Journal of Physiology (1992), 447, pp. 425-448 With 13 figures Printed in Great Britain

425

TENSION RESPONSES TO JOULE TEMPERATURE JUMP IN SKINNED RABBIT MUSCLE FIBRES

BY SERGEY Y. BERSHITSKY* AND ANDREY K. TSATURYANt From the *Department of Biophysics, Institute of Physiology, Urals Branch of Academy of Sciences of the USSR, Popova Street 30, 620014 Sverdlovsk, USSR and the tDepartment of Mechanics of Nature Processes, Institute of Mechanics, M. V. Lomonosov Moscow State University, Leninsky Gory, 119899 Moscow, USSR

(Received 25 February 1991) SUMMARY

1. Joule temperature jumps (T-jumps) from 5-9 °C up to 40 °C were used to study the cross-bridge kinetics and thermodynamics in skinned rabbit muscle fibres. To produce a T-jump, an alternating current pulse was passed through a fibre 5 s after removing the activating solution (pCa 4-5) from the experimental trough. The pulse frequency was 30 kHz, amplitude < 3 kV, and duration 0-2 ms. The pulse energy liberated in the fibre was calculated using a special analog circuit and then used for estimation of the T-jump amplitude. 2. The T-jump induced a tri-exponential tension transient. Phases 1 and 2 had rate constants k1 = 450-1750 s-1 and k2 = 60-250 s-1 respectively, characterizing the tension rise, whereas phase 3 had a rate constant k3 = 5-10 s-5 representing tension recovery due to the fibre cooling. 3. An increase from 13 to 40 °C for the final temperature achieved by the T-jump led to an increase in the amplitudes of phases 1 and 2. After T-jumps to 30-40 °C during phase 1, tension increased by 50-80 %. During phase 2 an approximately 2fold tension increase continued. Rate constants k. and k2 increased with temperature and temperature coefficients (Q1o) were 1P6 and 1-7, respectively. 4. To study which processes in the cross-bridges are involved in phases 1 and 2, a series of experiments were made where step length changes of -9 to +3 nm (hs)-1(nanometres per half-sarcomere length) were applied to the fibre 4 ms before the T-jump. 5. After the step shortening, the rate constant of phase 1 increased, whereas its amplitude decreased compared to those without a length change. This indicates that phase 1 is determined by some force-generating process in the cross-bridges attached to the thin filaments. This process is, most probably, the same as that producing the early tension recovery following the length change. The enthalpy change (AH) associated with the reaction controlling this process was estimated to be positive (15-30 kJ mol'). -

-

*t Present address to which all correspondence and reprint requests should be sent: Biophysics

Section, King's College London, 26-29 Drury Lane, London WC2B 5RL. MS 9178

426

S. Y BERSHITSKY AND A. K. TSATUR YAN

6. Both the rate constant k2 and the maximal tension achieved at the end of phase 2 were practically independent of the preceding length changes. This means that phase 2 is accompanied by the cross-bridge detachment and reattachment to new sites on the thin filaments. 7. A simple three-state model of the cross-bridge kinetics is proposed to explain the experimental data. INTRODUCTION

In 1971 Huxley and Simmons proposed a model of the force generation in muscle. They assumed that the cross-bridge can produce a reversible step movement while it is attached to the thin filament. This model explains the kinetics of the early partial tension recovery following a step length change (Huxley & Simmons, 1971; Ford, Huxley & Simmons, 1977, 1981, 1985). The main postulate in the Huxley & Simmons model is that the early tension recovery is due to a process in the crossbridges attached to the thin filament, not to the cross-bridge detachment and reattachment. Time-resolved X-ray experiments (Huxley, Simmons, Farugi, Kress, Bordas & Koch, 1983) confirmed this assumption. It was shown that the changes in the X-ray diffraction pattern induced by quick length change can be completely reversed by the length recovery to its initial value in 1-2 ms after the step, i.e. during or just after the early tension recovery. However, there is no evidence that the step movement of the attached cross-bridge can be made without a relative sliding of the filaments. So, it is not clear whether the step movement is involved in isometric force generation (Huxley, 1980). To synchronize the force-generating step of the cross-bridges, we used the joule temperature jump (T-jump) in single skinned muscle fibres (Bershitsky & Tsaturyan, 1985). In this method the T-jump is induced by the joule heat liberation in a fibre while it is suspended in air. The method permits a temperature change of up to 35 K with simultaneous monitoring of the mechanical events in the fibre. The fibre stiffness measurement before and after the T-jump (Bershitsky & Tsaturyan, 1986 a, 1989) showed that the stiffness drops immediately after the T-jump by about 0 5-1 % per 1 K. During a 3-4-fold tension rise initiated by the T-jump from 5-7 to 28-30 °C the stiffness also increases, but by only 50% (Bershitsky & Tsaturyan, 1989). So, the tension changes initiated by the T-jump are mainly due to the change in the cross-bridge force, not stiffness. The primary version of the joule T-jump method, as well as experiments similar to those presented here, were briefly described earlier, but were performed using muscle fibres from the frog (Bershitsky & Tsaturyan, 1986b, 1988; Tsaturyan & Bershitsky, 1988). At temperatures above 20 °C the tension transients in the frog fibres become too fast for their rate constants to be measured accurately. Thus a new series of experiments was performed using rabbit psoas muscle fibres whose T-jumpinduced tension transients are not as fast. Also, the isometric tension at maximal activation is more temperature sensitive in fibres from warm-blooded animals than those from cold-blooded animals (Woledge, Curtin & Homsher, 1985; Stephenson & Williams, 1985). -

JOULE TEMPERATURE JUMP IN MUSCLE FIBRE

427

METHODS

Principle of the method In order to make stepwise temperature changes in skinned muscle fibres, 0-2 ms, 30 kHz, up to 3 kV alternating current pulse was passed through the fibre segment suspended in air between two electrodes of the heating pulse generator. The joule heat liberated in the fibre was calculated with a special analog circuit and then used for the T-jump amplitude determination. The active electrode was fixed to the length-change generator and the ground electrode to the force transducer. When the fibre was fully activated (pCa 45), the activating solution was removed and the heating pulse applied within 5 s of the fibre being suspended in air. Tension transients initiated by the T-jumps from 5-9 to 13-40 °C were monitored. In some experiments step length changes from -9 to + 3 nm (hs)'- (nanometres per half-sarcomere) were applied 4 ms before the T-jump to study the cross-bridge processes producing the tension transients. -

Fibre preparation and solutions Muscle fibres were obtained from European grey rabbits of either sex weighing 2-5-3-5 kg. Animals were killed by a blow to the head. Thin fibre bundles (- 1 mm in diameter, 3 cm long) were tied to wooden sticks and cut loose from the psoas minor muscles. Then each bundle was put into a glass tube filled with the storage solution (Table 1) and rapidly cooled to -20 'C. After 24 h the bundles were transferred to a fresh storage solution and stored at -20 'C for 2-6 weeks. A segment of a single fibre was separated from the bundle under a long-focus microscope MBS-9 (LOMO Inc., Leningrad, USSR) in storage solution at 3-5 'C. Then the fibre was transferred to the experimental trough at 0-2 'C. The fibre ends were placed on dry nickel tube electrodes and moistened by droplets (= 0 05 ,ul) of shellac dissolved in ethanol (70/30, v/v). The trough was filled with cold relaxing solution (Table 1). As ethanol diffuses into the solution, the shellac hardens quickly providing reliable fixation and electric contact between the fibre segment (1P4-2-5 mm long) and the electrodes. The fibre glued to the nickel tube electrode is shown in the left inset in Fig. 1. The sarcomere length was adjusted to 2-5-2-6 ,um while being monitored by laser diffraction. The homogeneity of the fibre widths along the segment was inspected in two projections using an MBS-9 microscope and the optical system described below. The sarcomere length homogeneity was checked using laser diffraction at various fibre lengths in the relaxing solution. The fibre crosssectional area A) was determined twice: in air (A.) and in the relaxing solution (A8). A8 was used for the fibre tension (force per area) calculation, while A. was necessary for determination of the heated volume of the fibre surrounded by a thin layer of solution. The cross-sectional area was calculated using a formula A = 7Td1d2/4 (Blinks, 1965), where A is A8 or A., d4 and d2 are the fibre widths in two perpendicular projections in solution or in air. If the variation of the area along the fibre suspended in air was more than 10%, the fibre was replaced by another one. Before each experiment, the fibre was treated with 05-1 % (v/v) solution of non-ionic detergent Triton X-100 in the relaxing solution to ensure destruction of the sarcolemma and the membranes of the sarcoplasmic reticulum. The method of Moisescu (1976) was used for quick and homogeneous activation of the fibre. The composition of the solutions is similar to that previously described (Bershitsky & Tsaturyan, 1989) and is shown in Table 1. Cacodilic acid was used as a pH buffer because of the very low temperature coefficient of its pKa. This coefficient measured using an EV-74 ionometer was -00045 log units per 1 0C in the range 0-35 0C. So, the T-jump of 25 'C induced a decrease in pH of only about 0-1 log units. -

Mechanical instrumentation Trough. An experimental chamber with a 09 ml solution trough was made from anodized aluminum. The lower part of the chamber was placed into the thermoelectric thermostat which kept the chamber temperature at 0-4 'C. The trough width and depth were 4 and 8 mm respectively. The short distances from the fibre held in the middle of the trough to the walls and bottom of the massive cold chamber provided a temperature increase of not more than 5 K when the solution was removed from the trough. When cold, vapour in the trough was nearly saturated independently of vapour pressure in the surrounding air. The uncoated transistor covered with a thin layer of isolator was fixed 1 mm from the centre of the fibre and used as a thermometer in

o~ ~C

428

CD C) -4

S. Y. BERSHITSKY AND A. K. TSATURYAN

2

c
). The rate constants are plotted on a logarithmic ordinate against the reciprocal absolute temperature, T, on the abscissa. Straight lines represent the regression for each set of data points. Data are from four muscle fibres.

0

Responses to T-jumps of various amplitude To study the temperature dependence of the amplitudes and rate constants for phases 1 and 2, a series of four experiments was performed where T-jumps of various amplitudes were applied to the fibres. The records of the tension responses to the T-jumps of various amplitudes are shown in Fig. 6 at two oscilloscope sweep speeds. The starting temperature just before the T-jumps was 5-1-5-4 'C. The initial tension in air, P0, at the temperature was 50-54 kN m-2. An increase in the final temperature reached by the T-jump led to an increase in the maximal tension achieved during the tension transient and an acceleration of this transient. Sometimes, after T-jumps of an intermediate amplitude, a small tension drop during the heating pulse preceded the tension rise (Fig. 6, 16 K example). At T-jumps of a rather high amplitude (20-35 K), the drop was not seen because of an electric artifact during the heating pulse and the fast tension rise (phase 1) which began during the heating pulse. Figure 7A shows the temperature dependence of tension before (in the activating solution and air) and after the T-jumps from four experiments. The maximal tension

S. Y. BERSHITSKY AND A. K. TSA TUR YAN

436

achieved after the T-jump is plotted in Fig. 7A against the temperature which was corrected for fibre cooling during tension rise. The plot shows a nearly linear increase in tension from 15-40 to 170-210 kN m-2 when the temperature was increased from 1-5-3 to 30-40 °C. At the initial temperature 5-1-6-3 °C tension was 50-60 kN m2. B

A

1.0

1-0

05-

o

,0.5 -

o

0C14

CalX r0-0 ~ + 30 20 0 30 T-jump amplitude (K) Fig. 8. Normalized amplitudes of phases 1, aO/lP (A), and 2, aO/(Po+aO) (B), against the T-jump amplitude, AT. Data are from four muscle fibres.

0-0 i 0

10

20

T-jumps of a relatively high amplitude (> 15 K) induced a biexponential tension rise. For T-jumps of lower amplitude, phase 1 was not determinable (Fig. 6, 8 K) or the computer program (Provencher, 1976) showed that this phase was not significant. Both k1 and k2 increased with the final temperature. An Arrhenius plot for k1 and k2 obtained from four experiments is shown in Fig. 7B. The Qlo values determined by the least-squares method were 1-6 for k1 and 1-7 for k2, respectively. At any given temperature k1 was = 5 times k2. At 20 °C k, was 400-600 s-1 and k2 was 75-120 s-'. The dependence of normalized tension rise during phase 1, al/PO, on the T-jump amplitude, AT, is shown in Fig. 8A. The tension increment associated with phase 1 was a near linear function of AT. After 25-35 K T-jumps the increment achieved was 55-75 % of Po. Normalized tension increment during phase 2, al(Po + a'), is plotted in Fig. 8B, against AT. This increment increased quickly when AT rose to 15-20 K and then achieved a plateau at 70-100%. Effects of preceding length changes To examine what cross-bridge processes are responsible for phases 1 and 2 of the tension rise due to a T-jump, a series of five experiments was made with step length changes of amplitude ranging from -9 to + 3 nm (hs)-1 applied to the fibre 4 ms prior to the T-jump. Mechanical transients Typical records in an experiment of this series are shown in Fig. 9. In this experiment, the tension in air just before the length step, Po, at the starting temperature 8-7-9 °C was 80-88 kN m-2. Length steps completed within 0 35 ms

437 JOULE TEMPERATURE JUMP IN MUSCLE FIBRE induced a tension transient which was similar to those described by Huxley & Simmons (1971) and Ford et al. (1977). The subsequent T-jump induced a biexponential tension rise followed by a slow tension recovery similar to those without length change.

j....125K + 3 nm (hs)-1

*

100

I 500 -

50

-9

-6

-3

0

3

-9

Length step (nm

-6

-3

0

3

(hs)-')

Fig. 12. Variation of the rate constant of phases 1 (k,) and 2 (k2) with the length step amplitude. Bars show the standard deviations in the five experiments presented in Figs 10 and 11.

change. The amplitude of phase 2, a2, increased after fibre shortening. The increase in a2 as compared with aO (at y = 0) was significant (P < 0 02) at y values from -6 to -9 nm (hs)-. Figure 12B shows the rate constant k2 of the slow phase 2 compared to the preceding length change, y. It can be seen that k2 is practically independent of y. The scatter of the data was due to the variation of k2 values between fibres. Correlation between k2 and y was not significant for individual fibres. The fact that the rate constant and the final tension of phase 2 were independent of the preceding length changes means that during this phase the cross-bridges 'forgot' the relative sliding of the thin and thick filaments. Hence, it can be concluded that phase 2 is accompanied by the cross-bridge detachment and reattachment to the thin filaments. DISCUSSION

Joule T-jump method

Possible artifacts Electric artifacts. Some possible artifacts of the joule T-jump method were briefly described earlier (Bershitsky & Tsaturyan, 1985, 1989). The direct effect of the

JOULE TEMPERATURE JUMP IN MUSCLE FIBRE

441

electric field on the fibre was, most likely, insignificant. Taking the peak electric field intensity, E = 2 MV m-l, charge of a cross-bridge q = 1.6 x 1018 C (ten times unit charge), and the dielectric constant of the solution, e = 80, one can calculate the maximal electric force acting on a cross-bridge, Fe = 4 x 10-14 N. This force is only 1 % of the force per cross-bridge during an isometric contraction (Huxley & Simmons, 1971). Since up to twenty activations and T-jumps were applied to a fibre without a significant loss of tension, it can be concluded that the heating pulse did not harm the contractile proteins. There was a small effect of the electric field on the ionic composition of the activating solution due to electrolysis. Even for H+ ions, which are the most mobile ions, the displacement during a half-wave of the heating pulse of maximal amplitude was estimated to be < 5,m. This means that the thickness of a layer near the electrodes where the solution composition was changed due to electrolysis was not thicker than two sarcomere lengths. Changes in the solution composition in air. As the heating pulse was applied to the fibre suspended in air, possible effects of water evaporation from the fibre surface and the ATP hydrolysis in the fibre should be discussed. The fibre temperature in the cold trough was as low as 5-9 °C, and the evaporation was also small. Computer simulation showed that the increase in ionic strength due to evaporation was < 5 % in 5 s. At room temperature this effect is more significant (Ferenczi, 1985, 1986). The ATPase rate in the rabbit fibre at 5-10 "C is less than 1-3 s-1 per myosin head (Brenner, 1986). Taking the concentration of heads in the fibre to be 0-15 mM (Ferenczi, Homsher & Trentham, 1984), one can calculate the ATPase activity in the fibre to be < 0-2 mm s-'. This means that < 1 mM-MgATP is converted into MgADP in 5 s after the fibre had been suspended in air. The computer simulation taking into account MgATP hydrolysis and the CP/CPK regeneration system showed that in this system the MgATP concentration in air remains practically the same as that in the solution, and the MgADP concentration is < 0-15 mm. The inorganic phosphate (Pi) concentration increased from 0-5 mm in the solution to 1-5 mM 5 s after the fibre was suspended in air.

Temperature heterogeneity Possible reasons for heterogeneity of the electric field and the temperature distribution just after the T-jump are the 'skin-effect' and a variation of the crosssectional area along the fibre. At the current frequency of 30 kHz and the fibre conductivity 1 m1 2-1 the skin depth should be more than 1 m, i.e. four orders of magnitude greater than the fibre radius. Thus the field heterogeneity due to the 'skin-effect' was negligible. Therefore, the main reason for heterogeneity in the electric field and temperature just after the T-jump was the variation of the crosssectional area Aa along the fibre. This variation was shown in the Methods section to be < 15%. The temperature heterogeneity after the T-jump due to fibre cooling was estimated using computer simulation (see Methods). The temperature gradient across the fibre was estimated to be < 3 % at any time after the T-jump. Length of the cooled ends increased with time. At 20-30 ms, the cooled length was 40-50,tm or 3-6 % of the fibre length (see eqn (2)). The cooling of the fibre's ends after the T-

442

S. Y. BERSHITSKY AND A. K. TSATURYAN

jump is not likely to have a major affect on the tension transients described here. The maximal tension achieved after the T-jump (Fig. 6) was not less than the tension at the same temperature in solution (Goldman, McCray & Ranatunga, 1987, Ranatunga, 1990). The fact that a fibre-stiffness rise accompanied tension rise induced by the T-jump shows additionally an absence of the compliant end segments in the heated fibre (Bershitsky & Tsaturyan, 1989).

Comparison with other T-jump methods The laser T-jump method has been used by Smith, Goldman, Hibberd, Liquori, Luttmann & McCray (1984), Smith, McCray, Hibberd & Goldman (1989) and Davis & Harrington (1987a, b). Fibre heating with microwave radiation has been used by Lindley & Kuyel (1978) and Lindley & Goldthwait (1984). The time resolution of the joule T-jump method used here is 0-2 ms, which is about the same resolution as that of the laser T-jump methods. The time resolution of the microwave-radiation method is about one order of magnitude slower. On the other hand, the laser T-jump does not permit a temperature change of more than 8 K, while the magnitude of the joule heating is as much as 35 K. The main limitation of the joule T-jump method is the relatively fast fibre cooling after the T-jump. Thus this method is only useful for the study of rather fast processes. The infra-red laser pulse used by Goldman et al. 1987 induced heating of not only the fibre but also the surrounding solution and the metal hooks attached to the fibre. As we have discussed earlier (Bershitsky & Tsaturyan, 1989), the heating of the hooks led to thermal expansion. The effect of elongation of the hooks is comparable with that of fibre thermal expansion. Thus, after the laser pulse, a tension transient was induced by both the T-jump (of a rather small amplitude) and fibre length release due to the thermal expansion of the hooks as well as the fibre.

Comparison with earlier studies Temperature dependence of maximal tension Temperature dependence of isometric tension at maximal activation shown in Fig. 7A is similar to that obtained in steady-state experiments with skinned rabbit fibres at maximal activation (Goldman et al. 1987; Ranatunga, 1990). In steady-state experiments, a similar dependence was obtained with fibres from other warmblooded animals (Stephenson & Williams, 1985). The only difference in the tension-temperature relation between our experiments and those of Goldman et al. (1987) is the fact that in their experiments the relation became less steep at temperatures above 20 'C. This difference can be explained by disorder of the sarcomere length reducing tension in steady-state experiments at high temperature (Brenner, 1986). Also steady-state experiments where temperature was increased from 0 to 40 'C rather quickly (in about 50 s) showed a near linear tension-temperature relation (Ranatunga, 1990).

T-jump de ects A biexponential tension rise initiated by laser (Goldman et al. 1987; Davies & Harrington, 1987a) and joule (Bershitsky & Tsaturyan, 1986b, 1988) T-jumps has been described. In the laser T-jump experiments, tension rise was preceded by a

JOULE TEMPERATURE JUMP IN MUSCLE FIBRE 443 tension drop due to thermal expansion of the fibre and the hooks. The drop was expressed much less or was indeterminable after the joule T-jumps. The difference was, most probably, due to thermal expansion of the hooks in the laser T-jump experiments. In the experiments presented here, a fast tension rise of high amplitude beginning during the heating pulse masked the initial drop. That is why the drop was seen only during T-jumps of an intermediate amplitude (Fig. 6, 16 K) or after the fibre stretch (Fig. 9, + 3 nm (hs)-1). Stretch slowed down the fast tension rise and the drop became more evident. The rate constant k1 of the fast phase 1 of the tension rise was similar to that of the laser T-jump experiments (Goldman et al. 1987). However, in contrast to the experiments presented here (Fig. 7B), no temperature dependence of this rate constant was observed. Goldman et al. (1987) used relatively small T-jumps at various initial temperatures. As can be seen from Fig. 6, the tension rise initiated by an 8 K T-jump (the maximal value for the laser T-jump) is rather small. The k1 value cannot be determined accurately enough for such small T-jumps. For this reason, the data scatter in the experiments of Goldman et al. (1987) was significant (see Fig. 10 in their paper) and, possibly, masked the temperature dependence of kl. In the experiments presented here, the temperature dependence was studied using T-jumps of various amplitudes. At T-jumps > 15 K, the rate constant of phase 1 can be estimated exactly. In the experiments reported here, the rate constant of phase 2 was a few times greater than that of the laser T-jump experiments (Goldman et al. 1987; Davis & Harrington, 1987a). The difference cannot be explained by fibre cooling after the joule T-jump, because the estimation of the rate constants was made taking into consideration cooling kinetics. After laser T-jumps of a small amplitude, the tension obtained by the extrapolation of phase 2 to the T-jump moment was about the same as tension before the T-jump (Goldman et al. 1987). After joule T-jumps of high amplitude, the extrapolated tension was 1P5 times higher than that before the Tjump. It is possible that the cross-bridge processes controlling phase 2 in the laser and joule T-jump experiments are different due to the differences in initial conditions for the cross-bridges at the beginning of this phase (i.e. at the end of phase 1) after T-jumps of different amplitudes. The rate constants k1 and k2 at 20-25 °C are very close to the rate constants of exponential processes 'C' and 'B' in experiments with small-amplitude sinusoidal length changes in rabbit fibres at the same temperature (Kawai & Brandt, 1980). The k2 value is also close to the rate constant of cross-bridge attachment estimated by the 'Ca-jump' (Goldman & Kaplan, 1988) and the 'ATP-jump' (Goldman, Hibberd & Trentham, 1984) experiments with flash photolysis of 'caged-compounds' in the rabbit muscle fibres. Interpretation of the data Phase 1 The fast component of tension rise initiated by the T-jump (phase 1) is, probably, induced by some forced-generating process in the cross-bridges attached to the thin filaments. The main evidence for this conclusion is the fact that the rate constant of phase 1 increases after fibre shortening and decreases after stretching (Fig. 12A). The -

S. Y. BERSHITSKY AND A. K. TSATURYAN dependence of the rate constant on the preceding length change means that the crossbridges involved in phase 1 'remember' filament sliding and, therefore, they were attached to the thin filaments before the length step and T-jump. An absence of the cross-bridge reattachment during phase 1 is also indicated by measurements (Bershitsky & Tsaturyan, 1989) showing that the fibre stiffness remains practically constant during phase 1. The process controlling phase 1 is, most probably, the same as that controlling the early tension recovery following the step length change (Huxley & Simmons, 1971; Ford et al. 1977, 1981, 1985). The rate constants of these processes are similar and depend on the length change in a similar manner (Figs 9 and 12A). For frog fibres, the rate constant of phase 1 extrapolated to 0-2 °C (Bershitsky & Tsaturyan, 1988) was the same as the rate constant of the early tension recovery interpolated to zero length change (Ford et al. 1977). A similar conclusion was made by Goldman et al. (1987) who compared the tension responses to the T-jumps and length steps. The data presented in Fig. 11 are further evidence for identity of the processes controlling the fast responses to length and temperature perturbations. Tension dependencies on the length-step amplitude before the T-jump and at the end of phase 1 are very similar. Tension rise during phase 1 indicates that the enthalpy change, AH, associated with the force-generating process controlling this phase is positive. Goldman et al. (1987) have estimated it to be 9 kJ mol-1 in their laser T-jump experiments. In the experiments presented here, tension at the end of phase 1 was much higher than in their experiments. Therefore, our estimate of All is higher, AH = 15-30 kJ mol-1 (see below).

444

Phase 2 The slow component of the tension rise initiated by the T-jump (phase 2) is accompanied by cross-bridge detachment and reattachment because neither the maximal tension after the T-jump nor the rate constant of phase 2 depend on the preceding length change (Figs 9 and 12B). Thus, during phase 2, the force-generating cross-bridges 'forget' the filament sliding and, therefore, they reattach to new sites on the thin filaments. During phase 2, the fibre stiffness increases to a lesser extent than tension (Bershitsky & Tsaturyan, 1989). Since fibre stiffness is proportional to the number of cross-bridges attached to the thin filaments (Huxley & Simmons, 1973), an increase in the tension-to-stiffness ratio means that during phase 2 there is an increase in the force generated by a cross-bridge. The data of the experiments presented here and earlier (Bershitsky & Tsaturyan, 1988) cannot be explained by the Huxley & Simmons (1971) model or the four-state models of Eisenberg, Hill & Chiu (1980) and Pate & Cooke (1989). It is difficult to explain why the cross-bridge should reattach to the thin filament to generate more force. It will be shown below that the main features of the experimental data can be explained by a rather simple model joining the models of Huxley & Simmons (1971) and Huxley (1973).

JOULE TEMPERATURE JUMP IN MUSCLE FIBRE

445

Kinetic model The tension and stiffness transients initiated by the joule T-jump have been explained using a simple kinetic model based on a scheme of the cross-bridge cycle taken as follows D -->N N' F =>DI (5) where D is the detached state of the cross-bridge, N, N' and F are the attached states. Only state F is force-generating during isometric contraction, whereas N and N' are non-force-generating states. The cross-bridge stiffness is proposed to be equal in all three attached states N, N' and F. In the detached state D, the stiffness is zero. Thus, normalized tension, P, and stiffness, S, are as follows: (6) P = [F], S = [N] + [N'] + [F], where [N], [N'] and [F] are the probabilities that the cross-bridge is in states N, N' and F, respectively. The reversible attachment D * N is followed by a reversible transition between two stages of attachment N N' as proposed by Huxley (1973). The transition N N' may be the step of the inorganic phosphate release of the cross-bridge ATPase cycle (Huxley, 1980). The rapid reversible transition N' * F is the force-generating step postulated by the Huxley & Simmons (1971) model. The slow irreversible detachment F -= D is the rate-limiting step of the ATP hydrolysis and includes ADP release, ATP binding the cross-bridge detachment. A more detailed six-state kinetic scheme and a model describing mechanical responses to temperature and concentration perturbations has been characterized briefly (Tsaturyan, 1991). The rate constants kDN = 80 s-1 and kND = 50 s-1 at 20 °C were estimated from the kinetics of the stiffness transients in the experiments with the photolysis of 'caged ATP' (Goldman et al. 1984) and 'caged Ca' (Goldman & Kaplan, 1988). The kinetic constants of the transition N * N', kNN' = 130 s-1 and kN,N = 60 s-1 at 20 °C were estimated from rigor and active stiffness measurements (Goldman et al. 1984) and the delay between the stiffness and tension rise during an onset of contraction (Goldman & Kaplan, 1988). The rate constants kNTF = kFN' = 300 s-1 at 20 °C were estimated from experiments with sinusoidal length changes (Kawai & Brandt, 1980), and kFD = 10 s-1 was chosen to provide the ATPase rate ([F]kFD) equal to that in the experiments of Ferenezi et al. (1984). The Qlo values for the rate constants were chosen to approximate the data presented here, the stiffness transients initiated by the T-jump (Bershitsky & Tsaturyan, 1989) and the temperature dependence of the ATPase activity in the fibres (Brenner, 1986). The Q1o values for the rate constants kDN", kN'N, kNF and kFD were 1-5, 2, 2 and 1-5, respectively. To explain the experimental data it is necessary to accept that the enthalpy changes, AHNN, and AHN'F, associated with the transitions N N' and N' =>F are positive. In this case, an increase in temperature leads to a shift of the equilibrium between states N, N' and N', F to the right. Phase 1 of the tension rise is due to a rapid force-generating transition N' F. Phase 2 is explained by a decrease in the number of cross-bridges in the predominant state N due to a shift from state N to state N' and then to state F. Tension and stiffness rise in phase 2 is accompanied by --

,

=

=

=

S. Y. BERSHITSKY AND A. K. TSATUR YAN

446

a change in the population of attached cross-bridges due to the reversibility of steps N < N' and N' F. The enthalpy change values for the force-generating step, AHN'F = 15-30 kJ mol', and the predominant step, AHNN = 30-60 kJ mol2, provide the best fit of the experimental data. These estimated values depend on the equilibrium Stiffness

1.0

3 2

cn

0)

1

CA

.)

Tension

~~~~~~~~~~~~~~3

0)

0

0.5

2 1

E

_

0

z

-10

0

10 20 30 Time after T-jump (ms)

40

50

Fig. 13. Simulated stiffness and tension transients from the model described in the text. The starting temperature was 7 °C; the final temperatures after the T-jump applied at time zero were: 15 °C (1), 25 °C (2) and 35 °C (3). The enthalpy change associated with the force-generating step was AHN'F = 22-5 kJ mol-1, for the previous step AHN'N = 40 kJ mol-1, and for the cross-bridge attachment AHDN = -10 kJ mol-1. For the rate constants and their temperature coefficients see text.

constant K = kN F/kFN at 20 °C which cannot be determined accurately enough. It should be noted that heat measurements in frog muscle after step shortening (Gilbert & Ford, 1988) also showed a positive enthalpy change associated with a rapid forcegeneration step. Three simultaneous differential equations describing non-steady kinetics in accordance with scheme (5) were solved numerically. Figure 13 shows the results of simulation of tension and stiffness transients after T-jumps of various amplitudes. The main features of the experimental transients are well described by the above model. After high T-jumps the biphasic character of the tension rise is easily seen (compared to Fig. 6). The stiffness increase is near exponential with the rate constant being close to that of the slow component of tension rise as was found in the experiments of Bershitsky & Tsaturyan (1989). We wish to thank Professor Sir A. F. Huxley, Professor Y. E. Goldman and Dr K. W. Ranatunga for helpful discussions. We are grateful to Dr A. L. Drachev for assistance in the computer simulation and the experimental data analysis. We are also grateful to Dr J. Clark for his kind help in preparation of the manuscript.

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