l u i d which must move i n f o r a given s e p a r a t i o n , and the t h i n n e r the l a y e r the s m a l l e r the "pi p e " through which t h i s f l u i d must be t r a n s p o r t e d . These eg u a t i o n s may be used to provide an estimate of the adhesive a b i l i t y of k columbianus by using an average value f o r mucus i n i t s f l u i d s t a t e of 40 poise and assuming an a r b i t r a r y s e p a r a t i o n r a t e o f 1 mm/sec. Shear s t r e s s = 400 N/m2 t e n s i l e s t r e s s = 6 x 10 s N/m2 I t i s ev i d e n t t h a t i t i s much e a s i e r t o s l i d e the two d i s c s a p a r t than to p u l l them apart a x i a l l y and t h a t the a x i a l v a l u e s can be q u i t e l a r q e . In f a c t the a x i a l value here would i n r e a l i t y be l i m i t e d by the t e n s i l e s t r e n g t h of water, which has been estimated at 0.2 - 1.0 x 10 8 N/m2 (Hammel and S c h o l l a n d e r , 1976) t h i s e x p l a i n s at l e a s t on a q u a l i t a t i v e b a s i s the f i r s t two o b s e r v a t i o n s made on A. columbianus, t h a t i t adheres 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 the f o o t of a s l u g i s not l i f t e d when the animal i s 273 c r a w l i n g on a non-porous s u r f a c e (Chapter 3). The value f o r t e n s i l e s t r e s s c a l c u l a t e d here i s very l a r g e . I f t h i s estimate i s c o r r e c t i t would r e q u i r e the a p p l i c a t i o n of a weight o f 1.5 x 10 s kg to detach a 20 gram s l u g . While no a c c u r a t e f i g u r e i s a v a i l a b l e f o r the adhesive s t r e n g t h of the s l u g ' s f o o t i n t e n s i o n , t h i s c a l c u l a t e d value i s o b v i o u s l y many times too l a r g e . The reason f o r t h i s d i s c r e p a n c y i s t w o - f o l d : 1. The Stefan equation i s c a l c u l a t e d f o r d i s c s immersed i n a v i s c o u s f l u i d . Thus when the d i s c s are separated more f l u i d i s drawn i n . For a s l u g anchored by f l u i d mucus to a g l a s s p l a t e the most l i k e l y f l u i d t o be drawn i n as the s l u g i s p u l l e d away from the substratum i s a i r , the v i s c o s i t y of which i s roughly 1 x 10-s t h a t of mucus and w i l l t h e r e f o r e c o n t r i b u t e n e g l i g i b l y to adhesion. Thus the Ste f a n equation over estimates a slug* s adhesive a b i l i t y . The degree of o v e r e s t i m a t i o n cannot be determined without a c l e a r understanding of the flow p a t t e r n s of f l u i d s beneath the s l u g ' s f o o t when a f o r c e i s attempting t o p u l l t h e . f o o t away from the substratum. Data concerning these flow p a t t e r n s are not yet a v a i l a b l e . 2. Any flaws (such as a i r bubbles i n the mucus or dust on the g l a s s surface) i n the adhesive l a y e r w i l l form s t r e s s c o n c e n t r a t i o n s which w i l l lower the e f f e c t i v e adhesive s t r e n g t h of such a f l u i d system. Thus, while the system i s i n theory capable of tremendous adhesive s t r e n g t h , i n r e a l i t y t h e presence of unavoidable flaws w i l l impose - a much lower l i m i t on adhesive s t r e n g t h ; The theory o f s t r e s s 274 c o n c e n t r a t i o n s w i l l be d i s c u s s e d more f u l l y l a t e r i n t h i s c h a p ter. U n t i l the e f f e c t s o f these two f a c t o r s are q u a n t i f i e d the Stefan equation can only provide a very rough i n d i c a t i o n o f the adhesive a b i l i t y of the s l u g ' s f o o t . I t i s reasonably c l e a r , however, t h a t the simple presence of a v i s c o u s f l u i d beneath the f o o t provides the p o t e n t i a l f o r a high adhesive s t r e n g t h . Returning to the Stefan equation and remembering the assumptions used t o c a l c u l a t e the values c i t e d here, i t w i l l be seen t h a t the high s t r e s s f i g u r e obtained i s a t t r i b u t a b l e to the r e l a t i v e l y high r a t e of s e p a r a t i o n (coupled with the extremely t h i n l a y e r o f mucus). The lower the r a t e of s e p a r a t i o n the lower the s t r e s s . Thus a smal l s t r e s s a p p l i e d over a long p e r i o d of time w i l l r e s u l t i n a l a r g e s e p a r a t i o n o f the d i s c s . This f a c t l e a d s t o another aspect of the adhesive system of s l u g s . So f a r t h i s d i s c u s s i o n has assumed the presence of mucus i n i t s f l u i d form. How does the s i t u a t i o n d i f f e r f o r -mucus i n i t s o l i d form? Return to the s i t u a t i o n shown i n F i g u r e 8 . 1c. In t h i s case,however, the two d i s c s are held t o g e t h e r by a s o l i d mucus l a y e r 10 um t h i c k and a f o r c e a p p l i e d t o separate the d i s c s at 1 mm/second (an i n i t i a l t e n s i l e s t r a i n r a t e o f 100/sec) . At t h i s r a t e the y i e l d s t r e s s of A. columbianus pedal mucus i n shear i s about 1 x 10 3 N/m2 . The s t i f f n e s s of a m a t e r i a l i n t e n s i o n i s approximately 3 times t h a t i n shear so the y i e l d s t r e n g t h o f s o l i d mucus (at t h i s s t r a i n rate) i s about 3 x 10 3 N/m2 ; a 275 value much lower than t h a t c a l c u l a t e d by the Stef a n eguation. However t h i s i s only the s t r e s s r e q u i r e d to change the s o l i d mucus i n t o a f l u i d . Once the mucus behaves as a f l u i d the arguments o u t l i n e d above concerning the Stefan equation apply. Thus i f the s l u g i s adhering with s o l i d mucus, the problem of i t s u l t i m a t e adhesive s t r e n g t h i n r e s i s t i n g r a p i d deformation r e t u r n s i n the end to the que s t i o n o f the adhesive s t r e n g t h o f a v i s c o u s f l u i d . The s o l i d i t y o f mucus i s , however, an important f a c t o r i n r e s i s t i n g s m a l l e r f o r c e s on the time s c a l e (approximately 1 second) imposed duri n g locomotion as has been thoroughly d i s c u s s e d i n Chapter 7. The s o l i d i t y of mucus w i l l a l s o allow i t t o f u n c t i o n as an e f f e c t i v e adhesive a g a i n s t the f o r c e of g r a v i t y on the time s c a l e of minutes and hours. On t h i s time s c a l e a f l u i d adhesive would be i n e f f e c t i v e . The p r o p e r t i e s of mucus and the mucus 1 e f f e c t i v e n e s s as an adhesive at l a r g e times 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 o f t h i s d i s c u s s i o n i t seems reasonable to assume t h a t pedal mucus forms an e f f e c t i v e adhesive. I f t h i s i s so how does.the s l u g ever manage to detach part or a l l of i t s f o o t from the substratum? When f e e d i n g , s l u g s are o f t e n seen t o l i f t the a n t e r i o r 1/4 to 1/3 of the body i n order to reach a l e a f . A l s o , i f pedal mucus i s such a stro n g adhesive how i s i t p o s s i b l e t o so e a s i l y p e e l a s l u g from a piece of g l a s s ? The answer t o these q u e s t i o n s l i e s i n the form a t i o n of s t r e s s c o n c e n t r a t i o n s i n the mucus. Take f o r example the 276 s i t u a t i o n d e p i c t e d i n Figure 9.2. A t e n s i l e s t r e s s i s placed on a block of m a t e r i a l . I t can be imagined t h a t the 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 area on the top of the block can be t r a c e d , molecule t o molecule, through the m a t e r i a l t o an area on the bottom of the block. Thus the d i s t r i b u t i o n of f o r c e s w i t h i n the b l o c k can 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 as shown i n F i g u r e 9.2a. I f the f o r c e i s evenly d i s t r i b u t e d over the top and bottom s u r f a c e s of the block the s t r e s s t r a j e c t o r i e s w i l l be p a r a l l e l and evenly spaced and the f o r c e w i l l be spread u n i f o r m l y throughout the m a t e r i a l . Now i f a cra c k i s i n t r o d u c e d i n t o one edge of the m a t e r i a l the s i t u a t i o n i s changed. The f o r c e a c t i n g on the m a t e r i a l above the crack can no longer be passed d i r e c t l y to the m a t e r i a l below the c r a c k . I n s t e a d the s t r e s s t r a j e c t o r i e s must curve around the end of the crack and i n doing so squeeze t o g e t h e r . Thus a l l the f o r c e t h a t would normally be a p p l i e d around the area of the crack i s concentrated i n the area a t the crack t i p . The i n c r e a s e i n s t r e s s a t the crack t i p can be q u i t e l a r g e and i s expressed by St = S (1 + (21/w) ) (Wainright et a l , 1976; Gordon, 1972) where St i s the s t r e s s a t the crack t i p , S i s the o v e r a l l s t r e s s , and 1 and w are the dimensions of the crack as shown i n Figure 9.2b. T h i s equation can be a p p l i e d d i r e c t l y to adhesive s t r u c t u r e of a s l u g ( Figure 9.2c). The edge of the s l u g ' s f o o t provides a ready made crack ,. As a reasonable 277 FIGOBE 9.2.. S t r e s s c o n c e n t r a t i o n s . A) In a uni f o r m l y loaded sample t h e . s t r e s s t r a j e c t o r i e s are u n i f o r m l y spaced.„ B) A crack causes the 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 of a s l u g ' s f o o t w i l l a c t as a cra c k , c a u s i n g a s t r e s s c o n c e n t r a t i o n . f t t t t t t f f t t NOI1VH1N30NO0 . SS3UJLS n u u i i i i ! a t t t t t t t t t t t S3IU0103rVbl SS3H1S U U U U H l 2*6 9Jn5i j 279 example s e t the "crack l e n g t h " at 100um. The crack width cannot be any l a r g e r than the t h i c k n e s s of the mucus l a y e r and i s l i k e l y t o be c o n s i d e r a b l y s m a l l e r , f o r example set w c o n s e r v a t i v e l y at 5 um. Thus the s t r e s s c o n c e n t r a t i o n S/St = (1 + 200/5) = 41 Any s t r e s s a p p l i e d to the f o o t edge by the c o n t r a c t i o n of muscle w i l l be magnified 41 times a t the crack t i p . As the crack extends the s t r e s s c o n c e n t r a t i o n s w i l l grow l a r g e r and i t w i l l be e a s i e r t o detach a d d i t i o n a l areas of the f o o t . In t h i s manner the s l u g , by a p p l y i n g a r e l a t i v e l y s m a l l f o r c e a t i t s f o o t edge, can detach i t s f o o t from the substratum. In o r d e r to take advantage of the crack present at the edge of the f o o t the s l u g c o n t r a c t s muscles at t a c h e d to the edges. However when an i n q u i s i t i v e z o o l o g i s t attempts to grasp a s l u g and p u l l i t o f f a p i e c e of g l a s s he u s u a l l y p u l l s the s l u g from the center of i t s back i n which case very l i t t l e f o r c e i s a p p l i e d d i r e c t l y to the f o o t f r i n g e s and the edge c r a c k s are not propagated. I f however an edge of the f o o t i s p r i e d up and p u l l e d upon a l a r g e c r a c k i s c r e a t e d , a l a r g e f o r c e can be a p p l i e d t o t h a t crack area and the s l u g i s e a s i l y peeled o f f as the crack propagates. T h i s presence of s t r e s s c o n c e n t r a t i o n at crack t i p s can e x p l a i n the t h i r d o b s e r v a t i o n noted at the beginning of t h i s chapter. As a l r e a d y mentioned the e x i s t e n c e of other c r a c k s i n 280 the mucus l a y e r , such as a i r bubbles trapped as the s l u g moves, c a v i t i e s i n the substratum, or d i r t p a r t i c l e s w i l l form s t r e s s c o n c e n t r a t i o n s . The presence of a number of these s t r e s s c o n c e n t r a t i o n s would lower the adhesive s t r e n g t h of the mucus l a y e r to a value w e l l below i t s t h e o r e t i c a l maximum. A TEST As mentioned above the s t r u c t u r e of a s l u g ' s body does not l e n d i t s e l f t o the measurement of adhesive s t r e n g t h . In one case, however, i t proved p o s s i b l e t o measure the adhesive s t r e n g t h of s l u g s . I f a mass i s swung a t the end of a s t r i n g the path taken by the mass i s the r e s u l t of two f a c t o r s : 1. The mass i s t r a v e l l i n g at a c e r t a i n v e l o c i t y . I f the s t r i n g were not present the mass would t r a v e l i n a s t r a i g h t l i n e . 2. In order f o r the mass to t r a v e l i n a c i r c u l a r path a constant r a d i a l a c c e l e r a t i o n must be a p p l i e d t o the mass. T h i s r a d i a l a c c e l e r a t i o n l e a d s to the " c e n t r i f i g a l f o r c e " , F. F = ma where m i s mass and a i s a c c e l e r a t i o n . The a c c e l e r a t i o n i s c a l c u l a t e d as a = w zr 281 where w i s the angular v e l o c i t y of the mass as i t t r a v e l s i n i t s c i r c u l a r path and r i s the r a d i u s of the c i r c l e . Thus F = mw2r I f a s l u g i s placed on a d i s k , allowed to adhere, and the d i s k i s then r o t a t e d , a c e n t r i f u g a l f o r c e w i l l be exerted on the s l u g . As long as the s l u g remains s t a t i o n a r y r e l a t i v e to the d i s k 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 by the s o l i d adhesive mucus beneath the s l u g . When the d i s k i s r o t a t e d at s u f f i c i e n t speed, the s l u g w i l l be f o r c e d outwards on the d i s k . Thus i f the mass of the s l u g and i t s f o o t a r e a , the r a d i u s at which the s l u g i s placed on the d i s k and the angular v e l o c i t y r e g u i r e d t o move;the slug are a l l known the adhesive shear s t r e n g t h of the mucus can be c a l c u l a t e d . This experiment was c a r r i e d out u s i n g the apparatus shown i n F i g u r e 9.3 . . The f o o t area of a s m a l l A. columbianus (0.18 - 0.26 grams) was measured and the s l u g then placed on the d i s k at a measured r a d i u s and allowed to adhere., The d i s k was r o t a t e d by a Cole-Parmer Master Servodyne motor, and the frequency of r e v o l u t i o n matched manually with a c a l i b r a t e d stroboscope. The r a t e . o f r o t a t i o n was i n c r e a s e d u n t i l the s l u g ' s adhesive y i e l d e d and the s l u g was spun outwards to the r e t a i n i n g w a l l . The r a t e of r o t a t i o n was then read o f f the stroboscope and the y i e l d s t r e s s c a l c u l a t e d . Three t o f i v e t r i a l s were c a r r i e d out on each of f i v e s l u g s and the average y i e l d s t r e s s c a l c u l a t e d was 780 (+- 335) N/m2 . i t was not p o s s i b l e with t h i s 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 columbianus pedal mucus under the s l u g . The e l e c t r i c motor spi n s the d i s k at an angular v e l o c i t y , W, t h a t i s measured with the stroboscope. The f o r c e a c t i n g to s l i d e the s l u g r a d i a l l y outwards i s MW2R, where w i s the s l u g ' s mass, and R i s the r a d i u s . . In t h i s manner the f o r c e (and the s t r e s s ) a t which the mucus y i e l d s and the s l u g b egins t o s l i d e , can be measured. Figure 9.3 283 k S T R O B E Slug M a s s = M Foot Area = A F O R C E = MW R = F S T R E S S = F / A S L U G j^Z R f^;w~™>:^ ji~i^ aKi.,"r,!,rf,itiwit^  E L E C T R I C MOTOR RETAINING W A L L / / DISK S P E E D C O N T R O L 284 apparatus t o measure the shear r a t e : i n c u r r e d by c e n t r i f u g a t i o n . However, s i n c e the r a t e of r o t a t i o n was i n c r e a s e d s l o w l y the c e n t r i f u g a l f o r c e was a p p l i e d over a number of seconds. Consequently the shear r a t e should be q u i t e low. In Chapter 4 the y i e l d s t r e s s of A columbianus pedal mucus at a shear r a t e of approximately 5/second (the lowest measured) was 320 N/m2 . Thus qiven the crude nature of t h i s experiment the p r e d i c t e d and measured v a l u e s match q u i t e closely.. 285 CHAPTER TEN• Co n c l u s i o n s i T h i s study has examined i n c o n s i d e r a b l e d e t a i l the mechanism of adhesive locomotion found i n one s p e c i e s of s l u g , A r i o l i m a x columbianus . I s the mechainism d e s c r i b e d here unique to t h i s one s p e c i e s or can i t be g e n e r a l i z e d t o account f o r the locomotion of other types of gastropods? Before d e a l i n g d i r e c t l y with t h i s question i t w i l l be u s e f u l to review the fundamental requirements f o r adhesive locomotion. Any gastropod u t i l i z i n g muscular pedal waves w i l l have two types of areas present on the f o o t s o l e d u r i n g movement: 1. areas t h a t are moving forward, and 2. areas t h a t are s t a t i o n a r y . The moving segments of the f o o t must encounter some amount of s l i d i n g f r i c t i o n as they s l i d e a c r o s s the substratum.. The f o r c e r e g u i r e d t o overcome t h i s f r i c t i o n i n r e s i s t e d by the areas of the f o o t which are -s t a t i o n a r y . T h i s r e s i s t a n c e i s brought about by an i n t e r a c t i o n of the s t a t i o n a r y p o r t i o n s of the f o o t with the substratum beneath them. Thus, i f the r e s i s t a n c e of the s t a t i o n a r y p o r t i o n s of the foot to being moved backwards i s g r e a t e r than the r e s i s t a n c e of the moving p o r t i o n s of the f o o t to being moved forwards the animal w i l l be a b l e to c r a w l . T h i s i n e q u a l i t y of forward and backwards r e s i s t a n c e s can be brought about i n any of t h r e e ways: 1. I f the r e s i s t a n c e to movement per u n i t area i s the same f o r a l l p a r t s of the f o o t , i t i s necessary t h a t a s m a l l e r area be moved forwards than remains s t a t i o n a r y . 286 2. The r e s i s t a n c e t o movement per u n i t area can vary from one p o r t i o n of the f o o t t o the next such t h a t the moving areas o f the f o o t , taken as a whole, show l e s s r e s i s t a n c e than the s t a t i o n a r y p o r t i o n s . In t h i s case the moving segments of the f o o t c o u l d have a l a r g e r area than the s t a t i o n a r y segments provided t h a t the r e s i s t a n c e to movement was s u f f i c i e n t l y s m a l l e r under the moving areas. 3. Both 1 . and 2. c o u l d be a c t i n g s imultaneously. I t has been shown i n t h i s study t h a t A., columbianus i s a good example of t h i s t h i r d case. D i r e c t waves (as used bu A. columbianus ) s t a r t at the p o s t e r i o r end of the animal by compressing the f o o t . Areas o f forward movement (the waves) are thus n e c e s s a r i l y s m a l l e r than the s t a t i o n a r y areas. In a d d i t i o n , the p h y s i c a l p r o p e r t i e s o f the pedal mucus are such that the forward s l i d i n g r e s i s t a n c e i s c o n s i d e r a b l y s m a l l e r than the backwards r e s i s t a n c e . The r e s u l t i s an e f f e c t i v e locomotory system. We now r e t u r n to the o r i g i n a l q u e s t i o n of t h i s c hapter; c o u l d t h i s , or a s i m i l a r mechanism, be o p e r a t i n g i n other gastropod s p e c i e s ? The v a r i o u s s p e c i e s w i l l be d i s c u s s e d a c c o r d i n g to t h e i r locomotory types (as d e f i n e d i n Chapter 3). D i r e c t Monotaxic Waves The prominent members of t h i s group are the t e r r e s t r i a l s l u g s and s n a i l s . As regards the mechanism of locomotion the vast m a j o r i t y of these are very s i m i l a r i n a l l r e s p e c t s to A columbianus. Consequently, I see no reason why the model proposed here f o r A_. columbianus cannot be a p p l i e d 287 d i r e c t l y t o these other s p e c i e s . D i r e c t D i t a x i c Waves D i r e c t d i t a x i c waves (see F i g u r e 10.1b) are found i n r e l a t i v e l y few s p e c i e s of gastropods such as the abalones H a l i o t i d a e and some s p e c i e s of Th a i s . The best d e s c r p t i o n of d i t a x i c d i r e c t waves i s t h a t o f Lissman (1945a) using H a l i o t i s t u b e r c u l a t a , and t h i s study i s used as the b a s i s f o r t h i s d i s c u s s i o n . As with d i r c t monotaxic waves, the areas o f forward motion i n H a l i o t i s are compressed r e l a t i v e t o the s t a t i o n a r y areas so t h a t locomotion c o u l d occur even without a v a r i a t i o n i n f r i c t i o n a l r e s i s t a n c e under d i f f e r e n t areas o f the f o o t , , The abalone does, however, e x h i b i t a mechanism f o r lo w e r i n g the r e s i s t a n c e t o movement under the moving segments of the f o o t . In these animals the f o o t can c l e a r l y be seen t o l i f t during the passage of a wave. T h i s process i s f a c i l i t a t e d by the p o s i t i o n of the waves on the f o o t . U n l i k e the s l u g , where the waves are i n the center of the f o o t and enclosed by a rim, the abalone's wave moves along the edges o f the f o o t and are thus d i r e c t l y i n co n t a c t with the surrounding f l u i d . I t seems l i k e l y t h a t the water being sheared under the l i f t e d p o r t i o n of the f o o t w i l l o f f e r l e s s r e s i s t a n c e to movement than the mucus under the s t a t i o n a r y p o r t i o n s of the f o o t . Thus, at l e a s t i n the case of the abalone, animals u t i l i z i n g d i r e c t d i t a x i c waves employ a d i f f e r e n t mechanism than t h a t proposed f o r A columbianus . The end r e s u l t i s s i m i l a r but the requirement f o r s p e c i a l i z e d mucus p r o p e r t i e s i s absent. 288 FIGURE 10.1. A diagrammatic r e p r e s e n t a t i o n of the f o u r r e g u l a r forms of pedal waves. The s t i p p l e d areas r e p r e s e n t those areas on the f o o t which are moving, and the arrows i n d i c a t e the d i r e c t i o n of movement. 289 D. R E T R O G R A D E DITAXIC Patella vulgata R E T R O G R A D E MONOTAXIC Nerit ina recli vata 2 9 0 Retrograde D i t a x i c Waves Retrograde d i t a x i c waves (see F i g u r e 10.1c) are the most common form of pedal wave found among prosobranch gastropods ( M i l l e r , 1974b). Jones and Truman (1970) have s t u d i e d the locomotion of the l i m p e t P a t e l l a v u l g a t a , and t h e i r study w i l l form the b a s i s of t h i s d i s c u s s i o n . Retrograde waves, i n c o n t r a s t t o d i r e c t waves, are i n i t i a t e d a t the a n t e r i o r end of the f o o t as the f o o t i s extended forwards. The wave o f extension i s then passed p o s t e r i o r l y along the f o o t . The l e n g t h of a s i n g l e wave i s t y p i c a l l y one t h i r d of the f o o t l e n g t h or g r e a t e r ( M i l l e r , 1974a). I t seems l i k e l y t h a t the area of these l a r g e waves of extension i s l a r g e r than the area of the s t a t i o n a r y p o r t i o n s of the f o o t . Consequently these animals must possess a mechanism f o r l o wering the forward s l i d i n g r e s i s t a n c e r e l a t i v e t o the backwards . Jones and Trueman (1970) propose t h a t the f o o t i s l i f t e d d uring movement and that the space f i l l e d with water, as with abalones. Onlike abalones, however, the l i f t i n g o f the f o o t i s not v i s u a l l y apparent. Jones and Trueman (1970) based t h e i r c o n c l u s i o n s on measurements made as a li m p e t crawled over a hole i n a g l a s s p l a t e . . I t has been pointed out i n Chapter 3 t h a t measurements of f o o t l i f i t i n g made i n t h i s manner may not conform to the s i t u a t i o n when an animal i s c r a w l i n g over a s o l i d , i n f l e x i b l e s u r f a c e . I t i s h i g h l y probable, then, t h a t l i m p e t s (and presumably other prosobranchs) do not l i f t t h e i r f o o t during locomotion and must t h e r e f o r e . r e l y on the p r o p e r t i e s of t h e i r pedal mucus to a f f e c t movement. The 291 r e s o l u t i o n of t h i s q u e s t i o n awaits f u r t h e r study. Retrograde Monotaxic Waves While r e t r o g r a d e monotaxic waves are f a i r l y common i n gastropods ( M i l l e r , 1974b) they have r e c e i v e d r e l a t i v e l y l i t t l e a t t e n t i o n . The most e x t e n s i v e study to date i s that of Gainey (1976) d e a l i n g with Neratina r e c l i v a t a . As with d i t a x i c r e t r o g r a d e waves, monotaxic retrograde.waves are waves o f e x t e n s i o n (see F i g u r e 10.Id). Each wave i s t y p i c a l l y one t h i r d of the f o o t l e n g t h or g r e a t e r and one or two waves are present on the f o o t a t any one time ( M i l l e r , 1974a). In N. r e c l i v a t a only one wave i s present on the f o o t . As a consequence the area of the movinq segment of the f o o t i s l e s s than t h a t of the s t a t i o n a r y segments. I t i s not known whether t h i s i s t y p i c a l o f t h i s type of wave. I f indeed the s t a t i o n a r y area exceeds the moving area, no r e d u c t i o n i n r e s i s t a n c e beneath the moving area need n e c e s s a r i l y e x i s t . A r e d u c t i o n i n r e s i s t a n c e beneath the waves would however be advantageous. As with other wave forms, a lowering of r e s i s t a n c e could be brought about e i t h e r by a l i f t i n g o f the f o o t or the p r o p e r t i e s of the pedal mucus. To my knowledge no measurements have been made concerning t h i s problem. Thus, u n t i l more data have been gathered, the p o s s i b l e e x i s t e n c e i n these animals of a mechanism s i m i l a r t o t h a t i n A., columbianus cannot be determined. Summary 2 9 2 In summary, the mechanism of adhesive.locomotion proposed i n t h i s 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 . I t i s p o s s i b l e t h a t i t may apply to other forms o f pedal locomotion but u n t i l f u r t h e r i n f o r m a t i o n i s known about these forms of locomotion t h i s p o s s i b i l i t y remains u n c e r t a i n . 2 9 3 LITERATURE CITED Acker, R.F., B.F. Brown, J.R. DePalma, J.R. Iverson (eds.) 1973. Proceedings of the T h i r d I n t e r n a t i o n a l  Congress on Marine C o r r o s i o n and F o u l i n g . Northwestern Univ. P r e s s , Evanston, 111. 1031 pp. A k l o n i s , J . J . , W.J. MacKnight, and M. Shen. 1972. I n t r o d u c t i o n t o Polymer V i s c o e l a s t i c i t y . John Wiley and Sons, N.Y. 249 pp. Alexander, R.McN. 1965. Animal Mechanics.. Chapman and H a l l , London. 346 pp. . „_ and G. Gcldspink (eds.) 1977. Mechanics and E n e r g e t i c s of Animal Locomotion . 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