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State of sodium and water in single striated muscle fibers McLaughlin, Stuart Graydon Arthur 1968-08-19

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THE STATE OF SODIUM AND WATER IN SINGLE STRIATED MUSCLE FIBERS by STUART GRAYDON ARTHUR MCLAUGHLIN B. Sc., Un i v e r s i t y of 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 accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1968 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I ag ree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n  t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depa r tment The U n i v e r s i t y o f B r i t i s h Co lumb ia Vancouver 8, Canada ABSTRACT Cation s e n s i t i v e glass microelectrodes were inserted into s i n g l e s t r i a t e d muscle f i b e r s of the giant barnacle, Balanus nubilus, to measure d i r e c t l y the a c t i v i t i e s of sodium and potassium i n the myoplasm. The t o t a l sodium and potassium content of the i n d i v i d u a l experimental f i b e r s was de termined by flame photometry. From these measurements, the percentage of sodium i n the f i b e r which did not a f f e c t the microelectrodes and the per centage of water i n the f i b e r which was not a v a i l a b l e to act as solvent for the potassium ions were ca l c u l a t e d . The minimal percentages of "bound" sodium and water were 84% and 42% r e s p e c t i v e l y . I t was hypothesized that a s i g n i f i c a n t f r a c t i o n of th i s "bound" sodium was involved i n ion p a i r forma t i o n with carboxyl moieties on the myosin molecules x^hich comprise the thick filaments, and experiments were designed to te s t this hypothesis. In the second series of experiments, the a c t i v i t i e s of sodium, potassium and hydrogen i n the myoplasm were measured as the temperature of the s o l u t i o n bathing the f i b e r s was increased from 7 to 40°C. An i r r e v e r  s i b l e shortening occurred i n a l l f i b e r s between 37 and 40°C. When the f i b e r s shortened i n a sodium free Ringer s o l u t i o n , the mean a c t i v i t y of sodium increased by 130%, the mean a c t i v i t y of potassium remained r e l a t i v e  l y constant, and the pH decreased from 7.17 to 6.77. These experiments pro vided strong evidence that sodium i s bound to myosin i n the l i v i n g f i b e r , f o r extracted myosin i s known to denature at 37°C and release i t s a s s o c i  ated a l k a l i metal cations. In the t h i r d series of experiments, the o p t i c a l density, O.D., of the single s t r i a t e d muscle f i b e r s was measured at 50 m i x i n t e r v a l s between i i i 450 and 850 mp.. At a l l wavelengths, the O.D. decreased markedly when the normal Ringer bathing so l u t i o n was replaced by sodium free sucrose Ringer. For example, at 850 mu, the O.D. of the f i b e r s , r e l a t i v e to the i n i t i a l value i n normal Ringer, decreased from 1 to 0.21 ± 0.06 i n 25 minutes. The cor responding increase i n the transmittar.ee, T, (O.D. = -log T) was from 5% to 55%. This change in O.D. could be reversed by returning the normal Ringer bathing s o l u t i o n to the bath. Large, r e v e r s i b l e decreases i n O.D. were also observed when potassium and t r i s were used as substitutes for sodium. These changes i n O.D. are explained by the theory of l i g h t s c a t t e r i n g i f i t i s assumed that sodium i s bound to the main sc a t t e r i n g centers i n the myoplasm, the thick filaments. When the f i b e r s were bathed in sodium free, l i t h i u m substituted Ringer, a small r e v e r s i b l e increase i n the O.D. was observed, which may indicate that l i t h i u m i s complexed more strongly than sodium to the binding s i t e s on the thick filaments. In the f i n a l series of experiments, the number of sodium and potassium ions "bound" to the c o n t r a c t i l e proteins i n a glycerinated f i b e r was measured. The free concentrations of hydrogen, sodium and potassium were maintained at values s i m i l a r to those found in an i n t a c t f i b e r . The r e s u l t s indicated that s u b s t a n t i a l binding of both sodium and potassium occurred, and that p r o p o r t i o n a l l y more sodium than potassium ions were "bound". I f the r e s u l t s are extrapolated to the i n t a c t f i b e r , they imply that about as much sodium i s "bound" to the c o n t r a c t i l e proteins as i s free i n the myoplasm. This amount of "bound" sodium i s s u f f i c i e n t to explain the r e s u l t s of the denaturation and l i g h t s c a t t e r i n g experiments, but i n  s u f f i c i e n t to account for the anomalously low a c t i v i t y of sodium i n the myo plasm, as measured by a sodium s e n s i t i v e microelectrode. Thus, i t was i v concluded that e i t h e r some factor must enhance the binding of sodium to the c o n t r a c t i l e proteins i n a l i v i n g c e l l , or that sodium must be sequestered i n organelles which are destroyed by the g l y c e r i n a t i o n process. 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. Water 5 B. A l k a l i metal cations 14 CHAPTER I I I SCOPE AND PURPOSE OF THE INVESTIGATION 36 RESULTS AND DISCUSSION CHAPTER IV ACTIVITY OF SODIUM AND POTASSIUM IN THE MYOPLASM 40 A. Introduction 40 B. Methods '. . 41 C. Results . .„ 50 D. Discussion 54 CHAPTER V RELEASE OF BOUND SODIUM 62 A. Introduction 62 B. Methods „ „ 62 C. Results „. „ 66 D. Discussion „ 74 CHAPTER VI OPTICAL DENSITY CHANGES OF FIBERS IN SODIUM FREE SOLUTIONS 80 A. Introduction „ 80 B. Methods „ 81 C. Results 86 D B Discussion „ „ 100 CHAPTER VII BINDING OF SODIUM AND POTASSIUM IN GLYCEROL EXTRACTED FIBERS 104 A. Introduction 104 B. Methods 105 C. Results 107 D. Discussion I l l v i CONCLUSIONS CHAPTER VIII SIGNIFICANCE OF THE RESULTS 114 CHAPTER IX SUGGESTIONS FOR FUTURE WORK 122 BIBLIOGRAPHY ; 130 APPENDIX I „ 143 APPENDIX II 143 v i i LIST OF TABLES TABLE I Solutions „ 44 TABLE II Sodium and potassium i n si n g l e muscle f i b e r s 52 TABLE I I I Sodium concentration and a c t i v i t y i n sing l e muscle f i b e r s before and a f t e r shortening 69 TABLE IV Potassium concentration and a c t i v i t y i n sing l e muscle f i b e r s before and a f t e r shortening 72 TABLE V Solutions „ 82 TABLE VI The sodium and potassium content of f i b e r s extracted 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 containing [K] = 295 mM and [Na] = 10.4 mM 108 TABLE VII The sodium and potassium content of f i b e r s extracted i n 507o g l y c e r o l for 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 containing [K] = 295 mM and [Na] = 0.2 mM 110 v i i i LIST OF FIGURES Figure 1 Photograph of the t i p of a sodium s e n s i t i v e microelectrode 41 Figure 2 Diagram of a cannulated muscle f i b e r with inserted microelectrode 45 Figure 3 Photograph, of a single s t r i a t e d muscle f i b e r from the giant barnacle ..... ...... 46 Figure 4 Relation between the sodium and potassium contents of sin g l e muscle f i b e r s 51 Figure 5 Relation between membrane p o t e n t i a l and log [K] for a t y p i c a l muscle f i b e r . , 53 Figure 6 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 length with temperature and with time 67 Figure 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 of a t y p i c a l muscle f i b e r as the temperature was increased to 40°C „ „ 68 Figure 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 of potassium of 7 f i b e r s as the temperature was increased to 40°C ... 71 Figure 9 V a r i a t i o n i n the average pH of the myoplasm of 10 f i b e r s as the temperature was increased to 40°C 73 Figure 10 Diagram of a sing l e muscle f i b e r positioned i n the perspex bathing chamber, and plan view of the o p t i c a l pathway „ 84 Figure 11 The t o t a l concentrations of sodium and potassium i n f i b e r s bathed i n sodium free sucrose Ringer 87 Figure 12 The transmittance of si n g l e muscle f i b e r s i n normal Ringer and a f t e r 25 minutes i n sucrose Ringer as a function of wavelength „ 89 Figure 13 The o p t i c a l density of sing 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 value of the o p t i c a l density i n normal Ringer as a function of wavelength 90 Figure 14 The r e l a t i v e o p t i c a l density of sing l e muscle f i b e r s bathed i n t r i s Ringer and then i n normal Ringer 92 Figure 15 The r e l a t i v e o p t i c a l density of sing l e muscle f i b e r s bathed i n potassium Ringer and then i n normal Ringer ... 93 ix Figure 16 The r e l a t i v e o p t i c a l density of single muscle f i b e r s bathed i n l i t h i u m Ringer and i n pH = 9.6 Ringer 94 Figure 17 The t o t a l concentrations of 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 substituted Ringer 95 Figure 18 The a c t i v i t y of sodium i n the myoplasm of sing l e muscle f i b e r s bathed i n l i t h i u m Ringer or sucrose Ringer 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 of sodium when the f i b e r was bathed i n normal Ringer 98 Figure 19 The pH and membrane p o t e n t i a l of si n g l e muscle f i b e r s bathed i n pH = 9.6 Ringer and in normal Ringer 100 X ACKNOWLEDGEMENTS I wish to thank Dr. J . A. M. Hinke, my research d i r e c t o r , f o r the encouragement, assistance and constructive c r i t i c i s m s he offered throughout the course of this work; Mr. C. G. Lemon for the h e l p f u l suggestions and equipment he supplied during the performance of the o p t i c a l experiments reported i n Chapter VI; Dr. P. Taylor for the many hours of personal a t t e n t i o n I received at h i s seminars; Mrs. Irene Ingraham and Mr. Alan McLaughlin for the t e c h n i c a l assistance they rendered during various phases of the work. 1 CHAPTER I HISTORICAL INTRODUCTION Shortly before his death, S i r Isaac Newton remarked: "I do not know what I may appear to the world, but to myself I seem to have been only l i k e a boy playing on the seashore, and d i v e r t i n g myself in now and then f i n d i n g a smoother pebble or a p r e t t i e r s h e l l than ordinary w h i l s t the great th ocean of truth lay a l l undiscovered before me." What was true of 17 Cen- th tury mathematics and physics (and Newton was 17 Century mathematics and physics) i s also true of 20 ^  Century biology. Much time has been spent playing with c e l l s and organelles, but for the f i r s t h a l f of this century, the sea-like environment of these c e l l s and organelles was almost complete l y ignored. Water was considered merely as the i n e r t , i n t r a c e l l u l a r medium i n which the biochemical reactions of the c e l l occured. In the l a s t decade, however, many investigators recognized the importance of understand ing the role of water in c e l l physiology and biochemistry. As Szent-Gyorgyi has stated: "water i s not only the mater, mother, i t i s also the matrix of l i f e , and biology may have been unsuccessful i n understanding the most basic functions because i t focussed i t s attention only on the p a r t i c u l a t e matter..." (1). I t i s not f a i r to say that water was completely ignored by the e a r l i e r b i o l o g i s t s . There are sporadic references in the l i t e r a t u r e to the p o s s i b i l i t y that water i n the cytoplasm i s not in the same phys i c a l state as normal l i q u i d water. Over 60 years ago, Overton (2) observed that a muscle swelled to much less 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 pressure, and concluded that a sub-s t a n t i a l f r a c t i o n of c e l l u l a r water was osmotically i n a c t i v e . Twenty years l a t e r , Rubner (3) estimated the f r a c t i o n of water which could'not be frozen i n a muscle at -20° C, and deduced that 23% of the water i n frog muscle was "bound". In 1930, however, H i l l (4) concluded from vapor pressure measure ments that less than 47» of the water i n frog muscle was "bound". Interest i n the state of water i n c e l l s remained dormant f or another 20 years. I t i s i n t e r e s t i n g to note that i f an error i n H i l l ' s c a l c u l a t i o n s i s corrected, hi s data p r e d i c t that about 30% of the water i n frog muscle i s "bound" (5). In recent years, the i n t e r e s t of chemists i n the structure of water has stimulated the i n t e r e s t of ph y s i o l o g i s t s and biochemists i n th i s b i o l o g i c a l l y ubiquitous molecule. In the l a s t two years alone, several con ferences have been held (6, 7, 8) and books written (9, 10, 11) on the importance of the state of water i n the l i v i n g c e l l . Most phy s i o l o g i s t s have assumed that a i l the a l k a l i metal cations, as well as the water, i n a c e l l e x i s t i n a free s t a t e . Many years ago, how ever, several investigators suggested that the s e l e c t i v e potassium ion accumulation of c e l l s may be due to binding rather than a membrane phenom enon (12, 13, 14). In 1929 Hober (15) c r i t i c a l l y analyzed t h i s p o s s i b i l  i t y . He concluded that only the proteins i n a c e l l e x i s t i n large enough quantities to complex s u f f i c i e n t ions to explain the s e l e c t i v e accumulation of potassium by an absorption mechanism. For this reason, he examined the av a i l a b l e data on complexing of ions by extracted p r o t e i n s . He observed that the amount of ion binding by proteins i n s o l u t i o n was small. This observation i s s t i l l v a l i d , with the exception of a few proteins l i k e myosin (16). He also observed that there was no evidence of a marked pre ference of proteins for potassium over sodium ions. Thus, he concluded that the binding of ions to proteins could not explain the s e l e c t i v e accumulation of potassium i n l i v i n g c e l l s . In s p i t e of Hober's a n a l y s i s , there e x i s t today groups of i n v e s t i  gators i n A u s t r a l i a (17-20), Russia (21-23) and the USA (24-31) which do not accept the assumption that the i n t r a c e l l u l a r ions i n general, and the potassium ion i n p a r t i c u l a r , are free i n the cytoplasm. Ernst (32, page 311) has l i s t e d several other investigators who prefer, i n one form or another, a sorption theory of ion accumulation to the more generally accepted membrane theory. The proponents of the sorption theory base t h e i r hypotheses not so much on experimental evidence for ion binding as on c r i t i  cisms of the membrane theory and the a u x i l l i a r y postulates required by th i s theory. The necessity of postulating a wide v a r i e t y of "ion pumps" located i n the membrane, for example, leads to serious contradictions, as Troshin (21) and Ling (29, 30) have pointed out. These groups have speculated that most of the potassium, but not the sodium i n the c e l l e x i s t s i n a complexed or associated s t a t e . This speculation has never been widely accepted. Con way (33), f o r example, has c r i t i c i z e d the theory, d i r e c t i n g h i s c r i t i c i s m s mainly at L i n g . The microelectrode experiments reported i n this thesis also contradict the sorption theory, for they demonstrate that the a c t i v i t y of potassium i n the myoplasm of 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 higher than would be cal c u l a t e d by assuming that a l l the water and potassium ions are free i n the myoplasm. The mere r e j e c t i o n of the sorption theory does not, of course, remove the c r i t i c i s m s of the membrane theory. These c r i t i c i s m s w i l l be discussed further i n Chapter IX. This in v e s t i g a t o r c e r t a i n l y does not accept the sorption theory, but wishes to stress that the advocates of t h i s theory have performed an important function,, They have forced b i o l o g i s t s to examine more thoroughly the question of ion a s s o c i a t i o n i n l i v i n g c e l l s . The t h e o r e t i c a l aspects of the a s s o c i a t i o n of the a l k a l i metal cations with various anions have been studied by Eisenman (34, 35) and Ling (25). The development of cation sensi t i v e microelectrodes by Hinke (36) and the a p p l i c a t i o n of a nuclear magnetic resonance technique by Cope (37) has allowed b i o l o g i s t s to study d i r e c t l y for the f i r s t time the binding of sodium and potassium in l i v i n g c e l l s . The r e s u l t s of these studies (5, 36-40) indicate that a s u b s t a n t i a l amount of ion p a i r formation does occur i n the myoplasm of s t r i a t e d muscle f i b e r s , but that i t i s sodium and not potassium which i s preferred by the b i o l o g i c a l f i x e d charge system. 5 CHAPTER II PHYSICAL CHEMISTRY OF THE BINDING OF WATER AND THE ALKALI METAL CATIONS A. Water Introduction. This section consists of a b r i e f review of the structure of water and the e f f e c t s of various solutes on t h i s s t r u c t u r e . The possible e f f e c t s of proteins and membranes on the structure of water in the cytoplasm of a l i v i n g c e l l w i l l be considered, as w i l l the methods of examining these s t r u c t u r a l changes; The Structure of VJater. The structure of water was f i r s t d i s  cussed i n the modern c r y s t a l l o g r a p h i c sense by Bernal and Fowler (1) i n 1933. They postulated that extensive hydrogen bonding occurs between water molecules, and considered water as a disordered s o l i d having an i r r e g u l a r ' four co-ordinated st r u c t u r e . The view that water i s merely a broken-down form of the ice l a t t i c e , with the length of the hydrogen bonds increased, i s supported by a great deal of experimental evidence. The most d i r e c t evidence comes from X-ray s c a t t e r i n g measurements (2-8). Morgan and Warren (2) were the f i r s t to show that for short periods of time each water mole cule has four nearest neighbours, and, at temperatures below 30° C, a second set of twelve nearest neighbours. The distance at which these near est neighbours are found i s compatible with the view that water has a tetrahedral structure s i m i l a r to i c e . In 1957, Frank and Wen (9) presented what i s now the most gener a l l y accepted model of water. They based t h e i r model on the hypothesis that the formation of hydrogen bonds i n water i s a co-operative phenomenon. This i s a reasonable hypothesis because the hydrogen bond has a p a r t i a l covalent nature (10). They argued that when one hydrogen bond forms i n water, the formation of neighbouring bonds i s encouraged and s t a b i l i z e d . S i m i l a r l y , they argued that 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 tends to break up. Thus, they picture water as cons i s t i n g of minute " f l i c k e r i n g c l u s t e r s " of i c e - l i k e groups surrounded by non- hydrogen-bonded molecules (11, F i g . 1). They did not specif y the exact molecular arrangement within these groups, but Nemethy and Scheraga (12, 13) made the reasonable assumption that the t r i d y m i t e - l i k e structure of normal ice I occurs frequently. On the basis of t h i s assumption Nemethy and Scheraga (12, 13) made a d e t a i l e d s t a t i s t i c a l mechanical analysis of the structure of water. They concluded that at 20° C the average c l u s t e r con tains about 60 molecules and that at this temperature about 70% of the water molecules are i n the c l u s t e r s . These numbers increase as the temper ature i s lowered, and v i c e versa. A minimal estimate of the l i f e time of the c l u s t e r s can be made from experimental data. The c l u s t e r s must e x i s t long enough to be detected by X-ray (2) or Raman (14, 15) techniques; that -11 -12 i s , about 10 - 10 seconds. I t i s more d i f f i c u l t to make a maximal estimate of the l i f e time of the c l u s t e r s . I f , as Frank (16, 17) believes, the d i e l e c t r i c r e l a x a t i o n time of water i s equal to the h a l f l i f e of the c l u s t e r s , the l i f e time of the c l u s t e r s i s 10 ^ - 1 0 ~ ^ seconds (18). This i s 100 to 1000 times the period of a molecular v i b r a t i o n , hence the cl u s t e r s have a meaningful existence. I t should be stressed that many other models for the structure of water e x i s t . Kavanau (19, pages 178-190), i n a terse and l u c i d manner d i s  cusses the "vacant l a t t i c e point" model of F o r s l i n d (20, 21), the "water- hydrate" model of Pauling (22, 23) and the " d i s t o r t e d bond" model of Pople (24). He also l i s t s over a dozen reviews of s t i l l other models for the structure of water. None of these models w i l l be discussed here. For t h i s t h e s i s , i t i s s u f f i c i e n t to note that pure water does have a structure. Also, the f l i c k e r i n g c u l s t e r model i s the most highly developed, and appears to explain a l l the experimental data a v a i l a b l e . The values for the free energy, enthalpy and entropy calculated by Nemathy and Scheraga (12, 13) agree very well with the experimental data. The values they calculated f o r the heat capacity agree reasonably well with the experimental data, as do the c a l c u l a t e d curves for the r a d i a l d i s t r i b u t i o n function. The maximum i n the density of water at 4° C may also be predicted q u a l i t a t i v e l y from the theory. The i n f r a red studies of Buijs and Choppin (25) support the model, and i t i s s i g n i f i c a n t that these measurements were made a f t e r the formula t i o n of the model. The temperature dependence of v i s c o s i t y (26) agrees extremely well with Nemethy and Scheraga's treatment of the model. An ex planation e x i s t s for the f a c t the energy 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 , viscous flow, d i e l e c t r i c r e l a x a t i o n or s t r u c t u r a l r e l a x a t i o n f or excess u l t r a s o n i c absorption has approximately the same value (16, 17, 27). In terms of the model, most of the energy of a c t i v a t i o n for these processes i s required to break down the i n i t i a l structure; l i t t l e energy i s required to re o r i e n t the molecules. F i n a l l y , one can l o g i c a l l y explain why non-polar solutes enhance the i c e - l i k e nature of water i n terms of t h i s model. This l a s t f a c t leads to a discussion of the e f f e c t of solutes on the structure of water. The E f f e c t of Non-polar Solutes on the Structure of Water. Con sider f i r s t the evidence that the structure of water i s enhanced when non- polar solutes are added. I f the s o l u t i o n r e s u l t i n g from the ad d i t i o n of a non-polar solute to water was i d e a l , one would expect the changes i n volume and enthalpy to be zero, and the changes i n entropy and free energy to correspond to those for i d e a l mixing. For non-polar solutes, however, the changes in volume and enthalpy are negative and there i s a very large nega t i v e excess entropy change over the entropy of i d e a l mixing. This leads to a low s o l u b i l i t y . Frank and Evans (28) explained the negative enthalpy and excess negative entropy terms by postulating that the non-polar molecules enhance the structure of water. In other words, the f l i c k e r i n g c l u s t e r s are s t a b i l i z e d . This tends to be confirmed by the fa c t the d i e l e c t r i c relaxa t i o n time i s lengthened in aqueous solutions of non-polar molecules (16). Why should non-polar solutes s t a b i l i z e the " f l i c k e r i n g clusters"? Frank and Evans (28) offered the rather h e u r i s t i c explanation that non-polar solutes do not transmit disruptive e l e c t r i c a l influences well because of 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 the structure. Nemethy and Scheraga (12, 13) and Scheraga (11) offered a more precise explanation. They argued that a water molecule in pure water has f i v e energy le v e l s a v a i l a b l e to i t . These energy l e v e l s correspond to molecules with zero, one, two, three or four hydrogen bonds. A molecule with four hydrogen bonds can accept a non-polar molecule as a f i f t h neighbour. Thus, this energy l e v e l i s lowered because of the van der Waals energy of i n t e r a c t i o n . An unbonded water molecule, on the other hand, already has a high co-ordina t i o n number and can acquire a non-polar neighbour only at the expense of a water molecule. This implies that a dipole-dipole i n t e r a c t i o n w i l l be re placed with a much weaker van der Waals i n t e r a c t i o n . Hence, the energy l e v e l f o r the unbonded water molecules in contact with non-polar solutes i s increased. The energy le v e l s for molecules involved i n one, two or three hydrogen bonds are ra i s e d for the same reason (11, F i g . 8). I f a Boltzmann d i s t r i b u t i o n of the water molecules between the 5 energy l e v e l s i s assumed, i t i s apparent that the addition of non-polar solutes to water s h i f t s more molecules into the lower (four hydrogen bonds) energy s t a t e . Since the non- polar solute f i l l s a space which would be empty i n an ordinary i c e - l i k e c l u s t e r , there i s a decrease i n volume. The hydrogen bonded water mole cules i n the f i r s t layers about a non-polar solute are generally known as "icebergs" (28). The E f f e c t £f Ions on the Structure of Water. Ions have a dual e f f e c t on the structure of water. The f i r s t e f f e c t i s on the water mole cules close to the ion. These are generally regarded as being immobilized, p o l a r i z e d and compressed by the in t e r a c t i o n s of the dipole moment with the strong e l e c t r i c f i e l d of the ion (1, 3, 9, 28, 29, 30, 31). The term "immobilized" implies that the water molecules bound to cations l i k e cesium -8 -9 or l i t h i u m spend about 10 and 10 seconds r e s p e c t i v e l y attached to the ions (32). I t i s apparent that the ion imposes a d i f f e r e n t type of order on the c l o s e s t water molecules than the order inherent i n the normal water. Nevertheless, the ion does increase the order of these nearest neighbour water molecules. One would expect the ordering e f f e c t to be greatest for small and multivalent ions. Much experimental evidence supports the idea that small ions increase the net order of water. Perhaps the most d i r e c t evidence i s the f a c t that s a l t s l i k e L i F increase the v i s c o s i t y of water (33). Other evidence comes from measurements of the entropies of hydration (28), apparent molal heat capacities (34) and the temperature dependence of the l i m i t i n g d i f f u s i o n constant (35). A manifestation of the dual e f f e c t of ions on water i s the fa c t that monovalent cations larger than potassium (and most anions) disrupt the structure of water. They decrease the v i s c o s i t y of water (33). The entropy loss which occurs when a KC1 molecule i s dissolved in water i s less thaw 10 when two argon atoms are dissolved, even though they both have the same e l e c t r o n i c structure (28, 36). Other evidence for the net structure break ing a c t i v i t y of large ions comes from measurements of the ion 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 fa c t large ions reduce the r e l a x a t i o n time for the d i e l e c t r i c constant (37). The structure breaking e f f e c t of larger ions i s r e a d i l y explained i n terms of the " f l i c k e r i n g c l u s t e r " model. There exists- two regions of ordered water molecules about an ion. Far from the ion there e x i s t s a region with the structure of normal water. In the immediate v i c i n i t y of the ion the water molecules are oriented by the strong, s p h e r i c a l l y symmetric e l e c t r i c f i e l d of the ion. The buffer zone, or intermediate region between these two states of competing and incompatible order is i t s e l f i n a state of chaos. Thus, what i s often true i n i n t e r n a t i o n a l p o l i t i c s is true i n chem i s t r y . The lack of order of the water molecules i n this intermediate region explains the structure breaking e f f e c t of the larger ions. The smaller ions organize water molecules beyond the f i r s t layer of water, hence t h e i r net e f f e c t is to enhance the structure of water s l i g h t l y . Further discussion of the structure breaking action of ions can be found in the papers of Frank and Evans (28), Gurney (3), Frank and Wen (9) and Harris and O'Konski (38). The water which is oriented and bound by the e l e c t r i c f i e l d of ions i s often designated asC " s o f t i c e " , i n contrast to the term "icebergs", which i s used to describe the water organized by non-polar solutes. The E f f e c t of Proteins and Membranes on the Structure of Water. The structure of water w i l l also be influenced i f a solute contains s i t e s which can i n t e r a c t with water molecules through the formation of hydrogen 11 bonds. Hydrogen bonding w i l l occur at the peptide linkages of proteins. At most, four water molecules can be bound by each peptide group (39), but t h i s amount of i n t e r a c t i o n could only occur i n unfolded proteins, where the pep tide linkages are free to i n t e r a c t . In an a-helix, a l l of the peptide l i n k  ages are involved i n the maintenance of the molecular structure. In muscle the a-helix content of the proteins i s high (40), hence not much d i r e c t water binding to the peptide linkages would be expected. The amount of water bound d i r e c t l y to macromolecules v i a ion-dipole, hydrogen bonds and the weaker dipole-dipole interactions may thus be expected to be small. This does not mean, however, that these macromolecules do not organize r e l a  t i v e l y large amounts of water. / The consideration of the organization of water about a protein en t a i l s the consideration of the geometry of the protei n , and how i t w i l l f i t into the water l a t t i c e . For example, Berendsen and Migchelsen note that "Backbone structures able to form H-bonds to water w i l l have structure- breaking or structure-promoting e f f e c t s , depending on the geometry of the hydrogen-bonding s i t e s . I f the geometry i s such that the s i t e s , to which water may be bound, form an array f i t t i n g to an i c e - I structure, a structure- promoting influence i s to be expected. The same may be true i f other regu l a r water structures could be f i t t e d to the hydrogen bonding s i t e s . With hydrophobic backbones s i m i l a r e f f e c t s might occur i f short polar side-chains repeat i n a pattern f i t t i n g to a regular water l a t t i c e . The e f f e c t s w i l l be stronger for r i g i d backbones or side chains." (41). Collagen i s an example of a molecule with such a structure. The a x i a l l y repeating distance of the three f o l d h e l i x i s exactly s i x times the expected repeating distance of molecules i n chains of water (42). Thus, one would expect collagen to or ganize water, and NMR studies indicate that chains of water molecules are . 12 formed in the f i b e r d i r e c t i o n (41, 43). Water may also be oriented at the interfaces of extended surfaces, and there i s some evidence that these surface zones are tens and hundreds of molecules deep rather than monomolecular as commonly assumed. The water l a t t i c e i n a clay c r y s t a l , for example, appears to acquire an increased order and r i g i d i t y at distances of up to 300 X away from the surface of the clay (44, 21). The extent to which water i s organized about most proteins and b i o l o g i c a l membranes i s s t i l l unknown. I n i t i a l d i e l e c t r i c , and NMR measure ments on macromolecular solutions supported the concept that water i s im mobilized into thick, i c e - l i k e hydration crusts f o r large distances away from macromolecules (45, 46). Improvements i n the NMR technique and a recognition that the d i e l e c t r i c properties of macromolecules could l a r g e l y be explained i n terms of the p o l a r i z a t i o n of the d i f f u s e double layer, how ever, have l a r g e l y invalidated the concept of long range immobilization; on the other hand, most recent NMR experiments do indicate that the net time which solvent water molecules spend i n a given o r i e n t a t i o n i s lengthened to varying degrees in solutions of macromolecules (19, pages 207 - 217) . A f t e r a thorough l i t e r a t u r e search, Kavanau concluded that b i o l o g i c a l membranes and macromolecules "are encased in a th i n crust of bound water molecules at le a s t one molecule thick" (19, page 217). The State of Water i n the L i v i n g C e l l . The term "bound water", as used above, i s rather ambiguous. As noted in Chapter I, many investigators are now interested i n the f r a c t i o n of "bound water" i n the l i v i n g c e l l , but each seems to have his own d e f i n i t i o n of the term. In p r a c t i c e , the term i s defined by the technique u t i l i z e d to measure the f r a c t i o n of "bound water". 13 This i s apparent i f one considers that the values obtained for the water "bound" to a given p r o t e i n by d i f f e r e n t techniques are themselves quite d i f f e r e n t (47). In t h i s t h e s i s , the term "bound water" w i l l r e f e r to the f r a c t i o n of water i n the c e l l unavailable to act as solvent for the i n t r a c e l l u l a r solutes. I t should be stressed that t h i s d e f i n i t i o n i s as a r b i t r a r y as the other d e f i n i t i o n s a v a i l a b l e at present and that i t i s not meant to imply that water i n a l i v i n g c e l l 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 and only two s t a t e s . In s p i t e of the a r b i t r a r y nature of the d e f i n i t i o n , an accurate measurement of the f r a c t i o n of "bound water" i s important because of i t s relevance to the osmotic, permeability and transport measurements t y p i c a l l y made by p h y s i o l o g i s t s . I t seems u n l i k e l y that NMR (48) or desorption (49) measurements w i l l y i e l d much information about t h i s f r a c t i o n of "bound x-jater", for organ i z a t i o n and solute exclusion are not synonymous. In terms of the d e f i n i t i o n , however, t h i s quantity can be measured d i r e c t l y . A l l that i s required i s a knowledge of the free and t o t a l concentrations of the solute i n the c e l l . I f the free concentration i s greater than the t o t a l concentration, the d i f  ference may be a t t r i b u t e d to the "binding" of water, presumably to macro molecules and membranes. I t must of course be assumed that the solute i t  s e l f i s neither bound nor compartmentalized within the c e l l . Defined i n t h i s manner, the f r a c t i o n of "bound water" depends on the nature of the solute as well as on the state of water i n the c e l l . A small, polar solute l i k e urea, which i s capable of forming strong hydrogen bonds, xjould be expected to be soluble i n almost a l l of the i n t r a c e l l u l a r water. Conversely, a large, non-polar molecule would be expected to be ex-14 eluded from most of the organized water in the c e l l . I t would even be dangerous to assume that a l l the i o n i c species make use of the same f r a c t i o n of water. Ice I, for example, i s known to exclude sodium more than potas sium (50). As potassium i s the major cation i n muscle f i b e r s , a knowledge of the f r a c t i o n of water unavailable to act as solvent for t h i s ion i s of s p e c i a l importance. The development of glass microelectrodes s e n s i t i v e to potassium (51) made possible a d i r e c t measurement of the a c t i v i t y of potas sium i n the myoplasm of a large single muscle f i b e r (52, 53). When these measurements were coupled with accurate measurements of the t o t a l concentra t i o n of potassium i n the same single muscle f i b e r , an estimate of the f r a c  t i o n of "bound water" i n the c e l l could be made. To foreshadow the r e s u l t s , which are discussed in the following chapters, i t may be noted that Hearst and Vinograd (54, 55) measured the f r a c t i o n of water i n a DNA s o l u t i o n which excluded an a l k a l i metal s a l t . From t h e i r density gradient studies, they concluded that a region consisting of four layers of water molecules about the T-4 bacteriophage DNA molecule completely excluded a l i t h i u m s i l i c o - tungstate s a l t . B. The A l k a l i Metal Cations Introduction. This section i s concerned with evidence that the a l k a l i metal cations can form ion pa i r s with charged groups on macromole cules. F i r s t , the binding of these ions to p o l y e l e c t r o l y t e s and ion ex change resins i s considered. Next two theories of cation s e l e c t i v i t y are b r i e f l y discussed. F i n a l l y , the evidence that the a l k a l i metal cations form complexes with proteins i s appraised. Before any discussion can commence, the d e f i n i t i o n of an ion pair must be considered. The term i s not as ambiguous as the term "bound water", but i s s u f f i c i e n t l y abstruse to warrant comment. I f two oppositely charged ions are small or highly charged and also close together, the energy of the e l e c t r i c a l a t t r a c t i o n w i l l be greater than the thermal energy, and the ion p a i r w i l l survive a number of c o l l i s i o n s with solvent molecules. Bjerrum (56) investigated the problem of exactly how close a given p a i r of ions must be before they may be considered an ion p a i r . He concluded that the average e f f e c t of ion p a i r formation i s best represented i f two ions are considered to form an ion p a i r when they come, closer together than a distance 2 r . = (z z q )/(2DkT). In the d e f i n i t i o n , z and z represent the charges on the ions, q the e l e c t r o n i c charge, D the d i e l e c t r i c constant, k Boltzmann' constant and T the absolute temperature. At t h i s distance the mutual elec t r i c p o t e n t i a l energy i s equal to 2kT. The distance was chosen because the, p r o b a b i l i t y of fi n d i n g an oppositely charged ion about any given ion has a minimum at r . . Robinson and Stokes (57, Chapter 14) discuss b r i e f l y the mm mathematical basis of 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 i n an aqueous s o l u t i o n at 25° C have a value of r . = 3.57 X. Thus, i f the sum n mm » of the r a d i i of the ions of a monovalent e l e c t r o l y t e i s less than t h i s value-, ion p a i r formation w i l l occur to a c e r t a i n extent. I f the ions of a mono valent e l e c t r o l y t e have diameters greater than t h i s value, some form of the Debye-HUckel theory should be v a l i d . Several c r i t i c i s m s have been made of Bjerrum's theory, but only f;. need be noted here (58). The f i r s t c r i t i c i s m i s that the theory counts as ion p a i r s some ions which are not i n phys i c a l contact, and as Bjerrum him s e l f notes, " t h i s d e f i n i t i o n is rather a r b i t r a r y " (56). The second c r i t i c ! ' " i s that the distance of close s t approach of the ions predicted from the 16 Bjerrum theory varies from solvent to solvent. This implies that an ion p a i r can contain solvent molecules between the two ions. A b r i e f discussion of improvements to Bjerrum 1s d e f i n i t i o n and of other d e f i n i t i o n s of ion p a i r s may be found i n a book by Rice and Nagasawa (59, pages 441-446). Po l y e l e c t r o l y t e s and the A l k a l i Metal Cations. The a l k a l i metal cations form no strong or even moderately strong complexes with most common small molecules and ions. Exceptions are the complexes formed with strong chelating agents l i k e EDTA (60) and uranyl d i a c e t i c acid (61). The extent of ion p a i r formation with carboxyl or phosphate moieties on other small molecules i s c e r t a i n l y very s l i g h t . I t might therefore be suspected that the a l k a l i metal cations are e s s e n t i a l l y free in a s o l u t i o n of p o l y e l e c t r o  lytes containing carboxyl or phosphate groups. Under c e r t a i n conditions, however, exactly the converse i s true. The best known method of determining the extent of ion binding i s that of measuring the transference numbers of the polyions and the counter- ions using radioactive tracers (62). Measurements on p o l y a c r y l i c a c i d (a polycarboxylic acid) demonstrated that i n a 0.0151 N s o l u t i o n at 507o n e u t r a l i z a t i o n about 507o of the sodium i n the system was bound (62) . The percentage of sodium ions bound was a function 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 for determining the amount of counterion bind ing by p o l y e l e c t r o l y t e s was also developed by Wall and h i s coworkers (62). The t h e o r e t i c a l basis for t h i s technique i s given i n d e t a i l by Crank (63, pages 121-122) . I t must be assumed that the process of ion p a i r formation proceeds quickly compared to d i f f u s i o n . I f t h i s i s so, l o c a l e q uilibrium may be assumed to e x i s t between the free and the bound components. For 17 s i m p l i c i t y , a l i n e a r adsorption isotherm may be assumed. That i s , the con- centration of the immobilized substance, S, i s assumed to be d i r e c t l y pro p o r t i o n a l to the concentration of the substance free to d i f f u s e , C. S = RC [1] where R i s a constant. Other cases are discussed by Crank (63). The usual equation for d i f f u s i o n i n one dimension (Fick's Law) i s then modified to allow for adsorption, and becomes dC/dt = D d 2C/dx 2 - dS/dt [2] i f the d i f f u s i o n c o e f f i c i e n t , D, i s assumed to be constant. Eqn. [1] may be substituted into Eqn. [2] to y i e l d dC/dt = D/(R + 1) * d 2C/dx 2 [3] which i s the normal form of the d i f f u s i o n equation with D replaced by D/(R + 1 ) . Thus, the extent of binding can be c a l c u l a t e d from a measurement 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 . The amount of sodium bound to poly- a c r y l i c a c i d c a l c u l a t e d by t h i s technique was found to be almost i d e n t i c a l to the amount ca l c u l a t e d by the transference number technique (62). The v i s c o s i t y , osmotic pressure, t u r b i d i t y and 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 charge on the macroion. Thus, measurements of these parameters may y i e l d valuable information about the extent of ion binding in the s o l u t i o n . Strauss and h i s coworkers (64-70, see e s p e c i a l l y 65, 68-70), f o r example, used e l e c t r o  phoresis and membrane equilibrium techniques to determine that the binding of the a l k a l i metal cations to polyphosphates increases i n the order Li>Na>K. The s e l e c t i v i t y with which the a l k a l i metal cations are bound i s 18 i n t e r e s t i n g , but i t i s the magnitude of the binding that i s r e a l l y s u r p r i s  ing. The extensive binding of the a l k a l i metal cations i s of course par t i a l l y due to the high negative charge on the polyion, which enhances the concentration of cations i n the double layer surrounding i t . A co r r e c t i o n f o r t h i s f actor may be applied by considering the corrected a s s o c i a t i o n constant K = [MP]/[P][M] e f f [4] where [MP] represents the concentration of the ion p a i r s , [P] the concentra t i o n of the free s i t e s on the polyion and [M] the e f f e c t i v e concentration of the cation M near the polymer chain. This concentration is given by the Boltzmann r e l a t i o n [ M ] e f f = [M] expC-q^/kT) [5] where [M] represents the ca t i c n concentration f a r from the polymer chain, q the charge on the cation, k the Boltzmann constant, T the absolute tempera ture 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 at the surface of the p o l y e l e c t r o - l y t e . (To apply t h i s correction,V must be assumed to equal the zeta poten t i a l , which may be calculated from the ele c t r o p h o r e t i c mobility.) Even with a c o r r e c t i o n for the Boltzmann f a c t o r , the extent of binding i s extremely high. The a s s o c i a t i o n constants f o r the phosphate polyions and the a l k a l i metal cations range from about 1 to 5 moles"\ The experiments of Strauss argue against the e a r l i e r concept that ions are a t t r a c t e d to a polyion merely because of i t s high net charge (71) and are trapped i n a region where \qV/kTl>l. A d d i t i o n a l evidence that true ion p a i r formation occurs i n p o l y e l e c t r o l y t e solutions i s discussed by Rice and Nagasawa ( 5 9 , pages 4 5 0 - 4 5 5 ) . I t was noted above that the polymerization of phosphate or carbox- yla t e monomers into a p o l y e l e c t r o l y t e enhances the binding of the a l k a l i metal cations to these moieties. I t i s i n t e r e s t i n g that an analagous phenomenon has been known to c o l l o i d chemists for over 30 years. When c e r t a i n p a r a f f i n chain cations form micelles at a c r i t i c a l concentration (72), the number of anions bound to these cations i s markedly enhanced (73). This phenomenon has been discussed i n some d e t a i l by Ling (74). Studies on the binding of ions to p o l y e l e c t r o l y t e s are of great t h e o r e t i c a l i n t e r e s t , but there are many reasons why the r e s u l t s of these studies (the observed magnitude and s e l e c t i v i t y of binding) are of l i t t l e d i r e c t b i o l o g i c a l s i g n i f i c a n c e . Not the l e a s t of these reasons i s the f a c t the proteins i n a l i v i n g c e l l are not free i n s o l u t i o n , but more or less s p a t i a l l y f i x e d , and i n a muscle f i b e r at l e a s t , cross-linked to a f a i r l y high degree. Thus, i t i s l o g i c a l to investigate the binding of the a l k a l i metal cations to s p a t i a l l y f i x e d and cross-linked p o l y e l e c t r o l y t e s ; ion exchange r e s i n s . Ion Exchange Resins and the A l k a l i Metal Cations. In an ion ex change r e s i n , two ions generally exchange with one another in stoichiometric q u a n t i t i e s , but they are not generally held equally strongly by the ex changer (75). The stoichiometric exchange between two monovalent cations, A and B, present i n both the aqueous and the exchanger phase, may be repre sented by the equation A + B A + B [6] where the bars denote the exchanger phase. The e q u i l i b r i u m s e l e c t i v i t y c o e f f i c i e n t , K , may then be defined as 20 where X. and X„ represent the equivalent f r a c t i o n s of the counterions i n the A B exchanger and X. and X represent the equivalent f r a c t i o n s of these ions i n A B the s o l u t i o n (75). I t i s apparent that i f both counterions are monovalent, eit h e r the molar or molal concentrations of the ions in the exchanger or the s o l u t i o n phase could have been used i n Eqn. [7], since only the r a t i o of the quantities appears. 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 ions in the 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 be applied 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 corrected s e l e c t i v i t y c o e f f i c i e n t , K^y^, i s defined as v ^ w w •  Both the order i n which a r e s i n s e l e c t s the a l k a l i metal cations and the magnitude of the s e l e c t i v i t y depend on several f a c t o r s . The most important appear to be the nature of the anionic s i t e , the structure and degree, of c r o s s - l i n k i n g of the r e s i n and the r e l a t i v e concentrations of the two ions i n the r e s i n . The s p e c i f i c capacity of the r e s i n (the number of exchange groups per u n i t amount of exchanger), the i o n i c strength of the surrounding s o l u t i o n , and the temperature may also a f f e c t the s e l e c t i v i t y . The e f f e c t of the nature of the anionic s i t e on the s e l e c t i v i t y w i l l be d i s  cussed f i r s t , and the discussion w i l l be l i m i t e d to three cations; L i , Na and 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 cro s s - l i n k e d polystyrene resins for the above cations vary with the degree of c r o s s - l i n k i n g and the r e l a t i v e concentrations of the ions in the ex changer, but the order of s e l e c t i v i t y i s K>Na>Li (75). The r e s u l t s obtained 21 on carboxylic and phosphonic resins are of greater b i o l o g i c a l s i g n i f i c a n c e . The order, as w e l l as the magnitude of the s e l e c t i v i t y of a carboxylic r e s i n depends on several f a c t o r s . I f , however, the r e s i n i s moderately cross- linked, maintained at a neutral or a l k a l i n e pH and the two competing ions are present i n approximately the same concentrations i n the r e s i n , i t w i l l s e l e c t the cations i n the order Li>Na>K (76, 77). This order of s e l e c t i v i t y was observed on carboxylic resins with three d i f f e r e n t types of polymer matrix, d i f f e r e n t s p e c i f i c c a p acities and d i f f e r e n t degrees of c r o s s - l i n k i n g (75). The importance of the anionic group i n the determination of the s e l  e c t i v i t y i s i l l u s t r a t e d by the f a c t that no s u l f o n i c r e s i n i s known which prefers sodium to potassium (75). Bregman and Murata (78) have shown that phosphonic r e s i n s , under a l k a l i n e and neutral conditions, also prefer the a l k a l i metal cations i n the order Li>Wa>K. Below pH 6, when the r e s i n e x i s t s mainly i n the -P(OH)0~ instead of the -RPO^ form, the s e l e c t i v i t y order i s reversed, potassium being preferred to sodium (76, 78). The e f f e c t of v a r i a t i o n s i n the r e l a t i v e concentrations of the cations on the s e l e c t i v i t y of a r e s i n i s sometimes quite pronounced. As Bregman (76) has stated, "In general, for resins of a conventional degree of c r o s s - l i n k i n g and a p a i r of cations which d i f f e r s i g n i f i c a n t l y i n s i z e , i t has been found that the a f f i n i t y f o r a cation increases as i t s mole f r a c t i o n i n the r e s i n phase decreases". This statement i s c e r t a i n l y applicable to the s e l e c t i v i t y of the carboxylic and phosphonic resins for the three a l k a l i metal cations discussed above (76, 77). The s e l e c t i v i t y c o e f f i c i e n t ^ L i / K a c a r k ° x v 1 i° r e s i n cross-linked with 15.470 divinylbenzene (DVB), fo r example, increases by a factor of about 5 as the mole f r a c t i o n of L i i n the r e s i n decreases from .9 to .2 (76). 22 V a r i a t i o n s 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 (usually DVB) 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 v a r i a t i o n s i n the mole f r a c t i o n of a cation i n the r e s i n . In s u l f o n i c resins, increasing the percentage of c r o s s - l i n k i n g agent generally increases the s e l e c t i v i t y of the r e s i n (75)„ In carboxylic r e s i n s , increasing the percen tage of c r o s s - l i n k i n g agent increases K^/ic ^ u t decreases ^ a / K O^") • One of the most important v a r i a b l e s a f f e c t i n g the s e l e c t i v i t y of carboxylic and phosphonic resins appears to be the pH, or equivalently, the degree of n e u t r a l i z a t i o n , a, of the r e s i n . A carboxylic r e s i n with 6% DVB, for example, sel e c t s the a l k a l i metal cations i n the order Li>Na>K at pH 7.4 (a = .85), but the order of s e l e c t i v i t y i s reversed at pH 6.5 (a = .2) (77). S i m i l a r l y , the s e l e c t i v i t y of phosphonic resins i s reversed under acid con d i t i o n s (76, 78). Bregman (76) has discussed the e f f e c t s of ioni c strength and temperature on the s e l e c t i v i t y of a r e s i n and Reichenberg (75) has commented on the e f f e c t s of v a r i a t i o n s i n the s p e c i f i c capacity. Unfortunately, l i t t l e work has been done on the e f f e c t of v a r i a t i o n s i n the l a t t e r parameter. In deed, i t i s unfortunate, as Reichenberg (75) has stated, that "the under standing of s e l e c t i v i t y phenomenon with monovalent ions (the a l k a l i metal cations i n t h i s case) i s of r e l a t i v e l y l i t t l e importance t e c h n o l o g i c a l l y " , although i t " i s of the greatest importance in connection with b i o l o g i c a l phenomenon". Its b i o l o g i c a l importance, from the point of view of t h i s t h e s i s , l i e s i n the analogy between the. inorganic, f i x e d charge, ion exchange sys tems and the s p a t i a l l y f i x e d proteins i n the l i v i n g c e l l . A s o l u t i o n of px-oteins extracted from a c e l l may be considered to be analogous to a poly-23 e l e c t r o l y t e s o l u t i o n . As both the number of cations bound, and the selec t i v i t y with which the p o l y e l e c t r o l y t e s bind these cations can be a l t e r e d (and in general increased) by charge f i x a t i o n and c r o s s - l i n k i n g , one should not expect the binding c h a r a c t e r i s t i c s of extracted proteins to be i d e n t i c a l to those of proteins i n the l i v i n g c e l l . The theories discussed below i n  dicate the importance of the structure of a protein i n determining i t s bind- ind c h a r a c t e r i s t i c s . Theories of Cation S e l e c t i v i t y . The f i r s t "mechanistic" attempt to explain the s e l e c t i v i t y of an ion exchange r e s i n was made by Gregor (79, 80). The basic factor governing s e l e c t i v i t y was assumed to be the e l a s t i c forces i n the r e s i n , which would oppose the tendency of the r e s i n to swell. He reasoned that the cation with the smallest hydrated radius would cause the l e a s t swelling i n the r e s i n , hence be preferred i n the r e s i n phase. This led to the p r e d i c t i o n that a r e s i n would s e l e c t the a l k a l i metal cations i n the order Cs>Rb>K>Na>Li, a s e l e c t i v i t y order which i s indeed v a l i d f o r most sulfonate r e s i n s . The theory, however, now appears to be i n v a l i d because i t cannot adequately explain "crossovers" or " s e l e c t i v i t y r e v e r s a l s " (75, page 252). The hydration of ions also plays an important r o l e i n a theory of s e l e c t i v i t y developed by Eisenman and h i s co-workers (81-84). In t h i s theory, however, there i s no necessity to r e l y on the rather vague concept of the hydrated ion radius. (Kavanau (19, pages 224-248) may be consulted for a b i o l o g i c a l l y oriented review of the current concepts regarding the hydration of ions.) Glueckauf (85) had c r i t i c i z e d Gregor's theory on these grounds even before the other d i f f i c u l t i e s inherent i n Gregor's theory were apparent. Eisenman's theory w i l l f i r s t be considered i n r e l a t i o n to a 24 glass (or resin) which completely excludes water. The exchange of a cation, I, i n i t i a l l y i n combination with an anionic s i t e , X, i n the glass or r e s i n for another cation, J , i n i t i a l l y i n a d i l u t e s o l u t i o n may be represented as XI + J ^ XJ + I + £F° [9] where AF°^ represents the standard free energy change for the process (84, see equation 8). The standard free energy change, i n the id e a l case, i s r e l a t e d 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 glass or r e s i n by Eqn. [10] AF?. = -RT In K T / T • [10] i j I /J where R and T have t h e i r usual s i g n i f i c a n c e (84, 75). The standard free energy change i n the exchange process w i l l depend mainly on two f a c t o r s ; the diffe r e n c e in the p a r t i a l molal free energies of hydration of the two ions i n the aqueous phase, (.F^^ - P ^ y d ) , and the difference in the p a r t i a l molal x «J —slas s free energies of i n t e r a c t i o n of the cations with the glass, (F^ tfaSS). Thus AF?. = ( F ^ y d - F T y d ) - ( P f l a P S - P T l a S S ) [11] The values of the f i r s t term i n parenthesis are known experimentally. Nothing need be known about the exact manner i n which water i n t e r a c t s with the ions. Values are given in Eisenman's paper (84) r e f e r r e d to Cs. Eisenman points out that there are two independent methods of obtaining values for the second term i n parenthesis of Eqn. [11]; a rather empirical, thermochemical 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 considered here. I f the s i t e s on the glass or r e s i n are widely separated, the free energies of i n t e r a c t i o n between a cation and an anionic s i t e w i l l be given 25 to a f i r s t approximation by Coulomb's law for r i g i d s i t e s and counterions; f glass = _ 3 2 2 / ( r i + r ) ...[12] f g l a s s = _ 3 2 2 / ( r j + r j [ 1 3 ] where r and r are the naked r a d i i of the ions I and J , and r i s the i. J ~ "equivalent" radius of the anionic s i t e (84). These two equations, along with the known values f o r the free energies of hydration of the cations may be substituted into Eqn. [11]. Values of AF°^ may then be p l o t t e d as a function of one v a r i a b l e , r . This generates a serie s of s e l e c t i v i t y orders (84, see F i g . 16). I f the anionic s i t e s are very c l o s e l y spaced, the free energies of i n t e r a c t i o n w i l l be given by the following equations; -glass = ( _ 3 2 2 ) / ( r i + r_) ...[14] f | l a S S = 1.56 (-322) / ( r j + r_) [15] which are the Born-Lande expressions for the i n t e r n a l free energies of an a l k a l i h a l i d e c r y s t a l l a t t i c e . The s u b s t i t u t i o n of these equations instead of [12] and [13] into Eqn. [11] and the p l o t t i n g of the values of £F°.. against r y i e l d s almost the same s e l e c t i v i t y sequences (84, see F i g . 17). The value of r at which a given s e l e c t i v i t y sequence i s observed, however, i s s h i f t e d , and i t i s important to note that the s h i f t occurs i n such a d i r e c t i o n that 1 S enhanced (84, compare figures 16 and 17) . For example, i f the r of the anionic s i t e s has a value which implies that the s e l e c t i v i t y , K^^,, i s unity when the s i t e s are i s o l a t e d , the value of K^ja/£ w i l l be greater than unity of overlapping of the s i t e s occurs. The r e l a t i o n s h i p between r and the s e l e c t i v i t y may be made cl e a r e r by a consideration of two l i m i t i n g cases. Consider f i r s t the case when r i s large (r » r^., r j ) . This Eisenman terms a s i t e of low f i e l d . 26 strength. I r r e s p e c t i v e of the r e l a t i v e sizes of the two cations, the second term i n Eqn. [11] w i l l be small, and w i l l depend p r i m a r i l y on the p a r t i a l free energies of hydration. The glass or r e s i n would then prefer the a l k a l i metal cations i n the order Cs>Rb>K>Na>Li (84, see r i g h t of eit h e r f i g u r e 16 or 17). Conversely, when r i s small, that i s , a s i t e of high f i e l d strength, the second term i n Eqn. [11] w i l l predominate. The glass or r e s i n would then prefer the cation with the smallest naked radius, that i s , Li>Wa>K>RbX;s (84, see l e f t of e i t h e r f i g u r e 16 or 17). For intermediate values of r , 9 other possible sequences are predicted. Thus, 11 sequences out of a possible 5'. = 120 sequences are predicted by the theory. These t h e o r e t i c a l predictions have been almost completely confirmed by experiments conducted on glasses of various compositions (containing s i t e s of varying f i e l d strengths). The experimental confirmation of the theory w i l l not be discussed here (83, 84). I t need only be noted that "the general agreement between the t h e o r e t i c a l predictions and the experimental r e s u l t s i s s u f f i c i e n t l y good to j u s t i f y the opinion that Eisenman's theory i s b a s i c a l l y sound" (75). The above discussion has been l i m i t e d to glasses or resins which exclude water. Eisenman investigated t h e o r e t i c a l l y the e f f e c t of water on the s e l e c t i v i t y of glasses and resins by considering a water swollen r e s i n as analogous to a concentrated s o l u t i o n of a strong e l e c t r o l y t e (83, 84). This was e s s e n t i a l l y an extension of the i n v e s t i g a t i o n of Cruickshank and Meares (86). Eisenman's "assumption that the free energy data of an aqueous s o l u t i o n may be used to represent completely the s e l e c t i v i t y properties of an ion exchange phase containing comparable amounts of water" (83, page 313) appears debatable to t h i s i n v e s t i g a t o r , but the conclusion he derives from 27 the analysis i s adequately supported by experimental evidence. Eisenman concludes that the main e f f e c t of water swelling w i l l be on the magnitude of s e l e c t i v i t y (decreasing i t ) and that swelling w i l l have l i t t l e e f f e c t on the pattern of s e l e c t i v i t y . Support f o r t h i s conclusion comes from experiments on both glasses and r e s i n s . The s e l e c t i v i t y of glasses which prefer potas sium to sodium passes through a maximum as the f i e l d strength of the s i t e s i s lowered, whereas the t h e o r e t i c a l analysis indicates the s e l e c t i v i t y should be a monotonic function of f i e l d strength. This maximum corresponds to an observable increase i n the hydration of the gla s s , hence supports the conclusion that hydration lowers the magnitude of the s e l e c t i v i t y (84, see r i g h t of figures 8 and 9). The data of Reichenberg (75) indicates that the s e l e c t i v i t y of sulfonate resins i s a simple function of the average amount of water per exchange group. This r e s u l t also supports the conclusion that an increase i n hydration leads to a decrease i n the magnitude of s e l e c t i v i t y , but does not change the order of s e l e c t i v i t y . Eisenman's theory permits at l e a s t a q u a l i t a t i v e explanation of the dependence of s e l e c t i v i t y on the nature of the anionic s i t e . The equivalent r should be r e l a t e d to the pK of the ion exchange s i t e (84). Sites with a high pK should have a low r and v i c e versa. Thus i t i s a — reasonable that the s u l f o n i c resins (the s i t e s of which have a low pK a J low f i e l d strength or low equivalent r ) prefer the a l k a l i metal cations i n the order K>Na>Li. The pK of the s i t e s on the other resins considered i n t h i s a chapter increase i n the order -^(OH)©^, -C00~, -PO^. The magnitude of s e l e c t i v i t y i s reduced i n -P(OH)C~ r e s i n s , the order of s e l e c t i v i t y reversed i n -COO" resins (they generally prefer Li>Na;>K.), and the magnitude of t h i s reversed s e l e c t i v i t y enhanced i n -PC1., resins i n agreement with the theory. 28 Eisenman's theory was created s p e c i f i c a l l y to explain the selec- t i v i t y c h a r a c t e r i s t i c s of cation s e l e c t i v e glasses, and has been very successful i n doing t h i s . As Reichenberg (75) has pointed out, however, d e t a i l e d predictions made on the basis of t h i s theory about the s e l e c t i v i t y orders expected i n carboxylic resins have been far less s u c c e s s f u l . The s e l e c t i v i t y reversals i n carboxylic r e s i n s , for example, commence with the sodium-lithium r e v e r s a l rather than the cesium-potassium r e v e r s a l , as pre dicted by the theory (75). This i s perhaps not too s u r p r i s i n g , because p o l a r i z a t i o n and other e f f e c t s have been ignored i n Eisenman's theory. Some facets of Ling's theory (74) of cation s e l e c t i v i t y w i l l now be discussed. The theories of Ling and Eisenman are s i m i l a r i n many respects, but that of the former was s p e c i f i c a l l y formulated for a b i o l o g i c  a l f i x e d charge system. Ling, l i k e Eisenman. considered the f i e l d strength of the anionic s i t e to be of prime importance i n determining s e l e c t i v i t y . He used a parameter he termed a "c value" (which i s s i m i l a r to the r u t i l i z e d by Eisenman) to describe the f i e l d strength of the anionic s i t e . This c value, calculated i n A*, i s the distance that a u n i t negative charge on the anion should be thought of being moved (either towards or away from the cation) to simulate the induction, multipole, p o l a r i z a t i o n and d i r e c t e f f e c t s of other i o n i c and polar groups. In contrast to Eisenman, Ling included the p o s s i b l e e f f e c t s of induced dipole interactions in h i s a n a l y s i s . He also assumed that an i n  t e g r a l number of water molecules could be found between the anion and the cation, and considered t h i s e f f e c t s t a t i s t i c a l l y . The a t t r a c t i v e forces between the anion and the cation were balanced against the repulsive forces (one of the s i g n i f i c a n t l a t t e r forces being Born repulsion) and the theory 29 was developed i n one dimension. The correct value of the p o l a r i z a b i l i t y of the carboxyl s i t e s i s not known, hence a number of values were considered. 11 s e l e c t i v i t y sequences for the 5 a l k a l i metal cations as Eisenman's theory. This agreement, however, may be f o r t u i t o u s . Many of the terms in Ling's basic equations are only rough approximations to the actual p h y s i c a l forces involved. The values that Ling used for the p o l a r i z a b i l i t y term have re ceived s p e c i a l a t t e n t i o n , for Ling (87) noted that the use of d i f f e r e n t values f o r the p o l a r i z a b i l i t y of the carboxyl groups would generate d i f f e r  ent s e l e c t i v i t y orders. Reichenberg (75) comments that the use of higher values for the p o l a r i z a b i l i t y "comes closer to p r e d i c t i n g the sequences that are found experimentally" for carboxylic resins of high s p e c i f i c capacity. d i e t s the entry of water into an exchanger can increase, rather than de crease the s e l e c t i v i t y (74). Experiments performed on glasses (84) and resins (75) contradict t h i s conclusion, as discussed above. Ling was able to make th i s p r e d i c t i o n because he assumed at the s t a r t of h i s analysis that a l l the cations i n a b i o l o g i c a l f i x e d charge system are associated with f i x e d anions (74), a highly dubious assumption. Ling of course, must argue i n this manner to provide a t h e o r e t i c a l j u s t i f i c a t i o n for h i s contention that the l i v i n g c e l l as a whole i s analogous to an ion exchange r e s i n with an extremely high s e l e c t i v i t y f or potassium over sodium. (According to Ling (74, page 220) the ^-^^ a f ° r a muscle f i b e r must be about 300, even though he admits that no physical system i s known that has a greater , than 10.) Further c r i t i c i s m of Ling's theory may be found i n a paper by Conway I t i s s i g n i f i c a n t that Ling's analysis predicts exactly the same An equally important c r i t i c i s m of Ling's theory i s that i t pre- (88). 30 There i s no objection to considering a membrane-free b i o l o g i c a l system as an ion exchange r e s i n (and glycerinated f i b e r s w i l l be considered as such below), but i t does seem unreasonable, as Ling has done (74), to completely ignore the membrane surrounding a l i v i n g c e l l . I f , as Reichen- berg contends, "we may to a f i r s t approximation, regard the e f f e c t of addi t i o n a l water as merely to ' d i l u t e ' the processes giving r i s e to s e l e c t i v i t y " (75), i t would seem reasonable i n a l i v i n g c e l l to consider the proteins (including that water of hydration which excludes a l k a l i metal cations) as ion exchange p a r t i c l e s immersed i n an aqueous s a l t s o l u t i o n . This approach seems e s p e c i a l l y desirable now that accurate measurements of the a c t i v i t i e s of sodium, potassium and hydrogen i n the aqueous s o l u t i o n surrounding the proteins can be made. Proteins and the A l k a l i Metal Cations. The d i f f i c u l t i e s inherent i n the a p p l i c a t i o n of a theory of cation s e l e c t i v i t y to a b i o l o g i c a l macro- molecule are apparent. Even i f one accepted u n c r i t i c a l l y an e x i s t i n g theory, i t would be impossible to p r e d i c t whether a given p r o t e i n would pre f e r to bind sodium or potassium, and equally d i f f i c u l t to p r e d i c t the number of cations i t would bind. I t seems reasonable, however, to accept that the s e l e c t i v i t y of a p r o t e i n w i l l depend on the r value (in terms of Eisenman 1s theory) or the c value (in terms of Ling's theory) of the carboxylic s i t e s . I t was noted that s u l f o n i c resins (pK = 1.5) prefer to bind K>Na and that carboxylic resins (pK = 6) prefer to bind Na>K. As the pKs of the a s p a r t i c and glutamic residues of proteins l i e between these two values (89), the s i t e s could conceivably prefer to bind e i t h e r sodium or potassium. I t should be noted, however, that "the a l k a l i metal cations are scarcely bound at a l l " to most proteins (90, page 591). Thus, i f a given protein does bind s i g n i f i c a n t quantities of the a l k a l i metal cations, i t may be expected that the overlap and induction e f f e c t s considered by Eisenman and Ling are of im portance. Overlap e f f e c t s would be expected to depend much more c r i t i c a l l y on the secondary and t e r t i a r y structure of the protein than induction e f f e c t s . Some experimental studies on the binding of the a l k a l i metal cations to extracted muscle proteins w i l l now be discussed. Szent-Gyorgyi noted the extensive binding of the a l k a l i metal cations to extracted myosin (91). Furthermore, he noted that the a b i l i t y of myosin to bind the a l k a l i metal cations i s extremely l a b i l e . The binding decreases markedly a f t e r storage of myosin at 0° for only 24 hours, and i s completely abolished by a thermal denaturation of the p r o t e i n . Two con clusions may be made from these observations. F i r s t , they i l l u s t r a t e that the a b i l i t y of myosin to bind cations i s dependent on the secondary and t e r t i a r y structure of the molecule. Second, they indicate that the binding of cations to myosin i n the l i v i n g c e l l may be somewhat higher than that measured on the extracted protein because of denaturation during the extrac t i o n procedure. Lewis and Saroff (92) made c a r e f u l measurements of the binding of sodium and potassium to a c t i n , myosin and actomyosin. Although 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 points and amino acid compositions, i t was found that a c t i n does not bind potassium ions but that myosin binds both sodium and potassium ions quite strongly. The maximum number of a l k a l i metal cations that could be bound to myosin was about 50 moles/10^ g myosin. At a p h y s i o l o g i c a l pH of about 7.3 (see Chapter V) and a free Unfortunately, Lewis and Saroff (92) were not as c a r e f u l i n describing t h e i r experiments as they were i n performing them. They i n i t i a l l y defined potassium concentration of 0.100 M, about 35 moles of potassium are bound to 10^g of myosin (92). Myosin binds sodium even more strongly than i t binds potassium. At a pH of 7.7 and a temperature of 5° C, the apparent associa t i o n constant of myosin for sodium (225 ± 22) i s about twice that of myosin for potassium (98 ± 11). These "anomalously high a s s o c i a t i o n constants for the binding of Na and K to myosin" (92) and the f a c t the binding depends on the structure of the molecule imply that overlap e f f e c t s should account for most of the binding. According to theory (84), the overlapping of s i t e s should enhance K, , Thus, i t i s l o g i c a l that sodium i s bound more as the "average number of potassium ions found per mole of myosin" (92 page 2115) . I t i s apparent from figures 1 and 2 in t h e i r paper that XT' has a maximum value of about 50. On page 2116, however, (see Table II) the max imum number of ions bound per 10^g of myosin i s also stated to be equal to 50. Thus, i t i s not c l e a r whether 4.2 * 10^g (the approximate weight of one mole of myosin) or 10^ grams of myosin i s capable of binding about 50 moles of a l k a l i metal cations. Cope (93), for one, i n i t i a l l y accepted the former i n t e r p r e t a t i o n . A c a r e f u l reading of the paper, however, indicates that the l a t t e r i n t e r p r e t a t i o n i s correct. Lewis and Saroff mention the molecular weight of myosin only once i n t h e i r paper, and then only when they discuss the combination of a c t i n and myosin i n approximately molar r a t i o s . Further more, i n this (92) and a l a t e r paper (94) they c o r r e l a t e the r e s u l t s d i r e c t  l y with the f a c t that there are "15 h i s t i d i n e residues per 10^ grams of myosin". Cope (personal communication) has since agreed that the r e s u l t s of Lewis and Saroff indicate that 50 moles of cations are bound per 10^g of myosin. 33 strongly than potassium to myosin. (It i s also l o g i c a l that small molecules which, can form a l k a l i metal chelates (94) prefer these cations i n the order Li>Na>K.) In a l a t e r paper, Saroff (94) analyzed the dependence of the binding on pH, and concluded that "the binding of sodium and potassium ions appears to involve c a r b o x y l - a l k a l i metal-imidazole and c a r b o x y l - a l k a l i metal-amino chelates". This conclusion i s c e r t a i n l y reasonable, but the p o s s i b i l i t y that other pairs of s i t e s could be involved i n the binding can not be excluded on the basis of the a v a i l a b l e evidence. I t may be of i n t e r e s t to c a l c u l a t e roughly the maximum number of binding s i t e s i n the l i v i n g c e l l f o r the a l k a l i metal cations from the data of Lewis and Saroff (92). Myosin comprises about 39-577* (95, 96) of the t o t a l p r o t e i n i n a muscle. I t w i l l be assumed that i t comprises 507, of the protein i n a barnacle muscle f i b e r . These f i b e r s contain about 757> water by weight (Chapter IV). I t i s not unreasonable to assume that 807, of the s o l i d m a t e rial i n the c e l l i s p r o t e i n . Thus, about 107> of the weight of a barnacle muscle f i b e r consists of myosin. At the p h y s i o l o g i c a l pH of 7.3 (Chapter V), about 40 s i t e s should be a v a i l a b l e to bind sodium and potassium per 10^g of myosin (92). Thus, the r e s u l t s of Lewis and Saroff p r e d i c t that about 50 mMoles of a l k a l i metal cations/Kg of f i b e r water are bound to myosin i n a barnacle muscle f i b e r . The binding of sodium and potassium to muscle proteins i n glycer- inated f i b e r s w i l l now be considered. This system should be a better model of the l i v i n g c e l l than d i l u t e solutions of extracted proteins. In a glycerinated f i b e r the proteins are s p a t i a l l y f i x e d i n such a manner that the structure of the proteins (in the thick and t h i n filaments) i s s i m i l a r to that of the proteins in a l i v i n g muscle f i b e r . Fenn (97) e q u i l i b r a t e d 34 glycerinated muscle f i b e r s i n solutions containing equal concentrations of sodium and potassium, then measured the concentrations of these cations i n muscle f i b e r s . Two major conclusions may be drawn from h i s data. F i r s t , more sodium than potassium was accumulated by the muscle f i b e r s at a l l the ex ter n a l concentrations studied, the preference f o r sodium over potassium being most marked at the lower concentrations. S l i g h t l y more "binding" occured than would have been predicted from the r e s u l t s of Lewis and Saroff (92), but Fenn cautions that "the d e t a i l e d and quantitative i n t e r p r e t a t i o n of these figures must await further experiments" (97). The other i n t e r e s t  ing feature of the data i s the fac t the number of bound ions/Kg muscle appears to pass through a maximum, then decrease as the external concentra tions of the ions i s increased. The s i g n i f i c a n c e of th i s trend w i l l be con sidered i n more d e t a i l i n Chapter IX, but i t may be noted here that t h i s r e s u l t could be explained i f a f r a c t i o n of the water i n the g l y c e r o l extracted muscle f i b e r i s unavailable to act as solvent for the a l k a l i metal cations. One f i n a l point may be made about the binding of ions to the con t r a c t i l e proteins i n the l i v i n g c e l l . I t would be na'ive not to expect the binding of other charged species to influence the binding of the a l k a l i metal cations to these proteins. Thus, the binding of calcium and magnesium would i n t u i t i v e l y be expected to decrease the binding of the a l k a l i metal cations to myosin, whereas the binding of anions such as chloride would be expected to enhance the binding of the a l k a l i metal cations (91). Bound polyphosphates such as ATP (98, 99, 100) might be expected to act l i k e the anionic moieties on a phosphonic ion exchange r e s i n (76, 7S) and enhance the o v e r a l l K^ a /'£ °f t n e c o n t r a c t i l e proteins, but the experiments of Fenn ( 9 7 ) indicate that ATP has very l i t t l e e f f e c t on the binding of sodium and potassium to the c o n t r a c t i l e proteins i n a glycerinated muscle f i b e r . bind the a l k a l i metal cations (strong chelating agents being the exception), these cations can engage i n ion p a i r formation with b i o l o g i c a l l y s i g n i f i c a n t anionic moieties on p o l y e l e c t r o l y t e s and ion exchange r e s i n s . Carboxylic there was l i t t l e t h e o r e t i c a l j u s t i f i c a t i o n for an extrapolation of t h i s re s u l t to the proteins i n a l i v i n g c e l l . Induction and overlapping e f f e c t s (which depend on the structure of the protein) could change the anionic f i e l d strength of the s i t e s , hence the s e l e c t i v i t y and magnitude of the binding. Experimental studies on the binding c h a r a c t e r i s t i c s of the major pro t e i n i n a muscle f i b e r , myosin, indicate that this p rotein 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 for both sodium and potas sium, the former ion being bound more strongly than the l a t t e r . The c r i t i c a l dependence of the binding c h a r a c t e r i s t i c s of myosin on the struc ture of the molecule and the preference of myosin f o r sodium over potassium are compatible with the e x i s t i n g theories of cation s e l e c t i v i t y . As the binding c h a r a c t e r i s t i c s of extracted myosin are q u a l i t a t i v e l y s i m i l a r to those of the proteins i n a glycerinated muscle f i b e r , i t seems reasonable to expect that s i g n i f i c a n t quantities of both sodium and potassium w i l l be bound to myosin in the l i v i n g c e l l , and that the s e l e c t i v i t y of the protei n , w i l l be greater than unity. In summary, i t was noted that although very few small molecules resins prefer to bind sodium to potassium that 36 CHAPTER I I I SCOPE AND PURPOSE OF THE INVESTIGATION The main purpose of this i n v e s t i g a t i o n was to test experimentally the hypotheses that: i . a s i g n i f i c a n t f r a c t i o n of the a l k a l i metal cations i n a s t r i a t e d muscle f i b e r i s bound to myosin, i i . the binding s i t e s on the thick filaments i n a s t r i a t e d muscle f i b e r prefer to bind the a l k a l i metal cations i n the order Li>Na>K, i i i . some of the water i n a s t r i a t e d muscle f i b e r i s "bound" i n such a manner as to be unavailable to act as solvent for the a l k a l i metal cations free i n the myoplasm. Four separate experimental approaches, which are b r i e f l y outlined below, were adopted. Chapter IV. The hypotheses were f i r s t tested by comparing the a c t i v i t i e s of sodium and potassium i n the myoplasm to the values expected from a determination of the t o t a l sodium, and potassium content of the c e l l . The a c t i v i t i e s were measured d i r e c t l y by means of cation s e n s i t i v e glass microelectrodes and the t o t a l content of sodium and potassium in the same muscle f i b e r was determined by a conventional flame photometric a n a l y t i c technique. I t i s apparent that 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 less than the a c t i v i t y predicted from the a n a l y t i c measurements. I t i s also apparent that i f pro p o r t i o n a l l y more water than potassium i s "bound", the measured a c t i v i t y of potassium w i l l be greater than the a c t i v i t y of potassium predicted from the a n a l y t i c measurements. The r e s u l t s obtained are compatible with both of these p r e d i c t i o n s . 37 There were other reasons f o r performing the above experiment, A knowledge of the a c t i v i t i e s of sodium and potassium i n the myoplasm i s a pr e r e q u i s i t e to an accurate measurement of the membrane permeabilities and transport c h a r a c t e r i s t i c s of these ions. A proper evaluation of the membrane p o t e n t i a l of the c e l l , and the i n t r a c e l l u l a r reactions (ATPase a c t i v a t i o n , for example) these cations can undergo also depends on an accurate 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 electrode measurements pro vided d i r e c t experimental evidence which contradicted Ling's hypothesis (1) that potassium i s accumulated p r e f e r e n t i a l l y over sodium by muscle f i b e r s 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 binding s i t e s . The microelectrode measurements were compatible with, but did not prove the hypothesis that a s i g n i f i c a n t f r a c t i o n of sodium i n the c e l l was bound to myosin. A l l or part of the sodium i n the c e l l unavailable to the cation s e n s i t i v e microelectrode could have been sequestered i n i n t r a c e l l u l a r organelles. The next experiment was designed s p e c i f i c a l l y to test the hypothesis that at le a s t some of the "bound" sodium i n the c e l l was indeed bound to myosin. Chapter V. I t i s known that extracted myosin undergoes thermal denaturation at 37° C (2) and that t h i s denaturation causes the release of bound a l k a l i metal cations (2) and polyphosphate anions (3). I t was reasoned that i f a s i g n i f i c a n t f r a c t i o n of the i n t r a c e l l u l a r sodium was bound to myosin, a release of bound sodium, hence an increase i n the a c t i v  i t y of sodium i n the myoplasm, would occur when the muscle f i b e r was heated to 37° C. This p r e d i c t i o n was confirmed by measuring the a c t i v i t y of sodium i n the myoplasm of s t r i a t e d muscle f i b e r s by means of a cation sensi t i v e glass microelectrode while the temperature of the sodium free bathing 38 s o l u t i o n was rai s e d to 37° C. The experiments reported i n Chapter V provided strong evidence that much of.the sodium i n s t r i a t e d muscle f i b e r s was indeed bound to myosin, but i t was thought desirable to obtain experimental evidence independent of microelectrode measurements to substantiate t h i s conclusion. r Chapter VI. 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 of a s t r i a t e d muscle f i b e r on the basis of the hypothesis that sodium i s bound to the thick filaments. The t u r b i d i t y or o p t i c a l density of a so l u t i o n of macromolecules i s intimately r e l a t e d to the net charge on the macromolecules. I f the net charge i s increased, the t u r b i d i t y of the s o l u t i o n decreases (4, 5, 6). Thus, the t u r b i d i t y of a muscle f i b e r would be expected to decrease i f the net charge on the main sc a t t e r i n g centers i n the f i b e r , the thick filaments, was increased. Bathing the f i b e r i n a sodium free s o l u t i o n should cause sodium to move o f f the binding s i t e s on the thick filaments and out of the c e l l . I f no ion replaces sodium on the binding s i t e s , the net negative charge on the thick filaments should increase, and the t u r b i d i t y of the f i b e r should decrease. This p r e d i c t i o n was confirmed f o r f i b e r s bathed i n sodium free solutions containing sucrose, t r i s or potassium as substitutes for sodium. When l i t h i u m was used as a sub s t i t u t e f o r sodium i n the bathing s o l u t i o n , the t u r b i d i t y of the f i b e r s increased s l i g h t l y . This f i n d i n g i s also compatible with the working hypothesis, for the l i t h i u m entering the c e l l should be bound more strongly than sodium to the s i t e s on the thick filaments (7). Chapter VII. The l a s t series of experiments was designed to measure the s e l e c t i v i t y , K^a/j£j of the proteins i n a glycerinated f i b e r when the free concentrations of sodium, potassium and hydrogen were s i m i l a r to those found i n the myoplasm of a l i v i n g c e l l . The. concentrations of sodium and potassium accumulated by the glycerinated f i b e r s were measured by means of radioisotopes and a standard flame photometric technique. The r e s u l t s indicated that the s e l e c t i v i t y of the proteins, K j j a / j ^ J w a s indeed greater than unity, but also that the number of sodium ions bound to the proteins was not great enough to explain the extremely low a c t i v i t y of sodium i n the myoplasm of a l i v i n g f i b e r . Thus, i t was concluded that i n a l i v i n g muscle f i b e r e i t h e r some factor enhances the binding of sodium to the c o n t r a c t i l e proteins or sodium i s compartmentalized i n i n t r a c e l l u l a r organelles. 40 CHAPTER IV ACTIVITY OF SODIUM AND POTASSIUM IN THE MYOPLASM A. Introduction The motivation for measuring the a c t i v i t i e s of sodium and potas sium i n the myoplasm of s t r i a t e d muscle f i b e r s was discussed i n the previous two chapters. A means of measuring these a c t i v i t i e s was devised by Kinke (1) , who was the f i r s t to construct cation s e n s i t i v e glass microelectrodes from the glasses developed by Eisenman and h i s coworkers (2). The success of the experiments also depended on the use of the extremely large, ( t y p i c a l weight = 20 mg, t y p i c a l diameter = 1mm, t y p i c a l length = 4 cm) muscle f i b e r s of the giant barnacle, Balanus nubilus. Hoyle and Smyth (3) may be consulted f o r a d e s c r i p t i o n of the barnacle muscles. One advantage of performing experiments on the large barnacle muscle f i b e r s i s that r e l a t i v e l y large microelectrodes can be used. These electrodes are easier to construct than the extremely small cation s e n s i t i v e microelectrodes that Lev (4, 5) u t i l i z e d f o r measurements on frog muscle f i b e r s . Another advantage i s that the muscle f i b e r s can be dissected with out damage because they are held together with only a loose network of collagen. The tendon can be cannulated without damage to the f i b e r and the microelectrode inserted down the lo n g i t u d i n a l axis of the f i b e r ; a procedure which ensures that the cation s e n s i t i v e t i p i s far from the region of damaged membrane. I f the microelectrode i s inserted transversely, the t i p i s near a damaged area of membrane, and leakage of sodium into the f i b e r , or of potassium out of the f i b e r can occur. F i n a l l y , the t o t a l sodium and potassium content of a single barnacle muscle f i b e r can be accurately 41 determined by means of flame photometry because of the large size of the , f i b e r s . B. Methods Microelectrodes. The sodium sensitive microelectrodes were con structed from Corning KAS 11-18 (sodium sensitive) 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 sensitive t i p was formed by fusing the two glasses in a microforge. The sensitive tips of the sodium (and potas sium) microelectrodes were about 15u, in diameter and 150-300u, i n length, as shown in F i g . 1. A recent a r t i c l e by Hinke (6) contains details of the F i g . 1. Photograph of the t i p of a sodium sensitive microelectrode. The t i p i s about 15u, i n diameter and 300u. in length. construction procedure. The potassium sensitive microelectrodes were constructed from Corning NAS 27-3 (potassium sensitive) and 0120 (lead) glasses. Only a few microelectrodes were constructed by the method 42 described by Hinke (1, 6), which involved matching and fusing three sets of glasses (NAS 27-3, 0120 and pyrex) at a j o i n t . A new technique was devel oped by the author whereby a j o i n t was formed by melting beeswax between the outer lead glass shank and the inner potassium glass c a p i l l a r y . This method of construction requires much less s k i l l than the previous technique and the electrodes have s l i g h t l y superior c h a r a c t e r i s t i c s (a longer l i f e and better s e l e c t i v i t y , presumably because the glass i s heated l e s s ) . A d e s c r i p t i o n of t h i s technique w i l l appear in an a r t i c l e by Hinke (7). The equations which describe the behavior of the sodium and potassium s e n s i t i v e microelectrodes are • ^ a = ENa + S N a l o g 1 0 ( a N a + k N a V ' • [ 1 6 ] \ = EK + S K l o g 1 0 ( a K + VNP [ 1 7 ] where E„, and ET, are the measured po t e n t i a l s ( m i l l i v o l t s ) of the microelec-Na K trodes in solutions containing Na and K ions at a c t i v i t i e s a„ and aT, Na K r e s p e c t i v e l y ; the other terms are constant for a given electrode and are obtained by c a l i b r a t i o n i n the standard s o l u t i o n s . The sodium (potassium) s e n s i t i v e microelectrodes were c a l i b r a t e d i n the following f i v e standard solutions, which were buffered to either pH 7 or pH 8 with 0.01 M t r i s : 0.1 M NaCl (0.1 M KC1), 0.01 M NaCl (0.01 M KC1), 0.05 M KC1 plus 0.05 M NaCl, 0.20 M KC1 plus 0.05 M NaCl, and 0.40 M KC1 plus 0.05 M NaCl. The potentials from a microelectrode immersed in a standard s o l u t i o n of either pH 7 or pH 8 were i d e n t i c a l (±0.5 mV). Elec trodes were c a l i b r a t e d before and a f t e r each experimental reading, and the r e s u l t s were rejected i f the two c a l i b r a t i o n s did not coincide (+ 1 mV). The cation 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 constant ' Na K' , 1 • from day to day for a given microelectrode, but varied from electrode to electrode. For the sodium microelectrodes, the s e l e c t i v i t y , k ^ , varied from 1/50 to 1/1000; for the potassium microelectrodes, the s e l e c t i v i t y , k^ , v a r i e d from 1/1 to 1/2. The imperfect s e l e c t i v i t y of the electrodes necessitated measuring E^^ and on the same f i b e r , then solving the two simultaneous equations, [16] and [17] for the a c t i v i t i e s . The response of the sodium microelectrodes to a 10-fold change in the sodium a c t i v i t y , S , was always 59 mV, whereas the response of the potassium microelectrodes to a 10-fold change i n the potassium a c t i v i t y , S^, was 50-55 mV. The p o t e n t i a l from the sodium and potassium s e n s i t i v e microelectrodes were measured on a Vibron 33B electrometer and recorded on a Grass ink w r i t i n g o s c i l l o g r a p h . A l l electrodes used i n these experiments responded c o r r e c t l y (±1%) to an applied p o t e n t i a l , which indicated that the impedance of the electrodes was less than 1/100 of the impedance of the electrometer (input resistance of Vibron 33B = 1 0 1 3 ohms). Membrane p o t e n t i a l measurements were made with open t i p microelec trodes of the Ling and Gerard type. Only those microelectrodes with a t i p p o t e n t i a l of less than 5 mV were used, i n accordance with the c r i t e r i o n of Adrian (8). In a d d i t i o n , each microelectrode was tested to ensure the p o t e n t i a l reading in the Ringer s o l u t i o n and 0.40 M KC1 plus 0.05 M NaCl standard s o l u t i o n was i d e n t i c a l . F i n a l l y , membrane p o t e n t i a l measurements were r o u t i n e l y made with two d i f f e r e n t open t i p microelectrodes on the same f i b e r . The p o t e n t i a l from the open t i p microelectrode was recorded v i a a cathode follower and a Grass P6 DC a m p l i f i e r on a Grass ink w r i t i n g o s c i l l o g r a p h . Both this a m p l i f i e r and the Vibron electrometer were c a l i -44 brated. before each experiment with a v a r i a b l e voltage source, which i n turn was c a l i b r a t e d from a Standard Weston C e l l . Determination of Cation A c t i v i t y and Concentration. Single s t r i a t e d muscle f i b e r s from the depressor muscles of the giant barnacle were dissected free with a small piece of baseplate at the o r i g i n and a tendon at the i n s e r t i o n . A glass cannula was inserted into the tendon, but not through the muscle-tendon junction. A f t e r the cannula was l i g a t e d i n posi t i o n , the preparation was suspended v e r t i c a l l y i n an a r t i f i c i a l bathing s o l u t i o n (Table I) as shown in F i g . 2. Cation s e n s i t i v e microelectrodes TABLE I Solutions (mM) Barnacle Ringer* Sucrose Ringer** Na 450 K 8 8 Ca 20 20 Mg 10 10 CI 518 68 T r i s 25 25 Sucrose 649 pH = 7.6 for both s o l u t i o n s . Note the sub s t i t u t i o n of T r i s for HCO-j in the o r i g i n a l barnacle Ringer s o l u t i o n of Hoyle and Smith (3) . **Sucrose added to make s o l u t i o n isosmotic with barnacle Ringer s o l u t i o n . were manipulated through the cannulated tendon into the myoplasm u n t i l the s e n s i t i v e t i p was 1-2 cm from the puncture zone (See F i g . 3). This technique ensured 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 Open-tipped microelectrode!! S i l k tie Tendon -Single muscle fibre «-500 JLL F i g . Z. Diagram of a cannulated muscle f i b e r with inserted microelectrode. Note the cannula does not damage the f i b e r membrane. See text for explan a t i o n . 46 potential was always measured immediately adjacent to the electrode t i p , and i t was subtracted from the potential of the cation sensitive microelectrode. (The cation sensitive microelectrode registers of course the membrane poten t i a l as well as the potential 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 after an elec trode impalement. I f any damage was observed, the f i b e r was rejected. After completion of the electrode measurements, the fib e r was transferred to a P e t r i dish, c a r e f u l l y decannulated to avoid damage, and swirled for 15 seconds in isosmotic sucrose. The f i b e r was then blotted and placed i n a weighing b o t t l e . After drying, and digestion with n i t r i c acid, 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 fib 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 sensitive microelectrode was inserted into the fib e r v i a the cannulated tendon. Note a cation sensitive micro electrode in the fib e r and an open t i p microelectrode i n the bathing solu t i o n . The v e r t i c a l bar represents 1 mm. 47 was analyzed for t o t a l sodium and potassium content with a Unicam SP 900 flame spectrophotometer. Determination of Membrane P o t e n t i a l at High External Potassium  Concentration, Single muscle f i b e r s were dissected and suspended by t h e i r tendons in the v e r t i c a l plane. Eight bathing solutions with potassium con centrations ranging from 0 to 450 mM were used. The product of the potassium and chloride concentrations in each s o l u t i o n containing potassium was kept constant by replacing chloride with methanesulfonate. Magnesium, calcium and t r i s were present at the same concentrations as i n barnacle Ringer s o l u t i o n . To eliminate spurious 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 microelectrodes within the myoplasm, membrane p o t e n t i a l measurements were made at each potassium concentration with at l e a s t two d i f f e r e n t microelectrodes. The t o t a l potassium content of the muscle f i b e r was determined in the manner described in the previous para graph. Determination of Bound Sodium and Water. The separation of the sodium, potassium and water content of a single muscle f i b e r into a "bound" and " f r e e " f r a c t i o n i s expressed by the following equations C N a V = ^ a ' W + B N a [18] S^' + ^ [19] where ^„ and are the molal a c t i v i t y c o e f f i c i e n t s of sodium and potassium Na K J r i n the myoplasm; V i s the t o t a l water content (kilograms); a ^ a and are the f r a c t i o n s of 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 to act as solvent for the sodium and potassium ions r e s p e c t i v e l y ; C„T and C„ are the • Na K concentrations of sodium and potassium (moles per kilogram f i b e r water) .48 determined by flame photometry; and a R are the a c t i v i t i e s of sodium and potassium determined d i r e c t l y by the microelectrodes; B^ a and are the "bound" quantities of the cations (moles). I t should be stressed that any ion unavailable to a f f e c t the cation s e n s i t i v e microelectrode i s considered "bound". Thus, the ions compartmentalized in i n t r a c e l l u l a r organelles or "trapped" i n the e l e c t r o s t a t i c f i e l d of a negatively charged macromolecule, as well as those ions complexed by s p e c i f i c s i t e s i n the myoplasm are considered to be "bound". These two equations, which are v a l i d by d e f i n i t i o n , contain s i x quantities xvhich cannot be determined experimentally at present: "C-r . V,,, B„ and BT,. Four more equations are required. These following Na' K' Na , K n n ° equations are based on assumptions, and may be i n c o r r e c t . The f i r s t assump ti o n i s that the a c t i v i t y c o e f f i c i e n t s of sodium and potassium ions free i n the myoplasm are equal This assumption i s not based on t h e o r e t i c a l grounds. As Robinson and Stokes (9, page 454) state "The various p h y s i o l o g i c a l f l u i d s can be quoted as another example where a theory of mixed e l e c t r o l y t e solutions would lead to progress..". I t seems a reasonable assumption, i f only because the a c t i v i t y c o e f f i c i e n t s of a 0.2 M KC1 and NaCl s o l u t i o n d i f f e r by merely 3%. (One could, as Lev (5) has done, merely define the a c t i v i t y c o e f f i c i e n t s of sodium and potassium i n a muscle to be the r a t i o s of the measured a c t i v i t i e s to the measured concentrations. One i s then l e f t with the problem of ex p l a i n i n g why the a c t i v i t y c o e f f i c i e n t of sodium, defined 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 potassium i n the myo plasm.) 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 of the myoplasm i s equal to the a c t i v i t y c o e f f i c i e n t of the barnacle Ringer s o l u t i o n . tf= 0.65 [21] I t should be noted that the sum of the concentrations of sodium and potas sium i n a barnacle muscle i s , on the average, only about h a l f the sum of the concentrations of these ions i n the bathing s o l u t i o n (Table I and F i g . 4). Thus, the a c t i v i t y c o e f f i c i e n t could be as high as that of a 0.25M KC1 charged groups on proteins i n the myoplasm. Furthermore, the binding of a f r a c t i o n of the i n t r a c e l l u l a r water w i l l increase the free cation concentra t i o n , and lower the a c t i v i t y c o e f f i c i e n t . I t seems u n l i k e l y , however, that these factors could lower the value of the a c t i v i t y c o e f f i c i e n t 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 a 1.0 M KC1 s o l u t i o n ) . Thus, the assumption that the a c t i v i t y c o e f f i c i e n t of the myoplasm i s equal to 0.65 i s only a guess, but i t i s probable that the actual value l i e s between 0.6 and 0.7. An error i n the estimate, of 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 would a l t e r q u a n t i t a t i v e l y , but not q u a l i t a t i v e l y the conclusions of th i s chapter. The p o s s i b i l i t y that the macroscopic d i e l e c t r i c constant of the muscle f i b e r a f f e c t s the a c t i v i t y c o e f f i c i e n t w i l l be considered i n the Discussion. The next assumption i s that the f r a c t i o n of water a v a i l a b l e to act as solvent f o r sodium i n the myoplasm equals the f r a c t i o n of water a v a i l a b l e to act as solvent for potassium. This assumption may not be v a l i d . Sodium does not f i t as well as potassium s o l u t i o n (^=0.7). I t i s probably somewhat lower because of the many [22] 50 into the normal Ice I l a t t i c e , hence may be excluded from a larger f r a c t i o n of water i n the c e l l than potassium (10). The use of an overestimated value f o r i n Eqn. [18], however, w i l l merely cause the value of to be underestimated. For this reason, the assumption i s acceptable. The f i n a l assumption i s that there i s no binding of potassium. B R = 0.0 ...[23] This 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 for mathe matical, not physi c a l reasons. This assumption serves to maximize the value of O j , = C£, which i s calculated from Eqn. [19]. (In other words, i t i s the minimal f r a c t i o n of "bound" water that i s calculated.) When Eqns. [20-23] are substituted into Eqns. [18] and [19], the following equations r e s u l t . C N a V = («/0.65)a N aV + B N a [24] C K = (a/0.65)a R [25] From these two equations and the experimental data, the minimal f r a c t i o n of "bound" water and the minimal f r a c t i o n of "bound" sodium i n a barnacle muscle f i b e r may be c a l c u l a t e d . C. Results Concentration and A c t i v i t y Measurements. Consider now the r e s u l t s obtained from the concentration measurements made on the experimental and con t r o l f i b e r s . These are i l l u s t r a t e d i n F i g . 4. I t i s apparent that there i s a wide v a r i a t i o n of C„ and C„ i n muscle f i b e r s from d i f f e r e n t barnacles, as Na K ' we l l as a close c o r r e l a t i o n between the C.T and C„ of i n d i v i d u a l f i b e r s (cor- 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 barnacle shoxred l i t t l e v a r i a t i o n i n eit h e r C or CT,. This i s i l l u s t r a t e d i n Table I l a , which Na K 51 .250 ^.200 cn 150 .100 CK = .l82+.78(CNa-105) .050 .100 .150 .200 .250 CNo(M/Kg H20) F i g . 4. Relation between the sodium and potassium contents of sing l e muscle f i b e r s . 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. gives the a c t i v i t y , concentration and membrane p o t e n t i a l measurements made on f i b e r s from a single barnacle. The s a l i e n t features of Table I l a are that C^ a i s much larger than a ^ and that i s approximately equal to a^. These two features are common to a l l the f i b e r s investigated. The f r a c t i o n s of "bound" water and "bound" sodium were calculated f o r each i n d i v i d u a l f i b e r . That i s . the values of a„ , a,,. C„ and CT, ' Na' K' Na K obtained from each experimental f i b e r were used to solve Eqns. [24] and [25] f o r (1-a) and(B /V)/G^ a. By t h i s method of a n a l y s i s , the f r a c t i o n s of TABLE I I Sodium and potassium i n sin g l e muscle f i b e r s * K *K (moles/kg H 20) Na Na Membrane p o t e n t i a l (mV) Water content (%) (a) Barnacle Ringer s o l u t i o n 0.157 0.143 0.010 0.051 67.0 79.4 ±0.006 t(3) ±0.001(17) ±0.001(3) ±0.002(17) ±0.2(3) ±0.1(17) (b) Sucrose Ringer s o l u t i o n 0.170 0.174 0.007 0.039 61.8 72.8 ±0.005(8) ±0.002(16) ±0.001(8) ±0.003(16) ±0.5(8) ±0.2(14) Barnacle Ringer controls 0.158 0.056 70.7 75.8 ±0.004(8) ±0.006(8) ±0.4(8) ±0.7(8) *A11 experiments were done at 25°C t± S.E. NOTE: Table l i b shows average r e s u l t s . Table I l a shows only the r e s u l t s obtained from the muscle f i b e r s of a single barnacle. The C^ a and of a l l the f i b e r s i n t h i s series are shown in F i g . 4. Table I l a i s presented only to i n d i c a t e that there 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 values of C... and Na obtained from the muscle f i b e r s of a sin g l e barnacle. The number or determinations i s shown i n parentheses. •k "bound" water and "bound" sodium were found to be 0.41 ± 0.014 and 0.84 ± 0.001 r e s p e c t i v e l y (nine experiments). These r e s u l t s are s i m i l a r to the values obtained by Hinke in a series of preliminary experiments, which were also reported i n a paper by McLaughlin and Hinke (11). Hinke concluded from h i s measurements that the f r a c t i o n s of "bound" water and sodium were .43 and .85 r e s p e c t i v e l y . The small standard error for the f r a c t i o n of bound sodium i s worthy of note. I t indicates that this quantity remained constant even though the sodium content of 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 obtained from f i b e r s 5 3 +40h +20 £ 0 t 20 "o Q . - 4 0 § - 60 1-80 -100 SI ope =51 mV/log [K Log | 0 [KJ^CM/Kg H 20) F i g . 5 . Relation between membrane p o t e n t i a l and log [ K ] for a t y p i c a l muscle f i b e r . The product [ K ] Q [ C 1 ] O was maintained a constant. bathed for 4 5 minutes i n sodium free, sucrose substituted Ringer. When these r e s u l t s were used to solve Eqns. [ 2 4 ] and [ 2 5 ] for the f r a c t i o n s of "bound" water and sodium, the values obtained were s i m i l a r to those ob tained from f i b e r s bathed i n normal Ringer. The f r a c t i o n s of "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. The r e l a t i o n s h i p between the membrane p o t e n t i a l and the log of the external potassium concentration i s shown for a t y p i c a l barnacle muscle f i b e r i n F i g . 5 . The observed l i n e a r r e l a t i o n s h i p when [ K ] q i s greater than 0.016 M and the slope of 51 mV/log [ K ] Q indicate that the sarcolemma may have been acting as a semipermeable membrane to the potassium ion. (A l i n e a r r e l a t i o n s h i p was observed f o r each of the f i v e experimental f i b e r s . The average slope was 53 ± 1 mV/log [K] q.) I f the potassium concentration gradient i s the sole determinant of the membrane p o t e n t i a l at regions of high external potassium concentration (admittedly a questionable assumption, see Chapter V), the i n t e r n a l and external a c t i v i  t i e s of potassium should be i d e n t i c a l when the membrane p o t e n t i a l i s zero. The average value of [ K ] Q 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 experiments). This corresponds to an a c t i v i t y of 0.242(0.65) = 0.157, which i s assumed to equal the a c t i v i t y of potassium i n the myoplasm. I f th i s i s used with the average value of Cv 0.177 ± 0.006 moles/kg H^ O (15 experiments), to solve f o r Oi from Eqn. [25] the f r a c t i o n of "bound" water i s found to be 0.27. D. 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 of cation s e n s i t i v e microelectrodes have been advanced by Ling (12). His f i r s t c r i t i c i s m i s that the proteinaceous f i x e d charge network i n the immediate v i c i n i t y of the microelectrode may be damaged by the microelectrode, hence have i t s binding c h a r a c t e r i s t i c s a l t e r e d . I t i s apparent from F i g . 3 that the cation sensi t i v e glass microelectrodes used i n these experiments were much smaller than the muscle f i b e r s . A comparison of the a l k a l i metal cation concentrations and membrane p o t e n t i a l s of the control and experimental f i b e r s indicated that no gross damage was suffered by the c e l l s on impalement by the micro electrodes. I f a change i n the binding c h a r a c t e r i s t i c s of the proteins i n the immediate v i c i n i t y of the microelectrode did occur, sodium and potassium 55 ions would merely d i f f u s e down the concentration gradients set up i n the myoplasm. Any anomalous concentrations of these cations close to the micro electrode would be d i s s i p a t e d in time throughout the c e l l , and the error introduced would be expected to be n e g l i g i b l e . Ling's second c r i t i c i s m (12) i s that the electrodes may respond to other ions besides sodium and potassium and that they may be poisoned by high concentrations of amino acids or proteins. Hinke (7) recently i n v e s t i  gated this p o s s i b i l i t y . He studied the e f f e c t of high concentrations of ammonium, l y s i n e , arginine and albumin molecules on the response of sodium and potassium s e n s i t i v e microelectrodes. These molecules did a f f e c t the electrodes, p a r t i c u l a r l y the potassium s e n s i t i v e microelectrodes, but the magnitude of the e f f e c t was very small. In a s o l u t i o n containing potassium ions at a concentration of 0.253 M and NH^, l y s i n e or arginine at a concen t r a t i o n of 0.05 M, the potassium microelectrode predicted a f a l s e l y high potassium concentration of 2.1, 1.2 and 0.07, r e s p e c t i v e l y . In a s o l u t i o n containing potassium at the above concentration and albumin at a concentra t i o n of 20 gram 7>, the potassium microelectrode predicted' a f a l s e l y high potassium concentration of about 37,. Thus, i t seems u n l i k e l y that cation s e n s i t i v e glass microelectrodes are greatly affected by e i t h e r proteins or amino acids in the cytoplasm of l i v i n g c e l l s . Robinson (13) has noted that proteins and amino acids have large d i e l e c t r i c increments (of the order of 0.1-1.0 units of d i e l e c t r i c constant per gram/liter) and speculated that "the d i e l e c t r i c constants inside c e l l s may therefore be very considerably greater than those of the r e l a t i v e l y pro t e i n - f r e e solutions outside, with a consequent increase in the a c t i v i t y 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 ions". Three c r i t i c i s m s may be made of t h i s statement. F i r s t , although amino acids would increase the d i e l e c t r i c con stant of a c e l l , proteins may have the reverse e f f e c t i f they are s p a t i a l l y f i x e d . Schwan (14) should be consulted for an excellent review of the d i e l e c t r i c constants of l i v i n g c e l l s . Next, there i s l i t t l e evidence to support the contention that an increase i n the macroscopic d i e l e c t r i c con stant of a s o l u t i o n would r e s u l t in an increase in the a c t i v i t y c o e f f i c i e n t s of the ions i n the s o l u t i o n . (Presumably, the a c t i v i t y c o e f f i c i e n t of the ion i s r e f e r r e d to unity at i n f i n i t e d i l u t i o n of the ion i n water.) There i s a simple r e l a t i o n s h i p between the a c t i v i t y c o e f f i c i e n t s of ions and the d i e l e c t r i c constants of solutions containing molecules l i k e alcohols, which lower the d i e l e c t r i c constant. The a c t i v i t y c o e f f i c i e n t s of ions i n these solutions are markedly r a i s e d (9), not lowered, as one would a n t i c i p a t e from Robinson's statement. Some form of the Debye-Huckel equation would admittedly p r e d i c t a lowering of the a c t i v i t y c o e f f i c i e n t s when the d i  e l e c t r i c constant i s lowered (and v i c e versa), but this e f f e c t , the "secondary medium e f f e c t " i s g r e a t l y overshadowed by the "primary medium e f f e c t " , as discussed by Robinson and Stokes (9, pages 351-357). F i n a l l y , i t should be stressed that there i s not a simple r e l a t i o n s h i p between the d i e l e c t r i c constant and the a c t i v i t y c o e f f i c i e n t s of ions i n solutions of proteins and amino ac i d s . Glycine, for example, causes a marked increase i n the macroscopic d i e l e c t r i c constant of an aqueous solu t i o n (2Z.6 units per mole) but has only a small e f f e c t on the a c t i v i t y c o e f f i c i e n t of NaCl (15, 16). I t may e i t h e r enhance or decrease the a c t i v i t y c o e f f i c i e n t of t h i s s a l t , depending on the r e l a t i v e and t o t a l concentrations of the s a l t and amino acid (16). E d s a l l and Wyman (17, Chapters 5, 6) may be consulted for a discussion of some of the t h e o r e t i c a l approaches to the problem of the e f f e c t of proteins and amino acids on the a c t i v i t y c o e f f i c i e n t s of s a l t s . 57 At present, one can only state that the av a i l a b l e experimental evidence i n  dicates that although the concentrations of amino acids and proteins found i n a barnacle muscle may s i g n i f i c a n t l y a f f e c t the macroscopic d i e l e c t r i c constant of the c e l l , t h i s change should not gr e a t l y a f f e c t the a c t i v i t y c o e f f i c i e n t s of the ions i n the c e l l (16, 7), Bound Water. Many investigators have attempted to measure the f r a c t i o n of "bound water" i n b i o l o g i c a l t i s s u e s . Before some of these re su l t s are considered, i t should again be stressed that the water i n a c e l l probably does not e x i s t i n simple bound and free f r a c t i o n s and that d i f f e r  ent techniques measure d i f f e r e n t properties of the i n t r a c e l l u l a r water. Studies on the swelling of muscle f i b e r s i n hypotonic solutions such as Overton (18) performed can y i e l d l i t t l e information about the state of water i n the c e l l . The sarcolemma i s now known to be permeable to sodium, potas sium and other solutes, and a change i n the osmolarity of the bathing s o l u t i o n w i l l produce a d i f f e r e n t steady state d i s t r i b u t i o n of these s o l  utes. This d i f f i c u l t y was circumvented by H i l l (19), who soaked a muscle i n an approximately equal volume of twice normal strength Ringer s o l u t i o n and determined the vapor pressure of the bathing s o l u t i o n a f t e r e q u i l i b r a  t i o n . I f h i s experimental data are corrected for a numerical error (11) they p r e d i c t that about 27% of the water i n a muscle f i b e r i s "bound". Experiments have been performed on s t r i a t e d muscle to determine the f r a c t i o n of c e l l u l a r water a v a i l a b l e to act as solvent f o r urea (19). The r e s u l t s p r e dict a negative f r a c t i o n of "bound water". 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 molecules; both are small and are capable of forming hydrogen bonds. A s i m i l a r technique has been used by Bozler and Lavine (20) to demonstrate 58 that only about 207, of the c e l l u l a r water in smooth muscle i s a v a i l a b l e to act as solvent for fructose and sucrose. The argument that these sugars do not enter the f i b e r (21) has been countered i n a recent paper by Bozler (22). A nuclear magnetic resonance technique has been used to study the state of water i n muscle (23) and nerve (24). Bratton et a l (23) i n t e r  preted t h e i r r e s u l t s to mean that only about 0.157, of the water i n muscle was "bound" whereas Chapman and McLauchlan (24) concluded that "the bulk of water inside the nerve i s i n a p a r t i a l l y oriented s t a t e " . This technique should prove extremely valuable i n the near future f or i n v e s t i g a t i n g the state of water i n l i v i n g c e l l s , but at the present time there are many d i f f i c u l t i e s i n i n t e r p r e t i n g the r e s u l t s of such studies (25, pages 171- 248). Attempts have been made to c a l c u l a t e the f r a c t i o n of "bound water" i n muscle by free z i n g (26) and microwave (27) techniques, but the r e s u l t s obtained from these experiments may also be interpreted i n a v a r i e t y of ways. A technique has r e c e n t l y been borrowed from c o l l o i d chemistry by Scheuplein and Morgan (28) to measure the f r a c t i o n of "bound water" i n k e r a t i n membranes. They measured the rate of desorption from a hydrated tissue by means of a microbalance technique. Their r e s u l t s indicate that the amount of "bound water" i n f u l l y hydrated stratum corneum can be as much as f i v e times the dry weight of the t i s s u e . The r e s u l t s are i n t e r e s t i n g , but the r e l a t i o n s h i p between the "bound water" ca l c u l a t e d i n t h i s manner and the water unavailable to act as solvent f or solutes i s unknown at present. I t i s obviously important to know the f r a c t i o n of water i n a muscle f i b e r unavailable to act as solvent for the main i n t r a c e l l u l a r c a t i o n , potassium. I t was this f r a c t i o n that was determined d i r e c t l y at 59 25° C i n a normal bathing so l u t i o n by the use of cation s e n s i t i v e microelec trodes. The r e s u l t s indicate that at le a s t 42 ± 1.4% of the water i n the myoplasm i s "bound" i n such a manner that i t i s unavailable to act as solvent for the potassium ions. When the f i b e r s were bathed i n sucrose Ringer f o r 45 minutes the f r a c t i o n of "bound water" i n the c e l l decreased to 34 ± 3.67o. This decrease might r e f l e c t a true change i n the state of water i n the c e l l , but i t could also be due to s t a t i s t i c a l v a r i a t i o n s , an increase i n the a c t i v i t y c o e f f i c i e n t of the myoplasm or an increase i n the binding of potassium. Of these four 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 to be true because the f i b e r s did accumulate potassium i n the sodium free sucrose Ringer s o l u t i o n . The r e s u l t s of the membrane p o t e n t i a l experiments indicate that 27%. of the water i n the c e l l i s "bound". This value, however, should be regarded only 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 of microelectrode measurements, that water i s "bound" i n muscle f i b e r s from the giant barnacle. Bound Sodium. I t was found that at le a s t 84% of the sodium i n muscle f i b e r s from the giant barnacle was excluded from the myoplasm which surrounded the microelectrode. This i s q u a l i t a t i v e l y compatible with the value of 70% that Lev (5) obtained from s i m i l a r measurements on frog muscle, and agrees with Robertson's (29) observation that 82% of the sodium i n lobster muscle could not be extruded by subjecting the muscle to pressure. These r e s u l t s are thus i n accord with the hypothesis that s i g n i f i c a n t amounts of sodium are bound to 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 not of course prove the hypothesis, f o r s i m i l a r r e s u l t s would be expected i f sodium was compartmentalized i n i n t r a c e l l u l a r organ e l l e s rather than bound to proteins. 60 Nuclear magnetic resonance (NMR) measurements may prove useful i n di 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 . I t has been known for several years that the NMR spectrum of sodium i s broadened when sodium i s complexed to polyanions (30-33). The broadening i s presumably due to the o r i e n t a t i o n of the sodium nucleus with respect to the nucleus of a neigh bouring atom. This, i n turn, could be due to the p o l a r i z a t i o n of the outer s h e l l electrons by the proximity of a charge (an i o n i c bond), or the addi t i o n of electrons to the outer o r b i t a l s (a covalent bond). Cope (34, 35) performed experiments on frog muscles and concluded that 70% of the sodium did not contribute to the NMR spectrum. As the compartmentalization of sodium i n organelles should not broaden the NMR spectrum, the r e s u l t would seem to imply that 70% of the sodium i n frog s t r i a t e d muscle i s bound to macromolecules. Unfortunately, ion p a i r formation i s not the only factor which can cause broadening of the NMR spectrum of sodium. For example, i t broadens i n alcohol water mixtures as the volume f r a c t i o n of alcohol i n  creases, and becomes i n v i s i b l e i n 957o or absolute alcohols (33). The a c t i v  i t y of sodium i n a l c o h o l i c solutions i s c e r t a i n l y not lowered because of extensive ion p a i r formation. Indeed, as mentioned e a r l i e r i n this Chapter, the a c t i v i t i e s of ions i n general (9, page 355) and sodium i n p a r t i c u l a r (preliminary experiments) increase markedly i n a l c o h o l i c s o l u t i o n s . The broadening of the NMR spectrum i n a l c o h o l i c solutions requires a proper t h e o r e t i c a l explanation. Also, the p o s s i b i l i t y that the "nuclear spin resonance adsorption of sodium may be al t e r e d by pro t e i n s " (31) indicates that a series of control experiments on concentrated solutions of proteins which are known not to bind sodium should be made. Thus, at the present time, Cope's NMR experiments cannot be accepted as d e f i n i t i v e evidence that there i s no compartmentalization of sodium i n s t r i a t e d muscle f i b e r s . 61 Sodium w i l l of course be contained i n compartments which are formed by invaginations of the sarcolemma. Estimates of the volume of these compartments w i l l be discussed i n Chapter VI. I t need only be noted here that most of the sodium i n these compartments would be expected to d i f f u s e out within 45 minutes i f the f i b e r i s exposed to a sodium free solu t i o n . The f r a c t i o n of "bound sodium" i n f i b e r s bathed for 45 minutes i n sucrose Ringer (0.81) i s approximately the same as that of f i b e r s bathed i n normal Ringer (0.84). Thus, i t may s a f e l y be concluded that most of the sodium i n s i d e the sarcolemma of a s t r i a t e d muscle f i b e r i s e i t h e r bound to macromolecules or compartmentalized in i n t r a c e l l u l a r organelles such as n u c l e i , mitochondria or ciste r n a e . 62 CHAPTER V RELEASE OF BOUND SODIUM A. Inti'oduction The r e s u l t s presented i n the previous chapter indicate that over 80% of the sodium i n s t r i a t e d muscle f i b e r s from the giant barnacle i s not free i n the myoplasm. This f i n d i n g i s consistent with the hypothesis that a s i g n i f i c a n t f r a c t i o n of the sodium i n s t r i a t e d muscle f i b e r s i s bound to myosin. Since extracted myosin releases i t s associated a l k a l i metal cations when i t undergoes thermal denaturation (1), i t was reasoned that myosin i n the l i v i n g c e l l might release i t s associated a l k a l i metal cations during an i r r e v e r s i b l e shortening induced by a change i n temperature. To detect a release of cations from an i n t e r n a l source, the a c t i v  i t i e s of sodium, potassium and hydrogen ions i n the myoplasm were measured when the f i b e r s shortened at 37-40° C i n a sodium free Ringer s o l u t i o n . The t o t a l concentrations of sodium and potassium i n both control and experimen t a l f i b e r s were also measured. The main observation was that during the i r r e v e r s i b l e shortening of the f i b e r the a c t i v i t y of sodium i n the myoplasm increased even though the t o t a l concentration of sodium i n the experimental f i b e r s decreased. B. Methods Experimental Procedure. In each experiment, four muscle f i b e r s from a depressor muscle of Balanus nubilus were dissected free from one another. Before the s t a r t of an experiment, two f i b e r s were cut away from the baseplate, washed for 10 seconds in. isosmotic sucrose, b l o t t e d , and [ 63 placed i n pre-weighed stoppered b o t t l e s for flame photometric a n a l y s i s . One of the two remaining f i b e r s was cannulated as described i n the previous chapter, then transferred with i t s baseplate and companion f i b e r to the experimental chamber. The cation s e n s i t i v e microelectrode was inserted through the cannulated tendon into the myoplasm u n t i l i t s s e n s i t i v e t i p was about 1 cm from the puncture zone (Figs. 2, 3). Deeper penetration was avoided because i t increased the rate of breakage of the microelectrodes during contraction. The membrane p o t e n t i a l of the f i b e r was always measured adjacent to the t i p of the ca t i o n - s e n s i t i v e microelectrode. During an ex periment the open t i p microelectrode was inserted and removed frequently but the c a t i o n - s e n s i t i v e microelectrode was maintained i n i t s i n i t i a l p o s i t i o n . The frequent puncturing of the membrane at the 1 cm l e v e l produced no s i g  n i f i c a n t decrease i n the membrane p o t e n t i a l . From the 1 cm l e v e l to the tendon l e v e l the membrane p o t e n t i a l decreased less than 5 mV, i n d i c a t i n g that the membrane at the fiber-tendon junction was well sealed around the ca t i o n - s e n s i t i v e microelectrode. In the experiments, the muscle f i b e r was exposed to solutions at d i f f e r e n t temperatures. The bath temperature was f i r s t lowered from 25 to 5° C, then was r a i s e d to 40° C. Between 5 and 35° C, the bath temperature was rai s e d i n increments of approximately 5° C by replacing the bathing s o l u t i o n with one at a higher temperature. Above 35° C, the bath tempera ture was increased at the rate of 0.5° C per minute by means of a glass- insulated heating c o i l . The bathing solutions were normal barnacle Ringer s o l u t i o n below 35° C, and sodium free isosmotic sucrose Ringer s o l u t i o n above 35° C (see Table 1 for the composition of these s o l u t i o n s ) . At 40° C, the bath temperature was held constant (39-42° C) u n t i l the experiment was terminated. The experiments involving measurements of potassium and hydrogen 64 a c t i v i t y were terminated a f t e r 15 minutes at 40° C, but the experiments i n  volving measurements of sodium a c t i v i t y were continued u n t i l passed a maximum. Membrane p o t e n t i a l , cation a c t i v i t y , and f i b e r length were record ed at each new temperature. The bath temperature was measured by means of an iron-constantan thermocouple mounted i n the chamber, and f i b e r length was measured.by a m i l l i m e t e r scale. Since i t was c a l c u l a t e d that thermal eq u i l i b r i u m should be v i r t u a l l y 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 i n t e r v a l . Between 35 and 40° C, the microelectrode p o t e n t i a l and bath temperature were recorded continuous l y . During t h i s period, three to f i v e measurements of the membrane poten t i a l and f i b e r length were made. The t o t a l concentrations of sodium and potassium i n the experimen t a l , companion and control f i b e r s were determined by flame photometry i n the experiments i n which a„ and a„ were measured. The f i b e r s were dried, r Na K * digested i n concentrated n i t r i c a c i d , n e u t r a l i z e d with ammonia to prevent the formation of a f l o c c u l a n t p r e c i p i t a t e , and then d i l u t e d to 10 ml before being analyzed on a Unicam SP900 spectrophotometer. Microelectrodes. D e t a i l s of the construction (2, 3) and c a l i b r a  t i o n (Chapter IV) of the c a t i o n - s e n s i t i v e microelectrodes have been de scr i b e d . For these experiments the s e n s i t i v e t i p s of the microelectrodes were made r e l a t i v e l y large (30u. x 2C0fj.) to minimize breakage during contrac t i o n . Eqns. [16] and [17] describe the behavior of the sodium and potassium microelectrodes. The equation which describes the behavior of the 65 pH s e n s i t i v e microelectrode, i s ^ = 4 + S H l o g 1 0 a H [26] where E i s the measured p o t e n t i a l ( m i l l i v o l t s ) of the microelectrode i n a XI I s o l u t i o n containing hydrogen ions at an a c t i v i t y a^; E^ and are constants obtained by c a l i b r a t i o n . The po t e n t i a l s of the sodium and potassium sensi t i v e microelectrodes were not a l t e r e d when the pH was changed from 7 to 8. The p o t e n t i a l s of the pH microelectrodes i n standard pH solutions were not al t e r e d by gross changes i n the Na + and K + content. Since a ^ a and were not measured on the same muscle f i b e r , the following method of analysis was used to cal c u l a t e a M & from Eqn. [16]. The experiments presented i n the previous chapter indicated that a^ , = 1.15 when the f i b e r i s e q u i l i b r a t e d at 25° C in the barnacle Ringer s o l u t i o n . Thus, a^ was estimated from the values of the two con t r o l f i b e r s . I t was assumed that a^ remained constant throughout the experiment, an assumption j u s t i f i e d by the r e s u l t s obtained from the potassium s e n s i t i v e microelec trode ( F i g . 3). Once a^ was estimated, a M & could be calculated from Eqn. [16]. The values of a presented i n F i g . 8 and Table IV were ca l c u l a t e d is. from Eqn. [17], The mean calculated r e s u l t s f o r a m & were used to compensate for the imperfect s e l e c t i v i t y of the potassium electrode. The errors i n t r o  duced by t h i s a n a l y t i c technique should be small because a ^ i s small r e l a t i v e to a^, even though k^ , (Eqn. [17]) i s r e l a t i v e l y large (0.5). Each cation s e n s i t i v e microelectrode was c a l i b r a t e d i n the stan dard solutions before and a f t e r an experiment. I f the c a l i b r a t i o n s v a r i e d by more than ±1 mV the experiment was re j e c t e d . The microelectrodes were 66 c a l i b r a t e d i n the standard solutions at temperatures between 5 and 40° C3 and the appropriate temperature corrections were applied to the experimental microelectrode p o t e n t i a l readings. The precautions taken i n the s e l e c t i o n of open t i p microelectrodes were i d e n t i c a l to those described i n Chapter IV, as was the recording apparatus. The r e s u l t s were analyzed using Eqns. [24] and [25], which describe the separation of the sodium and water content of a sin g l e muscle f i b e r into a " f r e e " and a "bound" f r a c t i o n . To c a l c u l a t e the f r a c t i o n of "bound" sodium, B^ a/(C^ aV), from Eqn. [24], a numerical value must be assigned to OL because both a ^ a and a^ were not measured on the same f i b e r . The f r a c t i o n of water free i n the myoplasm was assumed to be the value ob tained i n the previous chapter (a = 0.57). Results from pure solutions i n d i c a t e that the a c t i v i t y c o e f f i c i e n t should be r e l a t i v e l y independent of temperature (4), but i t must be assumed that a i s independent of tempera ture. This l a t t e r assumption w i l l be j u s t i f i e d when the potassium r e s u l t s are discussed. C. Results Membrane P o t e n t i a l and Shortening. The mean r e s u l t s from the 27 experimental f i b e r s are p l o t t e d i n F i g . 6. When the temperature was r a i s e d from 7 to 25° C, the membrane p o t e n t i a l increased by about 13 mV. This change was found to be r e v e r s i b l e . As the temperature was ra i s e d above 30° C, the membrane p o t e n t i a l decreased. Replacement of the barnacle Ringer s o l u t i o n by sodium free sucrose Ringer at 35° C ("S" i n F i g . 6) did not produce any observable d i s c o n t i n u i t y i n the downward trend of the membrane p o t e n t i a l . 67 The length of the f i b e r s remained constant up to about 37° C. Between 37 and 40° C, a strong spontaneous shortening occurred i n a l l 27 f i b e r s . This event did not seem to be causally 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 following reasons. F i r s t , the membrane p o t e n t i a l v a r i e d from 68 to 33 mV at the onset of the shortening. Second, relaxed, depolarized f i b e r s i n a 250 mM potassium, calcium free Ringer s o l u t i o n did not shorten u n t i l the temperature of t h i s s o l u t i o n was r a i s e d to 37° C. The > < »— Z UJ Z < CO UJ 7 0 l 6 5 - 6 0 - 5 5 - 5 0 - 4 5 - 4 0 - — i — 1 0 — i — 2 0 -1— 3 0 — m 1— 40 : o 10 - 2 - 3 •4 * - 5 2 0 E u a: C O O X O z U J T E M P ( ° C ) T I M E ( m i n ) A T 4 0 ° C F i g . 6. V a r i a t i o n i n the average membrane p o t e n t i a l (closed c i r c l e s ) and f i b e r length (open c i r c l e s ) x^ith temperature and with time at 40° C. At S the barnacle Ringer so l u t i o n was replaced by sodium free sucrose s o l u t i o n . At C a spontaneous shortening occurred i n a l l 27 f i b e r s . V e r t i c a l bars through points are twice the standard error i n length. 63 experimental f i b e r which supported the weight of the baseplate shortened about 50% i n 1 minute, then continued to shorten another 10-20% over the next 15 minutes (Fig. 6). The companion f i b e r supported no weight and shortened from about 4.0 to 0.5 cm. Changes i n I n t r a c e l l u l a r Sodium. The r e s u l t s from a t y p i c a l exper imental f i b e r are shown i n F i g . 7. In t h i s f i b e r , the a c t i v i t y of sodium i n the myoplasm, a ^ a , increased from 0.003 to 0.006 as the temperature was r a i s e d from 7 to 35° C. The average r e s u l t s for t h i s temperature i n t e r v a l , 0 . 0 1 5 n 0 . 0 1 0 - 0 . 0 0 5 - a N a l ' — r 4 0 — i — 3 0 i — 4 0 - T — 1 0 ~ i — 2 0 ~ i — 3 0 i 1 0 i 2 0 T E M P ( ° C ) T I M E ( m i n ) A T 4 0 ° 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 ) . , of a t y p i c a l muscle f i b e r as the temperature was increased to 40° C. Tne~symbols S and C are defined i n F i g . 6. Open c i r c l e s represent the-measurements i n Table I I I . however, revealed no s i g n i f i c a n t increase i n & a^. When the normal Ringer s o l u t i o n was replaced by sodium free sucrose Ringer at 35° C ("S" i n the f i g u r e ) , a ^ a always decreased, i n d i c a t i n g that sodium ions were moving out of the f i b e r . A f t e r the f i b e r shortened at 37-40° C, a„T always increased. * Na J This increase was u s u a l l y recorded within 1 minute and always wi t h i n 5 minutes a f t e r shortening. In t h i s experiment, a ^ a increased from 0.004 to 0.015 i n 44 minutes. In other experiments, maximum a„ values were ob- ' Na tained e a r l i e r . (Table I I I ) . TABLE I I I Sodium concentration* and a c t i v i t y * i n single muscle f i b e r s before (25° C) and a f t e r (40° C) shortening. 1 " <e**J%a>t <CNa>25 ^Na^O Minutes at 40° CT ( aNa }25 (JW40 25° C 40° C 0.058 0.046 11 0.009 0.014 0.86 0.73 0.076 0.053 21 0.007 0.018 0.92 0.70 0.060 0.060 45 0.009 0.037 0.87 0.46 0.085 0.052 38 0.010 0.017 0.90 0.71 0.123 0.051 14 0.005 0.007 0.96 0.88 0.099 0.069 40 0.005 0.012 0.96 0.85 0.163 0.099 18 0.011 0.023 0.94 0.79 0.080 0.123 27 0.008 0.010 0.91 0.93 0.061 0.055 44 0.004 0.015 0.94 0.76 0.081 0.085 35 0.006 0.011 0.93 0.89 0.089 0.069 0.007 0.016 0.92 0.77 ±0.010$" ±0.008 ±0.001 ±0.003 ±0.01 ±0.04 *Moles/kg f i b e r water. *Time at 40 C f o r C 3 ^ ) ^ t o reach a maximum value. ^Fraction of bound Na calculated from Eqn. [24], §Mean ± standard error of the mean. Ind i v i d u a l data f o r the 10 experimental f i b e r s are presented i n Table I I I . The average t o t a l sodium concentration of the two control f i b e r s analyzed at the s t a r t of the experiment i s denoted as (^3)^5* s o c ^ u m a c t i v i t y i n the experimental f i b e r s measured at 25° C (open c i r c l e , F i g . 7) i s denoted as (a^T )-, r. The (C T ) l r . and (a_T columns l i s t the sodium con-N Na 25 Na 40 Na 40 centrations and a c t i v i t i e s i n the experimental f i b e r s at the end of the experiment (open c i r c l e , F i g . 7). The l a s t two columns of the table l i s t the bound f r a c t i o n s of sodium c a l c u l a t e d from the data by Eqn. [24], A comparison of (G.T )_.r and (C,T ),_ indicates that the f i b e r s l o s t r v Na'25 N Na'40 sodium during the experiment. A l l the sodium loss probably occurred a f t e r the f i b e r s were immersed i n the sodium free sucrose Ringer s o l u t i o n . A comparison of (^3)^5 a n < ^ ^aNa^40 ^ e i R o n s t r a t e s the consistent increase i n a a f t e r the onset of shortening ( F i g . 7). Since sodium could not enter the f i b e r from a sodium free bathing s o l u t i o n , and since i t has been shown that sodium ions were i n f a c t leaving the f i b e r , i t may be concluded that e i t h e r sodium ions were released from an i n t e r n a l s i t e , or that there was a large reduction i n the myoplasmic free water. Since t h i s l a t t e r a l t e r n a t i v e demands a proportional increase i n the a c t i v i t i e s of a l l myoplasmic cations, i t can be ruled out because a^ remained r e l a t i v e l y constant (Fig. 8). Thus, i t may be concluded that the increase i n a„ r e s u l t s from a release of 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 Table I show that the average percentage reduction i n the f r a c t i o n of "bound" sodium was 16 ± 4 (0.92 to 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 from seven experimental f i b e r s are 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, there was no s i g n i f i c a n t change i n a^. Immediately a f t e r shortening, changed only from an average of 0.130 ± 0.006 to an average of 0.140 ± 0.008. For 15 minutes a f t e r shortening, a^ decreased slowly. 71 0.160- 0.130- 0.100- (°K)i —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 of potassium, (su.) ., of seven f i b e r s as the temperature was increased to 40° C. The shape or the curve (broken l i n e ) between 35 and 40 C was deduced from indvidual experi ments. The symbols S and C are defined i n F i g . 6. Open c i r c l e s represent the measurements in Table IV. V e r t i c a l bars through points are twice the standard error i n length. I n d i v i d u a l data for the seven f i b e r s are given i n Table IV. The columns denoted as ( C j r ) ^ , ( GK?40' ^ ^ 2 5 a n d ^ AK^40 ^ a v e t h e s a m e S 1 § n i f i - cance as comparable columns for sodium i n Table I I I . Comparison of the (CL,)-,. and (C ) . values demonstrates that the f i b e r s l o s t s i g n i f i c a n t quantities of potassium ions, probably during the period of dep o l a r i z a t i o n at 40 C (Fig. 6); yet comparison of the ( a ^ ) ^ and ( a K ) ^ Q values shows that 72 TABLE IV Potassium concentration* and a c t i v i t y * i n si n g l e muscle f i b e r s before (25° C) and a f t e r (40° C) shortening. <CK>25 <CK>40 ( aK>25 <aK>40 0.176 0.144 0.123 0.146 0.184 0.155 0.154 0.133 0.174 0.167 0.150 0.127 0.160 0.134 0.108 0.105 0.162 0.124 0.137 0.121 0.172 0.141 0.150 0.133 0.163 0.147 0.147 0.150 0.170 0.145 0.138 0.131 +0.003f ±0.005 ±0.006 ±0.006 *Moles/kg f i b e r water. TA f t e r 15 minutes at 40° C. TMean ± standard error of the mean. the a c t i v i t y of potassium i n the myoplasm was not s i g n i f i c a n t l y a l t e r e d . There are two possible explanations for these r e s u l t s ; e i t h e r potassium ions are released into the myoplasm from an i n t e r n a l s i t e , or water i s removed from the myoplasm to an i n t e r n a l s i t e . I f i t i s assumed that the f i r s t explanation i s correct, and further assumed that a l l the bound potassium ions are released during shortening, Eqn. [19] predicts that only 107o of the t o t a l f i b e r potassium need be bound and released to explain the r e s u l t s . A l t e r n a t i v e l y , i f i t i s assumed that the second explanation i s corre c t , and further assumed that there i s no binding of potassium either at the beginning or the end of the experiment, Eqn. [19] predicts that the f r a c t i o n of bound water must increase by 107, at the expense of the myoplas- mic free water. I t should be emphasized that neither of these p o s s i b i l i t i e s a l t e r s the conclusions 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 ten 73 8.On 7.6- 7.2 6.8H pH EXTERNAL INTE ~ i — 10 1 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 of the myoplasm (internal) of 10 f i b e r s as the temperature was increased to 40° C. The v a r i a t i o n of pH in the bath s o l u t i o n with temperature (external) was also measured and is shown as a t h i n l i n e . The shape of the curve (broken l i n e ) between the experimental points at 35 and 40 C was deduced from i n d i v i d u a l experiments. The symbols S and C are defined i n F i g . 6. V e r t i c a l bars through points are twice the standard error i n length. experimental f i b e r s i n x^hich the pH was measured are plo t t e d i n F i g . 9. Be tween 7 and 30° C a l i n e a r decrease i n pH was observed in both the myoplasm and the bath s o l u t i o n . In both cases, the pH changes were probably due to the temperature dependence of the buffer systems. I t i s u n l i k e l y that the myoplasmic pH changes were due to an inward d i f f u s i o n of hydrogen ions because of the short time i n t e r v a l between measurements. Above 30 C the 74 rate of change of the i n t e r n a l pH increased s l i g h t l y . At 35° C, no change i n i n t e r n a l pH was observed when the bath s o l u t i o n was changed to sodium free sucrose Ringer. When shortening occurred ("C" i n the figures) the pH dropped suddenly i n a l l ten f i b e r s . The average drop i n pH was from an extrapolated value of 7.17 at 40° C to a measured value of 6.85 ± 0.04 at 40° C. Ten minutes a f t e r the onset of shortening the pH reached an average mininum value of 6.77 ± 0.05. These r e s u l t s leave l i t t l e doubt that a sudden reduction i n myoplasmic pH occurred at the onset of shortening. D. Discussion V a r i a t i o n s i n Membrane P o t e n t i a l . The changes in membrane poten t i a l with temperature ( F i g . 6) warrant comment even though they are secondary to 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  creased by 13.0 mV, yet there was no s i g n i f i c a n t change i n eit h e r a M ^ or a^. Assuming that membrane permeability to sodium and potassium remains constant, i t may be cal c u l a t e d from the Goldman equation (5) that the membrane poten t i a l should only increase 3.4 mV over this temperature range. This anomalous dependence of membrane p o t e n t i a l on temperature, also observed by Frumento (6) i n frog muscle, may be due to eit h e r a decrease i n the cation permeability r a t i o (P /P„) or the existence of an electrogenic pump (7-11). Na K. I n t r a c e l l u l a r Sodium and Water "Binding". The a c t i v i t y and con centration values measured here are s i m i l a r to those reported i n the previous chapter, hence they confirm q u a l i t a t i v e l y the o r i g i n a l conclusions about sodium and water "binding". The calculated mean f r a c t i o n of "bound" sodium was 0.92 ± 0.01 i n the present experiments and 0.84 ± 0.00 in the previous experiments (Chapter IV). The l a t t e r estimate i s probably more r e l i a b l e because i t was calculated from aA, a„. C M and C., measurements on Na K> Na K the same muscle f i b e r . The calculated mean f r a c t i o n of "bound" water, (i-Oc) , was 0.27 ± 0.03 i n the present experiments and 0.41 ± 0.01 i n the previous experiments (Chapter IV). Both c a l c u l a t i o n s were based on the assumptions leading to Eqns. [24] and [25]. The previous estimate is believed to be more r e l i a b l e f or reasons s i m i l a r to those given f or the bound sodium f r a c t i o n . I t i s p o s s i b l e , however, that the discrepancy between the r e s u l t s i s r e a l because the barnacles were c o l l e c t e d from d i f f e r e n t locations i n d i f f e r e n t seasons and stored i n sea water at d i f f e r e n t temperatures (4 and 10° C). Hinke (3), i n a recent independent series of measurements also found that the f r a c t i o n of "bound" water i n barnacles taken from the second l o c a t i o n and stored at 10° C was low; (1-a) = 0.26. (Note that i f a i s assumed to have a value of 0.73 instead of 0.59, the f r a c t i o n of "bound" sodium ca l c u l a t e d from the data of Table I I I changes by only a small amount; from 0.92 to 0.90.) Another p o s s i b i l i t y i s that an e l e c t r i c a l error 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 microelectrode measurements either i n the present or the previous experiments. I t can be- shown, for example, that a 6 mV err o r i n the potassium p o t e n t i a l (E^, i n Eqn. [17]) could produce the discrepancy i n the calculated "bound" water f r a c t i o n s whereas a 6 mV error i n the sodium p o t e n t i a l ( E ^ a i n Eqn. [16]) would not a l t e r the magnitude of the "bound" sodium f r a c t i o n . Such an error i s u n l i k e l y , however, because of the c a r e f u l s e l e c t i o n of open-tip microelectrodes, and the r e j e c t i o n of experiments when the c a t i o n - s e n s i t i v e microelectrode p o t e n t i a l s i n standard solutions deviated by more than 1 mV. Release of Bound Sodium. I t was demonstrated that an increase i n the mean a„ occurred when the muscle f i b e r s shortened due to exposure to 76 temperatures between 37 and 40° C (Fig, 6 and Table I I I ) . This increase was not due to an inward d i f f u s i o n of sodium ions because no sodium ions were in. the bathing s o l u t i o n . I t i s u n l i k e l y that the increase re 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 during shortening the p o t e n t i a l of the potassium s e n s i t i v e microelectrode did not change s i g n i f i c a n t l y ( F ig. 8) and the poten t i a l of the hydrogen s e n s i t i v e microelectrode changed more r a p i d l y than that of the sodium s e n s i t i v e microelectrode (Figs. 9 and 7). As a M Q decreases i n sucrose Ringer at 25° C ( F i g . 18), i t may be concluded that the increase i n a„ , and the corresponding 1670 reduction i n B„ / (C„ V) , observed i n the Na' Na Na '' present experiments are causally r e l a t e d to the shortening induced by a change in temperature. I t may also be concluded that the increase i n a^ a, or the release of "bound" sodium, i s c h a r a c t e r i s t i c of a temperature induced shortening, but probably not of a normal contracture. When barnacle muscle f i b e r s were contracted at 25° C by exposure to a s o l u t i o n containing 0.064 M KC1, a M ^ was found to be 98 ± 4% (9 experiments) of the i n i t i a l value of t n e same f i b e r bathed i n normal Ringer) a f t e r 4 minutes in the high potassium s o l u t i o n , and 97 ± 67o (9 experiments) of the i n i t i a l value a f t e r 8 minutes i n the high potassium s o l u t i o n (preliminary experiments). Myoplasmic pH. Since the pH of the myoplasm was 7.43 and the pH of the bathing s o l u t i o n was 7.54 at 25° C, the e q u i l i b r i u m p o t e n t i a l for the hydrogen ion was 6 mV. The average membrane p o t e n t i a l at t h i s temperature, however, was 66 mV. Thus, hydrogen ions are not d i s t r i b u t e d between the myoplasm and the bathing s o l u t i o n according to the Nernst equation. Similar r e s u l t s have been reported for muscles of the crab (12) and frog (1.3) , although not for r a t s k e l e t a l muscles (14). A large, rapid decrease in myoplasmic pH occurred when the muscle f i b e r s shortened. The r a p i d i t y of the decrease indicates that i t was not due to hydrogen ions d i f f u s i n g into the f i b e r from the bathing s o l u t i o n . Even i f hydrogen ions did d i f f u s e into the f i b e r , no change i n pH would be observed because of the large buffer capacity of the myoplasm. This was demonstrated i n experiments performed i n depolarized f i b e r s (12, 13), and also by the pH experiments reported i n Chapter VI of th i s t h e s i s . There fo r e , the pH change observed at 37-40° C i n these experiments was due to a change i n the pK of the organic buffers i n the myoplasm. Since the contrac t i l e proteins constitute the main organic buffer, the change in the pK values probably s i g n i f i e s a disruption of the myofilaments. Location of Bound Sodium. The basic hypothesis of t h i s report i s that a s i g n i f i c a n t f r a c t i o n of the sodium i n s t r i a t e d muscle f i b e r s i s bound to myosin. I t i s known (1) that extracted myosin undergoes thernal denatur ati o n at a lower temperature (37° C) than extracted a c t i n (50° C). I t i s also known that when extracted myosin i s exposed to temperatures above 37° C i t releases associated a l k a l i metal cations (1) and ATP molecules (15). Thus, the object of these experiments was to disrupt the thick or A f i l a  ments i n an i n t a c t f i b e r and observe any changes i n the f r a c t i o n of "bound" sodium. There are several reasons for b e l i e v i n g that e i t h e r the A or the I filaments were s t r u c t u r a l l y a l t e r e d at 37-40° C: (i) an i r r e v e r s i b l e shortening occurred at this temperature, ( i i ) calcium ions were not re quired i n the bathing s o l u t i o n for t h i s shortening, (page 67), ( i i i ) the shortening occurred independently of changes i n the membrane p o t e n t i a l and (iv) a large, r a p i d decrease i n pH accompanied the shortening. Experiments performed on glycerinated muscles, as well as on ex-tracted proteins, indicate that i t was the A and not the I filaments that were disrupted i n these experiments at 37-40° C. Thermal d i s r u p t i o n of the A filaments was observed by Aronson i n glycerinated muscles (16). A f t e r heating the muscles for 2 minutes at a c r i t i c a l temperature (which v a r i e d from 43.5° C for frog to 51° C for mouse muscle) he observed a decrease in the birefringence of the muscle, and a loss i n the A filament structure as seen under the electron microscope. The shortening and the decrease in the myoplasmic pH of barnacle muscle f i b e r s exposed to temperatures of 37-40° C are probably re l a t e d to the thermal d i s r u p t i o n of the A filaments that Aronson observed. The myosin molecules, themselves, however, need not be completely denatured when the breakdown of the A filaments occurs. In f a c t , a v a i l a b l e evidence indicates that a slow denaturation of the myosin mole- o cules should occur at 37 C, for i t takes about 1 hour f o r the v i s c o s i t y of extracted myosin to double at t h i s temperature (1). Consistent with t h i s f a c t i s the observation that in barnacle muscles the release of "bound" sodium at 37-40° C occurs over a period of about 1/2 hour. The r e s u l t s presented i n this chapter are thus i n excellent agree ment with the hypothesis that much of the sodium i n an i n t a c t s t r i a t e d muscle f i b e r i s bound to myosin. I t must be admitted, however, that the data could be interpreted i n a d i f f e r e n t manner. I t could be argued that the increase in a,T observed at 37-40° C was due to a release of sodium Na from i n t r a c e l l u l a r compartments such as n u c l e i , mitochondria or the c i s t e r - nae of the sarcoplasmic reticulum. This explanation seems u n l i k e l y f o r the following reasons. F i r s t , a ^ & does not increase following a potassium i n  duced contracture at 25° C (preliminary experiments). Thus, i t must be argued that the membranes are disrupted by the temperature, not the shorten ing, i n such a way as to allow sodium to e x i t from the compartments. Note 79 however, that a.T always decreased between 35° C and the temperature at which ' Na shortening occurred (Fig. 7). The membrane p o t e n t i a l v a r i e d between 68 and 33 mV at the time of shortening, but no increase i n a„ was noted u n t i l °> Na a f t e r the shortening occurred. Thus, there i s a f a r better 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 shortening and the increase i n a„ than there i s ° Na between the membrane p o t e n t i a l and the increase i n a., . r Na In summary, i t has been demonstrated that a s i g n i f i c a n t release of "bound" sodium occurs following an i r r e v e r s i b l e shortening induced by a temperature change. I t was argued that t h i s shortening was r e l a t e d to a dis r u p t i o n of the thick or A filaments, an i n d i c a t i o n that at le a s t part of the f r a c t i o n of "bound" sodium i n s t r i a t e d muscle f i b e r s i s associated with myosin. 80 CHAPTER VI / OPTICAL DENSITY CHANGES OF FIBERS IN SODIUM FREE SOLUTIONS A. Introduction The o p t i c a l experiments reported below were undertaken to obtain further evidence that some of the sodium i n s t r i a t e d muscle f i b e r s which i s unavailable to a sodium s e n s i t i v e microelectrode i s bound rather than com partmentalized. The idea of using l i g h t s c a t t e r i n g measurements to detect the binding of ions to macromolecules i s not new. E d s a l l and h i s coworkers (1) u t i l i z e d t h i s technique to measure the binding of ch l o r i d e , calcium and thiocyanate ions to protein serum albumin. L i g h t i s scattered from a c o l l o i d a l s o l u t i o n because of l o c a l f l u c t u a t i o n s i n r e f r a c t i v e index. These are due to f l u c t u a t i o n s i n concen t r a t i o n caused by random thermal motion, which in turn are counteracted by the increase i n free energy which a r i s e s from the f l u c t u a t i o n . Fluctuations i n concentration contribute p r o p o r t i o n a l l y to the square of the r e s u l t i n g f l u c t u a t i o n s i n r e f r a c t i v e index. E d s a l l et a l (1) extended the f l u c t u a  t i o n theory to multicomponent systems containing charged macromolecules, while Doty and Steiner (Z) approached the problem v i a the interference theory. Both these approaches are discussed i n a review a r t i c l e (3). The t h e o r e t i c a l basis for i n v e s t i g a t i n g the binding of ions to 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 2c) / (Zm3M2) [27] which describes the r e l a t i o n between the t u r b i d i t y , T, of an i d e a l three component system (consisting of water., s a l t and macro-ion s a l t ) and the net 81 charge, Z, on the macro-ion. The term H represents a c o l l e c t i o n of o p t i c a l constants and va r i e s inversely with the fourth power of the wavelength. The terms c and M represent r e s p e c t i v e l y the concentration and molecular weight of the macro-ion while m^  represents the concentration of the micro-ion of opposite charge. This simple r e l a t i o n can be derived by applying the con d i t i o n of Donnan equilibrium to a system for which the i o n i c strength i s not too low and by considering only e l e c t r o s t a t i c i n t e r a c t i o n s (1, 2, 3). I t i s apparent, from Eqn. [27] that increasing the net charge, Z, on the macro-ion decreases the turbidity,'?" , of the s o l u t i o n . I t was reasoned that i f sodium was bound to negatively charged macromolecules within the barnacle muscle, bathing the f i b e r i n a sodium free s o l u t i o n would cause sodium to move o f f the binding s i t e s and out of the f i b e r . I f no ion replaced sodium on the binding s i t e s , the net charge of the macromolecules would increase, and the t u r b i d i t y of the f i b e r would decrease. Thus, muscle f i b e r s bathed i n sodium free solutions were examined for any decrease i n t u r b i d i t y . B. Methods Determination of A c t i v i t i e s and Concentrations. The sodium sensi t i v e microelectrodes were c a l i b r a t e d i n solutions containing both sodium and potassium (Chapter IV) as well as i n solutions containing 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 . The hydrogen s e n s i t i v e micro electrodes were c a l i b r a t e d i n standard buffers of pH 7 and 8. The micro electrodes were c a l i b r a t e d before and a f t e r each experiment and the r e s u l t s were rejected unless the c a l i b r a t i o n s coincided (±1 mV). Conventional open t i p microelectrodes f i l l e d with 3 M KC1 were used to measure the membrane p o t e n t i a l of the f i b e r s . (The membrane p o t e n t i a l was of course subtracted from the p o t e n t i a l recorded from the. sodium s e n s i t i v e microelectrode i n the 82 TABLE V Solutions (M) * Normal Ringer Sucrose Ringer T r i s Ringer Calcium free Ringer Potassium Ringer Lithium Ringer NaCl .450 .000 .000 .480 .000 .000 C a C l 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 L i C l .000 .000 • .000 .000 .000 .450 Sucrose .000 .650 .000 .000 .000 .000 The pH of every s o l u t i o n i n t h i s table was 7.6. Normal Ringer buffered to pH = 9.6 with t r i s or to pH = 5.5 with CO., was also used f o r some experi ments . myoplasm.) The precautions taken i n the s e l e c t i o n of these microelectrodes, the c a l i b r a t i o n procedure and the recording apparatus were i d e n t i c a l to those described i n Chapter IV. The sodium s e n s i t i v e microelectrodes were used to measure the a c t i v i t y of sodium i n the myoplasm of f i b e r s bathed i n sucrose and l i t h i u m Ringer. The hydrogen s e n s i t i v e microelectrodes were used to measure the pH of the myoplasm of f i b e r s bathed i n pH = 9.6 and pH = 5.5 Ringer. The com pos i t i o n s of the bathing solutions used i n these experiments i s given i n Table IV. An a l y t i c measurements were not made on f i b e r s used for micro electrode experiments. Separate experiments were conducted to determine the movement of a l k a l i metal cations when the f i b e r s were bathed i n l i t h i u m and 83 sucrose Ringer. Seven f i b e r s attached to a sing l e baseplate were dissected free from one another i n normal Ringer. Two f i b e r s were taken as cont r o l s ; they were b l o t t e d , swirled for 30 seconds iniso-osmotic sucrose, b l o t t e d again, then placed i n pre-weighed b o t t l e s . The remaining 5 f i b e r s were suspended by t h e i r tendons i n the bath which contained e i t h e r sucrose or li t h i u m Ringer, removed at 1, 3, 5, 10 and 25 minutes and handled i n the same manner as the co n t r o l s . The f i b e r s were then dried and digested i n n i t r i c a c i d . The r e s u l t i n g s o l u t i o n was ne u t r a l i z e d with ammonia, d i l u t e d to 10 ml and analyzed for sodium and potassium (and l i t h i u m i f applicable) on a Unicam SP 900 flame spectrophotometer; Determination of Relative Optical Density. As shown i n F i g . 10, a single muscle f i b e r was suspended by i t s tendon i n a cl e a r perspex chamber containing normal Ringer. The baseplate of 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 stretched to about 120% of i t s r e s t i n g length. The chamber was then positioned i n a Beckman B spectrophotometer (Fig. 10) and the o p t i c a l density (O.D,,) measured for 10 minutes to ensure i t s con stancy. In the f i r s t series of experiments, the s l i t width remained con stant while the O.D. was determined at various wavelengths. Normal Ringer was then replaced by sucrose Ringer and the O.D. measured for 25 minutes at a sing l e wavelength. A f t e r this period of time the O.D. was again measured at various wavelengths. Sucrose Ringer was then replaced by normal Ringer, and a f i n a l scan of wavelengths made a f t e r 25 minutes. In a l l other exper iments, O.D. measurements were made only at 850 mu,. Some pertinent experimental d e t a i l s are as follows. The spectro photometer was equipped with a constant voltage transformer, and was always turned on one hour p r i o r to an experiment. The wavelength d i a l was 84 Cannula • gated tendon 5 c m Muscle fibre (diam. 1-3 mm) J ii/^~"t^~ Baseplate Drain Light from Ferry prism Variable slit «.l mm Perspex^chamber Shutter !' ^ Muscle fibre 1 1 / Lens 1 / Phototube 2mm c 1 slit , 6 m m  S I 1 T exit slit F i g . 10. Diagram of a sing l e muscle f i b e r positioned i n the perspex bathing chamber ( l e f t ) , and plan view of the o p t i c a l pathway ( r i g h t ) . c a l i b r a t e d with a mercury lamp. A l l bathing solutions were f i l t e r e d before use to remove dust p a r t i c l e s . The chamber f i l l e d with the bathing s o l u t i o n was used as the blank at a l l wavelengths. I f the f i n a l and i n i t i a l blank readings did not coincide ( ± 2 % ) , the experimental r e s u l t s were re j e c t e d . The width of the beam was always less than 1/2 the width of the f i b e r , and usu a l l y much less because large, f l a t f i b e r s were selected f o r these' experi ments. A l l experiments were conducted at room temperature ( 2 3 - 2 5 ° C ) . Limitations of the Experimental Apparatus and Method. The o p t i c a l 85 density, O.D., i s defined i n Eqn. [28] O.D. = - l o g 1 0 ( I / I o ) [28] where I / I D represents the transmittance, or the r a t i o of the transmitted to the incident i n t e n s i t y . The t u r b i d i t y , T, i s defined as the r a t i o of the t o t a l l i g h t scattered to the product of the incident i n t e n s i t y of l i g h t and volume of s o l u t i o n (or muscle) which scatters l i g h t . I t may be expressed as an e x t i n c t i o n c o e f f i c i e n t , and when absorption i s n e g l i g i b l e , where L i s the o p t i c a l path length-of the beam i n the muscle f i b e r . I t i s apparent from Eqns. [28] and [29] that i n the absence of absorption the t u r b i d i t y of the f i b e r r e l a t i v e to i t s i n i t i a l value i n normal Ringer i s equal to the O.D. of the f i b e r r e l a t i v e to i t s i n i t i a l value i n normal Ringer. In the presence of generalized absorption, Eqn. [29] must be modi f i e d , and to a f i r s t approximation 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 to absorption. A simple algebraic manipulation can then be made to show that the change i n r e l a t i v e t u r b i d i t y i s always greater than the change i n the r e l a t i v e O.D. (Appendix 1). Thus, a possible constant absorption was accepted as an error because the change i n the t u r b i d i t y of the f i b e r was underestimated. This error w i l l decrease as the wavelength of incident l i g h t increases because generalized absorption decreases Xfith increasing wavelength. In these experiments, the height of the l i g h t beam was 19 mm at the l a s t entrance s l i t , about 12 mm at the muscle and 6 mm at the e x i t s l i t . The theory of l i g h t s c a t t e r i n g assumes p a r a l l e l indicent l i g h t , but many T = -(2.303/O l o g 1 0 ( I / I o ) [29] = -(2.303/JL) l o g 1 ( ) ( I / I o ) [30] investigators use converging l i g h t for scattering measurements, and as Stacey (4) has stated " i n p r a c t i c e the error due to the use of converging l i g h t has not been a serious one." A more serious error a r i s e s from the f a c t that the l i g h t beam could not be p r e c i s e l y focussed. The width of the l i g h t beam increased from less than .2 mm at the entrance s l i t to .6 mm at the e x i t s l i t . Thus, the diverging width of the beam forced the e x i t s l i t to have a width of .6 mm. A smaller e x i t s l i t would have c o l l e c t e d less l i g h t scattered through very small angles. This error, however, implies that the measured change i n O.D, i s less than the change i n 'Y, hence i t was accepted (Appendix 2). In any hig h l y turbid medium l i k e a muscle f i b e r , secondary scatter ing complicates the i n t e r p r e t a t i o n of l i g h t s c a t t e r i n g measurements. When the s c a t t e r i n g p a r t i c l e s have one dimension greater than 1/20 of the wave length of the incident l i g h t , i n t e r n a l interference also occurs. Doty and Steiner (5) have discussed t h i s phenomenon i n an a r t i c l e on the spectro photometry measurement of t u r b i d i t y . Although both secondary s c a t t e r i n g and i n t e r n a l interference must be considered when the absolute t u r b i d i t y of a s o l u t i o n i s measured, these factors probably may be ignored when the r e l a t i v e t u r b i d i t y of muscle f i b e r s i n various solutions i s measured. The e f f e c t of i n t e r n a l interference on the t u r b i d i t y should remain constant throughout the experiment. The existence of secondary s c a t t e r i n g implies that the actual change i n t u r b i d i t y i s greater than the change i n 0 oD. that i s measured and t h i s e f f e c t can be minimized by making measurements at long wavelengths. C. Results Sucrose Ringer. F i g . 11 summarizes the flame photometric measure-87 ments of the sodium and potassium concentrations of f i b e r s soaked for vary ing times i n sodium free sucrose Ringer. The a c t i v i t y of sodium i n the myo plasm. a„ . i s also shown. Since the sodium s e n s i t i v e microelectrodes were c ' Na' not absolutely s e l e c t i v e for sodium a small c o r r e c t i o n for the a c t i v i t y of potassium i n the myoplasm, a^, was applied to the electrode readings (Eqn. [16]). The value of a^ . was not measured i n these experiments, but was 4 > o Z O < z o ,801 1 6 0 - ° 1 4 0 H 1 2 0 - 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0 - [ K + ] - 5 - 1 T r- 5 1 0 1 5 2 0 T I M E | m i n ) I N S O D I U M F R E E S U C R O S E R I N G E R 2 5 F i g . 11. The t o t a l concentrations of sodium and potassium i n f i b e r s bathed i n sodium free sucrose Ringer. I n i t i a l points are the average of measure ments from 20 f i b e r s . Other points are the average of measurements from 10 f i b e r s . 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 microelectrode, i s also shown. The number of experiments, n, was 5. The v e r t i c a l bars are twice the S.E. i n length. 88 estimated from the measured average concentration of potassium (Fig. 11) using the empirical r e l a t i o n a^ , = .87[K] (Chapter V). From the data presented i n Chapter IV, i t was calculated that the percentages of t o t a l f i b e r sodium unavailable to a microelectrode when f i b e r s were bathed i n normal and sucrose Ringer were 84% and 81% respective l y . In comparison, the calculated values from the data of F i g . 11 are 85%, and 807o. These estimates do not take into account the large e x t r a c e l l u l a r space which was recently discovered i n sing l e barnacle muscle f i b e r s (5). This compartment was found to comprise about 57, of the t o t a l f i b e r volume by two independent techniques, and i t presumably contains about .030 moles of sodium/kg f i b e r water (6). I f the t o t a l concentration of sodium i n f i b e r s bathed i n normal Ringer, .066 moles/kg f i b e r water (Fig. 11), i s corrected for the sodium i n the e x t r a c e l l u l a r compartment, the percentage of i n t r a c e l l u l a r sodium unavailable to the microelectrode i n normal Ringer becomes 72%. This value increased to 80% when the f i b e r s were bathed f o r 25 minutes i n sucrose Ringer. Thus, the previous observation (Chapter IV) that the f r a c t i o n of t o t a l f i b e r sodium unavailable to the microelectrode decreased 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- plained by the large e x t r a c e l l u l a r space of the f i b e r s . The transmittance of sing l e muscle f i b e r s i s graphed i n F i g . 12 as a function of wavelength. The lower curve i s the transmittance of the f i b e r s i n normal Ringer and the upper curve i s the transmittance of the same f i b e r s a f t e r 25 minutes i n sucrose Ringer. The apparent d i s c o n t i n u i t y i n the curves between 600 and 650 mu. i s an a r t i f a c t which arises because a d i f f e r e n t group of f i b e r s had to be used for the wavelengths below 600 and above 650 mu,. No d i s c o n t i n u i t y was observed i n the transmittances of two 6 0 I 1 1 1 1 1 1 1 1 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 W A V E L E N G T H (mM) F i g , 12. The transmittance of sing l e muscle f i b e r s i n normal Ringer (lower curve) and a f t e r 25 minutes i n sucrose Ringer (upper curve) as a function of wavelength. f i b e r s which were scanned from 600 to 900 imj. i n normal and sucrose Ringer. I t i s apparent from F i g . 12 that at a given wavelength the transmittance of a muscle f i b e r i s greater i n sucrose than i n normal Ringer. Note also that i n e i t h e r sucrose or normal Ringer, the transmittance increases with wave length. In an ide a l s o l u t i o n , 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 with the fourth power of the wavelength. This implies that a p l o t of the log of the t u r b i d i t y (or O.D.) against the log 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 with a slope of -4. This r e l a t i o n s h i p was not observed for si n g l e muscle f i b e r s , although the data of F i g . 12 i l l u s t r a t e s that the transmit tance does increase with the wavelength. The deviation from the inverse fourth power r e l a t i o n s h i p i s presumably due to the existence of i n t e r n a l i n  terference, secondary s c a t t e r i n g and absorption. Internal interference alone can change the inverse fourth power r e l a t i o n s h i p between t u r b i d i t y and wave length to an inverse square r e l a t i o n s h i p (4). The transmittance of a muscle f i b e r i s dependent on the thickness F i g . 13. The o p t i c a l density, O.D., of si 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 value of the O.D. i n normal Ringer as a function of wavelength. The data i n curve 2 are from f i b e r s bathed for 25 minutes i n sucrose Ringer; the data i n curve 3 are from the same f i b e r s 25 minutes a f t e r they were returned to normal Ringer. 91 of the f i b e r or o p t i c a l path length. This dependence on o p t i c a l path length can be avoided by considering the r e l a t i v e o p t i c a l density (O.D.) of a f i b e r ( F i g . 13) rather than the transmittance. The r e l a t i v e O.D. drops from an i n i t i a l value of 1 (curve 1, F i g . 13) i n normal Ringer to low values (curve 2, F i g . 13) a f t e r 25 minutes i n sucrose Ringer. The la r g e s t change occurs at the longest wavelength where the errors due to possible absorption, s c a t t e r i n g through small angles and secondary s c a t t e r i n g are minimal. Curve 3, F i g . 13, shows that t h i s phenomenon i s almost completely r e v e r s i b l e . When normal Ringer was returned to the chamber, the r e l a t i v e O.D. of the f i b e r s increased w i t h i n 25 minutes to over 90% of the i n i t i a l value. T r i s Ringer. In F i g . 14 the r e l a t i v e O.D. (at 850 mu.) of sing l e muscle f i b e r s bathed i n sodium f r e e , t r i s substituted Ringer i s graphed as a function of time. The time for the O.D. of the f i b e r s to reach a constant value i n eit h e r t r i s or sucrose Ringer was i d e n t i c a l (10-15 min., F i g . 14) but the magnitude of the decrease was not as great i n t r i s as i n sucrose Ringer. When normal Ringer was returned to the chamber, the O.D. of the f i b e r s increased r a p i d l y to i t s i n i t i a l value (Fig. 14). The recovery of the O.D. of f i b e r s bathed i n sucrose Ringer was also noted to be more rapid than the i n i t i a l decrease i n the O.D. Potassium Ringer. In F i g . 15 the r e l a t i v e O.D. (at 850 mu.) of singl e muscle f i b e r s bathed i n sodium free, calcium free, potassium sub s t i t u t e d Ringer i s graphed as a function of time. I t was necessary to pre- soak the f i b e r s i n a calcium free s o l u t i o n , and remove calcium from the sodium free, potassium substituted s o l u t i o n to prevent the contracture of the f i b e r s . The O.D. of the f i b e r s was f i r s t measured i n normal Ringer, then i n calcium free Ringer. Exposure to calcium free Ringer f o r 25 minutes 92 < u i — o. O 0 . 4 - -5 n=5 0 . 2 - " T " 1 0 I 1 5 — r — 2 0 2 5 / 0 5 1 0 1 5 2 0 2 5 —4- T I M E ( m i n ) I N N O R M A L R I N G E R — -- T I M E ( m i n ) I N T R I S R I N G E R - F i g . 14. The r e l a t i v e O.D. (850 imj.) of sing l e muscle f i b e r s bathed i n t r i s Ringer and then i n normal Ringer. lowered the O.D. s l i g h t l y (note the r e l a t i v e O.D. at zero time i n F i g . 15). When th i s s o l u t i o n was replaced by potassium Ringer, the O.D. decreased as shown i n F i g . 15. This decrease was greater than the decrease i n t r i s Ringer, but less than the decrease i n sucrose Ringer. The recovery of the O.D. was very slow compared to the recovery of the O.D. of f i b e r s i n i t i a l l y bathed i n sucrose or t r i s Ringer. The O.D. was s t i l l increasing s l i g h t l y a f t e r 50 minutes i n normal Ringer (Fig. 15). As potassium 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) of si n g l e muscle f i b e r s bathed i n potassium Ringer and then i n normal Ringer. 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 calcium free Ringer. a s u b s t a n t i a l increase i n the volume of the f i b e r s occurred when they were bathed i n the potassium Ringer s o l u t i o n . The volume of the f i b e r s did i n  crease i n t h i s s o l u t i o n , but the increase was so s l i g h t as to be n e g l i g i b l e . A co n t r o l experiment indicated that the percentage water content of f i b e r s bathed i n normal Ringer was 76.6 ± 0.1 (n=5) whereas the percentage water content of f i b e r s from the same muscle bathed f o r 25 minutes i n calcium free Ringer, then f o r 25 minutes i n potassium Ringer was 77.7 ± 0.2 (n=9) . Lithium Ringer. In F i g . 16 (upper curve) the r e l a t i v e O.D. 94 - T I M E ( m i n ) I N p H 9 . 6 R I N G E R 2 5 / 0 5 1 0 1 5 2 0 2 5 T I M E ( m i n ) I N N O R M A L R I N G E R - F i g . 16. The r e l a t i v e O.D. (850 1141) of sing l e muscle f i b e r s bathed i n li t h i u m Ringer (upper graph) and i n pH = 9.6 Ringer (lower graph). (at 850 mu.) of sing l e muscle f i b e r s bathed i n sodium free, l i t h i u m substitu ted Ringer i s graphed as a function of time. No decrease i n the O.D. was observed. In 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 s i g n i f i c a n t increase occur red, which was r e v e r s i b l e . A f t e r 25 minutes i n l i t h i u m Ringer, the r e l a t i v e O.D. increased to 1.033 ± .003 (n=7) and upon returning normal Ringer to the bathing chamber the r e l a t i v e O.D. decreased to 1.004 ± .008 (n=7). The changes i n the t o t a l concentrations of potassium, sodium and l i t h i u m i n single muscle, f i b e r s bathed 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 1 8 0 I n i t i a l Ov. = 6 + 2 ( n = 6 ) ~~r 1 0 T " 1 5 2 0 — I 2 5 T I M E ( m i n ) I N S O D I U M F R E E L I T H I U M R I N G E R , F i g . 17. The t o t a l concentrations of 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 substituted Ringer. I n i t i a l points are the average of measurements from 20 f i b e r s . Other points are the average of measurements from 10 f i b e r s . F i g . 17. The concentration of potassium i n the f i b e r s remained constant (F i g . 17) as i n f i b e r s bathed i n sucrose Ringer ( F i g . 11). A f t e r 25 minutes i n l i t h i u m Ringer the sodium concentration decreased by .080 - .044 = .036 moles/kg f i b e r water and the l i t h i u m concentration increased by 0.41 - .002 = .039 moles/kg f i b e r water ( F i g . 17). For comparison, i t should be r e c a l l e d that the decrease i n the sodium concentration a f t e r 25 minutes in.. • sucrose Ringer was .066 - .035 = .031 moles/kg f i b e r water ( F i g . 11). 96 One would l i k e to know how much of the decrease i n t o t a l sodium concentration of f i b e r s soaked i n l i t h i u m or sucrose Ringer was due to sodium leaving the e x t r a c e l l u l a r space and how much was due to sodium a c t u a l l y leaving the c e l l . As mentioned above, the e x t r a c e l l u l a r space com pr i s e s about 57„ of the volume of a sing l e muscle f i b e r , hence probably con tains .030 moles/kg f i b e r water of sodium. Thus, i n lit h i u m Ringer, about .006 moles/kg f i b e r water of i n t r a c e l l u l a r sodium leaves the c e l l and about .009 moles/kg f i b e r water of li t h i u m enters the c e l l through the sarco- lemma. These differences are not s i g n i f i c a n t . In sucrose Ringer about .001 moles/kg f i b e r water of sodium leaves the c e l l i n 25 minutes. I t should be stressed that the e x t r a c e l l u l a r space may have been s l i g h t l y overestimated (6) and that i t was not measured on the experimental f i b e r s . Thus, a d e f i n i t e value cannot be assigned to the concentration of i n t r a c e l l u l a r sodium l o s t i n eit h e r sucrose or t r i s Ringer. A reasonable estimate would appear to l i e between .005 and .010 moles/kg f i b e r water. The concentration of free i n t r a c e l l u l a r sodium l o s t i n eit h e r sucrose or t r i s Ringer is approximately i d e n t i c a l a f t e r 25 minutes ( F i g . 18) and equal to about .002 moles/kg f i b e r water. When this value i s subtracted from the estimate of the t o t a l loss of i n t r a c e l l u l a r sodium, i t i s apparent that only about .005 moles/kg f i b e r water of "bound" sodium was removed by the sucrose or l i t h i u m Ringer. As mentioned above, the a c t i v i t y of sodium i n the myoplasm, a M a > of s i x f i b e r s soaked i n li t h i u m Ringer was measured to determine the loss of the free i n t r a c e l l u l a r sodium i n t h i s s o l u t i o n . Measurements were made with the same microelectrode used i n the sucrose Ringer experiments (Fig. 11). Furthermore, measurements were made on altei'nate f i b e r s from the same barnacles; one f i b e r was bathed i n sucrose Ringer, the next i n l i t h i u m Ringer and so on. In l i t h i u m Ringer (see F i g . 17 for the i n i t i a l a ^ ) a rather unexpected, t r a n s i t o r y increase i n a occurred i n four out of s i x f i b e r s , whereas i n sucrose Ringer, a„ always decreased monotonically with » => J Na time. The sodium s e n s i t i v e microelectrode 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 the electrode readings were corrected f o r t h i s by assuming that the a c t i v i t y of l i t h i u m i n the myoplasm was equal to the t o t a l concentration of l i t h i u m i n the f i b e r . Obviously t h i s i s a maximal c o r r e c t i o n , because most of the f i b e r l i t h i u m should be i n the e x t r a c e l l u l a r space. The t r a n s i t o r y increase noted i n the a ^ a of f i b e r s bathed i n l i t h i u m Ringer warranted the construction of an electrode which had no measurable response to l i t h i u m i n the concentration range that could have occurred i n the myoplasm and the r e p e t i t i o n of the above experiments. Measurements were made with t h i s electrode on 5 f i b e r s bathed i n l i t h i u m Ringer and on 4 f i b e r s bathed i n sucrose Ringer. The r e s u l t s were s i m i l a r to those obtained previously. In l i t h i u m Ringer a t r a n s i t o r y increase i n a„ occurred i n 2 out of 5 f i b e r s whereas i n sucrose Ringer a„ always Na & Na J decreased monotonically with time. The r e s u l t s are summarized i n F i g . 18, which i s a graph of a as a function of time i n l i t h i u m Ringer (upper curve) and i n sucrose Ringer (lower curve) r e l a t i v e to the i n i t i a l value of a>T when the f i b e r i s i n normal Ringer. The differences between the two Na curves are only s t a t i s t i c a l l y s i g n i f i c a n t f o r the f i r s t 5 minutes. D i f f e r  ences i n the rate of decrease of a„ could have resulted from v a r i a t i o n s i n Na the s i z e of the f i b e r , the p o s i t i o n of the microelectrode i n the f i b e r , the a c t i v i t y of the "sodium pump" or the i n i t i a l a ^ a, but i t i s d i f f i c u l t to conceive how any of these factors could have caused a„, to increase i n J Na l i t h i u m Ringer. I t seems l i k e l y , therefore, that the increase i n a„ re-° ' Na f l e e t s a release of sodium from an i n t e r n a l binding s i t e . 98 1 . 2 H 0 5 1 0 1 5 2 0 T I M E ( m i n ) I N S U C R O S E 0 O R L I T H I U M ® R I N G E R F i g . 18. The a c t i v i t y of sodium i n the myoplasm, a M a » °^ sin g l e muscle f i b e r s bathed i n l i t h i u m Ringer (upper curve) or sucrose Ringer (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 Ringer. The i n i t i a l a ^ & of the f i b e r s bathed i n l i t h i u m Ringer was .006 ± .001 M. The i n i t i a l a of the f i b e r s bathed i n sucrose Ringer was .009 ± .002 M. Na pH = 9.6 and pH = 5.5 Ringer. A simple experiment which i l l u s  t rates the dependence of the O.D. of a muscle f i b e r on the charge of the macromolecules i t contains was performed on glycerinated f i b e r s . Fibers which had been bathed i n .01 M KC1 were placed i n .01 M KOH and observed under a d i s s e c t i n g microscope. Within 10 minutes they became almost trans parent. The change i n O.D. was r e v e r s i b l e . When the f i b e r was returned to normal Ringer, the O.D. of the f i b e r s increased. The decrease i n O.D. was 99 presumably due to the fac t that the macromolecules i n the f i b e r acquired a large net negative 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 glycerinated f i b e r s were bathed i n .01 M HC1. This decrease i n O.D. was presumably due to the fac t that the macromolecules acquired a large net p o s i t i v e charge i n .01 M HC1. The O.D. of a muscle f i b e r w i l l be a maximum when the pH of the myoplasm i s near the i s o e l e c t r i c pH of the main s c a t t e r i n g centers i n the f i b e r , which are presumably the thick filaments. I t i s e s s e n t i a l f o r the argument advanced beloxv that the thick filaments i n a muscle f i b e r bathed i n normal Ringer have a net negative charge. This assumption was tested by varying the pH of the myoplasm s l i g h t l y . Increasing the pH of the myoplasm should increase the net negative charge on the thick filaments, hence de crease the O.D. of the f i b e r . Decreasing the pH of the myoplasm up to, but not beyond the i s o e l e c t r i c point of the thick filaments should decrease t h e i r net negative charge, hence increase the O.D. of the f i b e r . The pH and membrane p o t e n t i a l measurements made on four f i b e r s bathed i n pH = 9.6 Ringer are i l l u s t r a t e d i n F i g . 19. The pH of the myo plasm when the f i b e r s were i n normal Ringer was 7.315 ± .009 (n=4). A f t e r 25 minutes i n pH = 9.6 Ringer i t increased to 7.378 ± .018 (n=4) . The O.D. changes that occurred i n pH = 9.6 Ringer are i l l u s t r a t e d i n F i g . 16 (lower graph). The r e l a t i v e O.D. decreased to .966 ± .011 a f t e r 25 minutes. Caldwell (7) has shown that the myoplasmic pH of 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 decreased by bathing the f i b e r s i n Ringer a c i d i f i e d with CO^. A s i m i l a r r e v e r s i b l e decrease i n the myoplasmic pH of barnacle muscle f i b e r s bathed i n Ringer which had been a c i d i f i e d with CO-, (pH of Ringer = 5.5) was observed. The myoplasmic pH decreased from 7.3 100 7.38 7.36- x a. 7.34- 7.32- T 10 T 15 T 20 r 25/0 5 10 15 20 25 -4* TIME (min) IN NORMAL RINGERS - > < z L U t — o c L U z < m 5 -TIME (mir.) IN pH 9.6 RINGERS- F i g . 19. The pH and membrane p o t e n t i a l of single muscle f i b e r s bathed i n pH = 9.6 Ringer and i n normal Ringer. to 6.3 i n 3 minutes. When normal Ringer (pH = 7.6) was returned to the bathing chamber, the pH of the myoplasm returned to 7.3 within 10 minutes (6). The r e l a t i v e O.D. of f i b e r s bathed i n pH = 5.5 Ringer increased to a stable value of 1.047 ± .006 (n=7) with i n three minutes. A f t e r 5 minutes i n the pH =5.5 Ringer, normal Ringer was returned to the bathing chamber. A f t e r 10 minutes i n normal Ringer, the r e l a t i v e O.D. decreased to 1.017 ± .004 (n=7) . D. Discussion 101 The o p t i c a l studies reported i n th i s paper were undertaken to obtain independent supporting evidence f o r the hypothesis that sodium i s bound to myosin i n s t r i a t e d muscle f i b e r s . Eqn. [27] i l l u s t r a t e s the re la t i o n s h i p that e x i s t s between the net charge, Z, on a small, o p t i c a l l y i n a c t i v e molecule and the t u r b i d i t y , T , of a s o l u t i o n when the concentration of the macromolecule i s low and the i o n i c strength of the s o l u t i o n i s high. For several reasons, neither Eqn. [27], nor more expanded and complete forms of i t (3, 8) are 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 . A f i b e r con tains not one, but many macromolecular species capable of s c a t t e r i n g l i g h t . The thick filaments, however, are probably the main s c a t t e r i n g centers because of t h e i r high "molecular" weight and concentration. These filaments form a highly concentrated s o l u t i o n or g e l , are large compared with the wavelength of incident l i g h t , and contain o p t i c a l l y a c t i v e molecules. These complicating factors make the quantitative a p p l i c a t i o n of l i g h t s c a t t e r i n g theory exceedingly d i f f i c u l t , but they should not destroy 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 serious complication a r i s e s from the f a c t that the thick filaments i n a muscle f i b e r are not free i n s o l u t i o n , but organized i n a p a r a l l e l hexagonal array. Increasing the net charge on macromolecules free i n s o l u t i o n decreases the randomness of the s o l u t i o n , or equivalently, de creases the concentration f l u c t u a t i o n s of the molecules, hence decreases the t u r b i d i t y of the system. Increasing the net charge on macromolecules which are i n i t i a l l y ordered w i l l not n e c e s s a r i l y decrease the concentration fluctu a tions. This w i l l only occur i f the i n i t i a l order i n the system i s one for X7hich the e l e c t r o s t a t i c free energy i s a minimum. Fortunately, the p a r a l l e l hexagonal array of the thick filaments i s exactly the minimum e l e c t r o s t a t i c free energy configuration for a system of charged rods (9, page 233). Thus, 102 increasing the net charge on the thick filaments should decrease the magni tude of the concentration f l u c t u a t i o n s of the filaments, hence decrease the t u r b i d i t y of the muscle f i b e r . I t i s also e s s e n t i a l for the argument that the thick filaments be negatively charged. T i t r a t i o n (10), electrophoresis (11, 12) and ATP binding studies (11, 13, 14) on myosin i n d i c a t e that t h i s requirement i s s a t i s f i e d at the myoplasmic pH of about 7.3 (Fig. 19). The experiments i n pH = 5.5 and pH = 9.6 Ringer also i n d i c a t e the thick filaments are negatively charged. In s p i t e of the inherent d i f f i c u l t i e s i n the a p p l i c a t i o n of l i g h t s c a t t e r i n g theory to l i v i n g muscle f i b e r s , i t seems reasonable to attempt to explain the o p t i c a l r e s u l t s i n terms of changes i n the net charge on the thi c k filaments. The s i g n i f i c a n c e of the exercise l i e s i n comparing the experimental r e s u l t s with the r e s u l t s predicted from the hypothesis that a s i g n i f i c a n t f r a c t i o n of sodium i n the f i b e r i s bound to the th i c k filaments, presumably to carboxyl moieties. When the f i b e r s are bathed i n sucrose, t r i s or potassium Ringer, sodium should move o f f the binding s i t e s and out of the c e l l , causing an increase i n the net negative charge on the thick filaments. This should decrease the t u r b i d i t y , hence the O.D. of the f i b e r s . Large, r e v e r s i b l e decreases i n the O.D. of f i b e r s bathed i n these solutions (Figs. 13, 14, 15) were indeed observed. The arguments advanced in Chapter I I indic a t e that the binding s i t e s on the thick filaments should prefer the a l k a l i metal cations i n the order Li>Na>iC (15). Thus, when the f i b e r s are bathed i n l i t h i u m Ringer, the l i t h i u m entering the myoplasm should more than compensate for the loss of the "bound" sodium. This should cause a s l i g h t decrease i n the net negative charge on the thick filaments, hence 103 the t u r b i d i t y and the O.D. of the f i b e r should increase. A small rever s i b l e increase i n the O.D. of f i b e r s bathed i n l i t h i u m Ringer was observed ( F i g . 16). Furthermore, there was an i n i t i a l increase of a ^ a i n f i b e r s bathed i n l i t h i u m Ringer ( F i g . 18) which may also be due to the displacement of bound sodium by l i t h i u m . I t should be emphasized, however, that these increases i n were small, and observed only i n about 507o of the f i b e r s bathed i n l i t h i u m Ringer. I t i s apparent then, that a l l the o p t i c a l re s u l t s are compatible with the hypothesis that sodium i s bound to the thick filaments. Unfortunately, a p r e d i c t i o n of how much sodium i s bound to the thick filaments cannot be made from these experiments. The o p t i c a l changes appear to be due to the movement of only about .005 moles/kg f i b e r water of sodium from the binding s i t e s , but there could be e i t h e r more or less than t h i s amount of sodium bound to the t h i c k filaments. I t should also be noted that other i n t e r p r e t a t i o n s of the experimental r e s u l t s are p o s s i b l e , f o r the t a c i t assumption has been made that the structure of the t h i c k filaments di d not change when the f i b e r s were bathed i n sodium free s o l u t i o n s . The p o s s i b i l i t y , however, that sodium or l i t h i u m i s necessary to maintain the i n t e g r i t y of c e r t a i n structures i n the myoplasm i s i t s e l f extremely i n t e r  e s t i n g . Obviously, much more experimental work remains to be done on the r e l a t i o n s h i p between the o p t i c a l properties of muscle f i b e r s and the ions they contain, but at present these experiments are o f f e r e d as q u a l i t a t i v e support for the hypothesis that a s i g n i f i c a n t f r a c t i o n of the sodium i n i n t a c t barnacle muscle f i b e r s i s bound to myosin. 104 CHAPTER VII BINDING OF SODIUM AND POTASSIUM IN GLYCEROL EXTRACTED FIBERS A. Introduction The experiments performed by Lewis and Saroff (1) on solutions of extracted myosin indi c a t e that t h i s protein has the capacity to bind large quantities (about 50 moles/lO"* grams myosin) of a l k a l i metal cations and that the a s s o c i a t i o n constant for the myosin-sodium complex i s about twice the a s s o c i a t i o n constant for the myosin-potassium complex. I t was noted i n Chapter I I , however, that one should be hesitant about using these r e s u l t s to 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 potassium are bound to myosin i n a l i v i n g c e l l . The s p a t i a l f i x a t i o n and cross-linkage that myosin under goes i n the l i v i n g c e l l may a l t e r i t s binding c h a r a c t e r i s t i c s , as experi ments on other macromolecules and p o l y e l e c t r o l y t e s have indicated. I t seemed reasonable, therefore, to study the influence of these two phenomenon on the capacity of myosin to bind sodium and potassium by measuring the binding c h a r a c t e r i s t i c s of the c o n t r a c t i l e proteins in a glycerinated f i b e r . As the membranes in a f i b e r are destroyed by g l y c e r i n a t i o n , and no source of metabolic energy remains, the p o s s i b i l i t y that ions are s e l e c t i v e l y accumulated i n i n t r a c e l l u l a r organelles may be ignored. When the experiments i n t h i s chapter were undertaken, the author was unaware of the work of Fenn (2). Fenn had already demonstrated that glycerinated f i b e r s s e l e c t i v e l y accumulate sodium over potassium when ex posed to solutions containing equal concentrations of these two ions. The free concentrations (or a c t i v i t i e s ) of sodium and potassium i n the myoplasm of an i n t a c t s t r i a t e d muscle f i b e r , however, are far from equal, as the 105 measurements reported i n Chapters IV, V and VI demonstrate. The s e l e c t i v i t y of many ion exchange resins depends on the r e l a t i v e concentrations of the a l k a l i metal cations in the exchanger (3). Thus, i f the glycerinated f i b e r i s to be considered a model, a l b e i t a crude model, of the l i v i n g c e l l , i t seemed appropriate to study the accumulation of sodium and potassium by glycerinated f i b e r s exposed to solutions containing these ions at approx imately the same a c t i v i t i e s as are found in the myoplasm of an i n t a c t f i b e r . The r e s u l t s of such a study are presented below. They are q u a l i t a t i v e l y compatible with the r e s u l t s of both Lewis and Saroff (1) and Fenn (Z) in that they demonstrate the s e l e c t i v i t y c o e f f i c i e n t , K^ a/ K, of the g l y c e r i n  ated f i b e r i s greater than 1.0 (see Eqn. [7] for a d e f i n i t i o n of the s e l e c t i v i t y c o e f f i c i e n t ) . B. Methods G l y c e r i n a t i o n . Approximately a dozen f i b e r s on a single base plate were dissected free from one another in normal Ringer (Table I) at 25° C and examined for damage. Only undamaged f i b e r s were used. The ten dons of these f i b e r s were l i g a t e d by thread to a rod and the baseplate t i e d to another rod so that the f i b e r s were f i x e d at rest length. The f i b e r s were then transferred to g l y c e r o l (507=, by volume, buffered to pH 7.33 at 25° C). The temperature of the g l y c e r o l was 2-3° C, and the f i b e r s were stored f or 20 hours at t h i s temperature. The f i b e r s were then transferred to fresh g l y c e r o l and stored at -20° C for 24 days. 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 that used by Szent-Gyorgyi (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 baseplate was tested f or c o n t r a c t i l i t y before experiments were performed on the other f i b e r s . The f i b e r was cut from the stone, bathed f o r 10 minutes i n d i s t i l l e d 106 water to remove most of the g l y c e r o l , then placed i n a s o l u t i o n containing .005 M ATP, .010 M C a C l 2 , .010 M MgCl 2, .200 M t r i s at a pH of 7.6. A l l f i b e r s tested f o r c o n t r a c t i l i t y did shorten. The contractions occurred slowly over a period of about 5 minutes, the f i b e r s shortening to about 1/2 t h e i r i n i t i a l length. Experimental Procedure. A l l experiments were performed i n a cold room at a temperature of 2-3° C. The f i b e r s were f i r s t transferred from the 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 containing .275 M KC1 and .025 M KiyPO^ at pH 7.4. They remained i n t h i s s o l u t i o n f o r 1 hour to allow the g l y c e r o l to d i f f u s e out of the f i b e r s . They were then transferred to a s o l u t i o n containing .275 M KC1, .025 M K^PO^ and e i t h e r a trace (.0002 M) concentra- 22 t i o n or .010 M Na CI at pH 7.4. The f i b e r s were e q u i l i b r a t e d i n one of these two solutions f o r 1-2 hours. A f t e r t h i s period of time the f i b e r s were cut from the baseplate, b l o t t e d b r i e f l y to remove excess bathing f l u i d and placed i n preweighed, stoppered weighing b o t t l e s . The b l o t t i n g and transfer procedure took about 10 seconds. The wet weight of the f i b e r was measured immediately, the f i b e r dried to a constant weight at 95° C, then the dry weight of the f i b e r measured. Aft e r d i g e s t i o n i n .2 ml of concen trated HNO^ and n e u t r a l i z a t i o n with ammonia, the l i q u i d was transferred to a v i a l used i n the Nuclear Chicago Automatic Gamma Well Counting System and d i l u t e d to 5 ml. The sodium content, i n counts per minute (cpm), of the experimental f i b e r was then measured. These measurements were alternated with measure ments of the cpm/ml of the bathing s o l u t i o n . Eight one ml samples of the bathing so l u t i o n were pipetted into v i a l s (samples were also weighed on a si x place balance to correct for any p i p e t t i n g e r r o r s ) , d i l u t e d to 5 ml, and 107 the cpm determined. Samples were counted f o r 10 minutes, and 5 r e p e t i t i o n s of the counts were made to ensure the s t a b i l i t y of the gamma counter. The background was less than 1% of the cpm i n the experimental samples. A f t e r the r a d i o a c t i v i t y of the samples was determined, they were d i l u t e d to 25 ml and analyzed for potassium content on a Unicam SP 900 flame spectrophotometer. Samples of the bathing s o l u t i o n were also analyzed f o r potassium content. C. Results A preliminary experiment was conducted to determine how long the 22 f i b e r s should be e q u i l i b r a t e d i n the solutions containing Na before they were removed for a n a l y s i s . Sixteen g l y c e r o l extracted f i b e r s were bathed fo r one hour i n a .275 M KC1 plus .025 M KH-,P0^ s o l u t i o n to remove the 22 g l y c e r o l , then transferred to a s i m i l a r s o l u t i o n containing Na . They were removed from t h i s s o l u t i o n at times ranging from 1/2 to 18 hours. The sodium and potassium concentrations i n the muscle reached a constant value a f t e r 1/2 hour. To ensure e q u i l i b r a t i o n i n the experimental s e r i e s , f i b e r s 22 were bathed i n the solutions containing Na for 1-2 hours. The r e s u l t s of the experiments are presented in Tables VI and VII. The f i r s t column i n Table VI gives the % water (by weight) of the f i b e r s . The average value i s 88.5%. The average 7» water content of an in t a c t barnacle muscle f i b e r , on the other hand, i s about 75% (average from the experimental f i b e r s u t i l i z e d i n the experiments described i n Chapters V and VI).. This implies that the g l y c e r o l extracted barnacle muscle f i b e r s have swelled to about twice t h e i r i n i t i a l volume. The next column l i s t s the dry weight of the f i b e r s . 108 TABLE VI The sodium and potassium content of f i b e r s extracted i n 50% g l y c e r o l for 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 containing [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 bathing s o l u t i o n due to the Na was 23,530 ± 540 (n = 8) cpm/ml. % Water Dry [Na] cpm/fiber [K] mMoles/fiber Na bound K bound i n Fiber Weight Measured Expected Measured Expected cpm/gm mMoles/ 10-3gms x lO-- 3 x 10*° dry weight gm dry weight 84.1 2.649 397 330 4.500 4.133 25,300 0.138 88.6 1.925 416 352 4.750 4.413 33,200 0.175 89.7 1.940 453 397 5.375 4.984 28,900 0.201 88.1 2.428 452 423 5.500 5.303 11,900 0.081 88.2 1.874 393 329 4.500 4.132 34,200 0.196 88.9 3.358 803 633 8.875 7.934 50,600 0.280 90.6 3.150 965 714 9.250 8.956 79,700 0.093 88.8 2.390 539 446 6.000 5.590 38,900 0.171 88.9 2.090 599 394 5.375 4.938 98,100 0.209 88.5 2.568 617 465 6.250 5.830 59,200 0.164 90.1 2.103 666 450 6.000 5.646 102,700 0.168 88.5 2.453 615 444 5.875 5.569 69,700 0.125 87.6 2.396 459 398 5.375 4.993 35,500 0.159 88.5 51,400 0.166 + 7,900* ± 0.014 S . E. The t h i r d column l i s t s the measured r a d i o a c t i v i t y of the indi v  i d u a l f i b e r s i n cpm. The fourth column l i s t s the values of the cpm expected on the basis of three assumptions. These assumptions are: (i) no sodium ions are bound to the c o n t r a c t i l e proteins, ( i i ) the a c t i v i t y c o e f f i c i e n t of sodium ions i n the glycerinated f i b e r i s equal to the a c t i v i t y c o e f f i c i e n t of sodium ions i n the bathing s o l u t i o n , ( i i i ) a l l the water i n the c e l l i s free to act as solvent f o r the sodium ions. The fourth column was calcu lated by multip l y i n g the weight of water i n the f i b e r by the measured value of 23,530 ± 540 (n=8) cpm/ml bathing s o l u t i o n , the r a d i o a c t i v i t y of the bathing s o l u t i o n . (The error of less than 1% that a r i s e s i n assuming that 1 109 gm of water contains the same number of water molecules as 1 ml of bathing s o l u t i o n i s ignored.) Note that i n each case the f i b e r contains more sodium than would be expected on the basis of the above three assumptions. Assump-* ti o n ( i i i ) " i s probably not v a l i d , but the e f f e c t of any water "binding" would be to reduce the concentration of sodium i n the f i b e r , hence the i n v a l i d i t y of th i s assumption could not lead to the observed r e s u l t s . I t w i l l be assumed that assumption ( i i ) i s v a l i d , and that the observed accumu l a t i o n of sodium by the glycerinated f i b e r s i s due to the binding of sodium to the c o n t r a c t i l e p roteins. The penultimate column l i s t s the amount of sodium bound (in cpm) per gram of dry weight of muscle. The r e s u l t s i n th i s column were obtained by subtracting the measured and the expected cpm and d i v i d i n g by the dry weight of the f i b e r . The average value of 51,400 ± 7,900 (n=13) cpm/gm dry weight i s equivalent to (51,400 cpm/gm dry weight)(0.0104 mMoles/23,530 cpm) = 0.023 mMoles bound sodium/gm dry weight. The f i f t h column i n Table VI l i s t s the measured amount of potas sium i n the muscle, as determined by flame photometry. The si x t h column l i s t s the mMoles of potassium expected i n the f i b e r on the basis of assump tions ( i , i i , i i i ) applied to potassium instead of sodium ions. The f i n a l column l i s t s the mMoles of bound potassium per gm of dry f i b e r weight. The average of th i s quantity i s 0.166 mMoles/gm dry weight. The glycerinated f i b e r s could be considered as highly hydrated ion exchange r e s i n s , and the s e l e c t i v i t y , as defined i n Eqn. [7] of these resins c a l c u l a t e d . The average s e l e c t i v i t y of the f i b e r s , c a l c ulated from the data of Table VI i s K^/jr = 1.18. There i s , however, a groxving body of evidence i n d i c a t i n g that "we may, to a f i r s t approximation, regard the 110 TABLE VII The sodium and potassium content of f i b e r s extracted 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 so l u t i o n containing [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 bathing s o l u t i o n due to the Na was 22,550 ± 630 (n = 8) cpm/ml. % Water Dry [Na] cpm/fiber [K] mMoles/fiber Na bound K bound i n Fiber Weight Measured Expected Measured Expected cpm/gm mMoles/ 10-3 x 10" J x 10"3 dry weight gm dry weight 87.3 2.463 415 382 5.375 5.000 13,400 0.152 90.1 3.164 716 649 8.500 8.495 21,200 0.002 90.2 2.775 690 576 7.875 7.535 41,100 0.122 88.0 2.936 581 485 6.625 6.352 32,700 0.093 90.2 2.214 623 459 6.250 6.012 74,100 0.107 90.4 2.816 665 598 7.875 7.823 23,800 0.018 89.8 2.458 602 488 6.500 6.384 46,400 0.047 88.4 1.230 249 211 3.250 2.765 30,900 0.394 88.3 3.298 763 561 7.750 7.343 61,200 0.123 86.9 2.559 468 383 5.375 5.008 33,200 0.143 90.6 3.813 920 828 11.625 10.842 24,100 0.205 87.1 2.878 555 438 6.125 5.732 40,700 0.136 87.6 2.542 473 404 5.625 5.298 27,100 0.128 88.9 2.360 555 426 6.000 5.576 54,700 0.180 88.8 37,500 0.132 ± 4,500* ±0.025 S. E. e f f e c t of ad d i t i o n water as merely to ' d i l u t e ' the processes giving r i s e to s e l e c t i v i t y " (5). Thus, i t seems reasonable to consider not only the s e l  e c t i v i t y of the f i b e r as a whole, but the s e l e c t i v i t y of the proteins as w e l l . The term ^ ^ y ^ ^ ^ may be defined as (mMoles of sodium bound per gm protein/mMoles sodium free per ml solution)/(mMoles of potassium bound per gm protein/mMoles potassium fr e s per ml s o l u t i o n ) . I t may be cal c u l a t e d from the data of Table VI that the s e l e c t i v i t y of the proteins, defined i n thi s manner i s (51,400/23,530)/(0.166/0.295) = 3.88. The r e s u l t s of another seri e s of experiments conducted i n a bath ing s o l u t i o n containing only a trace (0.2mM) concentration of sodium are I l l presented i n Table VII. 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 , Kja/ K H2°*°, c a l c u l a t e d from the data i n t h i s table 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 data of Table VI. D. Discussion Some of the factors which complicate the i n t e r p r e t a t i o n of the above measurements w i l l now be discussed. At a pH of about 7.4, the pro teins myosin and a c t i n are negatavely charged (4) and the conditions f o r a Donnan equ i l i b r i u m are established. The Donnan e f f e c t could not explain the s e l e c t i v e accumulation of sodium over potassium by the f i b e r s , but i t could account for the potassium and some of the sodium accumulation. I f the potas sium accumulation of the muscle f i b e r s was due to the Donnan e f f e c t , the f i b e r s should have a negative p o t e n t i a l AE = KI l n ( [ K ] s o l u t i o n / [ K ] f i b e r ) . F From Table I, the average value of [ K ] s o l u t i o n / [ K ] f i b e r i s 1.073, hence the f i b e r should have a negative p o t e n t i a l of about 1.8 mV. The measured poten t i a l of the muscle f i b e r s was 0.00 ± 0.05 mV, i n d i c a t i n g that i f the muscle f i b e r i s considered as a homogeneous e n t i t y , the Donnan e f f e c t plays a n e g l i g i b l e r o l e i n the accumulation of ions. The author f e e l s , however, that one should no longer consider e i t h e r an i n t a c t or a g l y c e r i n ated muscle f i b e r as a homogeneous e n t i t y . Rather, one should note that there are at least "two types of e l e c t r o s t a t i c binding, which d i f f e r i n the degree of s p e c i f i c i t y of binding between charged groups. One of these might be characterized as ion-pair formation and the other as a generalized domain binding with the small counterions associated as a mobile layer with the large, m u l t i p l y charged molecule." (6) The s e l e c t i v i t y of the binding argues for the former i n t e r p r e t a t i o n , but does not prove i t . 112 The p o s s i b i l i t y that the proteins could a f f e c t the a c t i v i t y co e f f i c i e n t s of sodium and potassium ions without a c t u a l l y "binding" these ions should be considered, but lack of information about this phenomenon necessitates the assumption that 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 unaffected by the p r o t e i n s . Also worthy of consideration i s the p o s s i b i l i t y that a f r a c t i o n of the water i n the g l y c e r o l extracted f i b e r s i s "bound" i n such a manner that i t i s unavailable to act as solvent for the a l k a l i metal cations. A method of measuring experimentally t h i s f r a c t i o n of water i s discussed i n Chapter IX. I t may be worthwhile to summarize the a v a i l a b l e information about the binding of sodium and potassium to extracted muscle p r o t e i n s . The ex periments of Lewis and Saroff (1) i n d i c a t e that a maximum of 0.50 mMoles of cations can be bound to 1 gm of myosin, and that myosin binds sodium more strongly than potassium. The electrophoresis experiments of M i l l e r et a l (7) also i n d i c a t e the sodium i s bound more strongly than potassium to myosin. In an abstract published in 1942, Mullins (8) reported that myosin preferred potassium to sodium, but Fenn, who repeated these experiments, concluded that "the published abstract was i n error for unknown reasons" (2). Both the-magnitude and the s e l e c t i v i t y of the binding that Fenn (2) observed i n g l y c e r o l extracted f i b e r s are compatible with the r e s u l t s of Lewis and Saroff (1). I f i t i s assumed that the g l y c e r o l extracted f i b e r s used by Fenn contained 75% water by weight, and further assumed that the concentrations he quotes i n meq/kg r e f e r to a kg of muscle and not f i b e r water, one may calculate' the l i m i t i n g s e l e c t i v i t y from the data presented i n 113 Table I I of h i s paper. The average value of K j ^ y ^ ^ ® = 2.8 ± .3. This s e l e c t i v i t y does not appear to be dependent on the concentration of sodium and potassium i n the bathing s o l u t i o n . In summary, a glycerinated f i b e r can be considered an ion exchange r e s i n and the s e l e c t i v i t y of the " r e s i n " , Kjj a^» c a l c u l a t e d . Fenn's exper iments demonstrated the s e l e c t i v i t y was greater than unity when the ions were present i n equal concentrations: the experiments presented here i l l u s  t r a t e i t i s also greater than u n i t y when sodium and potassium ions are present at concentrations s i m i l a r to those found i n an i n t a c t f i b e r . The average s e l e c t i v i t y of the proteins (not of the f i b e r as a whole) f or the two experimental ser i e s was ^^/y^^P'*^ = 3.8. I f the g l y c e r o l extracted f i b e r i s considered as a model of the i n t a c t f i b e r , the r e s u l t s of Table VI imply that an i n t a c t f i b e r (containing 75% water by weight) with a^ = 0.20 M and a = 0.007 M contains 0.055 moles/kg water of potassium and 0.008 Na moles/kg water of sodium "bound" to pro t e i n s . 114 CHAPTER VIII SIGNIFICANCE OF THE RESULTS Probably the most important conclusion that can be drawn from the experiments presented i n t h i s thesis i s that one can no longer consider the a l k a l i metal cations and water i n a s t r i a t e d muscle f i b e r to be i n exactly the same state as the ions and xjater i n the bathing s o l u t i o n surrounding the c e l l . Consider the sodium content of a sin g l e muscle f i b e r from the giant barnacle, Balanus nubilus. A t y p i c a l i n t a c t f i b e r contains about 70 mMoles/kg f i b e r water of sodium (Chapters IV, V, V I ) . About 30 mMoles/kg f i b e r water of sodium are contained i n a compartment which communicates with the bathing s o l u t i o n ; presumably the extensive invaginations of the sarco lemma which are v i s i b l e under the el e c t r o n microscope (1). Only about 10 of the remaining 40 mMoles/kg f i b e r water of sodium are " f r e e " i n the myoplasm, as was determined d i r e c t l y by cation s e n s i t i v e microelectrodes (Chapters IV, V, V I ) . Thus, about 3/4 of the i n t r a c e l l u l a r sodium i n barnacle muscle f i b e r s i s "bound". I t seems reasonable to extrapolate t h i s conclusion to a l l s t r i a t e d muscle f i b e r s because Lev (2), who used cation s e n s i t i v e micro electrodes to investigate the state of sodium i n frog s t r i a t e d muscle f i b e r s , obtained s i m i l a r r e s u l t s and Robertson (3) found that 3/4 of the sodium i n lobster muscle could not be extruded by pressure. Experiments performed with potassium s e n s i t i v e microelectrodes indicate that between 27 and 417» of the i n t r a c e l l u l a r water i s unavailable to act as solvent f or the potassium ions (Chapters IV, V). Thus, the microelectrode experiments re ported i n t h i s thesis provide strong evidence that there i s a hetrogeneous d i s t r i b u t i o n of sodium and water i n sin g l e s t r i a t e d muscle f i b e r s from the giant barnacle. 1.15 The d i v i s i o n of the sodium content of a s t r i a t e d muscle f i b e r into a free 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 there i s strong evidence that at l e a s t 1/3 of the "bound" sodium i s complexed to myosin. Experiments on solutions of extracted myosin (4) and glycerinated f i b e r s (Chapter VII) indi c a t e that about 10 mMoles/kg f i b e r water of sodium may be expected to be complexed to myosin i n an i n t a c t barnacle muscle f i b e r . This conclusion i s f u l l y supported by the denaturation and l i g h t s c a t t e r i n g ex periments reported i n Chapters V and VI r e s p e c t i v e l y . The l o c a t i o n of the remaining 20 mMoles/kg f i b e r water of sodium which i s unavailable to a sodium s e n s i t i v e microelectrode i s unknown at present. I t seems u n l i k e l y that t h i s f r a c t i o n of "bound" sodium i s contained i n n u c l e i or mitochondria, because these organelles comprise only a small f r a c t i o n of 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 potassium (5, pages 226-229). The cisternae and long i t u d i n a l tubules of frog muscle have been estimated to comprise about 13% of the c e l l by volume (6), but the experiments of Zadunaisky (7) i n d i c a t e that these compartments probably do not contain a high concentration of sodium. Furthermore, the sarcoplasmic reticulum appears to be less h i g h l y developed i n barnacle than frog muscle. Thus, there i s no evidence to i n  dicate that t h i s f r a c t i o n of "bound" sodium i s sequestered i n organelles, but there i s NMR evidence to indi c a t e that i t i s bound to macromolecules (8). As discussed i n Chapter IV, Cope's conclusion (8) that 3/4 of the sodium i n s t r i a t e d muscle f i b e r s i s bound to macromolecules must be regard ed as tentative at present, but t h i s i n v e s t i g a t o r knows of 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 contradicts the conclusion. The experiments performed on g l y c e r o l extracted f i b e r s (Chapter VII) do argue against t h i s conclusion, but the s e l e c t i v i t y of the binding s i t e s f o r 116 sodium over potassium could be greater i n the i n t a c t than i n the g l y c e r o l extracted f i b e r . What i s the s i g n i f i c a n c e of these r e s u l t s ? For one thing, they contradict the equilibrium or sorption theories of i o n i c accumulation put forward by i n d i v i d u a l s such as Nasonov (9), Troshin (10), Ling (5) and others. Ling (5), f o r example, contends that the carboxyl s i t e s on proteins i n the cytoplasm have a strong preference f o r potassium over sodium ions even though i t has been known for over a decade that extracted myosin pre fer s sodium to potassium (4) and that glycerinated f i b e r s p r e f e r e n t i a l l y accumulate sodium over potassium (11). I t i s the author's opinion that the experiments performed with cation s e n s i t i v e microelectrodes on crab (12), frog (2) and barnacle (Chapters IV, V, VI) muscles d i r e c t l y disprove Ling's theory. The a c t i v i t y of potassium i n the myoplasm of s t r i a t e d muscle f i b e r s i s not approximately equal to the a c t i v i t y of potassium i n the bathing solu t i o n , as Ling's theory demands. I t i s the a c t i v i t y of sodium, not potas sium, which has an anomalously low value. Although the microelectrode experiments reported i n t h i s thesis d i r e c t l y contradict the equilibrium theories of ion accumulation, they also strengthen a c r i t i c i s m of the more generally accepted membrane theory of ion accumulation. This c r i t i c i s m , which has been strongly advanced by Ling (5, 13, 14), i s concerned with the energy requirements of the postu lated "membrane pumps". Aside from Ling, four groups of workers have studied this problem i n r e l a t i o n to the postulated sodium pump i n s t r i a t e d muscle f i b e r s (15, 16, 17, 18). The consensus of opinion was that under p h y s i o l o g i c a l conditions about 20% of the t o t a l energy of the c e l l would be required to drive the sodium pump. This i s a minimal value because both the 117 energy-delivering mechanism and the pumping mechanisms were assumed to be 100% e f f i c i e n t and i t was further assumed chat the d i f f u s i o n of sodium i n the myoplasm was surface rather than bulk phase l i m i t e d . The d i r e c t measure ments of the a c t i v i t y of sodium i n the myoplasm indicate that the differ e n c e i n the chemical p o t e n t i a l of sodium across the sarcolemma i s about 4 times the value calculated from measurements of the t o t a l concentration of sodium i n the c e l l . Correction f o r t h i s factor alone raises the energy require ments of the sodium pump in frog muscle from 20% to 25% of the t o t a l energy output of the c e l l . I t i s known that calcium and magnesium, as well as sodium ions, are permeable and not- d i s t r i b u t e d across the sarcolemma accord ing to the Nernst equation. Ling (14), using only the f l u x data a v a i l a b l e i n the l i t e r a t u r e , c a l c ulated that the energy requirements of these three pumps i s 330% of the t o t a l energy expenditure of the c e l l . Many other s o l  utes such as hydrogen ions (Chapter VI), amino acids and sugars (14, 5) are also not d i s t r i b u t e d according to the Nernst equation, and presumably re quire energy expending "pumps" to maintain the d i s e q u i l i b r i u m . This i s a serious c r i t i c i s m of the membrane theory, but i t does not imply that i t must be rejected and. an equ i l i b r i u m theory of ion accumu l a t i o n accepted i n i t s place. Consider what i s meant by the term a c t i v e transport. I t i s usu a l l y defined as a process that can bring about a flow of a substance against an electrochemical p o t e n t i a l gradient of the substance (19, 20). The existence of such a flow, however, does not mean that metabol i c energy must be expended d i r e c t l y to cause the flow. As Katchalsky and Curran (21, page 199) point out "In p r i n c i p l e , such flow could be a n t i c i  pated on the basis of the thermodynamic equations without implying the operation of an act i v e transport. A d i f f u s i o n a l flow against i t s concentra t i o n gradient driven by d i s s i p a t i o n of another d i f f u s i o n a l process would be 118 regarded as an incongruent d i f f u s i o n , not as active transport. Thus, the th flow of the i component across a membrane may be wr i t t e n J i = L i i A ^ i + i i L i k ^ • k * i I f Au„ = 0, but V 0, a flow of i may s t i l l take place." In Eqn. [31], L^. represents the phenomenological c o e f f i c i e n t which r e l a t e s the di f f e r e n c e th i n the electrochemical p o t e n t i a l of the j species, AJJL ^, to the flow of the th i species, J \ . Spanner (22) also recognizes t h i s p o s s i b i l i t y and gives an example of a hypothetical process which could bring about a flow of a sub stance against i t s electrochemical p o t e n t i a l gradient, and furthermore be i n h i b i t e d by metabolic poison, yet s t i l l not be driven d i r e c t l y by metabolic energy. Salminen et a l (23, 24) have demonstrated experimentally that sodium and potassium ions may be made to flow i n opposite d i r e c t i o n s against t h e i r concentration gradients across a synthetic membrane when there i s a simultaneous f l u x of water and hydrogen ions i n the system. A recent phen omenological d e s c r i p t i o n of the act i v e transport of s a l t and water appears i n a paper by Hoshiko and Lindley (25). The above paragraph dealt with cases where a net flow of solute occurs against an electrochemical gradient, as i n the i n t e s t i n a l mucosa, the wall of kidney tubules, frog skins and sodium loaded muscle f i b e r s . The second law of thermodynamics d i c t a t e s that such a flow must occur at the expense of energy, but i t was noted that the energy need not be expended d i r e c t l y . (It i s obvious that there can be no c r i t i c i s m of the ultimate metabolic energy expended i n cases where a net transf e r occurs. The c e l l must have s u f f i c i e n t energy to bring about such a transfer.) I f a steady state system i s now considered (for example, a r e s t i n g muscle fiber)' there i s a complete range of energy the c e l l could expend to maintain t h i s steady 119 s t a t e . I f the steady state i n f a c t represents an equilibrium, as Ling con tends, no energy would be required. The author f e e l s t h i s p o s s i b i l i t y must be rejected, as stated above. The energy requirement of the c e l l (for a given set of fluxes and electrochemical p o t e n t i a l gradients) i s maximized i f the steady state i s maintained by a system of "pumps", each of which u t i l  izes metabolic energy d i r e c t l y to pump sodium, calcium, magnesium and hydrogen ions against an electrochemical gradient and wastes the free energy gained by the c e l l due to the passive movement of these ions down t h e i r electrochemical gradients. I t i s the energy requirements of such a postu lated system that Ling has repeatedly c r i t i c i z e d (5, 13, 14). I f Ling's c a l c u l a t i o n of the energy requirements of such a system of pumps i s accepted, the concept of pumps which are uncoupled, or coupled only to another "up h i l l " process (such as the postulated sodium potassium coupling i n muscle and nerve) must be r e j e c t e d . L i n g , however, i s not l o g i c a l i n s t a t i n g that "Unless we are w i l l i n g to venture that the second law of thermodynamics does not hold i n these l i v i n g c e l l s and that the l i v i n g c e l l s can generate free ^ de novo, then wi t h i n the confine of our understanding of the p h y s i c a l world there i s no a l t e r n a t i v e to discarding the pump mechanism f o r s e l e c t i v e i o n i c d i s t r i b u t i o n i n l i v i n g c e l l s " (14). The concepts of pumps need not be re jected at a l l . I t need only be modified to accept the f a c t that coupling does occur between the various fluxes of solutes. The equations of i r r e v e r s i b l e thermodynamics would seem to imply that no coupling can occur when a l l the net fluxes are zero across a b i o l o g i c a l membrane (26, page 44), that i s , when the c e l l i s i n a steady state at r e s t . This would be true i f the net f l u x of an ion through each microscopic path way i n the membrane was zero. The p o s t u l a t i o n of a pump of any kind, 120 One possible coupling process i s "exchange d i f f u s i o n " (27); i n such a process the i n f l u x of an ion would be d i r e c t l y coupled with the e f f l u x . I t i s apparent that the existence of "exchange d i f f u s i o n " would reduce the energy requirements of the sodium, calcium, magnesium, etc. pumps (for a given electrochemical p o t e n t i a l gradient and f l u x ) . I t should be stressed, however, that t h i s i s not the only possible mechanism whereby coupling can occur. Coupling could occur d i r e c t l y between the fluxes of two d i f f e r e n t ions i n the membrane, v i a the current generated by a pump ( r e c a l l the d i s  cussion i n Chapter V about the p o s s i b i l i t y of an electrogenic pump) or v i a the production of an intermediate such as ATP. With regard to the l a s t p o s s i b i l i t y , note that Garrahan and Glynn (28) have recently demonstrated that the i n f l u x of sodium ions i n red blood c e l l ghosts can lead to the pro duction of ATP. Further comment on the r e l a t i o n s h i p between the transport processes and chemical reactions that could occur in b i o l o g i c a l membranes would be mere speculation, for as Eisenman notes (29), i t i s not even known how ions permeate through b i o l o g i c a l membranes. A knowledge of the a c t i v i t i e s of sodium and potassium i n the myo plasm i s of value i n other f i e l d s of membrane study such as the measurement of p e r m e a b i l i t i e s and the evaluation of the membrane p o t e n t i a l . To trans- however, i s equivalent to postulating that the membrane i s a n i s o t r o p i c (Curie-Prigogine P r i n c i p l e ) , and furthermore implies that through at l e a s t two microscopic pathways there e x i s t non zero fluxes of the ion i n question. The vector sum of a l l the component fluxes i s of course equal to zero, but there i s no d i f f i c u l t y i n admitting that these i n d i v i d u a l fluxes are capable of being coupled. 121 form the f l u x rate of an ion into the permeability, for example, the d i f f e r  ence in the a c t i v i t i e s of the ion across the sarcolemma must be known. In the past, investigators have assumed that t h i s was equal to the diffe r e n c e i n the concentrations of the ion across the sarcolemma. The measurements presented i n Chapters IV, V and VI indi c a t e that f o r both sodium and potas sium ions, t h i s assumption i s erroneous. 0 122 CHAPTER IX j SUGGESTIONS FOR FUTURE WORK A Ion and Water Binding Intact F i b e r s . The studies on carboxylic resins (1, 2) discussed i n Chapter I I indicate that these resins prefer the a l k a l i metal cations i n the order Li>Na>KD I t i s now known that both extracted myosin (3) and g l y c e r o l extracted f i b e r s (4, Chapter VII) also prefer sodium to potassium and that the a c t i v i t y of sodium, but not potassium has an anomalously low value i n the myoplasm of s t r i a t e d muscle f i b e r s (Chapters IV, V, V I ) . I t would be simple to determine 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 . This experiment would support the tenta t i v e conclusion, based on the l i g h t s c a t t e r i n g experiments reported i n Chapter VI, that l i t h i u m i s bound more strongly to myosin than e i t h e r sodium or potassium, a conclusion compatible with the t u r b i d i t y measurements of Szent-Gyorgyi (5, page 42) on solutions of extracted myosin i n various con centrations of the a l k a l i metal c a t i o n s . Furthermore, the study would be of t h e o r e t i c a l value i n understanding the nature of the binding s i t e s . There i s no d i f f i c u l t y i n exchanging most of the sodium i n a barnacle muscle f i b e r f o r l i t h i u m . This can be accomplished by bathing the f i b e r s i n a sodium free, l i t h i u m substituted Ringer s o l u t i o n (preliminary experiments). There e x i s t glasses, s u f f i c i e n t l y s e n s i t i v e to l i t h i u m (sodium being the only important contaminant), from which microelectrodes could probably be constructed (6). Thus, the a c t i v i t y and t o t a l concentration of l i t h i u m i n the f i b e r could be measured, and the f r a c t i o n of "bound" l i t h i u m determined. Further information about the nature of the s i t e s to which sodium (and presumably potassium) ions are complexed with i n i n t a c t muscle f i b e r s could be obtained by measuring the a c t i v i t i e s of these ions i n the myoplasm under conditions of varying pH. The pH of the myoplasm can r a p i d l y be lowered by about 1 unit by exposing the'muscle f i b e r to solutions saturated with CO^ (Chapter V I ) . A few preliminary experiments indicated that the a c t i v i t y of sodium did not 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 of the a c t i v i t y of potassium. I t would be desirable to repeat, and extend these measurements to higher pH regions, i f a method of r a p i d l y increasing the pH of the myoplasm could be found. The t h e o r e t i c a l basis and experimental j u s t i f i c a t i o n of using a d i f f u s i o n technique to measure the f r a c t i o n of ions bound to macromolecules i n s o l u t i o n was given i n Chapter I I . D i f f u s i o n experiments have already y i e l d e d valuable information about the state of potassium i n giant axons. The elegant experiments of Hodgkin and Keynes (8) demonstrated that the d i f f u s i o n c o e f f i c i e n t of potassium i n giant axons i s about 1.5 x 10~^ cm^sec"^. 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 potassium i n .5 M KC1 i s 2.135 x 10" 5 c m 2 s e c - 1 (9) and i n .5 M KI 2.030 1 0 - 5 c m 2 s e c _ 1 (10). Thus, i t appears that less than 257o of the potassium i n giant axons i s bound of compartmentalized. Caution, however, must be used i n the i n t e r p r e t a t i o n of 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) points out that ion pair formation does not always decrease the d i f f u s i o n c o e f f i c i e n t of an ion. The d i f f u s i o n c o e f f i c i e n t of potassium on the sur face of a glass, f o r example, i s higher than that i n a d i l u t e s o l u t i o n (12). Presumably, this i s because potassium can "jump" from s i t e to s i t e on the gla s s . I t would be d i f f i c u l t , however, to argue that the anionic s i t e s i n a l i v i n g c e l l are close enough to permit the movement of potassium by th i s type of mechanism. Even Ling has attempted to measure the d i f f u s i o n c o e f f i c i e n t of ions i n muscle as a demonstration of binding (13), but the d i f f u s i o n experiments performed on muscle f i b e r s to date have been f a r from conclusive (13, 14, 15). The extremely large barnacle muscle f i b e r s would be i d e a l for measurements of the r e l a t i v e l o n g i t u d i n a l d i f f u s i o n c o e f f i c i e n t s of the a l k a l i metal cations i n the myoplasm. Two of these ions (lithium and r a d i o a c t i v e sodium or potassium, for example) could be simultaneously i n  jected into a f i b e r (16), the f i b e r sectioned a f t e r a given time, and the r e l a t i v e d i f f u s i o n c o e f f i c i e n t s determined. The extensive membraneous net work i n these s t r i a t e d muscle f i b e r s , however, would greatly impede the d i f f u s i o n of both species, making accurate measurements extremely d i f f i c u l t . I f i t was found necessary to make k i n e t i c measurements of the m o b i l i t i e s (as was done in the experiments of Hodgkin and Keynes), the experiments would have to be performed i n a calcium free medium to prevent contraction of the f i b e r s on a p p l i c a t i o n of a current. Thus, there are formidable technical d i f f i c u l t i e s to performing an experiment of t h i s type, but the experiment would provide an excellent independent test of the microelectrode r e s u l t s presented i n t h i s t h e s i s . D i f f u s i o n experiments on glycerinated f i b e r s , on the other hand, would be r e l a t i v e l y easy to perform and i n t e r p r e t . Glycerinated F i b e r s . There are several advantages to studying ion and water "binding" on glycerinated rather than i n t a c t f i b e r s . The pH and i o n i c concentrations may be r a p i d l y and r e v e r s i b l y v a r i e d and the pos s i b i l i t y of s e l e c t i v e accumulation i n i n t r a c e l l u l a r organelles need not be considered. The destruction of the sarcolemma implies that the state of water i n glycerinated f i b e r s can be investigated by a v a r i e t y of techniques not applicable to an i n t a c t f i b e r . One method would be to study desorption curves, as has been done on other non-membraneous tissues (17). Another would be to measure the imbibition pressure, as has been done on the corneal 125 stroma (18). One could study simultaneously the binding of ions and water to the proteins i n a glycerinated f i b e r by a simple technique. Consider Eqn. [19], I f both sides of t h i s equation are divided by the weight of s o l i d m a t e rial i n the glycerinated f i b e r , M r Q , the following equation r e s u l t s = C.V/M - O,aV/0f vM ) [32] K pro K pro K K K pro where B,,/M represents the moles of potassium ions bound per kg of s o l i d K pro ma t e r i a l . I t i s c e r t a i n l y reasonable to expect that Bj,/M q w i l l be a monotonically increasing function of a^/lf^ (the free concentration of potassium i n the muscle f i b e r , which i s equal to the concentration of potassium i n the external 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 are i d e n t i c  a l ) , and approach a constant value when saturation of the binding s i t e s occurs. This i s indeed the case for myosin, as F i g . 1 of Lewis and Saroff (3) i n d i c a t e s . As t h e i r studies were performed at protein concentrations of less than 1% (3) , t h e i r t a c i t assumption that the f r a c t i o n of water a v a i l a b l e to act as solvent for potassium, OL^, was uni t y was probably v a l i d . The value of i n a glycerinated f i b e r , however, may be s i g n i f i c a n t l y d i f f e r e n t from unity. I f CL, i s i n c o r r e c t l y assumed to be unity B /M is. Js. pro w i l l pass through a maximum, then f a l l instead of a t t a i n i n g a constant value. This indicates a method of measuring Bv/M and CL independently. A series Js. pro is. of measurements at varying external concentrations of potassium could be f i t t e d with a value of 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 at high concentrations. The experiments could be repeated with each of the a l k a l i metal cations. This would indicate two things; the amount of water un av a i l a b l e to act as solvent for each cation and the r e l a t i v e values of the ass o c i a t i o n constants. The data of Fenn (4) indicates that a s i g n i f i c a n t amount of water "binding" w i l l be found, for i f h i s data are p l o t t e d i n t h i s manner the apparent binding (that i s , the binding c a l c u l a t e d with the assumption that 0^, and o^ a = 1.0) of both sodium and potassium passes throug a maximum at concentrations of about .10 M. A s e r i e s of measurements of the r e l a t i v e binding constants of the a l k a l i metal cations to the proteins i n a glycerinated f i b e r , coupled with more s e l e c t i v i t y measurements of the type reported i n Chapter VII would be of great t h e o r e t i c a l value. They would allow one to examine c r i t i c a l l y a given theory of cation s e l e c t i v i t y as applied to a b i o l o g i c a l f i x e d charge system. Two such theories, those of Eisenman (19) and Ling (11) were b r i e f l y discussed i n Chapter I I . A c r i t i c a l examination of the theories of the binding of the a l k a l i metal cations to proteins would be of value, but i t would also be des i r a b l e to consider i n more d e t a i l how proteins can a f f e c t the a c t i v i t y c o e f f i c i e n t s of ions without a c t u a l l y "binding" these ions. In Chapter IV i t was noted that a knowledge of the macroscopic d i e l e c t r i c constant of a s o l u t i o n of proteins i s of l i t t l e value i n p r e d i c t i n g the e f f e c t of the pro 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 of the ions i n s o l u t i o n . Any theory of such e f f e c t s should, as E d s a l l and Wyman (20) point out, be "framed i n terms of the dimensions, dipole 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 of the i n d i v i d u a l molecules, rather than i n terms of the macroscopic d i e l e c t r i c constant, of the whole medium." B. Denaturation and Contraction The denaturation experiments reported i n Chapter V could be ex tended to include an EM i n v e s t i g a t i o n of the changes i n u l t r a s t r u c t u r e that 127 occur when a barnacle muscle f i b e r i s heated to 37-40° C. I t was postulated that the contraction and release of bound sodium and hydrogen ions that occurred at t h i s temperature were due to a breakdown of the thick filaments. This conclusion was based on experiments performed on extracted proteins and glycerinated f i b e r s . Either a confirmation or negation of th i s postulated breakdown of the thick filaments would be i n t e r e s t i n g , and could p o s s i b l y shed some l i g h t on the mechanism of normal p h y s i o l o g i c a l contractions. . I t was mentioned i n Chapter V that some preliminary measurements were made to determine i f the a c t i v i t i e s of sodium and potassium i n the myoplasm var i e d when the muscle f i b e r contracted. The f i b e r was contracted by exposure to a so l u t i o n containing 0.064 [K], and remained i n a state of contracture f o r about 10 minutes. No s i g n i f i c a n t change i n a^ , occurred during the isometric contracture (10 f i b e r s ) . In 3 out of 9 f i b e r s i n which a ^ a was measured, however, a large (100-500%) t r a n s i t o r y ( l a s t i n g about 30 seconds) increase i n a ^ was noted at the s t a r t of contracture. The experi ments were abandoned mainly because of two technical problems; the sodium electrodes were generally slow i n responding to p o t e n t i a l and a c t i v i t y changes and there was some doubt as to whether the observed p o t e n t i a l change on the sodium s e n s i t i v e microelectrode was due to an a c t i v i t y change or to a t r a n s i t o r y d epolarization of an i n t e r n a l system of membranes. These two d i f f i c u l t i e s could perhaps be circumvented by u t i l i z i n g open t i p cation sen s i t i v e microelectrodes and working with a depolarized preparation to which calcium could be added to produce contraction. C„ L i g h t Scattering The measurements reported i n Chapter VI could be extended to study the e f f e c t s of other ions on the O.D. of muscle f i b e r s ; cesium and rubidium 128 are obvious choices, but i t would be i n t e r e s t i n g to study the e f f e c t of calcium and magnesium i n more d e t a i l . I t would also be desirable to make measurements of the angular as w e l l as the wavelength dependence of the scattered l i g h t . This would require more elaborate instrumentation than a simple spectrophotometer, but would prove co n c l u s i v e l y that the phenomenon was due to s c a t t e r i n g and not absorption. Experimental measurements of the angular d i s t r i b u t i o n of the scattered l i g h t could also be corr e l a t e d with predictions made on the basis of the interference theory of 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 of the th i c k filaments i n a muscle f i b e r are known from electron microscopy.. The i n v e s t i g a t o r has also observed that during an isometric con tracture (induced by an increase i n the potassium concentration i n the bathing solution) the O.D. of the muscle f i b e r s increases markedly, then decreases on r e l a x a t i o n (preliminary experiments). This change may be due to the conjunction of the thick and t h i n filaments i n the muscle f i b e r , an analogous phenomenon being the r e v e r s i b l e increase i n the O.D. of solutions of g e l a t i n on s e t t i n g (21). I f further development of the theory of l i g h t s c a t t e r i n g i n muscle f i b e r s indicates that the tentative explanation offered f o r the increase i n O.D. i s cor r e c t , t h i s observation w i l l be of fundamental p h y s i o l o g i c a l importance. Light s c a t t e r i n g measurements may be made very _3 r a p i d l y (<10 seconds) hence i t would be pos s i b l e to measure r o u t i n e l y on the same f i b e r : (i) the stimulating a c t i o n p o t e n t i a l with an open t i p micro electrode, ( i i ) the conjunction of the thick and t h i n filaments by o p t i c a l measurements, ( i i i ) the c o n t r a c t i l e force with a transducer. 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Frank. B i o f i z i k a , 11, 58 (1966). 143 APPENDIX I Proof that a constant absorption decreases the experimentally observed changes i n o p t i c a l density. Let O.D.^ and be r e s p e c t i v e l y the o p t i c a l density and t u r b i d i t y of a f i b e r i n normal Ringer. Let 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 density and t u r b i d i t y of the f i b e r i n a d i f f e r  ent s o l u t i o n . Consider f i r s t the case where ^ 1«0. (This corres ponds to bathing the r i b e r i n sucrose, t r i s , potassium or pH = 9.6 Ringer.) From Eqn. [28] O.D. = - l o g 1 ( ) (I/I q) and from Eqn. [30] I/I = exp -(p +T)S. Therefore, O.D^/O.D^ = fl"2 + P) / (T^ + P) Now T 2 / f x < 1.0 Hence 1 + p / ^ < 1 + p/T 2 or ^ / ^ < CT 2 + P ) / ^ + P) = O.D^/O.D^ Thus, the r e l a t i v e O.D. does not decrease to as low a value as the r e l a t i v e t u r b i d i t y . S i m i l a r l y , i t may be shown that i f ^"/T^ > 1.0, the r e l a t i v e O.D. does not increase to as high a value as the r e l a t i v e t u r b i d i t y . APPENDIX I I Proof that the l i g h t scattered through small angles decreases the experimentally observed changes i n o p t i c a l density. Let the symbols have the same s i g n i f i c a n c e as i n Appendix I and consider f i r s t the case where O.D.^ > O.D..,. I f a l l other sources of error are ignored, O.D.^ = c r i ( t / 2 . 3 0 3 ) where 0 < c < 1.0. Now, 0.D.2 > c T 2(Jl/2.303) for two reasons. There i s less l i g h t scattered through small angles i n the second bathing s o l u t i o n , and the r e l a t i v e importance of the scattered l i g h t i s less because of the lower O.D. Therefore, t^/ < O.D.^/O.D The r e l a t i v e O.D. does not decrease to as low a value as the r e l a t i v e t u r b i d i t y . 144 S i m i l a r l y , i t may be shown that i f O.D.^ > O.D..,, the r e l a t i v e O.D. does not increase to as high a value as the r e l a t i v e t u r b i d i t y . 

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