The force-generation process in active muscle is strain sensitive and endothermic: a temperature-perturbation study

In their well-known experiments on active muscle, Huxley and Simmons (1971) attributed the quick tension recovery after a rapid (<1 ms), small shortening step (L-release) to the force-generating transition(s) (referring to a decrease in the slope of tension decline) in the attached cross-bridges; although many subsequent studies supported this interpretation (Ford et al., 1977), the underlying molecular deformation in the cross-bridge – as determined from X-ray diffraction studies in particular – remains unclear (Knupp et al., 2009). In general, force rises obtained by other rapid perturbations on active muscle, e.g. temperature jump (T-jump), pressure release, are significantly slower (see references in Ranatunga et al., 2002, 2010) than the quick tension recovery obtained after L-release. The original observations from several different laboratories and using T-jumps (Davis and Harrington, 1987; Goldman et al., 1987; Bershitsky and Tsaturyan, 1992; Davis, 1998) indicated that the active force-generation process in isometric muscle may be endothermic (tension rises on absorption of heat). The fact that the tension rise after a T-jump was much slower than the tension recovery after an L-release led to proposals that the underlying processes were: (1) different and remote from one another in the cross-bridge cycle (see Davis and Epstein, 2009 and refs therein), possibly in a parallel attached pathway (Tsaturyan et al., 1999; Huxley, 2000; Ferenczi et al., 2005; Woledge et al., 2009); or (2) of a different nature. For example, Huxley (2000) suggested that a T-jump caused rocking of the motor domain on the actin filament, whereas the early tension recovery after sudden shortening was caused by tilting of the lever arm. However, Tsaturyan et al. (1999) proposed that the T-jump raised tension by a transition from non-stereospecific to stereospecific binding of myosin heads to actin.

It may be argued that the quick tension recovery by L-release represents a force-generation event when cross-bridges are negatively strained (and hence fast), whereas the response to a T-jump (or pressure release) in isometric muscle reports the force generation without an externally induced strain (see Davis, 1998; Coupland et al., 2005). Indeed, when compared with the tension rise induced by a standard T-jump on the isometric muscle, the tension rise induced by the T-jump was more pronounced during steady shortening, whereas it was depressed (∼absent) during steady lengthening (Ranatunga et al., 2007). Thus, the force-generating process perturbed by a T-jump shows strain sensitivity, enhanced by negative strain and inhibited by positive strain. By modelling the effect of temperature on the cross-bridge cycle, containing two tension-generating steps of similar amplitude, we proposed a hypothesis in which the temperature rise after a T-jump and the tension recovery after L-release were produced by the same step, i.e. the first tension-generating step (Offer and Ranatunga, 2015). Rapid shortening, by making the strain on the cross-bridges more negative, activated the first tension-generating step directly. In contrast, we suggested that a T-jump speeded up this tension-generation step more indirectly via the two strongly endothermic steps preceding it: the ATP hydrolysis step; and the cross-bridge attachment step. The purpose of the present study was to extend our understanding of such findings. In the well-known experimental study dealing with tension transients to small, rapid shortening and lengthening steps, Ford et al. (1977) commented that the quick tension recovery following a small L-release was also observable at the beginning of ramp shortening. It was represented by a sharp decrease in the slope of tension decline (an inflection; see fig. 29 in Ford et al., 1977) before the subsequent gradual decrease in the slope to the steady-state tension at that shortening velocity. The X-ray diffraction studies by Yagi et al. (2006) have indeed shown that a conformational change of actin-attached cross-bridges occurs early (in <2 ms) in the transition from isometric to shortening in muscle fibres.

In the present study on maximally Ca²⁺-activated single muscle fibres at 8–9°C, we examine the tension, the time course and the length change characteristics of this initial transition at a range of shortening velocities. We also examine the temperature sensitivity of this initial tension decline by applying a T-jump coincident with the onset of ramp shortening. Results are discussed in relation to previous interpretations on the basis of the active force generation in muscle.

The experiments were done on segments of single skinned fibres from rabbit psoas muscle. Adult male rabbits were killed by an intravenous injection of an overdose of sodium pentobarbitone (Euthatal, Rhone Merieux Ltd, Harlow, UK), in accordance with the UK legislation, and fibre bundles from the psoas muscle were prepared and chemically skinned using 0.5% Brij 58, as described previously (Fortune et al., 1991). The procedures were approved by the University of Bristol Ethical Review Committee for animal use and care.

Detailed information on fibre dissection and fibre mounting for tension recording, the trough assembly (consisting of four troughs mounted on the stage of a binocular microscope) and the compositions of various buffer solutions have been published previously (see Ranatunga et al., 2002, 2007). Basically, the ends of a single fibre segment were glued (using nitrocellulose) to two metal hooks: one attached to a force transducer (resonant frequency ∼14 kHz); and the other to a motor to apply ramp length changes to one fibre end. The buffer solutions had β-glyerol phosphate as the (low temperature-sensitive) pH buffer, pH 7.1 and ionic strength 200 mmol l^–1. Using He-Ne laser diffraction, the fibre length was adjusted to a sarcomere length of 2.5–2.6 µm. A fibre, held isometrically, was maximally Ca²⁺-activated in the front trough where the temperature was clamped at 8–9°C and monitored by a thermocouple placed close to the muscle fibre. A laser pulse of 0.2 ms duration and near infrared (1.32 µm) in wavelength was used to induce a T-jump in the fibre and the solution bathing it in the front trough; the amplitude of the T-jump used in the experiments was ∼3°C and, following a laser pulse, the elevated temperature remained constant for >0.5 s. To minimise thermal expansion effects on fibre tension, care was taken to shadow the transducer hooks from the laser radiation (see Ranatunga, 2010). The sarcomere length was monitored by a diffractometer in a few experiments (see Ranatunga, 2001). As reported previously from measurements of the signal during and after the ramp length change (see Ranatunga et al., 2010), the average sarcomere shortening (owing to end compliance) would be ∼11% less than the induced fibre length change. Data analyses will be presented with regard to fibre length change, although the corresponding sarcomere length change will be occasionally considered, the error involved in such calculation is high (∼10%). As in previous studies, particular care was taken to ensure that fibres remained in good condition during the course of recording; thus, fibres were regularly examined under a binocular microscope and an experiment terminated if fibres showed damage or developed visible irregularities (or if there was a >10% drop in isometric force).

The outputs of the tension transducer, the thermocouple, the motor (fibre length) and, in a few experiments, the diffractometer (sarcomere length change) were examined on two cathode ray oscilloscopes and digital voltmeters and, using a CED micro-1401 (Mk II) laboratory interface and Signal 3 software (Cambridge Electronic Design Ltd, Cambridge, UK), collected and stored on a personal computer. Subsequent analyses, including measurements of force, temperature, length and curve fitting to tension records, were made using Signal software and further analyses made with Fig.P software (Biosoft, Great Shelford, Cambridgeshire, UK).

Various tensions given in this study refer to the active muscle fibre force measured above the baseline (resting) force. The nomenclature used in describing the force responses during ramp shortening is the same as in our previous studies (see Roots et al., 2007). Briefly, P₀ refers to the steady isometric force, and during a ramp shortening there is a gradual reduction in tension decline to a force level P₂ that can be used to determine the steady-state force versus shortening velocity relationship (see Ranatunga et al., 2010). In experiments with greater resolution, Ford et al. (1977) showed the occurrence of an initial sharper decrease of tension decline (an inflection) earlier after the onset of a ramp shortening. We examined the tension (P₁) at, time (t₁) to and length change (L₁) to the end of this initial P₁ transition; by applying a T-jump coincident with the onset of ramp shortening, we also examined the temperature sensitivity of this P₁ transition.

Data presented in the study are from experiments on 17 single fibres at 8–9°C. With average sarcomere length set at ∼2.5 μm, the mean (±s.e.m.) rest length (L₀) of the fibre segments was 1.55±0.09 mm and the mean (±s.e.m.) maximum Ca²⁺-activated isometric tension (P₀) was 199±14.3 kN m⁻². Two experimental studies were carried out. In study 1 (N=11), the characteristics of the initial P₁ transition were determined at a range of ramp shortening velocities up to the maximum shortening velocity (V_max), with near-zero isotonic force [the T-jump effect was examined after the slower P₂ transition to examine the T-jump force generation during steady shortening and the analyses were reported previously (Ranatunga et al., 2010)]. In study 2 (N=9), the tension response to T-jump applied coincident with onset of ramp shortening was recorded at various velocities and the changed tension response analysed. Unlike in all previous studies where T-jump was when force level was steady (isometric, steady shortening or lengthening, see Ranatunga, 2010), the experiments/analyses presented here required making two recordings at each velocity, i.e. one with and another without T-jump to correct for tension decline and difference traces were examined. Thus, two tension responses were recorded at any given velocity, i.e. one with a standard T-jump and another without a T-jump; such recordings were made at a wide range of velocities (ramp speeds). Feasibility of this method was carried out in some of the experiments in study 1, and data from three fibres were included in study 2 analysis.

In most figures, individual measurements (data points, N>90 for each study) are plotted to show the scatter and distributions and linear regressions were fitted (e.g. Fig. 3A and Fig. 6A) to these pools of individual data. Additionally, as given in the figure legends, means (±s.e.m.) were calculated for short velocity ranges and shown; they aided fitting curves by eye. In Tables 1 and 2, an attempt has been made to provide a suitable summary of the findings to compare and contrast T-jump and other data from ramp shortening, steady shortening and isometric. Any other relevant experimental details are outlined in the Results.

Fig. 1A shows the basic features of the tension response to a ramp shortening. The tension decline shows a gradual decrease in slope (the P₂ transition) to reach a near-steady tension P₂. The tension record also shows the occurrence of an inflection soon after the onset of a ramp length change and before the slower P₂ transition. This is thought to represent the force-generating transition in the attached cross-bridges on exposure to negative strain (see Ford et al., 1977; Bressler, 1985). As shown in Fig. 1B and C (see legend), three measurements were made to characterise this P₁ transition: (1) the time t₁ from the beginning of the ramp to the transition; (2) the force P₁ at the transition; and (3) from the length record, the length change L₁ to the transition.

Fig. 2 shows, for a range of velocities, the individual measurements and the mean (±s.e.m.) values for the P₁ tension and the time t₁ to the transition. Fig. 2A shows that the transition occurs at a lower tension level (or its amplitude P₀/P₁ becomes larger) when shortening velocity is increased. Fig. 2B shows that the time t₁ to the transition decreases sharply with increase of shortening velocity, i.e. the P₁ transition is faster with increased velocity.

Fig. 3A shows that the reciprocal of t₁ (1/t₁, proportional to the rate or the speed of the transition) increases linearly with shortening velocity, so that the approximate exponential rate (3/t₁, see Fig. 3 legend) would be >500 s⁻¹ at shortening velocities approaching V_max (1–2 L₀ s⁻¹). The extrapolated rate to zero velocity, i.e. for the isometric muscle, is 60–70 s⁻¹. The length change L₁ at which the end of the transition occurs is plotted against shortening velocity in Fig. 3B. The data show that L₁ increases with increase of shortening velocity but approaches a steady value of 0.75% L₀ at velocities >1.0 L₀ s⁻¹. Taking a half-sarcomere length of 1.25 μm (as in mammalian fibres), the steady L₁ corresponds to ∼8 nm half-sarcomere^–1 (or ∼9 nm half-sarcomere^–1 when corrected for end compliance).

Table 1 summarises the data for the measurements of various features of the P₁ transition from this study (study 1). Similar data for the transition were also collected in study 2 experiments (see below) that were used primarily for generating difference tension traces; the data (given as study 2 in Table 1) are essentially similar; at near V_max, the rate is ∼500 s⁻¹ and L₁ is ∼8 nm half-sarcomere^–1. [We previously reported an analysis of the P₁ transition in experiments on tetanised intact rat muscle fibres but at 20°C (see fig. 4A in Roots et al., 2007). Probably a result of the higher temperature used in that study, the P₁ transition occurred at a higher tension level, the transition was faster and the length change L₁ shorter at similar velocities.]

It was shown in a few experiments in a previous study that a standard T-jump induced a tension potentiating effect when applied at different times during the force decline by ramp shortening, i.e. prior to the steady-state shortening force (see fig. 6 in Ranatunga et al., 2007). Moreover, it was shown that the effect of a T-jump on tension could be analysed by recording the difference tension trace between two tension responses to the same velocity, i.e. one with and the other without a T-jump. Examples of such records from an experiment in the present study, and for three different shortening velocities, are shown superimposed in Fig. 4A–C: comparison of the superimposed tension traces with (upper trace) and without T-jump (lower) shows that the amplitude and time courses of the tension decline during subsequent shortening is markedly altered by a T-jump and in a velocity-dependent way.

The response without a T-jump was subtracted from that with a T-jump at the same velocity to obtain the difference tension response, representing the tension change produced by the T-jump alone during shortening. Frames in Fig. 4D–F show the corresponding difference tension records (and also the difference temperature and length records) so obtained. It is seen that each difference tension response is biphasic (and rising), with an initial fast component (indicated by downward arrows) and a delayed slower component. The separation in time between the two is perhaps clearer at higher velocity (Fig. 4D). A T-jump tension response in isometric muscle also consists of two components, phase 2b (fast) and phase 3 (slow), though not separated in time (Ranatunga, 2010). To be compatible with previous studies on isometric T-jump tension response, the two components in the difference tension records during ramp shortening in this study will also be identified as phase 2b (fast) and phase 3 (slow).

Fig. 5 shows the difference tension records generated from an experiment on another fibre in which a wider range of shortening velocities, from 0 L₀ s⁻¹ (isometric; Fig. 5F) to 0.9 L₀ s⁻¹ (Fig. 5A), was used. Basically, the difference tension traces show that the speed of the T-jump response increases with increase of shortening velocity. On each difference tension trace, a dotted curve is superimposed to indicate the initial fast phase or phase 2b. It is seen that, unlike in the isometric case where the two phases of tension rise seem to originate together, the two phases of tension rise to a T-jump at the onset of ramp shortening are separated in time. The separation is more evident at higher velocities. Consequently, whereas the tension response of the isometric case could be fitted with a double exponential function – as in previous studies, in difference tension records obtained at the onset of ramp shortening, two single exponential curves were fitted separately to phase 2b to characterise its rate and amplitude and to phase 3 for its rate and the total amplitude.

Fig. 6 illustrates the pooled data from experiments on nine fibres for the rate (Fig. 6A) and amplitude (Fig. 6B) of phase 2b (filled symbols) and phase 3 (open symbols) components from such analyses; they are plotted against shortening velocity. Both phase 2b and phase 3 rates were significantly correlated with shortening velocity (P<0.001). The observed rate of phase 2b increases with increase of shortening velocity so that at >1 L₀ s⁻¹ (near V_max), the rate is ∼600 s⁻¹. Given that in the isometric case, the phase 2b rate is ∼50 s⁻¹ the rate increase is >10-fold when shortening is near V_max. Because it is measured after the T-jump (∼3°C higher), the rate of phase 2b is higher than that for P₁ transition at each velocity. It is interesting to note that phase 2b rate at very low velocities is indeed lower than in the isometric case, as also found in the data for the rate of T-jump tension rise during steady shortening (see fig. 3A in Ranatunga et al., 2010). Despite much variability in the amplitude data in Fig. 6B, they indicate that both the phase 2b amplitude and the total (phase 2b+phase 3) amplitude at low velocities are larger than the corresponding amplitudes in the isometric case and they decrease to below isometric amplitudes at the higher velocities. Thus, the T-jump-induced tension response at the onset of ramp shortening also suggests a biphasic dependence on velocity of the tension amplitude, as also obtained in the previous steady shortening experiments (see fig. 5 in Ranatunga et al., 2010).

Fig. 7 was constructed using the data for phase 2b illustrated in Fig. 6A (see figure legend for details) to examine the approximate extent of shortening (strain) during the initial tension rise after a T-jump. This figure shows that the extent of shortening corresponding to nearly full amplitude of the initial tension rise induced by a T-jump increases with shortening velocity and approaches an approximate steady level: the mean value for shortening velocity of ∼1.0 L₀ s⁻¹ is ∼0.7% L₀ (see also Table 2), as for L₁ in the P₁ transition above.

In their classical study, Ford et al. (1977) stated in definitive terms that the tension recovery following a small rapid length release (cross-bridge force generation) was also observable at the beginning of ramp shortening and was represented by a sharp decrease in slope of the tension decline (commencing an inflection) in the tension record. The present study examined this initial tension transition (labelled P₁ transition) and the T-jump-induced changes in the tension decline during ramp shortening, thereby extending our previous findings on isometric, shortening and lengthening muscle under steady-state conditions (see Ranatunga et al., 2007, 2010).

The time t₁ to the initial (P₁) transition decreased markedly initially but less so as the shortening velocity was further increased (see Fig. 2); the outcome is that the rate 1/t₁ is a linear function of the velocity (Fig. 3A). Approximating the P₁ transition as a single exponential [i.e. t₁/3=τ (time constant)], the data show that the rate 1/τ of the P₁ transition increases and would be 500 s⁻¹ at a shortening velocity of ∼1 L₀ s⁻¹ (near V_max). The length change L₁ associated with the P₁ transition increased with shortening velocity to a steady value ∼8 nm half-sarcomere^–1 when corrected for ∼11% end-compliance effect (see Fig. 3B and Table 1). These basic findings would be consistent with the original thesis of Ford et al. (1977) that the P₁ transition at the onset of a ramp shortening reflects a force-generating transition in attached cross-bridges.

Basically, when a ramp shortening is applied to an isometric muscle, the strain in all the attached cross-bridges becomes increasingly negative, causing the pre-stroke cross-bridges to go through force-generation transition. Ignoring the effects of series end compliance, the tension decrease at the start of the ramp shortening would be due to the sarcomeric compliance because there would be no time for cross-bridge attachment/detachment steps to occur to an appreciable extent. The tension decline will not continue at this initial rate, due to cross-bridge force generation resulting in the P₁ transition (the inflection). This is generally consistent with the interpretations given in the X-ray diffraction studies of Yagi et al. (2006) and Radocaj et al. (2009). Indeed, Yagi et al. (2006) concluded that actin-attached myosin heads (cross-bridges) undergo a rapid (∼2 ms) conformation change at the onset of a ramp shortening. Our present study shows that the speed, the amplitude and the associated length change of this initial (P₁) transition are velocity sensitive so that its features at high velocities approach those expected from rapid length release experiments.

When applied coincident with the onset of ramp shortening, a small T-jump has a pronounced potentiating effect on the subsequent tension response and the effects are velocity sensitive (Fig. 4). There are two components in the tension change induced by such a T-jump, identified as phase 2b (fast) and phase 3 (slow) (see Fig. 5), where phase 2b is considered the T-jump-induced (endothermic) force generation in attached cross-bridges and phase 3 a subsequent slow step(s) in the cross-bridge cycle. Interestingly, compared with the isometric case (Fig. 5F), the two phases are more distinct and separated in time during shortening (particularly at higher velocities, see Fig. 5A–C). The rate of phase 2b and the rate of phase 3 are linearly correlated with shortening velocity, and the rate of phase 2b in particular increases markedly with increase of velocity (Fig. 6A). The amplitude of both phases (see Fig. 6B) shows a biphasic velocity sensitivity, being higher than isometric at low velocities but decreasing below isometric at higher velocities.

The length change associated with phase 2b with a T-jump was ∼8 nm half-sarcomere^–1 when corrected for end compliance (Fig. 7; see Tables 1 and 2). This is similar to that for the P₁ transition above, consistent with the notion that phase 2b after a T-jump and the P₁ transition at the onset of ramp shortening may represent the same process (although at post- and pre-T-jump temperatures). If indeed the filaments contribute ∼50% to the sarcomeric compliance, then the length change (motor stroke) would be ∼4 nm for this process. As suggested by Ford et al. (1977), the P₁ transition at the onset of ramp shortening represents the cross-bridge force generation in active muscle and our present results show that it is temperature sensitive and endothermic.

In two previous studies (Ranatunga et al., 2007, 2010), we examined the effect of a standard T-jump applied when tension during a ramp shortening had reached a steady level, i.e. after the slower second transition (the P₂ transition). For comparison with the present study, the relevant findings during steady shortening are also given in Table 2; the corresponding (but unpublished; K.W.R., H. Roots and G.O., unpublished data) P₁ data from the same experiments are shown in Table 1. The key findings worthy of note are the following. (1) During steady shortening, a T-jump induced a monophasic tension rise; the slower component (phase 3) seen in isometric contraction and in the present experiments at the onset of ramp shortening was not evident during steady shortening (see fig. 1 in Ranatunga et al., 2007, 2010). (2) The rate of T-jump force generation increased linearly with increased velocity, so that at a shortening velocity of ∼1 L₀ s⁻¹ it was ∼10× faster than in the isometric case (∼200 s⁻¹) [Ford et al. (1985) indeed found that, in frog fibres, the tension recovery after L-release increased linearly with increase of steady shortening velocity]. (3) The amplitude of the T-jump tension response showed a biphasic dependence on shortening velocity, basically as found in the present experiments at the onset of ramp shortening. (4) The extent of shortening associated with the T-jump tension rise at ∼1 L₀ s⁻¹ was ∼18 nm half-sarcomere^–1 (see Table 2), much higher than the ∼8 nm half-sarcomere^–1 obtained for P₁ and T-jump at the onset of shortening. This indicated that in steady shortening muscle there are contributions to filament sliding by events additional to force-generation process. The qualitative features of the T-jump-induced tension response in steady shortening muscle and at different velocities could be kinetically simulated assuming that the cross-bridge cycle becomes faster during shortening, as in the thesis of Huxley (1957) (see discussion in Ranatunga et al., 2010). The simulation of the present data, however, remains difficult on that basis, because strain-sensitive changes of attached cross-bridges at the onset of ramp shortening need to be considered.

As mentioned before, a T-jump on maximally activated isometric muscle induces a biphasic rise of tension; the initial rate has been experimentally shown to be sensitive to the level of inorganic phosphate (Pi) and of Mg.ADP, products of ATP hydrolysis released by cycling cross-bridges. An increase in phosphate level increased the initial rate of tension rise to a T-jump (Ranatunga, 1999), whereas an increase in Mg.ADP level had the opposite effect (Coupland et al., 2005). Of interest with respect to the present study are the findings that indicate that force recovery after rapid L-steps show qualitatively similar behaviours to the above. Thus, although there is some asymmetry between stretch and release, the tension recovery is faster when phosphate level is raised (Ranatunga et al., 2002; Nocella et al., 2017) whereas the tension recovery from L-step is slower when Mg.ADP level is increased (Coupland et al., 2005). Although detailed underlying mechanisms remain unresolved (see Smith, 2014), these observations could be simulated using a kinetic ATPase scheme where force generation occurred before rapid release of phosphate early in the cross-bridge cycle whereas ADP release was slow and occurred later (Coupland et al., 2005; Ranatunga, 2010).

Considerable progress has been made, in the last ∼50 years or so, in our understanding of the underlying processes of muscle contraction both from experimental work (Ford et al., 1977, 1985) and from modelling (Månsson, 2010a; see review by Månsson et al., 2015; Smith, 2014 and references therein). Compared with the time when Huxley and Simmons (1971) proposed their thesis, our understanding on sarcomere compliance and sarcomere mechanics has changed; thus, filaments also contribute to sarcomeric compliance (see refs in Offer and Ranatunga, 2013), compliance may be non-linear (see Edman, 2009; Nocella et al., 2014) and their effects could be complex (Bagni et al., 2005; Månsson, 2010b; Offer and Ranatunga, 2013). Additionally, there is considerable experimental evidence from a range of studies and from different laboratories (Davis and Harrington, 1987; Goldman et al., 1987; Kawai and Halvorson, 1991; Bershitsky and Tsaturyan, 1992; Davis, 1998; Griffiths et al., 2002; Colombini et al., 2008) that indicate that the active force-generation process in muscle is endothermic. However, its relationship to force generation induced by a length release, as in the Huxley and Simmons (1971) experiments, remains unclear (see Ranatunga, 2010). Indeed, Kawai and Halvorson (1991), Bershitsky and Tsaturyan (2002), Piazzesi et al. (2003) and Davis and Epstein (2009) concluded that endothermic force-generating process and L-release-induced force response represent different steps in the cross-bridge cycle of muscle. Also, Huxley (2000), Ferenczi et al. (2005) and Woledge et al. (2009) suggested that a temperature-sensitive step may possibly be present in a parallel attached pathway.

In contrast, the present study provides experimental evidence that the strain-sensitive cross-bridge force generation, or a step closely coupled to it, is temperature sensitive (endothermic). Gilbert and Ford (1988) indeed reported from direct measurement, in active frog muscle, that heat is absorbed during quick tension recovery after small length releases. Developing a model to simulate the force–velocity data, L-step force transients, cross-bridge stiffness and energetics in active frog muscle, we found that two force-generation steps (of similar magnitude) are essential in the cross-bridge cycle (see Offer and Ranatunga, 2013). Interestingly, when the same model was used to simulate the basic effects of temperature (Offer and Ranatunga, 2015), it was found that the strongly endothermic ATP hydrolysis and cross-bridge attachment steps may drive the increase of active tension in isometric and shortening muscle, but with some endothermic character given to the first force-generation step, as found here. A conformational change(s) absorbing heat (entropy driven) could also account for the force rise on release of hydrostatic pressure (volume increase), as we reported in some previous studies on skinned rabbit fibres (Fortune et al., 1991) and on intact frog fibres (Vawda et al., 1999). Although the present experiments were at ∼10°C, where temperature sensitivity of active force in (mammalian) isometric muscle is high, the general findings should be relevant for understanding muscle function at physiological temperatures (∼35–38°C). Clearly, it would be important to examine in future, by further modelling and experimentation, the underlying basis of the strain-sensitive endothermic character of the (first) force-generation step in the cross-bridge cycle.

We thank Professor M. A. Geeves (University of Canterbury, UK), Dr Gavin Pinniger (University of Western Australia, Perth, Australia), Dr Ivo Telley (Gulbenkian Research Institute, Portugal) and Dr Naoto Yagi (Synchrotron Radiation Research Institute, Sayo, Japan) for making valuable critical comments on earlier versions of the manuscript. An abstract of this study was communicated to the 39th European Muscle Conference held in Padua, Italy (2010).