163

The Absolute Value o f the Isometric Heat Coefficient Tl/H in a Muscle Tivitch, and the Effect o f Stimulation and Fatigue.

By A. V. H il l , F.R.S.

(From the Department of Physiology and Biochemistry, University College, London.)

It is not technically possible to determine directly the lactic acid set free in a single muscle twitch. I t is necessary to calculate it from the initial heat- production, or from the tension developed. The anaerobic liberation of 1 gramme of lactic acid in muscle is accompanied, according to Meyerhof, by the production of 385 calories of heat (1). This leads to the equation :—

1 gramme-cm. (heat) EE 6*14 X 10”s gramme lactic acid. (I)

The isometric coefficient of lactic acid, defined for a twitch or a series of twitches by the equation*

__ (grammes tension developed) (cms. muscle length) m (grammes lactic acid produced)

has been the subject of much investigation by Meyerhof and his colleagues (2, 3, 4, 5). Matsuoka, for the frog’s sartorius muscle in Ringer’s solution, found a mean value of 1*05 X 108 (variation 0*69 to 1-36). Meyerhof and Lohmann, for the frog’s gastrocnemius, gave 1*40 X 108 as a mean, while Meyerhof and Schulz gave 1*43 X 108 (variation 1-12 to 1*66). In the gastrocnemius, however, the fibres are not straight, and do not run parallel to the muscle length ; consequently it is necessary to multiply (see Mashino (6), A. V. Hill (7)) the value so found by a factor of roughly 0-63 to allow for the skew disposition of the fibres. This gives, when corrected, 0*9 X 108 for the gastrocnemius, so that taking account of the value 1*05 X 108 found by Matsuoka for the sartorius, the round figure 1 X 108 may be accepted. This leads to the equation :—

1 gramme-cm. (tension-length) EE 10” 8 gramme lactic acid. (II)

From equations (I) and (II) we may calculate at once the lactic acid produced in a twitch, given either (I) H, the heat produced, or (II) T, the tension developed. Combining them we find a mean value for Tl/H, viz.,

| = 6-14. (Ill)

* Meyerhof defines it in terms of kilogrammes of tension developed and milligrammes of lactic acid produced.

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164 A. Y. Hill.

It is assumed that H, the heat, is the “ initial heat.” I t will be shown in a subsequent paper that in a series of twitches there is little, or no, delayed anaerobic heat.

I t is of interest to compare the mean value of Tl/H so calculated with one deduced directly from simultaneous observations of T and H. By means of the methods described in the two preceding papers, such observations have been made more accurately than in previous investigations, (a) on Tl/H in single twitches in the usual way, and (b) on ST1/H in series of twitches, where STlis the sum of the tensions developed multiplied by muscle length, and H is total heat calculated from the observed area of the galvanometer deflection-time curve. In every case the muscle was in pure nitrogen, sometimes treated with cyanide, after having been immersed for some time previously in neutral phosphate-Ringer (usually 7 to 10 mgms. per cent. P). The muscle had not been stimulated previously, except for a few twitches.

Twelve values for Tl/H (each the mean of several observations) in twelve different experiments are as follows : 4-34, 4*58, 5*37, 6 • 03, 6-25, 6 • 30, 6-40, 6*70, 6*97, 7-40, 7*65, 8-30 ; mean value, 6*36.

Twelve values for 2T1/H in twelve different experiments are as follows, the number of twitches in each series being given in brackets after the value of 2T1/H: 4*60 (63), 4-75(65), 4-86 (31), 5-12 (60), 5-25(32), 5-47 (183),5-74(32), 6-10(77), 6-72 (78), 6-98 (50), 7-24 (63), 7-30 (62), 7-48(191); mean value, 5-97.

The average, therefore, of the two mean values, viz., 6*16, is in close agree­ment with that deduced above from Meyerhof’s lactic acid data, and the variation from one muscle to another is no greater than that observed in the lactic acid experiments. In the case, at any rate, of the myothermic observations, the variation from one experiment to another is not due to experimental error—the error cannot be more than 3 or 4 per cent, and the average must be much less—it should be attri buted to the unavoidable differ­ences existing between different muscles similarly treated and apparently in good condition.

The assumption has been made in the above comparison that stimulation to partial fatigue (as is necessary for lactic acid measurements) does not affect the isometric coefficient for lactic acid, so that a series of 100 to 200 twitches should give the same result as a group of three or four. Meyerhof (2) showed that in a muscle pushed to extreme fatigue the isometric coefficient falls considerably : two experiments may be quoted :—

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Isometric Heat Coefficient Tl/H in a Muscle Twitch. 165

(1) First 145 twitches, Km = 0*77 X 108 (after applying the correction factor of 0-63 for the gastrocnemius).

Succeeding 350 twitches, Kw = 0-52 X 108.(2) First 210 twitches, Km = 0-77 X 108.

Succeeding 590 twitches, Km = 0*52 X 108.

This effect can be confirmed by the myothermic method : there is no doubt that in the last stages of exhaustion the ratio Tl/H falls considerably. Over a more moderate range, however, in a muscle in good condition, it remains remarkably constant, as is shown in Tables I and II.

In Table I the degree of previous anaerobic activity is given by the amount of heat liberated (calories per gramme) : complete fatigue is usually reached when about 1 cal. per gm. (i.e., about 0-26 per cent, of lactic acid) has been produced. In Table II the heat set free in each series is given, so that the degree of previous activity can be inferred by adding up the previous heats. In Table I are given the results for Tl/H in single twitches, obtained as usual, in every case but one, in absolute units. In Table II are given results for ST1/H for series of twitches, 2T1 being obtained by simple addition, H from the area of the deflection-time curve of the galvanometer, as described in the preceding papers : 2T1/H is expressed in absolute units.

Table I.—Effect of Previous Stimulation on the Value of Tl/H in a SingleAnaerobic Twitch.

Experiment 1 of 27.10.27.—Pure N 2 after Ringer, 20 mgms. per cent. P, pH 7*6. Tetani inter­polated between groups of three test-shocks.

Duration interpolatedtetanus: seconds....... 0*45 0*45 0*45 0*90 1*8 1*8 1*8

Total cals, per gm. in pre­vious stimulation....... 0-009 0-064 0-117 0-169 0-242 0-350 0-447

Tl/H, mean of 3 twitches 3-54 3-62 3-51 3-51 3-42 3-21 3-341-8 1-8 1-8

0-530 0-600 0-654 0-7003-47 3-70 3-86 4-05

Experiment II of 26.10.27.—Pure N 2 after Ringer, 10 mgms. per cent. P, pH 7-4. Groups of three test-shocks and 1-second tetani alternating.

Previous cals, per gm. ......... ..... 0-018 0-124 0-194 0-258 0-315 0-366 0-410Tl/H .............................. ..... 4-20 4-30 4-07 4-10 4-27 4-36 4-28

0-450 0-481 0-510 0-535 0-555 0-5904-12 4-04 4-00 3-84 3-66 3-60

Experiment I of 26.10.27.—As Experiment II of 26.10.27 above. No calibration. T/H in arbitrary units. Groups of four test-shocks and single 4-second tetani alternating.

T/H arbitrary u n its.................................... 7-8 8-9 9-1 9-3 9-1 8-5 7-8 7-4Experiment II of 27.10.27.—Pure N 2 after Ringer, 20 mgms. per cent. P, pH 7-4. Groups of

three test-shocks and single 2-second tetani alternating.Previous cals, per gm................ 0-011 0-132 0-237 0-323 0-392 0-446 0-490

Tl/H .............. ..................... 3-38 3-74 3-74 3-80 3-80 4-11 4-04

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166 A. V. Hill,

Table II.—Effect of Previous Stimulation on the Value of ET1/H in a Series ofAnaerobic Twitches.

Experiment of 22.12.27.—Total heat in stimulation 0-53 cal. per gm.Number of twitches.............................. ..... 65 63 63 64Heat produced : cals, per gm.............. ..... 0*15 0*14 0*13 0*11

27T1/H.............................................. ..... 4*75 4*51 4*32 4-81Experiment of 14.10.27 and 15.10.27.—4 hours in Ringer + 20 mgms. per cent. P. Then 17 hours

in 0 2, then in N 2. Total heat in stimulation 0-82 cal. per gm.Number of twitches................... 37 38 79 159 122Heat produced: cals, per gm.... 0*063 0*075 0*177 0*334 0*168

27T1/H ....................................... 3*92 4*23 4*05 4*11 3*74Muscle then left in oxygen : after 10 hours contracted strongly to stimulation.

Experiment of 3.1.28.—In N 2-HCN. Total heat in stimulation 0*610 cal. per gm.Number of shocks............................ 31 31 64 62 188Heat produced: cals, per gm.... 0*086 0*081 0*137 0*121 0*185

27T1/H....................................... 4*86 4*56 4*52 4*72 4*56Experiment of 25.1.28.—In N 2-HCN. Total heat in stimulation 0*47 cal. per gm.

Number of shocks............................................. 32 32 32 64Heat produced : cals, per gm........................ 0*107 0*106 0*103 0*155

27T1/H...................................... 5*74 5*08 4*43 5*14Experiment of 4.1.28.—In N«-HCN. Total heat in stimulation 0*64 cal. per gm.

Number of shocks.................................... 63 310 to extreme fatigue.Heat produced : cals, per gm................. 0*108 0*53

ZT1/H................................................ 7*24 6*82

Except where stated, the muscle had been treated with neutralised phosphate-Ringer, 7 to 10 mgms. per cent. P. Except in the last experiment quoted, stimulation was not to extreme fatigue. The heat produced in each separate series is given.

One comment should be made on the data in Tables I and II. I t is quite easy to get a contrary result, viz., a large fall in Tl/H as fatigue sets in, by employing muscles which are rapidly deteriorating. In all the above cases the muscles behaved well, and gave a long series of responses without undue depreciation : the experiments quoted were chosen simply because the muscles were, judging from their mechanical response, in good condition up to the end of stimulation. In every case the resting heat-rate in nitrogen at the beginning (see the preceding paper) was low, which is a further sign of good condition.

The values given in Tables I and II have been shown graphically in the accompanying figure by the following treatment : The first entry for Tl/H in each experiment was taken as unity, and subsequent values were expressed as a fraction of the initial one. Each fraction was then plotted as a function of the amount of heat liberated in previous stimulation. The case of Table I needs no comment. In Table II the total heat liberated up to the middle of the series under consideration is taken as the “ previous ” heat.

The method of plotting exaggerates the “ scatter ” for two reasons : (a) any

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Isometric Heat Coefficient T l/H a Muscle Twitch. 167

error or abnormality in the first reading of an experiment is perpetuated throughout the experiment by dividing the other readings by it, and ( ) the

II 1'

! h i *■a1 0-9

^ ° - 8H 0-7

O

n o o cD

c){

O o oo °co <o

>H j U C X /v j —

O c o ° - ° -____ (2D— a

—6 ____° o 1

— ------- - O------o o o

o

Cals, per previous activityGraphic representation of results in Tables I and II. The first entry for Tl/H in each

experiment was taken as unity ; all subsequent entries were divided by the first, and then plotted as a function of the heat liberated in previous anaerobic activity. In the case of Table II, previous activity was reckoned to the middle of the series considered.

diagram is cut off at the value 0*7 instead of being continued down to zero. I t is obvious, nevertheless, that there is very little, if any, change in Tl/H as the result of previous activity: the line Tl/H = 1 runs practically through the middle of the points. There is apparently a slight tendency for the ratio to fall, and the broken line is so drawn as to have the same number of points above as below it. To half fatigue (say 0*5 cal. per gm.) there is only about 3 per cent, diminution in Tl/H, if we accept the broken line ; even at 80 per cent, fatigue (say 0*8 cal. per gm.) there is only about 6 per cent, diminution. Practically speaking, therefore, we may say that previous activity has no effect on the ratio Tl/H, except during the extreme stages of fatigue.

W e may conclude that in a single twitch the processes leading to the develop­ment of tension and heat are the same as in a long series of twitches : thus, in order to determine the lactic acid produced in a single average twitch we may employ equations (I) and (II) above. Any error involved in so doing will be almost entirely that due to the random variation of the tissues employed, and will not be affected by the fact that the constants of the equations were derived from long series of twitches.

A certain special importance attaches to these results at the present moment, owing to recent work on the chemistry of “ phosphagen.” Phosphagen is an unstable compound of creatine and phosphate—probably combined with other

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168 A. V. Hill.

substances—which has been found to break down during the activity of muscle, and to be rapidly reformed afterwards in the presence of oxygen. (See Eggleton and Eggleton (8), (9), (10).) Recent work from Prof. Meyerhof’s laboratory in Berlin has shown certain unexpected phenomena, which lead one to suspect that the phosphagen is not really broken down at all, but in some sense “ unstabilised ” by stimulation. This work will be published shortly in a paper by D. Nachmansohn, the MS. of which Prof. Meyerhof was kind enough to send to Mr. Eggleton. The essential points are as follows :—

At rest in a fresh muscle, 73 per cent., approximately, of the “ inorganic ” phosphate, as usually determined, really consists of phosphagen. The “ isometric coefficient ” for phosphagen,

__ (grammes tension) (cm. muscle length) v (grammes inorganic H3P 0 4 produced) 9

is not constant, or approximately constant, as is the “ isometric coefficient ” for lactic acid Km defined above, but increases rapidly as the degree of previous activity increases. For example, in 42 twitches it was 0-56 X 108, in 85 twitches 0-78 X 108, in 325 twitches 2*4 X 108 (all corrected by the reducing factor 0-63 for the gastrocnemius). Whereas in the short series 1*5 times as many phosphagen molecules . “ break down” as lactic acid molecules are formed, in the later stages of the long series the ratio, instead of being 1 -5, is only about 0-1. The same effect is shown in a tetanic stimulus : in a single 5-second tetanus, or in two, twice as much phosphagen may be broken down as lactic acid produced, while in a series of 6 or 12 the ratio may be reversed : indeed, in the later stimuli, practically no phosphagen appears to break down at all.

Now it has been shown by Meyerhof and Suranyi (1) that the breakdown of phosphagen in vitro leads to the liberation of 150 calories per gramme of H3PO4 set free. If the major portion of the phosphagen present in muscle really broke down in the early stages of a long series of twitches, one could scarcely fail to detect the fact from the gradual rise in Tl/H that would occur as the rate of phosphagen breakdown fell off. Such a rise definitely does not occur. There is no doubt that the isometric coefficient for lactic acid remains constant up to a fair degree of activity, while it has been shown above that the isometric heat coefficient is practically unchanged up to a high degree of activity. These facts seem to preclude the possibility that the heat observed is largely made up, in the early stages of activity, by a breakdown which is nearly as important (from the thermal aspect) as the reaction producing lactic

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acid, but during the later stages assumes a negligible importance. If the breakdown of phosphagen in the living muscle really liberated 150 calories per gramme of H3P 04 set free, we could not fail to detect its presence from the rise of Tl/H with advancing fatigue. I t seems necessary to assume either that purified phosphagen has very different thermal properties from the substance existing in the living muscle, or that the‘breakdown does not really occur; perhaps the “ breakdown” should be regarded rather as an “ unstabilisation ” of some kind, allowing the phosphagen to be broken down by the chemical treatment necessary for its estimation, to which it is normally resistant. This suggestion is, in fact, made by Nachmansohn in his paper, on other grounds.

Summary.

1. Meyerhof’s experimental results on the relations between heat, tension and lactic acid in a series of isometric muscle twdtches may be expressed by the following equations for the case of a muscle with fibres parallel to its length :—•

1 gramme-centimetre (initial heat) EE 6*14 X 10“8 gramme lactic acid.1 gramme-centimetre (tension-length) EE 10~8 gramme lactic acid.

Tl/H = 6-14.

2. Direct observations of T and H by the improved methods described in the previous papers give a mean value of the isometric heat coefficient, Tl/H = 6*16. The rather wide variations observed experimentally in this coefficient are not due to errors of observation but to differences occurring between the muscles employed, in spite of all precautions to ensure uniformity.

3. Previous anaerobic activity, liberating a large fraction of the whole energy available but not pushed to extreme fatigue, has little or no effect on the isometric heat coefficient Tl/H. The effect, if any, is in the direction of a slight reduction. In extreme fatigue, however, the reduction is large.

4. The equations, therefore, in (1) above, which were deduced from observa­tions on a large number of twitches, are applicable without change to the case of a single twitch.

5. Recent work on “ phosphagen ”—a labile phosphate-creatine compound which appears to break down in activity and to be re-formed in oxidative recovery—has shown (a) that in vitro the breakdown of purified phosphagen leads to the liberation of about 150 calories per gramme of H3P 0 4 set free, and (b) that in vivo the “ breakdown ” occurs preponderatingly in the early stages of a long series of twitches. If the phosphagen “ breakdown ” in vivo

Isometric Heat Coefficient T l/H in a Muscle Twitch. 169

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really liberated the heat found for the breakdown of the purified material in vitro, it could not fail to cause an obvious increase in the isometric heat coefficient as activity progressed and fatigue set in. Such an increase does not occur; either, therefore, purified phosphagen is to be regarded as a very different substance (from the thermal aspect) from that existing in the living muscle, or the phosphagen “ breakdown ” in vivo is to be regarded rather as an “ unstabilisation,” causing the material to break down under chemical treatment to which it is normally resistant.

The expenses of this research have been borne by a grant from the Foulerton Fund of the Royal Society.

170 Isometric Heat Coefficient Tl/H in a Muscle Twitch.

REFERENCES.

(1) Meyerhof and Suranyi, 4 Bioehem. Zeitsch.,’ vol. 191, p. 106 (1927).(2) Meyerhof, ‘ Pflugers Arch.,’ vol. 191, p. 128 (1921).(3) Meyerhof and Lohmann, 4 Bioehem. Zeitsch.,’ vol. 168, p. 128 (1926).(4) Matsuoka,4 Pflugers Arch.,’ vol. 202, p. 573 (1924).(5) Meyerhof and Schulz, 6 Pflugers Arch.,’ vol. 217, p. 556 (1927).(6) Mashimo, 6 Journ. Physiol.,’ vol. 59, p. 37 (1924).(7) A. V. Hill, 4 Roy. Soc. Proc.,’ B, vol. 98, p. 510 (1925).(8) Eggleton and Eggleton, 4 Bioehem. Journ.,’ vol. 21, p. 190 (1927).(9) Eggleton and Eggleton, 4 Journ. Physiol.,’ vol. 63, p. 155 (1927).

(10) Eggleton and Eggleton,4 Journ. Physiol.,’ vol. 65, p. 15 (1928).

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