Archibald Vivian Hill

The abrupt transition from rest to activity in muscle.

The internal mechanical condition of an excited muscle has been examined by applying quick stretches at various moments after a maximal shock. At the end of the latent period there is an abrupt change of state, the contractile component suddenly becoming capable of bearing a load equal to the maximum tension set up in an isometric tetanus. The intensity of the active state produced by a shock is greatest at the start, is maintained for a time and then declines as relaxation sets in. The properties of the fully active state are defined by the three constants of the characteristic equation relating speed of shortening to load. A muscle consists mechanically of three components: (1) a contractile one, (2) an undamped series elastic one and (3) a parallel elastic one. The complication provided by (3) is avoided by working with small initial loads. The load-extension relation of the series elastic component has been determined. Its extensibility is high at small loads, becoming much less at greater ones. The full isometric force produces an extension in it of about 10% of the muscle’s length. In an isometric tetanus the form of the myogram is fully determined by the characteristic force-velocity relation of the contractile component and the load-extension curve of the series elastic one, the former having to shorten and stretch the latter before an external tension can be manifested. In a twitch there is insufficient time, before relaxation sets in, for the full tension to be developed. When the tension is raised sufficiently by a quick stretch applied early after a shock the contractile component cannot shorten as it would normally and the heat of shortening is absent. The heat of activation is probably a by-product of the process by which the sudden change of state from rest to full activity occurs. When a muscle is subjected to a tension rather greater than it can bear it lengthens slowly; to a tension considerably greater it ‘gives’ or ‘slips’. When a muscle is stretched rapidly a transitory overshoot of tension occurs followed by ‘slip’. During the disappearance of this extra tension heat is produced, as in the ‘cold drawing’ of a wire or thread. An analogous process occurs in relaxation under a load. When two shocks are applied in succession, the second restores the active state to its full intensity, from which it has declined to an extent depending on the interval after the first one. If, under isometric conditions, the series elastic component is still partly stretched at the moment when the second response occurs, the total tension developed is greater. This is the origin of the so-called ‘supernormal phase’ and the basis of the greater tension maintained in atetanic contraction. During a tetanus each shock restores the active state of the muscle to its full intensity. It seems reasonably certain that excitation of a muscle fibre occurs at its surface. It has been suggested that contraction is set up inside by the arrival of some chemical substance diffusing inwards after liberation a t the surface. The onset, however, of full activity occurs so soon after a shock that diffusion is far too slow to account for it. A process, not a substance, must carry activation inwards.

The mechanics of active muscle

When a frog’s or toad’s sartorius is rapidly released during a maintained isometric contraction its tension drops immediately and is redeveloped later. The extent of release required to reduce the tension to zero is 3 to 4 % of the length of the muscle. This is much less than the 10 to 15 % originally stated by Gasser & Hill: the difference is explained. The amount of work done during release by the passive elastic element in series with the contractile element is affected only very slightly by speed of release: the damping of this element is small. The redevelopment of tension after release has been compared with the original development of tension when the stimulus began. Minor and variable differences only have been observed, and these are probably due to redistribution of length, during isometric contraction, between different regions of the muscle. At greater initial extensions the rise of tension during an isometric tetanus is much slower than at smaller initial extensions. This also is attributed to redistribution of length, within the muscle. At an initial extension not greater than that at which the developed tension is a maximum the system is ‘stable’ and the tension reaches its full value sharply: at extensions on the outer side of the maximum the system is ‘unstable’ and a long slow creep of rising tension occurs. The apparent complexity of the time-course of the heat production in an isometric twitch is discussed.

The Series Elastic Component of Muscle

The properties have been examined of the undamped elastic component which lies in series with the contractile component of muscle. At higher tensions the elasticity is normal; the form of the load-extension curve as a whole must be largely due to the statistical distribution of tendon length in different fibres. The mechanical (elastic) energy of a contracting muscle is expressed graphically as a function of its tension. Even under completely isometric conditions this elastic energy is a significant fraction of the heat production in a twitch.

THE EFFECT OF LOAD ON THE HEAT OF SHORTENING OF MUSCLE.

During the process of shortening against a load a muscle liberates extra energy as work and as heat. The methods used in measuring the extra heat due to shortening have been critically examined and are described in some detail. The constant α of the heat of shortening depends on P, the load lifted, according to an average linear relation for frog sartorii at 0 °C, α/P0 = 0·16( ± 0.015) + 0·18( ± 0·027) P/P0 P0 is the maximum force developed at constant length. The constant α of the heat of shortening can no longer be regarded as the same quantity as the constant α of the characteristic equation (P+a)v = b(P0-P), relating velocity (v) of shortening to load; but α/P0 and a/P0, being always of the same order of size, are almost certainly connected in some way. The original (Hill 1938) conclusion that α and a were the same was probably due to a persistent error in the measurement of α, making it about 30% too great. In the original (Hill 1938) hypothesis the rate of extra energy liberation (P+α)v during shortening was taken to be proportional to (P0-P), i. e. to the gap between the maximum force a muscle could exert and the actual load it had to lift. In its simple form this idea must be abandoned; but a modification is suggested which still provides the characteristic equation and supplies a connexion between α and a. The assumptions made in calculating the heat of shortening are examined; to regard it simply as a change, produced by shortening, in the maintenance heat would make little difference. Further advances in the chemistry of contraction may allow the facts to be expressed in more concrete terms.

The Efficiency of Mechanical Power Development during Muscular Shortening and Its Relation to Load

When shortening occurs during a maintained isotonic contraction, as Aubert (1956) found during shortening at constant speed, the ‘efficiency’ remains very constant throughout, even over a considerable range of length. The efficiency varies largely with the load P, being zero at P = 0 and P = P0 (isometric). Near its maximum around P /P0 = 0·5 the efficiency (in frog sartorii at 0 °C) is consistently about 0·45. The form of the relation between efficiency and load is discussed, particularly in view of recent findings on the heat of shortening of muscle. The mechanical power developed during shortening is greatest when P/P0 = v/v0 = about 0·3; but the efficiency here is only 3 to 5% less than its maximum.

The Heat of Activation and the Heat of Shortening in a Muscle Twitch

The heat produced in a single muscle twitch is made up of two parts, (1) the heat of activation, and (2) the heat of shortening. In the leg muscles of toad or frog at 0°C the heat per cm. of shortening is about 350 g. cm. (expressed .in mechanical units) per sq. cm. of muscle cross-section. The heat of activation is usually rather less than the maximum heat of shortening and depends little, if at all, on the length at which the stimulus was applied or on changes of length thereafter: it is equal to the heat which would be produced if shortening were altogether obviated, a condition approximately realized in a muscle brought to a very short length by previous stimulation under a very small load. The heat of shortening occurs at the same time as the shortening. The heat of activation has its maximum rate at the start, very soon after the stimulus, and falls off in rate from then onwards. The heat of maintenance in a tetanic contraction is the summated effect of the heats of activation resulting from successive elements of the stimulus. The effect on the heat production of a sudden arrest of an isotonic contraction is described. Under such conditions the contractile elements of a muscle continue to shorten but at a decreasing rate as the tension rises. The complications due to inequalities of length and contractility in the different fibres of a muscle are discussed.

The Influence of Temperature on the Tension Developed in an Isometric Twitch

In muscular contraction the development of tension requires that the contractile component should shorten and stretch the series elastic component. In an isometric twitch the maximum tension is reached as a balance between two opposing processes, internal shortening on the one hand and decay of the active state (relaxation) on the other. The fact that the maximum tension in a twitch is considerably less than in a tetanus has been attributed to oncoming relaxation allowing insufficient time for internal shortening to be completed. The maximum tension in a twitch is considerably reduced by a rise of temperature, while that in a tetanus is somewhat increased. This would require that the temperature coefficient of the velocity of shortening should be substantially less than that of the decay of activity. Evidence for this exists. On this view the effect of a quick stretch, applied during the early stage of a twitch, in increasing the tension ratio, stretch/isometric, should be much greater at a higher temperature. This expectation is confirmed on frogs’ muscles over the range 0 to 20°C. The effect of temperature, therefore, on the size of a twitch can be attributed to the difference between the temperature coefficients of velocity of shortening and rate of relaxation.

The Reversal of Chemical Reactions in Contracting Muscle during an Applied Stretch

When a toad muscle is stretched 11 to 20 % during the active phase of a twitch or a short tetanus, resisting strongly, the total heat (Hs) appearing in it up to the end of relaxation may be about equal to the total mechanical work (W0) done during the stretch. Since all the work has disappeared, and no elastic energy is left by the end of relaxation, the net energy (Hs – W0) liberated by the muscle itself is nil. It is concluded that the chemical products of the reaction provoked by the stimulus have been wholly returned to their initial state. This result depends on the amplitude and timing of the stretch. Often Hsis rather greater than W0, but (Hs – W0) is always much less than Hi, the total heat in an isometric contraction: in these circumstances most, but not all, of the chemical products of activity have been reinstated. During a contraction with stretch the contractile component begins to lengthen as soon as the tension reaches a value slightly greater than that in an isometric tetanus. It is during this lengthening that chemical energy is re-absorbed. When work W, up to any moment, is done on a contracting muscle, some of it is used in producing elastic energy E in the series elastic component and in the connexion to the ergometer. Only the net work Wn =(W –E) has been taken up by the contractile component. If H is the heat produced in the muscle by any moment (H–Wn) soon begins to fall when the stretch starts. In a twitch or a short tetanus (H – Wn)usually becomes substantially negative, remaining negative for a considerable period but finally returning to zero, or to a small positive value, by the end of relaxation. In a longer tetanus, with a stretch starting later and the stimulus outlasting it, (H – Wn)begins to fall directly the stretch starts, dropping sometimes to or below zero, but increasing rapidly when the stretch ends, as the stimulus continues. The fact that the net energy (H — Wn) liberated by a muscle up to any moment may reach large negative values during part of the cycle, while the total energy (Hs — W0) over the whole cycle never falls below zero, is difficult to explain on any simple theory of the reversal of a chemical reaction. The difficulty is resolved by assuming that whenever the tension rises by ∆P during contraction, for whatever cause, there is a corresponding ‘thermoelastic’ absorptionof heat ∆Q= 0.018l0∆P, and conversely when the tension falls. The constant 0.018 is that observed in earlier experiments on the thermal effect of a sudden release of tension. If this assumption is correct, the real heat produced by the muscle up to any moment is greater than H by Q = 0.018l0P, where P is the tension at that moment. Substituting (H + Q) for H, it is found that (H + Q— Wn) behaves in the same general way as (H—Wn) during and after a stretch but never becomes negative. Since Q is zero at the end of relaxation, when P = 0, the statement about total quantities stands unaltered. The results can be used to calculate the ratio of the energy absorbed in chemical resynthesis, during a stretch, to the work applied. In stretches of moderate extent, the ratio may be as high as 0.5, but in the longer and more vigorous stretches which gave complete reversal the ratio was considerably less. The thermodynamic implications are discussed.

The Absorption of Work by a Muscle Stretched during a Single Twitch or a Short Tetanus

When a stimulated muscle is stretched fairly quickly during the active phase of contraction, it resists strongly and mechanical work must be done in stretching it. What happens to this work? If the length to which the muscle is stretched is not too great no significant part of the work remains as mechanical (elastic) energy after the muscle has relaxed. The total heat produced up to the end of relaxation is greater than it would have been had no work been performed on the muscle, but the excess is too small to account for all the work done. It is concluded that the missing work, about half of the whole, is absorbed, presumably as chemical energy. If a stretch is applied entirely during the relaxation phase, when activity is over but tension is still present, the whole of the work performed reappears as heat. If the view is accepted that the missing work is absorbed in chemical synthesis, it appears that the physical system responsible for mechanical work is reversibly coupled, during the active state, with a chemical system providing the necessary energy; and that this coupling is broken when activity passes off. Other possible hypotheses, however, are discussed. The application to ordinary muscular movement is referred to.

The Influence of the External Medium on the Internal pH of Muscle

Isolated frog muscles were exposed to Ringer’s solution of widely varying pH. In the presence of oxygen they remained in good condition for a long time and continued to contract well at hydrogen-ion concentrations many times greater (up to x 200) than that of their normal environment in the body. If the Donnan equilibrium, which is believed to govern the K and Cl ion ratios across the fibre membrane, applied also to H and HCO3 ions, the internal pH in these circumstances would be 3.8 or less. It is difficult to believe that the contractile mechanism would function so well under such conditions, but the question could be examined experimentally as follows. Muscles in oxygen-free Ringer at pH 7.4 to 3.3 were stimulated in a regular series of twitches to complete exhaustion, and the total tension developed was used to measure the energy liberated. If the energy was less than 0.4 cal/g muscle it could have been derived solely from the splitting of creatine phosphate and other phosphorus compounds; if it was greater than 0.4 cal/g muscle it must have been obtained in part from lactic acid production. The formation of lactic acid in response to stimulation ceases when the internal pH falls below about 6.3; but experiments show that at external pH 6.0 adjusted by phosphate buffers, lactic acid can be produced in practically normal amount, while some lactic acid can be formed even when the external pH is as low as 4.5. When muscles are stimulated in a medium saturated with 100% CO2 and buffered with bicarbonate, there is seldom evidence of lactic acid formation at any external pH (from 6.8 downwards). The CO2 itself appears to reduce the internal pH to about the critical level below which lactic acid production is inhibited. At lower CO2 percentages (50% or less, in nitrogen) some lactic acid can be produced at all external pH’s, from 5.1 upwards. If the hydrogen-ion ratio across the fibre membrane were governed by the Donnan equilibrium, the internal pH of a normally excitable muscle would have to be at least 1.2 less than that of the outside fluid. At external pH 6.0 the internal pH would then be 4.8 or less, yet the nearly normal production of lactic acid shows that it must have been well above 6.3, while at external pH 4.5 the internal pH would not be greater than 3.3, yet some lactic acid was formed, so it cannot in fact have been less than 6.0 (allowing 0.3 for the increased alkalinity due to phosphagen splitting). When phosphate buffers are used, the internal pH certainly falls to some extent when the external pH is lowered, but far less than prescribed by the Donnan equilibrium. With CO2-bicarbonate buffers, there is no sign that the internal pH depends on anything but the partial pressure of CO2. Other evidence is considered, particularly that obtained by using an intracellular glass electrode (Caldwell, with crab fibres). The conclusion is that in normally excitable muscle the Donnan equilibrium does not control, and does not greatly influence, the distribution of hydrogen ions across the fibre membrane. In resisting diffusion and potential gradients the muscle fibre probably maintains its own internal pH, at least to a large extent, by active metabolic effort, If so, since CO2 penetrates freely, the internal HCO3-ion concentration also must be actively maintained. When the controlling mechanism fails, the contractile function of the muscle deteriorates. The observed variability of muscles exposed to abnormal external conditions may depend on differences in their capacity to maintain their internal state.