Adventures in Biophysics [Reprint 2016 ed.] 9781512802542

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THE ELDRIDGE REEVES FOUNDATION FOR MEDICAL

JOHNSON PHYSICS

ADVENTURES IN BIOPHYSICS

ADVENTURES IN

Biophysics By Α . V. SC.D.,

LL.D.,

Hill M.D.,

F.R.S.

Foulerton Research Professor of the Royal Society

Philadelphia U N I V E R S I T Y OF PENNSYLVANIA PRESS L O N D O N : H U M P H R E Y MILFORD: OXFORD U N I V E R S I T Y 1

9 3

1

PRESS

Copyright 1931 UNIVERSITY OF PENNSYLVANIA PRESS Printed in the United States oj America by Lancaster Press, Inc., Lancaster, Pa.

PREFACE If you go to Devonshire in September and wander in the lanes you saw at the end of March you will find it hard to believe that they are in fact the same. Reading now in February the proofs of the lectures given at Philadelphia in October I am equally astonished at the changes which a few short months have wrought in our outlook. It is fortunate to be concerned with a field of research in which one's colleagues are so active, but it makes it no easier to describe the present, or any other outlook. The last three years, indeed, have brought strange and precious growth in subjects which seemed to be reaching maturity. I have avoided any detailed alterations in the picture piesented in the lectures themselves, and have been content to show, in somewhat numerous footnotes, so far as I am able, the changes which have occurred in the meantime. No doubt the picture will be old-fashioned again in six months: but still, when the primroses return it may help to explain how they once gave place to blackberries, how— for example and for a season—lactic acid was replaced by phosphagen, equilibrium by steady state, bound water by free. Α. UNIVERSITY COLLEGE, LONDON,

February, 1931.

V

V.

HILL.

CONTENTS

Page

PREFACE

Ν

INTRODUCTION

ix

Some Adventures with Vapour Pressure " II. The State of Water in Tissues " III. The Conception of the Steady State. . " IV. The Time-Relations of Events in Muscular Contraction " V. The Mechanics of Muscular Contraction and Other Matters APPENDIX I. A Discussion of the Several Instrumental Factors Involved in the Attainment of the Greatest Possible Sharpness of Analysis of the Heat Production of Muscle A P P E N D I X II. The Effect on the Calibration of Nonuniformity of Cross-section of Muscle A P P E N D I X III. The Flow of Heat in a Plane Sheet of Muscle

146

BIBLIOGRAPHY

149

INDEX

159

LECTURE

I.

vii

ι 29 55 80 116

139 144

INTRODUCTION ' T ^ W E N T Y summers ago, on Sunday mornings, certain ·*· young Cambridge physiologists used to go and dig in Gaskell's garden on the Gog Magog hills, while he regaled them with histories of the great things he had seen, and the great days he had spent in Ludwig's laboratory and elsewhere. These stories supplied, what no paper in a scientific periodical can supply, a vivid picture of the human side of scientific research. In our journals we try, so far as we can, to present a concise and logical account of our alleged discoveries. The real reasons why we did the things we did, the delays and imperfections and perplexities which beset us, the misery of continual failure, the joy of occasional success, the faith that with patience and persistence we should find the unknown something we were sure was there—all these are unfitting in a scientific periodical, yet somewhere a hint at least of them should be recorded. Such lectures as these are not intended to take the place of reviews or of articles in abstracting journals: those are much better read than heard. I hope, therefore, that Professor Bronk will persuade my successors, as he has persuaded me, to tell you of their scientific adventures: for so, firstly I shall be in good company, and secondly you will see better into their minds, you will realize that for you as for them the pursuit of natural knowledge may be one of the great adventures of the human spirit. I t was Borelli two hundred and fifty years ago who affirmed that the study of the motion of animals, no less than Astronomy, is a part of physics, to be enlarged and adorned (note the word " a d o r n e d " ) by mathematical demonstrations. The Johnson Foundation for Medical Physics, in which I have the honour to inaugurate this annual Series of lectures, is intended to fulfil Borelli's precept. I wish it good fortune in its enviable task: may it adorn, as well as extend, the fields of biological and medical knowledge! ix

L E C T U R E SOME

ADVENTURES

WITH

I VAPOUR

PRESSURE

N the spring and summer of 1927, while I was at Cornell, my colleague and assistant Mr. A. C. Downing was busy in London with a new type of muscle thermopile, which he was preparing against my return. This instrument exceeded all our expectations and made it possible for the first time to measure, with reasonable accuracy, the rate of resting heat production of a muscle lying on it; it came into use just three years ago, in October, 1927. I need not describe it in detail now: it is sufficient to say that by greatly improved electrical insulation of the wires and by the use of material of high thermal conductivity for the framework, it avoided the troublesome zero-errors, and the differences of temperature within the instrument, which had dogged the footsteps of previous myothermic observations. (See fig. ι and Hill 1928a.) A resting muscle placed upon it and soaked in Ringer's solution for an hour or two, g a v e — w h e n the solution was replaced by oxygen or nitrogen—steadyreadings which agreed well with Meyerhof's recorded observations of the oxygen consumption, or of the lactic acid formation, under aerobic or anaerobic conditions respectively. (See Hill 1928 b.) This, with its very constant zero, made measurements of total heat, after stimulation in oxygen or in nitrogen, far more accurate than any previously possible. T h e object of the experiments undertaken was to test, by the myothermic method, a claim advanced from Embden's laboratory in Frankfurt (see Embden, HirschKauffmann, Lehnartz and Deuticke (1926); Embden, Lehnartz and Hentschel (1927)), that in a series of muscle twitches a considerable fraction of the lactic acid set free appears some time after the mechanical response is past. This 1

I

SILVER FRAME

Side

S I L V E R FRAME

front

FIG. I. Thermopile for frog's sartorius. Scale refers to centre and right only (a) Vulcanite carrier; (b) brass terminals to electrodes; {c) copper terminals to thermopile; (d) brass tube for thread to muscle; (e) glass tube carrying electrode leads; (/) glass tube carrying thermopile leads; (g) rubber stopper; (A) glass cover; (»

120 075

i^f

*

0-75 6/772. cm. 4000 Heat verGm.

8000

12000

16.000

2QP00

FIG. 2. Linear relation between anaerobic resting heat-rate and total heat liberated by a succession of tetanic stimuli at ίο-minute intervals. T e t a n u s duration shown in seconds. (Hill 1928^.)

nerve), or some anaerobic process such as the formation of lactic acid from carbohydrate supplies the energy directly. When further energy is unobtainable the cell dies. There are two ways of looking at the phenomenon, the dynamic and the structural. These are not necessarily different, but they start from different points of view. We speak of living matter: there is, as I said at a recent Discussion on Colloid Science at Cambridge (Hill i93od), a certain danger in the term, for it appears to imply that any given identical piece of matter may be, and may continue to be, "alive." It emphasises the matter rather than the process. To take a physical analogy, a wave is a sequence of events in matter—or space—depending on the properties of that matter or space: we should, however, only obscure the study of waves were we to attribute their characteristics to the specific properties of an "oscillatory matter" or an "oscillatory space." There is nothing peculiar about the matter—or space—in which waves are travelling: the peculiarity is in the sequence of events 2

5

A D V E N T U R E S IN

BIOPHYSICS

making up the waves. So also in biology: " l i f e " in the physico-chemical sense must be regarded as a self-perpetuating and generally periodic complex of events, recognisable by its results, not by its outward appearance at a given moment, occurring indeed in a medium of matter, depending absolutely on the properties of matter, but as distinct from matter as music is from the air in which it is propagated. From the dynamic point of view the energy required by a resting cell is used in " d r i v i n g " the sequence of invisible events which make up life. T o break the continuity of these events for more than the shortest time is like wetting a short length in the powder train of a fuse: normal reactions may cease altogether to be propagated, and " l i f e " may end. There must be some element of truth at least in this way of looking at things. T h e other point of view emphasises the known, or the imagined but invisible, structural elements of the living cell. There is no doubt, whatever the mechanism of their maintenance, of the continued existence of surfaces of separation (or of dynamic processes acting like surfaces of separation) in the living cell. L i v i n g tissue, kept aseptically after removal from an animal, gradually breaks down in a way unknown during life. In muscle, glycogen becomes lactic acid, " p h o s p h a g e n " yields creatine and phosphate, various changes take place in the several phosphorus compounds, and probably as yet unknown reactions occur (see, e. g., Meyerhof 1930a). Rigor mortis ultimately sets in, and then the tissue slowly and gradually breaks up, in the process known as " a u t o l y s i s . " All this can be prevented, almost indefinitely, by supplying oxygen and foodstuff's. In the living cell there are, undoubtedly, many highly reactive substances, which proceed to react as soon as they are given the opportunity. T h e opportunity may come, either (1) when the cell is injured by mechanical or chemical means, when in fact the surfaces of separation are positively

6

VAPOUR

PRESSURE

broken: the rapidity of lactic acid formation in injured muscle is a notorious example: or (2) when, by oxygen want or by deprival of energy-liberating substances, the surfaces of separation can no longer be maintained in their normal and orderly state. One is led therefore to think of oxidation in the healthy resting cell as employed in maintaining a certain dynamic status quo, in which highly reactive substances are confined to their proper spheres of action, hindered—so to say—from unsocial conduct, utilized in an organised scheme of things instead of being permitted to behave at random. The need of an oxidative maintenance of an orderly and cooperative system may be due simply to the place of oxidation in a normal sequence of events—here we return rather to the dynamic point of view: or, the oxygen may be used to liberate energy by which surfaces and interfaces are held in their normal, polarized, impermeable state. We may think of a house, or perhaps better of a business or a city, in which the normal architecture, the normal services, and the normal economic organization can be kept up only by continual expenditure. So long as these exist, ordinary life is possible: the inhabitants can go about their lawful business. Remove, however, the normal services and restraints, and chaos rapidly sets in, all kinds of reactions occur which are usually prevented, and recovery may become slow or impossible. These two hypotheses of the function of oxidation in maintaining the steady state of the normal resting cell had long been in my mind. Could it be that in the peculiar increase of the rate of resting heat production of a muscle, caused by anaerobic stimulation, we were witnessing the first stages in the breakdown of the living muscle cells? The greater the extent of activity induced by stimulation the greater would be the oxygen want, the greater the reducing power of the substances set free, the greater the degree to which the surfaces and interfaces of the living

7

ADVENTURES IN

BIOPHYSICS

cells were p u t out of action. If this were so, the increment in heat rate induced by anaerobic stimulation might be a sign of the chaotic reactions m a d e possible by the withdrawal of the normal restraining influence of surfaces, interfaces, or dynamic processes m a i n t a i n e d so long as oxygen was present. Looked at in perspective now, with the true and simple explanation of the phenomenon in mind, the hypothesis m a y appear fantastic. At the time no other seemed possible, nor (I would plead in extenuation) could any of my friends suggest a better. I t was not lightly proposed, and m a n y tests and experiments were made before it was m a d e public. Firstly one h a d to be sure t h a t it was not due to some defect of the i n s t r u m e n t s employed. Various chemical substances, particularly lactic acid, are produced by stimulation: could the effect be a galvanic one, induced for example by acid diffusing through the insulating material and reacting differently with the two metals of the thermopile? T h e thermopile was most carefully insulated with bakelite, shellac and paraffin wax: to avoid a n y possible effect of a diffusing substance a strip of tinfoil was introduced between the insulating layers: the phenomenon appeared u n c h a n g e d : it seemed impossible t h a t any reasonable chemical substance could pass through such protection. Moreover filling the chamber with C 0 2 would make the muscle as acid as extreme fatigue. I t caused only a very slight increment in resting heat rate. If the effect were due to chemical reactions occurring in the muscle it should have a high t e m p e r a t u r e coefficient: t h e increment in heat rate increased a b o u t 2.5 times for a rise of io° C.: a physical error would probably be only slightly affected by temperature. M o r e o v e r — a n d here was something certainly significant—the effect might be almost entirely abolished by allowing the muscle to recover in oxygen. An example, illustrative only, m a y make this clearer. 8

VAPOUR

PRESSURE

Fresh muscle initially in N 2 : resting heat rate, galvanometer scale divisions 20 Muscle fatigued in N 2 : final resting heat rate. 200 0 2 introduced: muscle allowed to recover: final resting heat rate in 0 2 50 N 2 introduced: resting heat rate 25 What could this be other than an effect of oxygen in restoring the normal status quo in the muscle, in reinstating those surfaces or agents which maintain an orderly sequence of events and prevent a biochemical chaos? How otherwise could we find a smaller heat production in oxygen than in nitrogen? The same reactions running to completion in the one would scarcely yield less heat than ending half way in the other. Clearly oxygen was inhibiting some unknown reactions. W h a t should those reactions be other than the ones which, in the absence of oxygen, are known to lead to the death and disintegration of the cell? The experiments could not be denied: the hypothesis— fantastic as even then it seemed—was the only one which I, or any of my friends, could propose, and an account was published in the early summer of 1928 (Hill 1928b). This publication had a most peculiar effect, which some of you, even in America, may have noted. M y colleague Professor Donnan had rashly promised to give a public lecture at the British Association on " T h e Mystery of L i f e " (Donnan 1928). In this, having read my paper, and wishing to refer to the role of oxygen in maintaining the normal life and architecture of the cell, he made a few incautious and far too flattering remarks about my work, with the result that the daily Press descended like an avalanche on me as I was taking my summer holiday in Devon. I was charged with creating life (or alternatively with creating souls 2 ) in the laboratory, I was invited to raise the dead (in America) by means of oxygen and to write half a dozen * Souls and cells sound much the same to a newspaper reporter.

9

ADVENTURES IN

BIOPHYSICS

books. M y friend Professor Meyerhof heard about it from two old ladies—strangers to him—travelling in a train in Switzerland, and wondered what had befallen me. In Frankfurt doubtless they attributed it to the imperfections of the " Hill-Meyerhof theory." Y o u see why I have called this lecture " Some adventures with vapour pressure." B y the autumn of 1928 difficulties began to appear. T h e existence of an increment in resting heat rate after anaerobic stimulation could not be confirmed by Meyerhof (Meyerhof, McCullagh, and Schulz (1930)) by experiments with masses of muscle in a calorimeter. The increment in resting heat rate could be abolished, not only by allowing the muscle to recover in oxygen, but by washing it with Ringer's solution completely free from oxygen. On the other hand the phenomenon itself was confirmed in every way, even with a delicate resistance thermometer to replace the thermopile: it had nothing to do with the particular instrument employed. Finally in the summer of 1929 a most preposterous thing happened—the increment in heat rate due to anaerobic stimulation was found to be several times as great in hydrogen 3 as in nitrogen (Hill 1929c). It was obvious that a muscle could not be using hydrogen for its metabolism—some physical effect must underlie the observation. It still took me several days to find the answer to the riddle—so stupid and slow are physiologists in solving physical problems, so urgently do we need places like the Johnson Foundation where we can get sympathetic help! Years before I had read a paper by J . S. Haldane (Haidane, Kellas and K e n n a w a y ( 1 9 1 5 ) ) in which he showed that the human subject can better stand a given low partial pressure of oxygen in rarefied air than in a gas ' Hydrogen had been previously avoided, as the thermopiles were hollow and it was feared that the gas would diffuse through the insulator and blow them out. This actually happened later when tried. T h e experiments with hydrogen were made with a special instrument which was not hollow.

10

VAPOUR

PRESSURE

mixture at normal atmospheric pressure. Oxygen diffusion is more rapid in a mixture of lower density. Could something be diffusing towards my muscle more rapidly in hydrogen than in nitrogen? On a warm night in July, suddenly and from nowhere, the answer came: water vapour. A book of physical constants gave one immediate assurance that the phenomenon could be explained by the transfer just of a few milligrammes of water per day, evaporating from the walls and condensing on the muscle with an evolution of heat. A couple of experiments next morning made it certain that at last the riddle was solved. Not one of the long line of physiologists, from Helmholtz downwards, who have applied the myothermic method had ever paid any attention to the vapour pressure of the muscles they used. I was in good company. We had all placed our muscles on a thermopile in a moist chamber, moistened preferably with physiological salt solution, to prevent them from drying. We all knew of the depression of vapour pressure caused by substances dissolved in water. We all were aware, at least since the days of Ranke (Ranke 1865), that during activity the osmotic pressure of muscles rises owing to the production of new chemical molecules in solution, such as lactic acid: and a rise of osmotic pressure means a fall of vapour pressure. If we had been asked we should all have admitted the logical necessity that after stimulation the vapour pressure of the muscle would be less, with the consequence that water vapour would pass over from the walls of the chamber and condense on it, with an evolution of heat (the " l a t e n t heat of evaporation")· But, we should have answered, the effect, though theoretically necessary, must be so small as to be completely negligible. For example at 20° C. the depression of vapour pressure due to dissolving 0.7 g. of N a C l in 100 g. of water (a solution about isotonic with Ringer's fluid) is only 0.069 m m * H g ; while the change of vapour pressure due to the production even of 0.32 p.c. of lactic 11

ADVENTURES IN BIOPHYSICS acid

( c o m p l e t e f a t i g u e ) w o u l d be o n l y a b o u t ο . ο ι α

of H g .

mm.

H o w c o u l d w e r e a s o n a b l y e x p e c t a fall o f v a p o u r

p r e s s u r e o f 12 μ of H g to c a u s e a t r a n s f e r o f w a t e r v a p o u r , a c o n d e n s a t i o n on t h e m u s c l e , s u f f i c i e n t to g i v e a m e a s u r a b l e heat production.

Y e t such indeed w a s the case: w i t h the

instruments

in use

now

1930, M a r g a r i a

1930)

(Hill

1930a, Hill

and

Kupalov

1 m m . on the g a l v a n o m e t e r

scale

c o r r e s p o n d s to a c h a n g e o f w a t e r v a p o u r p r e s s u r e o f t h e o r d e r of 0.1 μ o f H g , a f r a c t i o n o f a w a v e l e n g t h o f l i g h t . I h o p e I m a y be a c q u i t t e d o f g r o s s s t u p i d i t y in

having

b e e n d e c e i v e d for n e a r l y t w o y e a r s b y an e f f e c t so c o m pletely unexpected. I t is well k n o w n t h a t in o r d e r t o o b t a i n r e l i a b l e r e s u l t s w i t h i s o l a t e d m u s c l e s it is a d v i s a b l e to s o a k t h e m u s e in R i n g e r ' s

fluid.

before

T h i s has been the recognised practice

for m a n y years, and L u c a s about 1910 designed a special m u s c l e t r o u g h for class e x p e r i m e n t s in w h i c h t h e t i o n is k e p t b a t h e d .

prepara-

T h e p r i m a r y r e a s o n for this use o f

R i n g e r ' s fluid is t o a v o i d d r y i n g : b u t a p a r t f r o m t h i s t h e beneficial effect of previous soaking pirically

realised.

A

logical

a v a i l a b l e in r e c e n t w o r k .

basis

has long been for

the

em-

procedure

is

Duliere and H o r t o n (1929) h a v e

p r o v e d t h a t w i t h o u t s u c h s o a k i n g a m u s c l e is a p t to s h o w a s p o n t a n e o u s loss of i r r i t a b i l i t y , w h i c h c a n be r e c o v e r e d b y subsequent soaking: H o r t o n (1930) has traced the effect f a i r l y c o n c l u s i v e l y to t h e e s c a p e o f p o t a s s i u m f r o m c e r t a i n of

the

fibres:

and

Fenn

(1930)

has

demonstrated

that

d u r i n g t h e s p o n t a n e o u s l y n o n - i r r i t a b l e s t a t e t h e r e m a y be an a p p r e c i a b l y g r e a t e r o x y g e n c o n s u m p t i o n . are

mentioned,

not

because

they

have

any

These facts immediate

b e a r i n g on t h e q u e s t i o n o f v a p o u r p r e s s u r e , b u t the

empirical

recognition

that

a muscle

behaves

because better

a f t e r s o a k i n g h a d led m y c o l l e a g u e s a n d m y s e l f for m a n y y e a r s to s o a k t h e m u s c l e for an h o u r or t w o o n its t h e r m o p i l e before commencing myothermic observations.

This prac-

tice had, moreover, the a d v a n t a g e t h a t b y b u b b l i n g 12

gas

VAPOUR PRESSURE

through the fluid in which the muscle lay the attainment of thermal equilibrium was greatly quickened—which is an advantage when you are reading to o.ooooi 0 . Thus, it had become the regular practice to soak a muscle well on its thermopile before commencing observation of its heat production. Now the preliminary soaking had one effect, indeed one advantage, which was entirely unforeseen: it brought the muscle, particularly if thin, into fairly exact osmotic equilibrium with the fluid around it. When the fluid was withdrawn and replaced by a gas (oxygen or nitrogen) the muscle still possessed the same identical vapour pressure as the fluid remaining on the walls and on the instrument, with the result that no condensation (or evaporation) of water on (or from) the muscle occurred. Consequently the deflection of the galvanometer connected to the thermopile was due solely to the heat produced by the muscle itself, owing to its proper metabolism, and was unaffected by the heat of condensation of water-vapour—until the muscle was stimulated. Then its osmotic pressure rose, its vapour pressure fell, water passed over and condensed on it, with an evolution of heat which might be several times as great as that due to its own resting metabolism. So long, however, as the muscle continued at rest in oxygen, its osmotic pressure—and therefore its vapour pressure—remained constant and equal to that of the fluid in which it had been soaked; and its heat production was correctly measured. In nitrogen, on the other hand, even without stimulation, its osmotic pressure gradually rose, owing to the anaerobic formation of lactic acid and other substances, and in the course of hours its change of vapour pressure was sufficient to cause appreciable error due to condensation of water on it. One obvious way of testing the vapour pressure hypothesis of the origin of the increment in anaerobic heat rate caused by stimulation was to prohibit evaporation 13

ADVENTURES IN BIOPHYSICS altogether by filling the muscle c h a m b e r w i t h paraffin oil. A good brand of " m e d i c i n a l " oil is p e r f e c t l y harmless to l i v i n g tissue, at least within the few hours of such an experiment as this. T h e muscle w a s first soaked for an hour or two in R i n g e r ' s solution to render it p e r m a n e n t l y irritable in the sense of Duliere and H o r t o n (1929). The solution was then replaced by oil t h r o u g h w h i c h nitrogen w a s bubbled to stir it and to r e m o v e o x y g e n ( o x y g e n is v e r y soluble in oil). T h e rate of resting heat p r o d u c t i o n was read once more. T h e r e was no sign of a n y increment. When evaporation, therefore, was made impossible the phenomenon disappeared. T h e converse experiment also w a s n e c e s s a r y : if the rate of evaporation was altered the effect should change proportionally and in the appropriate sense. A muscle w a s placed on a thermopile and brought b y prolonged s o a k i n g into osmotic equilibrium w i t h Ringer's solution. T h e solution was rem o v e d , and in o x y g e n or nitrogen the true resting heat rate was read. T h e c h a m b e r and the i n s t r u m e n t in it were then v e r y rapidly washed o u t w i t h a new solution, w e a k e r or stronger than that originally used, and the gas r e t u r n e d . I f the new solution were w e a k e r its v a p o u r pressure would be greater, w a t e r w o u l d pass o v e r from the walls w e t with it and condense on the muscle, the heat of condensation would be added to the true physiological h e a t , and an increased deflection w o u l d result. Conversely if the new solution were the stronger its v a p o u r pressure w o u l d be less, water would now e v a p o r a t e from the muscle (with an absorption of heat) and condense on the walls, the physiological heat would be diminished b y the l a t e n t h e a t of evaporation, and a smaller deflection w o u l d result. T h e experiment w a s an easy one to m a k e , and was q u i t e decisive. A n y value w h a t e v e r , positive or n e g a t i v e , could be g i v e n to the g a l v a n o m e t e r deflection recording the r a t e of h e a t production of the muscle, b y an a p p r o p r i a t e a d j u s t m e n t of the strength of the solution used for w a s h i n g o u t 14

VAPOUR PRESSURE the chamber. Incredible as it seemed the riddle had really been solved at last! One last test was necessary—the quantitative one. Muscles had frequently been left for long periods, showing exaggerated values of their resting heat rates. If these were due to the condensation of water on them should there not be sufficient water deposited to be very obvious? An extreme value for the increment in resting heat rate in nitrogen, due to complete exhaustion of the muscle, could be accounted for by the condensation of only 6 mg. of water per day on a muscle of 100 mg. A more ordinary value would correspond to 3 or 4 mg. per day, 1 mg. perhaps during the course of an experiment. An increase of 1 or 1 p.c. in the weight of one of these small muscles would be quite inappreciable to the eye: indeed it would be difficult to measure at all with certainty. Clearly there was no quantitative difficulty in attributing the effect to the transfer of vapour in the chamber. The high latent heat of evaporation of water on the one hand, and the almost incredible sensitivity of the instrument as a wet-bulb thermometer (for such indeed it was) on the other, had combined to make it possible to produce all these complex effects, these fantastic hypotheses, these disturbances in the daily Press, with the aid of a few milligrammes of water! How now could the secondary phenomena be explained? {A) The effect of temperature on the increment in resting heat rate: the temperature coefficient of the vapour pressure of water is just the same as that of the observed increment in the muscle experiments. (Β) Meyerhof's failure to detect the effect in calorimetrical experiments: due of course to the fact that evaporation and condensation were not possible, or—if possible—occurring in the same chamber, the one exactly balanced the other. (C) The effect of hydrogen: caused simply by the more rapid diffusion of water molecules through hydrogen than through nitrogen. (D) The effect of oxygen: due to oxidative recovery and 15

ADVENTURES

IN

BIOPHYSICS

the removal of lactic acid, to restoration of " p h o s p h a g e n , " to the fall of the osmotic pressure and the rise of the vapour pressure to their initial values. Perfectly obvious once the riddle had been solved. T h e answers to a number of minor questions now appeared. W h y , for example, if a muscle had not been given a sufficient preliminary soaking, was it impossible to obtain a reasonable or constant value of its resting heat rate? because the muscle was not in osmotic equilibrium with the fluid in its chamber. F o r a long time my colleague Hartree, working at Cambridge with the older type of vulcanite thermopile chamber (Hartree and Hill 1920a), had noticed that, even after prolonged soaking, a muscle suspended in oxygen or nitrogen shows a continual temperature drift in the negative direction (Hartree and Hill 1924, p. 452). One less cautious than Hartree might have been tempted by the perfectly obvious fact to indulge in hypotheses as fantastic as those recorded earlier. T h e living muscle, lying in a moist chamber at constant temperature, was unquestionably slightly cooler than its surroundings: were we witnessing here the direct evasion by a living cell of the Second L a w of T h e r m o d y n a m i c s ? W h a t sport for the daily Press at the British Association! Hartree recorded the result and went on with his work like a reasonable man: being an engineer he was unwilling to attack the Second L a w than which nothing is more certain. T h e answer was really much simpler. T h e vulcanite walls of the chamber absorb a little water (but not salts) from the droplets of solution lying on them; these become slightly more concentrated: their vapour pressure falls: water vapour therefore passes from the muscle to the droplets on the wall: the surface of the muscle is subjected to continual slow evaporation, with an absorption of heat, increasing as time goes on. Hartree has abolished the effect completely, simply by coating the surface of the vulcanite with a film of paraffin wax. So ends the possibility of a temporary 16

VAPOUR

PRESSURE

discovery of great importance: a living cell at constant temperature taking heat from its surroundings! It might be better if other supposed discoveries were treated with similar caution. Here at least, in the Johnson Foundation for Medical Physics, you will be able to save your physiological and medical colleagues from mistaking physical for biological effects. Perhaps indeed some of you expect that they will all prove to be physical in the end! I was determined, however, that the matter should not end here. So utterly unexpected a phenomenon, a device so sensitive in doing a job for which it was not designed or intended, must be made to expiate its crimes and to repay the effort wasted on it by being turned to good account. Firstly it should be calibrated in some way, and used to tell us the absolute value of the rise of osmotic pressure in a stimulated muscle, for comparison with the heat liberated in activity: and secondly it should be applied in a modified form (a problem in design and manufacture for Mr. Downing) to the measurement of the vapour pressure of small quantities of an aqueous solution. The first task it satisfactorily performed as I will shortly recount. In the second task its performance was good beyond expectation, and an instrument and a method have been devised by which the depression of vapour pressure can be measured, in a fraction of ι cc. of an aqueous solution, e.g. in human blood, with a probable error in a single determination of the order of 0.2 or 0.3 p.c. B y its means molecular weights may be measured, " f r e e " water distinguished from " b o u n d , " activities in the physico-chemical sense determined, osmotic pressures and changes of osmotic pressure recorded, all on minimal quantities of liquid. I do not know how important all this is, that is for others to judge, but it is certainly a strange and amusing development of the original observation. This second phase will be discussed in the second and third lectures. The osmotic pressure Ρ of a solution is related to its 17

ADVENTURES IN BIOPHYSICS vapour pressure (for not too great concentrations) by the equation

logepo/p =

PFjRT,

where p0 is the vapour pressure of the pure solvent, p that of the solution and V the volume 4 occupied in the liquid state by one gramme molecule of the vapour of the solvent. For the case of dilute solutions in water this equation may, with sufficient accuracy for most purposes, be written

[Oo - p)lpo]r = PU-ζβΤ, where Ρ is reckoned in atmospheres, and [_{po — ρ)!ρο~\τ is the relative lowering of vapour pressure at absolute temperature T. We see therefore that the osmotic pressure may be simply calculated from the relative depression of vapour pressure (p0 — p)lpt>. The determining factor in a physiological salt solution is the concentration of N a C l , and the relative depression of vapour pressure of a solution of N a C l is easily obtained from its molal 5 concentration m, remembering that over the whole range of physiological importance the relative molal depression, (p0 — p)/mp0, is practically constant at 0.0330, and independent of temperature. It is convenient, therefore, in dealing with osmotic and vapour pressures, to define them simply in terms of the corresponding solutions of N a C l . The absolute values can be immediately calculated if desired. As we shall see in the next lecture the osmotic pressure of frog's blood is equal approximately to that of a solution containing 0.725 g. of NaCl in 100 g. of water. Soaked in a Ringer's fluid practically isotonic with this a thin frog's muscle comes quickly into equilibrium. Placed on a thermopile in nitrogen and stimulated, an "increment in heat r a t e " is measured which records its rise of osmotic pressure: this rise of osmotic pressure is practically a linear 4 To be precise, V is the increase of volume caused by condensing in a large quantity of the solution ι g. mol. of the vapour of the solvent. 6 g. mols. of solute to iooo g. of HiO.

18

rate of a muscle in nitrogen, due to a series of maximal tetani, is plotted (as ordinate) against the total heat set free by stimulation (as abscissa). Units arbitrary. Durations of successive stimuli shown in seconds along each curve. The muscle in every case finished appreciably (e.g. A, D) or very (e.g. C, H) fatigued, as shown by the amount of heat in the last contraction (5 sec.) as compared with the first (1.5 sec.) [Hill and Kupalov 1930.]

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function of the heat produced in the activity induced by stimulation, as shown in fig. 3. In other words, total heat produced in anaerobic activity is almost, but not quite, directly proportional to the total number of molecules simultaneously set free—right up to the stage of rather advanced exhaustion. This is in a normal muscle: what it would be in a muscle poisoned with mono-iodo-acetic acid (see Lundsgaard 1930a), in which lactic acid formation does not occur on stimulation, remains to be f o u n d : 6 the experiments of fig. 3 were made before L u n d s g a a r d ' s paper was published. I t is important, in any case, to know that in the normal muscle at least the energy is very nearly proportional to the number of molecules set free. T h e major chemical changes known to occur in normal stimulated muscle are lactic acid formation and phosphagen breakdown. According to Meyerhof (1930a, p. 233) the isometric coefficient of lactic acid (the ratio of the product of tension developed and length to lactic acid formed in an isometric twitch) is almost entirely unaffected by temperature, but depends to some degree on the initial tension and appreciably on the degree of fatigue of the muscle. B y plotting and differencing M e y e r h o f ' s data (1930a, p. 234) it can be calculated that in successive productions of 0.05 p.c. lactic acid (i.e. from o. to 0.05, 0.05 to 0 . 1 0 , o. 10 to 0 . 1 5 etc.) the isometric coefficient of lactic acid has the following values, all multiplied by io 6 : 162, 1 3 4 , 1 1 4 , 1 0 0 , 96, 88, 82. According to my own observations the isometric coefficient for heat ( T l j H ) also is independent of temperature (Hartree and Hill 1 9 2 1 b ) and is somewhat affected by initial tension (Hill 1925) but is practically constant throughout a long series of twitches (Hill 1928c), up to the beginning of fatigue: in a very fatigued muscle, however, it diminishes, probably owing to another cause, the failure of the contractile mechanism. Dividing the one • T h e same effect has been found in muscles poisoned with iodo-acetic acid. footnote 1 2 , p. 25 below and Hill & Parkinson ( 1 9 3 1 ) .

20

See

VAPOUR PRESSURE c o e f f i c i e n t b y t h e o t h e r w e o b t a i n t h e r a t i o o f h e a t to l a c t i c a c i d f o r m e d ; w e see t h a t t h i s d e c r e a s e s c o n s i d e r a b l y b e t w e e n t h e b e g i n n i n g a n d t h e e n d o f a l o n g series o f t w i t c h e s . It

is

very

unlikely,

indeed

impossible,

that

the

same

chemical reaction should yield different quantities of heat at different s t a g e s of a c t i v i t y : the e x p l a n a t i o n of the fall of t h e i s o m e t r i c c o e f f i c i e n t for l a c t i c a c i d is a l m o s t

certainly

in p a r t t h a t in t h e e a r l i e r s t a g e s o f a c t i v i t y a c o n s i d e r a b l e f r a c t i o n o f t h e e n e r g y is d e r i v e d f r o m p h o s p h a g e n

break-

d o w n , so t h a t t h e l a c t i c a c i d is less a n d t h e c a l o r i c q u o t i e n t (heat/lactic acid) greater.

A b o u t 1/5 o f t h e e n e r g y s e t f r e e

i n s t i m u l a t i n g a m u s c l e t o f a t i g u e (see L e c t u r e V ) m a y

be

derived from phosphagen

by

Eggleton

and

phosphagen

Eggleton

breakdown

breakdown.7 (1927b,

to lactic

It was shown

1928)

that

the

acid formation

ratio

of

decreases

r a p i d l y as a n a e r o b i c s t i m u l a t i o n is c o n t i n u e d , a n d t h i s h a s been

amply

confirmed

(see

Meyerhof

1930a,

p.

101).

D i r e c t d e t e r m i n a t i o n s of the caloric q u o t i e n t for lactic acid by

Meyerhof

203)

have

lactic 0.2

acid

and

shown the

p.c., 355

his colleagues the

same

quotient

cal.,

i.e.

for

(see M e y e r h o f

general

was

376

the

effect. cal.

second

per

0.1

1930a,

For

0.1

gramme,

p.c.

lactic

p.

p.c. for acid

3 3 4 cal.: w i t h c o n s i d e r a b l e f a t i g u e the v a l u e w a s still lower. I t is c l e a r t h a t in t h e e a r l i e r s t a g e s o f a n a e r o b i c

activity

e n e r g y is l i b e r a t e d t o a n a p p r e c i a b l e e x t e n t a t t h e e x p e n s e of

phosphagen

breakdown,

in

the

later

entirely b y the formation of lactic acid.

stages

The

almost

myothermic

o b s e r v a t i o n s s h o w , h o w e v e r , t h a t in b o t h s t a g e s , i.e. f r o m e i t h e r s o u r c e o f e n e r g y , t e n s i o n is d e v e l o p e d (a) w i t h a b o u t t h e s a m e t o t a l l i b e r a t i o n o f h e a t 8 a n d (b) w i t h a b o u t

the

s a m e t o t a l l i b e r a t i o n o f n e w m o l e c u l e s or i o n s . 'Probably more like one-third from sources other than lactic acid. See Hill and Parkinson (1931). 8 This conclusion is strikingly confirmed by the fact that in a muscle poisoned with iodo-acetic acid, in which no lactic acid is formed, the ratio Tl/H in a twitch is exactly the same as in a normal muscle. Fischer (1930a, 1931): Meyerhof, Lundsgaard & Blaschko (1930): confirmed by Feng and myself. 21 3

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With regard to the latter, so far as the lines of fig. 3 are not straight they suggest that energy, in the earlier stages of activity, is liberated with a rather smaller rise of osmotic pressure than in the later stages. T h i s cannot be explained, nor indeed can a linear relation, by assuming that in the earlier stages of activity the energy is derived more from phosphagen breakdown, in the later stages more from lactic acid formation. T h e energy liberated, per g. mol., in the splitting of phosphagen is about 1 1 0 0 0 cal. (Meyerhof 1 9 3 0 a , p. 94). If the breakdown be " p h o s p h a g e n " molecule —> creatine +

phosphate,

then one new gramme molecule is liberated per calories. If it be X — "phosphagen"

X + creatine

11000

phosphate,

where X is some other unknown substance, then two new gramme moleculcs are liberated per 1 1 0 0 0 calories. In the formation of lactic acid alone in muscle we have (say) 300 cal. per g. or 27000 cal. per g. mol. For a given amount of heat therefore the number of new molecules set free is much less in the case of glycogen than in that of phosphagen breakdown: this is the wrong w a y round 9 to explain the curvatures of fig. 3. T h e phosphagen breakdown occurring particularly at the beginning, i.e. to the left of each diagram, should give there a greater and not a smaller rate of rise in the osmotic pressure curve. Clearly there are other factors at work, hitherto unrecognised: indeed the observations which I will next discuss furnish a strong hint that during anaerobic activity, during fatigue, there is an appreciable excess of new molecules or ions produced, over • This conclusion is borne out to some degree by the observation (Hill and Parkinson 1 9 3 1 ) that the liberation of 1 cal. of heat per 1 g. by a muscle poisoned with iodo-acetic acid (in which no lactic acid is formed) is accompanied by a rise of osmotic pressure equivalent to that produced by adding 0.40 p.c. N a C l to Ringer's fluid: whereas 1 cal. per 1 g. in a normal muscle gives a rise of osmotic pressure equivalent only to 0.33 p.c. N a C l .

22

VAPOUR PRESSURE and above all those known at present to chemical analysis. We are not yet at the end of the biochemistry of muscle. The rise of osmotic pressure shown by the increment in heat rate can be measured in absolute units, and compared with the heat set free during preceding activity. By washing out the chamber with Ringer's fluids of different concentrations the apparent rate of heat production can be altered: and it is clear that the speed of condensation of water vapour on the muscle, owing to a given rise in its osmotic pressure, must be the same as that due to an equal fall in the osmotic pressure of the fluid in the moist chamber. For example, if a deflection of 200 mm. be given when a Ringer's fluid isotonic with 0.75 p.c. of NaCl is replaced on the walls of the chamber by one isotonic with 0.45 p.c. NaCl, then it is obvious that a deflection of 200 mm. obtained by stimulation is to be attributed to a rise of osmotic pressure equal to that caused by adding 0.3 p.c. of N a C l to the fluids of the muscle. Kupalov and I (1930a) have made a number of such observations and found that, on the average, for 1 calorie per gramme of heat set free in fatiguing a muscle, there is a rise of osmotic pressure equivalent to the addition of 0.335 8· NaCl to 100 g. of its fluids.10 In complete fatigue there may be 0.3 to 0.35 p.c. of lactic acid set free, 1.05 to 1.225 calories of heat liberated per gramme. Taking 0.3 p.c. of lactic acid as a standard, this degree of fatigue will lead, according to our results, to a rise of osmotic pressure equivalent to the addition of 0.35 p.c. of NaCl to the fluids of the muscle. It is interesting to compare this value with that calculated from all the substances known to be produced in fatigue. We will assume that the muscle is 77 p.c. " f r e e " water and that the lactate ion exerts a normal osmotic pressure; it is easy to calculate that the increase of osmotic pressure on stimulation to 10 Confirmed by Hill and Parkinson (1931) who found a mean value of 0.326 in similar experiments.

23

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fatigue is 2.8 times as great as the osmotic pressure of the lactate ions liberated. T o explain the discrepancy it might be argued that the lactate ion is necessarily accompanied by an alkali ion, e.g. K , and that before combination with lactate the Κ ion was not free in solution to affect the osmotic pressure. There is, however, grave difficulty in assuming that the Κ ions associated after stimulation with the lactate ions were not free in solution before. T h e existence of electrically undissociated compounds of Κ in muscle is unlikely, and even if the anions were unable to diffuse (e.g. if they were part of the protein structure of the muscle) the cations would be free to change partners and so to move about and presumably to affect the osmotic pressure. Moreover, as I shall show in my next lecture, the osmotic pressure o f resting muscle can be calculated fairly exactly from the known soluble constituents dissolved in the water of the muscle. I f we were to argue that the cations before stimulation were not free to affect the osmotic pressure we should be left with a serious deficit in our calculation. Finally, direct experiments in which an acid ( C 0 2 ) was added artificially to resting muscle caused an increase of osmotic pressure rather less than that of its anions alone, certainly not twice as great: an effect which has been confirmed by Margaria (1931b) by experiments in which the rise of osmotic pressure due to the combination of C 0 2 w i t h blood was found to be appreciably less than that calculated for the bicarbonate ions alone, certainly again not twice as great. I t is clear therefore that the cations play no part in the phenomenon described. Lactic acid, however, is not the only substance liberated in fatigue. T h e breakdown of phosphagen into creatine and phosphate, if we suppose it to occur according to the second scheme referred to earlier, 11 liberates two new 11 There is evidence from recent work of Eggleton (1930) that " p h o s p h a g e n " in living muscle is not a simple uncombined molecule: phospho-creatine can diffuse

24

VAPOUR P R E S S U R E molecules for every atom of Ρ set free. According to Parnas and Mozolowski (1927) the ammonia content of muscle increases in severe fatigue. According to Lohmann (1928), in exhausted muscle a certain amount, say, one third, of the pyrophosphate initially present in it is hydrolysed into orthophosphate; if this pyrophosphate had previously been combined with adenylic acid (Lohmann 1929) each molecule split would become three. Taking account, therefore, of every known possibility, and making a maximal allowance in each case, the increase in total molal concentration as the result of fatigue can be calculated as follows: L a c t a t e (0.3 p . c . )

0.043 Μ

Creatine

0.023 Μ

Phosphate

0.023 Μ

Ammonia

0.002 Μ

Pyrophosphate-adenylic acid

0.004 Μ

Total

°.°95 Μ

sum m Now 0.095 Μ ' s ° l a l concentrations of the ions of a solution of 0.28 g. of N a C l in 100 g. of water. This is only 80 p.c. of 0.35, the observed change. We have taken the most favourable view possible of all the reactions known, or supposed, to be involved, in order to provide as many new molecules as possible. In spite of it there is still a deficit. 12 The existence of this deficit has more

through a parchment membrane: phosphate and creatine can diffuse through the living muscle: phosphagen can not. Presumably the phosphagen breaks down from combination in a larger complex, X — phosphagen —1• X + phosphate + creatine. In muscles poisoned with iodo-acetic acid, in which lactic acid formation is impossible, the chemical changes known to occur are (Lundsgaard 1930b): (a) phosphagen becomes phosphate and creatine; ( i ) adenyl-pyrophosphoric acid becomes orthophosphate, inosinic acid and ammonia; (r) the phosphate formed is esterified with hexose derived from glycogen, about 70 p.c. as the di- and 30 p.c. as the mono-ester; (d) some glycogen is broken down to hexose. These changes, at the best, acu

25

A D V E N T U R E S IN BIOPHYSICS recently been confirmed by Meyerhof (1930b) in experiments in which the extra depression of freezing point, caused by stimulating muscles to fatigue, was compared with the various substances produced. Presumably, therefore, some other changes, at present unrecognized, are involved. It is indeed unlikely that, after the striking progress of the last few years, we should at this particular moment have discovered all the reactions involved in muscular activity. M a y not carnosine, for example, be found to supply part of the missing osmotic pressure? There is no evidence indeed as yet that it will, but for many years creatine had also apparently no particular role to play. Carnosine is present in considerable quantities, specifically in skeletal muscle. There is said to be 0.25 p.c. in frog's muscle, considerably more in the muscles of some mammals. Little attention has been paid to it, and methods of determining it are at present very uncertain. Its molecular weight is 226, so that if 0.25 p.c. of carnosine were set free in muscular activity it would form a 0.012 Μ solution in the water of the muscle—which is about half the quantity we require to complete the story. L e t me show you, in closing, how consistent nature is. We have seen a very considerable rise of osmotic pressure in a frog's muscle stimulated anaerobically. Cannot the same phenomenon be demonstrated in man? This, by the w a y , is always a good question to ask: it often leads you into work more interesting even than the original discovery. It is easy to make a man take exercise of the required nature: any very severe effort, lasting even for a minute, leaves behind it a considerable " o x y g e n debt." We should expect the muscles of a man exhausted by violent exercise count for 50 to 70 p.c. of the increase of osmotic pressure observed (Hill & Parkinson 1 9 3 1 ) , unless we assume that the phosphagen and perhaps the adenyl-pyrophosphoric acid were combined in some more complex form in the resting muscle, and so were unable to exert an osmotic pressure of their own. Otherwise it is necessary, as in the normal muscle, to suppose that some reaction, hitherto unknown, occurs during activity.

26

VAPOUR P R E S S U R E to have a very high osmotic pressure. This should rapidly be communicated to the blood, partly by diffusion outwards of the products of metabolism, but more particularly by the diffusion of water in. The experiments of Margaria (1930) to be referred to again in a later lecture have shown a surprisingly constant value in the osmotic pressure of the blood of men at rest: the mean value is equal to that of a solution containing 0.945 g. of NaCl in 100 g. of water: the probable deviation of an individual value from the mean is only ± 0.005. The of a runner who had competed in the Amateur Athletic Championships in London, withdrawn 75 sec. after the end of the two miles steeplechase, had a value of 1.048, more than 1 1 p.c. higher than the mean. Margaria himself, after 1 minute of standing running, showed a value of 0.989: he had to go slow, however, in order to be in a fit state at the end to withdraw his own blood: our colleague, Hukuda, who had no such obligation, after minutes of standing running, gave the following values: Blood withdrawn f min. afterwards Blood withdrawn i j min. afterwards Blood withdrawn 4} min. afterwards

J -°33 0.996 0.982

M y own blood, withdrawn 60 seconds after 1 minute only of standing running, gave a value of 1.028. Standing running at maximum speed is extremely exhausting exercise; correspondingly it raises the osmotic pressure of the blood, in a very short time, to astonishing values: after which the osmotic pressure slowly returns to normal as recovery proceeds. The increment recorded in these experiments is quite outside the range of normal resting values: it exceeds the probable deviation twentyfold or more. I have little doubt that the blood of a first class runner, taken shortly after a quarter or a half mile race, would show considerably greater increments than these: in fact I am inclined to put a value of 1 . 1 5 as well within the range of possible accomplishment, for exercise of ex27

ADVENTURES

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treme severity lasting for a minute or two in a first rate subject. It may be interesting to some of you, in this land of record-breaking, to try. One can never hope to obtain a value as high as that of the muscles themselves: diffusion is not rapid enough between muscle and blood, and recovery sets in too fast. But at least one m a y hope, in the blood of the human athlete, to show an increment of osmotic pressure which is 60 p.c. of that found in the isolated muscle driven to exhaustion. M a y not such a change of osmotic pressure, leading temporarily to a large upset in the water distribution of the organism, be the cause of some of the phenomena of fatigue? Might not, for example, an osmotic suction of one atmosphere, suddenly applied, considerably upset the central nervous system ?

28

L E C T U R E THE

STATE

OF W A T E R

II IN

TISSUES

O R the calculations given in the last lecture we assumed that the substances formed during muscular activity are simply and normally dissolved in the water of the tissue, which was taken as being 77 p.c. by weight. Actually there is 80 to 81 p.c. of total water in frog's muscle: the value 77 p.c. was chosen for reasons which will be referred to later. I f , however, the chemical bodies had been dissolved in water equal in weight to 61 j p.c. of the muscle and not to 77 p.c. they would have given the full value of the observed increase in osmotic pressure: there would have been no cause to argue that some chemical body still unknown is liberated in muscular activity. Alternatively, we might attribute the observed rise of osmotic pressure not entirely to an increase in the quantity of the dissolved substances themselves but partly to a decrease—caused by activity—in the volume of the solvent. F o r example, if the free water of the muscle, initially 77 p.c., were reduced b y some colloidal process occurring in fatigue to 72 p.c. the dissolved constituents initially isotonic with 0.725 p.c. N a C l would be confined to a smaller volume, and their osmotic pressure would rise to a value equivalent to that of 0.725 X 77/72 = 0.776 p.c. N a C l . T h e chemical substances formed in a c t i v i t y , moreover, instead of being dissolved in 0.77 g. of w a t e r per g. of muscle, would be dissolved in 0.72 g. of water, and their osmotic pressure would be that, not of a 0.28 p.c. N a C l solution, but of a 0.28 X 77/72 = 0.297 p.c. solution. T h u s the final osmotic pressure would be that of a solution of (0.776 + 0.297) = 1.073 P- c · N a C l . T h i s is about 0.35 p.c. in excess of the initial value 0.725 p.c., so that the whole of the deficit in the calculated osmotic pressure below the observed could

F

29

A D V E N T U R E S IN

BIOPHYSICS

be explained by the simple hypothesis that the " f r e e " water of the muscle diminishes from 0.77 g. to 0.72 g. per g. of muscle as the result of fatigue. Clearly this possibility could not be neglected: it required careful examination. Indeed if it could be shown to be a fact it might provide a factor of extraordinary potency in altering or adjusting the osmotic pressure of living tissues, or their fluids. It is easy to imagine colloidal changes to occur by which some of the water is removed from its normal state as a solvent, and combined in some other state with the colloid: the consequence would be that the substances dissolved would be confined to a smaller volume and their osmotic pressure would rise, without the liberation of any molecules at all. T h e possibility had indeed been claimed as a fact as long ago as 1910. Jensen and Fischer ( 1 9 1 0 ) and Jensen (1912) determined the " bound " water of muscle by making cooling curves and calculating from their areas the heat absorbed. A comparison of the results with those obtained with solutions of N a C l was believed to allow a calculation of the " b o u n d " water. In fresh muscle they found 4 p.c. of the total water to be " b o u n d , " in muscle killed by freezing and thawing 14 to 17 p.c., in muscle heated to ioo° C. 22 p.c. Changes much smaller than these, occurring in fatigue, would be sufficient to explain completely the observed excess of osmotic pressure. Since the publication of Overton's experiments (1902) it has been commonly supposed that a large proportion of the water of muscle exists in some " b o u n d " form, incapable of taking part in the osmotic changes which occur when the tissue is immersed in hypo- or hyper-tonic solutions. From the fact that a muscle swells to much less than double its initial weight when immersed in a solution of half the initial osmotic pressure Overton concluded that " o n l y part of the water found in muscle can be present as a solvent." Overton's experiments can easily be confirmed. 30

S T A T E OF WATER IN TISSUES Their explanation, however, as I have shown in a recent paper (Hill 1930b), is not a " b i n d i n g " of the water, but (a) progressive changes, owing to survival and immersion, {b) the slowness of diffusion, and (c) the loss of semipermeability in a considerable fraction of the fibres. Overton's experiments, in fact, provide no support for the theory of " b o u n d " water in muscle. They must be referred to, however, for they seem to have started the tradition. A very obvious objection was raised by Rubner (1922) to the experiments of Jensen and Fischer, viz., that thermal conduction may be quite different in muscle and in solutions of N a C l . Rubner proposed an alternative method based on the same general idea, viz. that " b o u n d " water may be defined as that which cannot be frozen out by cooling the tissue to such temperatures as — 20° C. The material to be investigated was cooled to a low temperature for two hours and then dropped into a water calorimeter, the heat required to melt it being measured. He found that 1 gramme of dry substance was associated with the following amounts of " b o u n d " water: Egg-white Blood corpuscles Elastic tissue Blood vessels Beef muscle (dead) Beef heart-muscle (dead) Frogs' muscle (alive)

0.33 g. 0.63 0.44 0.45 0.76 0.64 0.90

The frog's muscle was cooled to — i8° C. and 100 g. of muscle contained 61.7 g. of " f r e e " water (mean of 11 observations); similar muscle contained 79.8 p.c. of total water. 1 Rubner's method also is not free from possible objection: (i) it assumes that the " b o u n d " water is the same at 1 In dilatometric experiments carried out at —2o° C . Moran and Smith (i930) found " t h a t the amount of water remaining unfrozen cannot possibly be greater than 6 p.c. of the total water in the muscle." I t is "quite possible," they point out, " t h a t muscle contains no bound water," even at — 20° C .

31

ADVENTURES

IN

BIOPHYSICS

— 20° C . as at the ordinary t e m p e r a t u r e s in which we are interested; the " b i n d i n g " of w a t e r b y a hydrophilic colloid is likely to be an exothermic reaction, in which case it m i g h t proceed appreciably further at a low temperature t h a n at a high. (ii) it assumes t h a t no reactions other than the melting of ice occur when the temperature rises. (iii) the specific heats of the solid constituents of muscle m a y not be v e r y accurately k n o w n , nor the heats of their solution negligible. It is possible, moreover, that water p r e v e n t e d from freezing by association with hydrophilic colloids m a y nevertheless be c a p a b l e of dissolving substances present in the tissue, and so be in t h a t sense free. R u b n e r ' s method was e m p l o y e d b y T h o e n e s (1925); indeed it is continually a t t r i b u t e d b y A m e r i c a n writers to T h o e n e s . T h e latter found in a gelatin jelly about 2 g. of w a t e r " b o u n d " by each 1 g. of d r y m a t e r i a l ; in agar j e l l y a b o u t 4 g. In the muscles of y o u n g animals he found about 2 g. of " b o u n d " water per 1 g. of d r y substance, in those of old animals about 1 g. T h e muscles were frozen and the h e a t of t h a w i n g measured. " I n this w a y , " he claimed, " i t can be shown w i t h considerable c e r t a i n t y t h a t there is a change during rigor in the a m o u n t of water b o u n d . " Robinson (1927, 1928) applied the same method to invest i g a t i n g the hardiness of insects exposed to low temperatures during winter. In some insects as m u c h as one half of the w a t e r they contain m a y be " b o u n d , " in the sense that it is not frozen by cooling to — 20° C . In h a r d y insects (Promothea) exposed to low t e m p e r a t u r e s the proportion of w a t e r " b o u n d " m a y increase from a b o u t 8 p.c. at the s t a r t to o v e r 40 p.c. after t w o or three weeks' exposure. The m e t h o d e m p l o y e d by T h o e n e s and b y Robinson is discussed in detail by G o r t n e r (1929). It is open to the same possible objections as t h a t of R u b n e r . A n o t h e r definition of, and another m e t h o d of determining, the " f r e e " w a t e r were suggested by N e w t o n and 32

S T A T E OF W A T E R IN TISSUES Gortner (1922), who added a known amount of cane sugar to expressed plant juice and measured the resulting depression of freezing point. 2 T h e greater the amount of water " b o u n d " the less will be the volume of water free to dissolve the added cane sugar, and the greater will be the depression of freezing point. B y comparing the depression of freezing point observed with that caused by adding the same amount of cane sugar to an amount of water equal to the total quantity contained in the juice, they showed that an appreciable fraction of the water was " b o u n d , " in the sense that it took no part in the solution of the cane sugar. In one case in which the solids made up 0.178 g. per ι g. of juice, of the total water (0.822 g.) 0.130 g. was found to be " bound." Newton (referred to by Gortner (1929)) employed the same method of studying the state of water in the sap of winter wheat, in drought-resistant crops, and in the press juice of grasses. In a recent paper Gortner (1930) has emphasised his sense of the importance of the conception of " b o u n d " water in biology. T h e questions raised as to the status of water in various animals and plants are clearly of great interest and merit further research and thought. I have had no personal experience of the matter except in so far as it has been presented by the problem which I discussed in my first lecture: the observed changes in the osmotic pressure of muscle obviously demanded a knowledge of the amount (if any) of " b o u n d " water in muscle and of its changes (if such occurred) during and as the result of activity. In investigating the problem I have been led 1 This method has recently been criticised by Grollman (1931) and by Moran and Smith (1930), particularly on the ground of the anomalies occurring in salt solutions to which high concentrations of sucrose are added. Indeed, according to Grollman, the method employing high concentrations of sucrose may often be shown to lead to impossible results. He suggests that the addition of small quantities of N a C l or K C l and the use of a delicate means of measuring the depression of vapour pressure (see below) provide the most appropriate method of approaching this problem. With such a method he found that the amount of water bound in gelatin solutions at p H 7.0 is relatively small, and in gum acacia solutions negligible.

33

ADVENTURES IN BIOPHYSICS incidentally to study blood, the body fluids of invertebrates, casein solutions and eggs. The opinion, therefore, which I shall express, that in muscle, and in such fluids, the " b o u n d " water is of little, if any, importance, and that the " f r e e " water is nearly equal to the total water as measured by drying, must be understood at the moment to apply solely to such fluids. The methods which we will discuss could be applied to a variety of other problems, but the results of such applications must not be forestalled. 3 As a preliminary to the description of the experimental study of the problem, it is interesting to see how far the observed osmotic pressure of blood and muscle can be calculated from the known concentrations of their soluble constituents as determined by analysis, supposing these to be dissolved in the total water as measured by drying. Incidentally mammalian blood is an excellent physico-chemical " m o d e l " of muscle; it contains about the same relative amount of water, and its chief protein, haemoglobin, is an efficient buffer, being (like the proteins of muscle) the ionised alkali salt of a weak acid. Mammalian blood. The mean osmotic pressure of human blood, taken from men at rest, is very accurately known from the investigations of Margaria (1930), which will be referred to in detail in the next lecture. It is equal to that of a N a C l solution containing 0.945 g. in 100 g. of water. Abderhalden's (1898) analyses of the blood of two cattle, two sheep, two horses, two dogs, one goat, one pig, one rabbit and one cat, allow the following mean values to be calculated. It is realised that by taking the mean of his 12 values for each constituent we obtain a result which is true in detail for no particular animal; since, however, our only object is to find the sum of the molal concentrations for mammalian blood, no error is introduced by taking the mean, and the result is more accurate. • S e e , however, Grollman ( 1 9 3 1 ) .

34

STATE

OF

WATER

IN

TISSUES

TABLE I.—Mean Values Calculated from Abderhaldens Data for Mammalian Blood Substance

g. to

100 g. blood

80.2 12.5

HiO Hb Sugar Na Κ Ca Mg CI Total Ρ

0.0790 0.2460 0.0790 0.0044 0.0031 0.2890 0.0314

g. to

100 g. HjO —

15.6 0.0980 0.3060 0.0980 0.0055 0.0039 0.3604 0.0392

Molal concentration

Remarks

—

Ο.ΟΟ23

Molecular weight assumed 67000 (Adair (1925), (1928))

0.0054

—

O.I33J 0.0252 O.OO IO

— —

Assumed 70 p.c. as free Ca ions

O.OOL6

O.IOI5 0.0088

— —

See note

Sum. . Ο.2789 Note.—The molal concentration for total Ρ assumes that the number of dissolved molecules containing phosphorus is 70 p.c. of the number of phosphorus atoms. See Hill 1930b, p. 482. A b d e r h a l d e n ' s list, h o w e v e r , a l t h o u g h it m a k e s u p nearly 87 p.c. of the sum of the m o l a l c o n c e n t r a t i o n s , m u s t

be

s u p p l e m e n t e d b y the following d a t a , o b t a i n e d from v a r i o u s sources. TABLE I I . — C o n s t i t u e n t s of Mammalian

Substance

Concentration assumed

Mola] concentration

Blood

Remarks

Protein other than One third of the value 0.0008 A rough estimate, but the for Hb value is practically negliHb gible in any case Bicarbonate 50 c.c. combined COi per 0.0280 100 g. blood 16 mg. per 100 g. blood. 0.0022 Lactate 0.0003 SO. 0.0062 0.030 p.c. in blood Urea Amino acids 0.006 p.c. Ν in blood. . . 0.0053 One Ν atom assumed to each molecule 0.007 P-c· ' n blood 0.0006 Creatine O.OOOI 0.001 p.c. in blood Creatinine 0.002 p.c. in blood Uric acid 0.0002 Sum

0.0437

35

ADVENTURES IN BIOPHYSICS T h e s u m , therefore, of the molal c o n c e n t r a t i o n s of all c o n s t i t u e n t s , o b t a i n e d by a d d i n g the results of T a b l e s I a n d I I , is 0.3226. T h i s is equal to the sum of t h e molal c o n c e n t r a t i o n s of t h e ions of a 0 . 1 6 1 3 molal N a C l solution, which is 0.943 g. in 100 g. H 2 0 . T h i s is almost precisely equal to t h e m e a n value, 0.945, for h u m a n blood exposed to 5 p.c. C 0 2 , found by M a r g a r i a . T o o m u c h e m p h a s i s m u s t n o t be laid u p o n the exactness of t h e a g r e e m e n t , b u t it is clear t h a t we can, if we wish, explain the observed osmotic pressure of m a m m a l i a n blood as due to all its soluble c o n s t i t u e n t s dissolved in its total w a t e r . If it be asserted t h a t a fraction of t h e w a t e r is " b o u n d " it m u s t be a d m i t t e d t h a t a precisely equal fraction of the soluble cons t i t u e n t s is b o u n d also: a s o m e w h a t unlikely coincidence. Frog's muscle. Various m e t h o d s h a v e been used in an a t t e m p t to d e t e r m i n e t h e exact s t r e n g t h of a solution of N a C l which is isotonic with frog's muscle. T h e most reliable results, those of O v e r t o n (1902) a n d of F l e t c h e r (1904), are 0.70 p.c. a n d 0.75 p.c. respectively. T h e depression of freezing point of frog's muscle also h a s been d e t e r m i n e d by various observers: t h e results I h a v e s u m marised in a recent paper (Hill and K u p a l o v 1930). T h e most p r o b a b l e v a l u e for t h e freezing point is a b o u t — 0.43°, which corresponds to t h a t of a solution containing 0.725 g. of N a C l in 100 g. of water. By t h e m e t h o d which will be described later in this lecture t h e depression of v a p o u r pressure of frog's blood has been m e a s u r e d (Hill a n d K u p a lov 1930, p. 4 5 1 ) . W i t h t h e necessary corrections for C 0 2 its m e a n value corresponds to t h a t of a solution c o n t a i n i n g 0.75 g. of N a C l in 100 g. of H 2 0 . Muscle is necessarily in osmotic equilibrium with blood. T h e r e are good g r o u n d s , therefore, for t a k i n g the osmotic pressure of frog's muscle as e q u i v a l e n t to t h a t of a solution of N a C l c o n t a i n i n g 0.725 g. in 100 g. of water. T h e c o n c e n t r a t i o n s of the cations p r e s e n t in frogs' muscles, and of chloride a n d w a t e r , according to Meigs and 36

STATE

Ryan (1912)

WATER

IN

TISSUES

and according to Katz (1896) are as follows, expressed in mg. per 100 g. of

( R . catesbiana),

esculenta),

( R .

OF

fresh muscle:

Meigs and Ryan Katz Mean

Κ

Na

Ca

Mg

ci

H.O

35°

3o8

54 55

18 16

3° 2 3

66 40

79900 81600

329

54έ

11

261

53

80700

Assuming these cations to be freely dissolved in the water the molal concentrations corresponding to the mean values just given are:

Molal concentration

Κ

Na

Ca

Mg

Total

0.I04

0.030

O.OO7

0.013

Ο.154

For the anions a similar calculation can be made with the following data: (a) Chloride: assuming the mean value given above, the molal concentration is 0.018. (b) Bicarbonate: the bicarbonate content of fresh frog's muscle at pH 7.0, calculated from Stella's (1929) data, corresponds to 12 volumes p.c. of combined C0 2 , or 0.007 molal. (c) Lactate: assuming a resting value of 25 mg. per 100 g., the molal concentration is 0.003. id) Phosphate: the phosphate distribution of resting muscle may be taken as follows. PHOSPHORUS

COMPOUNDS

OF R E S T I N G

mg. Ρ Compound per 100 g. 18 Orthophosphate Pyrophosphate-adenylic acid complex (Lohmann 1929) · · 45 Creatine-phosphoric acid (phosphagen). . . 65 Hexose monophosphoric ester ·· 5

• '33

37 4

MUSCLE Molal concentration 0.008 0.006 0.026 0.002 0.042

ADVENTURES IN BIOPHYSICS F o r the anions therefore of resting muscle, we may summarise as follows:

Molal concentration

Cl

Η CO,

Lactate

Phosphate

Total

0.018

0.007

0.003

Ο.Ο42

0.070

T h e sum of the molal concentrations of all the ions, positive and negative, is 0.154 + 0.070 = 0.224. T o this we should add the molal concentration of free creatine, which is a b o u t equal to t h a t of orthophosphate (Duliere 1929), viz. 0.008, and t h a t of protein, which we can only estimate by assuming it to have the same value as the haemoglobin in mammalian blood, viz. 0.002. T h e sum, therefore, of the molal concentrations of all known soluble constituents is 0.234. N o w the sum of the molal concentrations of the ions of the N a C l solution which we decided earlier to take as isotonic with muscle (0.725 to i c o g. H 2 0 ) is 0.248. This is only slightly greater t h a n the value calculated from the soluble constituents. If we had assumed t h a t only 95 p.c. of the water of muscle is " f r e e , " instead of 100 p.c., if in fact we h a d calculated our concentrations in 0.765 g. of water per 1 g. of muscle instead of in 0.807 g., we should have obtained a value almost exactly equal to t h a t observed. T h e quantities assumed are not so certain as in the case of m a m m a l i a n blood referred to earlier. We dare not argue from them t h a t exactly 5 p.c. of the water of muscle is " b o u n d , " though we shall see later t h a t this happens to be almost precisely the a m o u n t obtained by another m e t h o d . I t is clear, however, t h a t we c a n n o t assert t h a t any considerable fraction of the water of muscle is " bound " w i t h o u t having to admit t h a t almost the same fraction of t h e soluble constituents is bound also—again a rather unlikely coincidence. Suggestive, however, as these calculations were t h e y were not conclusive, and it was decided to test the m a t t e r 38

S T A T E OF WATER IN TISSUES experimentally, starting with blood. Moreover, to tell the truth, the thermal method of measuring vapour pressure, devised as the result of the experiments referred to in my first lecture, was just ready to be tried out and this seemed to be a grand opportunity for trying it! Since its use has been the basis of much that follows I must make a digression to describe it.

A

it ί::ί:

d —c

F i c . I. Vapour pressure thermopile in moist chamber: (a) one line of junctions: (b) hole connecting through tube (J) to outside: (f) glass chamber with tube (d) for admitting gas if required; (e) copper terminals in vulcanite platform [Margaria 1930.]

The instrument is shown in fig. i. It is simply a symmetrical thermopile, extremely well insulated, one set of junctions lying in a line down one face, the other set of junctions in a line down the other. Each face contains about 70 junctions between silver and constantan, so that a 39

ADVENTURES

IN

BIOPHYSICS

difference of temperature of i ° C. between them would give about 2.5 millivolts; this, with a sensitive Zernicke (Zc by Kipp) moving coil galvanometer of 25 ohms resistance, allowing for 50 ohms in the thermopile, provides a deflection of 100,000 mm. or more per i ° C. The two faces are covered with strips of moist filter paper of standard size. These have been carefully dried and then soaked in two solutions the difference of vapour pressure of which it is desired to measure. T h e y are then laid carefully, as symmetrically and with as little excess of fluid as possible, on the two faces; a glass tube has been prepared to serve as a moist chamber, its surface having been covered with wet filter paper; the instrument is placed in this tube and sunk in a water thermostat and left to settle down. It is not too difficult, by means of rather vigorous stirring 4 and the good old-fashioned method of a big toluol 5 -mercury gas regulator (discarding all modern electrical inventions, which are not as accurate and provide electrical disturbances), to maintain the temperature of a large bath continuously constant to within o.ooi°. This bath will hold six of the instruments, which will arrive at a constant temperature and a steady reading within three quarters of an hour. 6 This reading, if small, can be recorded directly on the galvanometer scale: if large it can be measured by a potentiometer. Let the solution on face ( 1 ) have vapour face (2) vapour pressure pi,, and on the walls vapour pressure p0. In the chamber, once has been reached, the vapour pressure will po, except in the immediate neighbourhood 4

pressure pa, on of the chamber a steady state be everywhere of the faces of

Preferably by bubbling air. ' Chloroform is safer and as good: pentane has a greater coefficient of expansion. The jet from which the gas comes should be ground on the slant, so that the mercury rising cuts off the gas gradually: " o f f " and " o n " should be avoided and the regulation made continuous. • With later instruments (see below) this time can be reduced to about 20 minutes.

40

S T A T E OF WATER IN TISSUES the thermopile. If p0 be greater than pa and pb water vapour will pass over by diffusion and condense on faces (1) and (2) at rates depending on the difference of vapour pressure: on face (1) the rate will be k(p0 — pa), on face (2) k(po — pb), the k's being equal since the instrument is symmetrical and symmetrically placed in the tube. This condensation will liberate heat. Face (1) therefore will tend to warm, and after a certain time will reach a steady temperature above its surroundings determined by a balance between the heat liberated by condensation and that lost by conduction: the rise of temperature of face (1) will be Ki(po — pa), where Κι depends on: (1) (2) (3) (4) (5) (6)

the the the the the the

temperature. barometric pressure. nature of the gas in the tube. geometrical shape of the instrument. thermal conductivity of the wires to that face. thermal conductivity of the insulator.

(1), (2) and (3) refer to the fact that the rate of diffusion of water vapour depends on the temperature, and on the density, of the gas through which diffusion takes place. Similarly the rise of temperature of face (2) will be K^ipo — pb). The difference of temperature, therefore, between the two faces, which is what we read on the galvanometer scale, is Ki(po — pa) — Ki(p0 — pb)· Now, if the instrument be so symmetrical, mechanically and thermally, that Κι = Κ ι = Κ , this reduces to K(pb -

pa).

In other words, the difference of temperature between the two faces is a direct measure of the difference of vapour pressure between the two solutions. If one had not had the experience of the muscle thermopiles, described in my first lecture, one might have expected the sensitivity of such 41

ADVENTURES IN BIOPHYSICS a differential " w e t - b u l b thermometer" to be rather low. Actually it is easy to obtain iooo mm. deflection for the difference of vapour pressure between water and ι p.c. N a C l solution. T h e sensitivity of the instrument is actually far greater than required; and indeed, if needed, it could be largely increased either by working with the thermostat at a higher temperature or by employing a more sensitive galvanometer. There would be little advantage, however, in so doing, since the real accuracy of the method is limited by various errors and disturbances which creep in. 7 I t might be thought that condensation of water on the filter papers would rapidly dilute the solutions they contain. If the difference of vapour pressure between wall and face be great enough, this in fact can happen. With ζ p.c. N a C l on the face and water on the wall the transfer of vapour is rapid enough to produce a measurable effect. With solutions more dilute, however, the effect is very small within the interval required for a steady reading to be reached: and in practice it can be rendered completely negligible by the simple device of employing on the wall a solution as nearly isotonic as possible with the fluid on the faces. In its ideal form the method is practically a " n u l l m e t h o d . " T h e solution to be studied is placed on one face against a solution on the opposite face of nearly the same osmotic pressure: e.g. blood may be compared with 0.94 p.c. N a C l . T h e paper on the wall, moreover, is moistened with the same solution. T h e equilibrium is very nearly complete. T h e slight difference of vapour pressure between the two faces—an extremely small fraction usually of the total vapour pressure of water—causes a slight difference between their rates of evaporation, which is read on 7

According to G r o l l m a n ( 1 9 3 1 ) , w h o e m p l o y e d a more sensitive g a l v a n o m e t e r ,

the method can be used with quite dilute solutions (e.g. 0.03 to 0.05 M . N a C l ) without considerable liability to error.

T h i s m a k e s it possible to d e t e r m i n e the

" a c t i v i t y " of water in such dilute solutions, which is not easy in other w a y s .

42

STATE OF WATER IN TISSUES the galvanometer. The method is analogous to that by which resistances are found with a Wheatstone's bridge: the bridge is almost balanced, and the small inequality is read on the galvanometer scale. Calibration is carried out by means of two solutions of known vapour pressure, e.g. by water and a solution of NaCl. NaCl is the best substance to employ: it is readily obtainable in a pure form: it is easily dried: solutions of it keep for long periods. Its vapour pressure is accurately known, the relative molal depression over the range of physiological importance being very nearly constant at 0.0330. 8 T o take an example, human blood versus a solution of 0.920 g. of NaCl per 100 g. of water gave + 25 mm. on the galvanometer scale: the same solution versus water gave 800 mm.: the blood therefore was isotonic with a solution containing 0.920 + 0.920 X 25/800 = 0.951 g. of NaCl in 100 g. of water. We have assumed so far that the thermopile is accurately symmetrical, that K\ = K2. Actually it is rather difficult to attain complete symmetry. The degree of symmetry can be tested by using water on both faces, and a strong solution of NaCl (e.g. 5 p.c.) on the walls. With water on one face only the reading would be (say) 5000 mm.: with water on both faces it is (say) 50 mm. The values, therefore, of Ki and Ki differ by 1 p.c. Actually thermopiles have been made considerably better than this. Usually, however, they are not so good and for the highest degree of accuracy a method of allowing for the asymmetry is necessary. The method adopted is to make a second observation with the solutions reversed and to take the average of the two readings. The basis for this procedure is as follows. As shown above, the reading for solution (a) on face (1) and solution (b) on face (2) is 8

Κ i(po — pa) — K2(p 0 — pb). See also Grollman (1931). 43

ADVENTURES

IN

BIOPHYSICS

Reversing the solutions the reading (now in the reverse direction) is K2(pa — pa) — Κ i(po — pb). T h e average of these is the simple quantity +Kt){pb-pa), which is the difference of vapour pressure required, multiplied by the average of the K ' s of the two faces. Actually this procedure has been found to give a very high degree of accuracy: Margaria for example in recent work (1930) on the vapour pressure of human blood has found the probable error of the mean of a single pair of readings to be only about 0.2 to 0.3 p.c.: which corresponds to 2 or 3 mg. of N a C l in 100 g. of water for the case considered. T h e advantage which the method possesses lies in the very small quantity of liquid it requires: 0.5 c.c. is quite enough. I have no doubt at all that a " m i c r o " method could be devised, employing a smaller thermopile and v e r y narrow strips of filter paper, requiring not more than 1/5 to 1/10 of this a m o u n t ; perhaps a single drop of liquid. Whether the micro-method would be quite as accurate it remains for experiment to decide. 9 Such a method might be of value in determining the osmotic pressure of the v e r y small amounts of biological fluids sometimes available. In a micro-micro-form even Professor A . N . Richards m i g h t use it with the tiny drops of urine from his frogs' glomeruli! Another possible application lies in determining the molecular weights of substances of which only very small quantities can be spared. It seems to work just as well with viscous material like centrifuged blood corpuscles or casein solu• M r . D o w n i n g has recently made (a) a smaller instrument (about y i the area) which is nearly as sensitive and j u s t as accurate: and (b) a still smaller i n s t r u m e n t (about 1/10 the area) which is rather less sensitive. used with about ι mg. of liquid.

T h e smaller instrument can be

B o t h of these are screwed into brass covers, w h i c h

ensures a constant air-gap between face and wall, and quickens

equilibration.

Grollman (1931) found that a smaller air-gap g a v e greater sensitivity, a f a c t w h i c h has been used in the design of these " m i c r o " instruments.

44

STATE OF WATER IN TISSUES tions—or even with egg yolk—as with solutions of N a C l : the freezing point method notoriously does not. You must excuse me: you see that I make strong claims for my offspring—what fond parent does not? We will return to the problem of the state of water in biological fluids. The method adopted in the first experiments was to add various substances to blood and to compare the depression of vapour pressure so caused with that produced by adding the same substances in similar amounts to a ι p.c. N a C l solution. The depression of vapour pressure has been reckoned in both cases per gramme of substance added to ioo grammes of water, the water content of the blood being measured by drying. Results have been expressed in terms of the ratio: (Vapour pressure depression caused by adding ι g. of solute to ioo g. of water in ι p.c. N a C l solution) (Vapour pressure depression caused by adding ι g. of solute to ioo g. of water in blood). If the ratio be unity we conclude that the whole of the water of blood is free to dissolve in a normal manner chemical substances added to it. If the ratio be less than unity we must conclude that some of the water of blood is " b o u n d " by the colloidal or other bodies there present, and so is unable to assist in the solution. The ratio is equal to that of " free " water to total water, provided all the material added is dissolved. The " f r e e " water cannot be greater than the total water. If it appears to be, i.e. if the ratio is greater than unity, as sometimes happens, we can only assume that the substance added is somehow removed from free solution by the presence of other bodies, e.g. by surface adsorption, or by " s o l u t i o n " in or combination with the protein or lipins. A further test can be applied by adding to blood, not chemical bodies as described above but water. If we regard as fixed the total number of ions or molecules present in a 45

A D V E N T U R E S IN BIOPHYSICS given amount of blood, and add water to it, the depression of vapour pressure observed at any stage should be inversely proportional to the total volume of " f r e e " water present at that stage. It is found by experiment that the reciprocal of the difference of vapour pressure between water and a mixture of blood and water is a linear function of the amount of water added to a given amount of blood. This is an expression of the relation, true for dilute solutions, PV = a constant, Ρ being the total osmotic pressure of all the dissolved constituents and V the volume of water in the solution. B y plotting the relation between ι / Ρ and V and extrapolating it backwards to the axis of V it is possible to determine the amount of " f r e e " water in the original blood. The results so obtained agree with those found by the other method. The results were as follows: When small quantities of N a C l , K C l and cane sugar were added to blood or blood corpuscles the ratio (free water)/(total water) determined in this way was about unity, having a mean value of 0.97. The addition of water led to almost exactly the same result, viz. 0.95. Urea 10 and creatine gave a greater number, the mean value being 1 . 1 7 . In casein solutions and in egg white the ratio for urea was not far from unity. In blood, therefore, the lower value is probably due to the removal of part of the urea from solution, perhaps by adsorption to, or combination with, the colloidal material or the lipins present; urea is singularly capable of penetrating living cells, which is probably a sign of its readiness to be combined or adsorbed. It would be well worth while to spend some time in studying those bodies which, added to tissues or biological fluids, give a smaller depression of vapour pressure than they should. On the evidence, therefore, of the results obtained by adding N a C l , K C l , cane sugar and water, we may conclude that nearly the whole of the water of blood, say 97 p.c. 10

Grollman ( 1 9 3 1 ) has investigated recently the anomalies occurring with urea.

46

STATE OF WATER IN TISSUES of it, is free to exert its normal behaviour as a solvent. This agrees with the deduction made by comparing the analyses and the observed freezing point. Some substances, however, such as urea and creatine, and probably lactic and succinic acids, fail to exert their full effect on the vapour pressure owing to a slight degree of adsorption on, or combination with, the colloidal constituents or the lipins of the blood. It would, of course, be possible to argue that some of the NaCl, KCl, or cane sugar also is adsorbed, the effect being exactly compensated by the demobilisation {qua solvent) of part of the water. It is not easy, however, in that case to explain the fact that the addition of water leads to the same value of the ratio as the addition of any of these three bodies. It is simpler to suppose that nearly all the water is free and that these substances are normally dissolved in it. This view is confirmed by similar experiments on casein solutions and on egg white. With these the ratio " f r e e " water/total water for all substances added (NaCl, KCl, cane sugar, urea) was about unity, the mean value being 0.98. Apparently, therefore, at room temperature only about 2 p.c. of the water is " bound." This conclusion is important in itself. In dealing with the equilibria occurring in such fluids concentrations should be expressed, not as is sometimes done in grammes (or mols) per litre, but in grammes (or mols) per 1000 g. offree water. This has been the practice of van Slyke and his school, for the case of blood, taking total water and " f r e e " water as the same; their practice is thus seen to be justified. So far, therefore, as these solutions are good physico-chemical " m o d e l s " of muscle they suggest that in the latter " b o u n d " water is of insignificant importance. It was necessary, however, to make experiments specifically on muscle to find out. Two methods were employed, the "single" and the " d i f ferential." In the "single" method several small muscles (preferably the gastrocnemii and the vasti interni (Mar47

ADVENTURES IN BIOPHYSICS shall) of one or two small frogs, which can be p r e p a r e d practically w i t h o u t i n j u r y , were first soaked for several h o u r s in normal o x y g e n a t e d Ringer's solution (R). Since, a p a r t from C 0 2 , the muscles were already practically isotonic with this solution, 5 or 6 hours of soaking should bring t h e m fairly accurately into equilibrium with it. T h e y were t h e n w i t h d r a w n one by one from the solution, freed f r o m all a d h e r e n t fluid by rapidly blotting with filter p a p e r , a n d d r o p p e d into a weighed glass t u b e of c a p a c i t y a b o u t 10 c.c. W h e n the muscles were all in the t u b e the whole was weighed, and so the weight of the muscles o b t a i n e d to t h e nearest 1 mg. T o the muscles in the t u b e was now added an a c c u r a t e l y weighed a m o u n t of R i n g e r ' s solution of twice t h e n o r m a l s t r e n g t h (2R). I t can be shown m a t h e m a t i c a l l y t h a t t h e m e t h o d is most sensitive and a c c u r a t e when t h e q u a n t i t y of 2/?-solution a d d e d contains an a m o u n t of w a t e r e q u a l to t h e a m o u n t of " f r e e " w a t e r in t h e muscles. Since t h e l a t t e r is a b o u t 80 p.c. of their weight it p r o v e d conv e n i e n t in practice to add a q u a n t i t y of 2/?-solution c o n t a i n ing an a m o u n t of w a t e r precisely equal to 80 p.c. of t h e w e i g h t of the muscles. T h e t u b e was t h e n filled w i t h oxygen and s t o p p e r e d , and the muscles a n d the 2/?-soIution were left 15 to 20 hours, so as to come i n t o diffusion equilibrium with one a n o t h e r ; d u r i n g t h a t time t h e t u b e was k e p t slowly revolving so as to ensure a d e q u a t e mixing. T h e final result was t h a t muscles and solution a t t a i n e d an osmotic pressure a b o u t equal to t h a t of 1.5/?. T h e muscles weighed finally 10 to 20 p.c. less t h a n t h e y did a t t h e s t a r t , b u t were usually in excellent condition a n d v e r y excitable. I t is essential t h a t a sufficient period should be allowed for equilibrium to be a t t a i n e d ; with muscles of 0.2 to 0.3 g. it w a s best to leave the t u b e r o t a t i n g d u r i n g t h e n i g h t a n d to complete the observations next d a y . If sufficient t i m e be n o t allowed t h e osmotic w i t h d r a w a l of w a t e r f r o m t h e 48

STATE OF WATER IN TISSUES muscles will not be complete, the osmotic pressure of the solution will be too high, and the " free " water of the muscle calculated from it too low. It is not advisable to use muscles weighing more than 0.3 g., otherwise the time required for osmotic equilibrium to be attained (which for muscles of similar shape varies as the 2/3 power of the weight) will be so great that the muscles may have depreciated; moreover there is the difficulty of an adequate supply of oxygen to the interior if the muscles be too large. The process of equilibration consists partly of a diffusion of water from the muscle into the solution outside, and partly (so far as semi-permeable membranes allow) of a diffusion of salt from the solution into the muscle. It is impossible to imagine a difference of osmotic pressure to exist between two different parts of the system once equilibrium has been attained, for the membranes involved are far too thin to stand any considerable mechanical stress: unless indeed one is ready to invoke some kind of "secret o r y " activity in the sarcolemma. 11 After 15 to 20 hours' mixing the tube was opened, the muscles removed, and the difference of vapour pressure measured between the fluid left in the tube and the original Ringer's solution (R). Two or three readings of this vapour pressure difference were generally made, and on the same day the apparatus was calibrated with the solutions R and 2R on its two faces. To take an example, 2 g. of muscle after equilibrium with R was mixed with an amount of iR containing 1.6 g. of water. After 18 hours' mixing the final vapour pressure difference between the fluid in the tube and the solution R was 127 (arbitrary units). On the same day the vapour pressure difference between R and 11 In frog's skin J. B. Bateman working with me by a similar method has recently found an apparent 20 to 30 p.c. of the water to be " b o u n d . " This fact probably means that the cells of the frog's skin can control their own internal osmotic pressure, by some kind of "secretory" activity, just like the aquatic animals referred to in Lecture I I I . This mechanism, however, does not seem to exist in erythrocytes or in muscle cells.

49

ADVENTURES IN BIOPHYSICS iR gave 249 units. Thus the final osmotic pressure of the mixture in the tube was the same as that of a solution (i + H i ) * = 1 . 5 1 * . We may argue as follows, if χ be the amount of " f r e e " water per 1 g. of muscle: (χ X weight of muscles)/? + (weight of water in 1R added)2/? = (χ X weight of muscles -f- weight of water in iR added)i-5i/?. This merely expresses the fact that when equilibrium has been attained the dissolved substances originally present (a) in the muscle at osmotic pressure R, and (b) in the fluid added at osmotic pressure i R , have been redistributed to give a uniform osmotic pressure (observed) 1.51 R. Hence, X

ι —0.0 weight of water in 2R added - — /C : 0.51 weight of muscles = 0.49 X 0.8/0.51 = 0.77.

-

Therefore 1 g. of muscle contained 0.77 g. of " f r e e " water. This method is valid so long as the condition of the muscle may be assumed to remain constant during equilibration with 2R. It cannot be applied when the initial osmotic pressure is not accurately known (as in fatigue) or when the osmotic pressure alters of itself during equilibration (as when anaerobic conditions are necessary, in order to prevent recovery). In such cases the "differential" method must be employed, in which an unknown initial osmotic pressure, or progressive osmotic changes during equilibration, are automatically allowed for. In the "differential" method the muscles were divided into two lots, those from the right leg of an animal being allotted to one, those from the left leg to the other. T h e procedure was much as before, except that twice as many frogs and two tubes—instead of one—were used. In one tube (A) was placed one lot of muscles together with a SO

STATE OF WATER IN TISSUES weighed quantity of Ringer's solution (R), containing an amount of water equal to 0.8 of the weight of the muscles. In the other tube (Β) was placed the other lot of muscles, together with a weighed quantity of 2i?-solution containing the same relative quantity of water. After prolonged equilibration the vapour pressure difference was measured between the fluids in tubes A and B, and expressed as a fraction/ of that between R and iR. As before, if χ be the quantity of " f r e e " water in 1 g. of the original muscles, it can be shown that ι —/ /

weight of water in iR added weight of muscles

There are two advantages in the "differential" method: (a) A preliminary soaking in ^-solution is unnecessary; the initial osmotic pressure of the muscles need not be known; all that is necessary is that it should be the same in both lots. {b) Changes occurring in the muscles during the prolonged second equilibration, which would be fatal in the first method, balance out exactly in the second, since they affect the contents of tubes (Λ) and (Β) alike. In a few experiments, instead of using iR as the test solution, a solution of urea in Ringer's fluid was employed. This gave very consistent and accurate results, the muscles being in excellent condition after prolonged soaking even in fairly strong solutions. The value, however, of the " f r e e " water found by the use of urea tended to be rather higher than by that of the solution 2R, and it was recalled that in blood values for the " f r e e " water obtained with urea were slightly, but definitely, too high. Urea is a peculiar substance; its extreme ability to penetrate living cells may well imply a high solubility in the lipins of the tissue, or a great liability to adsorption; and if some of the urea in the test fluid were removed from free solution by adsorption or otherwise it would appear as if the " f r e e " 51

A D V E N T U R E S IN

BIOPHYSICS

water of the tissue were greater than it really is. Hence, although the method employing urea seemed to work so well, it was thought wiser to avoid its use for fear of introducing a small consistent error. There is little danger of this with the 2/?-solution, the chief constituent of which is N a C l , a substance very unlikely not to remain in free solution. The mean value of the " f r e e " water fraction in all the experiments made on resting muscles was 0.77. It is possible that the true value is slightly greater even than this: any error due to incomplete equilibration would make the result too low, and it is not certain that equilibration is quite complete even in 18 hours. The true value cannot, however, be higher than 0.80 or 0.81, which is that of the total water fraction. There is obviously very little water " b o u n d " in the resting muscle. So far as they go the urea experiments gave a slightly higher value than those made with 2R; it may be that this was the truer one, owing to the rapid penetration of urea. Experiments were made also on fatigued muscles and on muscles in heat rigor. The "differential" method alone was used. The experiments on fatigue were really experiments on rigor. Muscles severely fatigued will not long survive if deprived of oxygen; it was necessary, in order to make sure that equilibration was complete, to subject them to 15 hours or more of mixing; this means—since recovery would obviously have spoilt the experiment—a long period of oxygen want, during which they invariably passed into rigor. T o ensure that the fatigued muscles should be alive at the end of it, equilibration would need to last not longer than about 4 hours. Only by using exceedingly small muscles, weighing, say, 50 mg. apiece, would it be possible so to quicken diffusion that equilibration would be complete in that time. The difficulty of preparing a sufficient mass of such small muscles without injury was too great. It is open, therefore, to any who will, to argue that the 52

STATE OF WATER IN TISSUES " f r e e " water of fatigued muscles has not been measured at all. Strictly speaking this is so. The muscles could be properly described as fatigued during the earlier part of their equilibration, but during the later part they were certainly in rigor. Since, however, the " f r e e " water of muscles in rigor appears to be the same as that of muscles at rest, it is very unlikely that in fatigue, which in many respects may be regarded as an intermediate condition, the case is seriously different. The mean value of the " f r e e " water fraction for fatigued and rigor muscles was 0.77. This is identical with the mean value for resting muscles. Again it may be slightly too low, owing to equilibration being not quite complete. The fundamental point, therefore, brought out by these experiments is that nearly the whole of the water of muscle is " f r e e , " in the sense that it can dissolve in a normal manner substances added to it. 12 This is true, whether the muscles be at rest or in rigor. The mean value of the " f r e e " water is 77 p.c. of the weight of the muscle for both, 95 p.c. or so of the total water. The true value may be even slightly greater. It does not seem possible therefore to explain the considerable changes of osmotic pressure observed in stimulated muscle by invoking changes in the amount of water free to dissolve the soluble constituents. So far as muscles are concerned we can treat the water they contain, at least all except 5 p.c. of it, as ordinary free water capable of dissolving in a perfectly normal way anything which may be added to it. Many more experiments of this kind should be performed. 13 The question of the status of water in the economy of living tissues, and in biological fluids, is very 12 Which is confirmed by the dilatometric observations of Moran and Smith (193°)· 13 One recent experiment may be mentioned. Miss M . Hetherington has injected intravenously into anaesthetized cats a given quantity of NaCl and has measured the rise of osmotic pressure of the blood so caused. Diffusion of water and salt is complete, and a fairly steady value is reached, in about 40 minutes.

53 5

ADVENTURES

IN

BIOPHYSICS

fundamental. I f , as has been commonly supposed, a large part of the water present in muscle had really been in some different state, incapable of acting as a normal solvent, if a large part of the salts had been present in some adsorbed or combined form incapable of conducting electricity, of exerting osmotic pressure, or of taking part in the usual balance of physico-chemical reactions, we should have had an even more puzzling problem than we actually have. T h e physical chemistry of muscle is difficult enough: it is fortunate that at least one possible complication is ruled out. F r o m the o b s e r v e d rise of osmotic pressure the total water available for diluting the injected salt can be c a l c u l a t e d .

I t is a b o u t 63 p.c. of the body weight, nearly e q u a l

to the total w a t e r in the a n i m a l ' s b o d y .

54

L E C T U R E THE

CONCEPTION

OF

THE

III STEADY

STATE

Ε know of no living organisms which remain indefinitely in a state of equilibrium without the liberation of energy. Certain cells, e.g. the unnucleated red blood corpuscles of mammals, have only a very low metabolism, and in these there is strong evidence that at least approximately a state of thermodynamic equilibrium exists 1 between them and their environment, separated by a membrane of certain peculiar physico-chemical properties. In no ordinary sense, however, are they alive: they do not reproduce, or move, or respire, or repair injuries inflicted on them: they might be so many small bags of haemoglobin excreted by the red marrow. Important as their study is, they tell us little about active living cells as such; biologically they are of interest rather in reference to certain important functions of the animal as a whole. Consider the common hen's egg. The ovum, or " y o l k , " is an enormous single cell which passes from the ovary into the mouth of a convoluted tube, the oviduct. As it moves down the oviduct the yolk receives first a deposit of gelatinous albumen, the " w h i t e , " next a membranous sheath, and finally a hard calcareous shell. The yolk and the white are in contact with one another through the vitelline membrane. The characteristics of the steady state existing between them have been studied by J . Straub (1929). The membrane is certainly permeable to water: if a yolk be placed in water or diluted egg-white it swells: if it then be replaced in undiluted egg-white it 1

Preliminary experiments were made by Hill (1930^, p. 485) in which the vapour pressure difference between erythrocytes before and after laking was found to be negligible. This result has been fully confirmed by Bateman.

55

ADVENTURES

IN

BIOPHYSICS

shrinks again. T h e membrane is permeable also to some at least of the salts contained in the y o l k . W e should e x p e c t , therefore, that the yolk and the white would come rapidly into diffusive and osmotic equilibrium with one another. T h e y do not. A c c o r d i n g to S t r a u b , for m a n y d a y s the freezing-point of yolk corresponds a p p r o x i m a t e l y to t h a t of ι p.c. N a C l in water, of w h i t e to t h a t of 0.75 p.c. N a C l . T h e r e is an " o s m o t i c p r e s s u r e " difference of about t w o atmospheres. It is inconceivable, h o w e v e r , that the delicate membrane around the y o l k could stand in fact a pressure of two atmospheres: m e c h a n i c a l l y there is no such pressure: hence the system cannot be in equilibrium, there m u s t be some hindrance to the free flow of w a t e r , provided b y the membrane, or perhaps b y the structure or a c t i v i t y of the y o l k . I t might be argued that the m e m b r a n e of a y o l k placed in diluted egg-white is in some w a y injured so t h a t it takes up w a t e r to which it is normally i m p e r m e a b l e . T h i s o b j e c tion cannot explain the following o b s e r v a t i o n s by S t r a u b : Freezing-points Yolk

White

-0.58° C.

- 0 . 4 6 ° C.

{A)

Initially, steady

(fi)

W h i t e diluted

-0.58°

-0.22°

(C)

A f t e r 48 h o u r s

-0.38°

-0.23

(D)

Undiluted white replaced.

—0.38°

—0.47°

(£)

A f t e r 48 h o u r s

—0.51°

— 0.44°

0

T h e yolk, initially (.Λ) of higher " o s m o t i c p r e s s u r e " than the white, when immersed ( Β ) in diluted e g g - w h i t e , g r a d u a l l y itself became diluted ( C ) , t h o u g h retaining still a higher osmotic pressure than the white. N o w placed ( D ) once more in undiluted egg-white it tended to revert ( Ε ) to its initial condition (Λ), and in so doing passed from an osmotic pressure lower (D) than the egg-white in which it lay to one which was higher ( Ε ) . N o leaks or i n j u r y to t h e m e m b r a n e could explain the change w h i c h occurred be56

C O N C E P T I O N OF T H E S T E A D Y

STATE

tween (D) and ( Ε ) : osmotic work was done, and energy must h a v e been supplied. 2 According to S t r a u b , this difference of freezing-point always occurs in the normal living egg, tending, however, to disappear with age and becoming practically zero in eggs preserved in lime. Straub attributed the phenomenon to oxidation taking place at the membrane around the yolk, and suggested a mechanism involving a galvanic combustion element, by which the naturally occurring process of diffusion of water and salts is reversed by electrical means and by the provision of energy at the membrane. Such a mechanism may exist, but I have failed to find any evidence of it by v a p o u r pressure measurements on oxygen-free eggs. Vapour pressure difference between egg-yolk and egg-white, measured by thermal method (Hill 1930), and expressed in terms of the percentage of NaCl which would have to be added to 0.7 p.c. NaCl solution to produce the same difference of vapour pressure. Eggs unfertilised: kept at 15 0 C. to 18 0 C., first in moist air, and then in moist hydrogen which was streaming continuously over heated copper to remove oxygen. Eggs in perfect condition to end. I I I I I Days in air I 16 44 30 if — 29 Days in hydrogen 29 29 — — — — 4 '3 Equivalent vapour pressure difference: per cent NaCl 0.292 0.291 0.260 ο·343 0.255 0.206 0.184 0.184 0.159 0.178

These results are an excellent confirmation of Straub's, which were obtained by freezing-point measurements; they * Dr. J . Needham informs me that he and his colleagues at Cambridge have recently investigated further the questions raised by Straub's work. The mechanism of the experiment just quoted is as follows. When the yolk is placed in diluted white a layer of dilute solution is formed inside the vitelline membrane which does not mix with the yolk. If the yolk is broken up to find its freezing point this layer is mixed with the undiluted material and the Δ is diminished. If, however, the yolk with its layer of diluted solution is put back in undiluted egg white the layer is absorbed, and so the original Δ regained. See Needham, Smith and others (1931).

57

ADVENTURES

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show also that the difference between yolk and white gradually diminishes with age; they indicate, however, no difference between eggs kept in air and eggs kept completely free from oxygen. Apparently, therefore, if a continual liberation of energy is the means by which the egg evades the attainment of osmotic equilibrium between yolk and white, that energy must be derived from some source not involving the use of free molecular oxygen. 3 Dr. Straub (1930a), commenting on these results at a recent meeting in Cambridge, pointed out that any electromotive force at the membrane, however produced, might be a sufficient cause of the concentration differences observed: it is just as easy to imagine an E . M . F . to be due to an anaerobic as to be an oxidative process. " I t is quite e a s y , " as he said, " t o realize, by an electric current through a membrane, steady concentration-differences of the same irregular seeming nature as are found in biological s y s t e m s . " He gave the following examples: Steady state at cellophane membrane. E.M.F. 4 volts. Concentrations constant in 7 hours. No difference of level. Analyses in milli-ions per 100 c.c. Ν —

Η"

HäSO« with traces of NH» and Ca.

Current 0.65 amp.

Anode

Cathode

Ratio

13.8

8.6 6.15 2.12 Ο.79 Ο.25 0

1.6

SO,"

8.4

NH.· Ca" Δ

1.66 0.61 0-345°

1

-35

0.78 0.77 1.38

s D r . Needham informs me that he has found a formation of lactic acid in the yolk sufficiently great to do the " w o r k " of reversing the naturally occurring diffusion process. Whether this " w o r k , " which certainly is not done at the membrane, but in the body of the yolk, can really be responsible for the steady state observed, or whether the latter is due to a physical membrane of extreme thinness lying inside the vitelline membrane and hindering the passage of water and salts, cannot yet be stated. It is curious that no electrical potential difference can be

58

CONCEPTION

OF

THE

STEADY

— NaHsPOt with traces of NH« and SO«. 10 Anode

Total Ρ Na" ΝΗ->

O

Ο Ο

O

1-C

PI

"t? *co Ο co —

Ο Ο

Μ ο Ο

Ο

ο. Ν Ό

ο

ο> 00 ΙΛ

CH CH I I

ο

0

ο

"ο k· C ο υ (j ) a low electrical resistance, due to the short distance between junctions: (c) a relatively low thermal conductivity, so avoiding heat loss: silver is very objectionable in this respect, as compared with i r o n : 1 1 u It has only recently been realized how important this factor is. A thermopile of silver-constantan elements constructed by Downing, at least as thin as that of Hartree, with no higher resistance and with about the same thermo-E.M.F. per i°,

91

ADVENTURES IN BIOPHYSICS (id) the thinness of the wires and insulation as finally employed. Let us return to the analysis of results. We have seen how all the resources of instrument design and construction have been devoted to making the curve of galvanometer deflection in the heating control, i.e. in the tool by which the analysis is carried out, rise as rapidly as possible. There is one further resource, to make the duration of the heating as short as possible. The following examples will illustrate the argument. B y "instantaneous" control is meant heating by a single break induction shock. Time: sec.

0

0

0.05

"Instantaneous" control

0

16

0.05 sec. control 0.10 sec. control

0 0

3

Time: sec. "Instantaneous" control 0.05 sec. control 0.10 sec. control Live twitch

0.7

0.2

0.15

85 41 22

0

Live twitch

I

I 96

326

!

253

33

!

0.3

459 386

0.9

1.0

93

I.I

0.4

579 514 450 212

75

7 0.8

0.25

1.2

1.3

980 993 999 IOOO 998 994 989 9 7 1 991 998 IOOO IOOO 997 993 9 6 3 987 997 9995 IOOO 998 994 896 655 746 831 943 9 7 1 987

766 720 673 360

0.5

0.6

882

947 854 9 3 2 824* 481

570

1-5

1.6

984 979 989 984

974 978

1.4

990 985Ϊ 9792 996 999 999h

It is obvious from this Table that the "instantaneous" control rises from the base line far more sharply than those for 0.05 or for 0.10 sec. heating: consequently, as Hartree insists, " i t must give a more definite (and therefore a better) analysis." In this he differs from Amberson (1930) who asserts that " i t is important to use, as a control curve, the form of galvanometer deflection given by a control heating enduring for the same period as the time unit of gave far inferior results to Hartree's: the only possible explanation seems to be that the silver carries away the heat so fast that the instrument is made slower and less sensitive.

For this kind of work not only a high thermo-E.M.F., a small heat-

capacity and a low electrical resistance are required but also a low (sideways) thermal conductivity.

92

T I M E - R E L A T I O N S OF E V E N T S analysis." Hartree's evidence will be given in detail in a paper to be published later (1931). In the last row of the Table given above are numbers for the deflection due to the heat in a single twitch of a frog's sartorius muscle at o° C. T h e "instantaneous cont r o l " is the mean of six curves in good agreement: the " l i v e t w i t c h " also of six such curves. T h e sensitivity was such that ι mm. on the record was 5.1 Χ i o - 5 cal. per gramme. T h e following is Hartree's solution, obtained by an application of the " i n s t a n t a n e o u s " control. Time: sec.

0

0.05

0.1

0.2

0.3

0.4

o.S

0.6

Heat Remainder.. .

0.05 0

0.18

0.28 0

0.105 0

0.035 1 5

0 0

0.105 0

0.155

—

Ο

T i m e : sec.

Heat Remainder..

0.045

ο

o.o3

0.015

Ο.ΟΟζ

ο

—I

0.005

ο

o.oo5

T h e remainders can easily be found by calculation. T h e y are as shown in the third row. T h e y could not be much smaller. T h e solution is given in Fig. 3. Again, as in Fig. 2, we see a sharp division of the heat into two

Time

seconds

FIG. 3. Full curve, results of analysis of rate of heat production in single twitch of frog's sartorius at o° C . Broken curve, record of tension in isometric contraction.

93

A D V E N T U R E S IN

BIOPHYSICS

separate phases, those of contraction and of relaxation respectively. In Fig. 3 the relaxation heat is about 35 p.c. of the whole initial heat. A striking result is shown in the curves of Fig. 4 which represent (plotted from the original records) the galvanometer deflections from {A) the mean of 6 twitches of the live

FIG. 4. Galvanometer deflections plotted, each from the mean of 6 records, for ( A ) the twitch of the live muscle at o° C. and ( S ) the " i n s t a n t a n e o u s " heating of the dead muscle. For result of analysis see Fig. 5.

94

TIME-RELATIONS

OF

EVENTS

muscle at o° C., and (Β) the mean of 6 " i n s t a n t a n e o u s " controls for the analysis. T h e means, the solution and the remainders are as follows: Time: sec.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Control Live Heat Remainder....

0 ο O.II ο

86 8 ο·59 -Ii

333 88

588 202

777 436

996 736

ι

0.02 Ο

953 646

9«3 697

Ο.ΟΙ 1 ϊ

892 5^3 0.01

2

Time: sec.

0.9

Ι.Ο

Ι.Ι

1.2

Control Live Heat Remainder....

ΙΟΟΟ

999

995 9*3

98 9

79 1

0.02J Ο

856 0.02

1 2

956 1

0

2

1 2

0.015

ο

0.12 1 2

Ο.ΙΟ Ο

1-3

1.4

1.5

1.6

977 995

97°

963

982 ο

0

ΙΟΟΟ

ΙΟΟΟ

T h e results of the analysis are shown in Fig. 5. Here again there is a very obvious separation of the two phases, corresponding to contraction and relaxation respectively;

Time • seconds

FIG. J. Full curve, results of analysis of rate of heat production in single twitch of frog's sartorius at o° C. Broken curve, record of tension in isometric contraction. For description of state of muscle see text. Made from the same muscle as Fig. 6 but later.

95

ADVENTURES

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BIOPHYSICS

as indeed it is o b v i o u s t h a t there m u s t be from a mere inspection of the curves of F i g . 4. T h e relaxation heat is 31 p.c. o f the whole initial heat. T h e muscle in this experim e n t w a s in a v e r y peculiar s t a t e : those w h o o b j e c t to experiments w h e n the tissues are not " n o r m a l " are certainly entitled to o b j e c t to this, t h o u g h the results were q u i t e consistent and h a v e been o b t a i n e d on other occasions. T h e tension d e v e l o p e d on a p p l y i n g a shock had fallen, a f t e r four hours of s u r v i v a l , to a b o u t one third of its original v a l u e , while the total initial heat had remained p r a c t i c a l l y unchanged. In the earlier records of such experiments there is not (see F i g . 6) the same clear i n t e r v a l between the t w o separate o u t b u r s t s of heat. T h e most peculiar t h i n g a b o u t this e x p e r i m e n t — a n d it has been seen in o t h e r s — i s t h a t the relaxation heat is here a b o u t the same as it had been w h e n the tension w a s p r e v i o u s l y three times as great. I f relaxation heat represents d e g r a d e d p o t e n t i a l e n e r g y it would seem in such cases, as H a r t r e e s u g g e s t s , t h a t internal stresses are present, p e r h a p s in some less organized form, and are p r e v e n t e d by u n k n o w n causes from exhibiting themselves externally as a regular longitudinal tension. T h e p h e n o m e n o n , its progressive o n s e t ,

«0

OZ

o*

06

Time'

F i o . 6.

OS

/. ο

12

seconds

F u l l c u r v e , results of analysis of rate of heat production in single t w i t c h

of frog's sartorius at o ° C .

B r o k e n c u r v e , record of tension in isometric c o n t r a c t i o n .

D o t t e d line, assumed beginning of relaxation heat. F i g . 5, b u t earlier.

96

M a d e from the same muscle as

TIME-RELATIONS OF EVENTS and its association with the peculiar shape of the curve in Fig. 5, are worthy of further contemplation. The results of the analyses given in Figs. 2, 3 and 5 are simple and straightforward. Unfortunately this is not always the case. Not infrequently results are found similar to those of Figs. 6 and 7. For Fig. 6 the records and results were as follows: Time: sec.

"Instantaneous" control Live twitch Heat Remainder Time: sec.

"Instantaneous" control Live twitch Heat Remainder Time: sec.

"Instantaneous" control Live twitch Heat Remainder

0 0 0

0.05 O.IO .15 86

17

81

.50

.60

.40

•45

466 588 6 93 7 7 7 843 194 315 O.I I 0.045 0.55 0 .70

.65

0 •75

892 928 95 3 971 9 8 3 9 9 1 427 525 619 0.09 0.13 0.065 0

- i

.35

77

0

•55

• 25 .30

199 3 3 3

0.041 Ο.25 0.14 0

.20

- 1

0

.80

.85

.90

996 9 9 9 IOOO 807 717 0.005 0.065

i

i

1.0

1.05

1.10

I.I5 1.20 1.25 1.30 1.4c

IOOO 9 9 9

997

995

992 989 986 980 977 970 968 988 997 IOOO

-95

881

O.OOJ 0

935 O.OIO

1.50

0

If we assume that the heat due to loss of tension-energy starts somehow as shown by the dotted line, the relaxation heat is about 33 p.c. of the whole initial heat. What the intermediate heat is due to it is impossible at present to say. It is worthy of note that the curves of Fig. 5 and of Fig. 6 were made from the same muscle., the former after and the latter before the onset of the peculiar state in which tension was diminished while heat remained unaltered.

97

ADVENTURES

H

IN

BIOPHYSICS

—

Ύι/nf seconds FIG. 7.

Full curve, results of analysis of rate of heat production in single twitch

o f frog's sartorius at 0 ° C .

Broken curve, record of tension in isometric contraction. N o t e : the control being for 0.05 sec.

D o t t e d line assumed beginning of relaxation.

heating, and the first two steps of the analysis being of 0.05 sec., the results from these are plotted as blocks.

For Fig. 7 the records and results are as follows: 0

0.0s

O.IO

o.rs

0.20 0.2s

0.05 sec. control

0

3i

33

105

204

L i v e 0.1 sec. tetanus

0

—

Time: sec.

3

0.08 0.25 0.04

Heat Remainder

0

—

—

- i

-—

322

44 O.I2

—

— —

0

—

0.80

0.8s

0.60

0.65

0.70

0.7s

0.05 sec. control

796

850 893

926

95 1

968

L i v e 0.1 sec. tetanus

347

—

0.060

Heat Remainder Time: sec. 0.05 sec. control L i v e 0.1 sec, tetanus Heat Remainder

0

—

0

—

0.105

— —

553

—

0.090

-

0

—

0.40

0 0.90

0

—

0

—

I.OS

1.10

IIS

1.20

1.30

I.4O

1-50

1000 819 0.020 0

IOOO

999

997

995

990

984

978

937

973

99 1

999

886

—

0

—

—

0.95

980 989 995 998 647 — — 737 0.050 — 0.025 —

1.00

—

0.4s

438 548 645 728 127 — — 234 0.095 — 0.085 - i

O.SS

455

0.35

—

0.50

Time: sec.

0.30

—

1.60 97 1 IOOO

If we assume once more that the heat due to loss of tension-energy starts somehow as shown by the dotted line, the relaxation heat is about 3 4 p.c. of the whole initial heat. 98

T I M E - R E L A T I O N S OF E V E N T S Again, as in Fig. 6, the results of the analysis show a relatively large amount of heat between the initial and the relaxation outbursts. It is not easy to account for this. It may be, now that we have both lactic acid formation and phosphagen breakdown, not to mention other possible reactions, occurring during the course of contraction, that some chemical process will prove to be available to explain it. It is certainly not an error of analysis. No ingenuity, however persistently applied, will twist a solution with reasonable remainders to avoid the intermediate heat of Figs. 6 and 7. Nor is it an error of the records, of which a number, in either case, were in good agreement. It is possibly due to a persistent irregularity, as between the case of the live muscle contracting and that of the dead control, in respect of thermal contact of muscle with thermo-j unctions. We have long feared that such an effect may finally prevent the method we have used from being pushed any farther. It is conceivable that the living muscle contracting and hardening may be in different degrees of thermal contact with the thermopile at different stages of contraction: if so, a single control would not be adequate to carry out the analysis, a different control would in theory be required at every stage, and the method would fail. 12 The curves of the analysis of the heat production given in Figs. 2, 3, 5, 6 and 7 all agree in showing that the first outburst of heat, rapid at the start and then tailing off, practically coincides with the development of the isometric response. (We shall see later that when work is performed the time distribution of heat may be considerably altered.) It is a striking thing that, with all the resources of chemistry 12 Another possible cause of irregularity might be non-uniformity of heat-production through the substance of the live muscle, due e.g. to damage in dissection or to inadequate stimulation of some part. T h e calculations given in Appendix I I I show that heat non-uniformly produced, even in quite a thin muscle, will not be so rapidly redistributed as to cause no error at the short times with which the analysis is concerned.

99

ADVENTURES IN BIOPHYSICS and physics, we cannot yet say whether the cause of the contraction heat is the breakdown of phosphagen, or the liberation of lactic acid, or both. It is clear that the first phase of the heat-production is not complete in the very short time found by Gasser and myself (1924) to cover the onset of the inextensible stage: nor does it coincide with the volume change found by Ernst (1926) to occur right at the beginning of contraction. The first phase of the heatproduction is obviously connected with the development of the mechanical response, the relaxation phase of the heatproduction with its disappearance. More than this it is impossible at present to say. Perhaps further light may be obtained by analyzing the initial heat in muscles, (a) in which phosphagen breakdown is largely prevented by a heavy dose of curare, or of trimethyl-octylammonium-iodide (Nachmansohn 1929), or (,b) in which lactic acid formation is prevented by treatment with mono-iodo-acetic acid 1 3 (Lundsgaard 193°)· We have dealt so far only with the case of the isometric contraction: the distribution of heat in the initial phase may, however, be largely affected by allowing the muscle to shorten. It was shown by Fenn (1923, 1924) that the total energy given out by an excited muscle is increased if mechanical work be done. This simple statement of the matter requires qualification, as we shall find later (see particularly Hill 1930-c), but there is no doubt in general of the Fenn effect. Hartree (1925) applied the methods 13 Hartree has made such experiments. There is no recognizable difference, in respect of the distribution of initial heat, between muscles which have and muscles which have not been poisoned with iodo-acetic acid. A n y type of result which occurs in one may occur also in the other. Whether this means that the initial process in contraction is not concerned with lactic acid at all, the lactic acid production supplying the energy later for phosphagen resynthesis, or whether it implies that alternative methods of supplying the energy for contraction exist side by side in the normal muscle, one of which is abolished by the poison, it is impossible at present to say. See Hartree ( 1 9 3 1 ) for further details.

100

T I M E - R E L A T I O N S OF E V E N T S described earlier in this lecture (not yet in so perfect a form) to an analysis of the heat-production of a muscle doing work. He chose the case described by Fenn of a short tetanus of a frog's sartorius in which, when work was done, the extra energy set free was equal to the work. T h e tetanus was for o . i sec., the temperature was o° C., a load was lifted by the muscle through a fixed distance

FIG. 8. Rate of heat production in frog's sartorius, o.i sec. tetanus, o° C. Full line, course of heat production in isometric contraction; broken-line, course of heat production when work equal to 26 p.c. of the initial heat was done. The unit of heat rate is the whole initial heat per second. Dotted line, isometric mechanical response (Hartree 1925).

(limited by stops) and held up (not allowed to stretch the muscle in relaxation), and the muscle relaxed to its initial length under a small load only. T h e mean result of a number of experiments is shown in Fig. 8. When the load was lifted, about 15 p.c. more of the total initial heat was 101 8

A D V E N T U R E S IN

BIOPHYSICS

produced in the first 0.2 sec. of the contraction: during that interval, moreover, work was done equal to about 26 p.c. of the initial heat. During relaxation, on the other hand, the heat production in the muscle which had done work was less by about 15 p.c. of the initial heat. Taking the heat set free in the isometric case as 100, the heat produced in the isotonic case was also 100 but the energy was 126; the energy in the contraction phase was increased by 4 1 , in the relaxation phase diminished by 15, as a consequence of the performance of work. 14 The matter was further investigated by Hartree and myself (1928-c). We also, like Fenn, were unaware of the existence of another factor, the length of the muscle, in the effect of shortening on energy set free (see Hill 1930-r). We happened to work at such an initial length that, in a single twitch, the total energy was the same whether work was done or not. Under these conditions the relaxation heat was diminished by an amount equal to the work done, the contraction heat was unaffected; the energy, however, set free in the first phase was greater by the mechanical work performed. We also carried out a series of experiments with tetanic stimuli. Here the usual Fenn effect was obvious: excess energy was liberated equal (on the average, for the duration of stimulus adopted) to about 70 p.c. of the work performed. Here again the approximate relation held: (Relaxation heat^metnc = (Relaxation heat)wurklug + (work) and excess energy, due to work, appeared as an increment in the first (contraction) phase. It is clear, therefore, that the distribution in time of the energy liberated in the " i n i t i a l " phases of muscular contraction may depend largely on mechanical conditions af14 1 have recently found the Fenn effect, and the relation of energy to length, to be just as obvious in a muscle poisoned with iodo-acetic acid as in a normal one. These adjustments therefore are not dependent on the lactic acid mechanism.

102

TIME-RELATIONS OF EVENTS a

υ

CQ

tV ε σ (Λ

'UiD-S V

Ι

3 >B5]SJ O} 31np OdJDUl 5s 3 J 3d

I