UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

State of sodium and water in single striated muscle fibers McLaughlin, Stuart Graydon Arthur 1968-12-31

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1968_A1 M24.pdf [ 7.62MB ]
Metadata
JSON: 1.0104613.json
JSON-LD: 1.0104613+ld.json
RDF/XML (Pretty): 1.0104613.xml
RDF/JSON: 1.0104613+rdf.json
Turtle: 1.0104613+rdf-turtle.txt
N-Triples: 1.0104613+rdf-ntriples.txt
Original Record: 1.0104613 +original-record.json
Full Text
1.0104613.txt
Citation
1.0104613.ris

Full Text

THE STATE OF SODIUM AND WATER IN  SINGLE STRIATED MUSCLE FIBERS  by STUART GRAYDON ARTHUR MCLAUGHLIN B. Sc., U n i v e r s i t y o f B r i t i s h Columbia,  1964  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS'FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of ANATOMY  We a c c e p t t h i s  t h e s i s as conforming  to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA January,  1968  In  presenting  advanced  Library  agree  this  degree  shall  that  thesis  at the U n i v e r s i t y  make  for extensive  p u r p o s e s may be g r a n t e d  It  financial  gain  of  copying  not  for  I agree  the  of  this  thesis  I  o r by h i s  represen-  this  thesis  permission.  an  further  scholarly  be a l l o w e d w i t h o u t my w r i t t e n  Columbia  that  for  that copying or p u b l i c a t i o n of  Depa r t m e n t The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  requirements  r e f e r e n c e and s t u d y .  by t h e Head o f my D e p a r t m e n t  is understood  shall  the  B r i t i s h Columbia,  it freely available for  permission  tatives.  in p a r t i a l f u l f i l m e n t o f  for  ABSTRACT  C a t i o n s e n s i t i v e g l a s s m i c r o e l e c t r o d e s were i n s e r t e d  into  single  s t r i a t e d muscle f i b e r s o f the g i a n t b a r n a c l e , Balanus n u b i l u s , to measure d i r e c t l y the a c t i v i t i e s  o f sodium and p o t a s s i u m i n the myoplasm.  The t o t a l  sodium and p o t a s s i u m c o n t e n t o f the i n d i v i d u a l e x p e r i m e n t a l f i b e r s was determined by flame photometry.  From these measurements,  sodium i n the f i b e r which d i d not a f f e c t  the m i c r o e l e c t r o d e s and the p e r -  centage o f water i n the f i b e r which was n o t a v a i l a b l e the p o t a s s i u m ions were c a l c u l a t e d .  t o a c t as s o l v e n t f o r  The minimal p e r c e n t a g e s o f "bound"  sodium and water were 84% and 42% r e s p e c t i v e l y . significant  the p e r c e n t a g e o f  I t was h y p o t h e s i z e d t h a t a  f r a c t i o n o f t h i s "bound" sodium was i n v o l v e d i n i o n p a i r  forma-  t i o n w i t h c a r b o x y l m o i e t i e s on the myosin m o l e c u l e s x^hich comprise the t h i c k f i l a m e n t s , and experiments were d e s i g n e d to t e s t  this  hypothesis.  In t h e second s e r i e s o f e x p e r i m e n t s , the a c t i v i t i e s p o t a s s i u m and hydrogen i n the myoplasm were measured  as the temperature o f  the s o l u t i o n b a t h i n g the f i b e r s was i n c r e a s e d from 7 to 40°C. s i b l e shortening occurred i n a l l  f i b e r s between  o f sodium,  37 and 40°C.  An i r r e v e r When the  f i b e r s s h o r t e n e d i n a sodium f r e e R i n g e r s o l u t i o n , the mean a c t i v i t y o f sodium i n c r e a s e d by 130%, the mean a c t i v i t y o f p o t a s s i u m remained r e l a t i v e l y c o n s t a n t , and the pH d e c r e a s e d from 7.17 t o 6.77. v i d e d s t r o n g e v i d e n c e t h a t sodium i s bound  These experiments p r o -  t o myosin i n the l i v i n g  fiber,  f o r e x t r a c t e d myosin i s known t o denature a t 37°C and r e l e a s e i t s a s s o c i ated a l k a l i metal c a t i o n s .  In the t h i r d  s e r i e s o f experiments, the o p t i c a l d e n s i t y , O.D., o f  the s i n g l e s t r i a t e d muscle f i b e r s was measured  a t 50 m i x i n t e r v a l s  between  iii 450 and normal  850 mp..  At a l l wavelengths,  R i n g e r b a t h i n g s o l u t i o n was  F o r example, a t 850 mu, the O.D. i n normal  the O.D.  o f the f i b e r s , r e l a t i v e to the i n i t i a l  R i n g e r , decreased from 1 t o 0.21  T h i s change i n O.D.  ± 0.06  i n 25 minutes.  (O.D.  The  value cor-  from 5%  = - l o g T) was  c o u l d be r e v e r s e d by r e t u r n i n g  b a t h i n g s o l u t i o n to the b a t h .  when the  r e p l a c e d by sodium f r e e s u c r o s e R i n g e r .  r e s p o n d i n g i n c r e a s e i n the transmittar.ee, T, 55%.  decreased markedly  the normal  L a r g e , r e v e r s i b l e d e c r e a s e s i n O.D.  Ringer were a l s o  observed when p o t a s s i u m and t r i s were used as s u b s t i t u t e s f o r sodium. changes i n O.D.  are e x p l a i n e d by the t h e o r y o f l i g h t  scattering  to  These  i f i t is  assumed t h a t sodium i s bound to the main s c a t t e r i n g c e n t e r s i n the myoplasm, the t h i c k f i l a m e n t s .  When the f i b e r s were bathed  s u b s t i t u t e d Ringer, a small r e v e r s i b l e w h i c h may  i n sodium f r e e ,  i n c r e a s e i n the O.D.  was  lithium  observed,  i n d i c a t e t h a t l i t h i u m i s complexed more s t r o n g l y than sodium to  the b i n d i n g s i t e s on the t h i c k  In the f i n a l  filaments.  s e r i e s o f experiments,  the number of sodium and  p o t a s s i u m i o n s "bound" to the c o n t r a c t i l e p r o t e i n s i n a g l y c e r i n a t e d was  measured.  The  f r e e c o n c e n t r a t i o n s o f hydrogen,  sodium and  fiber  potassium  were m a i n t a i n e d a t v a l u e s s i m i l a r to those found i n an i n t a c t  fiber.  results  potassium  i n d i c a t e d t h a t s u b s t a n t i a l b i n d i n g o f both sodium and  o c c u r r e d , and "bound".  The  t h a t p r o p o r t i o n a l l y more sodium than p o t a s s i u m i o n s were  I f the r e s u l t s a r e e x t r a p o l a t e d to the i n t a c t  fiber,  they imply  t h a t about as much sodium i s "bound" to the c o n t r a c t i l e p r o t e i n s as i s f r e e i n the myoplasm.  T h i s amount o f "bound" sodium i s s u f f i c i e n t  the r e s u l t s o f the d e n a t u r a t i o n and l i g h t s c a t t e r i n g sufficient  to account f o r the anomalously  to e x p l a i n  experiments, but i n -  low a c t i v i t y o f sodium i n the myo-  plasm, as measured by a sodium s e n s i t i v e m i c r o e l e c t r o d e .  Thus, i t was  iv concluded  t h a t e i t h e r some f a c t o r must enhance  contractile proteins in a l i v i n g i n o r g a n e l l e s which a r e d e s t r o y e d  cell,  the b i n d i n g o f sodium to the  or t h a t sodium must be  sequestered  by the g l y c e r i n a t i o n p r o c e s s .  V  TABLE OF CONTENTS  INTRODUCTION CHAPTER I  HISTORICAL INTRODUCTION  1  CHAPTER I I  PHYSICAL CHEMISTRY OF THE BINDING OF WATER AND THE ALKALI METAL CATIONS ,  5  A. B. CHAPTER I I I  Water A l k a l i metal cations  5 14  SCOPE AND PURPOSE OF THE INVESTIGATION  36  RESULTS AND DISCUSSION CHAPTER IV  CHAPTER V  ACTIVITY OF SODIUM AND POTASSIUM IN THE MYOPLASM  40  A.  Introduction  40  B. C. D.  Methods Results . .„ Discussion  RELEASE OF BOUND SODIUM A. B. C. D.  CHAPTER V I  Introduction Methods Results Discussion  B  Introduction Methods Results Discussion  „  „ „.  62 62 66 74  „ „  80  „ „ „  „  BINDING OF SODIUM AND POTASSIUM IN GLYCEROL EXTRACTED FIBERS A. B. C. D.  Introduction Methods Results Discussion  41 50 54 62  OPTICAL DENSITY CHANGES OF FIBERS IN SODIUM FREE SOLUTIONS A. B. C. D  CHAPTER V I I  '. .  80 81 86 100  104 104 105 107 I l l  vi CONCLUSIONS CHAPTER V I I I  SIGNIFICANCE OF THE RESULTS  114  CHAPTER IX  SUGGESTIONS FOR FUTURE WORK  122  BIBLIOGRAPHY APPENDIX I APPENDIX I I  ; „  130 143 143  vii L I S T OF TABLES  TABLE I  Solutions  TABLE I I  Sodium and p o t a s s i u m  TABLE I I I  Sodium c o n c e n t r a t i o n and a c t i v i t y i n s i n g l e muscle f i b e r s b e f o r e and a f t e r s h o r t e n i n g  69  P o t a s s i u m c o n c e n t r a t i o n and a c t i v i t y f i b e r s b e f o r e and a f t e r s h o r t e n i n g  72  TABLE IV  „  44  i n s i n g l e muscle f i b e r s  52  i n s i n g l e muscle  TABLE V  Solutions  TABLE V I  The sodium and potassium content o f f i b e r s e x t r a c t e d i n 507o g l y c e r o l f o r 24 days then e q u i l i b r a t e d i n a s o l u t i o n c o n t a i n i n g [K] = 295 mM and [Na] = 10.4 mM  108  The sodium and potassium content o f f i b e r s e x t r a c t e d i n 507o g l y c e r o l f o r 24 days then e q u i l i b r a t e d i n a s o l u t i o n c o n t a i n i n g [K] = 295 mM and [Na] = 0.2 mM  110  TABLE V I I  „  82  viii LIST OF FIGURES  Figure 1  Figure 2  Figure 3  Photograph o f the t i p o f a sodium microelectrode  Figure 5  Figure 7  Figure 8  Figure 9  F i g u r e 10  F i g u r e 11  F i g u r e 12  F i g u r e 13  F i g u r e 14  F i g u r e 15  inserted 45  Photograph, o f a s i n g l e s t r i a t e d muscle f i b e r .....  from the  ......  46  R e l a t i o n between the sodium and p o t a s s i u m c o n t e n t s o f s i n g l e muscle f i b e r s R e l a t i o n between membrane p o t e n t i a l and l o g [K] t y p i c a l muscle f i b e r  Figure 6  41  Diagram o f a c a n n u l a t e d muscle f i b e r w i t h microelectrode  giant barnacle Figure 4  sensitive  51  for a  .  ,  53  V a r i a t i o n i n the average membrane p o t e n t i a l and f i b e r l e n g t h w i t h temperature and w i t h time  67  V a r i a t i o n i n the i n t e r n a l a c t i v i t y o f sodium o f a t y p i c a l muscle f i b e r as the temperature was i n c r e a s e d t o 40°C „ „  68  V a r i a t i o n i n the average i n t e r n a l a c t i v i t y o f p o t a s s i u m o f 7 f i b e r s as the temperature was i n c r e a s e d to 40°C ...  71  V a r i a t i o n i n the average pH o f the myoplasm o f 10 f i b e r s as the temperature was i n c r e a s e d to 40°C  73  Diagram o f a s i n g l e muscle f i b e r p o s i t i o n e d i n the p e r s p e x b a t h i n g chamber, and p l a n view o f the o p t i c a l pathway „  84  The t o t a l c o n c e n t r a t i o n s o f sodium and p o t a s s i u m i n f i b e r s bathed i n sodium f r e e s u c r o s e R i n g e r  87  The t r a n s m i t t a n c e o f s i n g l e muscle f i b e r s i n normal R i n g e r and a f t e r 25 minutes i n s u c r o s e R i n g e r as a f u n c t i o n o f wavelength „  89  The o p t i c a l d e n s i t y o f s i n g l e muscle f i b e r s r e l a t i v e to the i n i t i a l v a l u e o f the o p t i c a l d e n s i t y i n normal R i n g e r as a f u n c t i o n o f wavelength  90  The r e l a t i v e o p t i c a l d e n s i t y o f s i n g l e muscle f i b e r s bathed i n t r i s R i n g e r and then i n normal R i n g e r  92  The r e l a t i v e o p t i c a l d e n s i t y o f s i n g l e muscle f i b e r s bathed i n p o t a s s i u m R i n g e r and then i n normal R i n g e r  ...  93  ix F i g u r e 16  F i g u r e 17  F i g u r e 18  F i g u r e 19  The r e l a t i v e o p t i c a l d e n s i t y o f s i n g l e muscle f i b e r s bathed i n l i t h i u m R i n g e r and i n pH = 9.6 R i n g e r  94  The t o t a l c o n c e n t r a t i o n s o f potassium, sodium and l i t h i u m i n f i b e r s bathed i n sodium f r e e , l i t h i u m s u b s t i t u t e d Ringer  95  The a c t i v i t y o f sodium i n the myoplasm o f s i n g l e muscle f i b e r s bathed i n l i t h i u m R i n g e r or s u c r o s e R i n g e r r e l a t i v e to the i n i t i a l a c t i v i t y o f sodium when the f i b e r was bathed i n normal R i n g e r  98  The pH and membrane p o t e n t i a l o f s i n g l e muscle f i b e r s bathed i n pH = 9.6 R i n g e r and i n normal R i n g e r  100  X  ACKNOWLEDGEMENTS  I w i s h to thank Dr. J . A. M. Hinke, my  r e s e a r c h d i r e c t o r , f o r the  encouragement, a s s i s t a n c e and c o n s t r u c t i v e c r i t i c i s m s he o f f e r e d the course o f t h i s work; Mr.  throughout  C. G. Lemon f o r the h e l p f u l s u g g e s t i o n s and  equipment he s u p p l i e d d u r i n g the performance  o f the o p t i c a l  experiments  r e p o r t e d i n Chapter V I ; Dr. P. T a y l o r f o r the many hours o f p e r s o n a l a t t e n t i o n I r e c e i v e d a t h i s seminars; Mrs. I r e n e Ingraham and Mr. A l a n M c L a u g h l i n f o r the t e c h n i c a l a s s i s t a n c e they r e n d e r e d d u r i n g v a r i o u s phases o f the work.  1 CHAPTER I  HISTORICAL INTRODUCTION  S h o r t l y b e f o r e h i s death, S i r I s a a c Newton remarked: know what I may  appear  " I do not  to the w o r l d , but to m y s e l f I seem to have been o n l y  l i k e a boy p l a y i n g on the seashore, and d i v e r t i n g myself f i n d i n g a smoother pebble or a p r e t t i e r  i n now  and  then  s h e l l than o r d i n a r y w h i l s t the g r e a t  ocean o f t r u t h l a y a l l u n d i s c o v e r e d b e f o r e me."  What was  t r u e of 17  th  Cen-  th t u r y mathematics and p h y s i c s (and Newton was p h y s i c s ) i s a l s o t r u e o f 20 ^  17  Century b i o l o g y .  Century mathematics and Much time has been spent  p l a y i n g w i t h c e l l s and o r g a n e l l e s , but f o r the f i r s t the s e a - l i k e environment ly  ignored.  Water was  h a l f of t h i s century,  of these c e l l s and o r g a n e l l e s was  c o n s i d e r e d merely as the i n e r t ,  i n which the b i o c h e m i c a l r e a c t i o n s o f the c e l l  occured.  almost  i n t r a c e l l u l a r medium In the  decade, however, many i n v e s t i g a t o r s r e c o g n i z e d the importance ing  the r o l e o f water i n c e l l  has  stated:  life,  complete-  p h y s i o l o g y and b i o c h e m i s t r y .  As  last  o f understandSzent-Gyorgyi  "water i s not o n l y the mater, mother, i t i s a l s o the m a t r i x of  and b i o l o g y may  have been u n s u c c e s s f u l i n u n d e r s t a n d i n g the most  b a s i c f u n c t i o n s because  i t f o c u s s e d i t s a t t e n t i o n o n l y on the p a r t i c u l a t e  matter..." (1). It  i s not f a i r  earlier biologists. possibility as normal  to say t h a t water was  c o m p l e t e l y i g n o r e d by  the  There are s p o r a d i c r e f e r e n c e s i n the l i t e r a t u r e  t h a t water i n the c y t o p l a s m i s not i n the same p h y s i c a l  l i q u i d water.  Over 60 years ago, Overton  (2) observed  to the state  that a  muscle s w e l l e d to much l e s s than twice i t s i n i t i a l weight when immersed i n a s o l u t i o n of h a l f  the i n i t i a l  osmotic p r e s s u r e , and concluded t h a t a  sub-  stantial  f r a c t i o n o f c e l l u l a r water was o s m o t i c a l l y  l a t e r , Rubner  inactive.  Twenty years  (3) e s t i m a t e d the f r a c t i o n o f water which c o u l d ' n o t be f r o z e n  i n a muscle a t -20° C, and deduced t h a t 23% o f the water i n f r o g muscle was "bound".  I n 1930, however, H i l l  (4) concluded from vapor p r e s s u r e  ments t h a t l e s s than 47» o f the water i n f r o g muscle was "bound".  measureInterest  i n the s t a t e o f water i n c e l l s remained dormant f o r another 20 y e a r s . interesting  to note t h a t  i f an e r r o r i n H i l l ' s  It is  calculations i s corrected,  h i s data p r e d i c t t h a t about 30% o f the water i n f r o g muscle i s "bound" ( 5 ) .  In r e c e n t water has s t i m u l a t e d  years,  the i n t e r e s t o f chemists i n the s t r u c t u r e o f  the i n t e r e s t o f p h y s i o l o g i s t s and b i o c h e m i s t s i n t h i s  b i o l o g i c a l l y ubiquitous  molecule.  ferences  (6, 7, 8) and books w r i t t e n  have been h e l d  I n the l a s t two years a l o n e ,  importance of the s t a t e o f water i n the l i v i n g  several  (9, 10, 11) on the  cell.  Most p h y s i o l o g i s t s have assumed t h a t a i l the a l k a l i metal as w e l l as the water, i n a c e l l e x i s t i n a f r e e s t a t e . ever, several  enon (12, 13, 14). I n 1929 Hober He c o n c l u d e d t h a t o n l y  o f p o t a s s i u m by an a b s o r p t i o n  rather  t h a t the amount o f i o n b i n d i n g  ference  (16).  than a membrane phenom-  ions  in a cell  this  possibil-  e x i s t i n l a r g e enough  to e x p l a i n the s e l e c t i v e a c c u m u l a t i o n  mechanism.  F o r t h i s r e a s o n , he examined the  a v a i l a b l e data on complexing o f ions by e x t r a c t e d  myosin  Many years ago, how-  (15) c r i t i c a l l y a n a l y z e d  the p r o t e i n s  q u a n t i t i e s t o complex s u f f i c i e n t  observation  cations,  i n v e s t i g a t o r s suggested t h a t the s e l e c t i v e potassium i o n  a c c u m u l a t i o n o f c e l l s may be due to b i n d i n g  ity.  con-  by p r o t e i n s  proteins.  He observed  i n s o l u t i o n was s m a l l .  i s s t i l l v a l i d , w i t h the e x c e p t i o n  of a few p r o t e i n s  This like  He a l s o observed that there was no evidence o f a marked  of proteins  f o r potassium over sodium i o n s .  pre-  Thus, he concluded  that  the b i n d i n g  of ions  to p r o t e i n s c o u l d n o t e x p l a i n the s e l e c t i v e a c c u m u l a t i o n  of potassium i n l i v i n g  cells.  I n s p i t e o f Hober's a n a l y s i s , there gators  i n A u s t r a l i a (17-20), R u s s i a  e x i s t today groups o f i n v e s t i -  (21-23) and the USA (24-31) which do n o t  a c c e p t the assumption that the i n t r a c e l l u l a r  ions i n g e n e r a l ,  p o t a s s i u m i o n i n p a r t i c u l a r , a r e f r e e i n the c y t o p l a s m . 311)  has l i s t e d  s e v e r a l other  and the  Ernst  (32, page  i n v e s t i g a t o r s who p r e f e r , i n one form o r  another, a s o r p t i o n theory  o f i o n a c c u m u l a t i o n to the more g e n e r a l l y  a c c e p t e d membrane t h e o r y .  The proponents o f the s o r p t i o n theory  hypotheses n o t so much on e x p e r i m e n t a l evidence f o r i o n b i n d i n g cisms o f the membrane theory theory.  and the a u x i l l i a r y p o s t u l a t e s  base  their  as on c r i t i -  r e q u i r e d by t h i s  The n e c e s s i t y o f p o s t u l a t i n g a wide v a r i e t y of " i o n pumps" l o c a t e d  i n the membrane, f o r example, leads  to s e r i o u s  (21)  out.  and L i n g  (29, 30) have p o i n t e d  c o n t r a d i c t i o n s , as T r o s h i n  These groups have s p e c u l a t e d  most o f the potassium, but n o t the sodium i n the c e l l or a s s o c i a t e d  state.  This  contradict  e x i s t s i n a complexed  s p e c u l a t i o n has never been w i d e l y a c c e p t e d .  way (33), f o r example, has c r i t i c i z e d mainly a t L i n g .  that  The m i c r o e l e c t r o d e  the s o r p t i o n theory,  the theory,  Con-  directing his criticisms  experiments r e p o r t e d  i n this thesis also  f o r they demonstrate t h a t the a c t i v i t y o f  p o t a s s i u m i n the myoplasm o f s t r i a t e d muscle f i b e r s i s a c t u a l l y h i g h e r  than  would be c a l c u l a t e d by assuming t h a t a l l the water and p o t a s s i u m ions a r e f r e e i n the myoplasm.  The mere r e j e c t i o n o f the s o r p t i o n theory  of c o u r s e , remove the c r i t i c i s m s o f the membrane t h e o r y . will  be d i s c u s s e d  This  does n o t ,  These c r i t i c i s m s  f u r t h e r i n Chapter IX.  i n v e s t i g a t o r c e r t a i n l y does n o t a c c e p t the s o r p t i o n  but wishes to s t r e s s t h a t the advocates o f t h i s theory  theory,  have performed an  important function,, the  q u e s t i o n of  o f the  They have f o r c e d b i o l o g i s t s to examine more t h o r o u g h l y  ion a s s o c i a t i o n  in living  by  Eisenman  (34,  35)  and  Ling  t i v e m i c r o e l e c t r o d e s by Hinke (36) resonance t e c h n i q u e by Cope (37) for  the  The  r e s u l t s of  but  The  t h e o r e t i c a l aspects  a s s o c i a t i o n of the a l k a l i metal c a t i o n s w i t h v a r i o u s  studied  of  cells.  first  time the b i n d i n g these s t u d i e s  (25).  and  has  The  anions have been  development of c a t i o n  sensi-  the a p p l i c a t i o n of a n u c l e a r magnetic  a l l o w e d b i o l o g i s t s to study d i r e c t l y  of sodium and  potassium i n l i v i n g  cells.  (5, 36-40) i n d i c a t e t h a t a s u b s t a n t i a l amount  i o n p a i r f o r m a t i o n does occur i n the myoplasm of s t r i a t e d muscle f i b e r s , that  i t i s sodium and  f i x e d charge system.  not  p o t a s s i u m which i s p r e f e r r e d  by  the b i o l o g i c a l  5 CHAPTER I I  PHYSICAL CHEMISTRY OF THE  BINDING OF WATER AND  THE  ALKALI METAL CATIONS  A. Water Introduction. s t r u c t u r e o f water and  T h i s s e c t i o n c o n s i s t s of a b r i e f r e v i e w o f the the e f f e c t s o f v a r i o u s s o l u t e s on t h i s  structure.  The p o s s i b l e e f f e c t s o f p r o t e i n s and membranes on the s t r u c t u r e of water i n the c y t o p l a s m o f a l i v i n g examining  c e l l w i l l be c o n s i d e r e d , as w i l l  these s t r u c t u r a l  The  the methods of  changes;  S t r u c t u r e of VJater.  The  s t r u c t u r e o f water was  first  cussed i n the modern c r y s t a l l o g r a p h i c sense by B e r n a l and Fowler 1933.  They p o s t u l a t e d t h a t e x t e n s i v e hydrogen bonding  (1) i n  occurs between water  m o l e c u l e s , and c o n s i d e r e d water as a d i s o r d e r e d s o l i d having an four co-ordinated structure.  dis-  irregular '  The view t h a t water i s merely a broken-down  form o f the i c e l a t t i c e , w i t h the l e n g t h of the hydrogen bonds i n c r e a s e d , i s supported by a g r e a t d e a l o f e x p e r i m e n t a l e v i d e n c e . evidence comes from X-ray (2) were the f i r s t c u l e has second  s c a t t e r i n g measurements  (2-8).  direct  Morgan and Warren  to show t h a t f o r s h o r t p e r i o d s o f time each water mole-  four nearest neighbours,  and,  a t temperatures  s e t o f twelve n e a r e s t n e i g h b o u r s .  e s t neighbours  The most  a r e found  The  below 30° C, a  d i s t a n c e a t which these near-  i s compatible w i t h the view t h a t water has  a  t e t r a h e d r a l s t r u c t u r e s i m i l a r to i c e .  I n 1957,  Frank and Wen  a l l y accepted model of water.  (9) p r e s e n t e d what i s now  They based  the most  gener-  t h e i r model on the h y p o t h e s i s  t h a t the f o r m a t i o n o f hydrogen bonds i n water i s a c o - o p e r a t i v e phenomenon. T h i s i s a r e a s o n a b l e h y p o t h e s i s because the hydrogen bond has a p a r t i a l  covalent  n a t u r e (10).  They argued t h a t when one hydrogen bond forms i n  water, the f o r m a t i o n o f n e i g h b o u r i n g bonds i s encouraged and s t a b i l i z e d . Similarly,  they argued t h a t when one bond i s broken by thermal a g i t a t i o n ,  the e n t i r e group o f minute  tends to break up.  "flickering  hydrogen-bonded  Thus,  they p i c t u r e water as c o n s i s t i n g  c l u s t e r s " o f i c e - l i k e groups surrounded by non-  m o l e c u l e s (11, F i g . 1 ) . They d i d n o t s p e c i f y the e x a c t  m o l e c u l a r arrangement w i t h i n these groups, but Nemethy and Scheraga (12, 13) made the r e a s o n a b l e assumption t h a t the t r i d y m i t e - l i k e s t r u c t u r e o f normal  ice I occurs frequently.  and Scheraga  On the b a s i s o f t h i s assumption Nemethy  (12, 13) made a d e t a i l e d s t a t i s t i c a l m e c h a n i c a l a n a l y s i s o f the  s t r u c t u r e o f water.  They concluded t h a t a t 20° C the average c l u s t e r con-  t a i n s about 60 m o l e c u l e s and t h a t a t t h i s temperature about 70% o f the water m o l e c u l e s a r e i n the c l u s t e r s . a t u r e i s lowered, and v i c e v e r s a .  These numbers i n c r e a s e  A minimal e s t i m a t e o f the l i f e  the c l u s t e r s can be made from e x p e r i m e n t a l d a t a . long enough t o be d e t e c t e d by X-ray -11 is,  about 10  The c l u s t e r s must e x i s t  (2) o r Raman (14, 15) t e c h n i q u e s ; t h a t  - 10  seconds.  I t i s more d i f f i c u l t  time o f the c l u s t e r s .  the d i e l e c t r i c r e l a x a t i o n time o f water  This  time o f  -12  e s t i m a t e o f the l i f e  clusters,  as the temper-  the l i f e  to make a maximal  I f , as Frank (16, 17)  i s e q u a l to the h a l f l i f e  time o f the c l u s t e r s i s 10 ^  believes, o f the  - 1 0 ~ ^ seconds ( 1 8 ) .  i s 100 t o 1000 times the p e r i o d o f a m o l e c u l a r v i b r a t i o n , hence the  c l u s t e r s have a m e a n i n g f u l It water e x i s t .  existence.  s h o u l d be s t r e s s e d Kavanau (19, pages  that many o t h e r models f o r the s t r u c t u r e o f 178-190),  i n a t e r s e and l u c i d manner d i s -  c u s s e s the "vacant l a t t i c e p o i n t " model o f F o r s l i n d (20, 2 1 ) , the "waterh y d r a t e " model o f P a u l i n g (24).  He a l s o l i s t s  (22, 23) and the " d i s t o r t e d bond" model of P o p l e  over a dozen reviews o f s t i l l  o t h e r models f o r the  s t r u c t u r e o f water.  None of these models w i l l  thesis, i t i s sufficient Also,  the f l i c k e r i n g  be d i s c u s s e d  For  this  to note t h a t pure water does have a s t r u c t u r e .  c u l s t e r model i s the most h i g h l y developed, and  to e x p l a i n a l l the e x p e r i m e n t a l data a v a i l a b l e . energy,  here.  The v a l u e s f o r the f r e e  e n t h a l p y and e n t r o p y c a l c u l a t e d by Nemathy and  agree v e r y w e l l w i t h the e x p e r i m e n t a l d a t a .  appears  Scheraga  (12,  13)  The v a l u e s they c a l c u l a t e d f o r  the heat c a p a c i t y agree r e a s o n a b l y w e l l w i t h the e x p e r i m e n t a l d a t a , as the c a l c u l a t e d curves f o r the r a d i a l d i s t r i b u t i o n f u n c t i o n . the d e n s i t y o f water a t 4° C may theory. and  The  t i o n of the model.  The maximum i n  q u a l i t a t i v e l y from  i n f r a r e d s t u d i e s of B u i j s and Choppin  i t is significant  The  temperature  p l a n a t i o n e x i s t s f o r the f a c t  (25) support the model,  dependence o f v i s c o s i t y (26)  Scheraga's  the energy  treatment  agrees  of the model.  An  ex-  of a c t i v a t i o n f o r s e l f d i f f u s i o n ,  flow, d i e l e c t r i c r e l a x a t i o n o r s t r u c t u r a l r e l a x a t i o n f o r excess  ultrasonic absorption  has a p p r o x i m a t e l y  terms o f the model, most o f the energy required  t o break down the i n i t i a l  reorient  the m o l e c u l e s .  the same v a l u e  (16, 17, 27).  o f a c t i v a t i o n f o r these p r o c e s s e s i s  s t r u c t u r e ; l i t t l e energy  F i n a l l y , one  In  i s required  can l o g i c a l l y e x p l a i n why  fact  leads to a d i s c u s s i o n of the e f f e c t o f s o l u t e s on the  to  non-polar  s o l u t e s enhance the i c e - l i k e n a t u r e of water i n terms o f t h i s model. last  the  t h a t these measurements were made a f t e r the formula-  extremely w e l l w i t h Nemethy and  viscous  a l s o be p r e d i c t e d  do  This  structure  o f water.  The sider f i r s t  E f f e c t o f Non-polar  o f Water.  Con-  the evidence t h a t the s t r u c t u r e of water i s enhanced when non-  p o l a r s o l u t e s are added. non-polar  S o l u t e s on the S t r u c t u r e  I f the s o l u t i o n r e s u l t i n g from the a d d i t i o n o f a  s o l u t e to water was  and e n t h a l p y to be z e r o ,  and  i d e a l , one would expect  the changes i n volume  the changes i n entropy and f r e e energy  to  c o r r e s p o n d to those f o r i d e a l m i x i n g .  F o r non-polar s o l u t e s , however, the  changes i n volume and e n t h a l p y are n e g a t i v e and  t h e r e i s a v e r y l a r g e nega-  t i v e excess entropy change over the entropy of i d e a l m i x i n g . a low s o l u b i l i t y .  Frank and Evans  T h i s l e a d s to  (28) e x p l a i n e d the n e g a t i v e e n t h a l p y and  excess n e g a t i v e entropy terms by p o s t u l a t i n g t h a t the non-polar  molecules  enhance the s t r u c t u r e o f water.  c l u s t e r s are  stabilized.  In o t h e r words, the f l i c k e r i n g  T h i s tends to be confirmed by the f a c t  the d i e l e c t r i c  relaxa-  t i o n time i s lengthened i n aqueous s o l u t i o n s o f non-polar m o l e c u l e s  Why  s h o u l d non-polar s o l u t e s s t a b i l i z e  Frank and Evans  t h e i r low p o l a r i z a b i l i t y , hency s t a b i l i z e (12, 13) and Scheraga  They argued  i n f l u e n c e s w e l l because  the s t r u c t u r e .  t h a t a water molecule  to i t .  one,  t h r e e or f o u r hydrogen  Nemethy and  i n pure water has f i v e energy  levels  These energy l e v e l s c o r r e s p o n d to molecules w i t h z e r o , bonds.  A molecule w i t h f o u r hydrogen  can a c c e p t a n o n - p o l a r molecule as a f i f t h n e i g h b o u r . level  of  (11) o f f e r e d a more p r e c i s e e x p l a n a t i o n .  available two,  clusters"?  (28) o f f e r e d the r a t h e r h e u r i s t i c e x p l a n a t i o n that n o n - p o l a r  s o l u t e s do not t r a n s m i t d i s r u p t i v e e l e c t r i c a l  Scheraga  the " f l i c k e r i n g  (16).  i s lowered because  Thus, t h i s  bonds  energy  o f the van der Waals energy o f i n t e r a c t i o n .  An  unbonded water m o l e c u l e , on the o t h e r hand, a l r e a d y has a h i g h c o - o r d i n a t i o n number and can a c q u i r e a non-polar neighbour water m o l e c u l e .  o n l y a t the expense o f a  This implies that a d i p o l e - d i p o l e i n t e r a c t i o n w i l l  p l a c e d w i t h a much weaker van der Waals i n t e r a c t i o n . l e v e l f o r the unbonded water molecules increased. hydrogen  The  energy  Hence, the  l e v e l s f o r molecules  involved  bonds are r a i s e d f o r the same r e a s o n  i s apparent  energy  i n contact with non-polar solutes i s i n one,  (11, F i g . 8 ) .  d i s t r i b u t i o n o f the water molecules between the 5 energy it  be r e -  two  or t h r e e  I f a Boltzmann  levels  i s assumed,  that the a d d i t i o n of non-polar s o l u t e s to water s h i f t s more  molecules  i n t o the lower  polar solute f i l l s cluster,  (four hydrogen  bonds) energy s t a t e .  S i n c e the  non-  a space which would be empty i n an o r d i n a r y i c e - l i k e  t h e r e i s a decrease i n volume.  c u l e s i n the f i r s t  The hydrogen  bonded water mole-  l a y e r s about a n o n - p o l a r s o l u t e are g e n e r a l l y known as  " i c e b e r g s " (28).  The E f f e c t £f Ions on the S t r u c t u r e of Water. e f f e c t on the s t r u c t u r e of water. c u l e s c l o s e to the i o n .  The  first  effect  Ions have a d u a l  i s on the water mole-  These are g e n e r a l l y regarded as b e i n g i m m o b i l i z e d ,  p o l a r i z e d and compressed by the i n t e r a c t i o n s of the d i p o l e moment w i t h the strong e l e c t r i c  of the i o n (1,  field  3, 9, 28, 29, 30, 3 1 ) .  The  term  " i m m o b i l i z e d " i m p l i e s t h a t the water molecules bound to c a t i o n s l i k e -8 or  l i t h i u m spend about  ions  (32).  -9  10  I t i s apparent  cesium  and  10  seconds  r e s p e c t i v e l y a t t a c h e d to the  t h a t the i o n imposes a d i f f e r e n t  on the c l o s e s t water molecules  type of o r d e r  than the o r d e r i n h e r e n t i n the normal  water.  N e v e r t h e l e s s , the i o n does i n c r e a s e the o r d e r o f these n e a r e s t neighbour water m o l e c u l e s .  One would expect the o r d e r i n g e f f e c t  s m a l l and m u l t i v a l e n t  ions.  Much e x p e r i m e n t a l evidence supports the  t h a t s m a l l ions i n c r e a s e the n e t o r d e r of water. e v i d e n c e i s the f a c t (33). (28),  t o be g r e a t e s t f o r  that s a l t s  Perhaps  the most  idea  direct  l i k e L i F i n c r e a s e the v i s c o s i t y of water  Other e v i d e n c e comes from measurements of the e n t r o p i e s o f h y d r a t i o n apparent m o l a l heat c a p a c i t i e s  (34) and the temperature  dependence of  the l i m i t i n g d i f f u s i o n c o n s t a n t (35). A m a n i f e s t a t i o n o f the d u a l e f f e c t of ions on water i s the t h a t monovalent c a t i o n s l a r g e r than p o t a s s i u m s t r u c t u r e of water.  (and most anions) d i s r u p t  They decrease the v i s c o s i t y of water  l o s s which o c c u r s when a KC1  molecule  fact  i s dissolved  (33).  The  the  entropy  i n water i s l e s s thaw  10 when two argon atoms a r e d i s s o l v e d , even though they both have the same electronic structure  (28, 36).  Other e v i d e n c e f o r the n e t s t r u c t u r e break-  i n g a c t i v i t y of l a r g e ions comes from measurements of the i o n m o b i l i t i e s ( 3 ) , measurements of the s e l f - d i f f u s i o n c o e f f i c i e n t of water i n e l e c t r o l y t e solutions  (35) and the f a c t l a r g e ions reduce the r e l a x a t i o n time f o r the  d i e l e c t r i c constant  (37).  The s t r u c t u r e b r e a k i n g i n terms o f the " f l i c k e r i n g  e f f e c t o f l a r g e r ions  c l u s t e r " model.  o r d e r e d water m o l e c u l e s about an i o n .  There e x i s t s - two r e g i o n s  these two s t a t e s o f competing and i n c o m p a t i b l e Thus, what i s o f t e n t r u e  istry.  The l a c k o f order  organize  water m o l e c u l e s beyond the f i r s t  Frank and Evans (38).  is itself  region  The s m a l l e r  ions  l a y e r o f water, hence t h e i r net Further  ( 3 ) , Frank and Wen  discussion  (9) and H a r r i s and O'Konski  The water which i s o r i e n t e d and bound by the e l e c t r i c as " s o f t i c e " , i n c o n t r a s t C  which i s used to d e s c r i b e  i n chem-  a c t i o n o f ions can be found i n the papers o f  (28), Gurney  i s often designated  between  i n a state of  i s true  e f f e c t o f the l a r g e r i o n s .  the s t r u c t u r e o f water s l i g h t l y .  of the s t r u c t u r e b r e a k i n g  region  o f the water m o l e c u l e s i n t h i s i n t e r m e d i a t e  the s t r u c t u r e b r e a k i n g  i s to enhance  order  in international politics  explains  effect  s p h e r i c a l l y symmetric  The b u f f e r zone, or i n t e r m e d i a t e  chaos.  of  I n the immediate v i c i n i t y o f the  i o n the water m o l e c u l e s a r e o r i e n t e d by the s t r o n g , f i e l d o f the i o n .  explained  F a r from the i o n there e x i s t s a  r e g i o n w i t h the s t r u c t u r e of normal water.  electric  is readily  the water o r g a n i z e d  The E f f e c t o f P r o t e i n s  to the term  f i e l d o f ions  "icebergs",  by n o n - p o l a r s o l u t e s .  and Membranes on the S t r u c t u r e  The s t r u c t u r e o f water w i l l a l s o be i n f l u e n c e d  of Water.  i f a solute contains  which can i n t e r a c t w i t h water m o l e c u l e s through the f o r m a t i o n  sites  o f hydrogen  11 bonds.  Hydrogen bonding w i l l occur  a t the p e p t i d e  linkages of proteins.  most, f o u r water m o l e c u l e s can be bound by each p e p t i d e amount o f i n t e r a c t i o n c o u l d o n l y occur t i d e l i n k a g e s a r e f r e e to i n t e r a c t .  i n unfolded  content  water b i n d i n g  o f the p r o t e i n s  I n an a - h e l i x ,  to the p e p t i d e  water bound d i r e c t l y  i s high  (39), but t h i s  p r o t e i n s , where the pepa l l o f the p e p t i d e  ages a r e i n v o l v e d i n the maintenance o f the m o l e c u l a r the a - h e l i x  group  At  structure.  link-  I n muscle  (40), hence n o t much d i r e c t  l i n k a g e s would be e x p e c t e d .  The amount o f  to macromolecules v i a i o n - d i p o l e , hydrogen bonds and  the weaker d i p o l e - d i p o l e i n t e r a c t i o n s may thus be expected to be s m a l l . T h i s does n o t mean, however, t h a t these macromolecules do not o r g a n i z e  rela-  t i v e l y l a r g e amounts o f water. /  The tails  c o n s i d e r a t i o n o f the o r g a n i z a t i o n o f water about a p r o t e i n en-  the c o n s i d e r a t i o n o f the geometry o f the p r o t e i n , and how i t w i l l f i t  i n t o the water l a t t i c e .  For example, Berendsen and M i g c h e l s e n note t h a t  "Backbone s t r u c t u r e s a b l e to form H-bonds t o water w i l l have s t r u c t u r e breaking  or structure-promoting  hydrogen-bonding s i t e s .  e f f e c t s , depending on the geometry o f the  I f the geometry i s such t h a t the s i t e s ,  water may be bound, form an a r r a y f i t t i n g promoting i n f l u e n c e i s to be e x p e c t e d . l a r water s t r u c t u r e s c o u l d be f i t t e d  t o an i c e - I s t r u c t u r e , a s t r u c t u r e -  The same may be t r u e i f other  to the hydrogen bonding s i t e s .  h y d r o p h o b i c backbones s i m i l a r e f f e c t s might occur repeat  i n a pattern f i t t i n g  stronger  i f short polar  t o a r e g u l a r water l a t t i c e .  f o r r i g i d backbones or s i d e c h a i n s . "  of a molecule with  such a s t r u c t u r e .  o f water  (42).  reguWith  side-chains  The e f f e c t s w i l l be  (41). Collagen  The a x i a l l y r e p e a t i n g  t h r e e f o l d h e l i x i s e x a c t l y s i x times the expected r e p e a t i n g m o l e c u l e s i n chains  to which  i s an example  d i s t a n c e o f the distance of  Thus, one would expect c o l l a g e n to o r -  g a n i z e water, and NMR s t u d i e s i n d i c a t e t h a t chains  o f water molecules a r e .  12 formed i n the f i b e r d i r e c t i o n  Water may  (41, 43).  a l s o be o r i e n t e d a t the i n t e r f a c e s of extended s u r f a c e s ,  and t h e r e i s some e v i d e n c e t h a t these s u r f a c e zones are tens and hundreds of m o l e c u l e s deep r a t h e r than monomolecular lattice  as commonly assumed.  i n a c l a y c r y s t a l , f o r example, appears to a c q u i r e an  The water  increased  o r d e r and r i g i d i t y a t d i s t a n c e s of up to 300 X away from the s u r f a c e o f the clay  (44, 2 1 ) .  The e x t e n t to which water i s o r g a n i z e d about most p r o t e i n s and b i o l o g i c a l membranes i s s t i l l  unknown.  Initial  d i e l e c t r i c , and NMR  measure-  ments on macromolecular s o l u t i o n s supported the concept t h a t water i s immobilized  into  t h i c k , i c e - l i k e h y d r a t i o n c r u s t s f o r l a r g e d i s t a n c e s away  from macromolecules r e c o g n i t i o n that  (45, 46).  Improvements i n the NMR  t e c h n i q u e and a  the d i e l e c t r i c p r o p e r t i e s o f macromolecules c o u l d  largely  be e x p l a i n e d i n terms o f the p o l a r i z a t i o n o f the d i f f u s e double l a y e r , howe v e r , have l a r g e l y  i n v a l i d a t e d the concept of long range i m m o b i l i z a t i o n ; on  the o t h e r hand, most r e c e n t NMR  experiments do i n d i c a t e that the n e t time  which s o l v e n t water m o l e c u l e s spend i n a g i v e n o r i e n t a t i o n i s lengthened to v a r y i n g degrees i n s o l u t i o n s o f macromolecules a thorough l i t e r a t u r e s e a r c h , Kavanau  (19, pages 207 - 217) .  After  concluded t h a t b i o l o g i c a l membranes  and macromolecules "are encased i n a t h i n c r u s t o f bound water m o l e c u l e s a t l e a s t one m o l e c u l e t h i c k "  (19, page 217).  The S t a t e of Water  i n the L i v i n g C e l l .  used above, i s r a t h e r ambiguous. are now  interested  The term "bound water", as  As noted i n Chapter I , many i n v e s t i g a t o r s  i n the f r a c t i o n of "bound water" i n the l i v i n g  each seems to have h i s own  d e f i n i t i o n of the term.  d e f i n e d by the t e c h n i q u e u t i l i z e d  cell,  but  I n p r a c t i c e , the term i s  to measure the f r a c t i o n o f "bound water".  13 This  i s apparent i f one  considers  t h a t the v a l u e s  obtained  "bound" to a g i v e n p r o t e i n by d i f f e r e n t techniques are different  t h e s i s , the  o f water i n the c e l l  other  quite  I t should  term "bound water" w i l l r e f e r to the f r a c t i o n  unavailable be  to a c t as s o l v e n t  states.  f o r the  s t r e s s e d that t h i s d e f i n i t i o n  d e f i n i t i o n s a v a i l a b l e at present  t h a t water i n a l i v i n g two  themselves  (47).  In t h i s  solutes.  f o r the water  cell  and  intracellular  i s as a r b i t r a r y as  t h a t i t i s not meant to  i s p h y s i c a l l y p a r t i t i o n e d between two  the  imply and  In s p i t e of the a r b i t r a r y n a t u r e of the d e f i n i t i o n , an  only accurate  measurement o f the f r a c t i o n of "bound w a t e r " i s important because of i t s relevance  to the o s m o t i c , p e r m e a b i l i t y  and  t r a n s p o r t measurements  typically  made by p h y s i o l o g i s t s .  It will  seems u n l i k e l y t h a t NMR  y i e l d much i n f o r m a t i o n  i z a t i o n and  quantity  knowledge of the If  the  ference  be  m o l e c u l e s and self  synonymous.  can be measured d i r e c t l y .  f r e e and  free concentration may  or d e s o r p t i o n  (49)  measurements  about t h i s f r a c t i o n of "bound x-jater", f o r organ-  s o l u t e e x c l u s i o n are not  however, t h i s  (48)  t o t a l concentrations i s greater  than the  In terms of the  A l l that i s required  o f the  s o l u t e i n the  t o t a l concentration,  is a  cell. the  dif-  a t t r i b u t e d to the " b i n d i n g " of water, presumably to macromembranes.  i s n e i t h e r bound nor  Defined the n a t u r e of the  I t must o f course be assumed t h a t the compartmentalized w i t h i n  the  solute i t -  cell.  i n t h i s manner, the f r a c t i o n of "bound w a t e r " depends  on  s o l u t e as w e l l as on the  A  s t a t e of water i n the c e l l .  s m a l l , p o l a r s o l u t e l i k e u r e a , which i s c a p a b l e of forming s t r o n g bonds, xjould be water.  definition,  expected to be  s o l u b l e i n almost a l l o f the  C o n v e r s e l y , a l a r g e , n o n - p o l a r molecule would be  hydrogen  intracellular  expected to be  ex-  14 e l u d e d from most of the o r g a n i z e d water i n the c e l l .  I t would even be  dangerous to assume t h a t a l l the i o n i c s p e c i e s make use o f the same f r a c t i o n of  water.  sium  I c e I , f o r example, i s known to exclude sodium more than p o t a s -  (50).  As p o t a s s i u m  i s the major c a t i o n i n muscle f i b e r s , a knowledge o f  the f r a c t i o n o f water u n a v a i l a b l e to a c t as s o l v e n t f o r t h i s special  importance.  potassium  The  ion i s of  development of g l a s s m i c r o e l e c t r o d e s s e n s i t i v e to  (51) made p o s s i b l e a d i r e c t measurement of the a c t i v i t y o f p o t a s -  sium i n the myoplasm o f a l a r g e s i n g l e muscle f i b e r  (52, 53).  When these  measurements were coupled w i t h a c c u r a t e measurements of the t o t a l t i o n of potassium  i n the same s i n g l e muscle f i b e r , an e s t i m a t e of the  t i o n of "bound water" i n the c e l l  c o u l d be made.  To foreshadow the  which are d i s c u s s e d i n the f o l l o w i n g c h a p t e r s , i t may and V i n o g r a d  the T-4  B.  results,  s o l u t i o n which  From t h e i r d e n s i t y g r a d i e n t s t u d i e s ,  t h a t a r e g i o n c o n s i s t i n g of f o u r l a y e r s o f water molecules  b a c t e r i o p h a g e DNA  tungstate  salt.  molecule  frac-  be noted t h a t H e a r s t  (54, 55) measured the f r a c t i o n of water i n a DNA  e x c l u d e d an a l k a l i metal concluded  concentra-  c o m p l e t e l y excluded a l i t h i u m  they about  silico-  salt.  The A l k a l i M e t a l C a t i o n s  Introduction. a l k a l i metal cules.  c a t i o n s can form i o n p a i r s w i t h charged  First,  change r e s i n s  T h i s s e c t i o n i s concerned w i t h evidence  b r i e f l y discussed.  Finally,  Next two  i o n ex-  t h e o r i e s o f c a t i o n s e l e c t i v i t y are  the evidence  complexes w i t h p r o t e i n s i s a p p r a i s e d .  the  groups on macromole-  the b i n d i n g of these ions to p o l y e l e c t r o l y t e s and i s considered.  that  that the a l k a l i metal  c a t i o n s form  pair  Before any d i s c u s s i o n can commence, the d e f i n i t i o n o f an i o n must be c o n s i d e r e d . but  i s s u f f i c i e n t l y a b s t r u s e to warrant comment.  ions a r e s m a l l o r h i g h l y charged electrical attraction will pair w i l l (56)  water",  The term i s n o t as ambiguous as the term "bound  I f two o p p o s i t e l y charged  and a l s o c l o s e t o g e t h e r , the energy of the  be g r e a t e r than the thermal  energy, and the i o n  s u r v i v e a number of c o l l i s i o n s w i t h s o l v e n t m o l e c u l e s .  Bjerrum  i n v e s t i g a t e d the problem o f e x a c t l y how c l o s e a g i v e n p a i r o f ions must  be b e f o r e they may be c o n s i d e r e d an i o n p a i r . e f f e c t of i o n p a i r formation  He concluded  i s best represented  average  t h a t the  i f two ions a r e c o n s i d e r e d  to form an i o n p a i r when they come, c l o s e r t o g e t h e r  than a d i s t a n c e  2 r  .  = (z z q )/(2DkT).  I n the d e f i n i t i o n , z  on the i o n s , q the e l e c t r o n i c charge,  and z  r e p r e s e n t the charges  D the d i e l e c t r i c c o n s t a n t , k Boltzmann'  c o n s t a n t and T the a b s o l u t e temperature. t r i c p o t e n t i a l energy i s equal t o 2kT.  A t t h i s d i s t a n c e the mutual  elec-  The d i s t a n c e was chosen because the,  p r o b a b i l i t y o f f i n d i n g an o p p o s i t e l y charged i o n about any g i v e n i o n has a minimum a t r . . Robinson and Stokes (57, Chapter 14) d i s c u s s b r i e f l y the mm mathematical b a s i s o f t h i s d e f i n i t i o n .  Monovalent e l e c t r o l y t e s  aqueous s o l u t i o n a t 25° C have a v a l u e of r . mm n  = 3.57 X.  o f the r a d i i of the ions o f a monovalent e l e c t r o l y t e i o n p a i r f o r m a t i o n w i l l occur  to a c e r t a i n e x t e n t .  v a l e n t e l e c t r o l y t e have diameters  i n an  Thus, i f the sum »  i s less  than t h i s  value-,  I f the i o n s o f a mono-  g r e a t e r than t h i s v a l u e , some form o f the  Debye-HUckel theory s h o u l d be v a l i d .  S e v e r a l c r i t i c i s m s have been made o f Bjerrum's t h e o r y , but o n l y f;. need be noted here  (58).  The f i r s t  criticism  i s t h a t the t h e o r y counts as  i o n p a i r s some i o n s which a r e n o t i n p h y s i c a l c o n t a c t , and as Bjerrum s e l f notes,  "this definition  i s rather arbitrary"  (56).  The second  him-  critic!'"  i s t h a t the d i s t a n c e o f c l o s e s t approach o f the ions p r e d i c t e d from the  16 Bjerrum theory p a i r can of  v a r i e s from s o l v e n t  contain  to s o l v e n t .  s o l v e n t molecules between the  improvements to B j e r r u m s d e f i n i t i o n and 1  p a i r s may  be  found i n a book by R i c e and  P o l y e l e c t r o l y t e s and cations  form no  strong  s m a l l m o l e c u l e s and  the a l k a l i m e t a l c a t i o n s lytes containing  and  (59,  ion  discussion  d e f i n i t i o n s of  ion  pages 441-446).  The  a l k a l i metal  complexes w i t h most common  the complexes formed w i t h (61).  or phosphate m o i e t i e s  slight.  t h a t an  A brief  uranyl d i a c e t i c acid  with carboxyl  i s c e r t a i n l y very  ions.  of other  Nagasawa  implies  the A l k a l i M e t a l C a t i o n s .  E x c e p t i o n s are  c h e l a t i n g agents l i k e EDTA (60)  molecules  two  or even m o d e r a t e l y s t r o n g  ions.  of ion p a i r formation  This  I t might t h e r e f o r e  The  on other  be  strong extent small  suspected  that  are e s s e n t i a l l y f r e e i n a s o l u t i o n of p o l y e l e c t r o -  carboxyl  or phosphate groups.  Under c e r t a i n c o n d i t i o n s ,  however, e x a c t l y the converse i s t r u e .  The  b e s t known method of d e t e r m i n i n g the extent  t h a t o f measuring the ions using  transference  radioactive tracers  polycarboxylic acid)  of i o n b i n d i n g  numbers of the p o l y i o n s  (62).  and  the  is  counter-  Measurements on p o l y a c r y l i c a c i d  (a  demonstrated that i n a 0.0151 N s o l u t i o n a t 507o  n e u t r a l i z a t i o n about 507 of the sodium i n the o  p e r c e n t a g e of sodium ions bound was  system was  bound  (62) .  The  a f u n c t i o n of the degree of n e u t r a l -  i z a t i o n of the p o l y e l e c t r o l y t e .  A d i f f u s i o n method f o r d e t e r m i n i n g the amount of c o u n t e r i o n i n g by p o l y e l e c t r o l y t e s was The  a l s o developed by W a l l and  theoretical basis for this  pages 121-122) .  technique i s g i v e n  be  i n d e t a i l by Crank  I t must be assumed t h a t the p r o c e s s of i o n p a i r  proceeds q u i c k l y compared to d i f f u s i o n . may  h i s coworkers  assumed to e x i s t between the  If this  f r e e and  i s so,  local  bind(62). (63,  formation  equilibrium  the bound components.  For  17 s i m p l i c i t y , a linear adsorption c e n t r a t i o n o f the portional  immobilized  i s o t h e r m may  substance, S,  be assumed.  That i s , the  i s assumed to be d i r e c t l y  to the c o n c e n t r a t i o n of the substance f r e e to d i f f u s e ,  conpro-  C.  S = RC where R i s a c o n s t a n t . equation  [1] Other cases  f o r d i f f u s i o n i n one  a l l o w f o r a d s o r p t i o n , and  dimension  2  2  the d i f f u s i o n c o e f f i c i e n t , D,  s u b s t i t u t e d i n t o Eqn.  ( F i c k ' s Law)  The  i s then m o d i f i e d  - dS/dt  [2]  i s assumed to be  constant.  Eqn.  [1] may  + 1)  * d C/dx 2  be  [3]  2  which i s the normal form o f the d i f f u s i o n e q u a t i o n w i t h D r e p l a c e d +1).  to  [2] to y i e l d  dC/dt = D/(R  D/(R  usual  becomes  dC/dt = D d C / d x if  a r e d i s c u s s e d by Crank (63).  by  Thus, the e x t e n t o f b i n d i n g can be c a l c u l a t e d from a measurement  o f the s e l f d i f f u s i o n c o e f f i c i e n t . a c r y l i c a c i d c a l c u l a t e d by  amount of sodium bound to p o l y -  t h i s technique  to the amount c a l c u l a t e d by the  The  The  was  found to be almost  t r a n s f e r e n c e number technique  v i s c o s i t y , osmotic p r e s s u r e ,  t u r b i d i t y and  identical  (62).  electrophoresis  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 s o l u t i o n depend on the e f f e c t i v e on the m a c r o i o n .  Thus, measurements of these parameters may  i n f o r m a t i o n about the extent h i s coworkers  of i o n b i n d i n g  (64-70, see e s p e c i a l l y 65,  yield  i n the s o l u t i o n .  p h o r e s i s and membrane e q u i l i b r i u m techniques  to determine that the  o f the a l k a l i m e t a l c a t i o n s to polyphosphates i n c r e a s e s  i n the  valuable  Strauss  68-70), f o r example, used  charge  and  electrobinding  order  Li>Na>K.  The  s e l e c t i v i t y w i t h which the a l k a l i m e t a l c a t i o n s are bound i s  18 i n t e r e s t i n g , but i t i s the magnitude o f the b i n d i n g t h a t i s r e a l l y ing.  surpris-  The e x t e n s i v e b i n d i n g of the a l k a l i metal c a t i o n s i s of course  t i a l l y due to the h i g h n e g a t i v e  par-  charge on the p o l y i o n , which enhances the  c o n c e n t r a t i o n o f c a t i o n s i n the double l a y e r surrounding  i t . A correction  f o r t h i s f a c t o r may be a p p l i e d by c o n s i d e r i n g the c o r r e c t e d a s s o c i a t i o n constant K = [MP]/[P][M] where [MP] r e p r e s e n t s  [4]  e f f  the c o n c e n t r a t i o n o f the i o n p a i r s ,  t i o n o f the f r e e s i t e s on the p o l y i o n and [M] of the c a t i o n M near the polymer c h a i n . Boltzmann  [P] the c o n c e n t r a -  the e f f e c t i v e  This concentration  concentration  i s g i v e n by the  relation [M]  e f f  where [M] r e p r e s e n t s  = [M] expC-q^/kT)  [5]  the c a t i c n c o n c e n t r a t i o n f a r from the polymer c h a i n , q  the charge on the c a t i o n , k the Boltzmann c o n s t a n t ,  T the a b s o l u t e  tempera-  t u r e and Y the e l e c t r o s t a t i c p o t e n t i a l a t the s u r f a c e of the p o l y e l e c t r o lyte.  (To a p p l y  this  correction,V  must be assumed to equal  the z e t a poten-  t i a l , which may be c a l c u l a t e d from the e l e c t r o p h o r e t i c m o b i l i t y . ) a c o r r e c t i o n f o r the Boltzmann f a c t o r , the e x t e n t o f b i n d i n g high.  The a s s o c i a t i o n c o n s t a n t s  Even w i t h  i s extremely  f o r the phosphate p o l y i o n s and the a l k a l i  m e t a l c a t i o n s range from about 1 to 5 m o l e s " \  The  experiments o f S t r a u s s argue a g a i n s t  the e a r l i e r  concept t h a t  ions a r e a t t r a c t e d to a p o l y i o n merely because o f i t s h i g h n e t charge (71) and  a r e trapped  i n a r e g i o n where  ion p a i r formation and Nagasawa  occurs  ( 5 9 , pages  \qV/kTl>l.  A d d i t i o n a l evidence  that  true  i n p o l y e l e c t r o l y t e s o l u t i o n s i s d i s c u s s e d by R i c e  450-455).  I t was  noted above t h a t the p o l y m e r i z a t i o n  of phosphate or  y l a t e monomers i n t o a p o l y e l e c t r o l y t e enhances the b i n d i n g metal cations  to these m o i e t i e s .  phenomenon has  I t i s i n t e r e s t i n g t h a t an  form m i c e l l e s a t a c r i t i c a l  (72), the number of anions bound to these c a t i o n s T h i s phenomenon has  Studies  been d i s c u s s e d  on  the b i n d i n g  t h e o r e t i c a l i n t e r e s t , but  of ions  direct biological  analagous  in a living  s p a t i a l l y f i x e d , and  When  concentration  the  c e l l are not  Thus, i t i s l o g i c a l  metal cations  to s p a t i a l l y  l e a s t of these reasons i s the  f r e e i n s o l u t i o n , but more or  to i n v e s t i g a t e the b i n d i n g  f i x e d and  these little  i n a muscle f i b e r a t l e a s t , c r o s s - l i n k e d to a  h i g h degree.  great  the r e s u l t s of  s e l e c t i v i t y of b i n d i n g ) are of  Not  (73).  (74).  to p o l y e l e c t r o l y t e s are of  t h e r e are many reasons why  significance.  alkali  i s markedly enhanced  i n some d e t a i l by L i n g  (the observed magnitude and  the p r o t e i n s  the  been known to c o l l o i d chemists f o r over 30 y e a r s .  c e r t a i n p a r a f f i n chain cations  studies  of  carbox-  fact  less fairly  of the  alkali  cross-linked polyelectrolytes; ion  exchange r e s i n s .  Ion Exchange R e s i n s and change r e s i n , two q u a n t i t i e s , but changer A and  (75).  sented by  the  ions g e n e r a l l y exchange w i t h one  they are not The  B, p r e s e n t  the A l k a l i M e t a l C a t i o n s .  generally held equally  ex-  s t r o n g l y by  the  ex-  monovalent c a t i o n s ,  the exchanger phase, may  be  repre-  equation A + B  A + B  [6]  where the bars denote the exchanger phase. coefficient, K  ion  another i n s t o i c h i o m e t r i c  s t o i c h i o m e t r i c exchange between two  i n both the aqueous and  In an  ,  may  then be d e f i n e d  as  The  equilibrium  selectivity  20  where X. and X„ r e p r e s e n t the e q u i v a l e n t f r a c t i o n s of the c o u n t e r i o n s i n the A B exchanger and X. and X r e p r e s e n t the e q u i v a l e n t f r a c t i o n s o f these A B the s o l u t i o n either  (75).  I t i s apparent  ions i n  t h a t i f both c o u n t e r i o n s are monovalent,  the molar or m o l a l c o n c e n t r a t i o n s of the i o n s i n the exchanger o r  s o l u t i o n phase c o u l d have been used i n Eqn. q u a n t i t i e s appears.  the  [ 7 ] , s i n c e o n l y the r a t i o of  I f the a c t i v i t y c o e f f i c i e n t s of the two  s o l u t i o n phase are d i f f e r e n t , a c o r r e c t i o n may  the  ions i n the  be a p p l i e d by m u l t i p l y i n g the  s e l e c t i v i t y c o e f f i c i e n t by the r a t i o of the a c t i v i t y c o e f f i c i e n t s ,  (^/^g)-  t  Thus, the c o r r e c t e d s e l e c t i v i t y c o e f f i c i e n t , K^y^,  v^ww  i s d e f i n e d as  ••  Both the o r d e r i n which a r e s i n s e l e c t s the a l k a l i metal and  the magnitude o f the s e l e c t i v i t y depend on s e v e r a l f a c t o r s .  important  appear to be  the n a t u r e of the a n i o n i c s i t e ,  degree, of c r o s s - l i n k i n g of the r e s i n and two  ions i n the r e s i n .  The  The  e f f e c t of the n a t u r e  cussed and  s o l u t i o n , and  first,  and  most  the s t r u c t u r e and  s p e c i f i c c a p a c i t y o f the r e s i n  the temperature may  also affect  be l i m i t e d  the  (the number of  the i o n i c s t r e n g t h of  of the a n i o n i c s i t e on  the d i s c u s s i o n w i l l  The  the r e l a t i v e c o n c e n t r a t i o n s o f  exchange groups per u n i t amount of exchanger), surrounding  cations  the  the  selectivity.  the s e l e c t i v i t y w i l l be  dis-  to three c a t i o n s ; L i , Na  K.  The magnitudes of the s e l e c t i v i t y c o e f f i c i e n t s of monosulfonated c r o s s - l i n k e d p o l y s t y r e n e r e s i n s f o r the above c a t i o n s v a r y w i t h the degree of c r o s s - l i n k i n g and changer, but  the r e l a t i v e c o n c e n t r a t i o n s o f the i o n s i n the  the o r d e r of s e l e c t i v i t y  i s K>Na>Li (75).  The  results  exobtained  21 on c a r b o x y l i c and The  order,  phosphonic r e s i n s are of g r e a t e r b i o l o g i c a l s i g n i f i c a n c e .  as w e l l as  the magnitude of the s e l e c t i v i t y o f a c a r b o x y l i c r e s i n  depends on s e v e r a l f a c t o r s .  I f , however, the r e s i n i s m o d e r a t e l y c r o s s -  l i n k e d , m a i n t a i n e d a t a n e u t r a l or a l k a l i n e pH are p r e s e n t select was  and  the  i n a p p r o x i m a t e l y the same c o n c e n t r a t i o n s  the c a t i o n s  i n the order Li>Na>K (76,  77).  two  competing  ions  i n the r e s i n , i t w i l l  T h i s order  of  selectivity  observed on c a r b o x y l i c r e s i n s w i t h three d i f f e r e n t types o f polymer  m a t r i x , d i f f e r e n t s p e c i f i c c a p a c i t i e s and (75).  The  ectivity  d i f f e r e n t degrees of c r o s s - l i n k i n g  importance of the a n i o n i c group i n the d e t e r m i n a t i o n  i s i l l u s t r a t e d by  p r e f e r s sodium to p o t a s s i u m  the f a c t t h a t no (75).  a l k a l i metal c a t i o n s  Below pH  e x i s t s m a i n l y i n the -P(OH)0~ i n s t e a d of the -RPO^ order  i s reversed,  The  p o t a s s i u m being  (78) have shown t h a t  neutral conditions, also prefer  i n the order Li>Wa>K.  sel-  s u l f o n i c r e s i n i s known which  Bregman and Murata  phosphonic r e s i n s , under a l k a l i n e and  o f the  the  6, when the r e s i n  form, the  p r e f e r r e d to sodium (76,  selectivity 78).  of  the  c a t i o n s on the s e l e c t i v i t y of a r e s i n i s sometimes q u i t e pronounced.  As  Bregman (76)  e f f e c t o f v a r i a t i o n s i n the r e l a t i v e c o n c e n t r a t i o n s  has  s t a t e d , "In g e n e r a l ,  c r o s s - l i n k i n g and has  f o r r e s i n s of a conventional  a p a i r of c a t i o n s which d i f f e r s i g n i f i c a n t l y  been found t h a t the a f f i n i t y f o r a c a t i o n i n c r e a s e s  i n the r e s i n phase d e c r e a s e s " . the s e l e c t i v i t y of the  c a r b o x y l i c and  a l k a l i metal c a t i o n s d i s c u s s e d ^Li/K  a  c  a  r  k°  x  v  This  as  in size, i t  i t s mole f r a c t i o n  statement i s c e r t a i n l y a p p l i c a b l e phosphonic r e s i n s f o r the  above (76,  77).  The  selectivity 0  by a f a c t o r o f about 5 as  the r e s i n d e c r e a s e s from .9 to  .2  (76).  to  three coefficient  1 i° r e s i n c r o s s - l i n k e d w i t h 15.47 d i v i n y l b e n z e n e  f o r example, i n c r e a s e s  degree o f  (DVB),  the mole f r a c t i o n o f L i i n  22 Variations ( u s u a l l y DVB)  i n the percentage of c r o s s - l i n k i n g agent i n a r e s i n  r e s u l t i n less predictable  changes i n the s e l e c t i v i t y than  variations  i n the mole f r a c t i o n o f a c a t i o n  increasing  the p e r c e n t a g e of c r o s s - l i n k i n g agent g e n e r a l l y  s e l e c t i v i t y o f the r e s i n  (75)„  In c a r b o x y l i c  tage o f c r o s s - l i n k i n g agent i n c r e a s e s  One carboxylic  K^/ic  ^  resins, u t  example, s e l e c t s  increases  increasing  ditions  the p e r c e n -  or e q u i v a l e n t l y ,  A carboxylic  the a l k a l i m e t a l c a t i o n s  the  r e s i n w i t h 6%  DVB,  i n the o r d e r Li>Na>K a t pH  the s e l e c t i v i t y of phosphonic r e s i n s  7.4  ( a = .2) (77).  i s r e v e r s e d under a c i d  con-  (76, 78).  Bregman (76) has d i s c u s s e d the e f f e c t s of i o n i c s t r e n g t h temperature on the s e l e c t i v i t y of a r e s i n and Reichenberg on the e f f e c t s o f v a r i a t i o n s  i n the s p e c i f i c c a p a c i t y .  work has been done on the e f f e c t o f v a r i a t i o n s deed, i t i s u n f o r t u n a t e , as Reichenberg  a l t h o u g h i t " i s o f the g r e a t e s t  importance  commented  Unfortunately,  (75) has s t a t e d ,  i n t h i s case) i s o f r e l a t i v e l y l i t t l e  (75) has  and  little  i n the l a t t e r parameter. I n -  s t a n d i n g o f s e l e c t i v i t y phenomenon w i t h monovalent ions cations  the  a f f e c t i n g the s e l e c t i v i t y o f  ( a = .85), but the o r d e r o f s e l e c t i v i t y i s r e v e r s e d a t pH 6.5 Similarly,  resins,  O^") •  decreases ^ / K  and phosphonic r e s i n s appears to be the pH, a, of the r e s i n .  In s u l f o n i c  a  o f the most important v a r i a b l e s  degree o f n e u t r a l i z a t i o n , for  i n the r e s i n .  that "the under(the a l k a l i metal  importance  technologically",  i n connection with b i o l o g i c a l  phenomenon".  Its lies  b i o l o g i c a l importance, from the p o i n t  i n the analogy between the. i n o r g a n i c ,  tems and the s p a t i a l l y f i x e d p r o t e i n s px-oteins e x t r a c t e d  from a c e l l may  o f view o f t h i s  thesis,  f i x e d charge, i o n exchange  i n the l i v i n g  cell.  sys-  A s o l u t i o n of  be c o n s i d e r e d to be analogous  to a p o l y -  23 electrolyte solution.  As both the number of c a t i o n s bound, and  the s e l e c -  t i v i t y w i t h which the p o l y e l e c t r o l y t e s b i n d these  c a t i o n s can be a l t e r e d  (and  c r o s s - l i n k i n g , one  not to  i n general  by charge f i x a t i o n and  expect the b i n d i n g c h a r a c t e r i s t i c s of e x t r a c t e d p r o t e i n s to be those  of p r o t e i n s i n the l i v i n g c e l l .  d i c a t e the ind  increased)  The  should  identical  t h e o r i e s d i s c u s s e d below i n -  importance of the s t r u c t u r e of a p r o t e i n i n d e t e r m i n i n g  i t s bind-  characteristics.  Theories  of C a t i o n S e l e c t i v i t y .  to e x p l a i n the s e l e c t i v i t y (79, 80).  The  of an  The  first  i o n exchange r e s i n was  b a s i c f a c t o r governing  s e l e c t i v i t y was  elastic  f o r c e s i n the r e s i n , which would oppose the  swell.  He  reasoned t h a t the c a t i o n w i t h  cause the l e a s t  "mechanistic"  attempt  made by Gregor  assumed to be  the  tendency o f the r e s i n  the s m a l l e s t h y d r a t e d  to  r a d i u s would  s w e l l i n g i n the r e s i n , hence be p r e f e r r e d i n the r e s i n phase.  T h i s l e d to the p r e d i c t i o n t h a t a r e s i n would s e l e c t the a l k a l i m e t a l cations valid  i n the o r d e r Cs>Rb>K>Na>Li, a s e l e c t i v i t y  f o r most s u l f o n a t e r e s i n s .  The  i n v a l i d because i t cannot a d e q u a t e l y reversals"  (75, page  The selectivity  o r d e r which i s  t h e o r y , however, now  appears to  e x p l a i n " c r o s s o v e r s " or  developed by Eisenman and h i s co-workers  t h e o r y , however, t h e r e  "selectivity  role  (81-84).  i n a theory In  this  (Kavanau (19, pages 224-248) may  be  consulted  f o r a b i o l o g i c a l l y o r i e n t e d review of the c u r r e n t concepts r e g a r d i n g  grounds even b e f o r e apparent.  of  i s no n e c e s s i t y to r e l y on the r a t h e r vague concept  ion radius.  h y d r a t i o n of i o n s . )  be  252).  h y d r a t i o n o f ions a l s o p l a y s an important  of the h y d r a t e d  indeed  Glueckauf the other  (85) had  the  c r i t i c i z e d Gregor's t h e o r y on  d i f f i c u l t i e s inherent  Eisenman's t h e o r y w i l l f i r s t be  these  i n Gregor's theory were  considered  i n r e l a t i o n to a  24 glass  (or r e s i n ) which completely excludes water.  The  exchange of a c a t i o n , I , i n i t i a l l y  a n i o n i c s i t e , X,  i n the g l a s s or r e s i n f o r another  d i l u t e s o l u t i o n may  ^  The  change f o r the p r o c e s s  to the s e l e c t i v i t y c o e f f i c i e n t of the g l a s s or r e s i n by Eqn. In K  T / T  I/J  (84,  change, i n the i d e a l case, i s [10]  •  [10]  where R and T have t h e i r u s u a l s i g n i f i c a n c e  (84, 75).  The  standard  change i n the exchange p r o c e s s w i l l depend mainly on two  free  factors;  d i f f e r e n c e i n the p a r t i a l m o l a l f r e e e n e r g i e s of h y d r a t i o n of the two in  the aqueous phase,  (.F^^  x  - P^  y d  aSS  the  ions  ) , and the d i f f e r e n c e i n the p a r t i a l  molal  «J  —slas s  f r e e e n e r g i e s of i n t e r a c t i o n of the c a t i o n s w i t h the g l a s s ,  tf ).  in a  [9]  standard f r e e energy  AF?. = -RT ij  energy  cation, J , i n i t i a l l y  XJ + I + £ F °  where A F ° ^ r e p r e s e n t s the s t a n d a r d f r e e energy  related  an  be r e p r e s e n t e d as  XI + J  see e q u a t i o n 8 ) .  i n combination w i t h  (F^  Thus AF?. =  (F^  The v a l u e s of the f i r s t  y d  - F  y d T  ) - (Pf  l a P S  - P  l a S S T  )  [11]  term i n p a r e n t h e s i s are known e x p e r i m e n t a l l y .  Nothing need be known about the exact manner i n which water i n t e r a c t s w i t h the i o n s .  V a l u e s are g i v e n i n Eisenman's paper  Eisenman p o i n t s out t h a t t h e r e a r e two v a l u e s f o r the second thermochemical  (84) r e f e r r e d to Cs.  independent  term i n p a r e n t h e s i s of Eqn.  methods of o b t a i n i n g [11]; a r a t h e r e m p i r i c a l ,  method, and a more t h e o r e t i c a l , atomic method.  Only  the  l a t t e r approach w i l l be c o n s i d e r e d h e r e .  If  the s i t e s on the g l a s s o r r e s i n are w i d e l y s e p a r a t e d , the f r e e  e n e r g i e s of i n t e r a c t i o n between a c a t i o n and an a n i o n i c s i t e w i l l be g i v e n  25 to a f i r s t a p p r o x i m a t i o n  where r  i.  by Coulomb's law f o r r i g i d  f  glass  =  _  3  2  2  /  (  r  i  +  f  glass  =  _  3  2  2  /  (  r  j  +  )  r  r  s i t e s and c o u n t e r i o n s ; ...[12]  j  [  1  3  ]  and r a r e the naked r a d i i o f the ions I and J , and r i s the J ~  " e q u i v a l e n t " r a d i u s o f the a n i o n i c s i t e  (84).  These two e q u a t i o n s ,  along  w i t h the known v a l u e s f o r the f r e e e n e r g i e s o f h y d r a t i o n o f the c a t i o n s may be s u b s t i t u t e d i n t o Eqn. [ 1 1 ] . f u n c t i o n o f one v a r i a b l e , r .  Values  o f A F ° ^ may then be p l o t t e d as a  T h i s generates  a series of s e l e c t i v i t y  (84, see F i g . 1 6 ) . I f the a n i o n i c s i t e s a r e v e r y c l o s e l y spaced,  orders  the f r e e  e n e r g i e s o f i n t e r a c t i o n w i l l be g i v e n by the f o l l o w i n g e q u a t i o n s ; -glass  f|  =  (  _322)/(  = 1.56 (-322) / (  l a S S  which a r e the Born-Lande e x p r e s s i o n s a l k a l i halide crystal of  lattice.  + _)  r i  ...[14]  r  r j  + r_)  [15]  f o r the i n t e r n a l f r e e e n e r g i e s o f an  The s u b s t i t u t i o n o f these e q u a t i o n s  instead  [12] and [13] i n t o Eqn. [11] and the p l o t t i n g o f the v a l u e s o f £F°..  against r  y i e l d s almost  The v a l u e o f r  the same s e l e c t i v i t y sequences  a t which a g i v e n s e l e c t i v i t y sequence i s observed,  i s s h i f t e d , and i t i s important d i r e c t i o n that  1  example, i f the r s e l e c t i v i t y , K^^,,  S  enhanced  to note  t h a t the s h i f t  (84, compare f i g u r e s  i n such a  o f the a n i o n i c s i t e s has a v a l u e which i m p l i e s t h a t the i s u n i t y when the s i t e s a r e i s o l a t e d ,  r e l a t i o n s h i p between r  i s large (r »  r^., r j ) .  the v a l u e o f K^j /£ a  occurs.  and the s e l e c t i v i t y may be made  c l e a r e r by a c o n s i d e r a t i o n o f two l i m i t i n g when r  occurs  however,  16 and 17) . F o r  w i l l be g r e a t e r than u n i t y o f o v e r l a p p i n g of the s i t e s  The  (84, see F i g . 1 7 ) .  cases.  Consider  first  the case  T h i s Eisenman terms a s i t e o f low f i e l d .  26 strength.  I r r e s p e c t i v e o f the r e l a t i v e s i z e s o f the two c a t i o n s , the second  term i n Eqn. [11] w i l l be s m a l l , and partial  free energies  of hydration.  the a l k a l i m e t a l c a t i o n s  will  The g l a s s o r r e s i n would then p r e f e r  i n the order  Cs>Rb>K>Na>Li  f i g u r e 16 o r 1 7 ) . C o n v e r s e l y , when r field  strength,  depend p r i m a r i l y on the  (84, see r i g h t o f e i t h e r  i s small, that i s , a s i t e of high  the second term i n Eqn. [11] w i l l predominate.  The g l a s s o r  r e s i n would then p r e f e r the c a t i o n w i t h the s m a l l e s t naked r a d i u s , Li>Wa>K>RbX;s values out  (84, see l e f t  of r , 9 other  o f e i t h e r f i g u r e 16 o r 1 7 ) . F o r  p o s s i b l e sequences a r e p r e d i c t e d .  that i s ,  intermediate  Thus, 11 sequences  o f a p o s s i b l e 5'. = 120 sequences a r e p r e d i c t e d by the t h e o r y .  These t h e o r e t i c a l p r e d i c t i o n s have been almost c o m p l e t e l y by experiments conducted on g l a s s e s of v a r y i n g  field  strengths).  w i l l n o t be d i s c u s s e d  here  of various  compositions  The e x p e r i m e n t a l c o n f i r m a t i o n  confirmed  (containing  sites  o f the t h e o r y  (83, 8 4 ) . I t need o n l y be noted t h a t " t h e  general  agreement between the t h e o r e t i c a l p r e d i c t i o n s and the e x p e r i m e n t a l  results  i s s u f f i c i e n t l y good to j u s t i f y  the o p i n i o n  that Eisenman's  theory  i s b a s i c a l l y sound" ( 7 5 ) .  The exclude water. the  above d i s c u s s i o n has been l i m i t e d to g l a s s e s  Eisenman i n v e s t i g a t e d t h e o r e t i c a l l y the e f f e c t o f water on  s e l e c t i v i t y of glasses  and r e s i n s by c o n s i d e r i n g  as analogous to a c o n c e n t r a t e d  s o l u t i o n of a strong  T h i s was e s s e n t i a l l y an e x t e n s i o n Meares  a water s w o l l e n  resin  e l e c t r o l y t e (83, 8 4 ) .  o f the i n v e s t i g a t i o n o f C r u i c k s h a n k and  ( 8 6 ) . Eisenman's "assumption t h a t the f r e e energy d a t a o f an aqueous  s o l u t i o n may be used t o r e p r e s e n t an  o r r e s i n s which  i o n exchange phase c o n t a i n i n g  appears d e b a t a b l e to t h i s  c o m p l e t e l y the s e l e c t i v i t y p r o p e r t i e s o f comparable amounts o f water" (83, page 313)  i n v e s t i g a t o r , b u t the c o n c l u s i o n he d e r i v e s  from  27 the a n a l y s i s i s a d e q u a t e l y concludes  supported  by e x p e r i m e n t a l  t h a t the main e f f e c t o f water s w e l l i n g w i l l  selectivity  (decreasing  e f f e c t on the  Support f o r t h i s c o n c l u s i o n comes from experiments  on b o t h g l a s s e s and r e s i n s .  The s e l e c t i v i t y  o f g l a s s e s which p r e f e r  sium to sodium passes through a maximum as the f i e l d  potas-  s t r e n g t h o f the s i t e s  lowered, whereas the t h e o r e t i c a l a n a l y s i s i n d i c a t e s the s e l e c t i v i t y  should be a monotonic f u n c t i o n o f f i e l d to an o b s e r v a b l e  The data o f Reichenberg  o f s u l f o n a t e r e s i n s i s a simple  o f water p e r exchange group. i n c r e a s e i n h y d r a t i o n leads  but does n o t change the o r d e r  the dependence of s e l e c t i v i t y  reasonable field  f u n c t i o n o f the average amount the c o n c l u s i o n t h a t  of s e l e c t i v i t y .  a t l e a s t a q u a l i t a t i v e e x p l a n a t i o n of  on the n a t u r e  o f the a n i o n i c s i t e .  The  o f the i o n exchange s i t e ( 8 4 ) .  should have a low r and v i c e v e r s a . —  a  (84, see  to a decrease i n the magnitude o f s e l e c t i v i t y ,  should be r e l a t e d to the pK  S i t e s w i t h a h i g h pK  the  (75) i n d i c a t e s t h a t the  T h i s r e s u l t a l s o supports  Eisenman's theory p e r m i t s  equivalent r  T h i s maximum corresponds  lowers the magnitude o f the s e l e c t i v i t y  r i g h t o f f i g u r e s 8 and 9 ) . selectivity  strength.  i n c r e a s e i n the h y d r a t i o n o f the g l a s s , hence supports  conclusion that hydration  an  Eisenman  be on the magnitude o f  i t ) and t h a t s w e l l i n g w i l l have l i t t l e  p a t t e r n of s e l e c t i v i t y .  is  evidence.  Thus  i tis  t h a t the s u l f o n i c r e s i n s (the s i t e s o f which have a low p K  a J  low  s t r e n g t h or low e q u i v a l e n t r ) p r e f e r the a l k a l i m e t a l c a t i o n s i n the  o r d e r K>Na>Li.  The pK  of the s i t e s on the other r e s i n s c o n s i d e r e d  in this  a chapter  i n c r e a s e i n the o r d e r -^(OH)©^,  selectivity  -C00~,  -PO^.  The magnitude o f  i s reduced i n -P(OH)C~ r e s i n s , the o r d e r o f s e l e c t i v i t y  reversed  i n -COO"  r e s i n s (they g e n e r a l l y p r e f e r Li>Na;>K.), and the magnitude o f t h i s  reversed  selectivity  enhanced i n -PC., r e s i n s i n agreement w i t h 1  the  theory.  28 Eisenman's theory was  created  specifically  to e x p l a i n the  t i v i t y c h a r a c t e r i s t i c s of c a t i o n s e l e c t i v e g l a s s e s , and s u c c e s s f u l i n doing t h i s .  As Reichenberg  d e t a i l e d p r e d i c t i o n s made on orders  the b a s i s of t h i s  d i c t e d by  the  reversal rather theory  p o l a r i z a t i o n and  discussed.  r e s p e c t s , but  (75).  other  This  The  i s perhaps not  theory  t h e o r i e s o f L i n g and  t h a t of the former was Ling,  of the a n i o n i c s i t e to be used a parameter he  on  the c a t i o n )  (74)  be  In c o n t r a s t  selectivity. r  of the a n i o n i c  that a u n i t negative  site. charge  ( e i t h e r towards or away from  polar  groups.  included He  the p o s s i b l e e f f e c t s o f a l s o assumed t h a t an i n -  found between the a n i o n and  this effect s t a t i s t i c a l l y .  The  the c a t i o n were b a l a n c e d a g a i n s t  significant  strength  i n d u c t i o n , m u l t i p o l e , p o l a r i z a t i o n and d i r e c t  t e g r a l number o f water m o l e c u l e s c o u l d be  of the  strength  moved  induced d i p o l e i n t e r a c t i o n s i n h i s a n a l y s i s .  between the a n i o n and  now  for a biologic-  (which i s s i m i l a r to the  the f i e l d  to Eisenman, L i n g  considered  pre-  theory.  the f i e l d  of prime importance i n d e t e r m i n i n g  the  i o n i c and  i n Eisenman's  s p e c i f i c a l l y formulated  thought of being  the  Eisenman are s i m i l a r i n many  termed a "c v a l u e "  to s i m u l a t e  e f f e c t s of o t h e r  c a t i o n , and  The  of c a t i o n s e l e c t i v i t y w i l l  c a l c u l a t e d i n A*, i s the d i s t a n c e  the a n i o n should  (one  selectivity  s u r p r i s i n g , because  l i k e Eisenman. c o n s i d e r e d  u t i l i z e d by Eisenman) to d e s c r i b e c value,  too  e f f e c t s have been ignored  f i x e d charge system.  This  about the  however,  than the cesium-potassium r e v e r s a l , as  Some f a c e t s of L i n g ' s  He  theory  out,  very  r e v e r s a l s i n c a r b o x y l i c r e s i n s , f o r example, commence w i t h  sodium-lithium  al  pointed  been  expected i n c a r b o x y l i c r e s i n s have been f a r l e s s s u c c e s s f u l .  selectivity  be  (75) has  has  selec-  latter  f o r c e s being  the  a t t r a c t i v e forces the r e p u l s i v e  Born r e p u l s i o n )  and  the  forces theory  29 was  developed i n one  the c a r b o x y l  sites  It  dimension.  The  correct value  o f the p o l a r i z a b i l i t y  i s not known, hence a number o f v a l u e s  i s s i g n i f i c a n t that Ling's  were  considered.  a n a l y s i s p r e d i c t s e x a c t l y the same  11 s e l e c t i v i t y sequences f o r the 5 a l k a l i m e t a l c a t i o n s as Eisenman's T h i s agreement, however, may  be  fortuitous.  Many of the  The  values  special attention, for Ling  values  f o r the p o l a r i z a b i l i t y of the c a r b o x y l  s e l e c t i v i t y orders.  values are  (87) n o t e d t h a t the use  Reichenberg  (75)  of d i f f e r e n t  groups would g e n e r a t e  comments t h a t the use  f o r the p o l a r i z a b i l i t y "comes c l o s e r to p r e d i c t i n g the  found e x p e r i m e n t a l l y "  An  equally  forces  t h a t L i n g used f o r the p o l a r i z a b i l i t y term have r e -  ceived  ent  theory.  terms i n L i n g ' s  b a s i c e q u a t i o n s are o n l y rough a p p r o x i m a t i o n s to the a c t u a l p h y s i c a l involved.  f o r c a r b o x y l i c r e s i n s of h i g h  important c r i t i c i s m of L i n g ' s  d i e t s the e n t r y of water i n t o an exchanger can crease  the s e l e c t i v i t y  resins  (75)  (74).  higher  sequences  i t pre-  i n c r e a s e , r a t h e r than  as d i s c u s s e d  above.  the c a t i o n s  f i x e d anions  (84)  deand  L i n g was  i n a b i o l o g i c a l f i x e d charge system are a s s o c i a t e d  (74), a h i g h l y dubious assumption.  i n t h i s manner to p r o v i d e t h a t the  living  able  a theoretical j u s t i f i c a t i o n for his  f o r p o t a s s i u m over sodium.  (74, page 220)  muscle f i b e r must be  about 300,  he admits t h a t no p h y s i c a l system i s known t h a t has  a greater  10.) (88).  Further  f°  r  a  c r i t i c i s m of L i n g ' s  theory  may  be  with  contention  i o n exchange r e s i n w i t h  an e x t r e m e l y h i g h s e l e c t i v i t y a  that  L i n g of c o u r s e , must argue  c e l l as a whole i s analogous to an  the ^ - ^ ^  that  capacity.  i s that  Experiments performed on g l a s s e s  contradict this conclusion,  of  specific  theory  differ-  to make t h i s p r e d i c t i o n because he assumed a t the s t a r t of h i s a n a l y s i s all  of  (According  to L i n g  even though ,  than  found i n a paper by Conway  30 There i s no system as an as  o b j e c t i o n to c o n s i d e r i n g  a membrane-free  i o n exchange r e s i n (and g l y c e r i n a t e d f i b e r s w i l l  such below), but  completely ignore  i t does seem u n r e a s o n a b l e , as L i n g has  the membrane s u r r o u n d i n g a l i v i n g  berg contends, "we  may  to a f i r s t  t i o n a l water as m e r e l y to  cell.  approximation, regard  'dilute'  be  considered  done (74),  to  I f , as R e i c h e n -  the e f f e c t of  the p r o c e s s e s g i v i n g r i s e  (75), i t would seem r e a s o n a b l e i n a l i v i n g c e l l  biological  to c o n s i d e r  to  addi-  selectivity"  the  proteins  ( i n c l u d i n g t h a t water of h y d r a t i o n which excludes a l k a l i metal c a t i o n s ) i o n exchange p a r t i c l e s immersed i n an aqueous s a l t seems e s p e c i a l l y d e s i r a b l e now o f sodium, p o t a s s i u m and proteins  and  the A l k a l i M e t a l C a t i o n s .  m o l e c u l e are a p p a r e n t . i t would be  f e r to b i n d of cations  impossible  theory) or the  c value  glutamic  s i t e s could  at a l l "  the  depend on the r  of p r o t e i n s  significant  pre-  to p r e d i c t the number  value  1  p r e f e r to b i n d K>Na and As  the pKs  l i e between these two  p r e f e r to b i n d  sites. that  of the a s p a r t i c  values  (89),  e i t h e r sodium or p o t a s s i u m .  a l k a l i metal c a t i o n s are  (90, page 591).  the  ( i n terms of Eisenman s  theory) of the c a r b o x y l i c  (pK = 1.5)  be noted, however, t h a t "the to most p r o t e i n s  to a b i o l o g i c a l macro-  equally d i f f i c u l t  ( i n terms o f L i n g ' s  conceivably  inherent  a c c e p t e d u n c r i t i c a l l y an e x i s t i n g  (pK = 6) p r e f e r to b i n d Na>K.  residues  difficulties  I t seems r e a s o n a b l e , however, to a c c e p t t h a t  noted that s u l f o n i c r e s i n s  carboxylic resins  should  activities  to p r e d i c t whether a g i v e n p r o t e i n would  sodium or potassium, and i t would b i n d .  The  of c a t i o n s e l e c t i v i t y  Even i f one  s e l e c t i v i t y of a p r o t e i n w i l l  and  measurements of the  approach  hydrogen i n the aqueous s o l u t i o n s u r r o u n d i n g  i n the a p p l i c a t i o n o f a t h e o r y  I t was  This  can be made.  Proteins  theory,  that accurate  solution.  as  the It  s c a r c e l y bound  Thus, i f a g i v e n p r o t e i n does b i n d  q u a n t i t i e s of the a l k a l i m e t a l c a t i o n s , i t may  be  expected  that  the o v e r l a p portance. on  and i n d u c t i o n e f f e c t s c o n s i d e r e d  by Eisenman and L i n g a r e o f im-  O v e r l a p e f f e c t s would be expected to depend much more  t h e secondary and t e r t i a r y s t r u c t u r e o f the p r o t e i n than  effects. cations  Some e x p e r i m e n t a l s t u d i e s on the b i n d i n g  induction  o f the a l k a l i metal  to e x t r a c t e d muscle p r o t e i n s w i l l now be d i s c u s s e d .  S z e n t - G y o r g y i n o t e d the e x t e n s i v e cations  critically  t o e x t r a c t e d myosin  myosin to b i n d  (91).  completely abolished  i s extremely l a b i l e .  c l u s i o n s may be made from these o b s e r v a t i o n s . cations  t e r t i a r y s t r u c t u r e o f the m o l e c u l e . of cations  to myosin i n the l i v i n g  measured on the e x t r a c t e d  metal  The b i n d i n g  o f myosin a t 0 ° f o r o n l y 24 h o u r s , and i s  by a thermal d e n a t u r a t i o n  the a b i l i t y o f myosin to b i n d  of the a l k a l i  Furthermore, he n o t e d t h a t the a b i l i t y o f  the a l k a l i metal c a t i o n s  decreases markedly a f t e r s t o r a g e  binding  o f the p r o t e i n . First,  Two con-  they i l l u s t r a t e  that  i s dependent on the secondary and Second, they i n d i c a t e t h a t  c e l l may be somewhat h i g h e r  p r o t e i n because o f d e n a t u r a t i o n  the b i n d i n g than t h a t  during  the e x t r a c -  t i o n procedure.  Lewis and S a r o f f  (92) made c a r e f u l measurements o f the b i n d i n g o f  sodium and p o t a s s i u m to a c t i n , myosin and actomyosin.  A l t h o u g h a c t i n and  myosin have s i m i l a r i s o e l e c t r i c p o i n t s and amino a c i d c o m p o s i t i o n s , i t was found t h a t a c t i n does n o t b i n d p o t a s s i u m ions but t h a t myosin b i n d s both sodium and p o t a s s i u m ions metal cations myosin.  quite strongly.  The maximum number o f a l k a l i  t h a t c o u l d be bound to myosin was about 50 moles/10^ g  A t a p h y s i o l o g i c a l pH o f about 7.3  Unfortunately,  Lewis and S a r o f f  (see Chapter V) and a f r e e  (92) were n o t as c a r e f u l i n d e s c r i b i n g  t h e i r experiments as they were i n p e r f o r m i n g them.  They i n i t i a l l y  defined  p o t a s s i u m c o n c e n t r a t i o n of 0.100 10^g o f myosin potassium.  (92).  M,  about 35 moles o f p o t a s s i u m are bound to  Myosin b i n d s sodium even more s t r o n g l y than i t b i n d s  A t a pH o f 7.7  and a temperature o f 5° C, the apparent a s s o c i a -  t i o n c o n s t a n t o f myosin f o r sodium f o r p o t a s s i u m (98 ± 11).  (225 ± 22) i s about twice t h a t o f myosin  These "anomalously h i g h a s s o c i a t i o n c o n s t a n t s f o r  the b i n d i n g o f Na and K t o myosin"  (92) and the f a c t the b i n d i n g depends on  the s t r u c t u r e o f the m o l e c u l e imply t h a t o v e r l a p e f f e c t s s h o u l d account f o r most of the b i n d i n g . s h o u l d enhance K,  ,  A c c o r d i n g to t h e o r y (84), the o v e r l a p p i n g o f s i t e s Thus, i t i s l o g i c a l  t h a t sodium i s bound more  as the "average number of p o t a s s i u m ions found per mole o f myosin" page 2115) .  I t i s apparent from f i g u r e s 1 and 2 i n t h e i r paper t h a t  a maximum v a l u e of about 50.  On page 2116,  Thus,  i t i s not c l e a r whether  4.2  mole of myosin) o r 10^ grams o f myosin o f a l k a l i metal c a t i o n s . interpretation. latter  Cope  XT'  has  however, (see T a b l e I I ) the max-  imum number o f ions bound per 10^g o f myosin 50.  (92  * 10^g  i s a l s o s t a t e d to be e q u a l to (the approximate weight o f one  i s c a p a b l e o f b i n d i n g about 50 moles  (93), f o r one,  i n i t i a l l y a c c e p t e d the former  A c a r e f u l r e a d i n g o f the paper, however, i n d i c a t e s t h a t the  interpretation i s correct.  Lewis and S a r o f f mention the m o l e c u l a r  weight o f myosin o n l y once i n t h e i r paper, and then o n l y when they d i s c u s s the c o m b i n a t i o n of a c t i n and myosin more, i n t h i s  (92) and a l a t e r paper  l y w i t h the f a c t myosin".  i n a p p r o x i m a t e l y molar r a t i o s . (94) they c o r r e l a t e  Cope ( p e r s o n a l communication)  myosin.  direct-  t h a t t h e r e are "15 h i s t i d i n e r e s i d u e s per 10^ grams o f has s i n c e agreed t h a t the r e s u l t s  of Lewis and S a r o f f i n d i c a t e t h a t 50 moles of  the r e s u l t s  Further-  o f c a t i o n s a r e bound per  10^g  33 s t r o n g l y than p o t a s s i u m to myosin.  (It i s also l o g i c a l  which, can  form a l k a l i metal c h e l a t e s  Li>Na>K.)  In a l a t e r paper, S a r o f f  binding  on pH,  and  (94) (94)  that small molecules  p r e f e r these c a t i o n s analyzed  concluded t h a t "the b i n d i n g  i n the  the dependence o f  of sodium and  order  the  potassium  ions  appears to i n v o l v e c a r b o x y l - a l k a l i m e t a l - i m i d a z o l e and c a r b o x y l - a l k a l i metal-amino c h e l a t e s " .  This conclusion  p o s s i b i l i t y t h a t other not  be  i s c e r t a i n l y r e a s o n a b l e , but  p a i r s of s i t e s c o u l d be  e x c l u d e d on  the b a s i s of the a v a i l a b l e e v i d e n c e .  I t may  i n t e r e s t to c a l c u l a t e r o u g h l y  binding  sites  of Lewis and  be of  i n the Saroff  living (92).  cell  weight  I t i s not  i n the  cell  of myosin  Thus, about 107>  s i t e s should  (92).  The  of the  living  be  the p h y s i o l o g i c a l pH o f  by  solid  sodium and  7.3  potassium  Saroff p r e d i c t that  of f i b e r water are bound to  p o t a s s i u m to muscle p r o t e i n s  considered.  This  system should  than d i l u t e s o l u t i o n s of e x t r a c t e d  g l y c e r i n a t e d f i b e r the p r o t e i n s are the s t r u c t u r e of the p r o t e i n s to t h a t of the p r o t e i n s  the  fiber.  b i n d i n g of sodium and  cell  At  Thus, the r e s u l t s of Lewis and  muscle  i n a t e d f i b e r s w i l l now  the  of the weight o f a  be a v a i l a b l e to b i n d  about 50 mMoles of a l k a l i metal c a t i o n s / K g myosin i n a b a r n a c l e  of  data  These f i b e r s c o n t a i n about 757> water  b a r n a c l e muscle f i b e r c o n s i s t s of myosin.  10^g  96)  unreasonable to assume t h a t 807, of the  is protein.  (Chapter V ) , about 40  from the  I t w i l l be assumed t h a t i t comprises 507, of  muscle f i b e r .  material  can-  the maximum number of  f o r the a l k a l i m e t a l c a t i o n s  p r o t e i n i n a barnacle (Chapter I V ) .  i n the b i n d i n g  Myosin comprises about 39-577* (95,  t o t a l p r o t e i n i n a muscle.  per  involved  the  in glycer-  be a b e t t e r model  proteins.  In a  s p a t i a l l y f i x e d i n such a manner t h a t  ( i n the  t h i c k and  thin filaments)  i n a l i v i n g muscle f i b e r .  Fenn  is similar  (97) e q u i l i b r a t e d  34 g l y c e r i n a t e d muscle  fibers  i n s o l u t i o n s containing equal c o n c e n t r a t i o n s of  sodium and potassium, then measured the c o n c e n t r a t i o n s o f these c a t i o n s i n muscle  fibers.  Two major c o n c l u s i o n s may be drawn from h i s d a t a . sodium  than p o t a s s i u m was accumulated  by the muscle  F i r s t , more  f i b e r s a t a l l the ex-  t e r n a l c o n c e n t r a t i o n s s t u d i e d , the p r e f e r e n c e f o r sodium over p o t a s s i u m b e i n g most marked a t the lower c o n c e n t r a t i o n s . S l i g h t l y more " b i n d i n g " o c c u r e d than would have been p r e d i c t e d from the r e s u l t s o f Lewis and S a r o f f (92), but Fenn c a u t i o n s t h a t " t h e d e t a i l e d and q u a n t i t a t i v e o f these f i g u r e s must await f u r t h e r experiments"  (97).  interpretation  The o t h e r  i n g f e a t u r e o f the d a t a i s the f a c t the number o f bound ions/Kg appears  muscle  t o pass through a maximum, then decrease as the e x t e r n a l c o n c e n t r a -  t i o n s o f the ions i s i n c r e a s e d . sidered  interest-  i n more d e t a i l  The s i g n i f i c a n c e o f t h i s t r e n d w i l l be con-  i n Chapter IX, but i t may be noted here t h a t  r e s u l t c o u l d be e x p l a i n e d i f a f r a c t i o n o f the water e x t r a c t e d muscle  fiber  this  i n the g l y c e r o l  i s u n a v a i l a b l e to a c t as s o l v e n t f o r the a l k a l i  metal  cations.  One  f i n a l p o i n t may be made about  t r a c t i l e p r o t e i n s i n the l i v i n g  cell.  the b i n d i n g of ions to the con-  I t would be na'ive n o t to expect the  b i n d i n g o f o t h e r charged s p e c i e s to i n f l u e n c e the b i n d i n g o f the a l k a l i metal c a t i o n s to these p r o t e i n s .  Thus, the b i n d i n g o f c a l c i u m and magnesium  would i n t u i t i v e l y be expected to decrease the b i n d i n g o f the a l k a l i cations  metal  to myosin, whereas the b i n d i n g o f anions such as c h l o r i d e would be  expected to enhance the b i n d i n g o f the a l k a l i metal c a t i o n s polyphosphates  such as ATP (98, 99, 100) might  a n i o n i c m o i e t i e s on a phosphonic  (91).  Bound  be expected to a c t l i k e the  i o n exchange r e s i n  (76, 7S) and enhance the  o v e r a l l K^ '£ °f  t  n  e  a/  c o n t r a c t i l e p r o t e i n s , but the experiments o f Fenn ( 9 7 )  i n d i c a t e t h a t ATP has v e r y  little  e f f e c t on the b i n d i n g  p o t a s s i u m to the c o n t r a c t i l e p r o t e i n s  i n a g l y c e r i n a t e d muscle  In summary, i t was noted t h a t a l t h o u g h v e r y bind  the a l k a l i metal c a t i o n s  these c a t i o n s  t h e r e was l i t t l e  with b i o l o g i c a l l y  significant  Carboxylic that  sodium to p o t a s s i u m  t h e o r e t i c a l j u s t i f i c a t i o n f o r an e x t r a p o l a t i o n of t h i s r e -  s u l t t o the p r o t e i n s  in a living  cell.  Induction  (which depend on the s t r u c t u r e o f the p r o t e i n ) field  molecules  the e x c e p t i o n ) ,  on p o l y e l e c t r o l y t e s and i o n exchange r e s i n s .  r e s i n s p r e f e r to b i n d  fiber.  few s m a l l  ( s t r o n g c h e l a t i n g agents being  can engage i n i o n p a i r f o r m a t i o n  anionic moieties  o f sodium and  and o v e r l a p p i n g  effects  c o u l d change the a n i o n i c  s t r e n g t h o f the s i t e s , hence the s e l e c t i v i t y and magnitude o f the  binding. protein  E x p e r i m e n t a l s t u d i e s on the b i n d i n g  c h a r a c t e r i s t i c s o f the major  i n a muscle f i b e r , myosin, i n d i c a t e t h a t t h i s p r o t e i n i s unique i n  possessing  r e l a t i v e l y high a s s o c i a t i o n constants  sium, the former i o n being critical  f o r both sodium and p o t a s -  bound more s t r o n g l y than the l a t t e r .  dependence of the b i n d i n g  c h a r a c t e r i s t i c s o f myosin on the s t r u c -  t u r e o f the m o l e c u l e and the p r e f e r e n c e  o f myosin f o r sodium over p o t a s s i u m  are compatible w i t h the e x i s t i n g t h e o r i e s o f c a t i o n s e l e c t i v i t y . binding  The  As the  c h a r a c t e r i s t i c s o f e x t r a c t e d myosin a r e q u a l i t a t i v e l y s i m i l a r to  those o f the p r o t e i n s  i n a g l y c e r i n a t e d muscle f i b e r ,  to expect t h a t s i g n i f i c a n t  q u a n t i t i e s o f both sodium and p o t a s s i u m w i l l be  bound to myosin i n the l i v i n g w i l l be g r e a t e r  i t seems r e a s o n a b l e  cell,  than u n i t y .  and t h a t the s e l e c t i v i t y o f the p r o t e i n ,  36 CHAPTER I I I  SCOPE AND  PURPOSE OF THE  The main purpose of t h i s the  hypotheses  that:  fiber ii.  s t r i a t e d muscle  i n v e s t i g a t i o n was  i .a significant  i n a s t r i a t e d muscle  INVESTIGATION  to t e s t e x p e r i m e n t a l l y  f r a c t i o n o f the a l k a l i metal  cations  i s bound to myosin,  the b i n d i n g s i t e s on the t h i c k f i l a m e n t s i n a  f i b e r p r e f e r to b i n d the a l k a l i metal c a t i o n s  i n the o r d e r  Li>Na>K, iii.  some o f the water  i n a s t r i a t e d muscle  fiber is  "bound" i n such a manner as to be u n a v a i l a b l e to a c t as s o l v e n t f o r the a l k a l i metal c a t i o n s f r e e i n the myoplasm.  Four s e p a r a t e e x p e r i m e n t a l  approaches, which are b r i e f l y o u t l i n e d below, were adopted.  Chapter IV.  The hypotheses were f i r s t  t e s t e d by comparing  the  a c t i v i t i e s o f sodium and p o t a s s i u m i n the myoplasm to the v a l u e s expected from a d e t e r m i n a t i o n o f the t o t a l  sodium, and p o t a s s i u m c o n t e n t of the  The a c t i v i t i e s were measured d i r e c t l y by means o f c a t i o n s e n s i t i v e m i c r o e l e c t r o d e s and muscle  f i b e r was  technique.  cell.  glass  the t o t a l c o n t e n t of sodium and p o t a s s i u m i n the same  determined by a c o n v e n t i o n a l flame p h o t o m e t r i c a n a l y t i c  I t i s apparent t h a t i f p r o p o r t i o n a l l y more sodium  than water i s  "bound", the measured a c t i v i t y of sodium w i l l be l e s s than the a c t i v i t y p r e d i c t e d from the a n a l y t i c measurements. p o r t i o n a l l y more water  I t i s a l s o apparent t h a t i f pro-  than potassium i s "bound", the measured a c t i v i t y o f  p o t a s s i u m w i l l be g r e a t e r than the a c t i v i t y o f p o t a s s i u m p r e d i c t e d from the a n a l y t i c measurements. these p r e d i c t i o n s .  The  r e s u l t s o b t a i n e d are compatible w i t h both of  37 There were o t h e r reasons  f o r performing  the above experiment,  knowledge o f the a c t i v i t i e s o f sodium and p o t a s s i u m prerequisite  i n the myoplasm i s a  to an a c c u r a t e measurement o f the membrane p e r m e a b i l i t i e s and  transport characteristics potential  A  o f the c e l l ,  o f these i o n s .  A proper e v a l u a t i o n o f the membrane  and the i n t r a c e l l u l a r r e a c t i o n s (ATPase  activation,  f o r example) these c a t i o n s can undergo a l s o depends on an a c c u r a t e knowledge of  the i n t r a c e l l u l a r a c t i v i t i e s .  F i n a l l y , the e l e c t r o d e measurements pro-  v i d e d d i r e c t e x p e r i m e n t a l evidence which c o n t r a d i c t e d L i n g ' s h y p o t h e s i s (1) that potassium  i s accumulated  preferentially  over sodium by muscle  fibers  because i t i s s e l e c t i v e l y adsorbed.on i n t r a c e l l u l a r b i n d i n g s i t e s .  The m i c r o e l e c t r o d e measurements were compatible w i t h , b u t d i d n o t prove  the h y p o t h e s i s t h a t a s i g n i f i c a n t f r a c t i o n o f sodium i n the c e l l was  bound to myosin. cation sensitive organelles.  A l l or p a r t o f the sodium i n the c e l l  u n a v a i l a b l e to the  m i c r o e l e c t r o d e c o u l d have been s e q u e s t e r e d  The next experiment  h y p o t h e s i s that a t l e a s t  in intracellular  was designed s p e c i f i c a l l y to t e s t the  some o f the "bound" sodium i n the c e l l was indeed  bound to myosin.  Chapter V.  I t i s known t h a t e x t r a c t e d myosin undergoes  d e n a t u r a t i o n a t 37° C (2) and t h a t t h i s d e n a t u r a t i o n causes bound a l k a l i metal reasoned  c a t i o n s (2) and polyphosphate  anions  thermal  the r e l e a s e o f  (3).  I t was  t h a t i f a s i g n i f i c a n t f r a c t i o n o f the i n t r a c e l l u l a r sodium was  bound to myosin, a r e l e a s e o f bound sodium, hence an i n c r e a s e i n the a c t i v ity  o f sodium i n the myoplasm, would occur when the muscle f i b e r was heated  to 37° C.  T h i s p r e d i c t i o n was confirmed by measuring  the a c t i v i t y o f  sodium i n the myoplasm o f s t r i a t e d muscle f i b e r s by means o f a c a t i o n t i v e g l a s s m i c r o e l e c t r o d e w h i l e the temperature  sensi-  o f the sodium f r e e b a t h i n g  38 s o l u t i o n was r a i s e d t o 37° C.  The experiments r e p o r t e d  i n Chapter V  provided  s t r o n g e v i d e n c e t h a t much o f . t h e sodium i n s t r i a t e d muscle f i b e r s was bound to myosin, but i t was thought d e s i r a b l e to o b t a i n e v i d e n c e independent o f m i c r o e l e c t r o d e  indeed  experimental  measurements to s u b s t a n t i a t e  this  conclusion. r  Chapter V I .  A p r e d i c t i o n can be made about the l i g h t s c a t t e r i n g  c h a r a c t e r i s t i c s o f a s t r i a t e d muscle f i b e r on the b a s i s o f the h y p o t h e s i s t h a t sodium i s bound to the t h i c k f i l a m e n t s .  The t u r b i d i t y or o p t i c a l  d e n s i t y o f a s o l u t i o n o f macromolecules i s i n t i m a t e l y r e l a t e d to the n e t charge on the macromolecules. o f the s o l u t i o n decreases  I f the n e t charge i s i n c r e a s e d ,  the t u r b i d i t y  (4, 5, 6 ) . Thus, the t u r b i d i t y o f a muscle  fiber  would be expected to decrease i f the n e t charge on the main s c a t t e r i n g centers  i n the f i b e r ,  the t h i c k f i l a m e n t s , was i n c r e a s e d .  i n a sodium f r e e s o l u t i o n should  sites,  the n e t n e g a t i v e  I f no i o n r e p l a c e s  tris  decrease.  should  This p r e d i c t i o n  c o n f i r m e d f o r f i b e r s bathed i n sodium f r e e s o l u t i o n s c o n t a i n i n g o r p o t a s s i u m as s u b s t i t u t e s f o r sodium.  s t i t u t e f o r sodium i n the b a t h i n g increased  slightly.  hypothesis,  sites  sodium on  charge on the t h i c k f i l a m e n t s  i n c r e a s e , and the t u r b i d i t y o f the f i b e r should was  the f i b e r  cause sodium t o move o f f the b i n d i n g  on the t h i c k f i l a m e n t s and out o f the c e l l . the b i n d i n g  Bathing  sucrose,  When l i t h i u m was used as a sub-  s o l u t i o n , the t u r b i d i t y o f the f i b e r s  T h i s f i n d i n g i s a l s o compatible w i t h  f o r the l i t h i u m e n t e r i n g  the c e l l  should  the working  be bound more s t r o n g l y  than sodium t o the s i t e s on the t h i c k f i l a m e n t s ( 7 ) . Chapter V I I .  The l a s t  s e r i e s o f experiments was designed to  measure the s e l e c t i v i t y , K^ /j£j o f the p r o t e i n s a  the f r e e c o n c e n t r a t i o n s  i n a g l y c e r i n a t e d f i b e r when  o f sodium, p o t a s s i u m and hydrogen were s i m i l a r t o  those found i n the myoplasm of a l i v i n g c e l l . and  p o t a s s i u m accumulated by  of radioisotopes indicated  t h a t the  than u n i t y , but was  not  and  great  The. c o n c e n t r a t i o n s  the g l y c e r i n a t e d f i b e r s were measured by means  a standard  flame p h o t o m e t r i c t e c h n i q u e .  s e l e c t i v i t y of the p r o t e i n s , j j / j ^ K  a  w  a  J  s  The  indeed  a l s o that the number of sodium ions bound to the  enough to e x p l a i n the extremely low  myoplasm of a l i v i n g  fiber.  of sodium  Thus, i t was  greater proteins  a c t i v i t y o f sodium i n the  concluded t h a t i n a l i v i n g muscle  f i b e r e i t h e r some f a c t o r enhances the b i n d i n g p r o t e i n s or sodium i s compartmentalized  results  of sodium to the c o n t r a c t i l e  in intracellular  organelles.  40 CHAPTER IV  ACTIVITY OF SODIUM AND POTASSIUM IN THE MYOPLASM  A.  Introduction  The m o t i v a t i o n f o r measuring sium i n the myoplasm o f s t r i a t e d two c h a p t e r s .  muscle f i b e r s was d i s c u s s e d  A means o f measuring  (1) , who was the f i r s t  to construct cation sensitive glass microelectrodes  the experiments a l s o depended  weight = 20 mg, t y p i c a l fibers  i n the p r e v i o u s  these a c t i v i t i e s was d e v i s e d by Kinke  from the g l a s s e s developed by Eisenman of  the a c t i v i t i e s o f sodium and p o t a s -  and h i s coworkers  ( 2 ) . The success  on the use o f the extremely large,  diameter = 1mm,  typical  o f the g i a n t b a r n a c l e , Balanus n u b i l u s .  (typical  l e n g t h = 4 cm) muscle Hoyle and Smyth (3) may be  c o n s u l t e d f o r a d e s c r i p t i o n o f the b a r n a c l e muscles.  One advantage muscle f i b e r s  of p e r f o r m i n g experiments on the l a r g e b a r n a c l e  i s that r e l a t i v e l y  l a r g e m i c r o e l e c t r o d e s can be used.  e l e c t r o d e s a r e e a s i e r t o c o n s t r u c t than the e x t r e m e l y s m a l l c a t i o n m i c r o e l e c t r o d e s t h a t L e v (4, 5) u t i l i z e d f o r measurements on f r o g fibers. out  Another advantage  i s t h a t the muscle  damage because they a r e h e l d  collagen.  fibers  These sensitive  muscle  can be d i s s e c t e d w i t h -  t o g e t h e r w i t h o n l y a l o o s e network o f  The tendon can be c a n n u l a t e d w i t h o u t damage t o the f i b e r and the  m i c r o e l e c t r o d e i n s e r t e d down the l o n g i t u d i n a l a x i s o f the f i b e r ; a procedure which ensures t h a t the c a t i o n s e n s i t i v e t i p i s f a r from t h e r e g i o n o f damaged membrane.  I f the m i c r o e l e c t r o d e i s i n s e r t e d  t r a n s v e r s e l y , the t i p  i s near a damaged a r e a o f membrane, and leakage o f sodium i n t o of p o t a s s i u m out o f the f i b e r  can o c c u r .  Finally,  p o t a s s i u m c o n t e n t o f a s i n g l e b a r n a c l e muscle  the f i b e r , o r  the t o t a l sodium and  f i b e r can be a c c u r a t e l y  41  determined by means of flame photometry because of the large s i z e of the , fibers. B.  Methods Microelectrodes.  The sodium s e n s i t i v e microelectrodes were con-  structed from Corning KAS 11-18  (sodium s e n s i t i v e ) and 0120  (lead) glasses  by a method f i r s t described by Hinke (1). The j o i n t between the outer lead glass shank and the sodium s e n s i t i v e t i p was formed by fusing the two glasses i n a microforge.  The s e n s i t i v e t i p s of the sodium (and potas-  sium) microelectrodes were about 15u, i n diameter and 150-300u, i n length, as shown i n F i g . 1.  A recent a r t i c l e by Hinke (6) contains d e t a i l s of the  F i g . 1. Photograph of the t i p of a sodium s e n s i t i v e microelectrode. t i p i s about 15u, i n diameter and 300u. i n length. construction procedure.  The potassium s e n s i t i v e microelectrodes were  constructed from Corning NAS 27-3 glasses.  The  (potassium s e n s i t i v e ) and 0120  (lead)  Only a few microelectrodes were constructed by the method  42 d e s c r i b e d by Hinke  (1, 6 ) , which i n v o l v e d matching and  glasses  (NAS  0120  oped by  the author whereby a j o i n t was  outer  27-3,  and  l e a d g l a s s shank and  pyrex) a t a j o i n t .  the  f u s i n g three  A new  technique was  formed by m e l t i n g  of  devel-  beeswax between  inner potassium glass c a p i l l a r y .  of c o n s t r u c t i o n r e q u i r e s much l e s s s k i l l  sets  than the p r e v i o u s  the  T h i s method  technique and  e l e c t r o d e s have s l i g h t l y s u p e r i o r c h a r a c t e r i s t i c s (a l o n g e r  life  s e l e c t i v i t y , presumably because the g l a s s i s heated l e s s ) .  A description  of this  technique w i l l  The  appear i n an a r t i c l e by Hinke  e q u a t i o n s which d e s c r i b e  potassium s e n s i t i v e microelectrodes  the behavior  and  the  better  (7).  of the  sodium  and  are  •  ^a \ where E„, Na trodes  and  =  E  =  E  Na  K  E , are K T  +  0.05  l o g  l o g  10  10  ( a  K  +  ( a  sodium  8 w i t h 0.01 M KC1  standard  k  +  M NaCl.  0.1  VNP  and K ions at a c t i v i t i e s a„ Na  M NaCl  The  M KC1  trodes were c a l i b r a t e d b e f o r e  and  r e s u l t s were r e j e c t e d i f the two  1  6  ]  microelec-  and  a, K T  f o r a g i v e n e l e c t r o d e and  are  solutions.  (0.1 M KC1), p l u s 0.05  0.01  were c a l i b r a t e d to e i t h e r pH  M NaCl  (0.01  M N a C l , and 0.40  p o t e n t i a l s from a m i c r o e l e c t r o d e 7 or pH  [  [ 1 7 ]  s o l u t i o n s , which were b u f f e r e d  M N a C l , 0.20  s o l u t i o n of e i t h e r pH  The  '•  (potassium) s e n s i t i v e m i c r o e l e c t r o d e s  M tris:  p l u s 0.05  N a V  terms are constant  f o l l o w i n g f i v e standard  p l u s 0.05  Na  by c a l i b r a t i o n i n the standard The  or pH  K  Na  i n s o l u t i o n s c o n t a i n i n g Na  obtained  the  S  S  the measured p o t e n t i a l s ( m i l l i v o l t s ) of the  r e s p e c t i v e l y ; the o t h e r  in  +  8 were i d e n t i c a l  a f t e r each e x p e r i m e n t a l c a l i b r a t i o n s d i d not  M  M  KC1),  KC1  immersed i n a (±0.5  mV).  Elec-  reading,  coincide  and  (+ 1  c a t i o n s e l e c t i v i t y . k„ or k , remained r e l a t i v e l y ' Na K' , 1  7  the  mV).  constant •  from day  to day  electrode. from 1/50 k^,  f o r a g i v e n m i c r o e l e c t r o d e , but v a r i e d from e l e c t r o d e to  For  the sodium m i c r o e l e c t r o d e s ,  to 1/1000; f o r the potassium  v a r i e d from 1/1  to 1/2.  The  simultaneous  equations,  was  always 59 mV,  k^,  varied  selectivity,  of the e l e c t r o d e s  then s o l v i n g the The  two  response of  to a 1 0 - f o l d change i n the sodium a c t i v i t y ,  whereas the response of the potassium  from the sodium and potassium  All  the  [17] f o r the a c t i v i t i e s .  a 1 0 - f o l d change i n the potassium  V i b r o n 33B  selectivity  on the same f i b e r ,  [16] and  the sodium m i c r o e l e c t r o d e s  microelectrodes,  imperfect  n e c e s s i t a t e d measuring E^^ and  the s e l e c t i v i t y ,  e l e c t r o m e t e r and  activity,  microelectrodes  50-55 mV.  The  V i b r o n 33B  of the  = 10  1 3  to  potential  on a Grass ink w r i t i n g o s c i l l o g r a p h .  experiments responded c o r r e c t l y  (±1%)  to an  a p p l i e d p o t e n t i a l , which i n d i c a t e d t h a t the impedance of the e l e c t r o d e s l e s s than 1/100  ,  s e n s i t i v e m i c r o e l e c t r o d e s were measured on a  recorded  e l e c t r o d e s used i n these  S^, was  S  impedance o f the e l e c t r o m e t e r  was  ( i n p u t r e s i s t a n c e of  ohms).  Membrane p o t e n t i a l measurements were made w i t h open t i p m i c r o e l e c trodes of the L i n g and Gerard p o t e n t i a l of l e s s than 5 mV Adrian  (8).  Only those m i c r o e l e c t r o d e s w i t h a t i p  were used, i n accordance w i t h the c r i t e r i o n  I n a d d i t i o n , each m i c r o e l e c t r o d e was  p o t e n t i a l reading standard  type.  i n the Ringer  s o l u t i o n was  identical.  were r o u t i n e l y made w i t h  two  s o l u t i o n and 0.40 Finally,  t e s t e d to ensure M KC1  p l u s 0.05  of  the M NaCl  membrane p o t e n t i a l measurements  d i f f e r e n t open t i p m i c r o e l e c t r o d e s  on  the same  fiber.  The  p o t e n t i a l from the open t i p m i c r o e l e c t r o d e was  a cathode f o l l o w e r and oscillograph.  a Grass P6 DC  recorded v i a  a m p l i f i e r on a Grass i n k w r i t i n g  Both t h i s a m p l i f i e r and  the V i b r o n e l e c t r o m e t e r were  cali-  44 brated. b e f o r e each experiment  w i t h a v a r i a b l e v o l t a g e s o u r c e , which i n t u r n  was c a l i b r a t e d from a Standard Weston  Cell.  D e t e r m i n a t i o n o f C a t i o n A c t i v i t y and C o n c e n t r a t i o n . s t r i a t e d muscle f i b e r s  Single  from the d e p r e s s o r muscles o f the g i a n t b a r n a c l e were  d i s s e c t e d f r e e w i t h a s m a l l p i e c e o f b a s e p l a t e a t the o r i g i n and a tendon a t the i n s e r t i o n .  A g l a s s cannula was i n s e r t e d  through the muscle-tendon j u n c t i o n . tion,  into  A f t e r the cannula was  the p r e p a r a t i o n was suspended v e r t i c a l l y  solution  the tendon,  (Table I ) as shown i n F i g . 2.  but n o t  ligated  i n an a r t i f i c i a l  i n posi-  bathing  Cation sensitive microelectrodes  TABLE I Solutions  (mM)  Barnacle Ringer* Na  Sucrose  Ringer**  450  K  8  8  Ca  20  20  Mg  10  10  CI  518  68  25  25  Tris Sucrose  649  pH = 7.6 f o r both s o l u t i o n s . Note the subs t i t u t i o n o f T r i s f o r HCO-j i n the o r i g i n a l b a r n a c l e Ringer s o l u t i o n o f Hoyle and Smith (3) . **Sucrose added to make s o l u t i o n i s o s m o t i c w i t h b a r n a c l e Ringer s o l u t i o n .  were manipulated s e n s i t i v e t i p was ensured  through the c a n n u l a t e d tendon  i n t o the myoplasm u n t i l the  1-2 cm from the puncture  zone (See F i g . 3 ) .  T h i s technique  that undamaged membrane surrounded  the s e n s i t i v e t i p .  The membrane  45  Cation-selective microelectrode  i/  i i  I  Glass cannula  S i l k tie Tendon  Open-tipped microelectrode!!  -Single muscle fibre «-500 JLL  F i g . Z. Diagram o f a c a n n u l a t e d muscle f i b e r w i t h i n s e r t e d m i c r o e l e c t r o d e . Note the cannula does not damage the f i b e r membrane. See t e x t f o r explanation.  46  p o t e n t i a l was always measured immediately adjacent to the electrode t i p , and i t was subtracted  from the p o t e n t i a l of the c a t i o n s e n s i t i v e  microelectrode.  (The cation s e n s i t i v e microelectrode r e g i s t e r s of course the membrane potent i a l as w e l l as the p o t e n t i a l due to the a l k a l i metal cations.)  The same  external reference electrode was used for both the experiment and the c a l i brations.  Fibers were examined for damage spots before and a f t e r an e l e c -  trode impalement.  I f any damage was observed, the f i b e r was r e j e c t e d .  A f t e r completion of the electrode measurements, the f i b e r was transferred to a P e t r i d i s h , c a r e f u l l y decannulated to avoid damage, and swirled for 15 seconds i n isosmotic sucrose. weighing b o t t l e .  The f i b e r was then b l o t t e d and placed i n a  A f t e r drying, and d i g e s t i o n with n i t r i c a c i d , the f i b e r  F i g . 3. Photograph of a single s t r i a t e d muscle f i b e r from the giant barnacle. The f i b e r was suspended v e r t i c a l l y by l i g a t i n g i t s tendon to a glass cannula (not shown). The cation s e n s i t i v e microelectrode was inserted into the f i b e r v i a the cannulated tendon. Note a c a t i o n s e n s i t i v e microelectrode i n the f i b e r and an open t i p microelectrode i n the bathing solut i o n . The v e r t i c a l bar represents 1 mm.  47 was  analyzed f o r t o t a l  flame  sodium and p o t a s s i u m c o n t e n t w i t h a Unicam SP  900  spectrophotometer.  D e t e r m i n a t i o n of Membrane P o t e n t i a l at High E x t e r n a l P o t a s s i u m Concentration,  S i n g l e muscle f i b e r s were d i s s e c t e d and suspended by  tendons i n the v e r t i c a l p l a n e .  E i g h t bathing s o l u t i o n s with potassium  c e n t r a t i o n s r a n g i n g from 0 to 450 mM p o t a s s i u m and was  were used.  con-  The product of the  c h l o r i d e c o n c e n t r a t i o n s i n each s o l u t i o n c o n t a i n i n g p o t a s s i u m  kept c o n s t a n t by r e p l a c i n g c h l o r i d e w i t h methanesulfonate.  c a l c i u m and  their  Magnesium,  t r i s were p r e s e n t a t the same c o n c e n t r a t i o n s as i n b a r n a c l e  Ringer s o l u t i o n .  To e l i m i n a t e s p u r i o u s r e s u l t s due  to the development of  t r a n s i t o r y t i p p o t e n t i a l s on m i c r o e l e c t r o d e s w i t h i n the myoplasm, membrane p o t e n t i a l measurements were made a t each potassium c o n c e n t r a t i o n w i t h a t l e a s t two  different microelectrodes.  muscle f i b e r was  determined  The  t o t a l p o t a s s i u m c o n t e n t of the  i n the manner d e s c r i b e d i n the p r e v i o u s p a r a -  graph.  D e t e r m i n a t i o n of Bound Sodium and Water.  The  s e p a r a t i o n of the  sodium, p o t a s s i u m and water content o f a s i n g l e muscle f i b e r and  " f r e e " f r a c t i o n i s expressed by the f o l l o w i n g  C  Na = V  S^' where ^„ and Na  K  ^  a  '  W  +  equations  [18]  B N  +  i n t o a "bound"  a  ^  [19]  are the m o l a l a c t i v i t y c o e f f i c i e n t s o f sodium and J  i n the myoplasm; V i s the t o t a l water content  (kilograms); a ^  a  the f r a c t i o n s o f water " f r e e " , or more s p e c i f i c a l l y , a v a i l a b l e  and  r  potassium are  to a c t as  s o l v e n t f o r the sodium and potassium ions r e s p e c t i v e l y ; C„ and C„ are the • Na K c o n c e n t r a t i o n s o f sodium and p o t a s s i u m (moles per k i l o g r a m f i b e r water) T  .48 determined by flame photometry;  and a  R  are the a c t i v i t i e s o f sodium  p o t a s s i u m determined d i r e c t l y by the m i c r o e l e c t r o d e s ; B^ "bound" q u a n t i t i e s o f the c a t i o n s ion  (moles).  a  and  are  and  the  I t should be s t r e s s e d t h a t  any  u n a v a i l a b l e to a f f e c t the c a t i o n s e n s i t i v e m i c r o e l e c t r o d e i s c o n s i d e r e d  "bound".  Thus, the ions compartmentalized i n i n t r a c e l l u l a r o r g a n e l l e s o r  " t r a p p e d " i n the e l e c t r o s t a t i c as w e l l as those ions complexed  field  o f a n e g a t i v e l y charged  by s p e c i f i c s i t e s  macromolecule,  i n the myoplasm a r e  c o n s i d e r e d to be "bound".  These  two e q u a t i o n s , which are v a l i d by d e f i n i t i o n , c o n t a i n s i x  q u a n t i t i e s xvhich cannot be determined e x p e r i m e n t a l l y a t p r e s e n t : "C-r . V,,, B„ and B ,. Na' K' Na , K T  Four more e q u a t i o n s are r e q u i r e d . n  n  e q u a t i o n s are based on assumptions, and may  be i n c o r r e c t .  These  following °  The f i r s t assump-  t i o n i s t h a t the a c t i v i t y c o e f f i c i e n t s o f sodium and p o t a s s i u m ions f r e e i n the  myoplasm a r e e q u a l  T h i s assumption i s not based on t h e o r e t i c a l grounds.  As Robinson and Stokes  (9,  can be quoted as  page 454)  s t a t e "The v a r i o u s p h y s i o l o g i c a l f l u i d s  another example where a t h e o r y of mixed e l e c t r o l y t e s o l u t i o n s would progress..".  I t seems a r e a s o n a b l e assumption, i f o n l y because the a c t i v i t y  c o e f f i c i e n t s o f a 0.2 M KC1 c o u l d , as Lev  and NaCl s o l u t i o n d i f f e r by merely 3%.  the measured c o n c e n t r a t i o n s .  p l a i n i n g why  (One  (5) has done, merely d e f i n e the a c t i v i t y c o e f f i c i e n t s o f  sodium and p o t a s s i u m i n a muscle t o be the r a t i o s o f the measured to  l e a d to  One  activities  i s then l e f t w i t h the problem o f ex-  the a c t i v i t y c o e f f i c i e n t of sodium,  d e f i n e d i n t h i s manner,  d i f f e r s markedly from the a c t i v i t y c o e f f i c i e n t of p o t a s s i u m i n the myoplasm.)  49 The  second assumption i s that the a c t i v i t y c o e f f i c i e n t  myoplasm i s e q u a l to the a c t i v i t y c o e f f i c i e n t  o f the b a r n a c l e  o f the  Ringer  solution.  0.65  tf= I t s h o u l d be noted  [21]  t h a t the sum o f the c o n c e n t r a t i o n s o f sodium and p o t a s -  sium i n a b a r n a c l e muscle i s , on the average, c o n c e n t r a t i o n s o f these  ions i n the b a t h i n g s o l u t i o n  Thus, the a c t i v i t y c o e f f i c i e n t solution charged fraction  (^=0.7).  the sum o f the  (Table I and F i g . 4 ) .  c o u l d be as h i g h as t h a t o f a 0.25M KC1  I t i s probably  somewhat lower because o f the many  groups on p r o t e i n s i n the myoplasm. o f the i n t r a c e l l u l a r water w i l l  t i o n , and lower  o n l y about h a l f  the a c t i v i t y c o e f f i c i e n t .  Furthermore, the b i n d i n g o f a  i n c r e a s e the f r e e c a t i o n c o n c e n t r a I t seems u n l i k e l y ,  however, t h a t  these f a c t o r s c o u l d lower  the v a l u e o f the a c t i v i t y c o e f f i c i e n t  (the  o f a 1.0 M KC1 s o l u t i o n ) .  activity coefficient  t h a t the a c t i v i t y c o e f f i c i e n t guess, b u t i t i s p r o b a b l e  Thus, the assumption  o f the myoplasm i s e q u a l to 0.65 i s o n l y a  t h a t the a c t u a l v a l u e l i e s between 0.6 and 0.7.  An e r r o r i n the estimate, o f the a c t i v i t y c o e f f i c i e n t would a l t e r chapter.  quantitatively,  but n o t q u a l i t a t i v e l y  The p o s s i b i l i t y t h a t the macroscopic  muscle f i b e r a f f e c t s  to below 0.6  the a c t i v i t y c o e f f i c i e n t  of less  than ± 0.05  the c o n c l u s i o n s o f t h i s  d i e l e c t r i c c o n s t a n t o f the w i l l be c o n s i d e r e d i n the  Discussion.  The next assumption i s t h a t the f r a c t i o n as s o l v e n t f o r sodium i n the myoplasm equals to a c t as s o l v e n t f o r  o f water a v a i l a b l e t o a c t  the f r a c t i o n  o f water a v a i l a b l e  potassium. [22]  T h i s assumption may n o t be v a l i d .  Sodium does n o t f i t as w e l l as potassium  50 i n t o the normal I c e I l a t t i c e , hence may be excluded from a l a r g e r of water for  i n the c e l l  than p o t a s s i u m (10).  The use o f an o v e r e s t i m a t e d v a l u e  i n Eqn. [ 1 8 ] , however, w i l l merely cause the v a l u e o f  underestimated.  fraction  F o r t h i s r e a s o n , the assumption i s a c c e p t a b l e .  t o be The f i n a l  assumption i s t h a t t h e r e i s no b i n d i n g o f p o t a s s i u m . B  = 0.0  R  ...[23]  T h i s assumption i s almost c e r t a i n l y i n c o r r e c t , but i t was made f o r mathem a t i c a l , not p h y s i c a l reasons.  T h i s assumption s e r v e s to maximize  of O j , = C£, which i s c a l c u l a t e d from Eqn.  [19].  the v a l u e  (In o t h e r words, i t i s the  minimal f r a c t i o n o f "bound" water t h a t i s c a l c u l a t e d . )  When Eqns.  [20-23] a r e s u b s t i t u t e d i n t o Eqns.  [18] and [ 1 9 ] , the  f o l l o w i n g equations r e s u l t . C C  N a  K  V=  («/0.65)a V  = (a/0.65)a  Na  B  +  [24]  N a  [25]  R  From these two e q u a t i o n s and the e x p e r i m e n t a l d a t a , the minimal f r a c t i o n o f "bound" water and the minimal f r a c t i o n o f "bound" sodium i n a b a r n a c l e muscle f i b e r may be c a l c u l a t e d .  C.  Results C o n c e n t r a t i o n and A c t i v i t y Measurements.  C o n s i d e r now the r e s u l t s  o b t a i n e d from the c o n c e n t r a t i o n measurements made on the e x p e r i m e n t a l and control fibers.  These a r e i l l u s t r a t e d  i n F i g . 4.  I t i s apparent t h a t t h e r e i s  a wide v a r i a t i o n o f C„ and C„ i n muscle f i b e r s from d i f f e r e n t b a r n a c l e s , as Na K ' w e l l as a c l o s e c o r r e l a t i o n between the C. and C„ o f i n d i v i d u a l f i b e r s ( c o r Na K r e l a t i o n c o e f f i c i e n t = 0.95). Muscle f i b e r s from the same b a r n a c l e shoxred T  l i t t l e variation  i n either C or C ,. Na K T  This i s i l l u s t r a t e d  i n Table I l a ,  which  51  .250  ^.200 cn  C = .l82+.78(C -105) K  Na  150  .100  .050  .100  .150 CNo(M/Kg  F i g . 4. fibers.  .200  .250  H 0) 2  R e l a t i o n between the sodium and p o t a s s i u m c o n t e n t s o f s i n g l e muscle The c o r r e l a t i o n c o e f f i c i e n t i s 0.95.  g i v e s the a c t i v i t y , c o n c e n t r a t i o n and membrane p o t e n t i a l measurements made on  f i b e r s from a s i n g l e b a r n a c l e .  that C^  a  i s much l a r g e r  These two f e a t u r e s  The  The s a l i e n t f e a t u r e s  than a ^ and that  of Table I l a are  i s a p p r o x i m a t e l y equal to a ^ .  a r e common to a l l the f i b e r s  investigated.  f r a c t i o n s o f "bound" water and "bound" sodium were  f o r each i n d i v i d u a l f i b e r .  That i s . the v a l u e s o f a„ , a,,. C„ and C , ' Na' K' Na K T  o b t a i n e d from each e x p e r i m e n t a l f i b e r were used to s o l v e for  (1-a) and(B  /V)/G^ . a  calculated  By t h i s method o f a n a l y s i s ,  Eqns. [24] and [25]  the f r a c t i o n s o f  TABLE I I Sodium and p o t a s s i u m i n s i n g l e muscle  K (moles/kg  *K  (a) B a r n a c l e R i n g e r 0.157 ±0.006 (3)  2  (b) Sucrose R i n g e r 0.170 ±0.005(8)  Na  0.010 ±0.001(3)  0.051 ±0.002(17)  67.0 ±0.2(3)  79.4 ±0.1(17)  0.039 ±0.003(16)  61.8 ±0.5(8)  72.8 ±0.2(14)  solution  0.174 ±0.002(16)  Barnacle Ringer  Water content (%)  Membrane potential (mV)  solution  0.143 ±0.001(17)  t  Na  H 0)  fibers*  0.007 ±0.001(8)  controls  0.158  0.056  ±0.004(8)  ±0.006(8)  70.7  75.8  ±0.4(8)  ±0.7(8)  *A11 experiments were done a t 25°C t± S.E. NOTE: T a b l e l i b shows average r e s u l t s . T a b l e I l a shows o n l y the r e s u l t s o b t a i n e d from the muscle f i b e r s o f a s i n g l e b a r n a c l e . The C ^ and of a l l the f i b e r s i n t h i s s e r i e s a r e shown i n F i g . 4. T a b l e I l a i s p r e s e n t e d o n l y to i n d i c a t e t h a t t h e r e i s no s u b s t a n t i a l v a r i a t i o n i n the v a l u e s o f C... and Na o b t a i n e d from the muscle f i b e r s o f a s i n g l e b a r n a c l e . The number or d e t e r m i n a t i o n s i s shown i n p a r e n t h e s e s . •k a  "bound" water and "bound" sodium were found to be 0.41 0.84  ± 0.001  respectively  (nine e x p e r i m e n t s ) .  ± 0.014  and  These r e s u l t s a r e s i m i l a r  to the v a l u e s o b t a i n e d by Hinke i n a s e r i e s o f p r e l i m i n a r y experiments, which were a l s o r e p o r t e d i n a paper by M c L a u g h l i n and Hinke ( 1 1 ) .  Hinke  c o n c l u d e d from h i s measurements t h a t the f r a c t i o n s o f "bound" water and sodium were .43 and  .85 r e s p e c t i v e l y .  The s m a l l s t a n d a r d e r r o r f o r the  f r a c t i o n o f bound sodium i s worthy o f n o t e .  I t i n d i c a t e s that this  quantity  remained c o n s t a n t even though the sodium c o n t e n t o f the f i b e r s v a r i e d from 0.040 to 0.200 moles/kg H^O  (Fig. 4).  Table l i b i l l u s t r a t e s  the average r e s u l t s o b t a i n e d from f i b e r s  53  +40h +20 £  0  t  SI ope =51 mV/log [K  20  "o Q. - 4 0  § -60  1-80 -100 Log  |0  [KJ^CM/Kg H 0) 2  Fig. 5 . R e l a t i o n between membrane p o t e n t i a l and l o g [ K ] f o r a t y p i c a l muscle f i b e r . The p r o d u c t [ K ] [ C 1 ] was m a i n t a i n e d a c o n s t a n t . Q  O  bathed f o r 4 5 minutes i n sodium f r e e , sucrose s u b s t i t u t e d these r e s u l t s were used to s o l v e Eqns. [ 2 4 ] and  Ringer.  When  [ 2 5 ] f o r the f r a c t i o n s of  "bound" water and sodium, the v a l u e s o b t a i n e d were s i m i l a r t o those obtained  from f i b e r s bathed i n normal R i n g e r .  The f r a c t i o n s o f  "bound"  water and sodium were found to be 0 . 3 4 and 0 . 8 1 r e s p e c t i v e l y .  Membrane P o t e n t i a l  Study.  p o t e n t i a l and the l o g of the e x t e r n a l  The r e l a t i o n s h i p between  the membrane  p o t a s s i u m c o n c e n t r a t i o n i s shown f o r  a t y p i c a l b a r n a c l e muscle f i b e r i n F i g . 5 .  The o b s e r v e d l i n e a r r e l a t i o n s h i p  when [ K ] i s g r e a t e r than 0.016 M and the s l o p e o f 51 mV/log  [K]  q  Q  indicate  t h a t the sarcolemma may have been a c t i n g as a semipermeable membrane to the potassium  ion.  experimental potassium  (A l i n e a r r e l a t i o n s h i p was observed  fibers.  The average s l o p e was 53 ± 1 mV/log  c o n c e n t r a t i o n g r a d i e n t i s the s o l e determinant  p o t e n t i a l a t r e g i o n s o f h i g h e x t e r n a l potassium questionable  Q  I f the  of the membrane  concentration  (admittedly a  T h i s corresponds  0.242(0.65) = 0.157, which i s assumed to equal the myoplasm.  I f this  to an a c t i v i t y o f  the a c t i v i t y o f potassium i n  i s used w i t h the average v a l u e o f C  v  (15 e x p e r i m e n t s ) ,  "bound" water i s found  i s zero.  when the membrane p o t e n t i a l was zero was 0.242 ±  0.012 moles/kg H-,0 ( f i v e e x p e r i m e n t s ) .  D.  q  should be i d e n t i c a l when the membrane p o t e n t i a l  average v a l u e o f [ K ]  moles/kg H^O  [K] .)  assumption, see Chapter V ) , the i n t e r n a l and e x t e r n a l a c t i v i -  t i e s o f potassium The  f o r each o f the f i v e  0.177 ± 0.006  t o s o l v e f o r Oi from Eqn. [25] the f r a c t i o n o f  t o be 0.27.  Discussion  Two major c r i t i c i s m s of the i n t r a c e l l u l a r use o f c a t i o n s e n s i t i v e m i c r o e l e c t r o d e s have been advanced by L i n g t h a t the p r o t e i n a c e o u s  (12).  His f i r s t  criticism i s  f i x e d charge network i n the immediate v i c i n i t y o f the  m i c r o e l e c t r o d e may be damaged by the m i c r o e l e c t r o d e , hence have i t s b i n d i n g characteristics altered. tive glass microelectrodes the muscle f i b e r s .  I t i s apparent from F i g . 3 that the c a t i o n s e n s i used i n these experiments were much s m a l l e r  A comparison o f the a l k a l i metal c a t i o n c o n c e n t r a t i o n s  and membrane p o t e n t i a l s o f the c o n t r o l and e x p e r i m e n t a l t h a t no gross electrodes.  than  fibers indicated  damage was s u f f e r e d by the c e l l s on impalement by the microI f a change i n the b i n d i n g c h a r a c t e r i s t i c s o f the p r o t e i n s i n  the immediate v i c i n i t y o f the m i c r o e l e c t r o d e d i d o c c u r , sodium and p o t a s s i u m  55 i o n s would merely d i f f u s e down the c o n c e n t r a t i o n myoplasm.  Any  anomalous c o n c e n t r a t i o n s  gradients  s e t up  i n the  of these c a t i o n s c l o s e to the m i c r o -  e l e c t r o d e would be d i s s i p a t e d i n time throughout the c e l l ,  and  the  error  i n t r o d u c e d would be expected to be n e g l i g i b l e .  Ling's to o t h e r  second c r i t i c i s m  ions b e s i d e s  high concentrations  sodium and  i s t h a t the e l e c t r o d e s may  p o t a s s i u m and  of amino a c i d s or p r o t e i n s .  gated t h i s p o s s i b i l i t y .  He  t h a t they may Hinke  respond  be p o i s o n e d  albumin molecules on  potassium s e n s i t i v e microelectrodes.  by  (7) r e c e n t l y i n v e s t i -  s t u d i e d the e f f e c t of h i g h c o n c e n t r a t i o n s  ammonium, l y s i n e , a r g i n i n e and and  (12)  of  the response of sodium  These m o l e c u l e s d i d a f f e c t  the  e l e c t r o d e s , p a r t i c u l a r l y the potassium s e n s i t i v e m i c r o e l e c t r o d e s ,  but  magnitude of the e f f e c t was  potassium  ions at a concentration t r a t i o n of 0.05  M,  very  small.  In a s o l u t i o n c o n t a i n i n g  of 0.253 M and NH^,  l y s i n e or a r g i n i n e a t a concen-  the p o t a s s i u m m i c r o e l e c t r o d e  potassium concentration  of 2.1,  1.2  and  0.07,  predicted a f a l s e l y  respectively. and  t i o n of 20 gram 7>, the potassium m i c r o e l e c t r o d e  predicted' a f a l s e l y  of about 37,.  s e n s i t i v e glass microelectrodes amino a c i d s  dielectric  per g r a m / l i t e r ) and may  (of the order  speculated  t h e r e f o r e be v e r y  high  amino a c i d s have l a r g e  of 0.1-1.0 u n i t s of d i e l e c t r i c d i e l e c t r i c constants  greater  constant  inside cells  than those o f the r e l a t i v e l y  t e i n - f r e e s o l u t i o n s o u t s i d e , w i t h a consequent i n c r e a s e ions".  or  cells.  t h a t "the  considerably  c o e f f i c i e n t s of i n t r a c e l l u l a r  concentra-  are g r e a t l y a f f e c t e d by e i t h e r p r o t e i n s  (13) has n o t e d t h a t p r o t e i n s and  increments  albumin at a  Thus, i t seems u n l i k e l y t h a t c a t i o n  i n the c y t o p l a s m o f l i v i n g  Robinson  high  In a s o l u t i o n  c o n t a i n i n g p o t a s s i u m a t the above c o n c e n t r a t i o n  potassium concentration  the  i n the  Three c r i t i c i s m s may  pro-  activity  be made of  this  statement.  F i r s t , a l t h o u g h amino a c i d s would i n c r e a s e the  s t a n t of a c e l l , fixed.  p r o t e i n s may  Schwan (14)  should be  d i e l e c t r i c c o n s t a n t s of support the  have the  c o n s u l t e d f o r an  living cells.  c o n t e n t i o n t h a t an  the  ion  ions i n the  is referred  solution.  to u n i t y at  i s a simple r e l a t i o n s h i p dielectric  c o n s t a n t s of  between the solutions  solutions  are markedly r a i s e d  from Robinson's statement.  e l e c t r i c constant  i n an  it  The  (9), not  a l o w e r i n g of  stressed  p r o t e i n s and  the  amino a c i d s .  (and  the  the  16).  has  I t may  vice  s a l t , depending on amino a c i d  (16).  a d i s c u s s i o n of  some of  e f f e c t of p r o t e i n s and  i n water.) of  of  Stokes  the  There  ions and  the which  i o n s i n these  would  anticipate  Debye-Huckel e q u a t i o n would  this effect, the  "primary medium  a simple r e l a t i o n s h i p of  di-  the  (9, pages 351-357).  activity coefficients  Finally,  between  the  ions i n s o l u t i o n s  of  G l y c i n e , f o r example, causes a marked i n c r e a s e  r e l a t i v e and  Edsall  ion  one  v e r s a ) , but  the  aqueous s o l u t i o n  and the  (2Z.6  a c t i v i t y c o e f f i c i e n t of  t o t a l c o n c e n t r a t i o n s of  Wyman (17, theoretical  amino a c i d s on  units  Chapters 5,  6) may  approaches to  the  the  the be  (15,  this  salt  and  consulted  problem of  activity coefficients  of  in  per  a c t i v i t y c o e f f i c i e n t o f NaCl  enhance or decrease the the  the  overshadowed by  o n l y a s m a l l e f f e c t on either  coefficients  a c t i v i t y c o e f f i c i e n t s when the  the m a c r o s c o p i c d i e l e c t r i c c o n s t a n t of an mole) but  to  a c t i v i t y c o e f f i c i e n t of  lowered, as  t h a t t h e r e i s not  d i e l e c t r i c c o n s t a n t and  evidence  activity  activity coefficients  d i s c u s s e d by Robinson and  s h o u l d be  the  containing molecules l i k e a l c o h o l s ,  Some form of  i s lowered  spatially  review of  activity coefficients  "secondary medium e f f e c t " i s g r e a t l y e f f e c t " , as  i n c r e a s e i n the  i n f i n i t e d i l u t i o n of  d i e l e c t r i c constant.  admittedly predict  excellent  Next, there i s l i t t l e  (Presumably, the  lower the  i f they are  i n c r e a s e i n the m a c r o s c o p i c d i e l e c t r i c con-  s t a n t of a s o l u t i o n would r e s u l t of  reverse e f f e c t  d i e l e c t r i c con-  for  the  salts.  57 A t p r e s e n t , one can o n l y s t a t e t h a t the a v a i l a b l e e x p e r i m e n t a l evidence i n dicates  t h a t a l t h o u g h the c o n c e n t r a t i o n s o f amino a c i d s and p r o t e i n s found  i n a b a r n a c l e muscle may s i g n i f i c a n t l y a f f e c t c o n s t a n t o f the c e l l ,  the macroscopic  t h i s change s h o u l d n o t g r e a t l y a f f e c t  c o e f f i c i e n t s o f the ions i n the c e l l  Bound Water.  dielectric  the a c t i v i t y  (16, 7 ) ,  Many i n v e s t i g a t o r s have attempted  f r a c t i o n o f "bound water" i n b i o l o g i c a l t i s s u e s .  t o measure the  B e f o r e some o f these r e -  s u l t s a r e c o n s i d e r e d , i t should a g a i n be s t r e s s e d t h a t the water i n a c e l l p r o b a b l y does n o t e x i s t  i n simple bound and f r e e f r a c t i o n s and t h a t  differ-  ent t e c h n i q u e s measure d i f f e r e n t p r o p e r t i e s o f the i n t r a c e l l u l a r water. S t u d i e s on the s w e l l i n g o f muscle f i b e r s Overton  (18) performed  i n the c e l l .  can y i e l d  little  i n h y p o t o n i c s o l u t i o n s such as i n f o r m a t i o n about  the s t a t e o f water  The sarcolemma i s now known to be permeable to sodium, p o t a s -  sium and o t h e r s o l u t e s , and a change i n the o s m o l a r i t y o f the b a t h i n g s o l u t i o n w i l l produce utes.  a different  steady s t a t e d i s t r i b u t i o n o f these  T h i s d i f f i c u l t y was circumvented  (19), who soaked  a muscle  i n an a p p r o x i m a t e l y equal volume o f twice normal s t r e n g t h R i n g e r  solution  and determined tion.  by H i l l  sol-  the vapor p r e s s u r e o f the b a t h i n g s o l u t i o n a f t e r  equilibra-  I f h i s e x p e r i m e n t a l data a r e c o r r e c t e d f o r a n u m e r i c a l e r r o r (11)  they p r e d i c t t h a t about  Experiments  27% o f the water i n a muscle f i b e r  have been performed  i s "bound".  on s t r i a t e d muscle t o determine  the f r a c t i o n o f c e l l u l a r water a v a i l a b l e to a c t as s o l v e n t f o r urea ( 1 9 ) . The r e s u l t s p r e d i c t a n e g a t i v e f r a c t i o n o f "bound w a t e r " .  This obviously  i n c o r r e c t r e s u l t may be due to the s i m i l a r i t i e s between the urea and the water m o l e c u l e s ; both a r e s m a l l and a r e capable o f forming hydrogen bonds. A s i m i l a r technique has been used by B o z l e r and L a v i n e  (20) to  demonstrate  58 t h a t o n l y about 207, o f the c e l l u l a r water  i n smooth muscle  a c t as s o l v e n t f o r f r u c t o s e and s u c r o s e .  The argument t h a t these sugars do  n o t e n t e r the f i b e r  i s a v a i l a b l e to  (21) has been c o u n t e r e d i n a r e c e n t paper by B o z l e r (22).  A n u c l e a r magnetic resonance t e c h n i q u e has been used to study the s t a t e of water  i n muscle  preted their results was  (23) and nerve  (24).  t o mean t h a t o n l y about 0.157, o f the water  "bound" whereas Chapman and McLauchlan  water  B r a t t o n e t a l (23)  inter-  i n muscle  (24) c o n c l u d e d t h a t "the b u l k of  i n s i d e the nerve i s i n a p a r t i a l l y o r i e n t e d s t a t e " .  This technique  s h o u l d prove e x t r e m e l y v a l u a b l e i n the near f u t u r e f o r i n v e s t i g a t i n g s t a t e o f water difficulties 248).  in living  the  c e l l s , but a t the p r e s e n t time t h e r e a r e many  in interpreting  the r e s u l t s o f such s t u d i e s  (25, pages  171-  Attempts have been made t o c a l c u l a t e the f r a c t i o n o f "bound water"  i n muscle by f r e e z i n g  (26) and microwave (27) t e c h n i q u e s , but the r e s u l t s  o b t a i n e d from these experiments may  a l s o be i n t e r p r e t e d  i n a v a r i e t y of  ways.  A t e c h n i q u e has r e c e n t l y been borrowed  from c o l l o i d  c h e m i s t r y by  S c h e u p l e i n and Morgan (28) to measure the f r a c t i o n o f "bound water" i n k e r a t i n membranes.  They measured the r a t e o f d e s o r p t i o n from a h y d r a t e d  t i s s u e by means o f a m i c r o b a l a n c e t e c h n i q u e .  Their results  indicate  that  the amount o f "bound water" i n f u l l y h y d r a t e d s t r a t u m corneum can be as much as f i v e times the d r y weight of the t i s s u e .  The r e s u l t s are  interesting,  but the r e l a t i o n s h i p between the "bound water" c a l c u l a t e d i n t h i s manner and the water u n a v a i l a b l e to a c t as s o l v e n t f o r s o l u t e s i s unknown a t p r e s e n t .  I t i s o b v i o u s l y important to know the f r a c t i o n of water muscle  f i b e r u n a v a i l a b l e to a c t as s o l v e n t f o r the main  c a t i o n , potassium.  I t was  t h i s f r a c t i o n t h a t was  in a  intracellular  determined d i r e c t l y a t  59 25° C i n a normal b a t h i n g s o l u t i o n by the use o f c a t i o n s e n s i t i v e m i c r o e l e c trodes.  The r e s u l t s i n d i c a t e t h a t a t l e a s t 42 ± 1.4% o f the water i n the  myoplasm i s "bound" i n such a manner that i t i s u n a v a i l a b l e to a c t as s o l v e n t for  the p o t a s s i u m i o n s .  When the f i b e r s were bathed i n s u c r o s e R i n g e r f o r  45 minutes the f r a c t i o n o f "bound water" i n the c e l l d e c r e a s e d t o 34 ± 3.67o. T h i s d e c r e a s e might r e f l e c t a t r u e change but  i n the s t a t e o f water i n the c e l l ,  i t c o u l d a l s o be due t o s t a t i s t i c a l v a r i a t i o n s , an i n c r e a s e i n the  a c t i v i t y c o e f f i c i e n t o f the myoplasm or an i n c r e a s e i n the b i n d i n g o f potassium.  Of these f o u r p o s s i b i l i t i e s ,  the l a s t seems most l i k e l y  t r u e because the f i b e r s d i d accumulate p o t a s s i u m i n the sodium f r e e Ringer s o l u t i o n .  to be sucrose  The r e s u l t s o f the membrane p o t e n t i a l experiments i n d i c a t e  t h a t 27%. o f the water i n the c e l l  i s "bound".  T h i s v a l u e , however,  should  be r e g a r d e d o n l y as a q u a l i t a t i v e i n d i c a t i o n , by a method independent o f m i c r o e l e c t r o d e measurements, giant  t h a t water i s "bound" i n muscle f i b e r s from the  barnacle.  Bound Sodium.  I t was found t h a t a t l e a s t 84% o f the sodium i n  muscle f i b e r s from the g i a n t b a r n a c l e was e x c l u d e d from the myoplasm which surrounded the m i c r o e l e c t r o d e .  T h i s i s q u a l i t a t i v e l y c o m p a t i b l e w i t h the  v a l u e o f 70% t h a t L e v (5) o b t a i n e d from s i m i l a r measurements on f r o g muscle, and agrees w i t h Robertson's (29) o b s e r v a t i o n t h a t 82% o f the sodium i n l o b s t e r muscle c o u l d n o t be e x t r u d e d by s u b j e c t i n g the muscle t o p r e s s u r e . These r e s u l t s a r e thus i n a c c o r d w i t h the h y p o t h e s i s that amounts o f sodium a r e bound  significant  t o myosin i n i n t a c t s t r i a t e d muscle f i b e r s . . The  measurements do n o t o f course prove the h y p o t h e s i s , f o r s i m i l a r  results  would be expected i f sodium was compartmentalized i n i n t r a c e l l u l a r organe l l e s r a t h e r than bound  to p r o t e i n s .  60 N u c l e a r magnetic resonance  (NMR) measurements may prove u s e f u l i n  d i s t i n g u i s h i n g between these two p o s s i b i l i t i e s . s e v e r a l years t h a t the NMR complexed  I t has been known f o r  spectrum o f sodium i s broadened when sodium i s  to p o l y a n i o n s (30-33).  The broadening i s presumably due to the  o r i e n t a t i o n o f the sodium n u c l e u s w i t h r e s p e c t to the n u c l e u s o f a n e i g h b o u r i n g atom.  T h i s , i n t u r n , c o u l d be due to the p o l a r i z a t i o n o f the o u t e r  s h e l l e l e c t r o n s by the p r o x i m i t y o f a charge t i o n o f e l e c t r o n s t o the o u t e r o r b i t a l s  (an i o n i c bond), or the a d d i -  (a c o v a l e n t bond).  Cope (34, 35)  performed experiments on f r o g muscles and c o n c l u d e d t h a t 70% o f the sodium d i d n o t c o n t r i b u t e to the NMR  spectrum.  As the c o m p a r t m e n t a l i z a t i o n o f  sodium i n o r g a n e l l e s s h o u l d n o t broaden the NMR  spectrum, the r e s u l t  seem to imply t h a t 70% o f the sodium i n f r o g s t r i a t e d muscle macromolecules.  broadens  i s bound t o  U n f o r t u n a t e l y , i o n p a i r f o r m a t i o n i s n o t the o n l y  which can cause broadening o f the NMR  spectrum o f sodium.  would  factor  F o r example, i t  i n a l c o h o l water m i x t u r e s as the volume f r a c t i o n o f a l c o h o l i n -  c r e a s e s , and becomes i n v i s i b l e  i n 957o o r a b s o l u t e a l c o h o l s  (33). The a c t i v -  i t y o f sodium i n a l c o h o l i c s o l u t i o n s i s c e r t a i n l y n o t lowered because o f extensive i o n p a i r formation. the a c t i v i t i e s  Indeed, as mentioned  o f ions i n g e n e r a l  earlier  i n t h i s Chapter,  (9, page 355) and sodium i n p a r t i c u l a r  ( p r e l i m i n a r y experiments) i n c r e a s e markedly i n a l c o h o l i c s o l u t i o n s . broadening o f the NMR  The  spectrum i n a l c o h o l i c s o l u t i o n s r e q u i r e s a p r o p e r  theoretical explanation.  A l s o , the p o s s i b i l i t y t h a t the " n u c l e a r  resonance a d s o r p t i o n o f sodium may be a l t e r e d by p r o t e i n s "  spin  (31) i n d i c a t e s  t h a t a s e r i e s o f c o n t r o l experiments on c o n c e n t r a t e d s o l u t i o n s o f p r o t e i n s which a r e known n o t to b i n d sodium s h o u l d be made.  Thus, a t the p r e s e n t  time, Cope's NMR experiments cannot be a c c e p t e d as d e f i n i t i v e e v i d e n c e t h a t t h e r e i s no  c o m p a r t m e n t a l i z a t i o n o f sodium i n s t r i a t e d muscle  fibers.  61 Sodium w i l l  o f course be c o n t a i n e d i n compartments which are  formed by i n v a g i n a t i o n s of the sarcolemma. these compartments w i l l here  be d i s c u s s e d i n Chapter V I .  I t need o n l y be  t h a t most o f the sodium i n these compartments would be expected  d i f f u s e out w i t h i n 45 minutes i f the f i b e r tion.  E s t i m a t e s of the volume o f  The  normal R i n g e r  (0.81) i s a p p r o x i m a t e l y (0.84).  Thus, i t may  n u c l e i , m i t o c h o n d r i a or c i s t e r n a e .  solu-  f o r 45 minutes i n  the same as t h a t of f i b e r s bathed i n  s a f e l y be concluded  sodium i n s i d e the sarcolemma o f a s t r i a t e d muscle f i b e r macromolecules or compartmentalized  to  i s exposed to a sodium f r e e  f r a c t i o n o f "bound sodium" i n f i b e r s bathed  sucrose Ringer  noted  t h a t most o f the i s e i t h e r bound to  i n i n t r a c e l l u l a r o r g a n e l l e s such  as  62 CHAPTER V  RELEASE OF BOUND SODIUM  A.  Inti'oduction  The r e s u l t s p r e s e n t e d i n the p r e v i o u s c h a p t e r i n d i c a t e t h a t over 80% o f the sodium i n s t r i a t e d muscle f i b e r s from the g i a n t b a r n a c l e i s n o t f r e e i n the myoplasm.  This finding  i s c o n s i s t e n t w i t h the h y p o t h e s i s t h a t a  s i g n i f i c a n t f r a c t i o n o f the sodium i n s t r i a t e d muscle f i b e r s myosin.  S i n c e e x t r a c t e d myosin r e l e a s e s  i t s associated a l k a l i metal  c a t i o n s when i t undergoes thermal d e n a t u r a t i o n myosin i n the l i v i n g  i s bound t o  ( 1 ) , i t was reasoned t h a t  c e l l might r e l e a s e i t s a s s o c i a t e d a l k a l i m e t a l c a t i o n s  d u r i n g an i r r e v e r s i b l e s h o r t e n i n g  induced by a change i n temperature.  To d e t e c t a r e l e a s e o f c a t i o n s from an i n t e r n a l s o u r c e , the ities  activ-  o f sodium, p o t a s s i u m and hydrogen ions i n the myoplasm were measured  when the f i b e r s s h o r t e n e d a t 37-40° C i n a sodium f r e e R i n g e r s o l u t i o n .  The  t o t a l c o n c e n t r a t i o n s o f sodium and p o t a s s i u m i n b o t h c o n t r o l and experimental  f i b e r s were a l s o measured.  The main o b s e r v a t i o n was t h a t d u r i n g the  i r r e v e r s i b l e s h o r t e n i n g o f the f i b e r  the a c t i v i t y o f sodium i n the myoplasm  i n c r e a s e d even though the t o t a l c o n c e n t r a t i o n o f sodium i n the e x p e r i m e n t a l f i b e r s decreased.  B. Methods  Experimental Procedure.  I n each experiment, f o u r muscle  fibers  from a d e p r e s s o r muscle o f Balanus n u b i l u s were d i s s e c t e d f r e e from one another. the  B e f o r e the s t a r t o f an experiment, two f i b e r s were c u t away from  b a s e p l a t e , washed f o r 10 seconds in. i s o s m o t i c s u c r o s e , b l o t t e d , and  [  63 p l a c e d i n pre-weighed stoppered b o t t l e s f o r flame p h o t o m e t r i c a n a l y s i s . of  the two remaining  One  f i b e r s was c a n n u l a t e d as d e s c r i b e d i n the p r e v i o u s  c h a p t e r , then t r a n s f e r r e d w i t h i t s b a s e p l a t e and companion f i b e r to the e x p e r i m e n t a l chamber.  The c a t i o n s e n s i t i v e m i c r o e l e c t r o d e was  through the c a n n u l a t e d tendon about  1 cm from the puncture  i n t o the myoplasm u n t i l zone  inserted  i t s s e n s i t i v e t i p was  ( F i g s . 2, 3 ) . Deeper p e n e t r a t i o n was  a v o i d e d because i t i n c r e a s e d the r a t e of breakage o f the m i c r o e l e c t r o d e s during c o n t r a c t i o n .  The membrane p o t e n t i a l o f the f i b e r was always measured  a d j a c e n t t o the t i p o f the c a t i o n - s e n s i t i v e m i c r o e l e c t r o d e . periment  the open t i p m i c r o e l e c t r o d e was i n s e r t e d and removed f r e q u e n t l y but  the c a t i o n - s e n s i t i v e m i c r o e l e c t r o d e was m a i n t a i n e d The  D u r i n g an ex-  in its initial  f r e q u e n t p u n c t u r i n g o f the membrane a t the 1 cm l e v e l produced  nificant tendon  decrease  i n the membrane p o t e n t i a l .  position. no s i g -  From the 1 cm l e v e l to the  l e v e l the membrane p o t e n t i a l d e c r e a s e d  l e s s than 5 mV,  indicating  t h a t the membrane a t the f i b e r - t e n d o n j u n c t i o n was w e l l s e a l e d around the cation-sensitive microelectrode.  In different  the experiments,  temperatures.  the muscle f i b e r was exposed to s o l u t i o n s a t  The bath temperature  5° C, then was r a i s e d t o 40° C. was r a i s e d  i n increments  was f i r s t  lowered  Between 5 and 35° C, the bath  from 25 to temperature  o f a p p r o x i m a t e l y 5° C by r e p l a c i n g the b a t h i n g  s o l u t i o n w i t h one a t a h i g h e r temperature.  Above 35° C, the bath  tempera-  t u r e was i n c r e a s e d a t the r a t e o f 0.5° C p e r minute by means o f a g l a s s insulated heating c o i l .  The b a t h i n g s o l u t i o n s were normal b a r n a c l e R i n g e r  s o l u t i o n below 35° C, and sodium f r e e i s o s m o t i c s u c r o s e R i n g e r s o l u t i o n above 35° C (see T a b l e 1 f o r the c o m p o s i t i o n o f these s o l u t i o n s ) . bath temperature terminated.  was h e l d c o n s t a n t  The experiments  (39-42° C) u n t i l  A t 40° C, the  the experiment  was  i n v o l v i n g measurements o f p o t a s s i u m and hydrogen  64 a c t i v i t y were t e r m i n a t e d  a f t e r 15 minutes a t 40° C, but  the experiments i n -  v o l v i n g measurements of sodium a c t i v i t y were c o n t i n u e d u n t i l  passed  a  maximum.  Membrane p o t e n t i a l , c a t i o n a c t i v i t y , and ed a t each new  temperature.  The  fiber  bath temperature was  l e n g t h were r e c o r d -  measured by means o f  an i r o n - c o n s t a n t a n thermocouple mounted i n the chamber, and was  measured.by a m i l l i m e t e r s c a l e .  e q u i l i b r i u m s h o u l d be v i r t u a l l y  S i n c e i t was  fiber  calculated  that  interval.  Between 35 and 40°  the m i c r o e l e c t r o d e p o t e n t i a l and bath temperature were r e c o r d e d During  tial  and  t o t a l c o n c e n t r a t i o n s o f sodium and p o t a s s i u m  companion and  c o n t r o l f i b e r s were determined  r  a„ were measured. K  digested i n concentrated n i t r i c  b e i n g a n a l y z e d on a Unicam SP900  Microelectrodes. (Chapter  i n the experimen-  by flame photometry i n the  The  f i b e r s were d r i e d , *  a c i d , n e u t r a l i z e d w i t h ammonia t o p r e v e n t  the f o r m a t i o n o f a f l o c c u l a n t p r e c i p i t a t e , and  scribed.  continuous-  f i b e r l e n g t h were made.  experiments i n which a„ and Na  tion  C,  t h i s p e r i o d , t h r e e to f i v e measurements o f the membrane poten-  The tal,  thermal  complete 2 minutes a f t e r a s o l u t i o n change,  a l l measurements were taken a f t e r t h i s time  ly.  length  then d i l u t e d  to 10 ml  before  spectrophotometer.  D e t a i l s o f the c o n s t r u c t i o n (2, 3) and  calibra-  IV) o f the c a t i o n - s e n s i t i v e m i c r o e l e c t r o d e s have been  For these experiments the s e n s i t i v e  de-  t i p s o f the m i c r o e l e c t r o d e s  were made r e l a t i v e l y l a r g e (30u. x 2C0fj.) to minimize breakage d u r i n g c o n t r a c tion.  Eqns. [16] and potassium  [17] d e s c r i b e the b e h a v i o r  microelectrodes.  The  of the sodium  and  e q u a t i o n which d e s c r i b e s the b e h a v i o r o f the  65 pH s e n s i t i v e m i c r o e l e c t r o d e , i s  ^ where E  4  =  +  S  H  l o g  10 H  [26]  a  i s the measured p o t e n t i a l  ( m i l l i v o l t s ) o f the m i c r o e l e c t r o d e i n a  XI I  s o l u t i o n c o n t a i n i n g hydrogen ions a t an a c t i v i t y a^; E ^ and o b t a i n e d by c a l i b r a t i o n .  are constants  The p o t e n t i a l s o f the sodium and p o t a s s i u m  sensi-  t i v e m i c r o e l e c t r o d e s were n o t a l t e r e d when the pH was changed from 7 t o 8. The  p o t e n t i a l s o f the pH m i c r o e l e c t r o d e s i n s t a n d a r d pH s o l u t i o n s were n o t  a l t e r e d by gross changes i n the N a Since a ^  a  and  and K  +  content.  +  were n o t measured on the same muscle f i b e r , the  f o l l o w i n g method o f a n a l y s i s was used to c a l c u l a t e a experiments p r e s e n t e d when the f i b e r  i n the p r e v i o u s c h a p t e r  &  from Eqn. [ 1 6 ] . The  indicated  t h a t a^, = 1.15  i s e q u i l i b r a t e d a t 25° C i n the b a r n a c l e R i n g e r  Thus, a ^ was e s t i m a t e d  from the  solution.  v a l u e s o f the two c o n t r o l f i b e r s .  assumed t h a t a ^ remained c o n s t a n t throughout  ( F i g . 3 ) . Once a ^ was e s t i m a t e d , a  M  &  I t was  the experiment, an assumption  j u s t i f i e d by the r e s u l t s o b t a i n e d from the p o t a s s i u m trode  M  sensitive microelec-  c o u l d be c a l c u l a t e d from Eqn.  [16].  The v a l u e s o f a p r e s e n t e d is.  i n F i g . 8 and T a b l e IV were c a l c u l a t e d  from Eqn. [ 1 7 ] , The mean c a l c u l a t e d r e s u l t s f o r a f o r the i m p e r f e c t s e l e c t i v i t y o f the p o t a s s i u m duced by t h i s a n a l y t i c technique relative  m  &  were used t o compensate  electrode.  The e r r o r s i n t r o -  s h o u l d be s m a l l because a ^ i s s m a l l  to a^, even though k^, (Eqn. [17]) i s r e l a t i v e l y  large  Each c a t i o n s e n s i t i v e m i c r o e l e c t r o d e was c a l i b r a t e d dard s o l u t i o n s b e f o r e and a f t e r an experiment. by more than ±1 mV the experiment was r e j e c t e d .  (0.5).  i n the s t a n -  I f the c a l i b r a t i o n s v a r i e d The m i c r o e l e c t r o d e s were  66 calibrated  i n the s t a n d a r d s o l u t i o n s a t temperatures between 5 and 40°  C  3  and the a p p r o p r i a t e temperature c o r r e c t i o n s were a p p l i e d to the e x p e r i m e n t a l microelectrode potential readings.  The p r e c a u t i o n s taken i n the s e l e c t i o n  o f open t i p m i c r o e l e c t r o d e s were i d e n t i c a l to those d e s c r i b e d i n Chapter IV, as was  the r e c o r d i n g a p p a r a t u s .  The r e s u l t s were a n a l y z e d u s i n g Eqns.  [24] and  [ 2 5 ] , which  d e s c r i b e the s e p a r a t i o n o f the sodium and water c o n t e n t o f a s i n g l e fiber  i n t o a " f r e e " and a "bound" f r a c t i o n .  "bound" sodium, B ^ / ( C ^ V ) , a  assigned The  a  from Eqn.  to OL because both a ^  f r a c t i o n o f water  a  and a ^ were not measured on the same f i b e r .  f r e e i n the myoplasm was  i n d i c a t e t h a t the a c t i v i t y c o e f f i c i e n t  ture.  To c a l c u l a t e the f r a c t i o n o f  [ 2 4 ] , a n u m e r i c a l v a l u e must be  t a i n e d i n the p r e v i o u s c h a p t e r (a = 0.57).  temperature  muscle  assumed to be the v a l u e ob-  R e s u l t s from pure  s h o u l d be r e l a t i v e l y  solutions  independent o f  ( 4 ) , but i t must be assumed t h a t a i s independent o f  tempera-  T h i s l a t t e r assumption w i l l be j u s t i f i e d when the p o t a s s i u m r e s u l t s  are  discussed.  C.  Results  Membrane P o t e n t i a l and S h o r t e n i n g . e x p e r i m e n t a l f i b e r s a r e p l o t t e d i n F i g . 6.  The mean r e s u l t s from the 27  When the temperature was  raised  from 7 to 25° C, the membrane p o t e n t i a l i n c r e a s e d by about  13 mV.  change was  r a i s e d above  found to be r e v e r s i b l e .  As the temperature was  30° C, the membrane p o t e n t i a l d e c r e a s e d .  Replacement  s o l u t i o n by sodium f r e e s u c r o s e R i n g e r a t 35° C ("S"  This  o f the b a r n a c l e R i n g e r i n F i g . 6) d i d not  produce any o b s e r v a b l e d i s c o n t i n u i t y i n the downward t r e n d o f the membrane potential.  67 The  l e n g t h o f the f i b e r s remained c o n s t a n t up to about 37° C.  Between 37 and 40° C, a s t r o n g spontaneous s h o r t e n i n g o c c u r r e d i n a l l 27 fibers.  T h i s event  d i d n o t seem t o be c a u s a l l y r e l a t e d to the decrease i n  membrane p o t e n t i a l f o r the f o l l o w i n g r e a s o n s .  First,  the membrane p o t e n t i a l  v a r i e d from 68 t o 33 mV a t the onset of the s h o r t e n i n g . depolarized fibers not  shorten u n t i l  i n a 250 mM potassium, the temperature o f t h i s  Second, r e l a x e d ,  calcium f r e e Ringer  solution did  s o l u t i o n was r a i s e d t o 37° C.  The  7 0 l  65-  >  60-  < »— Z  55-  -2  E u -3  a: C O  UJ Z <  50-  O •4  CO UJ  45-  *  X  O z U J  -5 4 0 -  — i — 10  30  20 T E M P  F i g . 6. V a r i a t i o n f i b e r l e n g t h (open the b a r n a c l e R i n g e r A t C a spontaneous through p o i n t s a r e  -1—  — i —  (°C)  — m  1—  40 : o TIME  10 (min) A T  20 4 0 ° C  i n the average membrane p o t e n t i a l ( c l o s e d c i r c l e s ) and c i r c l e s ) x^ith temperature and w i t h time a t 40° C. A t S s o l u t i o n was r e p l a c e d by sodium f r e e sucrose s o l u t i o n . s h o r t e n i n g o c c u r r e d i n a l l 27 f i b e r s . V e r t i c a l bars twice the s t a n d a r d e r r o r i n l e n g t h .  63 e x p e r i m e n t a l f i b e r which supported the weight o f the b a s e p l a t e s h o r t e n e d about 50% i n 1 minute, then c o n t i n u e d to s h o r t e n another 10-20% over the next 15 minutes  ( F i g . 6).  from about 4.0  t o 0.5  The companion f i b e r supported no weight and s h o r t e n e d cm.  Changes i n I n t r a c e l l u l a r i m e n t a l f i b e r a r e shown i n F i g . 7. the  Sodium.  The r e s u l t s  from a t y p i c a l  I n t h i s f i b e r , the a c t i v i t y o f sodium i n  myoplasm, a ^ , i n c r e a s e d from 0.003 t o 0.006 as the temperature a  r a i s e d from 7 to 35° C.  exper-  The average r e s u l t s  for this  temperature  was  interval,  0.015n  0.010-  0 . 0 0 5 -  a  N a l '  -T— 10  ~i— 20 TEMP  (°C)  ~ i — 30  — r 40  i  10 TIME  — i —  i 20 (min)  30  A T  i — 40  40°C  F i g . 7. V a r i a t i o n i n the i n t e r n a l a c t i v i t y of sodium, (a ) . , o f a t y p i c a l muscle f i b e r as the temperature was i n c r e a s e d to 40° C. Tne~symbols S and C a r e d e f i n e d i n F i g . 6. Open c i r c l e s r e p r e s e n t the-measurements i n T a b l e III.  however, r e v e a l e d no s i g n i f i c a n t  i n c r e a s e i n &^ .  When the normal  a  s o l u t i o n was r e p l a c e d by sodium f r e e sucrose Ringer figure), a^  always decreased, i n d i c a t i n g  a  of the f i b e r .  A f t e r the f i b e r shortened  Ringer  a t 35° C ("S" i n the  t h a t sodium ions were moving out a t 37-40° C, a„ always * Na T  increased.  J  This  i n c r e a s e was u s u a l l y r e c o r d e d w i t h i n 1 minute and always w i t h i n 5  minutes a f t e r s h o r t e n i n g . 0.015 i n 44 m i n u t e s . tained e a r l i e r .  I n t h i s experiment, a ^  I n other  a  i n c r e a s e d from 0.004 to  experiments, maximum a„ v a l u e s were ob' Na  (Table I I I ) .  TABLE I I I Sodium c o n c e n t r a t i o n * and a c t i v i t y * i n s i n g l e muscle f i b e r s b e f o r e and  after  (40° C) s h o r t e n i n g . 1  Minutes < Na>25  ^Na^O  0.058 0.076 0.060 0.085 0.123 0.099 0.163 0.080 0.061 0.081  0.046 0.053 0.060 0.052 0.051 0.069 0.099 0.123 0.055 0.085  C  0.089 ±0.010$"  ( a  a t 40° C T  11 21 45 38 14 40 18 27 44 35  0.069 ±0.008  (25° C)  Na 25 }  W 4 0 J(  "  <e**J%a>t  25° C  40° C  0.009 0.007 0.009 0.010 0.005 0.005 0.011 0.008 0.004 0.006  0.014 0.018 0.037 0.017 0.007 0.012 0.023 0.010 0.015 0.011  0.86 0.92 0.87 0.90 0.96 0.96 0.94 0.91 0.94 0.93  0.73 0.70 0.46 0.71 0.88 0.85 0.79 0.93 0.76 0.89  0.007 ±0.001  0.016 ±0.003  0.92 ±0.01  0.77 ±0.04  *Moles/kg f i b e r w a t e r . *Time a t 40 C f o r C ^ ) ^ r e a c h a maximum v a l u e . ^ F r a c t i o n o f bound Na c a l c u l a t e d from Eqn. [ 2 4 ] , §Mean ± s t a n d a r d e r r o r o f the mean. 3  t  o  I n d i v i d u a l data Table  III.  The average t o t a l  f o r the 10 e x p e r i m e n t a l  f i b e r s are presented i n  sodium c o n c e n t r a t i o n o f the two c o n t r o l f i b e r s  a n a l y z e d a t the s t a r t o f the experiment i s denoted as (^3)^5*  s  o  c  ^  u  m  a c t i v i t y i n the e x p e r i m e n t a l f i b e r s measured a t 25° C (open c i r c l e , F i g . 7) is  denoted as (a^ ) - , . Na 25 T  N  r  The ( C ) . and (a_ columns l i s t Na 40 Na 40 T  c e n t r a t i o n s and a c t i v i t i e s experiment the  l r  T  the sodium con-  i n the e x p e r i m e n t a l f i b e r s a t the end o f the  (open c i r c l e , F i g . 7 ) . The l a s t two columns o f the t a b l e  list  bound f r a c t i o n s o f sodium c a l c u l a t e d from the data by Eqn. [ 2 4 ] ,  A comparison o f (G. )_. and (C, ) , _ i n d i c a t e s t h a t the f i b e r s Na'25 Na'40 r  T  v  sodium d u r i n g the experiment. the  r  T  N  A l l the sodium l o s s p r o b a b l y o c c u r r e d a f t e r  f i b e r s were immersed i n the sodium f r e e s u c r o s e R i n g e r s o l u t i o n .  comparison o f (^3)^5  a n <  lost  ^ ^ Na^40 ^ a  e  i  R  o  n  s  t  r  a  t  e  s  A  the c o n s i s t e n t i n c r e a s e i n  a  a f t e r the onset o f s h o r t e n i n g  ( F i g . 7 ) . S i n c e sodium c o u l d n o t e n t e r  the  f i b e r from a sodium f r e e b a t h i n g s o l u t i o n , and s i n c e i t has been shown  t h a t sodium ions were i n f a c t l e a v i n g the f i b e r ,  i t may be concluded t h a t  e i t h e r sodium i o n s were r e l e a s e d from an i n t e r n a l s i t e , o r t h a t t h e r e was a l a r g e r e d u c t i o n i n the myoplasmic demands a p r o p o r t i o n a l it  f r e e water.  Since t h i s l a t t e r  alternative  i n c r e a s e i n the a c t i v i t i e s o f a l l myoplasmic  cations,  can be r u l e d o u t because a ^ remained r e l a t i v e l y c o n s t a n t ( F i g . 8 ) . Thus,  i t may be concluded t h a t the i n c r e a s e i n a„ r e s u l t s from a r e l e a s e o f Na sodium from an i n t e r n a l s i t e .  The c a l c u l a t i o n s i n T a b l e I show t h a t the  average p e r c e n t a g e r e d u c t i o n i n the f r a c t i o n o f "bound" sodium was 16 ± 4 (0.92 t o 0.77). Changes i n I n t r a c e l l u l a r Potassium.  The average r e s u l t s  seven e x p e r i m e n t a l f i b e r s a r e p l o t t e d i n F i g . 8.  When the f i b e r s were  heated from 7 to 35° C, t h e r e was no s i g n i f i c a n t change i n a ^ . a f t e r shortening,  changed  average o f 0.140 ± 0.008. slowly.  from  Immediately  o n l y from an average o f 0.130 ± 0.006 t o an  F o r 15 minutes a f t e r s h o r t e n i n g , a ^ decreased  71  0.160-  0.130-  0.100-  (° )i K  —i—  10  20 TEMP (°C)  —  30  r  40  0  10  20  TIME (min ) AT 40°C  F i g . 8. V a r i a t i o n i n the average i n t e r n a l a c t i v i t y o f p o t a s s i u m , (su.) ., o f seven f i b e r s as the temperature was i n c r e a s e d to 40° C. The shape or the c u r v e (broken l i n e ) between 35 and 40 C was deduced from i n d v i d u a l e x p e r i ments. The symbols S and C are d e f i n e d i n F i g . 6. Open c i r c l e s r e p r e s e n t the measurements i n T a b l e IV. V e r t i c a l bars through p o i n t s a r e t w i c e the standard error i n length.  I n d i v i d u a l data f o r the seven f i b e r s columns  denoted as  (Cjr)^,  cance as comparable (CL,)-,. and  (C ) .  columns  ( K?40' ^ ^ 2 5 G  a  n  d  a r e g i v e n i n T a b l e IV. ^ K^40 ^ A  a  f o r sodium i n T a b l e I I I .  v  e  t  h  e  s  a  m  e  Comparison  v a l u e s demonstrates t h a t the f i b e r s  lost  S  1  §  n  The i  f  i  -  o f the  significant  q u a n t i t i e s o f p o t a s s i u m i o n s , p r o b a b l y d u r i n g the p e r i o d o f d e p o l a r i z a t i o n at  40  C  ( F i g . 6 ) ; y e t comparison o f the  ( a ^ ) ^ and  (  a K  )^  Q  v a l u e s shows t h a t  72 TABLE IV P o t a s s i u m c o n c e n t r a t i o n * and a c t i v i t y * i n s i n g l e muscle and a f t e r  (25° C)  (40° C) s h o r t e n i n g .  < K>25  < K>40  K>25  < K>40  0.176 0.184 0.174 0.160 0.162 0.172 0.163  0.144 0.155 0.167 0.134 0.124 0.141 0.147  0.123 0.154 0.150 0.108 0.137 0.150 0.147  0.146 0.133 0.127 0.105 0.121 0.133 0.150  0.170 +0.003f  0.145 ±0.005  0.138 ±0.006  0.131 ±0.006  C  C  f i b e r s before  (a  a  *Moles/kg f i b e r water. T A f t e r 15 minutes a t 40° C. TMean ± s t a n d a r d e r r o r o f the mean.  the a c t i v i t y o f p o t a s s i u m i n the myoplasm was n o t s i g n i f i c a n t l y a l t e r e d .  There a r e two p o s s i b l e e x p l a n a t i o n s  f o r these r e s u l t s ; e i t h e r  p o t a s s i u m ions a r e r e l e a s e d i n t o the myoplasm from an i n t e r n a l s i t e , o r water  i s removed from the myoplasm to an i n t e r n a l s i t e .  t h a t the f i r s t  explanation  i s c o r r e c t , and f u r t h e r assumed t h a t a l l the  bound p o t a s s i u m ions a r e r e l e a s e d d u r i n g s h o r t e n i n g , o n l y 107o o f the t o t a l the r e s u l t s .  I f i t i s assumed  Eqn. [19] p r e d i c t s t h a t  f i b e r p o t a s s i u m need be bound and r e l e a s e d t o e x p l a i n  A l t e r n a t i v e l y , i f i t i s assumed t h a t the second e x p l a n a t i o n i s  c o r r e c t , and f u r t h e r assumed t h a t t h e r e i s no b i n d i n g o f p o t a s s i u m e i t h e r a t the b e g i n n i n g  o r t h e end o f the experiment, Eqn. [19] p r e d i c t s t h a t the  f r a c t i o n o f bound water must i n c r e a s e by 107, a t the expense mic f r e e water. alters  I t s h o u l d be emphasized  the conclusions  of the myoplas-  t h a t n e i t h e r o f these p o s s i b i l i t i e s  from the experiments i n which a ^ was measured.  Changes i n I n t r a c e l l u l a r Hydrogen.  The average r e s u l t s  from t e n  73  8.On  EXTERNAL 7.6INTE  7.2  6.8H pH 1  ~ i —  10  20 TEMP (°C)  — i —  30  i • i 40 vO  —  «  —  10  — I  20  TIME (min) AT 40°C  F i g . 9. V a r i a t i o n i n the average pH o f the myoplasm ( i n t e r n a l ) o f 10 f i b e r s as the temperature was i n c r e a s e d to 40° C. The v a r i a t i o n o f pH i n the bath s o l u t i o n w i t h temperature ( e x t e r n a l ) was a l s o measured and i s shown as a thin line. The shape o f the curve (broken l i n e ) between the e x p e r i m e n t a l p o i n t s a t 35 and 40 C was deduced from i n d i v i d u a l experiments. The symbols S and C a r e d e f i n e d i n F i g . 6. V e r t i c a l bars through p o i n t s a r e twice the standard e r r o r i n length.  experimental f i b e r s  i n x^hich the pH was measured a r e p l o t t e d  tween 7 and 30° C a l i n e a r decrease i n pH was observed and  the bath s o l u t i o n .  the temperature  i n F i g . 9.  i n both the myoplasm  I n both c a s e s , the pH changes were p r o b a b l y due to  dependence o f the b u f f e r systems.  I t is unlikely  myoplasmic pH changes were due to an inward d i f f u s i o n o f hydrogen because  Be-  o f the s h o r t time i n t e r v a l between measurements.  Above 30  that the ions C the  74 r a t e o f change o f the i n t e r n a l pH i n c r e a s e d s l i g h t l y . in  A t 35° C, no change  i n t e r n a l pH was observed when the bath s o l u t i o n was changed  free sucrose Ringer.  When s h o r t e n i n g o c c u r r e d  dropped suddenly i n a l l t e n f i b e r s .  to sodium  ("C" i n the f i g u r e s ) the pH  The average drop i n pH was from an  e x t r a p o l a t e d v a l u e o f 7.17 a t 40° C to a measured v a l u e o f 6.85 ± 0.04 a t 40° C.  Ten minutes a f t e r  the o n s e t o f s h o r t e n i n g  the pH reached an average  mininum v a l u e o f 6.77 ± 0.05.  These r e s u l t s l e a v e l i t t l e  sudden  pH o c c u r r e d a t the onset o f s h o r t e n i n g .  D.  r e d u c t i o n i n myoplasmic  Discussion  Variations t i a l w i t h temperature to  doubt t h a t a  i n Membrane P o t e n t i a l .  The changes  i n membrane poten-  ( F i g . 6) warrant comment even though they a r e secondary  the main f i n d i n g s .  From 7 to 25° C, the average membrane p o t e n t i a l i n -  c r e a s e d by 13.0 mV, y e t there was no s i g n i f i c a n t change i n e i t h e r a ^ or a ^ . M  Assuming  t h a t membrane p e r m e a b i l i t y to sodium and p o t a s s i u m remains c o n s t a n t ,  i t may be c a l c u l a t e d from the Goldman e q u a t i o n (5) that the membrane potential  s h o u l d o n l y i n c r e a s e 3.4 mV over t h i s  temperature range.  This  anomalous dependence o f membrane p o t e n t i a l on temperature, a l s o observed by Frumento  (6) i n f r o g muscle, may be due to e i t h e r a d e c r e a s e i n the c a t i o n  permeability ratio  (P /P„) or the e x i s t e n c e o f an e l e c t r o g e n i c pump (7-11). Na K.  Intracellular  Sodium and Water " B i n d i n g " .  c e n t r a t i o n v a l u e s measured here a r e s i m i l a r p r e v i o u s c h a p t e r , hence  to those r e p o r t e d i n the  they c o n f i r m q u a l i t a t i v e l y  about sodium and water " b i n d i n g " .  The a c t i v i t y and con-  the o r i g i n a l  conclusions  The c a l c u l a t e d mean f r a c t i o n o f "bound"  sodium was 0.92 ± 0.01 i n the p r e s e n t experiments and 0.84 ± 0.00 i n the p r e v i o u s experiments r e l i a b l e because  (Chapter I V ) .  i t was c a l c u l a t e d  The l a t t e r e s t i m a t e i s p r o b a b l y more from a , A  Na  a„. C K>  M  Na  and C., measurements on K  the same muscle  The 0.03  fiber.  c a l c u l a t e d mean f r a c t i o n o f "bound" water,  i n the p r e s e n t experiments and 0.41  ± 0.01  (i-Oc) , was  Both c a l c u l a t i o n s were based on the assumptions  Eqns.  [25].  The p r e v i o u s e s t i m a t e i s b e l i e v e d  leading to  to be more r e l i a b l e  f o r reasons s i m i l a r to those g i v e n f o r the bound sodium f r a c t i o n . p o s s i b l e , however, that the d i s c r e p a n c y between the r e s u l t s the b a r n a c l e s were c o l l e c t e d from d i f f e r e n t and s t o r e d i n sea water a t d i f f e r e n t  It is  is real  locations in different  temperatures  (4 and 10° C ) .  10° C was 0.73  low;  because seasons  Hinke ( 3 ) ,  i n a r e c e n t independent s e r i e s of measurements a l s o found t h a t the of "bound" water  fraction  i n b a r n a c l e s taken from the second l o c a t i o n and s t o r e d a t  (1-a) = 0.26.  i n s t e a d of 0.59,  (Note t h a t  i f a i s assumed to have a v a l u e of  the f r a c t i o n o f "bound" sodium c a l c u l a t e d from the  data o f T a b l e I I I changes by o n l y a s m a l l amount; from 0.92  Another p o s s i b i l i t y  i s t h a t an e l e c t r i c a l  to 0.90.)  e r r o r was  introduced i n  the c a t i o n s e n s i t i v e or open t i p m i c r o e l e c t r o d e measurements e i t h e r p r e s e n t o r the p r e v i o u s experiments. 6 mV  error  ±  i n the p r e v i o u s experiments  (Chapter I V ) . [24] and  0.27  I t can be-  i n the p o t a s s i u m p o t e n t i a l  (E^, i n Eqn.  d i s c r e p a n c y i n the c a l c u l a t e d "bound" water i n the sodium p o t e n t i a l  (E^  the "bound" sodium f r a c t i o n .  a  i n Eqn.  shown, f o r example,  i n the that a  [17]) c o u l d produce the  f r a c t i o n s whereas a 6 mV  [16]) would not a l t e r  error  the magnitude  of  Such an e r r o r i s u n l i k e l y , however, because o f  the c a r e f u l s e l e c t i o n o f o p e n - t i p m i c r o e l e c t r o d e s , and the r e j e c t i o n o f experiments when the c a t i o n - s e n s i t i v e m i c r o e l e c t r o d e p o t e n t i a l s s o l u t i o n s d e v i a t e d by more than 1  R e l e a s e of Bound Sodium. the mean a„  i n standard  mV.  I t was  o c c u r r e d when the muscle  demonstrated  t h a t an i n c r e a s e i n  f i b e r s s h o r t e n e d due  to exposure to  76 temperatures not due  between 37 and  to an inward  40°  C ( F i g , 6 and T a b l e I I I ) .  d i f f u s i o n of sodium ions because no  the b a t h i n g s o l u t i o n .  This increase  was  sodium i o n s were in.  I t i s u n l i k e l y t h a t the i n c r e a s e r e s u l t e d from an  e l e c t r i c a l a r t i f a c t because d u r i n g s h o r t e n i n g the p o t e n t i a l of the  potassium  s e n s i t i v e m i c r o e l e c t r o d e d i d not change s i g n i f i c a n t l y  the  tial of  the sodium s e n s i t i v e m i c r o e l e c t r o d e  a„ , and Na'  a t 25°  C  ( F i g . 18),  the c o r r e s p o n d i n g  167  0  ( F i g s . 9 and  i t may  be concluded  a l s o be concluded  decreases  in  t h a t the i n c r e a s e i n  t h a t the i n c r e a s e i n a ^ ,  i n the  or the r e l e a s e  a  "bound" sodium, i s c h a r a c t e r i s t i c of a temperature induced  c o n t r a c t e d a t 25° found  to be  s o l u t i o n , and  98 ± 4%  When b a r n a c l e muscle f i b e r s were  (9 experiments) o f the i n i t i a l  i n normal Ringer)  value  of  a f t e r 4 minutes i n the h i g h  a ^ M  t  n  e  potassium  97 ± 67o (9 experiments) o f the i n i t i a l v a l u e a f t e r 8 minutes  the h i g h p o t a s s i u m  solution  Myoplasmic pH.  hydrogen i o n was  6 mV.  (preliminary experiments).  Since the pH of the myoplasm was  the b a t h i n g s o l u t i o n was The  7.54  a t 25°  C,  7.43  and  the e q u i l i b r i u m p o t e n t i a l  average membrane p o t e n t i a l a t t h i s  however, was  66 mV.  myoplasm and  the b a t h i n g s o l u t i o n a c c o r d i n g to the N e r n s t  f o r r a t s k e l e t a l muscles  A l a r g e , r a p i d decrease  (12)  equation.  and  frog  the  pH  f o r the  temperature,  Thus, hydrogen i o n s are not d i s t r i b u t e d between  r e s u l t s have been r e p o r t e d f o r muscles of the c r a b a l t h o u g h not  shortening,  C by exposure to a s o l u t i o n c o n t a i n i n g 0.064 M KC1,  same f i b e r bathed  of  M Q  to the s h o r t e n i n g induced by a change  but p r o b a b l y not of a normal c o n t r a c t u r e .  in  As a  temperature. I t may  was  7).  r e d u c t i o n i n B„ / (C„ V) , observed Na Na ''  p r e s e n t experiments are c a u s a l l y r e l a t e d  of  poten-  of the hydrogen s e n s i t i v e m i c r o e l e c t r o d e changed more r a p i d l y than t h a t  sucrose Ringer  in  ( F i g . 8) and  the Similar  (1.3) ,  (14).  i n myoplasmic pH o c c u r r e d when the muscle  f i b e r s shortened. due  t o hydrogen  Even i f hydrogen  The r a p i d i t y o f the decrease i n d i c a t e s that i t was n o t  ions d i f f u s i n g  i n t o the f i b e r from the b a t h i n g  ions d i d d i f f u s e i n t o the f i b e r , no change i n pH would be  observed because o f the l a r g e b u f f e r c a p a c i t y o f the myoplasm. demonstrated  i n experiments performed  a l s o by the pH experiments r e p o r t e d fore,  solution.  i n depolarized  fibers  i n Chapter V I o f t h i s  T h i s was  (12, 13), and  thesis.  There-  the pH change observed a t 37-40° C i n these experiments was due to a  change i n the pK o f the o r g a n i c b u f f e r s i n the myoplasm.  Since  the c o n t r a c -  t i l e p r o t e i n s c o n s t i t u t e the main o r g a n i c b u f f e r , the change i n the pK values  p r o b a b l y s i g n i f i e s a d i s r u p t i o n of the m y o f i l a m e n t s .  L o c a t i o n o f Bound Sodium.  The b a s i c h y p o t h e s i s o f t h i s r e p o r t i s  t h a t a s i g n i f i c a n t f r a c t i o n o f the sodium to myosin.  i n s t r i a t e d muscle  I t i s known (1) t h a t e x t r a c t e d myosin undergoes  a t i o n a t a lower temperature  (37° C) than e x t r a c t e d a c t i n  a l s o known t h a t when e x t r a c t e d myosin  i s exposed  i t r e l e a s e s a s s o c i a t e d a l k a l i metal c a t i o n s  fibers  i s bound  t h e r n a l denatur-  (50° C ) .  It is  to temperatures above 37° C  (1) and ATP m o l e c u l e s ( 1 5 ) .  Thus, the o b j e c t o f these experiments was t o d i s r u p t the t h i c k or A ments i n an i n t a c t f i b e r and observe any changes  fila-  i n the f r a c t i o n o f "bound"  sodium.  There a r e s e v e r a l reasons f o r b e l i e v i n g t h a t e i t h e r the A o r the I f i l a m e n t s were s t r u c t u r a l l y a l t e r e d a t 37-40° C: shortening quired  occurred  a t t h i s temperature,  i n the b a t h i n g  shortening  occurred  solution for this  ( i ) an i r r e v e r s i b l e  ( i i ) calcium shortening,  i n d e p e n d e n t l y o f changes  ions were n o t r e -  (page 67), ( i i i ) the  i n the membrane p o t e n t i a l and  ( i v ) a l a r g e , r a p i d decrease i n pH accompanied  the s h o r t e n i n g .  Experiments performed on g l y c e r i n a t e d muscles, as w e l l as on ex-  tracted proteins, were d i s r u p t e d  i n d i c a t e t h a t i t was  the A and n o t the I f i l a m e n t s  i n these experiments a t 37-40° C.  A f i l a m e n t s was  observed by Aronson  h e a t i n g the muscles  Thermal d i s r u p t i o n o f the  i n g l y c e r i n a t e d muscles  f o r 2 minutes a t a c r i t i c a l  that  temperature  (16).  After  (which v a r i e d  from 43.5° C f o r f r o g to 51° C f o r mouse muscle) he observed a d e c r e a s e i n the b i r e f r i n g e n c e o f the muscle, and a l o s s seen under  the e l e c t r o n m i c r o s c o p e .  myoplasmic  pH of b a r n a c l e muscle  are p r o b a b l y r e l a t e d Aronson o b s e r v e d .  i n the A f i l a m e n t s t r u c t u r e as  The s h o r t e n i n g and the decrease i n the  f i b e r s exposed  t o temperatures o f 37-40° C  to the thermal d i s r u p t i o n o f the A f i l a m e n t s  that  The myosin m o l e c u l e s , themselves, however, need not be  c o m p l e t e l y denatured when the breakdown o f the A f i l a m e n t s o c c u r s .  In f a c t ,  a v a i l a b l e e v i d e n c e i n d i c a t e s t h a t a slow d e n a t u r a t i o n o f the myosin moleo c u l e s s h o u l d occur a t 37 e x t r a c t e d myosin  C, f o r i t takes about  to double a t t h i s  temperature  1 hour f o r the v i s c o s i t y o f (1).  Consistent with this  f a c t i s the o b s e r v a t i o n t h a t i n b a r n a c l e muscles  the r e l e a s e o f "bound"  sodium a t 37-40° C o c c u r s over a p e r i o d o f about  1/2  hour.  The r e s u l t s p r e s e n t e d i n t h i s c h a p t e r are thus i n e x c e l l e n t ment w i t h the h y p o t h e s i s t h a t much of the sodium muscle  fiber  i s bound to myosin.  d a t a c o u l d be i n t e r p r e t e d  i n an i n t a c t  striated  I t must be a d m i t t e d , however, t h a t the  i n a d i f f e r e n t manner.  the i n c r e a s e i n a, observed a t 37-40° C was Na T  due  I t c o u l d be argued to a r e l e a s e of  following reasons. duced  First, a^  &  that  sodium  from i n t r a c e l l u l a r compartments such as n u c l e i , m i t o c h o n d r i a or the nae o f the s a r c o p l a s m i c r e t i c u l u m .  agree-  cister-  T h i s e x p l a n a t i o n seems u n l i k e l y f o r the  does not i n c r e a s e f o l l o w i n g a p o t a s s i u m i n -  c o n t r a c t u r e a t 25° C ( p r e l i m i n a r y e x p e r i m e n t s ) .  Thus,  i t must be  argued t h a t the membranes are d i s r u p t e d by the temperature, not the s h o r t e n i n g , i n such a way  as to a l l o w sodium  to e x i t  from the compartments.  Note  79 however, t h a t a. always decreased between 35° C and the temperature a t which ' Na T  shortening  occurred  ( F i g . 7 ) . The membrane p o t e n t i a l v a r i e d between 68 and  33 mV a t the time o f s h o r t e n i n g , °> after  the s h o r t e n i n g  occurred.  b u t no i n c r e a s e Thus, there  i n a„ was n o t e d Na  until  i s a f a r b e t t e r c o r r e l a t i o n be-  tween the i r r e v e r s i b l e s h o r t e n i n g and the i n c r e a s e i n a„ than t h e r e i s ° Na between the membrane p o t e n t i a l and the i n c r e a s e i n a., . Na r  I n summary, i t has been demonstrated t h a t a s i g n i f i c a n t r e l e a s e o f "bound" sodium occurs temperature change.  f o l l o w i n g an i r r e v e r s i b l e s h o r t e n i n g I t was argued t h a t t h i s s h o r t e n i n g  induced  by a  was r e l a t e d t o a  d i s r u p t i o n o f the t h i c k o r A f i l a m e n t s , an i n d i c a t i o n t h a t a t l e a s t p a r t o f the f r a c t i o n o f "bound" sodium i n s t r i a t e d muscle f i b e r s myosin.  i s associated  with  80  /  CHAPTER V I  OPTICAL DENSITY CHANGES OF FIBERS IN SODIUM FREE SOLUTIONS  A.  Introduction  The o p t i c a l experiments r e p o r t e d below were undertaken t o o b t a i n f u r t h e r e v i d e n c e t h a t some o f the sodium i n s t r i a t e d muscle unavailable  to a sodium s e n s i t i v e m i c r o e l e c t r o d e  partmentalized.  The i d e a of u s i n g  light  the b i n d i n g o f ions t o macromolecules (1) u t i l i z e d thiocyanate  this  s c a t t e r i n g measurements to d e t e c t  i s n o t new.  increase  i s s c a t t e r e d from a c o l l o i d a l  in refractive  index.  s o l u t i o n because o f l o c a l  These a r e due to f l u c t u a t i o n s i n concen-  t i o n theory  by  Fluctuations  c o n t r i b u t e p r o p o r t i o n a l l y t o the square o f the r e s u l t i n g  in refractive  index.  to multicomponent  w h i l e Doty and S t e i n e r theory.  i n turn are counteracted  i n f r e e energy which a r i s e s from the f l u c t u a t i o n .  in concentration fluctuations  E d s a l l and h i s coworkers  t e c h n i q u e t o measure the b i n d i n g o f c h l o r i d e , c a l c i u m and  t r a t i o n caused by random thermal motion, which the  i s bound r a t h e r than com-  ions to p r o t e i n serum albumin.  Light fluctuations  f i b e r s which i s  E d s a l l e t a l (1) extended the f l u c t u a -  systems c o n t a i n i n g  (Z) approached  charged macromolecules,  the problem v i a the i n t e r f e r e n c e  Both these approaches a r e d i s c u s s e d  i n a review a r t i c l e ( 3 ) .  The t h e o r e t i c a l b a s i s f o r i n v e s t i g a t i n g the b i n d i n g o f ions t o macromolecules  by l i g h t s c a t t e r i n g measurements i s i l l u s t r a t e d  by Eqn. [Z7]  Hc/T = 1/M + ( Z c ) / (Zm M ) 2  2  3  which d e s c r i b e s component system  the r e l a t i o n between the t u r b i d i t y , T , o f an i d e a l  [27] three  ( c o n s i s t i n g of water., s a l t and macro-ion s a l t ) and the n e t  81 charge,  Z, on the macro-ion.  The term H r e p r e s e n t s a c o l l e c t i o n of o p t i c a l  c o n s t a n t s and v a r i e s i n v e r s e l y w i t h terms c and M r e p r e s e n t r e s p e c t i v e l y  the f o u r t h power o f the wavelength. the c o n c e n t r a t i o n and m o l e c u l a r  The  weight  o f the macro-ion w h i l e m^ r e p r e s e n t s the c o n c e n t r a t i o n o f the m i c r o - i o n o f o p p o s i t e charge.  T h i s simple r e l a t i o n can be d e r i v e d by a p p l y i n g the con-  d i t i o n o f Donnan e q u i l i b r i u m to a system f o r which the i o n i c too low and by c o n s i d e r i n g o n l y e l e c t r o s t a t i c  interactions  apparent, from Eqn. [27] t h a t i n c r e a s i n g the n e t charge, decreases  the turbidity,'?" , o f the s o l u t i o n .  sodium was bound to n e g a t i v e l y charged muscle, b a t h i n g the f i b e r  and  Z, on the macro-ion that i f  macromolecules w i t h i n the b a r n a c l e  i n a sodium f r e e s o l u t i o n would cause sodium to I f no i o n r e p l a c e d sodium  the n e t charge of the macromolecules would i n c r e a s e ,  the t u r b i d i t y o f the f i b e r would d e c r e a s e .  Thus, muscle f i b e r s  i n sodium f r e e s o l u t i o n s were examined f o r any decrease  B.  (1, 2, 3 ) . I t i s  I t was reasoned  move o f f the b i n d i n g s i t e s and out o f the f i b e r . on the b i n d i n g s i t e s ,  strength i s not  bathed  in turbidity.  Methods  Determination  o f A c t i v i t i e s and C o n c e n t r a t i o n s .  t i v e m i c r o e l e c t r o d e s were c a l i b r a t e d potassium  (Chapter  The sodium s e n s i -  i n s o l u t i o n s c o n t a i n i n g both  sodium and  IV) as w e l l as i n s o l u t i o n s c o n t a i n i n g 0.200 M KC1, 0.010  M NaCl and e i t h e r 0.004 or 0.040 M L i C l . e l e c t r o d e s were c a l i b r a t e d  The hydrogen s e n s i t i v e  i n s t a n d a r d b u f f e r s o f pH 7 and 8.  micro-  The m i c r o -  e l e c t r o d e s were c a l i b r a t e d b e f o r e and a f t e r each experiment and the r e s u l t s were r e j e c t e d u n l e s s the c a l i b r a t i o n s c o i n c i d e d (±1 mV).  Conventional  open  t i p m i c r o e l e c t r o d e s f i l l e d w i t h 3 M KC1 were used t o measure the membrane p o t e n t i a l o f the f i b e r s .  (The membrane p o t e n t i a l was o f course  from the p o t e n t i a l r e c o r d e d  subtracted  from the. sodium s e n s i t i v e m i c r o e l e c t r o d e i n the  82 TABLE V Solutions  * Normal Ringer NaCl  Sucrose Ringer  (M)  Tris Ringer  Calcium free Ringer  Potassium Ringer  Lithium Ringer  .450  .000  .000  .480  .000  .000  CaCl  2  .020  .020  .020  .000  .000  .020  MgCl  2  .010  .010  .010  .010  .010  .010  KC1  .008  .008  .008  .008  .488  .008  T r i s CI  .025  .025  .475  .025  .025  .025  LiCl  .000  .000  • .000  .000  .000  .450  Sucrose  .000  .650  .000  .000  .000  .000  The pH o f every s o l u t i o n i n t h i s t a b l e was 7.6. Normal R i n g e r b u f f e r e d t o pH = 9.6 w i t h t r i s o r t o pH = 5.5 w i t h CO., was a l s o used f o r some e x p e r i ments .  myoplasm.)  The p r e c a u t i o n s taken i n the s e l e c t i o n o f these m i c r o e l e c t r o d e s ,  the c a l i b r a t i o n procedure  and the r e c o r d i n g apparatus were i d e n t i c a l to  those d e s c r i b e d i n Chapter IV.  The  sodium s e n s i t i v e m i c r o e l e c t r o d e s were used  a c t i v i t y o f sodium i n the myoplasm o f f i b e r s bathed Ringer. of  i n sucrose and l i t h i u m  The hydrogen s e n s i t i v e m i c r o e l e c t r o d e s were used  the myoplasm o f f i b e r s bathed  t o measure the  to measure the pH  i n pH = 9.6 and pH = 5.5 R i n g e r .  p o s i t i o n s o f the b a t h i n g s o l u t i o n s used  i n these experiments  The com-  i s given i n  Table IV.  A n a l y t i c measurements were n o t made on f i b e r s used e l e c t r o d e experiments. movement o f a l k a l i metal  Separate experiments  were conducted  c a t i o n s when the f i b e r s were bathed  f o r micro-  to determine the i n l i t h i u m and  83 sucrose Ringer.  Seven f i b e r s a t t a c h e d to a s i n g l e b a s e p l a t e were d i s s e c t e d  f r e e from one another i n normal R i n g e r .  Two f i b e r s were taken as c o n t r o l s ;  they were b l o t t e d , s w i r l e d f o r 30 seconds a g a i n , then p l a c e d i n pre-weighed suspended  by t h e i r tendons  iniso-osmotic sucrose, b l o t t e d  bottles.  The remaining 5 f i b e r s were  i n the bath which c o n t a i n e d e i t h e r s u c r o s e o r  l i t h i u m R i n g e r , removed a t 1, 3, 5, 10 and 25 minutes same manner as the c o n t r o l s . nitric to  acid.  The r e s u l t i n g  The f i b e r s were then d r i e d and d i g e s t e d i n s o l u t i o n was n e u t r a l i z e d w i t h ammonia, d i l u t e d  10 ml and a n a l y z e d f o r sodium and p o t a s s i u m  on a Unicam SP 900 flame  (and l i t h i u m i f a p p l i c a b l e )  spectrophotometer;  Determination of R e l a t i v e Optical Density. a s i n g l e muscle  and handled i n the  f i b e r was suspended  c o n t a i n i n g normal R i n g e r .  by i t s tendon  As shown i n F i g . 10,  i n a c l e a r perspex chamber  The b a s e p l a t e o f the f i b e r was f i r m l y embedded i n  p l a s t i c i n e and the f i b e r was s t r e t c h e d t o about 120% o f i t s r e s t i n g The  chamber was then p o s i t i o n e d  and the o p t i c a l d e n s i t y stancy.  I n the f i r s t  i n a Beckman B spectrophotometer  (O.D,,) measured f o r 10 minutes  s e r i e s o f experiments, the s l i t w i d t h remained  con-  Normal R i n g e r  then r e p l a c e d by s u c r o s e R i n g e r and the O.D. measured f o r 25 minutes a t  a s i n g l e wavelength. at  ( F i g . 10)  to ensure i t s con-  s t a n t w h i l e the O.D. was determined a t v a r i o u s wavelengths. was  length.  After  v a r i o u s wavelengths.  and a f i n a l  t h i s p e r i o d o f time t h e O.D. was a g a i n measured  Sucrose R i n g e r was then r e p l a c e d by normal R i n g e r ,  scan o f wavelengths  made a f t e r 25 minutes.  I n a l l o t h e r exper-  iments, O.D. measurements were made o n l y a t 850 mu,.  Some p e r t i n e n t e x p e r i m e n t a l d e t a i l s a r e as f o l l o w s . photometer  The s p e c t r o -  was equipped w i t h a c o n s t a n t v o l t a g e t r a n s f o r m e r , and was always  t u r n e d on one hour p r i o r  to an experiment.  The wavelength  d i a l was  84  Cannula  Light from Ferry prism Perspex^chamber  • gated tendon Muscle fibre (diam. 1-3 mm)  J 5 cm  ii/^~"t^~  Baseplate  Variable slit «.l mm  1  !  1 1  /  Lens 2mm slit S I 1 T  Drain  ' ^  Shutter  Muscle fibre  /  c , 6  Phototube  1 m  m  exit slit  F i g . 1 0 . Diagram o f a s i n g l e muscle f i b e r p o s i t i o n e d i n the perspex b a t h i n g chamber ( l e f t ) , and p l a n view o f the o p t i c a l pathway ( r i g h t ) .  c a l i b r a t e d w i t h a mercury  lamp.  use t o remove dust p a r t i c l e s .  A l l b a t h i n g s o l u t i o n s were f i l t e r e d b e f o r e The chamber f i l l e d w i t h the b a t h i n g s o l u t i o n  was used as the b l a n k a t a l l wavelengths. readings d i d not coincide  (±2%),  The w i d t h o f the beam was always u s u a l l y much l e s s because ments.  I f the f i n a l and i n i t i a l  blank  the e x p e r i m e n t a l r e s u l t s were r e j e c t e d . l e s s than 1/2 the w i d t h o f the f i b e r , and  l a r g e , f l a t f i b e r s were s e l e c t e d f o r these' e x p e r i -  A l l experiments were conducted a t room temperature  L i m i t a t i o n s o f the E x p e r i m e n t a l Apparatus  (23-25° C).  and Method.  The o p t i c a l  85 d e n s i t y , O.D.,  i s d e f i n e d i n Eqn. [28] O.D. = - l o g  where I / I  represents  D  light  [28]  (I/I ) o  the t r a n s m i t t a n c e ,  the i n c i d e n t i n t e n s i t y . total  1 0  o r the r a t i o o f the t r a n s m i t t e d t o  The t u r b i d i t y ,  s c a t t e r e d to the p r o d u c t  T, i s d e f i n e d as the r a t i o o f the  o f the i n c i d e n t i n t e n s i t y o f l i g h t and  volume o f s o l u t i o n (or muscle) which s c a t t e r s l i g h t . an e x t i n c t i o n c o e f f i c i e n t , and when a b s o r p t i o n  T  = -(2.303/O  where L i s the o p t i c a l path  I t may be expressed  is negligible, [29]  log (I/I ) 1 0  as  o  l e n g t h - o f the beam i n the muscle f i b e r .  It is  apparent from Eqns. [28] and [29] t h a t i n the absence o f a b s o r p t i o n the t u r b i d i t y o f the f i b e r r e l a t i v e t o i t s i n i t i a l equal  t o the O.D. o f the f i b e r r e l a t i v e  Ringer.  value  i n normal Ringer i s  to i t s i n i t i a l  i n normal  I n the p r e s e n c e o f g e n e r a l i z e d a b s o r p t i o n , Eqn. [29] must be modi-  f i e d , and to a f i r s t  approximation = -(2.303/JL) l o g  1 ( )  (I/I )  [30]  o  where £i i s an e x t i n c t i o n c o e f f i c i e n t due t o a b s o r p t i o n . manipulation  A simple  algebraic  can then be made t o show t h a t the change i n r e l a t i v e  turbidity  i s always g r e a t e r than the change i n the r e l a t i v e O.D. a p o s s i b l e constant in  value  a b s o r p t i o n was accepted  Thus,  as an e r r o r because the change  the t u r b i d i t y o f the f i b e r was u n d e r e s t i m a t e d .  as the wavelength o f i n c i d e n t l i g h t  (Appendix 1 ) .  This error w i l l  i n c r e a s e s because g e n e r a l i z e d  decrease absorption  d e c r e a s e s Xfith i n c r e a s i n g wavelength.  I n these experiments, the h e i g h t o f the l i g h t beam was 19 mm a t the  l a s t entrance  slit,  about 12 mm a t the muscle and 6 mm a t the e x i t  The  t h e o r y o f l i g h t s c a t t e r i n g assumes p a r a l l e l  slit.  i n d i c e n t l i g h t , but many  i n v e s t i g a t o r s use c o n v e r g i n g l i g h t Stacey  f o r s c a t t e r i n g measurements, and as  (4) has s t a t e d " i n p r a c t i c e the e r r o r due to the use o f c o n v e r g i n g  l i g h t has n o t been a s e r i o u s one."  A more s e r i o u s e r r o r a r i s e s from the  f a c t t h a t the l i g h t beam c o u l d n o t be p r e c i s e l y f o c u s s e d . l i g h t beam i n c r e a s e d the e x i t s l i t .  from l e s s than  A smaller  s c a t t e r e d through v e r y  to .6 mm a t  the e x i t  slit  e x i t s l i t would have c o l l e c t e d l e s s  small angles.  t h a t the measured change i n O.D, accepted  .2 mm a t the e n t r a n c e s l i t  Thus, the d i v e r g i n g w i d t h o f the beam f o r c e d  to have a w i d t h o f .6 mm. light  The w i d t h o f the  T h i s e r r o r , however,  implies  i s l e s s than the change i n 'Y, hence i t was  (Appendix 2 ) .  I n any h i g h l y t u r b i d medium l i k e a muscle f i b e r , secondary s c a t t e r ing  complicates  the i n t e r p r e t a t i o n o f l i g h t s c a t t e r i n g measurements.  the s c a t t e r i n g p a r t i c l e s have one dimension g r e a t e r l e n g t h o f the i n c i d e n t l i g h t , Steiner  (5) have d i s c u s s e d  p h o t o m e t r y measurement and  than 1/20 o f the wave-  i n t e r n a l interference also occurs.  of t u r b i d i t y .  A l t h o u g h both secondary s c a t t e r i n g when the a b s o l u t e  a s o l u t i o n i s measured, these f a c t o r s p r o b a b l y may be ignored t u r b i d i t y o f muscle f i b e r s i n v a r i o u s  The e x i s t e n c e  t u r b i d i t y of when the  s o l u t i o n s i s measured.  e f f e c t o f i n t e r n a l i n t e r f e r e n c e on the t u r b i d i t y s h o u l d throughout the experiment.  Doty and  t h i s phenomenon i n an a r t i c l e on the s p e c t r o -  i n t e r n a l i n t e r f e r e n c e must be c o n s i d e r e d  relative  When  remain  constant  o f secondary s c a t t e r i n g  t h a t the a c t u a l change i n t u r b i d i t y i s g r e a t e r  The  implies  than the change i n 0 D.  i s measured and t h i s e f f e c t can be minimized by making measurements  o  that  a t long  wavelengths.  C.  Results  Sucrose R i n g e r .  F i g . 11 summarizes the flame p h o t o m e t r i c measure-  87 ments of the sodium and p o t a s s i u m ing  times  plasm. a„ '  c  concentrations of f i b e r s  i n sodium f r e e sucrose R i n g e r . . i s a l s o shown.  The  soaked f o r v a r y -  a c t i v i t y of sodium i n the myo-  S i n c e the sodium s e n s i t i v e m i c r o e l e c t r o d e s were  Na'  n o t a b s o l u t e l y s e l e c t i v e f o r sodium a s m a l l c o r r e c t i o n f o r the a c t i v i t y potassium (Eqn.  i n the myoplasm, a^, was  [16]).  1  ,80  of  a p p l i e d to the e l e c t r o d e r e a d i n g s  The v a l u e of a^. was  not measured i n these experiments,  but  was  [K ] +  160-  °  140H  120-  4 >  o  100-  8 0 Z O  <  60-  z o  4 0 -  -5-  2 0 -  1  r-  T  5  10 TIME  | min)  IN  S O D I U M  15 FREE  S U C R O S E  20  25  RINGER  F i g . 11. The t o t a l c o n c e n t r a t i o n s of sodium and p o t a s s i u m i n f i b e r s bathed i n sodium f r e e s u c r o s e R i n g e r . I n i t i a l p o i n t s are the average of measurements from 20 f i b e r s . Other p o i n t s are the average of measurements from 10 fibers. The a c t i v i t y of sodium i n the myoplasm, a , as measured by a sodium s e n s i t i v e m i c r o e l e c t r o d e , i s a l s o shown. The number o f experiments, n, was 5. The v e r t i c a l bars are twice the S.E. i n l e n g t h .  88 e s t i m a t e d from the measured average  c o n c e n t r a t i o n of potassium  ( F i g . 11)  u s i n g the e m p i r i c a l r e l a t i o n a^, = .87[K] (Chapter V ) .  From the data p r e s e n t e d percentages  of total fiber  f i b e r s were bathed ly. and  I n comparison, 807o.  i n Chapter  IV, i t was c a l c u l a t e d  t h a t the  sodium u n a v a i l a b l e t o a m i c r o e l e c t r o d e when  i n normal and s u c r o s e R i n g e r were 84% and 81% r e s p e c t i v e the c a l c u l a t e d v a l u e s from the data o f F i g . 11 a r e 85%,  These e s t i m a t e s do n o t take i n t o account  the l a r g e  extracellular  space which was r e c e n t l y d i s c o v e r e d i n s i n g l e b a r n a c l e muscle f i b e r s (5). T h i s compartment was found by two independent  about  57, o f the t o t a l f i b e r volume  t e c h n i q u e s , and i t presumably c o n t a i n s about  of sodium/kg f i b e r water f i b e r s bathed  to comprise  .030 moles  (6). I f the t o t a l c o n c e n t r a t i o n o f sodium i n  i n normal R i n g e r ,  .066 moles/kg f i b e r water  ( F i g . 11), i s  c o r r e c t e d f o r the sodium i n the e x t r a c e l l u l a r compartment, the percentage o f i n t r a c e l l u l a r sodium u n a v a i l a b l e to the m i c r o e l e c t r o d e i n normal R i n g e r becomes 72%.  T h i s v a l u e i n c r e a s e d t o 80% when the f i b e r s were bathed f o r  25 minutes i n s u c r o s e R i n g e r . t h a t the f r a c t i o n o f t o t a l decreased  Thus, the p r e v i o u s o b s e r v a t i o n (Chapter IV)  f i b e r sodium u n a v a i l a b l e to the m i c r o e l e c t r o d e  s l i g h t l y when the f i b e r s were bathed  i n sucrose Ringer  i s ex-  p l a i n e d by the l a r g e e x t r a c e l l u l a r space o f the f i b e r s .  The  t r a n s m i t t a n c e o f s i n g l e muscle f i b e r s  a f u n c t i o n o f wavelength. fibers  i s graphed  i n F i g . 12 as  The lower curve i s the t r a n s m i t t a n c e o f the  i n normal R i n g e r and the upper curve i s the t r a n s m i t t a n c e o f the same  f i b e r s a f t e r 25 minutes i n sucrose R i n g e r .  The apparent  discontinuity in  the curves between 600 and 650 mu. i s an a r t i f a c t which a r i s e s because a d i f f e r e n t group o f f i b e r s had to be used above 650 mu,.  f o r the wavelengths below 600 and  No d i s c o n t i n u i t y was observed  i n the t r a n s m i t t a n c e s o f two  60  1  I 5 0 0  1  1  600 W A V E  1  1  7 0 0 L E N G T H  1  1  8 0 0  1 900  (m ) M  F i g , 12. The t r a n s m i t t a n c e of s i n g l e muscle f i b e r s i n normal R i n g e r (lower curve) and a f t e r 25 minutes i n sucrose R i n g e r (upper curve) as a f u n c t i o n o f wavelength.  f i b e r s which were scanned from 600 to 900 imj. i n normal and s u c r o s e It  i s apparent  a muscle f i b e r  Ringer.  from F i g . 12 t h a t a t a g i v e n wavelength the t r a n s m i t t a n c e o f i s g r e a t e r i n sucrose than i n normal R i n g e r .  Note a l s o t h a t  i n e i t h e r s u c r o s e o r normal R i n g e r , the t r a n s m i t t a n c e i n c r e a s e s w i t h wavelength.  In an i d e a l s o l u t i o n , f o u r t h power of the wavelength. turbidity  (or O.D.)  the t u r b i d i t y v a r i e s  i n v e r s e l y w i t h the  T h i s i m p l i e s t h a t a p l o t o f the l o g o f the  a g a i n s t the l o g of the wavelength w i l l y i e l d a s t r a i g h t  90 l i n e w i t h a s l o p e o f -4.  T h i s r e l a t i o n s h i p was  muscle f i b e r s , a l t h o u g h the data of F i g . 12 tance does i n c r e a s e w i t h the wavelength. f o u r t h power r e l a t i o n s h i p t e r f e r e n c e , secondary  illustrates  The  i s presumably due  not observed  for single  t h a t the t r a n s m i t -  d e v i a t i o n from the i n v e r s e  to the e x i s t e n c e of i n t e r n a l i n -  s c a t t e r i n g and a b s o r p t i o n .  Internal  i n t e r f e r e n c e alone  can change the i n v e r s e f o u r t h power r e l a t i o n s h i p between t u r b i d i t y and wavel e n g t h to an i n v e r s e square The  relationship  (4).  t r a n s m i t t a n c e of a muscle f i b e r  i s dependent on the t h i c k n e s s  F i g . 13. The o p t i c a l d e n s i t y , O.D., o f s i n g l e muscle f i b e r s r e l a t i v e to the i n i t i a l v a l u e of the O.D. i n normal R i n g e r as a f u n c t i o n of wavelength. The data i n curve 2 are from f i b e r s bathed f o r 25 minutes i n s u c r o s e R i n g e r ; the d a t a i n curve 3 a r e from the same f i b e r s 25 minutes a f t e r they were r e t u r n e d to normal R i n g e r .  91 of  the f i b e r or o p t i c a l path l e n g t h .  T h i s dependence on o p t i c a l p a t h l e n g t h  can be a v o i d e d by c o n s i d e r i n g the r e l a t i v e o p t i c a l d e n s i t y (O.D.) o f a f i b e r (Fig.  13) r a t h e r than the t r a n s m i t t a n c e .  The r e l a t i v e O.D. drops  i n i t i a l v a l u e o f 1 (curve 1, F i g . 13) i n normal R i n g e r 2, F i g . 13) a f t e r 25 minutes i n s u c r o s e R i n g e r . at  t h e l o n g e s t wavelength  scattering  from an  t o low v a l u e s  (curve  The l a r g e s t change o c c u r s  where the e r r o r s due t o p o s s i b l e a b s o r p t i o n ,  through s m a l l a n g l e s and secondary  s c a t t e r i n g are minimal.  3, F i g . 13, shows t h a t t h i s phenomenon i s almost c o m p l e t e l y  Curve  reversible.  When normal R i n g e r was r e t u r n e d to t h e chamber, the r e l a t i v e O.D. o f t h e fibers  i n c r e a s e d w i t h i n 25 minutes t o over  T r i s Ringer.  90% o f the i n i t i a l  value.  I n F i g . 14 the r e l a t i v e O.D. ( a t 850 mu.) o f s i n g l e  muscle f i b e r s bathed  i n sodium f r e e , t r i s  s u b s t i t u t e d R i n g e r i s graphed as  a f u n c t i o n o f time.  The time f o r t h e O.D. o f the f i b e r s to r e a c h a c o n s t a n t  value i n either t r i s  or s u c r o s e R i n g e r was i d e n t i c a l  (10-15 min.,  but the magnitude o f the decrease was n o t as g r e a t i n t r i s Ringer.  F i g . 14)  as i n s u c r o s e  When normal R i n g e r was r e t u r n e d t o t h e chamber, the O.D. o f the  f i b e r s i n c r e a s e d r a p i d l y to i t s i n i t i a l v a l u e  ( F i g . 1 4 ) . The r e c o v e r y o f  the O.D. o f f i b e r s bathed  i n s u c r o s e R i n g e r was a l s o noted  than the i n i t i a l  i n t h e O.D.  decrease  Potassium Ringer.  I n F i g . 15 the r e l a t i v e O.D. (at 850 mu.) o f  s i n g l e muscle f i b e r s bathed s t i t u t e d R i n g e r i s graphed soak the f i b e r s  i n sodium f r e e , c a l c i u m f r e e , p o t a s s i u m as a f u n c t i o n o f time.  sub-  I t was n e c e s s a r y t o p r e -  i n a c a l c i u m f r e e s o l u t i o n , and remove c a l c i u m from the  sodium f r e e , p o t a s s i u m the f i b e r s .  t o be more r a p i d  s u b s t i t u t e d s o l u t i o n to p r e v e n t the c o n t r a c t u r e o f  The O.D. o f the f i b e r s was f i r s t  then i n c a l c i u m f r e e R i n g e r .  Exposure  measured i n normal R i n g e r ,  t o c a l c i u m f r e e R i n g e r f o r 25 minutes  92  -5  u< i—  o.  O  0 . 4 -  n=5 0 . 2 -  " T " 10 -TIME  —r— 20  I 15  (min) I N TRIS  R I N G E R -  2 5 / 0 —4-  5 TIME  10  2 0  15  (min) I N N O R M A L  F i g . 14. The r e l a t i v e O.D. (850 imj.) o f s i n g l e muscle f i b e r s bathed Ringer and then i n normal R i n g e r .  lowered  shown i n F i g . 15.  the O.D. decreased as  T h i s decrease was g r e a t e r than the decrease  R i n g e r , b u t l e s s than the decrease  i n sucrose Ringer.  in tris  The r e c o v e r y o f the  O.D. was v e r y slow compared to the r e c o v e r y o f the O.D. o f f i b e r s  after  in tris  the O.D. s l i g h t l y (note the r e l a t i v e O.D. a t z e r o time i n F i g . 15).  When t h i s s o l u t i o n was r e p l a c e d by p o t a s s i u m R i n g e r ,  bathed  25  R I N G E R — -  i n sucrose or t r i s Ringer. 50 minutes i n normal R i n g e r  As p o t a s s i u m  The O.D. was s t i l l  initially  increasing s l i g h t l y  ( F i g . 15).  i s more permeable than sodium, one might expect  that  93  1.0-  F i g . 15. The r e l a t i v e O.D. (850 lmx) o f s i n g l e muscle f i b e r s bathed i n p o t a s s i u m R i n g e r and then i n normal R i n g e r . The f i b e r s were i n i t i a l l y bathed f o r 25 minutes i n c a l c i u m f r e e R i n g e r .  a substantial bathed  i n c r e a s e i n the volume o f the f i b e r s o c c u r r e d when they were  i n the p o t a s s i u m R i n g e r s o l u t i o n .  crease i n t h i s s o l u t i o n , A control bathed  experiment  The volume o f the f i b e r s d i d i n -  but the i n c r e a s e was so s l i g h t as t o be n e g l i g i b l e .  indicated  t h a t the p e r c e n t a g e water  content of f i b e r s  i n normal R i n g e r was 76.6 ± 0.1 (n=5) whereas the percentage  content of f i b e r s  from the same muscle  R i n g e r , then f o r 25 minutes  Lithium Ringer.  bathed f o r 25 minutes  water  i n calcium free  i n p o t a s s i u m R i n g e r was 77.7 ± 0.2 (n=9) .  I n F i g . 16 (upper curve) the r e l a t i v e  O.D.  94  25/0 -TIME  (min) IN  pH  9.6  5  RINGER  10  TIME  15  (min) IN  N O R M A L  2 0  25  RINGER  -  F i g . 16. The r e l a t i v e O.D. (850 1141) o f s i n g l e muscle f i b e r s bathed i n l i t h i u m R i n g e r (upper graph) and i n pH = 9.6 R i n g e r (lower g r a p h ) .  (at 850 mu.) o f s i n g l e muscle f i b e r s bathed ted R i n g e r i s graphed observed.  as a f u n c t i o n  i n sodium f r e e , l i t h i u m  o f time.  No decrease  I n f a c t , a s l i g h t , but s t a t i s t i c a l l y  r e d , which was r e v e r s i b l e .  After  substitu-  i n the O.D. was  s i g n i f i c a n t increase occur-  25 minutes i n l i t h i u m R i n g e r , the r e l a t i v e  O.D. i n c r e a s e d t o 1.033 ± .003 (n=7) and upon r e t u r n i n g  normal R i n g e r t o the  b a t h i n g chamber the r e l a t i v e O.D. decreased t o 1.004 ± .008 (n=7).  The  changes i n t h e t o t a l c o n c e n t r a t i o n s o f p o t a s s i u m ,  l i t h i u m i n s i n g l e muscle, f i b e r s bathed  sodium and  i n l i t h i u m Ringer are i l l u s t r a t e d i n  95  180  Initial  Ov.  =6+2  (n=6)  T "  ~~r  TIME  (min)  — I  15  10  IN S O D I U M  FREE LITHIUM  20  25  RINGER  , F i g . 17. The t o t a l c o n c e n t r a t i o n s o f p o t a s s i u m , sodium and l i t h i u m i n f i b e r s bathed i n sodium f r e e , l i t h i u m s u b s t i t u t e d R i n g e r . I n i t i a l p o i n t s a r e the average o f measurements from 20 f i b e r s . Other p o i n t s a r e the average o f measurements from 10 f i b e r s .  F i g . 17.  The c o n c e n t r a t i o n of p o t a s s i u m i n the f i b e r s remained c o n s t a n t  ( F i g . 17) as i n f i b e r s bathed i n s u c r o s e R i n g e r ( F i g . 11).  A f t e r 25 minutes  i n l i t h i u m R i n g e r the sodium c o n c e n t r a t i o n d e c r e a s e d by .080 - .044 = .036 moles/kg f i b e r water and the l i t h i u m .002 = .039 moles/kg f i b e r water recalled  c o n c e n t r a t i o n i n c r e a s e d by 0.41 -  ( F i g . 17).  F o r comparison, i t s h o u l d be  t h a t the d e c r e a s e i n the sodium c o n c e n t r a t i o n a f t e r  s u c r o s e R i n g e r was  .066 - .035 = .031 moles/kg f i b e r water  25 minutes in.. •  ( F i g . 11).  96 One would l i k e to know how much o f the decrease i n t o t a l concentration of f i b e r s sodium l e a v i n g actually  soaked i n l i t h i u m  the e x t r a c e l l u l a r  l e a v i n g the c e l l .  o r s u c r o s e R i n g e r was due to  space and how much was due to sodium  As mentioned above, the e x t r a c e l l u l a r  p r i s e s about 57„ o f the volume o f a s i n g l e tains  .006 moles/kg f i b e r water o f i n t r a c e l l u l a r .009 moles/kg f i b e r water o f l i t h i u m  Thus, i n l i t h i u m  e n t e r s the c e l l  moles/kg f i b e r water o f sodium l e a v e s the c e l l  (6)  t h a t the e x t r a c e l l u l a r  through the s a r c o -  I n s u c r o s e R i n g e r about .001 i n 25 minutes.  on the e x p e r i m e n t a l f i b e r s .  i n either  sucrose or t r i s  Ringer.  Thus, a  A r e a s o n a b l e e s t i m a t e would  appear t o l i e between .005 and .010 moles/kg f i b e r water. free i n t r a c e l l u l a r  sodium l o s t  approximately i d e n t i c a l moles/kg f i b e r water. the  I t should be  v a l u e cannot be a s s i g n e d t o the c o n c e n t r a t i o n o f i n t r a c e l l u l a r  sodium l o s t  of  and about  space may have been s l i g h t l y o v e r e s t i m a t e d  and t h a t i t was n o t measured  definite  R i n g e r , about  sodium l e a v e s the c e l l  These d i f f e r e n c e s a r e n o t s i g n i f i c a n t .  stressed  space com-  muscle f i b e r , hence p r o b a b l y con-  .030 moles/kg f i b e r water o f sodium.  lemma.  sodium  t o t a l loss  after  i n either  25 minutes  The c o n c e n t r a t i o n  s u c r o s e or t r i s R i n g e r i s  ( F i g . 18) and equal to about .002  When t h i s v a l u e i s s u b t r a c t e d from the e s t i m a t e o f  of i n t r a c e l l u l a r  sodium, i t i s apparent t h a t o n l y about .005  moles/kg f i b e r water o f "bound" sodium was removed by the s u c r o s e o r  lithium  Ringer.  As mentioned above, the a c t i v i t y o f sodium i n the myoplasm, of  s i x fibers  soaked i n l i t h i u m  of  the f r e e i n t r a c e l l u l a r  R i n g e r was measured  sodium i n t h i s  solution.  a  M  a  >  to determine the l o s s Measurements were made  w i t h the same m i c r o e l e c t r o d e used i n the s u c r o s e R i n g e r experiments ( F i g . 11).  Furthermore, measurements were made on altei'nate  fibers  from the same  b a r n a c l e s ; one f i b e r was bathed i n sucrose R i n g e r , the next i n l i t h i u m  R i n g e r and so on.  I n l i t h i u m Ringer  (see F i g . 17 f o r the i n i t i a l  r a t h e r unexpected,  transitory increase i n a  a^) a  occurred i n four out of s i x  f i b e r s , whereas i n s u c r o s e R i n g e r , a „ always decreased m o n o t o n i c a l l y w i t h » => J Na time.  The sodium s e n s i t i v e m i c r o e l e c t r o d e was s l i g h t l y s e n s i t i v e to l i t h i u m ,  but t h e e l e c t r o d e r e a d i n g s were c o r r e c t e d f o r t h i s by assuming t h a t the a c t i v i t y o f l i t h i u m i n t h e myoplasm was e q u a l t o the t o t a l c o n c e n t r a t i o n o f l i t h i u m i n the f i b e r . of  O b v i o u s l y t h i s i s a maximal c o r r e c t i o n , because most  the f i b e r l i t h i u m s h o u l d be i n t h e e x t r a c e l l u l a r  The  transitory  l i t h i u m R i n g e r warranted measurable response  i n c r e a s e noted  i n the a ^  space.  o f f i b e r s bathed i n  a  the c o n s t r u c t i o n o f an e l e c t r o d e which had no  to l i t h i u m i n the c o n c e n t r a t i o n range  o c c u r r e d i n the myoplasm and the r e p e t i t i o n o f the above  t h a t c o u l d have experiments.  Measurements were made w i t h t h i s e l e c t r o d e on 5 f i b e r s bathed R i n g e r and on 4 f i b e r s bathed to  those o b t a i n e d p r e v i o u s l y .  i n sucrose Ringer.  i n lithium  The r e s u l t s were s i m i l a r  In l i t h i u m Ringer a t r a n s i t o r y increase i n  a„ o c c u r r e d i n 2 out o f 5 f i b e r s whereas i n s u c r o s e R i n g e r a„ Na Na &  d e c r e a s e d m o n o t o n i c a l l y w i t h time. which i s a graph o f a  a when t h e f i b e r Na >T  (lower curve) r e l a t i v e  i s i n normal R i n g e r .  curves a r e o n l y s t a t i s t i c a l l y  J  The r e s u l t s a r e summarized i n F i g . 18,  as a f u n c t i o n o f time i n l i t h i u m R i n g e r  curve) and i n s u c r o s e R i n g e r  always  significant  (upper  to the i n i t i a l v a l u e o f  The d i f f e r e n c e s between t h e two f o r the f i r s t  5 minutes.  Differ-  ences  i n the r a t e o f decrease o f a„ c o u l d have r e s u l t e d from v a r i a t i o n s i n Na the s i z e o f the f i b e r , t h e p o s i t i o n o f the m i c r o e l e c t r o d e i n the f i b e r , the  a c t i v i t y o f t h e "sodium pump" o r the i n i t i a l  a ^ , but i t i s d i f f i c u l t to a  c o n c e i v e how any o f these f a c t o r s c o u l d have caused a„, to i n c r e a s e i n Na J  l i t h i u m Ringer. °  I t seems l i k e l y ,  t h e r e f o r e , that '  the i n c r e a s e i n a„ r e Na  f l e e t s a r e l e a s e o f sodium from an i n t e r n a l b i n d i n g s i t e .  98  1.2H  0  5  10 TIME  (min)  15  IN S U C R O S E  0  O R  20  LITHIUM®  RINGER  F i g . 18. The a c t i v i t y o f sodium i n the myoplasm, » °^ s i n g l e muscle f i b e r s bathed i n l i t h i u m R i n g e r (upper curve) o r s u c r o s e R i n g e r (lower curve) r e l a t i v e to the i n i t i a l a when the f i b e r was bathed i n normal R i n g e r . The i n i t i a l a ^ o f the f i b e r s bathed i n l i t h i u m R i n g e r was .006 ± .001 M. The i n i t i a l a o f the f i b e r s bathed i n s u c r o s e R i n g e r was .009 ± .002 M. Na a  M a  &  pH = 9.6 trates  and pH = 5.5  Ringer.  the dependence o f the O.D.  macromolecules  i t c o n t a i n s was  A simple experiment which  o f a muscle  performed  f i b e r on the charge o f the  on g l y c e r i n a t e d f i b e r s .  which had been bathed i n .01 M KC1 were p l a c e d i n .01 M KOH under a d i s s e c t i n g parent.  The  microscope.  change i n O.D.  normal R i n g e r , the O.D.  was  W i t h i n 10 minutes reversible.  o f the f i b e r s  illus-  and  observed  they became almost  When the f i b e r was  increased.  Fibers  trans-  r e t u r n e d to  The decrease i n O.D.  was  99 presumably due to the f a c t  t h a t the macromolecules i n the f i b e r a c q u i r e d  a l a r g e n e t n e g a t i v e charge when i t was bathed  i n .01 M KOH.  Similar  large  r e v e r s i b l e changes i n O.D. were observed when g l y c e r i n a t e d f i b e r s were bathed  i n .01 M HC1.  T h i s decrease  i n O.D. was presumably due to the f a c t  t h a t the macromolecules a c q u i r e d a l a r g e n e t p o s i t i v e charge  i n .01 M HC1.  The O.D. o f a muscle f i b e r w i l l be a maximum when the pH o f the myoplasm i s near  the i s o e l e c t r i c pH o f the main s c a t t e r i n g c e n t e r s i n the  f i b e r , which a r e presumably the t h i c k f i l a m e n t s .  I t i s e s s e n t i a l f o r the  argument advanced beloxv t h a t the t h i c k f i l a m e n t s i n a muscle f i b e r i n normal R i n g e r have a n e t n e g a t i v e charge. v a r y i n g the pH o f the myoplasm s l i g h t l y .  T h i s assumption  bathed  was t e s t e d by  I n c r e a s i n g the pH o f the myoplasm  s h o u l d i n c r e a s e the n e t n e g a t i v e charge on the t h i c k f i l a m e n t s , hence dec r e a s e the O.D. o f the f i b e r .  D e c r e a s i n g the pH o f the myoplasm up t o , but  n o t beyond the i s o e l e c t r i c p o i n t o f the t h i c k f i l a m e n t s s h o u l d  decrease  t h e i r n e t n e g a t i v e charge, hence i n c r e a s e the O.D. o f the f i b e r .  The pH and membrane p o t e n t i a l measurements made on f o u r f i b e r s bathed  i n pH = 9.6 R i n g e r a r e i l l u s t r a t e d  i n F i g . 19.  The pH o f the myo-  plasm when the f i b e r s were i n normal R i n g e r was 7.315 ± .009 (n=4). 25 minutes i n pH = 9.6 R i n g e r changes t h a t o c c u r r e d graph).  i t i n c r e a s e d to 7.378 ± .018 (n=4) .  i n pH = 9.6 R i n g e r a r e i l l u s t r a t e d  The r e l a t i v e O.D. decreased  Caldwell  After The O.D.  i n F i g . 16 (lower  t o .966 ± .011 a f t e r 25 minutes.  (7) has shown t h a t the myoplasmic pH o f crab muscle  f i b e r s may be r a p i d l y and r e v e r s i b l y d e c r e a s e d by b a t h i n g the f i b e r s i n R i n g e r a c i d i f i e d w i t h CO^.  A s i m i l a r r e v e r s i b l e decrease  pH o f b a r n a c l e muscle f i b e r s bathed  i n the myoplasmic  i n R i n g e r which had been a c i d i f i e d  CO-, (pH o f R i n g e r = 5.5) was o b s e r v e d .  with  The myoplasmic pH decreased from 7.3  100  7.38  >  7.36-  < x  z  a.  LU t—  7.34-  o c  z< m  LU  5  7.32-  T 10  T 15  T 20  -TIME (mir.) IN pH 9.6 RINGERS-  r 25/0 -4*  5  10  15  20  TIME (min) IN NORMAL RINGERS  25 -  F i g . 19. The pH and membrane p o t e n t i a l o f s i n g l e muscle f i b e r s bathed i n pH = 9.6 R i n g e r and i n normal R i n g e r .  to 6.3 i n 3 m i n u t e s .  When normal R i n g e r  (pH = 7.6) was r e t u r n e d to t h e  b a t h i n g chamber, t h e pH o f the myoplasm r e t u r n e d to 7.3 w i t h i n 10 minutes (6).  The r e l a t i v e O.D. o f f i b e r s bathed  i n pH = 5.5 Ringer  a s t a b l e v a l u e o f 1.047 ± .006 (n=7) w i t h i n three m i n u t e s .  i n c r e a s e d to A f t e r 5 minutes  i n the pH = 5 . 5 R i n g e r , normal R i n g e r was r e t u r n e d to the b a t h i n g A f t e r 10 minutes i n normal R i n g e r , .004 (n=7) .  D.  Discussion  the r e l a t i v e O.D. decreased  chamber.  to 1.017 ±  101 The  o p t i c a l studies reported  o b t a i n independent s u p p o r t i n g  evidence  i n t h i s paper were undertaken t o f o r the h y p o t h e s i s  bound t o myosin i n s t r i a t e d muscle f i b e r s .  t h a t sodium i s  Eqn. [27] i l l u s t r a t e s  l a t i o n s h i p t h a t e x i s t s between the n e t charge, Z, on a s m a l l ,  the r e -  optically  i n a c t i v e m o l e c u l e and the t u r b i d i t y , T , o f a s o l u t i o n when the c o n c e n t r a t i o n o f the macromolecule i s low and the i o n i c s t r e n g t h o f the s o l u t i o n i s h i g h . For s e v e r a l reasons,  n e i t h e r Eqn. [ 2 7 ] , n o r more expanded and complete forms  o f i t (3, 8) a r e q u a n t i t a t i v e l y a p p l i c a b l e to a muscle f i b e r . t a i n s not one, b u t many macromolecular s p e c i e s capable The  t h i c k f i l a m e n t s , however, a r e p r o b a b l y  because o f t h e i r h i g h " m o l e c u l a r " form a h i g h l y c o n c e n t r a t e d  A fiber  of scattering l i g h t .  the main s c a t t e r i n g c e n t e r s  weight and c o n c e n t r a t i o n .  These f i l a m e n t s  s o l u t i o n o r g e l , a r e l a r g e compared w i t h the  wavelength o f i n c i d e n t l i g h t , and c o n t a i n o p t i c a l l y a c t i v e m o l e c u l e s . complicating  con-  These  f a c t o r s make the q u a n t i t a t i v e a p p l i c a t i o n o f l i g h t s c a t t e r i n g  theory exceedingly  difficult,  but they s h o u l d n o t d e s t r o y  the q u a l i t a t i v e  r e l a t i o n between macromolecular charge and t u r b i d i t y .  A more s e r i o u s c o m p l i c a t i o n a r i s e s from the f a c t t h a t the t h i c k f i l a m e n t s i n a muscle f i b e r a r e n o t f r e e i n s o l u t i o n , b u t o r g a n i z e d p a r a l l e l hexagonal a r r a y .  in a  I n c r e a s i n g the n e t charge on macromolecules f r e e  i n s o l u t i o n d e c r e a s e s the randomness o f the s o l u t i o n , o r e q u i v a l e n t l y , decreases  the c o n c e n t r a t i o n f l u c t u a t i o n s o f the m o l e c u l e s ,  t u r b i d i t y o f the system. are  Increasing  hence d e c r e a s e s the  the n e t charge on macromolecules which  i n i t i a l l y o r d e r e d w i l l n o t n e c e s s a r i l y decrease the c o n c e n t r a t i o n  ations.  T h i s w i l l o n l y occur  i f the i n i t i a l  order  X7hich the e l e c t r o s t a t i c f r e e energy i s a minimum.  fluctu-  i n the system i s one f o r F o r t u n a t e l y , the p a r a l l e l  hexagonal a r r a y o f the t h i c k f i l a m e n t s i s e x a c t l y the minimum e l e c t r o s t a t i c f r e e energy c o n f i g u r a t i o n f o r a system o f charged rods  (9, page 2 3 3 ) .  Thus,  102 i n c r e a s i n g the n e t charge on the t h i c k f i l a m e n t s tude o f the c o n c e n t r a t i o n t u r b i d i t y o f t h e muscle  It  d e c r e a s e the magni-  f l u c t u a t i o n s o f the f i l a m e n t s , hence decrease the fiber.  i s a l s o e s s e n t i a l f o r t h e argument t h a t the t h i c k  be n e g a t i v e l y binding  should  charged.  studies  Titration  (10), e l e c t r o p h o r e s i s  filaments  (11, 12) and ATP  (11, 13, 14) on myosin i n d i c a t e t h a t t h i s requirement i s  s a t i s f i e d a t the myoplasmic pH o f about 7.3 ( F i g . 1 9 ) . The experiments i n pH = 5.5 and pH = 9.6 R i n g e r a l s o i n d i c a t e the t h i c k f i l a m e n t s  are negatively  charged.  I n s p i t e o f the i n h e r e n t scattering  theory  difficulties  t o l i v i n g muscle f i b e r s ,  i n the a p p l i c a t i o n o f l i g h t  i t seems r e a s o n a b l e t o attempt t o  e x p l a i n the o p t i c a l r e s u l t s i n terms o f changes i n the n e t charge on the thick filaments.  The s i g n i f i c a n c e o f the e x e r c i s e  e x p e r i m e n t a l r e s u l t s w i t h the r e s u l t s p r e d i c t e d a s i g n i f i c a n t f r a c t i o n o f sodium i n the f i b e r presumably t o c a r b o x y l m o i e t i e s .  lies  i n comparing the  from the h y p o t h e s i s  i s bound to the t h i c k  When the f i b e r s a r e bathed  t r i s o r p o t a s s i u m R i n g e r , sodium should move o f f the b i n d i n g o f the c e l l , filaments. fibers. solutions  causing This  an i n c r e a s e  should  i n the n e t n e g a t i v e  that filaments,  i n sucrose, s i t e s and o u t  charge on the t h i c k  decrease the t u r b i d i t y , hence the O.D. o f the  L a r g e , r e v e r s i b l e d e c r e a s e s i n the O.D. o f f i b e r s bathed i n these ( F i g s . 13, 14, 15) were indeed o b s e r v e d .  i n Chapter I I i n d i c a t e t h a t the b i n d i n g p r e f e r the a l k a l i m e t a l c a t i o n s  The arguments advanced  s i t e s on the t h i c k f i l a m e n t s  i n the o r d e r Li>Na>iC (15).  should  Thus, when the  f i b e r s a r e bathed i n l i t h i u m R i n g e r , the l i t h i u m e n t e r i n g  the myoplasm  more than compensate f o r the l o s s o f the "bound" sodium.  This  a s l i g h t decrease i n the n e t n e g a t i v e  should  should cause  charge on the t h i c k f i l a m e n t s , hence  103 the t u r b i d i t y and  the O.D.  o f the f i b e r s h o u l d i n c r e a s e .  s i b l e i n c r e a s e i n the O.D. ( F i g . 16). bathed  Furthermore,  i n l i t h i u m Ringer  o f f i b e r s bathed t h e r e was  increases i n bathed  an i n i t i a l  increase of a ^ a l s o be due  a  observed  in fibers  to the  displacement  I t s h o u l d be emphasized, however, t h a t  were s m a l l , and observed  i n l i t h i u m Ringer.  i n l i t h i u m R i n g e r was  ( F i g . 18) which may  o f bound sodium by l i t h i u m .  A small rever-  I t i s apparent  o n l y i n about  507o o f the  these fibers  then, t h a t a l l the o p t i c a l r e -  s u l t s a r e compatible w i t h the h y p o t h e s i s t h a t sodium i s bound to the  thick  filaments.  U n f o r t u n a t e l y , a p r e d i c t i o n o f how  much sodium i s bound t o the  t h i c k f i l a m e n t s cannot be made from these experiments. appear t o be due  to the movement o f o n l y about  .005  The  optical  changes  moles/kg f i b e r water o f  sodium from the b i n d i n g s i t e s , but t h e r e c o u l d be e i t h e r more o r l e s s t h i s amount o f sodium bound to the t h i c k f i l a m e n t s .  than  I t s h o u l d a l s o be  noted  t h a t o t h e r i n t e r p r e t a t i o n s o f the e x p e r i m e n t a l r e s u l t s a r e p o s s i b l e , f o r the t a c i t assumption  has been made t h a t the s t r u c t u r e o f the t h i c k f i l a m e n t s  d i d n o t change when the f i b e r s were bathed  i n sodium f r e e s o l u t i o n s .  The  p o s s i b i l i t y , however, t h a t sodium or l i t h i u m i s n e c e s s a r y to m a i n t a i n the i n t e g r i t y o f c e r t a i n s t r u c t u r e s i n the myoplasm i s i t s e l f esting.  O b v i o u s l y , much more e x p e r i m e n t a l work remains  extremely  to be done on  r e l a t i o n s h i p between the o p t i c a l p r o p e r t i e s o f muscle f i b e r s and they c o n t a i n , but a t p r e s e n t these experiments support f o r the h y p o t h e s i s t h a t a s i g n i f i c a n t i n t a c t b a r n a c l e muscle f i b e r s  inter-  a r e o f f e r e d as  the  the ions  qualitative  f r a c t i o n o f the sodium i n  i s bound to myosin.  104 CHAPTER V I I  BINDING OF  A.  SODIUM AND  POTASSIUM IN GLYCEROL EXTRACTED FIBERS  Introduction The  extracted  myosin i n d i c a t e t h a t t h i s p r o t e i n has  quantities that  experiments performed by Lewis and  Saroff the  (1) on  capacity  I t was  should be h e s i t a n t about u s i n g  t o p r e d i c t q u a n t i t a t i v e l y how  much sodium and  in a living  cell.  The  goes i n the  living  cell  s p a t i a l f i x a t i o n and may  alter  ments on o t h e r macromolecules and seemed r e a s o n a b l e , t h e r e f o r e ,  and  the  capacity  of myosin to b i n d  binding  c h a r a c t e r i s t i c s of the  fiber.  As  cross-linkage  accumulated i n i n t r a c e l l u l a r o r g a n e l l e s  experiIt phenomenon  p o t a s s i u m by measuring in a  the  glycerinated  d e s t r o y e d by g l y c e r i n a t i o n , and  may  be  Fenn had  ignored.  already  demonstrated  author that  f i b e r s s e l e c t i v e l y accumulate sodium over p o t a s s i u m when  posed to s o l u t i o n s c o n t a i n i n g free concentrations  no  ions are s e l e c t i v e l y  experiments i n t h i s c h a p t e r were undertaken, the  unaware o f the work of Fenn ( 2 ) .  o f an  t h a t myosin under-  i n f l u e n c e of these two  source of m e t a b o l i c energy remains, the p o s s i b i l i t y t h a t  glycerinated  these r e s u l t s  c h a r a c t e r i s t i c s , as  c o n t r a c t i l e proteins  the membranes i n a f i b e r are  When the  noted i n  p o l y e l e c t r o l y t e s have i n d i c a t e d .  sodium and  twice  p o t a s s i u m are bound to myosin  i t s binding  to study the  of  large  the a s s o c i a t i o n c o n s t a n t f o r the myosin-sodium complex i s about  Chapter I I , however, t h a t one  was  to b i n d  (about 50 moles/lO"* grams myosin) of a l k a l i m e t a l c a t i o n s  the a s s o c i a t i o n c o n s t a n t f o r the myosin-potassium complex.  on  solutions  equal c o n c e n t r a t i o n s  (or a c t i v i t i e s ) of sodium and  i n t a c t s t r i a t e d muscle f i b e r , however, are  o f these two  ex-  ions.  The  p o t a s s i u m i n the myoplasm f a r from e q u a l ,  as  the  105 measurements r e p o r t e d i n Chapters IV, V and VI demonstrate. o f many i o n exchange r e s i n s depends on the r e l a t i v e a l k a l i metal cations  i n the exchanger  (3).  Thus,  The  selectivity  c o n c e n t r a t i o n s o f the  i f the g l y c e r i n a t e d  i s to be c o n s i d e r e d a model, a l b e i t a crude model, o f the l i v i n g  fiber  cell, i t  seemed a p p r o p r i a t e to study the a c c u m u l a t i o n of sodium and p o t a s s i u m by g l y c e r i n a t e d f i b e r s exposed  to s o l u t i o n s c o n t a i n i n g these i o n s a t approx-  i m a t e l y the same a c t i v i t i e s  as are found i n the myoplasm o f an i n t a c t  The r e s u l t s o f such a study are p r e s e n t e d below.  They are  qualitatively  compatible w i t h the r e s u l t s of both Lewis and S a r o f f  (1) and Fenn  t h a t they demonstrate  a  ated f i b e r  B.  (Z) i n  the s e l e c t i v i t y c o e f f i c i e n t , K ^ / , o f the g l y c e r i n -  i s g r e a t e r than 1.0  selectivity  fiber.  (see Eqn.  K  [7] f o r a d e f i n i t i o n o f the  coefficient).  Methods  Glycerination.  A p p r o x i m a t e l y a dozen f i b e r s on a s i n g l e  base-  p l a t e were d i s s e c t e d f r e e from one another i n normal R i n g e r (Table I) a t 25° C and examined f o r damage.  Only undamaged f i b e r s were used.  The  ten-  dons o f these f i b e r s were l i g a t e d by t h r e a d to a r o d and the b a s e p l a t e t i e d to another rod so t h a t the f i b e r s were f i x e d a t r e s t were then t r a n s f e r r e d t o g l y c e r o l 25° C ) .  The  The  fibers  (507=, by volume, b u f f e r e d t o pH 7.33  temperature of the g l y c e r o l was  s t o r e d f o r 20 hours a t t h i s  length.  temperature.  at  2-3° C, and the f i b e r s were  The  f i b e r s were then  to f r e s h g l y c e r o l and s t o r e d a t -20° C f o r 24 days.  transferred  This g l y c e r i n a t i o n pro-  cedure i s s i m i l a r to t h a t used by S z e n t - G y o r g y i ( 4 ) .  Test of C o n t r a c t i l i t y .  At l e a s t one  f i b e r from each b a s e p l a t e was  t e s t e d f o r c o n t r a c t i l i t y b e f o r e experiments were performed on the o t h e r fibers.  The f i b e r was  c u t from the s t o n e , bathed f o r 10 minutes  in distilled  106 water to remove most o f the g l y c e r o l , then p l a c e d i n a s o l u t i o n .005 M ATP,  .010 M C a C l , 2  fibers tested  o f about 5 minutes,  The c o n t r a c t i o n s  room a t a temperature of 2-3° C.  They remained  1/2  A l l experiments were performed i n a c o l d The f i b e r s were f i r s t t r a n s f e r r e d  .275 M KC1,  .275 M KC1  and  from  .025 M KiyPO^  i n t h i s s o l u t i o n f o r 1 hour to a l l o w the g l y c e r o l  to d i f f u s e out o f the f i b e r s . containing  occurred  the f i b e r s s h o r t e n i n g to about  g l y c e r o l s o l u t i o n to a s o l u t i o n c o n t a i n i n g  a t pH 7.4.  All  length.  Experimental Procedure.  the  .200 M t r i s a t a pH o f 7.6.  2  f o r c o n t r a c t i l i t y d i d shorten.  s l o w l y over a p e r i o d their i n i t i a l  .010 M M g C l ,  containing  They were then t r a n s f e r r e d  .025 M K^PO^  and e i t h e r a t r a c e  to a s o l u t i o n  (.0002 M) c o n c e n t r a -  22 t i o n or .010 M Na these two s o l u t i o n s  CI a t pH 7.4.  The f i b e r s were e q u i l i b r a t e d  f o r 1-2 h o u r s .  After  this period  were cut from the b a s e p l a t e , b l o t t e d b r i e f l y  measured immediately, the f i b e r d r i e d the  dry weight of the f i b e r measured.  t r a t e d HNO^  o f time the f i b e r s  to remove excess b a t h i n g  and p l a c e d i n preweighed, s t o p p e r e d w e i g h i n g b o t t l e s . t r a n s f e r procedure took about 10 seconds.  i n one o f  fluid  The b l o t t i n g and  The wet weight o f the f i b e r was  to a c o n s t a n t weight a t 95° C, then After  digestion  i n .2 ml o f concen-  and n e u t r a l i z a t i o n w i t h ammonia, the l i q u i d was  transferred  v i a l used i n the N u c l e a r Chicago Automatic Gamma W e l l Counting System  to a  and  d i l u t e d to 5 ml. The sodium c o n t e n t , i n counts per minute f i b e r was  then measured.  These measurements were a l t e r n a t e d  ments o f the cpm/ml o f the b a t h i n g s o l u t i o n . b a t h i n g s o l u t i o n were p i p e t t e d six  (cpm), of the e x p e r i m e n t a l  p l a c e b a l a n c e to c o r r e c t  Eight  w i t h measure-  one ml samples  o f the  i n t o v i a l s (samples were a l s o weighed  f o r any p i p e t t i n g  on a  e r r o r s ) , d i l u t e d to 5 ml, and  107 the of  cpm determined.  Samples were counted f o r 10 minutes, and 5 r e p e t i t i o n s  the counts were made to ensure the s t a b i l i t y o f the gamma c o u n t e r .  background  was l e s s than 1% o f the cpm i n the e x p e r i m e n t a l  The  samples.  A f t e r the r a d i o a c t i v i t y o f the samples was determined, they were diluted  t o 25 ml and a n a l y z e d f o r p o t a s s i u m c o n t e n t on a Unicam SP 900 flame  spectrophotometer.  Samples o f the b a t h i n g s o l u t i o n were a l s o a n a l y z e d f o r  potassium content.  C.  Results  A p r e l i m i n a r y experiment was conducted to determine how l o n g the 22 f i b e r s s h o u l d be e q u i l i b r a t e d were removed f o r a n a l y s i s . for  one hour  glycerol,  i n the s o l u t i o n s c o n t a i n i n g Na  b e f o r e they  S i x t e e n g l y c e r o l e x t r a c t e d f i b e r s were bathed  i n a .275 M KC1 p l u s .025 M KH-,P0^ s o l u t i o n t o remove the 22  then t r a n s f e r r e d  to a s i m i l a r s o l u t i o n c o n t a i n i n g Na  .  removed from t h i s s o l u t i o n a t times r a n g i n g from 1/2 t o 18 h o u r s . sodium and p o t a s s i u m c o n c e n t r a t i o n s i n the muscle a f t e r 1/2 hour.  They were The  reached a c o n s t a n t v a l u e  To ensure e q u i l i b r a t i o n  i n the e x p e r i m e n t a l s e r i e s , 22 were bathed i n the s o l u t i o n s c o n t a i n i n g Na f o r 1-2 h o u r s . The r e s u l t s o f the experiments The  first  b a r n a c l e muscle  This  (by weight) o f the f i b e r s .  The average 7» water  c o n t e n t of an i n t a c t  f i b e r , on the o t h e r hand, i s about  experimental f i b e r s u t i l i z e d VI)..  a r e p r e s e n t e d i n T a b l e s V I and V I I .  column i n T a b l e V I g i v e s the % water  The average v a l u e i s 88.5%.  i n the experiments  75% (average from the  d e s c r i b e d i n Chapters V and  i m p l i e s t h a t the g l y c e r o l e x t r a c t e d b a r n a c l e muscle  s w e l l e d to about  twice t h e i r  weight o f the f i b e r s .  initial  fibers  volume.  f i b e r s have  The next column l i s t s  the d r y  108 TABLE V I The sodium and p o t a s s i u m c o n t e n t o f f i b e r s e x t r a c t e d i n 50% g l y c e r o l f o r 24 days then e q u i l i b r a t e d i n a s o l u t i o n c o n t a i n i n g [K] = 295 mM_,|nd [Na] = 10.4 mM. The r a d i o a c t i v i t y i n the b a t h i n g s o l u t i o n due to the Na was 23,530 ± 540 (n = 8) cpm/ml.  Dry % Water i n F i b e r Weight 10-3gms  [Na] cpm/fiber Measured Expected  84.1 88.6 89.7 88.1 88.2 88.9 90.6 88.8 88.9 88.5 90.1 88.5 87.6  397 416 453 452 393 803 965 539 599 617 666 615 459  2.649 1.925 1.940 2.428 1.874 3.358 3.150 2.390 2.090 2.568 2.103 2.453 2.396  K bound Na bound cpm/gm mMoles/ dry weight gm d r y weight  [K] m M o l e s / f i b e r Measured Expected x lO-x 10*° 3  330 352 397 423 329 633 714 446 394 465 450 444 398  4.500 4.750 5.375 5.500 4.500 8.875 9.250 6.000 5.375 6.250 6.000 5.875 5.375  4.133 4.413 4.984 5.303 4.132 7.934 8.956 5.590 4.938 5.830 5.646 5.569 4.993  51,400 + 7,900*  88.5  S .  i d u a l f i b e r s i n cpm.  The f o u r t h  the measured  r a d i o a c t i v i t y o f the i n d i v -  column l i s t s  the v a l u e s o f the cpm e x p e c t e d  on the b a s i s o f t h r e e assumptions. i o n s a r e bound  These assumptions a r e : ( i ) no sodium  t o the c o n t r a c t i l e p r o t e i n s ,  sodium ions i n the g l y c e r i n a t e d  The f o u r t h  column was  calcu-  the weight o f water i n the f i b e r by the measured  23,530 ± 540 (n=8) cpm/ml b a t h i n g s o l u t i o n ,  bathing s o l u t i o n .  coefficient  ( i i i ) a l l the water i n the c e l l i s  to a c t as s o l v e n t f o r the sodium i o n s .  l a t e d by m u l t i p l y i n g  ( i i ) the a c t i v i t y c o e f f i c i e n t o f  f i b e r i s e q u a l to the a c t i v i t y  o f sodium ions i n the b a t h i n g s o l u t i o n ,  of  0.166 ± 0.014  E.  The t h i r d column l i s t s  free  0.138 0.175 0.201 0.081 0.196 0.280 0.093 0.171 0.209 0.164 0.168 0.125 0.159  25,300 33,200 28,900 11,900 34,200 50,600 79,700 38,900 98,100 59,200 102,700 69,700 35,500  (The e r r o r  of less  value  the r a d i o a c t i v i t y of the  than 1% t h a t  arises  i n assuming t h a t  1  109 gm o f water c o n t a i n s t h e same number o f water m o l e c u l e s as 1 ml o f b a t h i n g s o l u t i o n i s ignored.)  Note  t h a t i n each case the f i b e r c o n t a i n s more  than would be expected on the b a s i s o f the above three assumptions. tion  (iii)"is  p r o b a b l y n o t v a l i d , b u t the e f f e c t o f any water  sodium  Assump-*  "binding"  would be to reduce the c o n c e n t r a t i o n o f sodium i n the f i b e r , hence the i n v a l i d i t y o f t h i s assumption c o u l d n o t l e a d t o the observed r e s u l t s . w i l l be assumed t h a t assumption  ( i i ) i s v a l i d , and t h a t the observed accumu-  l a t i o n o f sodium by t h e g l y c e r i n a t e d f i b e r s to  the c o n t r a c t i l e  i s due t o the b i n d i n g o f sodium  proteins.  The p e n u l t i m a t e column per  It  gram o f d r y weight o f muscle.  lists  the amount o f sodium bound  The r e s u l t s  ( i n cpm)  i n t h i s column were o b t a i n e d  by s u b t r a c t i n g the measured and the expected cpm and d i v i d i n g by the d r y weight o f the f i b e r .  The average v a l u e o f 51,400 ± 7,900 (n=13) cpm/gm d r y  weight i s e q u i v a l e n t t o (51,400 cpm/gm d r y weight)(0.0104 mMoles/23,530 cpm)  = 0.023 mMoles bound sodium/gm d r y w e i g h t .  The f i f t h  column  i n Table V I l i s t s  the measured amount o f p o t a s -  sium i n the muscle, as determined by flame photometry.  The s i x t h  column  lists  the mMoles o f p o t a s s i u m expected i n the f i b e r on the b a s i s o f assump-  tions  ( i , i i , i i i ) applied  column  lists  to p o t a s s i u m i n s t e a d o f sodium  ions.  The f i n a l  the mMoles o f bound p o t a s s i u m p e r gm o f d r y f i b e r w e i g h t .  The  average o f t h i s q u a n t i t y i s 0.166 mMoles/gm d r y w e i g h t .  The g l y c e r i n a t e d f i b e r s c o u l d be c o n s i d e r e d as h i g h l y h y d r a t e d ion  exchange  r e s i n s , and the s e l e c t i v i t y , as d e f i n e d i n Eqn.  resins calculated. the  The average s e l e c t i v i t y o f the f i b e r s , c a l c u l a t e d  data of Table V I i s K^/jr  evidence i n d i c a t i n g  [7] o f these  =  1.18.  from  There i s , however, a groxving body o f  t h a t "we may, t o a f i r s t a p p r o x i m a t i o n , r e g a r d the  110 TABLE V I I The sodium and p o t a s s i u m c o n t e n t o f f i b e r s e x t r a c t e d i n 50% g l y c e r o l f o r 24 days then e q u i l i b r a t e d i n a s o l u t i o n c o n t a i n i n g [K] = 295 mM and [Na] = 0.2 mM. The r a d i o a c t i v i t y i n the b a t h i n g s o l u t i o n due to the Na was 22,550 ± 630 (n = 8) cpm/ml. Dry % Water i n F i b e r Weight 10-3  cpm/fiber [Na] Measured Expected  87.3 90.1 90.2 88.0 90.2 90.4 89.8 88.4 88.3 86.9 90.6 87.1 87.6 88.9  415 716 690 581 623 665 602 249 763 468 920 555 473 555  [K] m M o l e s / f i b e r Measured Expected x 10"3 x 10" J  2.463 3.164 2.775 2.936 2.214 2.816 2.458 1.230 3.298 2.559 3.813 2.878 2.542 2.360  382 649 576 485 459 598 488 211 561 383 828 438 404 426  5.375 8.500 7.875 6.625 6.250 7.875 6.500 3.250 7.750 5.375 11.625 6.125 5.625 6.000  5.000 8.495 7.535 6.352 6.012 7.823 6.384 2.765 7.343 5.008 10.842 5.732 5.298 5.576  88.8  K bound Na bound cpm/gm mMoles/ d r y weight gm d r y weight 13,400 21,200 41,100 32,700 74,100 23,800 46,400 30,900 61,200 33,200 24,100 40,700 27,100 54,700 37,500 ± 4,500*  0.152 0.002 0.122 0.093 0.107 0.018 0.047 0.394 0.123 0.143 0.205 0.136 0.128 0.180 0.132 ±0.025  S. E.  e f f e c t o f a d d i t i o n water selectivity"  as m e r e l y t o ' d i l u t e '  the p r o c e s s e s g i v i n g r i s e t o  ( 5 ) . Thus, i t seems r e a s o n a b l e to c o n s i d e r n o t o n l y the s e l -  e c t i v i t y o f the f i b e r as a whole, b u t the s e l e c t i v i t y o f the p r o t e i n s as well.  The term ^ ^ y ^ ^ ^ may be d e f i n e d as (mMoles o f sodium bound p e r gm  protein/mMoles  sodium f r e e p e r ml s o l u t i o n ) / ( m M o l e s o f p o t a s s i u m bound p e r  gm protein/mMoles  p o t a s s i u m f r e s p e r ml s o l u t i o n ) .  I t may be c a l c u l a t e d  from t h e d a t a o f T a b l e V I t h a t the s e l e c t i v i t y o f the p r o t e i n s , d e f i n e d i n t h i s manner i s (51,400/23,530)/(0.166/0.295) = 3.88.  The r e s u l t s o f another s e r i e s of experiments ing s o l u t i o n c o n t a i n i n g o n l y a t r a c e  conducted i n a b a t h -  (0.2mM) c o n c e n t r a t i o n o f sodium a r e  Ill presented  i n Table V I I .  Kja/ 2°*°, H  K  The  s e l e c t i v i t y c o e f f i c i e n t of the p r o t e i n s ,  c a l c u l a t e d from the d a t a i n t h i s t a b l e i s (37,500/22,550)/  (0.132/0.295) = 3.72,  not s i g n i f i c a n t l y d i f f e r e n t from the s e l e c t i v i t y  co-  e f f i c i e n t c a l c u l a t e d from the d a t a of T a b l e V I .  D.  Discussion  Some of the f a c t o r s which c o m p l i c a t e the i n t e r p r e t a t i o n o f above measurements w i l l now  be d i s c u s s e d .  A t a pH o f about 7.4,  t e i n s myosin and a c t i n are n e g a t a v e l y charged Donnan e q u i l i b r i u m a r e e s t a b l i s h e d . s e l e c t i v e accumulation account  and  by the f i b e r s , but  due  f i b e r s h o u l d have a n e g a t i v e p o t e n t i a l of about 1.8 0.00  ± 0.05  mV,  i s c o n s i d e r e d as a homogeneous e n t i t y ,  n e g l i g i b l e r o l e i n the a c c u m u l a t i o n t h a t one  s h o u l d no  i s 1.073, hence the  mV.  The measured  indicating  poten-  t h a t i f the muscle  the Donnan e f f e c t p l a y s a  of ions.  Rather,  The  author  one  s h o u l d note  types o f e l e c t r o s t a t i c b i n d i n g , which d i f f e r  s p e c i f i c i t y o f b i n d i n g between charged c h a r a c t e r i z e d as i o n - p a i r f o r m a t i o n and  f e e l s , however,  groups.  One  t h a t t h e r e are a t i n the degree of  of these might  l a r g e , m u l t i p l y charged m o l e c u l e . " f o r the former  (6)  be  the o t h e r as a g e n e r a l i z e d domain  b i n d i n g w i t h the s m a l l c o u n t e r i o n s a s s o c i a t e d as a mobile  argues  the  l o n g e r c o n s i d e r e i t h e r an i n t a c t or a g l y c e r i n a t e d muscle  f i b e r as a homogeneous e n t i t y . l e a s t "two  I f the p o t a s -  ([K]solution/[K]fiber).  v a l u e of [ K ] s o l u t i o n / [ K ] f i b e r  t i a l of the muscle f i b e r s was  i t could  to the Donnan e f f e c t ,  f i b e r s s h o u l d have a n e g a t i v e p o t e n t i a l AE = KI l n F  fiber  the c o n d i t i o n s f o r a  some o f the sodium a c c u m u l a t i o n .  o f the muscle f i b e r s was  From T a b l e I , the average  the p r o -  The Donnan e f f e c t c o u l d not e x p l a i n the  of sodium o v e r p o t a s s i u m  f o r the p o t a s s i u m  sium a c c u m u l a t i o n  (4) and  the  The  layer with  the  s e l e c t i v i t y of the b i n d i n g  i n t e r p r e t a t i o n , but does not prove i t .  112 The  possibility  e f f i c i e n t s o f sodium and ions should  be  necessitates  t h a t the p r o t e i n s  c o u l d a f f e c t the a c t i v i t y  potassium ions without a c t u a l l y "binding"  considered,  but  lack of information  co-  these  about t h i s phenomenon  the assumption t h a t the a c t i v i t y c o e f f i c i e n t s of the " f r e e "  ions are u n a f f e c t e d  by  the  proteins.  A l s o worthy of c o n s i d e r a t i o n  i s the p o s s i b i l i t y t h a t a f r a c t i o n of  the water i n the g l y c e r o l e x t r a c t e d  f i b e r s i s "bound" i n such a manner t h a t  it  f o r the a l k a l i m e t a l c a t i o n s .  is unavailable  to a c t as  o f measuring e x p e r i m e n t a l l y  solvent  t h i s f r a c t i o n o f water i s d i s c u s s e d  A method  i n Chapter  IX.  I t may the b i n d i n g  be worthwhile to summarize the a v a i l a b l e i n f o r m a t i o n  of sodium and  periments of Lewis and  p o t a s s i u m to e x t r a c t e d muscle p r o t e i n s .  Saroff  c a t i o n s can be bound to 1 gm s t r o n g l y than p o t a s s i u m . (7)  The  (1) i n d i c a t e t h a t a maximum o f 0.50 of myosin, and  The  about ex-  mMoles o f  t h a t myosin b i n d s sodium more  electrophoresis  experiments o f M i l l e r  et a l  a l s o i n d i c a t e the sodium i s bound more s t r o n g l y than p o t a s s i u m to  myosin.  I n an a b s t r a c t p u b l i s h e d  i n 1942,  Mullins  p r e f e r r e d p o t a s s i u m to sodium, but Fenn, who concluded t h a t "the  published  a b s t r a c t was  (8) r e p o r t e d  t h a t myosin  r e p e a t e d these experiments, i n e r r o r f o r unknown r e a s o n s "  (2).  Both the-magnitude and  the  (2) observed i n g l y c e r o l e x t r a c t e d o f Lewis and  Saroff  (1).  water, one  may  he  f i b e r s are  t h a t Fenn  compatible w i t h the r e s u l t s  I f i t i s assumed t h a t the g l y c e r o l e x t r a c t e d  f i b e r s used by Fenn c o n t a i n e d the c o n c e n t r a t i o n s  s e l e c t i v i t y of the b i n d i n g  75% water by weight, and  f u r t h e r assumed  quotes i n meq/kg r e f e r to a kg o f muscle and  c a l c u l a t e ' the  limiting  not  that fiber  s e l e c t i v i t y from the data p r e s e n t e d i n  113 T a b l e I I o f h i s paper.  The average v a l u e o f K j ^ y ^ ^  ® = 2.8 ± .3.  This  s e l e c t i v i t y does n o t appear to be dependent on the c o n c e n t r a t i o n o f sodium and potassium  i n the b a t h i n g  solution.  I n summary, a g l y c e r i n a t e d f i b e r can be c o n s i d e r e d an i o n exchange r e s i n and the s e l e c t i v i t y o f the " r e s i n " , K j j ^ » c a l c u l a t e d . a  Fenn's exper-  iments demonstrated the s e l e c t i v i t y was g r e a t e r than u n i t y when the ions were p r e s e n t  i n equal c o n c e n t r a t i o n s : the experiments p r e s e n t e d here  t r a t e i t i s a l s o g r e a t e r than u n i t y when sodium and potassium p r e s e n t a t c o n c e n t r a t i o n s s i m i l a r t o those average s e l e c t i v i t y o f the p r o t e i n s two  experimental  s e r i e s was  found  t h a t an i n t a c t f i b e r  ions are  i n an i n t a c t f i b e r .  The  (not o f the f i b e r as a whole) f o r the  ^^/y^^P'*^  = 3.8.  I f the g l y c e r o l  f i b e r i s c o n s i d e r e d as a model o f the i n t a c t f i b e r , imply  illus-  extracted  the r e s u l t s o f T a b l e V I  ( c o n t a i n i n g 75% water by weight) w i t h a ^ = 0.20 M  and a = 0.007 M c o n t a i n s 0.055 moles/kg water o f p o t a s s i u m Na moles/kg water o f sodium "bound" t o p r o t e i n s .  and 0.008  114 CHAPTER V I I I  SIGNIFICANCE OF THE RESULTS  P r o b a b l y the most important c o n c l u s i o n t h a t can be drawn from the experiments p r e s e n t e d i n t h i s t h e s i s i s t h a t one can no l o n g e r c o n s i d e r the a l k a l i m e t a l c a t i o n s and water i n a s t r i a t e d muscle f i b e r  to be i n e x a c t l y  the same s t a t e as the ions and xjater i n the b a t h i n g s o l u t i o n the c e l l .  surrounding  C o n s i d e r the sodium c o n t e n t of a s i n g l e muscle f i b e r  g i a n t b a r n a c l e , Balanus n u b i l u s . mMoles/kg f i b e r water o f sodium  A typical  intact  from the  f i b e r c o n t a i n s about 70  (Chapters IV, V, V I ) .  About 30 mMoles/kg  f i b e r water o f sodium a r e c o n t a i n e d i n a compartment which communicates  with  the b a t h i n g s o l u t i o n ; presumably the e x t e n s i v e i n v a g i n a t i o n s o f the s a r c o lemma which a r e v i s i b l e under the e l e c t r o n m i c r o s c o p e ( 1 ) .  Only about 10 o f  the r e m a i n i n g 40 mMoles/kg f i b e r water o f sodium are " f r e e " i n the myoplasm, as was  determined d i r e c t l y by c a t i o n s e n s i t i v e m i c r o e l e c t r o d e s  V, V I ) . fibers all  (Chapters IV,  Thus, about 3/4 o f the i n t r a c e l l u l a r sodium i n b a r n a c l e muscle  i s "bound".  I t seems r e a s o n a b l e to e x t r a p o l a t e t h i s c o n c l u s i o n to  s t r i a t e d muscle f i b e r s because L e v  ( 2 ) , who  used c a t i o n s e n s i t i v e m i c r o -  e l e c t r o d e s to i n v e s t i g a t e the s t a t e of sodium i n f r o g s t r i a t e d  muscle  f i b e r s , o b t a i n e d s i m i l a r r e s u l t s and R o b e r t s o n (3) found t h a t 3/4 o f the sodium i n l o b s t e r muscle c o u l d not be e x t r u d e d by p r e s s u r e . performed w i t h p o t a s s i u m s e n s i t i v e m i c r o e l e c t r o d e s  Experiments  i n d i c a t e t h a t between 27  and 417» o f the i n t r a c e l l u l a r water i s u n a v a i l a b l e to a c t as s o l v e n t f o r the p o t a s s i u m ions  (Chapters IV, V ) .  Thus, the m i c r o e l e c t r o d e experiments r e -  p o r t e d i n t h i s t h e s i s p r o v i d e s t r o n g e v i d e n c e that t h e r e i s a hetrogeneous d i s t r i b u t i o n o f sodium and water i n s i n g l e s t r i a t e d muscle f i b e r s giant  barnacle.  from the  1.15 The d i v i s i o n o f the sodium c o n t e n t of a s t r i a t e d muscle f i b e r  into  a f r e e and a "bound" f r a c t i o n i s an o v e r s i m p l i f i c a t i o n , but t h e r e i s s t r o n g e v i d e n c e t h a t a t l e a s t 1/3 of the "bound"  sodium i s complexed  Experiments on s o l u t i o n s o f e x t r a c t e d myosin  to myosin.  (4) and g l y c e r i n a t e d  fibers  (Chapter V I I ) i n d i c a t e t h a t about 10 mMoles/kg f i b e r water of sodium may expected to be complexed conclusion i s f u l l y  to myosin i n an i n t a c t b a r n a c l e muscle f i b e r .  s u p p o r t e d by the d e n a t u r a t i o n and l i g h t  be This  scattering  ex-  periments r e p o r t e d i n Chapters V and V I r e s p e c t i v e l y .  The l o c a t i o n o f the r e m a i n i n g 20 mMoles/kg f i b e r water o f sodium which i s u n a v a i l a b l e to a sodium s e n s i t i v e m i c r o e l e c t r o d e i s unknown a t present.  I t seems u n l i k e l y t h a t t h i s f r a c t i o n o f "bound" sodium i s c o n t a i n e d  i n n u c l e i or m i t o c h o n d r i a , because these o r g a n e l l e s comprise o n l y a s m a l l f r a c t i o n o f the c e l l by volume, and do not appear to accumulate sodium p r e f e r e n t i a l l y over p o t a s s i u m (5, pages 226-229). itudinal of  t h a t these compartments  p r o b a b l y do not c o n t a i n a h i g h c o n c e n t r a t i o n o f  Furthermore, the s a r c o p l a s m i c r e t i c u l u m appears to be l e s s  f r a c t i o n o f "bound"  but  e v i d e n c e to i n d i c a t e t h a t i t i s bound  ed  sodium i s s e q u e s t e r e d i n o r g a n e l l e s ,  As d i s c u s s e d i n Chapter IV, Cope's  sodium i n s t r i a t e d muscle f i b e r s  i s bound  as t e n t a t i v e a t p r e s e n t , but t h i s  highly  Thus, there i s no e v i d e n c e t o i n -  d i c a t e that t h i s t h e r e i s NMR  13%  ( 6 ) , but the experiments o f Z a d u n a i s k y (7) i n d i c a t e  developed i n b a r n a c l e than f r o g muscle.  (8).  long-  t u b u l e s o f f r o g muscle have been e s t i m a t e d to comprise about  the c e l l by volume  sodium.  The c i s t e r n a e and  conclusion  to macromolecules  (8) t h a t 3/4 o f the  to macromolecules must be r e g a r d -  i n v e s t i g a t o r knows o f no experiment  performed on i n t a c t s t r i a t e d muscle f i b e r s which c o n t r a d i c t s the c o n c l u s i o n . The experiments performed on g l y c e r o l e x t r a c t e d f i b e r s  (Chapter V I I ) do  argue a g a i n s t t h i s c o n c l u s i o n , but the s e l e c t i v i t y o f the b i n d i n g s i t e s f o r  116 sodium over p o t a s s i u m c o u l d be g r e a t e r i n the i n t a c t extracted  than i n the g l y c e r o l  fiber.  What i s the s i g n i f i c a n c e o f these r e s u l t s ?  F o r one t h i n g ,  they  c o n t r a d i c t the e q u i l i b r i u m o r s o r p t i o n t h e o r i e s o f i o n i c a c c u m u l a t i o n p u t forward by i n d i v i d u a l s such as Nasonov others.  Ling  ( 9 ) , T r o s h i n (10), L i n g  ( 5 ) , f o r example, contends  (5) and  t h a t the c a r b o x y l s i t e s on p r o t e i n s  i n the c y t o p l a s m have a s t r o n g p r e f e r e n c e f o r p o t a s s i u m o v e r sodium i o n s even though  i t has been known f o r over a decade t h a t e x t r a c t e d myosin p r e -  f e r s sodium t o p o t a s s i u m accumulate  sodium over p o t a s s i u m  experiments frog  (4) and t h a t g l y c e r i n a t e d f i b e r s (11).  I t i s the author's o p i n i o n t h a t the  performed w i t h c a t i o n s e n s i t i v e m i c r o e l e c t r o d e s on crab ( 1 2 ) ,  (2) and b a r n a c l e (Chapters IV, V, VI) muscles  theory.  preferentially  d i r e c t l y disprove Ling's  The a c t i v i t y o f p o t a s s i u m i n the myoplasm o f s t r i a t e d muscle  fibers  i s n o t a p p r o x i m a t e l y e q u a l to the a c t i v i t y o f p o t a s s i u m i n the b a t h i n g s o l u t i o n , as L i n g ' s t h e o r y demands. sium, which has an anomalously  I t i s the a c t i v i t y o f sodium, n o t p o t a s -  low v a l u e .  A l t h o u g h the m i c r o e l e c t r o d e experiments  reported i n this  thesis  d i r e c t l y c o n t r a d i c t the e q u i l i b r i u m t h e o r i e s o f i o n a c c u m u l a t i o n , they a l s o s t r e n g t h e n a c r i t i c i s m o f the more g e n e r a l l y a c c e p t e d membrane t h e o r y o f ion accumulation. Ling  T h i s c r i t i c i s m , which has been s t r o n g l y advanced  by  (5, 13, 1 4 ) , i s concerned w i t h the energy requirements o f the p o s t u -  l a t e d "membrane pumps". s t u d i e d t h i s problem muscle f i b e r s  A s i d e from L i n g , f o u r groups o f workers have  i n r e l a t i o n to the p o s t u l a t e d sodium pump i n s t r i a t e d  (15, 16, 17, 1 8 ) . The consensus  p h y s i o l o g i c a l c o n d i t i o n s about required  o f o p i n i o n was t h a t under  20% o f the t o t a l energy o f the c e l l would be  to d r i v e the sodium pump.  T h i s i s a minimal v a l u e because  b o t h the  117 e n e r g y - d e l i v e r i n g mechanism and the pumping mechanisms were assumed to be 100%  e f f i c i e n t and i t was f u r t h e r assumed chat the d i f f u s i o n o f sodium i n  the myoplasm was s u r f a c e r a t h e r than b u l k phase l i m i t e d .  The d i r e c t measure-  ments o f the a c t i v i t y o f sodium i n the myoplasm i n d i c a t e t h a t the d i f f e r e n c e in  the c h e m i c a l p o t e n t i a l o f sodium a c r o s s the sarcolemma i s about 4 times  the v a l u e c a l c u l a t e d from measurements o f the t o t a l c o n c e n t r a t i o n o f sodium in  the c e l l .  C o r r e c t i o n f o r t h i s f a c t o r a l o n e r a i s e s the energy r e q u i r e -  ments o f the sodium pump i n f r o g muscle from 20% to 25% o f the t o t a l o u t p u t o f the c e l l .  energy  I t i s known t h a t c a l c i u m and magnesium, as w e l l as  sodium i o n s , a r e permeable and not- d i s t r i b u t e d a c r o s s the sarcolemma a c c o r d ing in  t o the N e r n s t  equation.  Ling  the l i t e r a t u r e , c a l c u l a t e d  t h a t the energy requirements  pumps i s 330% o f the t o t a l energy u t e s such as hydrogen i o n s  (14), u s i n g o n l y the f l u x data  e x p e n d i t u r e o f the c e l l .  q u i r e energy  expending  of these  three  Many o t h e r  (Chapter V I ) , amino a c i d s and sugars  a l s o n o t d i s t r i b u t e d a c c o r d i n g t o the N e r n s t  available  sol-  (14, 5) a r e  e q u a t i o n , and presumably r e -  "pumps" t o m a i n t a i n the d i s e q u i l i b r i u m .  T h i s i s a s e r i o u s c r i t i c i s m o f the membrane t h e o r y , b u t i t does n o t imply t h a t i t must be r e j e c t e d and. an e q u i l i b r i u m theory o f i o n accumul a t i o n accepted transport. of  i n i t s place.  C o n s i d e r what i s meant by the term  active  I t i s u s u a l l y d e f i n e d as a p r o c e s s t h a t can b r i n g about a f l o w  a substance  a g a i n s t an e l e c t r o c h e m i c a l p o t e n t i a l g r a d i e n t o f the substance  (19, 2 0 ) . The e x i s t e n c e o f such a f l o w , however, does n o t mean t h a t i c energy must be expended d i r e c t l y to cause the f l o w . Curran  (21, page 199) p o i n t out " I n p r i n c i p l e ,  As K a t c h a l s k y and  such f l o w c o u l d be a n t i c i -  p a t e d on the b a s i s o f the thermodynamic e q u a t i o n s w i t h o u t o p e r a t i o n o f an a c t i v e  transport.  metabol-  i m p l y i n g the  A d i f f u s i o n a l flow a g a i n s t i t s concentra-  t i o n g r a d i e n t d r i v e n by d i s s i p a t i o n o f another  d i f f u s i o n a l p r o c e s s would be  118 regarded  as an incongruent  th flow o f the i  Thus, the  component a c r o s s a membrane may be w r i t t e n i  J  I f Au„ = 0, but L^. r e p r e s e n t s  d i f f u s i o n , n o t as a c t i v e t r a n s p o r t .  =  L  i i  A  ^ i  +  i i i k ^ k*i  •  L  V 0, a flow o f i may s t i l l  take p l a c e . "  I n Eqn.  [31],  the phenomenological c o e f f i c i e n t which r e l a t e s the d i f f e r e n c e th  i n the e l e c t r o c h e m i c a l p o t e n t i a l o f the j  s p e c i e s , AJJL ^, to the flow o f the  th i  species, J \ .  Spanner  (22) a l s o r e c o g n i z e s  t h i s p o s s i b i l i t y and g i v e s an  example o f a h y p o t h e t i c a l p r o c e s s which c o u l d b r i n g about a flow o f a substance a g a i n s t i t s e l e c t r o c h e m i c a l p o t e n t i a l g r a d i e n t , and furthermore i n h i b i t e d by m e t a b o l i c energy.  poison, y e t s t i l l  be  n o t be d r i v e n d i r e c t l y by m e t a b o l i c  Salminen e t a l (23, 24) have demonstrated e x p e r i m e n t a l l y  sodium and p o t a s s i u m i o n s may be made to f l o w i n o p p o s i t e  that  d i r e c t i o n s against  t h e i r c o n c e n t r a t i o n g r a d i e n t s a c r o s s a s y n t h e t i c membrane when there i s a simultaneous f l u x o f water and hydrogen ions i n the system. omenological  A r e c e n t phen-  d e s c r i p t i o n o f the a c t i v e t r a n s p o r t o f s a l t and water appears  i n a paper by Hoshiko and L i n d l e y ( 2 5 ) . The occurs  above paragraph d e a l t w i t h cases where a n e t f l o w o f s o l u t e  a g a i n s t an e l e c t r o c h e m i c a l g r a d i e n t , as i n the i n t e s t i n a l mucosa, the  w a l l of kidney  t u b u l e s , f r o g s k i n s and sodium loaded muscle f i b e r s .  The  second law o f thermodynamics d i c t a t e s t h a t such a f l o w must occur a t the expense o f energy, b u t i t was noted t h a t the energy need n o t be expended directly. metabolic  ( I t i s obvious t h a t t h e r e can be no c r i t i c i s m o f the u l t i m a t e energy expended i n cases where a n e t t r a n s f e r o c c u r s .  must have s u f f i c i e n t energy t o b r i n g about such a t r a n s f e r . ) s t a t e system i s now c o n s i d e r e d  The c e l l  If a  steady  ( f o r example, a r e s t i n g muscle f i b e r ) ' there  i s a complete range o f energy the c e l l c o u l d expend to m a i n t a i n  this  steady  119 state.  I f the steady s t a t e i n f a c t r e p r e s e n t s  tends, no energy would be r e q u i r e d . be r e j e c t e d , as s t a t e d above.  an e q u i l i b r i u m , as L i n g  The author f e e l s t h i s p o s s i b i l i t y must  The energy requirement o f the c e l l  g i v e n s e t o f f l u x e s and e l e c t r o c h e m i c a l p o t e n t i a l g r a d i e n t s )  (for a  i s maximized i f  the steady s t a t e i s m a i n t a i n e d by a system o f "pumps", each o f which izes metabolic  energy d i r e c t l y  con-  util-  to pump sodium, c a l c i u m , magnesium and  hydrogen ions a g a i n s t an e l e c t r o c h e m i c a l g r a d i e n t and wastes the f r e e energy gained  by the c e l l due t o the p a s s i v e movement o f these ions down t h e i r  electrochemical  gradients.  I t i s the energy requirements o f such a p o s t u -  l a t e d system t h a t L i n g has r e p e a t e d l y  criticized  (5, 13, 1 4 ) . I f L i n g ' s  c a l c u l a t i o n o f the energy requirements o f such a system o f pumps i s a c c e p t e d , the concept o f pumps which a r e uncoupled, o r c o u p l e d h i l l " process and  (such as the p o s t u l a t e d  nerve) must be r e j e c t e d .  "Unless we a r e w i l l i n g  only  t o another "up-  sodium p o t a s s i u m c o u p l i n g  i n muscle  L i n g , however, i s n o t l o g i c a l i n s t a t i n g t h a t  t o v e n t u r e t h a t the second law o f thermodynamics does  not h o l d i n these l i v i n g  c e l l s and t h a t the l i v i n g c e l l s  can g e n e r a t e f r e e  de novo, then w i t h i n the c o n f i n e o f our u n d e r s t a n d i n g o f the p h y s i c a l w o r l d there  i s no a l t e r n a t i v e t o d i s c a r d i n g the pump mechanism f o r s e l e c t i v e i o n i c  distribution i n living jected at a l l . does o c c u r  The  cells"  The concepts o f pumps need n o t be r e -  I t need o n l y be m o d i f i e d  between the v a r i o u s  equations o f i r r e v e r s i b l e  coupling  (14).  to accept  the f a c t t h a t  coupling  fluxes of solutes.  thermodynamics would seem to imply  can occur when a l l the n e t f l u x e s a r e zero a c r o s s  membrane (26, page 4 4 ) , t h a t i s , when the c e l l  t h a t no  a biological  i s i n a steady s t a t e a t r e s t .  T h i s would be t r u e i f the n e t f l u x o f an i o n through each m i c r o s c o p i c way i n the membrane was z e r o .  The p o s t u l a t i o n o f a pump o f any k i n d ,  path-  ^  120 One a process  p o s s i b l e coupling process  the i n f l u x of an  i s "exchange d i f f u s i o n "  i o n would be d i r e c t l y coupled  i s apparent t h a t the e x i s t e n c e  with  (27); i n such  the e f f l u x .  of "exchange d i f f u s i o n " would reduce  It  the  energy requirements of the sodium, c a l c i u m , magnesium, e t c . pumps ( f o r a given  electrochemical p o t e n t i a l gradient  however, occur. ions  that t h i s Coupling  i s not  and  flux).  I t s h o u l d be  stressed,  the o n l y p o s s i b l e mechanism whereby c o u p l i n g  c o u l d occur  d i r e c t l y between the f l u x e s of two  can  different  i n the membrane, v i a the c u r r e n t generated by a pump ( r e c a l l the  dis-  c u s s i o n i n Chapter V about the p o s s i b i l i t y o f an e l e c t r o g e n i c pump) or v i a the p r o d u c t i o n  o f an  intermediate  such as ATP.  p o s s i b i l i t y , note t h a t Garrahan and t h a t the  Glynn  processes  and  Further  chemical  comment on  c e l l ghosts can  last  l e a d to the  the r e l a t i o n s h i p between the  r e a c t i o n s that could occur  would be mere s p e c u l a t i o n , f o r as Eisenman notes how  to the  (28) have r e c e n t l y demonstrated  i n f l u x of sodium ions i n r e d b l o o d  d u c t i o n o f ATP.  With r e g a r d  pro-  transport  i n b i o l o g i c a l membranes (29), i t i s not  even known  ions permeate through b i o l o g i c a l membranes.  A knowledge o f the a c t i v i t i e s plasm i s of v a l u e  i n other  o f p e r m e a b i l i t i e s and  however, i s e q u i v a l e n t  microscopic  The  vector  there  sum  i s no  o f being  p o t a s s i u m i n the myo-  f i e l d s o f membrane study such as  the measurement  the e v a l u a t i o n of the membrane p o t e n t i a l .  zero  f l u x e s of the  ion i n  o f a l l the component f l u x e s i s of course equal  coupled.  trans-  f u r t h e r m o r e i m p l i e s t h a t through a t  pathways there e x i s t non  difficulty  To  to p o s t u l a t i n g t h a t the membrane i s a n i s o t r o p i c  ( C u r i e - P r i g o g i n e P r i n c i p l e ) , and two  o f sodium and  i n admitting  least  question.  to z e r o ,  t h a t these i n d i v i d u a l f l u x e s are  but  capable  121 form the f l u x r a t e o f an i o n i n t o the p e r m e a b i l i t y , f o r example, the d i f f e r ence i n the a c t i v i t i e s  o f the i o n a c r o s s the sarcolemma must be known.  the p a s t , i n v e s t i g a t o r s have assumed t h a t t h i s was  equal to the d i f f e r e n c e  i n the c o n c e n t r a t i o n s o f the i o n a c r o s s the sarcolemma. presented  i n Chapters  In  The  measurements  IV, V and VI i n d i c a t e t h a t f o r both sodium and p o t a s -  sium i o n s , t h i s assumption i s e r r o n e o u s .  0  122 CHAPTER IX j  SUGGESTIONS FOR FUTURE WORK  A  I o n and Water B i n d i n g  Intact Fibers.  The s t u d i e s on c a r b o x y l i c r e s i n s  (1, 2) d i s c u s s e d  i n Chapter I I i n d i c a t e t h a t these r e s i n s p r e f e r the a l k a l i metal c a t i o n s i n the o r d e r Li>Na>K  D  I t i s now known t h a t both e x t r a c t e d myosin  glycerol extracted fibers  (3) and  (4, Chapter V I I ) a l s o p r e f e r sodium to p o t a s s i u m  and t h a t the a c t i v i t y o f sodium, b u t n o t p o t a s s i u m has an anomalously low v a l u e i n the myoplasm o f s t r i a t e d muscle f i b e r s would be simple to determine  (Chapters I V , V, V I ) .  It  i f p r o p o r t i o n a l l y more l i t h i u m than sodium i s  "bound" i n an i n t a c t muscle f i b e r .  T h i s experiment  would support the t e n t a -  t i v e c o n c l u s i o n , based on the l i g h t  s c a t t e r i n g experiments  reported i n  Chapter V I , t h a t l i t h i u m i s bound more s t r o n g l y to myosin than e i t h e r  sodium  o r potassium, a c o n c l u s i o n compatible w i t h the t u r b i d i t y measurements o f S z e n t - G y o r g y i (5, page 42) on s o l u t i o n s o f e x t r a c t e d myosin i n v a r i o u s conc e n t r a t i o n s o f the a l k a l i metal c a t i o n s .  Furthermore,  the study would be  o f t h e o r e t i c a l v a l u e i n u n d e r s t a n d i n g the n a t u r e o f the b i n d i n g s i t e s . There  i s no d i f f i c u l t y  fiber for lithium.  i n exchanging most o f the sodium i n a b a r n a c l e muscle  T h i s can be a c c o m p l i s h e d by b a t h i n g the f i b e r s  sodium f r e e , l i t h i u m s u b s t i t u t e d R i n g e r s o l u t i o n  in a  (preliminary experiments).  There e x i s t g l a s s e s , s u f f i c i e n t l y s e n s i t i v e t o l i t h i u m  (sodium b e i n g the  o n l y important c o n t a m i n a n t ) , from which m i c r o e l e c t r o d e s c o u l d p r o b a b l y be constructed  (6).  Thus, the a c t i v i t y and t o t a l c o n c e n t r a t i o n o f l i t h i u m i n  the f i b e r c o u l d be measured, and the f r a c t i o n o f "bound" l i t h i u m  F u r t h e r i n f o r m a t i o n about  determined.  the n a t u r e o f the s i t e s t o which sodium  (and  presumably potassium) ions a r e complexed w i t h i n i n t a c t muscle  c o u l d be o b t a i n e d by measuring  the a c t i v i t i e s  under c o n d i t i o n s o f v a r y i n g pH.  o f these ions i n t h e myoplasm  The pH o f t h e myoplasm can r a p i d l y be  lowered by about 1 u n i t by exposing the'muscle f i b e r t o s o l u t i o n s w i t h CO^ (Chapter V I ) .  fibers  saturated  A few p r e l i m i n a r y experiments i n d i c a t e d t h a t t h e  a c t i v i t y o f sodium d i d n o t change s i g n i f i c a n t l y when the pH was lowered ( 7 ) , but  no measurements were made o f the a c t i v i t y o f p o t a s s i u m .  I t would be  d e s i r a b l e t o r e p e a t , and extend these measurements t o h i g h e r pH r e g i o n s , i f a method o f r a p i d l y i n c r e a s i n g  the pH o f t h e myoplasm c o u l d be found.  The t h e o r e t i c a l b a s i s and e x p e r i m e n t a l j u s t i f i c a t i o n o f u s i n g a d i f f u s i o n t e c h n i q u e t o measure the f r a c t i o n o f ions bound to macromolecules i n s o l u t i o n was g i v e n i n Chapter I I .  D i f f u s i o n experiments have a l r e a d y  y i e l d e d v a l u a b l e i n f o r m a t i o n about the s t a t e o f p o t a s s i u m i n g i a n t The e l e g a n t experiments o f Hodgkin and Keynes  (8) demonstrated  d i f f u s i o n c o e f f i c i e n t o f p o t a s s i u m i n g i a n t axons cm^sec"^. 2.135  axons.  t h a t the  i s about 1.5 x 10~^  The s e l f d i f f u s i o n c o e f f i c i e n t o f p o t a s s i u m i n .5 M KC1 i s  x 10" c m s e c 5  2  - 1  (9) and i n .5 M KI 2.030 1 0  - 5  cm sec 2  _ 1  i t appears t h a t l e s s than 257o o f the p o t a s s i u m i n g i a n t axons compartmentalized.  (10).  Thus,  i s bound o f  C a u t i o n , however, must be used i n t h e i n t e r p r e t a t i o n o f  d i f f u s i o n measurements made i n b i o l o g i c a l m a t e r i a l .  Ling  (11, page 338)  p o i n t s out t h a t i o n p a i r f o r m a t i o n does n o t always d e c r e a s e t h e d i f f u s i o n c o e f f i c i e n t o f an i o n .  The d i f f u s i o n c o e f f i c i e n t o f p o t a s s i u m on the s u r -  f a c e o f a g l a s s , f o r example, Presumably, glass. living  this  i s h i g h e r than t h a t  i n a d i l u t e s o l u t i o n (12).  i s because p o t a s s i u m can "jump" from s i t e  I t would be d i f f i c u l t ,  to s i t e on the  however, to argue t h a t the a n i o n i c s i t e s  c e l l a r e c l o s e enough t o p e r m i t the movement o f p o t a s s i u m by t h i s  type o f mechanism.  Even L i n g has attempted to measure the d i f f u s i o n  i na  c o e f f i c i e n t of  ions i n muscle as  a d e m o n s t r a t i o n of b i n d i n g  d i f f u s i o n experiments performed on muscle f i b e r s conclusive  (13,  14,  15).  The  be  i d e a l f o r measurements of  of  the  jected  (16),  the  to date have been f a r  the  relative longitudinal Two  of  the  diffusion  these ions  sodium or potassium, f o r example) c o u l d be  into a fiber  but  from  e x t r e m e l y l a r g e b a r n a c l e muscle f i b e r s would  a l k a l i m e t a l c a t i o n s i n the myoplasm.  radioactive  (13),  coefficients (lithium  simultaneously i n -  f i b e r s e c t i o n e d a f t e r a g i v e n time, and  relative diffusion coefficients  determined.  The  and  the  e x t e n s i v e membraneous n e t -  work i n these s t r i a t e d muscle f i b e r s , however, would g r e a t l y  impede  the  d i f f u s i o n o f b o t h s p e c i e s , making a c c u r a t e measurements e x t r e m e l y d i f f i c u l t . If was  i t was  found n e c e s s a r y to make k i n e t i c measurements of  done i n the  have to be f i b e r s on  experiments of Hodgkin and  application  to p e r f o r m i n g an  would p r o v i d e an  the  of a c u r r e n t .  in this  excellent thesis.  o t h e r hand, would be  experiment o f  and  Diffusion  considered.  The  d e s t r u c t i o n of  a p p l i c a b l e to an  c u r v e s , as has would be  be  rapidly  experiment  the m i c r o e l e c t r o d e  experiments on  There are  the  results  glycerinated fibers,  reversibly  intact  been done on  to measure the  can  the be  fiber.  sarcolemma i m p l i e s investigated One  by  studying  fibers.  varied  and  t h a t the  a variety  method would be  The the  pH  pos-  p r e s s u r e , as has  of  state  be of  techniques  to study d e s o r p t i o n  o t h e r non-membraneous t i s s u e s  imbibition  on  interpret.  s e v e r a l advantages to  and  the  technical  a c c u m u l a t i o n i n i n t r a c e l l u l a r o r g a n e l l e s need not  water i n g l y c e r i n a t e d f i b e r s not  type, but  g l y c e r i n a t e d r a t h e r than i n t a c t  i o n i c c o n c e n t r a t i o n s may selective  formidable  r e l a t i v e l y easy to p e r f o r m and  water " b i n d i n g " on  s i b i l i t y of  this  independent t e s t o f  Glycerinated Fibers. i o n and  Thus, t h e r e are  (as  experiments would  performed i n a c a l c i u m f r e e medium to p r e v e n t c o n t r a c t i o n o f  difficulties  presented  K e y n e s ) , the  the m o b i l i t i e s  (17).  been done on  Another the  corneal  125 stroma (18).  One the p r o t e i n s [19],  could  study s i m u l t a n e o u s l y  the b i n d i n g  o f ions and water t o  i n a g l y c e r i n a t e d f i b e r by a simple t e c h n i q u e .  C o n s i d e r Eqn.  I f both s i d e s o f t h i s e q u a t i o n a r e d i v i d e d by the weight o f s o l i d  material  i n the g l y c e r i n a t e d f i b e r , M  r  Q  , the f o l l o w i n g e q u a t i o n r e s u l t s  = C.V/M - O,aV/0f M ) K pro K K K pro  [32]  v  K  pro  where B,,/M represents K pro material.  the moles o f p o t a s s i u m i o n s bound p e r kg o f s o l i d  I t i s c e r t a i n l y r e a s o n a b l e t o expect t h a t Bj,/M  monotonically  q  w i l l be a  i n c r e a s i n g f u n c t i o n o f a ^ / l f ^ (the f r e e c o n c e n t r a t i o n o f  p o t a s s i u m i n the muscle f i b e r , which i s e q u a l to the c o n c e n t r a t i o n o f p o t a s s i u m i n the e x t e r n a l s o l u t i o n i f the a c t i v i t y c o e f f i c i e n t s a r e i d e n t i c a l ) , and approach a c o n s t a n t occurs. (3)  This  v a l u e when s a t u r a t i o n o f the b i n d i n g  sites  i s indeed the case f o r myosin, as F i g . 1 o f Lewis and S a r o f f  indicates.  As t h e i r s t u d i e s were performed a t p r o t e i n  concentrations  o f l e s s than 1% (3) , t h e i r t a c i t assumption t h a t the f r a c t i o n o f water a v a i l a b l e t o a c t as s o l v e n t The  value  of  f o r potassium, O L ^ , was u n i t y was p r o b a b l y v a l i d .  i n a g l y c e r i n a t e d f i b e r , however, may be s i g n i f i c a n t l y  I f CL, i s i n c o r r e c t l y assumed t o be u n i t y B /M is. Js. p r o w i l l pass through a maximum, then f a l l i n s t e a d o f a t t a i n i n g a c o n s t a n t v a l u e . d i f f e r e n t from u n i t y .  T h i s i n d i c a t e s a method o f measuring B /M and CL i n d e p e n d e n t l y . Js. p r o is.  A series  v  o f measurements a t v a r y i n g f i t t e d with a value concentrations. metal c a t i o n s .  of  external concentrations  o f p o t a s s i u m c o u l d be  which y i e l d s a h o r i z o n t a l l i n e f o r By/M  q  a t high  The experiments c o u l d be r e p e a t e d w i t h each o f the a l k a l i T h i s would i n d i c a t e two t h i n g s ;  a v a i l a b l e to a c t as s o l v e n t association constants.  the amount o f water un-  f o r each c a t i o n and the r e l a t i v e v a l u e s  The data o f Fenn  (4)  o f the  i n d i c a t e s that a s i g n i f i c a n t  amount o f water  " b i n d i n g " w i l l be found, f o r i f h i s data a r e p l o t t e d i n t h i s  manner the apparent b i n d i n g assumption  t h a t 0^, and o ^  a  (that i s , the b i n d i n g c a l c u l a t e d w i t h the = 1.0)  o f both sodium and p o t a s s i u m passes throug  a maximum a t c o n c e n t r a t i o n s o f about  .10  M.  A s e r i e s o f measurements o f the r e l a t i v e b i n d i n g c o n s t a n t s o f the a l k a l i m e t a l c a t i o n s to the p r o t e i n s  in a glycerinated fiber,  coupled w i t h  more s e l e c t i v i t y measurements o f the type r e p o r t e d i n Chapter V I I would be of great t h e o r e t i c a l value.  They would a l l o w one  to examine c r i t i c a l l y a  g i v e n t h e o r y o f c a t i o n s e l e c t i v i t y as a p p l i e d to a b i o l o g i c a l f i x e d system. briefly  Two  such t h e o r i e s , those o f Eisenman (19) and L i n g  charge  (11) were  d i s c u s s e d i n Chapter I I .  A critical  examination o f the t h e o r i e s o f the b i n d i n g o f the  a l k a l i m e t a l c a t i o n s to p r o t e i n s would be o f v a l u e , but i t would a l s o d e s i r a b l e to c o n s i d e r i n more d e t a i l how  p r o t e i n s can a f f e c t the  c o e f f i c i e n t s o f ions w i t h o u t a c t u a l l y " b i n d i n g " these i o n s . i t was  be  activity  In Chapter IV  n o t e d t h a t a knowledge o f the m a c r o s c o p i c d i e l e c t r i c c o n s t a n t o f a  s o l u t i o n o f p r o t e i n s i s o f l i t t l e v a l u e i n p r e d i c t i n g the e f f e c t o f the p r o t e i n on the a c t i v i t y c o e f f i c i e n t s o f the ions i n s o l u t i o n .  Any  theory o f  such e f f e c t s s h o u l d , as E d s a l l and Wyman (20) p o i n t out, be "framed o f the dimensions, d i p o l e moments, and e l e c t r i c a l p o l a r i z a b i l i t i e s i n d i v i d u a l m o l e c u l e s , r a t h e r than i n terms o f the m a c r o s c o p i c  i n terms o f the  dielectric  constant, o f the whole medium."  B.  D e n a t u r a t i o n and  Contraction  The d e n a t u r a t i o n experiments r e p o r t e d i n Chapter V c o u l d be tended to i n c l u d e an EM  i n v e s t i g a t i o n o f the changes i n u l t r a s t r u c t u r e  exthat  127 o c c u r when a b a r n a c l e  muscle f i b e r  i s heated to 37-40° C.  I t was p o s t u l a t e d  t h a t the c o n t r a c t i o n and r e l e a s e o f bound sodium and hydrogen occurred  at this  ions  that  temperature were due t o a breakdown o f the t h i c k f i l a m e n t s .  T h i s c o n c l u s i o n was based on experiments performed on e x t r a c t e d p r o t e i n s and glycerinated fibers.  Either a confirmation  or negation  of this  postulated  breakdown o f the t h i c k f i l a m e n t s would be i n t e r e s t i n g , and c o u l d p o s s i b l y shed some l i g h t on the mechanism o f normal p h y s i o l o g i c a l c o n t r a c t i o n s .  . I t was mentioned  i n Chapter V t h a t some p r e l i m i n a r y measurements  were made t o determine i f the a c t i v i t i e s o f sodium and p o t a s s i u m i n the myoplasm v a r i e d when the muscle  f i b e r contracted.  The f i b e r was  by exposure to a s o l u t i o n c o n t a i n i n g 0.064 [ K ] , and remained contracture during a^  a  f o r about 10 minutes.  the i s o m e t r i c c o n t r a c t u r e  i n a state of  No s i g n i f i c a n t change i n a^, o c c u r r e d (10 f i b e r s ) .  was measured, however, a l a r g e  seconds) i n c r e a s e  contracted  I n 3 out o f 9 f i b e r s  i n which  (100-500%) t r a n s i t o r y ( l a s t i n g about 30  i n a ^ was noted a t the s t a r t o f c o n t r a c t u r e .  The e x p e r i -  ments were abandoned m a i n l y because o f two t e c h n i c a l problems; the sodium e l e c t r o d e s were g e n e r a l l y slow i n r e s p o n d i n g to p o t e n t i a l and a c t i v i t y changes  and t h e r e was some doubt as t o whether  on the sodium s e n s i t i v e m i c r o e l e c t r o d e  the observed p o t e n t i a l change  was due to an a c t i v i t y change o r t o a  t r a n s i t o r y d e p o l a r i z a t i o n o f an i n t e r n a l system o f membranes. difficulties  c o u l d perhaps be circumvented by u t i l i z i n g  These two  open t i p c a t i o n sen-  s i t i v e microelectrodes  and working w i t h a d e p o l a r i z e d p r e p a r a t i o n  c a l c i u m c o u l d be added  t o produce c o n t r a c t i o n .  C„  to which  Light Scattering  The measurements r e p o r t e d the e f f e c t s o f o t h e r  i n Chapter V I c o u l d be extended t o s t u d y  ions on the O.D. o f muscle  f i b e r s ; cesium and r u b i d i u m  128 a r e obvious c h o i c e s , b u t i t would be i n t e r e s t i n g to study c a l c i u m and magnesium i n more d e t a i l . measurements o f the angular scattered l i g h t . simple  the e f f e c t o f  I t would a l s o be d e s i r a b l e to make  as w e l l as the wavelength dependence o f the  T h i s would r e q u i r e more e l a b o r a t e  instrumentation  than a  s p e c t r o p h o t o m e t e r , but would prove c o n c l u s i v e l y t h a t the phenomenon  was due t o s c a t t e r i n g and n o t a b s o r p t i o n . angular  d i s t r i b u t i o n o f the s c a t t e r e d l i g h t  Experimental  measurements o f the  c o u l d a l s o be c o r r e l a t e d w i t h  p r e d i c t i o n s made on the b a s i s o f the i n t e r f e r e n c e theory o f l i g h t s c a t t e r i n g because the s i z e and d i s t r i b u t i o n o f the t h i c k f i l a m e n t s i n a muscle  fiber  a r e known from e l e c t r o n microscopy..  The tracture bathing  i n v e s t i g a t o r has a l s o observed t h a t d u r i n g an i s o m e t r i c con-  (induced by an i n c r e a s e i n the p o t a s s i u m c o n c e n t r a t i o n  i n the  s o l u t i o n ) the O.D. o f the muscle f i b e r s i n c r e a s e s markedly, then  d e c r e a s e s on r e l a x a t i o n ( p r e l i m i n a r y e x p e r i m e n t s ) .  T h i s change may be due  to t h e c o n j u n c t i o n o f the t h i c k and t h i n f i l a m e n t s i n the muscle f i b e r , an analogous phenomenon b e i n g o f g e l a t i n on s e t t i n g scattering  the r e v e r s i b l e i n c r e a s e i n the O.D. o f s o l u t i o n s  ( 2 1 ) . I f f u r t h e r development o f the t h e o r y o f l i g h t  i n muscle f i b e r s  i n d i c a t e s t h a t the t e n t a t i v e e x p l a n a t i o n o f f e r e d  f o r the i n c r e a s e i n O.D. i s c o r r e c t , t h i s o b s e r v a t i o n w i l l physiological  importance.  be o f fundamental  L i g h t s c a t t e r i n g measurements may be made v e r y  _3 rapidly  (<10  seconds) hence i t would be p o s s i b l e to measure r o u t i n e l y on  the same f i b e r : electrode,  ( i ) the s t i m u l a t i n g a c t i o n p o t e n t i a l w i t h an open t i p m i c r o -  ( i i ) the c o n j u n c t i o n o f the t h i c k and t h i n f i l a m e n t s by o p t i c a l  measurements, ( i i i )  the c o n t r a c t i l e f o r c e w i t h a t r a n s d u c e r .  o f the v a l u e o f k i n e t i c o p t i c a l measurements i n s t u d y i n g omena, c o n s i d e r recognized  As an example  c o n t r a c t i l e phen-  the r e c e n t experiments o f Yefimov and F r a n k (22).  the f a c t t h a t the c r o s s s t r i a t i o n s  They  i n a muscle f i b e r make i t  129 analogous to a d i f f r a c t i o n g r i d , grid  c o n s t a n t t h a t o c c u r r e d on c o n t r a c t i o n .  teresting; with  and measured k i n e t i c a l l y  time.  they found  The r e s u l t s  the changes i n the were extremely i n -  t h a t s h o r t e n i n g o c c u r s not m o n o t o n i c a l l y , but  stepwise  130 BIBLIOGRAPHY  Chapter I  1.  A. S z e n t - G y o r g y i .  2.  E. O v e r t o n .  3.  M.  4.  A. V. H i l l .  5.  S. G. A. M c L a u g h l i n and J . A. M. H i n k e . 837 (1966).  6.  H. E. Whipple, e d i t o r . Forms o f water Acad. S c i . V o l . 25, A r t . 2 (1965).  7.  R. E. S t o w e l l , e d i t o r . 15 (1965).  8.  G. E. Fogg, e d i t o r .  9.  Academic P r e s s I n c . , New  P f l u e g e r s A r c h . Ges. P h y s i o l .  Rubner.  isms.  Bioenergetics.  Abh.  P r e u s s . Akad. W i s s . No.  P r o c . Roy.  The  Soc.  Cryobiology.  E. G. Olmstead. 1966.  11.  S. J . Webb.  Springfield.  1, 1 (1922). 477  (1930).  Can. J . P h y s i o l . Pharm. 44,  in biologic  systems.  Ann. N.  F e d e r a t i o n P r o c . V o l . 24,  in living  B u t t e r w o r t h , I n c . , Washington.  Suppl.  organ-  1966.  Lea and F e b i g e r , P h i l a d e l p h i a .  in biological  integrity.  C h a r l e s C. Thomas,  1965.  12.  B. Moore and H. E. Roaf.  Kolloid-Z.  13.  H. F i s h e r and G. Moore.  14.  M. N e u s c h l o s s .  15.  R. Hbber.  16.  M.  17.  F. H. Shaw and S. E. Simon. 33, 153 (1955).  18.  S. E. Simon, F. H. Shaw, S. Bennett and M. M u l l e r . 40, 753 (1957).  19.  S. E. Simon.  Am.  13, 133  (1913).  J . P h y s i o l . 20, 330  (1915).  P f l u e g e r s A r c h . Ges. P h y s i o l . 204,  P f l u e g e r s A r c h . Ges. P h y s i o l . 221, 478  S. Lewis and H. A. S a r o f f .  N a t u r e . 184,  J . Am.  374  (1924).  (1929).  Chem. Soc. 79_, 2112  (1957).  A u s t r a l i a n J . E x p t l . B i o l . Med. S c i .  1978  Y.  (1965).  Mammalian c e l l water.  Bound water  1957.  (1902).  s t a t e and movement o f water  C e l l water.  10.  115  (London), S e r . B, 106,  S. E. B. Symposia XIX  D. A. T. D i c k .  92,  York.  (1959).  J . Gen.  Phvsiol.  131 20.  S. E . Simon, B. M. Johnstone, K. H. Shankly and F. H. Shaw. P h y s i o l . 43, 55 (1959).  21.  A. T r o s h i n . Problems o f c e l l p e r m e a b i l i t y . Pergamon P r e s s , London, 1966. ( O r i g i n a l R u s s i a n e d i t i o n p u b l i s h e d i n 1965)  22.  A. S. T r o s h i n . I n Membrane t r a n s p o r t and metabolism. E d i t e d by A. K l e i n z e l l e r and A. Kotyk. Academic P r e s s I n c . , London. 1961.  23.  D. N. Nasonov. L o c a l r e a c t i o n o f p r o t o p l a s m and g r a d u a l e x c i t a t i o n . N a t i o n a l S c i e n c e F o u n d a t i o n , Washington, D„ C. 1962. (Original R u s s i a n e d i t i o n p u b l i s h e d i n 1959)  24.  G. N. L i n g . I n Phosphorus metabolism, V o l . I . E d i t e d by W. D. M c E l r o y and B. G l a s s . Johns Hopkins P r e s s , B a l t i m o r e . 1952.  25.  G. N. L i n g .  A p h y s i c a l t h e o r y o f the l i v i n g  i n g Co., New York.  state.  J . Gen.  Blaisdell  Publish-  1962.  26.  G. N. L i n g .  E i o p o l y m e r s , 1_, 91 (1964).  27.  G. N. L i n g and M. M. O c h s e n f e l d .  28.  G. N. L i n g .  Ann. N. Y. Acad. S c i . 125, 401 (1965).  29.  G. N. L i n g .  F e d e r a t i o n P r o c . 24, S103 (1965).  30.  G. N. L i n g .  P e r s p e c t i v e s B i o l . Med. _9, 87 (1965).  31.  G. N. L i n g and M. M. O c h s e n f e l d .  32.  E. E r n s t .  B i o p h y s . J . 5, 777 (1965).  J . Gen. P h y s i o l . 49, 819 (1966).  I n Membrane t r a n s p o r t and metabolism.  K l e i n z e l l e r and A. Kotyk. 33.  E . J . Conway.  34.  G. Eisenman.  E d i t e d by A.  Academic P r e s s I n c . , London. 1961.  P h y s i o l . Revs. 37, 84 (1957). I n Membrane t r a n s p o r t and metabolism.  K l e i n z e l l e r and A. Kotyk.  E d i t e d by A.  Academic P r e s s I n c . , London. 1961.  35.  G. Eisenman.  36.  J . A. M. Hinke.  37.  F. W. Cope.  38.  A. A. L e v . Nature, 201_, 1132 (1964).  39.  J . A. M. Hinke and S. G. A. M c L a u g h l i n . Can. J . P h y s i o l . Pharm. 44, 837 (1967). F. W. Cope. J . Gen. P h y s i o l . 50, 1354 (1967).  40.  B i o p h y s . J . 2, 259 (1962). Nature, 184, 1257 (1959).  P r o c . N a t l . Acad. S c i . U.S. 54, 225 (1965).  132 Chapter I I /  1.  J . D. B e r n a l and R. H. F o w l e r .  2.  J . Morgan and B. E . Warren.  3.  R. W. Gurney.  J . Chem. Phys.  I, 515 (1933).  J . Chem. Phys. 6, 666 (1938).  Ionic processes i n s o l u t i o n .  M c G r a w - H i l l , New York.  1953. 4.  G. W. Brady and J . T. K r a u s e .  5.  G. W. Brady.  J . Chem. Phys. 28, 464 (1958).  6.  G. W. Brady.  J . Chem. Phys. 29, 1371 (1958).  7.  G. W. Brady and W. J . Romanow.  8.  M. D. Danford and H. A. L e v y .  9.  H. S. Frank and W. Y. Wen.  10.  C. A. C o u l s o n . Thompson.  J . Chem. Phys. 27, 304 (1957).  J . Chem. Phys. 32, 306 (1960). J . Am. Chem. Soc. 84, 3965  (1962).  D i s c . Faraday Soc. 24, 133 (1957).  I n Hydrogen b o n d i n g .  E d i t e d by D. H a d z i and H. W.  Pergamon P r e s s , New York. 1959.  11.  H. A. Scheraga.  12.  G. Nemethy and H. A. Scheraga.  J . Chem. Phys. 36, 3382 (1962).  13.  G. Nemethy and H. A. Scheraga.  J . Phys. Chem. 66, 1773 (1962).  14.  M. Magat.  C. J . P h y s i q u e , 6, 179 (1935).  15.  M. Magat.  D i s c u s s i o n s Faraday Soc. j!3, 114 (1937).  16.  H. S. F r a n k .  P r o c . Roy. Soc. (London), S e r . A, 247, 481 (1958).  17.  H. S. F r a n k .  NAS-NRC Pub. 942, 141 (1963).  18.  C. H. C o l l i e , J . B. Hasted and D. M. R i t s o n . P r o c . Phys. Soc. (London), 60, 145 (1948). J . L . Kavanau. S t r u c t u r e and f u n c t i o n i n b i o l o g i c a l membranes, V o l I .  19.  Ann. New York Acad. S c i . 125, 253 (1965).  Holden-Day, I n c . , San F r a n c i s c o . 1965. 20.  E. F o r s l i n d .  21.  E. F o r s l i n d . I n P r o c e e d i n g s of the second i n t e r n a t i o n a l congress on Rheology. E d i t e d by V. G. W. H a r r i s o n . B u t t e r w o r t h s , London. 1954. L. Pauling. I n Hydrogen b o n d i n g . E d i t e d by D. H a d z i and H. W. Thompson. Pergamon P r e s s New York. 1959,  22.  A c t a P o l y t e c h . 115, 9 (1952).  133 23.  L. Pauling.  The n a t u r e o f the c h e m i c a l bond, 3 r d e d i t i o n .  Cornell  U n i v e r s i t y P r e s s , New York. 1960. 24.  J . A. P o p l e .  25.  K. B u i j s and G. R. Choppin.  26.  A. A. M i l l e r .  27.  K. S. Singwi and A. Sj'olander.  28.  H. S. Frank and M. W. Evans.  29.  D. D. E l e y and M. G. Evans.  30.  J . N. S h o o l e r y and B. J . A l d e r .  31.  M. S. B e r g q v i s t and E. F o r s l i n d .  32.  M. E i g e n .  33.  M. Kaminsky.  34.  M. E i g e n and L . De Maeyer. I n The s t r u c t u r e o f e l e c t r o l y t e s o l u t i o n s , E d i t e d by W. J . Hamer. John W i l e y and Sons, I n c . , New York. 1959.  35.  J . H. Wang.  36.  R. E . P o w e l l and M. W. L a t i m e r .  37.  G. H. Haggis, J . B. Hasted and T. J . Buchanan. 1452  P r o c . Roy. Soc. (London), S e r . A, 205, 163 (1951). J . Chem. Phys. 39, 2035  (1963).  J . Chem. Phys. 38, 1568 (1963). Phys. Rev. 119, 863 (1960).  J . Chem. Phys.  13, 507 (1945).  T r a n s . Faraday Soc. 34, 1093 (1938). J . Chem. Phys. 23, 805 (1955). A c t a Chem. Scand.  16, 2096  (1962).  Pure A p p l . Chem. _6, 97 (1963). D i s c . Faraday Soc. 24, 171 (1957).  J . Phys. Chem. _58, 686 (1954). J . Chem. Phys.  19, 1139 (1951). J . Chem. Phys. 20,  (1952).  38.  F . E . H a r r i s and C. T. O'Konski.  J . Phys. Chem. 61, 310 (1957).  39.  0. L . S p o n s l e r , J . D. Bath and J . W. E l l i s .  J . Phys. Chem. 35, 2053  (1940). 40.  N. Azuma and Y. Tonomura.  41.  H. J . C. Berendsen 365  B i o c h i m . B i o p h y s . A c t a , 73, 499 (1963).  and C. M i g c h e l s e n .  Ann. New York Acad. S c i . 25,  (1965).  42.  A. R i c h and F . H. C. C r i c k .  43.  H. J . C„ Berendsen.  44.  J . D. B e r n a l . Thompson.  J . M o l . B i o l . 3, 483 (1961).  J . Chem. F h y s . 36, 3297  I n Hydrogen bonding.  (1962).  E d i t e d by D. H a d z i and H. W.  Pergamon P r e s s , New York.  1959.  45.  B. J a c o b s o n .  A c t a Chem. Scand. _9, 191 (1955),  46.  B. J a c o b s o n .  J . Am. Chem. Soc. 77, 2919 (1955).  134 47.  J . T. E d s a l l . I n The p r o t e i n s , V o l . 1. E d i t e d by H. Neurath and K. B a i l e y . Academic P r e s s , New York. 1953.  48.  C. B. B r a t t o n , A. L . Hopkins (1965).  49.  R. J . S c h e u p l e i n and L . J . Morgan.  50.  W. S. M c C u l l o c h and W. M. Brody. I n The g r e a t i d e a s today, 1966. E d i t e d by R. M. H u t c h i n s and M. J . A d l e r . P r a e g e r , I n c . , New York. 1966.  51.  J . A. M. Hinke.  52.  S. G. A. M c L a u g h l i n and J . A. M. H i n k e . 837 (1966).  Can. J . P h y s i o l . Pharm. 44,  53.  J . A. M. Hinke and S. G. A. M c L a u g h l i n .  Can. J . P h y s i o l . Pharm. 45,  655  and J . W. Weinberg.  S c i e n c e , 147, 738  Nature, 214, 456 (1967).  Nature, 184, 1257 (1959).  (1967).  54.  J . E . H e a r s t and J . V i n o g r a d .  P r o c . N a t l . Acad. S c i . 47, 825 (1961).  55.  J . E . H e a r s t and J . V i n o g r a d .  P r o c . N a t l . Acad. S c i . 47, 1005 (1961).  56.  N. Bjerrum. K danske v i d e n s k . S e l s k . 7_, No. 9 (1926); S e l e c t e d p a p e r s , page 108. K i n a r Munksgaard, Copenhagen. 1949.  57.  R. A. Robinson and R. H. S t o k e s . London.  Electrolyte solutions.  Butterworths,  1959.  58.  R. M. F u o s s .  J . Am. Chem. Soc. 80, 5059  59.  S. A. R i c e and M. Nagasawa. P r e s s , New York.  (1958).  Polyelectrolyte solutions.  Academic  1961.  60.  G. Schwarzenbach and H. Ackermann.  61.  G. Schwarzenbach, E . Kampitsch and R. S t e i n e r . H e l v . Chim. A c t a , 29, 364 (1946). J . R. Huizenga, P. F. G r i e g e r and F . T. W a l l . J . Am. Chem. Soc. _72, 2636 (1950).  62.  H e l v . Chim. A c t a , 30, 1798 (1947).  63.  J . Crank. The mathematics o f d i f f u s i o n . London. (1956).  Oxford U n i v e r s i t y P r e s s ,  64.  U. P. S t r a u s s , N. L . G e r s h f e l d and H. S p i e r a . 76, 5909 (1954).  65.  U. P. S t r a u s s , D. Woodside and P. Wineman. (1957).  66.  U. P. S t r a u s s and P. L . Wineman.  J . Am. Chem. Soc.  J . Phys. Chem. 61, 1353  J . Am. Chem. Soc. 80, 2366  (1958).  135 67.  U. P. S t r a u s s and P. Ander.  J . Am. Chem. Soc. 80, 6494 (1958).  68.  U. P. S t r a u s s and S. B l u e s t o n e .  69.  U. P. S t r a u s s and P. D. Ross.  J . Am. Chem. Soc. 81, 5299  (1959).  70.  U. P. S t r a u s s and P. D. Ross.  J . Am. Chem. Soc. 81, 5295  (1959).  71.  R. M. Fuoss, A. K a t c h a l s k y and S. L i f s o n .  J . Am. Chem. Soc. _81, 5292 (1959).  P r o c . N a t l . Acad. S c i . U.S.  37, 579 (1951). 72.  J . W. McBain.  T r a n s . Faraday Soc. 9, 99 (1913).  73.  G. S. H a r t l e y . Aqueous s o l u t i o n s o f p a r a f f i n - c h a i n s a l t s . P a r i s . 1936.  74.  G. N. L i n g . A p h y s i c a l t h e o r y o f the l i v i n g i n g Co., New York. 1962.  75.  D. R e i c h e n b e r g .  I n Ion exchange.  Dekker, I n c . , New York.  state.  Herman,  Blaisdell  E d i t e d by J . A. M a r i n s k y .  Publish-  Marcel  1966.  76.  J . I . Bregman.  Ann. N. Y. Acad. S c i . 57, 125 (1953).  77.  H. P. Gregor, M. J . H a m i l t o n , R. J . Oza and F. B e r n s t e i n .  J . Phys.  Chem. 60, 263 (1956). 78.  J . I . Bregman and Y. Murata.  79.  H. P. G r e g o r .  J . Am. Chem. Soc. 70, 1293 (1948).  80.  H. P. G r e g o r .  J . Am. Chem. Soc. 73, 642 (1950).  81.  G. Eisenman, D. 0. Rudin and J . U. Casby.  82.  D. 0. Rudin and G. Eisenman. A b s t r a c t s , 21 I n t e r n a t i o n a l Congress o f P h y s i o l o g i c a l S c i e n c e s , 237 (1959). G. Eisneman. I n Membrane t r a n s p o r t and metabolism. E d i t e d by A.  83.  K l e i n z e l l e r and A. Kotyk.  J . Am. Chem. Soc. M ,  1867 (1952).  S c i e n c e , 126, 831 (1957).  Academic P r e s s I n c . , London.  84.  G. Eisenman.  85.  E. Glueckauf.  86.  E . H. C r u i c k s h a n d and P. Meares.  87.  G. N. L i n g .  88.  E . J . Conway.  89.  E . J . Cohn and J . T. E d s a l l , e d i t o r s . p e p t i d e s as ions and d i p o l a r i o n s .  1961.  B i o p h y s . J . 2, 259 (1962). P r o c . Roy. Soc. London, S e r . A, 214, 207 (1952). T r a n s . Faraday Soc. 53, 1299 (1957).  J . Gen. P h y s i o l . 43, 149 (1960). P h y s i o l . Rev. 37 , 84 (1957). P r o t e i n s , amino a c i d s and R e i n h o l d , New York. 1943.  136 90.  J . T. E d s a l l and J . Wyman. P r e s s , New York. 1958.  91.  A. S z e n t - G y o r g y i . New York.  contraction.  Academic P r e s s ,  1951.  M. Lewis and H. A. S a r o f f .  93.  F . W. Cope.  94.  H. A. S a r o f f .  95.  H. H. Weber and K. Meyer.  96.  E . C. Bate Smith.  97.  W. 0. Fenn.  98.  J . Brahms and J . B r e z n e r .  99.  L . B. Nanninga. W. S. Lynn.  c h e m i s t r y , V o l . I . Academic  Chemistry o f muscular  92.  100.  Biophysical  J . Am. Chem. Soc. 7_9, 2112 (1957).  J . Gen. P h y s i o l . 50, 1354 (1967). A r c h . Biochem. B i o p h y s . '71, 194 (1957). Biochem. Z. 266, 137 (1933).  P r o c . Roy. Soc. (London), S e r . B, 124, 136 (1937).  P r o c . Soc. Exp. B i o l . Med. 96, 783 (1957). A r c h . Biochem. B i o p h y s . _95, 219 (1952).  Nature, 194, 187 (1962).  A r c h . Biochem. B i o p h y s . 110, 262 (1965).  Chapter I I I  1.  G. N. L i n g . A p h y s i c a l t h e o r y o f the l i v i n g i n g Co., New York. 1962.  2.  A. S z e n t - G y o r g y i . New York.  C h e m i s t r y o f muscular  state.  Blaisdell  contraction.  Publish-  Academic P r e s s ,  1951.  3.  L . B. Nanninga.  Nature, 194, 187 (1962).  4.  J . T. E d s a l l , H. E d e l h o c k , R. L o n t i e  and P. M o r r i s o n .  J . Am. Chem.  Soc. 72, 4641 (1950). 5.  P. Doty and R. F . S t e i n e r .  6.  P. Doty and J . T. E d s a l l .  7.  H. A. S a r o f f .  J . Chem. Phys. 20, 85 (1952). Advan. P r o t e i n Chem. 6., 35 (1951).  A r c h . Biochem. B i o p h y s . 71, 194 (1957). Chapter IV  1.  J  2.  G. Eisenman, D. 0. Rudin and J . U. Casby.  0  A. M. Hinke.  Nature, 184, 1257 (1959). S c i e n c e , 126, 831 (1957)  137 3.  G. Hoyle and T. Smyth J r .  4„  A. A. Lev and E. P. Buzhinsky.  5  A. A. L e v . Nature, 201,  6„  J . A. M. H i n k e . In G l a s s e l e c t r o d e s f o r hydrogen and o t h e r c a t i o n s . E d i t e d by G. Eisenman. M a r c e l Dekker, New York. 1967.  7.  J . A. M. H i n k e . In I n t r a c e l l u l a r g l a s s m i c r o e l e c t r o d e c o n f e r e n c e ( M o n t r e a l , 1967). E d i t e d by N. C. Hebert and M. L a v a l l e e . To be p u b l i s h e d by John W i l e y and Sons I n c .  8.  R. H. A d r i a n .  9.  R. A. Robinson and R. H. S t o k e s . London. 1959.  0  S c i e n c e , 139,  1132  49  (1963).  C y t o l o g y (USSR), 3, 614  (1961).  (1964).  J . P h y s i o l . London, !L33, 631  (1956).  Electrolyte solutions.  10.  W.  11.  S. G. A. M c L a u g h l i n and J . A. M. Hinke.  Butterworths,  S. M c C u l l o c h and W. M. Brody. I n The g r e a t i d e a s today, 1966. E d i t e d by R. M. H u t c h i n s and M. J . A d l e r . P r a e g e r , I n c . , New York. 1966.  837  Can. J . P h y s i o l . Pharm. 44,  (1966).  12.  G. N. L i n g .  13.  J . R. Robinson.  14.  H. P. Schwan.  Advan. B i o l . Med.  15.  N. R. J o s e p h .  J . B i o l . Chem. I l l , 489  16.  E. J . Cohn and J . T. E d s a l l , P r o t e i n s , amino a c i d s and p e p t i d e s as ions and d i p o l a r i o n s . Hafner P u b l i s h i n g Company, New York. 1943.  17.  J . T. E d s a l l and J . Wyman. New  York.  Ann. N. Y. Acad. S c i . 125, 401 P h y s i o l . Rev.  40, 112  (1965).  (1960).  Phys. 5, 147  (1957).  (1935).  Biophysical chemistry.  Academic P r e s s ,  1958.  18.  E. O v e r t o n .  P f l u e g e r s A r c h . Gen.  19.  A. V . H i l l .  P r o c . Roy.  20.  E. B o z l e r and D. L a v i n e .  21.  P. J . Goodford and E. H. L e a c h .  J . P h y s i o l . r75,  22.  E. B o z l e r .  1459  23.  C. B. B r a t t o n , A. L . Hopkins (1965).  24.  G. Chapman and K. A. McLauchlan.  Soc Am.  P h y s i o l . 92, 115  (London), S e r . B, 106, J . P h y s i o l . .L95, 45  J . Gen. P h y s i o l . 50,  (1902). 477  (1930).  (1958). 38P  (1964).  (1967).  and J . W. Weinberg. Nature, 215,  391  S c i e n c e , 147, (1967).  738  138 25.  J . L . Kavanau.  S t r u c t u r e and f u n c t i o n i n b i o l o g i c a l membranes, V o l . 1.  Holden-Day, I n c . , San F r a n c i s c o . 1965. 26.  M. Rubner.  Abh. P r e u s s . Akad. Wiss. No. 1, 1 (1922).  27.  P. 0. V o g e l h u t .  28.  R. J . S c h e u p l e i n and L . J . Morgan.  29.  J . D. R o b e r t s o n .  30.  0. J a r d e t s k y and J . E . Wertz.  A r c h . Biochem. B i o p h y s . 65, 569 (1956).  31.  0. J a r d e t s k y and J . E . Wertz.  Am. J . P h y s i o l . _187, 608 (1956).  32.  J . E . Wertz and 0. J a r d e t s k y .  J . Chem. Phys, 25, 357 (1956).  33.  0. J a r d e t s k y and J . E . Wertz.  J . Am. Chem. Soc. 82, 318 (1960).  34.  F. W. Cope.  P r o c . N a t l . Acad. S c i . U. S. 54, 225 (1965).  35.  F. W. Cope.  J . Gen. P h y s i o l . 50, 1353 (1967).  Nature, 203, 1169 (1964). Nature, 214, 456 (1967).  J . Exp. B i o l . 38, 707 (1961).  Chapter V  1.  A. S z e n t - G y o r g y i . C h e m i s t r y o f muscular New York, 1962.  2.  J . A. M. Hinke. I n G l a s s e l e c t r o d e s f o r hydrogen and o t h e r c a t i o n s . E d i t e d by G. Eisenman. M a r c e l Dekker, I n c . , New York. 1967.  3.  J . A. M. Hinke, In I n t r a c e l l u l a r glass m i c r o e l e c t r o d e conference ( M o n t r e a l , 1967). E d i t e d by N. C. Hebert and M. L a v a l l e e . To be p u b l i s h e d by John W i l e y and Sons I n c .  4.  R. A. Robinson and R. H. S t o k e s . London.  contraction.  Academic P r e s s ,  Electrolyte solutions.  Butterworths,  1959.  5.  A. L . Hodgkin  and B. K a t z .  J . P h y s i o l . 108, 37 (1949).  6.  A. S. Frumento.  7.  R. P. Kernan.  8.  R. D. Keynes and R. Rybova.  9.  L . J . M u l l i n s ' a n d M. Z. Awad.  S c i e n c e , 147, 1442 (1965). Nature, 193, 986 (1962). J . P h y s i o l . _168, 58P (1963). J . Gen. P h y s i o l . 48, 761 (1965).  10.  S. R. C r o s s , R. D. Keynes and R. Rybova.  11.  R. H. A d r i a n and C. L . Slayman.  J . P h y s i o l . 181, 865 (1965).  J . P h y s i o l . 184, 970 (1966).  139 12.  P. C. C a l d w e l l .  J . P h y s i o l . 142, 22 (1958).  13.  P.. G. Kostyuk and Z. A. S o r o k i n a . I n Membrane t r a n s p o r t and metabolism. E d i t e d by A. K l e i n z e l l e r and A. Kotyk. Academic P r e s s I n c . , London. 1961.  14.  N. W. C a r t e r , F. C. R e c t o r J r . , D. S. Campion and D. W.  Seldin.  J . C l i n . I n v e s t . 46, 920 (1967). 15.  L . B. Nanninga.  16.  J . F . Aronson.  Nature, 1_94, 187 (1962). Nature, 210, 995 (1966).  Chapter V I  1.  J . T. E d s a l l , H. Edelhock, R. L o n t i e and P. M o r r i s o n .  J . Am. Chem.  Soc. 72, 4641 (1950). 2.  P. Doty and R. F. S t e i n e r .  3.  P. Doty and J . T. E d s a l l .  4.  K. A. S t a c e y . L i g h t - s c a t t e r i n g London. 1956.  5.  P. Doty and R. F. S t e i n e r .  6.  J . A. M. H i n k e . In I n t r a c e l l u l a r glass microelectrode conference ( M o n t r e a l , 1967). E d i t e d by N. C. Hebert and M. L a v a l l e e . To be p u b l i s h e d by John W i l e y and Sons I n c .  7.  P. C. C a l d w e l l .  8.  J . T h . G. Overbeek, A. V r i j and H. F . Huisman. scattering.  9.  J . Chem. Phys. 20, 85 (1952). Advan. P r o t e i n Chem. _6, 35 (1951). i n p h y s i c a l chemistry.  Butterworths,  J . Chem. Phys. _18, 1211 (1950).  J . P h y s i o l . 142, 22 (1958).  E d i t e d by M. K e r k e r .  R i c e and Nagasawa.  Pergamon.  Polyelectrolyte solutions.  10.  N. K. S a r k a r .  Enzymologia,  11.  J . Brahms and J . B r e z n e r .  12.  M. Dubuisson.  *13.  L . B. Nanninga.  14.  W. S. Lynn.  15.  H. A. S a r o f f .  In Electromagnetic 1962. Academic P r e s s .  1961,  15, 237 (1950). A r c h . Biochem. B i o p h y s . 95, 219 (1961).  B i o l . Rev. Cambridge P h i l . Soc. 25, 46 (1950). Nature, 1_94, 187 (1962).  A r c h . Biochem. B i o p h y s . U 0 , 262 (1965). A r c h . Biochem. B i o p h y s . 71, 194 (1957).  140 Chapter V I I  J . Am. Chem. Soc. 79,  1.  M. S. Lewis and H. A. S a r o f f .  2112 (1957).  2.  W. 0 . Fenn. P r o c . Soc. Exp. B i o l . Med. 96, 783 (1957).  3.  J . I . Bregman.  4.  A. S z e n t - G y d r g y i . Chemistry o f muscular New York, 1951.  5.  D. R e i c h e n b e r g . I n I o n exchange. Dekker, I n c . , New York. 1966.  E d i t e d by J . A. M a r i n s k y .  Marcel  6.  L . S. G o l d r i n g . I n I o n exchange. Dekker, New York. 1966.  E d i t e d by J . A. M a r i n s k y .  Marcel  7.  G. L . M i l l e r , R. H. G o l d e r , E-. S. E i t e l m a n and E . E. M i l l e r . Biochem. B i o p h y s . 41, 125 (1952).  8.  J . L. Mullins.  Ann. N. Y. Acad. S c i . 57, 125 (1953).  Federation Proc. l  t  contraction.  Academic P r e s s ,  Arch.  61 (1942).  Chapter V I I I  1.  J . A. M. H i n k e . I n I n t r a c e l l u l a r g l a s s m i c r o e l e c t r o d e conference (Montreal, 1967). E d i t e d by N. C. Hebert and M. L a v a l l e e . To be p u b l i s h e d by John W i l e y and Sons I n c .  2.  A. A. L e v . Nature, 201, 1132 (1964).  3.  J . D. R o b e r t s o n .  4.  M. S. Lewis and H. A. S a r o f f .  5.  G. N. L i n g . A p h y s i c a l t h e o r y o f the l i v i n g s t a t e . ing Co., New York. 1962.  6.  L . D. Peachey.  7.  J . A. Zadunaisky.  8.  F . W. Cope.  9.  D. N. Nasonov.  J . Exp. B i o l . 38, 707 (1961).  J . Cell  J . Am. Chem. Soc. _79 2112 (1957). Blaisdell  Publish-  B i o l . 25, 209 (1965).  J . C e l l B i o l . 31, C l l (1966).  J . Gen. P h y s i o l . 50, 1353 (1967). L o c a l r e a c t i o n o f p r o t o p l a s m and g r a d u a l e x c i t a t i o n .  N a t i o n a l S c i e n c e F o u n d a t i o n , Washington, R u s s i a n e d i t i o n p u b l i s h e d i n 1959). 10.  t  D. C.  1962.  (Original  A. T r o s h i n . Problems o f c e l l p e r m e a b i l i t y . Pergamon P r e s s , London. 1966. ( O r i g i n a l R u s s i a n e d i t i o n p u b l i s h e d i n 1965).  141 P r o c . Soc. Exp. B i o l . Med. 96,  11.  W. 0. Fenn.  12.  J . A. M. H i n k e .  13.  G. N. L i n g .  P e r s p e c t i v e s B i o l . Med. 9, 87 (1965).  14.  G. N. L i n g .  F e d e r a t i o n P r o c . 24, S103 (1965).  15.  R. D. Keynes and G. W. M a i s e l . 142,  783 (1957).  Nature, 184, 1257 (1959).  P r o c . Roy. Soc. (London), S e r . B,  383 (1945).  16.  E . J . Conway.  Nature, 157, 715 (1946).  17.  H. L e v i and H. H. U s s i n g .  18.  E . J . H a r r i s and G. P. Burns.  19.  T. Rosenberg.  A c t a Chem. Scan. 2, 14 (1948).  20.  T. Rosenberg.  Symp. Soc. E x p t l . B i o l .  21.  A. K a t c h a l s k y and P. F. C u r r a n . biophysics.  A c t a P h y s i o l . Scand.  16, 232 (1948).  T r a n s . Faraday Soc. 45, 508 (1949).  8, 27 (1954).  N o n e q u i l i b r i u m thermodynamics i n  H a r v a r d U n i v e r s i t y P r e s s , Cambridge.  22.  D. C. Spanner.  I n t r o d u c t i o n t o thermodynamics.  23.  S. Salminen.  24.  A. Ekman, J . Rastas and S. Salminen.  25.  T. Hoshiko and B. L i n d l e y .  26.  D. A. T. D i c k .  27.  H. U s s i n g .  28.  P. J . Garrahan and I . M. G l y n n .  29.  G. Eisenman, J . P. Sandbloom and J . D. Walker, 965 (1967).  1965.  Academic P r e s s .  1954.  N a t u r e , 200, 1069 (1963).  C e l l water.  Advan. Enzymol.  Nature, 200, 1073 (1963).  J . Gen. P h y s i o l . 50, 729 (1967). B u t t e r w o r t h s , Washington.  1966.  13, 21 (1952). J . P h y s i o l . 192, 237 (1967). Jr.  S c i e n c e , 155,  i  Chapter IX  1.  J . I . Bregman.  Ann. N. Y. Acad.  S c i . 57, 125 (1953).  2.  H. P. Gregor, M. J . H a m i l t o n , R. J . Oza and F. B e r n s t e i n . Chem. 60, 263 (1956).  3.  M. Lewis and H. A. S a r o f f .  J . Phys.  J . Am. Chem. Soc. _79, 2112 (1957).  142 4.  W. 0. Fenn.  P r o c . Soc. Exp. B i o l .  96, 783 (1957).  5.  A. S z e n t - G y o r g y i . Chemistry o f muscular New York. 1951.  6.  G. Eisenman. I n Advances i n a n a l y t i c a l c h e m i s t r y and i n s t r u m e n t a t i o n V o l . 4. E d i t e d by C. N. R e i l l e y . I n t e r s c i e n c e , New York. 1965.  7.  J . A. M. H i n k e . In I n t r a c e l l u l a r glass microelectrode conference (Montreal, 1967). E d i t e d by N. C. Hebert and M. L a v a l l e e . To be p u b l i s h e d by John W i l e y and Sons I n c .  8.  A. L . Hodgkin and R. D. Keynes.  9.  A. M. Friedman  contraction.  Academic  Press,  J . P h y s i o l . 119, 513 (1953).  and J . W. Kennedy.  J . Am. Chem. Soc. 77, 4499  10.  R. M i l l s and J . W. Kennedy.  J . Am. Chem. Soc. 75, 5696  11.  G. N. L i n g . A p h y s i c a l t h e o r y o f the l i v i n g i n g Co., New York. 1962.  12.  J . M. N i e l s e n , A. W. Adamson and J . W. C o b b l e .  state.  (1955).  (1953).  Blaisdell  Publish-  J . Am. Chem. Soc.  74, 446 (1952). 13.  G. N. L i n g .  Ann. New York Acad. S c i . 137, 837 (1966).  14.  E. J . H a r r i s .  15.  A. L . Hodgkin  16.  F. J . B r i n l e y J r .  J . P h y s i o l . 124, 248 (1954). and R. D. Keynes.  J . P h y s i o l . 131, 592 (1956).  I n Membranes and t r a n s p o r t phenomena.  Biophysical  Soc. 1966. 17.  R. J . S c h e u p l e i n and L . J . Morgan.  18.  B. 0. Hedbys, S. Mishima  Nature, 214 456 (1967).  and D„ M. M a u r i c e .  Exp. Eye. Res. 2, 99  (1963). 19.  G. Eisenman.  B i o p h y s . J . 2, 259 (1962).  20.  J . T„ E d s a l l and J . Wyman. P r e s s , New York.  B i o p h y s i c a l c h e m i s t r y , V o l . I . Academic  1958.  21.  H. Boedtker and P. Doty.  22.  V. N. Yefimov  J . Phys. Chem. 58, 968 (1954).  and G„ M. F r a n k .  B i o f i z i k a , 11, 58 (1966).  143 APPENDIX I  P r o o f t h a t a c o n s t a n t a b s o r p t i o n decreases the e x p e r i m e n t a l l y observed changes i n o p t i c a l d e n s i t y .  L e t O.D.^ and  be r e s p e c t i v e l y the  o p t i c a l d e n s i t y and t u r b i d i t y o f a f i b e r i n normal R i n g e r .  L e t O.D.^, and T  be r e s p e c t i v e l y the o p t i c a l d e n s i t y and t u r b i d i t y o f t h e f i b e r i n a d i f f e r ent  solution.  Consider f i r s t  ponds t o b a t h i n g the r i b e r From Eqn.  [28]  T /f 2  Hence  1 ( )  (I/I ) q  = exp - ( p  x  (This  corres-  and from Eqn. [30]  +T)S.  O.D^/O.D^ = fl"  Therefore,  ^ 1«0.  i n s u c r o s e , t r i s , p o t a s s i u m o r pH = 9.6 R i n g e r . )  O.D. = - l o g I/I  Now  the case where  2  + P) / (T^  + P)  < 1.0  1 + p / ^ < 1 + p/T  2  o r ^ / ^ < CT + P ) / ^ + P) = O.D^/O.D^ 2  Thus, the r e l a t i v e O.D. does n o t decrease to as low a v a l u e as t h e r e l a t i v e turbidity.  Similarly,  i t may be shown t h a t i f ^"/T^ > 1.0,  O.D. does n o t i n c r e a s e t o as h i g h a v a l u e as the r e l a t i v e  the r e l a t i v e turbidity.  APPENDIX I I  P r o o f t h a t the l i g h t s c a t t e r e d through s m a l l a n g l e s decreases the e x p e r i m e n t a l l y observed changes i n o p t i c a l d e n s i t y . the same s i g n i f i c a n c e O.D.^ > O.D..,. i  0 < c < 1.0.  There i s l e s s  bathing s o l u t i o n , because  I and c o n s i d e r f i r s t  the case where  I f a l l o t h e r sources o f e r r o r a r e i g n o r e d ,  c r ( t / 2 . 3 0 3 ) where reasons.  as i n Appendix  L e t the symbols have  O.D.^ =  Now, 0.D. > c T (Jl/2.303) f o r two 2  2  l i g h t s c a t t e r e d through s m a l l a n g l e s i n the second  and the r e l a t i v e importance  o f the lower O.D.  T h e r e f o r e , t^/  o f the s c a t t e r e d l i g h t < O.D.^/O.D  O.D. does n o t decrease to as low a v a l u e as the r e l a t i v e  i s less  The r e l a t i v e turbidity.  144 Similarly,  i t may  be shown t h a t i f O.D.^  > O.D..,, the r e l a t i v e O.D.  i n c r e a s e to as h i g h a v a l u e as the r e l a t i v e  turbidity.  does not  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Country Views Downloads
United States 9 0
China 9 6
Japan 5 0
Algeria 3 0
Russia 3 0
Germany 2 6
City Views Downloads
Ashburn 6 0
Shenzhen 5 6
Unknown 5 6
Tokyo 5 0
Beijing 4 0
Saint Petersburg 3 0
Redmond 2 0
Wilmington 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0104613/manifest

Comment

Related Items