Endothermic force generation, temperature-jump experiments and effects of increased [MgADP] in rabbit psoas muscle fibres
1 Muscle Contraction Group, Department of Physiology, School of Medical Sciences, University of Bristol, Bristol BS8 1TD, UK
Abstract
We studied, by experiment and by kinetic modelling, the characteristics of the force increase on heating (endothermic force) in muscle. Experiments were done on maximally Ca2+-activated, permeabilized, single fibres (length 2 mm; sarcomere length, 2.5 μm) from rabbit psoas muscle; [MgATP] was 4.6 mM, pH 7.1 and ionic strength was 200 mM. A small-amplitude (3°C) rapid laser temperature-jump (0.2 ms T-jump) at 8–9°C induced a tension rise to a new steady state and it consisted of two (fast and slow) exponential components. The T-jump-induced tension rise became slower as [MgADP] was increased, with half-maximal effect at 0.5 mM[MgADP]; the pre- and post-T-jump tension increased 20% with 4 mM added [MgADP]. As determined by the tension change to small, rapid length steps (<1.4%L0 complete in <0.5 ms), the increase of force by [MgADP] was not associated with a concomitant increase of stiffness; the quick tension recovery after length steps (Huxley–Simmons phase 2) was slower with added MgADP. In steady-state experiments, the tension was larger at higher temperatures and the plot of tension versus reciprocal absolute temperature was sigmoidal, with a half-maximal tension at 10–12°C; the relation with added 4 mM MgADP was shifted upwards on the tension axis and towards lower temperatures. The potentiation of tension with 4 mM added MgADP was 20–25% at low temperatures (5–10°C), but 10% at the physiological temperatures (30°C). The shortening velocity was decreased with increased [MgADP] at low and high temperatures. The sigmoidal relation between tension and reciprocal temperature, and the basic effects of increased [MgADP] on endothermic force, can be qualitatively simulated using a five-step kinetic scheme for the crossbridge/A-MATPase cycle where the force generating conformational change occurs in a reversible step before the release of inorganic phosphate (Pi), it is temperature sensitive (Q10 of 4) and the release of MgADP occurs by a subsequent, slower, two-step mechanism. Modelling shows that the sigmoidal relation between force and reciprocal temperature arises from conversion of preforce-generating (A-M.ADP.Pi) states to force-bearing (A-M.ADP) states as the temperature is raised. A tension response to a simulated T-jump consists of three (one fast and two slow) components, but, by combining the two slow components, they could be reduced to two; their relative amplitudes vary with temperature. The model can qualitatively simulate features of the tension responses induced by large-T-jumps from low starting temperatures, and those induced by small-T-jumps from different starting temperatures and, also, the interactive effects of Pi and temperature on force in muscle fibres.
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Introduction
It has been known for over half a century (Hadju, 1951) that active force in mammalian skeletal muscle increases as the temperature is raised. Subsequent studies have confirmed and extended this finding to different muscles (e.g. fast and slow muscles, Ranatunga & Wylie, 1983), species (including peripheral muscles of the human body, see references in Ranatunga et al. 1987) and to different types of preparations (e.g. Ca2+-activated skinned fibres, Stephenson & Williams, 1981, 1985). The finding indicated the endothermic nature of active muscle force, i.e. force increases as heat is absorbed. This fundamental characteristic has received considerable attention in a number of studies (see references in Davis, 1998; Kawai, 2003; Ranatunga & Coupland, 2003b), and the basic findings and conclusions that have emerged from mammalian muscle fibre studies, and uncertainties and unknowns that remain, may be briefly summarized as follows. (1) Whereas the rigor force (when crossbridges are strongly attached but not cycling) decreases linearly, the active isometric force (when crossbridges are cycling) increases twofold when the temperature is raised from 10°C to high physiological (>30°C) temperatures (Ranatunga, 1994). The active force versus reciprocal absolute temperature (1/T) is sigmoidal (Davis, 1998; Kawai, 2003; also, see references in Coupland & Ranatunga, 2003) with indication of saturation at physiological temperatures; the latter feature, however, has not been observed in the experiments of Bershitsky & Tsaturyan (1992, 2002) who used force measurements after large temperature-jumps (T-jumps) to high temperatures. Interestingly, a sigmoidal relation between maximum force and temperature is seen also in frog fibres but with a low temperature for the half-maximal tension, 2°C (i.e. 8–10°C lower than for mammalian fibres, see Piazzesi et al. 2003). (2) Increase of active muscle force on heating is not accompanied by a concomitant increase of stiffness (Goldman et al. 1987), indicating that it is not due to a significant increase in the fraction of attached crossbridges, but due to an increase of average force per crossbridge; this has been examined and confirmed in studies on rabbit (Bershitsky & Tsaturyan, 1995, 2002) and frog muscle fibres (Bershitsky et al. 1997; Tsaturyan et al. 1999; Piazzesi et al. 2003). (3) A rapid T-jump induces a bi-exponential (labelled phase 2b and phase 3) rise in force to a level as expected from steady-state experiments; the (faster) phase 2b is identified as ‘endothermic force generation’ in attached crossbridges (Davis & Harrington, 1987; Goldman et al. 1987; Bershitsky & Tsaturyan, 1989, 1992; Ranatunga, 1996). From more recent experiments, however, Bershitsky & Tsaturyan (2002) challenged the validity of identification of two (or more) phases in a T-jump-induced force response, and they analysed the entire tension response as a ‘single process’. (4) Phase 2b has been compared with a slow component of the phase 2 or T1–T2 tension recovery (Huxley & Simmons, 1971) obtained in length-release experiments (Davis & Harrington, 1993; Davis & Rodgers, 1995). However, exact quantitative comparison of the T-jump force response with the T1–T2 transition has proved difficult; on the basis of a number of observations; Bershitsky & Tsaturyan (2002) indeed concluded that tension transients induced by T-jumps and length steps are caused by different processes in crossbridges (see, however, Piazzesi et al. 2003 and Ferenczi et al. 2005). (5) In so far that it is not directly coupled to the release of inorganic phosphate (Pi) in the actomyosin (AM) ATPase cycle that underlies muscle contraction, the phase 2b (after T-jumps) is considered to represent a ‘de novo force generation’ in attached crossbridges (Davis & Rodgers, 1995; Davis, 1998). Subsequent T-jump studies identified this endothermic force generation step as a molecular step before the rapid Pi release (i.e. a transition between two AM.ADP.Pi states) in isometric muscle fibres (Ranatunga, 1999a). This is in agreement with the conclusion reached using other perturbations on muscle fibres (Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992) and on myofibrils (Tesi et al. 2000) that the force generation occurs prior to Pi release by cycling crossbridges. However, whether this unified thesis would be sustained when the ATPase cycle is perturbed in other ways (e.g. increased [MgADP]) remains unknown.
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It is known that MgADP is a product released later in the AM-ATPase cycle; it binds to nucleotide-free (AM) crossbridges, potentiates active force (Cooke & Pate, 1985; Fortune et al. 1989; Dantzig et al. 1991; Lu et al. 1993), decreases maximum shortening velocity and ATPase rate in muscle fibres (Cooke & Pate, 1985; Pate & Cooke, 1989a,b; He et al. 1997; Seow & Ford, 1997; Morris et al. 2003) and in myofibrils (Tesi et al. 1999). However, MgADP effects on endothermic force generation are not known, although such data would be essential for the development of a more complete kinetic model. These were the aims of our study, and they also enable us to address some discrepancies (see above) that remain unresolved among the different T-jump studies.
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Thus, we have examined in single psoas fibres: the force generation induced by a small rapid (0.2 ms) T-jump, force responses to small rapid length steps, and active force and shortening velocity at different temperatures (range 5–30°C) when the [MgADP] was increased, and used a five-step kinetic model to qualitatively simulate some of the findings. Preliminary data from this study have been reported in abstract form (Ranatunga & Coupland, 2003a; Coupland & Ranatunga, 2004).
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Methods
Fibre preparation and solutions
Adult male rabbits were killed by an intravenous injection of an overdose of sodium pentobarbitone, and other tissues were harvested for different experiments by other researchers. Fibre bundles from the psoas muscle were prepared and chemically skinned using 0.5% Brij 58, as previously described (Fortune et al. 1989). Control buffer solutions (with no MgADP) contained 10 mM glycerol 2-phosphate (a temperature-insensitive pH buffer; pH 7.1), 4.6 mM MgATP, 12 mM creatine phosphate, 15 mM EGTA (relaxing solution), CaEGTA (activating solution) or HDTA (preactivating solution), 9 mM glutathione and 50 mM potassium acetate. The MgADP buffer solutions additionally contained 4 mM MgADP with a reduced potassium acetate concentration (12 mM). The compositions of solutions were calculated using a computer program for solving multiequilibria, maintaining ionic strength (200 mM) and a free [Ca2+] in the activating solutions of 0.032 mM. Solutions with MgADP concentrations lower than 4 mM were obtained by mixing 4 mM ADP buffer solution with the control solution. Adenosine pentaphosphate (100 μM) was added to the solutions containing 0.5 mM MgADP; adenosine pentaphosphate inhibits the myofibrillar adenylate kinase reaction that catalyses ADP to AMP and ATP (Cooke & Pate, 1985; see Dantzig et al. 1991). However, we did not notice significant differences in these experiments when tension was measured with and without adenosine pentaphosphate. Creatine kinase (1–2 mg ml–1) (300 units mg–1; Sigma) was added to control buffer solutions before use to decrease [MgADP], and [MgADP] was assumed to be reduced to 10 μM. All solutions also contained 4% dextran (molecular mass 500 kDa) in order to compress the filament lattice spacing to normal dimensions (Maughan & Godt, 1979).
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Apparatus and laser T-jump technique
Details of the trough assembly, design of the force transducer (natural resonant frequency, 14 kHz), and other aspects of the experimental apparatus have been previously described (Ranatunga, 1996, 1999a; Coupland et al. 2001). Briefly, the trough assembly was mounted on the stage of an optical microscope and, by means of a mechanical lever mechanism, the fibre could be moved and immersed in the different trough solutions. The solution temperature in the front experimental trough was clamped at the desired temperature (5–30°C) using thermo-electric modules (Peltier units) with feedback from a small thermistor and monitored with a thermocouple. In order to maintain fibre stability, the temperature in the other troughs containing relaxing and preactivating solutions was kept at 5°C by cooling fluid circulating through the assembly.
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The principle of the laser T-jump technique is similar to that used by Davis & Harrington (1987), and its details have been previously described (Ranatunga, 1996, 1999a). The temperature of the front (glass) experimental trough was clamped at 8–9°C and the T-jump was induced by a 0.2 ms laser pulse radiation of a standard energy (the maximum pulse energy available was 2 J). The laser pulse, of 6 mm in diameter and circular in cross-section, from a Nd-YAG laser (Schwartz Electro-Optics) passed through a long-focal-length (300 mm) cylindrical lens and entered the experimental trough through the front glass window. The pulse cross-section at the level of the fibre was a horizontal ellipse of 6 mm x 2.5 mm; to prevent extraneous thermal expansion effects, the transducer hooks were shadowed from the laser radiation by Al-flags placed outside the trough window. A laser pulse heated the buffer solution in the trough and the muscle fibre bathed in it; the fibre/heated fluid volume ratio was >2500. The wavelength of the radiation was 1.32 μm, similar to that of the iodine laser used by Davis & Harrington (1987): the water extinction length at this wavelength is 10 mm, so that the pulse radiation passed across the trough solution (3 mm) and was reflected back through the solution by platinum foil that lined the trough back-wall; the characteristics of absorption of laser radiation were such that temperature gradients in the trough solution were small. A small thermocouple placed near the fibre showed that after a laser pulse the elevated solution temperature remained constant for at least 500 ms and decreased only slowly (half-time longer than 5 s) afterwards (see Fig. 1 in Ranatunga, 1996).
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A, a fibre was maximally Ca2+-activated in control solution (no added MgADP) at 9°C and, during the steady tension plateau (pre-T-jump tension), a T-jump of 3°C was induced by a laser pulse (indicated by the arrow). The elevated temperature remained constant for at least 500 ms and decreased slowly afterwards (half-time of decrease >5 s; see Fig. 1 of Ranatunga, 1996). The T-jump induced a tension rise to a new steady level (post-T-jump tension) and the tension rise was fitted with a bi-exponential curve extracting two components, phase 2b and phase 3 (see Methods). B, an identical T-jump was induced when the same fibre was activated in the presence of 4 mM added MgADP. For easy comparison with the control, only the initial 500 ms of a 5 s sweep is shown; the tension reached at 500 ms was >99% of that at 700 ms when the temperature had decreased by 0.1°C. Note that compared with the control, the pre-T-jump tension is higher, but the T-jump-induced tension rise is slower in the presence of 4 mM MgADP, whereas the actual amplitude of the tension rise is similar.
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The outputs of the force transducer, the thermocouple and the motor were monitored on digital cathode ray oscilloscopes and digital voltmeters, and recorded using a PC with a CED 1401 (plus) laboratory interface (Cambridge Design Ltd, UK). In some length step experiments, the position of the first-order He–Ne laser diffraction was also monitored by means of a position detector, and the output of this diffractometer was used only as an index of sarcomere length change during length steps (see Ranatunga et al. 2002). A continuous record of the tension was also made on a chart recorder.
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Experimental protocols and data analysis
Using dark-field illumination on the stage of a binocular microscope, single fibres were dissected under paraffin oil. A short fibre segment was attached using nitrocellulose glue between two metal hooks, one connected to the force transducer and the other to the motor. The sarcomere length was set to 2.5 μm using He–Ne laser diffraction, and the fibre width and length were measured under light microscope; fibre length (L0) was 2 mm in most experiments. Several types of experiment were carried out on a total of 24 fibres, and in a given protocol the final control tension was within 12% of the initial control. The different experimental protocols used are summarized below.
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Laser T-jump experiments. The force transients induced by a standard laser T-jump of 3°C and from an initial temperature of 8–9°C were recorded in each fibre after activation to steady state in control conditions, with different added [MgADP], and finally in control conditions. The force rose to a new steady level after a T-jump, and each tension response was fitted with a double exponential function (FigP, Biosoft), and the rate and the amplitude of the two components were determined. For comparability with previous nomenclature, the two components will be referred to as phase 2b (fast, endothermic force generation) and phase 3 (slow). A very fast tension recovery component (phase 2a) was not clearly discernible in this study; it is observed following length release (see below) and after T-jump – if there is a large thermal expansion producing an apparent length-release effect (see Davis & Harrington, 1993; Ranatunga, 1999b).
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Tension responses to length steps. Some observations were also made in the above experiments on the tension transients induced by small rapid length steps, as in Huxley & Simmons, (1971) type of experiments. These were done at the pre-T-jump temperature (8–9°C) with control activation and with activation in the presence of 4 mM added MgADP. In a given fibre, a length step complete in <0.5 ms and of the same amplitude (0.3–1.4%L0, in different fibres) was applied to one end of the fibre under both conditions and the tension transients were recorded. The tension change at the end of length step (T1) was measured and the quick tension recovery afterwards (T2 or phase 2 recovery, Huxley & Simmons, 1971) was characterized by fitting a bi-exponential function isolating two components, phase 2a (very fast) and phase 2b as in our previous study (see Ranatunga et al. 2002).
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[MgADP] on isometric tension at different temperatures. This was examined at a range of added [MgADP]. Many experiments were done at 10°C, but data were also obtained at other temperatures, particularly with and without 4 mM added MgADP. After at least 5 min in relaxing solution, the fibre was transferred to preactivating solution (5 min) before being activated and, soon after maximal tension was reached, the fibre was transferred back to the relaxing solution. The relaxing, preactivating and activating solutions all contained the same added [MgADP].
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[MgADP] on shortening velocity. In a few control experiments, the ‘slack test’ method (Edman, 1979) was used to determine the unloaded shortening velocity (Vu) in fibres that were activated in control solutions and in the presence of 4 mM MgADP. The fibre was shortened using length releases (90% step complete in <1 ms) that were sufficiently large to reduce the fibre tension to zero when applied on the plateau of steady maximal tension. The duration of unloaded shortening from the start of the length release until tension redevelopment was measured, and Vu was estimated from the slope of plot of length change versus duration of unloaded shortening. The Vu determined from three fibres in control solutions and three fibres in the presence of 4 mM MgADP clearly showed that Vu was decreased with added [MgADP], as reported in previous studies (see Introduction).
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Based on the aforementioned experiments, and in order to obtain data from the same fibre at different MgADP levels, we examined the duration of unloaded shortening following a standard length release (5–10%L0 in different fibres) applied on the tension plateau. In each fibre, measurements were made in control solutions and in the presence of different concentrations of added MgADP using the same length step amplitude, and the length step amplitude divided by the duration of the slack period was taken as the Vu. This measurement from a single length step would overestimate the shortening velocity since the intercept on the length axis is not allowed for; nevertheless, it was considered adequate for comparative purposes.
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Some general considerations and uncertainties
(1) During an experiment, a muscle fibre was regularly examined under the microscope and data discarded if there was evidence of development of fibre damage. However, routine continuous monitoring of sarcomere length or its clamping was not made in the present experiments, and hence there is uncertainty, particularly at high temperatures, as to what extent our data were affected by the development of sarcomere nonuniformities. (2) As emphasized in previous studies (see Cooke & Pate, 1985, Pate & Cooke, 1989a), there are difficulties involved in quantitative analyses in muscle fibres of the effects of products (MgADP and Pi) of AM-ATPase cycle due to their generation after activation and accumulation from diffusion-limited equilibration with the bathing solution. We assumed that, under control conditions (i.e. with creatine phosphokinase plus creatine phosphate present), [MgADP] is low (10 μM) and [MgATP] remains constant at 4 mM. Using the principles of the calculations made by Pate & Cooke(1989a), we previously noted that the [Pi] within an active fibre at 10°C would rise to 0.5–0.7 mM at steady state under control conditions and to higher values as the temperature is raised (Coupland et al. 2001). With increased [MgADP] (i.e. with no creatine phosphokinase present), [MgADP] would rise and [MgATP] would fall after activation (Cooke & Pate, 1985); Cooke & Pate (1985) noted that 0.9 mM[MgADP] would be generated at steady state at 10°C, and it is likely to be higher at raised temperatures. However, three further observations are noteworthy. Firstly, comparison with data from intact fibres, in which contractions are brief and electrically evoked, provides some validity of the control observations. Secondly, experiments of He et al. (1997) show that 50–70% of isometric force is developed in the first turnover of the cycle (i.e. before any MgADP is released), and hence [MgADP] as calculated for steady-state accumulation may overestimate its increase when steady force is measured briefly after activation. Thirdly, important meaningful and detailed data have been obtained in muscle fibre studies using similar procedures to ours (see Zhao & Kawai, 1994). Nevertheless, the uncertainties regarding the [MgADP] level within fibres under different conditions restrict our discussions to the differences seen between the control and 4 mM added [MgADP] rather than the quantitative concentration dependence of the effects.
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Simulating T-jump transients and isometric tension behaviour
To qualitatively model our findings, we used a minimal five-step scheme for the crossbridge/AM-ATPase cycle (Scheme 1) which is an extension of the three-step scheme used previously. A number of previous studies by different groups, and using different techniques, proposed that the crossbridge force generation occurs prior to rapid Pi release by cycling crossbridges in muscle (Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992; He et al. 1997). By making the rate of (pre-Pi-release) force generation temperature sensitive (endothermic), the scheme could also account for the Pi effects on T-jump-induced tension transients (Ranatunga, 1999a) and Pi effects on steady force at different temperatures (Coupland et al. 2001). In a detailed examination of mechanokinetic models, Smith & Sleep (2004) indeed ruled out the alternative possibility that force generation follows Pi release, although they preferred a case where a fast force generation step is followed by a slow Pi release. In so far that they did not identify a specific temperature-sensitive step, however, we have retained the original case where the force generation step is followed by a rapid Pi release.
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Thus, the forward rate constant of step 1 (k+1) is a moderately fast (20 s–1 at 10–15°C) temperature-sensitive (endothermic) force generation, whereas the reverse rate constant (k–1, 120 s–1) is not temperature sensitive. Increasing the forward rate constant k+1 with a Q10 of 4, corresponding to an activation enthalpy of 100 kJ K–1, simulates temperature effects. Step 2 is rapid Pi release, where k+2 is set as 0.8 x 103 s–1 and altering k–2 simulates [Pi] changes; the range of k–2 values corresponds to a second-order rate constant of 1.4 x 105M–1 s–1 for Pi binding in step 2 (similar to Dantzig et al. 1992 and Gutfreund & Ranatunga, 1999). Steps 3 and 4 represent the slow two-step ADP release: k+3/k–3 was forward biased and set at 15 s–1/5 s–1 to fit the data distribution in the present study (see discussion). k+4 was set low (2 s–1), and changing k–4 simulates [MgADP] changes; the values of k–4 used for control correspond to a second-order rate constant for ADP binding of 2 x 105M–1 s–1 which is similar to the values used in other studies (Dantzig et al. 1991). Step 5 is irreversible and includes all the steps after ADP release that are necessary to reprime a crossbridge for the next cycle. The overall rate in this route is low (k+5, 10 s–1), probably limited by the M.ATP M.ADP.Pi cleavage step after detachment (see He et al. 2000) which is not separately identified in our scheme, but the initial AM-dissociation step per se would be fast in the presence of millimolar levels of MgATP (>1000 s–1, see Goldman et al. 1984; He et al. 2000). Thus, although AM is a strongly bound state, [AM] as such was considered small, and hence its occupancy was not included for the calculation of force; moreover, He et al. (2000) considered the force per AM state to be small. Also, the effect of inclusion of this state can be inferred from its occupancy changes shown in Fig. 9B. According to the scheme, states II, III and IV (AM*.ADP.Pi, AM*ADP and AM*'.ADP) are equal-force-bearing states (F) and the sum of their fractional occupancy is taken as force.
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A, Arrhenius plots of the two rate constants of the model (see Scheme 1) that were increased to simulate temperature effects. The rate of the force generation step (k+1) increased markedly (see Zhao & Kawai, 1994; Q104) and that of ADP-release step (k+4) slightly (Q10 of 1.3). The symbols show values for a selected number of temperatures. Note that the marked temperature sensitivity of k+1 implies that it would not be very much slower than inorganic phosphate (Pi) release (see Methods) at high temperatures. B, the fractional occupancy of the five states under control conditions (low [MgADP]10 μM and 0.5 mM Pi) calculated for a selected number of temperatures, and plotted against reciprocal absolute temperature. Open symbols show states (V and I) that do not contribute to force (, AM + M.ATP + M.ADP.Pi that are not separately identified in the model; and , AM.ADP.Pi, the pre-force-generating state). Note the dominance of pre-force-generating state (AM.ADP.Pi) at the low temperatures (e.g. 10°C), and the decrease of its occupancy with warming. Filled symbols represent force-bearing states (, AM*.ADP.Pi; , AM*.ADP; and , AM*'.ADP); note the increased occupancy of AM.ADP (post-power stroke) states as the temperature is raised. For any temperature, the sum of the occupancies of the five states is 1. C, filled circles show simulated, steady-state (at 1–2 s) tension (as the sum of the fractional occupancies of states II, III and IV) under control conditions (0.5 mM Pi and 10 μM ADP) at 5°C intervals. Note the approximate sigmoidal relation with half-maximal at 10–12°C, as found experimentally; force at 0°C is 20%. If force is determined at short intervals after large T-jumps to a high temperature, the apparent saturation of force at high temperature is reduced (crosses and dotted line). Open diamonds with dashed curve show that with simulated 4 mM[MgADP] (k–4 set to a higher value), the sigmoidal relation is shifted to the right (compare with Fig. 7A).
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The linear kinetic Scheme 1 was solved by the matrix method using Mathcad 2000 software (Mathsoft), as previously described (Gutfreund & Ranatunga, 1999); it gives results in the form of apparent rate constants (reciprocal relaxation times) and amplitudes for the sum of exponentials representing the formation and decay of each of the states in the system. After a steady state is reached, the method can be used to simulate a relaxation phenomenon by changing the rate constant of the step(s) appropriately (e.g. increasing k+1 with a Q10 of 4 and k+4 with a Q10 of 1.3 for a T-jump in the present study) and the approach to the new steady state obtained. Although a perturbation of a five-step system yields five rate constants, their values were such that only three were practically useful, with values ranging from >10–2 s–1 to <103 s–1. Of these three, two rate constants were small (slow), similar and could be combined, so that a T-jump-induced tension rise is effectively characterized by two rates: a fast rate and a (combined) slow rate as in the experiments. For calculation of the steady tensions at a new steady state, the occupancies of the states were determined 1–2 s after a perturbation.
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For clarity in the presentation, the first section in the Results presents the experimental data, where tension or force in Figs 1–8 refers to the measured values from muscle fibres. The second section in the Results, with Figs 9–12, contains the model simulations where tension or force refers to the sum of the fractional occupancies of the three force-bearing states without normalization to any experimental measurement.
Results
, http://www.100md.com Experimental data
T-jump induced (endothermic) force generation. In experiments on five muscle fibres, we examined the effect of [MgADP] on the force generation induced by a standard laser T-jump of 3°C applied during the tension plateau after maximal Ca2+ activation at 8–9°C; Fig. 1A shows the tension response induced by a T-jump in control activation (no added MgADP); as found in previous studies, the tension rose to a new steady level following a T-jump, and the tension trace could be fitted with a bi-exponential function (drawn through the trace). Figure 1B shows from the same fibre the tension response after activation in the presence of 4 mM added MgADP and it is qualitatively similar to the control. It is seen, however, that compared to the control, the tension before the T-jump is higher but the T-jump-induced tension rise to a new level is slower with increased [MgADP].
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In each fibre experiment, a tension transient to the same T-jump was recorded with control activation and with separate activations in the presence of different levels of MgADP and finally with a control activation. Figure 2 shows the pooled data (mean ±S.E.M.) for the steady active tension measured before the T-jump (8–9°C, open symbols) and after the T-jump (11–12°C, filled symbols) plotted against added [MgADP], where the tensions are normalized to the first pre-T-jump control tension in each fibre. The data show that the both pre- and post-T-jump tension is potentiated by 20% with increase of [MgADP] to 4 mM MgADP.
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Pooled (means ±S.E.M.) tension data are shown for different [MgADP] from five fibres that were maximally Ca2+-activated at 8–9°C () and a T-jump induced; a full data set was obtained from each fibre. The new steady tension data at the elevated temperature of 11–12°C (post-T-jump) are shown by . Tensions are given as ratios of the pre-T-jump tension of the first control (i.e. with no added MgADP) in each fibre. A hyperbolic curve was fitted to each pooled data set. Note that the active tension is increased by about 20% with 4 mM MgADP at both pre- and post-T-jump temperatures. The T-jump increased force by 6% per degree Celsius.
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In Fig. 3, the rates and the amplitudes of the two exponential components derived by curve fitting to the T-jump-induced tension responses (as in Fig. 1) are plotted against added [MgADP]. The rate of endothermic force generation (phase 2b, filled symbols in Fig. 3A) decreased towards a lower level as [MgADP] was increased; a hyperbolic curve was fitted to the pooled individual data for phase 2b rate and it gave a maximum rate of 40 s–1, a minimum of 16 s–1 and 50% decrease at [MgADP] of 0.5 mM. The rate of the slower phase (phase 3) was relatively insensitive to or only slightly decreased with increased [MgADP]. As shown in Fig. 3B, the amplitudes of the two components (normalized to post-T-jump tension) remained similar at different [MgADP] and showed no significant correlation with increased [MgADP] (P > 0.05).
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The tension responses induced by standard T-jumps in control conditions (no added MgADP) and at a range of added [MgADP] were analysed by curve fitting as shown in Fig. 1. A, the mean (±S.E.M.) rate constants (reciprocal time constant) from five fibres are plotted against different [MgADP]. Filled symbols show data for endothermic force generation (phase 2b). A hyperbolic curve was fitted to the pooled individual data for phase 2b gives a maximum rate of 40 s–1, a minimum of 16 s–1 and half-maximal effect at 0.5 mM[MgADP]. Open symbols represent data for the slow phase 3, and show relative insensitivity (or slight decrease) to [MgADP]. B, the amplitudes of the two exponential components (fast phase 2b, filled symbols; slow phase 3, open symbols) are plotted against [MgADP]; the amplitudes of phase 2b and 3 show minimal sensitivity to [MgADP].
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Tension responses to length steps and stiffness estimates. In the aforementioned experiments, the tension responses to 2–4 small length steps per fibre (<1.4%L0 complete in <0.5 ms) were also recorded at 8–10°C, and they were analysed to obtain estimates of fibre stiffness. Figure 4A shows, from a fibre in control activation, the tension responses (top panel) that were elicited when two length steps (bottom panel) were applied to one end of the fibre. As is well known (Huxley & Simmons, 1971), the tension reaches a peak at the end of a length step (T1), but then recovers quickly to T2, which is only partial recovery towards the pre-length step tension level (T0); the tension change (i.e. T1–T0 from a stretch and T0–T1 from a release) divided by the length step amplitude (L) was taken as stiffness. In order to pool the data from different fibres, this ratio was normalized to L0 and control T0. Figure 4B shows records from a fibre activated in the presence of 4 mM MgADP; it can be seen that the initial quick tension recovery is slower than under control conditions, even though the length step amplitude is larger. The quick tension recovery (T1 to T2 phase of the tension transient) was fitted with a double exponential function isolating phase 2a (very fast) and phase 2b; such fitted curves are drawn through the tension traces in Fig. 4.
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A, a fibre was activated to steady state in control solution and a length-release and a length-stretch step of the same amplitude (0.25%L0) was applied; the resultant tension responses are shown on the top panel. A length step was complete in <0.5 ms; the position of the first-order He–Ne laser diffraction for release only, shown in the middle panel (in arbitrary units), indicates sarcomere length shortening induced by the fibre-length release. Temperature 9°C. B, sample traces from an experiment on another fibre, activated in the presence of 4 mM added MgADP, where the length step amplitude was 0.9%L0. The diffractometer signals in the middle panel indicate sarcomere length changes, but the slow oscillations in them are probably artefacts. Note that the tension recovery is slower with MgADP. Temperature 10°C. In each tension response, the tension reaches a peak (T1) at the end of a length step and then quickly but partially recovers to a level referred to as T2 (Huxley & Simmons, 1971). The peak tension change (T) due to a length step (L) was measured as T1–T0 for stretch and T0–T1 for release (T0, steady tension before length step) and stiffness calculated as (T/L); in order to pool the data from different fibres, L was normalized to L0 and T normalized to control T0. The initial rapid tension recovery after length-step (Huxley–Simmons phase 2 or T1–T2 recovery; Huxley & Simmons, 1971) was characterized by fitting a bi-exponential curve isolating two components referred to as phase 2a (very fast) and phase 2b; a curve is drawn through each trace.
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Figure 5A shows, in the form of histograms, the pooled data from three fibres in each of which stiffness estimates were made using the same lengthstep amplitude both in the control and in the presence of 4 mM added MgADP; the length step amplitudes used, however, were different in different fibres. The histograms on the left show that, compared with the control (open column), the steady tension was potentiated 20% with MgADP. Histograms on the right show the mean (±S.E.M.) stiffness ratios (calculated as above): the ratio is 163 (±17.8, n= 8) for the control and it is higher, 171 (±15.5, n= 8), with MgADP, but the difference is not significant (paired t test, P > 0.05). Thus, the increase of force by 4 mM MgADP is not due to a concomitant increase of stiffness.
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A, data from three fibres in each of which the tension responses to 2–4 stretch and release steps of the same amplitude (0.3–1.3%L0, in different fibres) were examined under control conditions (open columns) and in the presence of added 4 mM MgADP (double hatched columns). The columns on the left show (MgADP/control) percentage tension ratios; tension in the presence of ADP is 20% higher. The columns on the right show the mean (±S.E.M., n= 8) stiffness from the fibres (see Fig. 4 legend), normalized to L0 and control T0 of each fibre; the slightly higher stiffness with ADP (178 ± 15.5 T0/L0) is not significantly different (paired t test, P > 0.05) from control stiffness (163 ± 17.8 T0/L0). Thus, the tension potentiation by MgADP is not associated with a corresponding increase of stiffness. B, pooled data for the reciprocal time constants of the two exponential components (phase 2a, squares; phase 2b, circles) isolated by curve fitting to the initial tension recovery after a length step; they are plotted on a logarithmic ordinate against the length step amplitude as percentage L0. Data are from five fibres in three of which data were obtained both in control (filled symbols) and with 4 mM added MgADP (open symbols); each fibre contributed data for release and stretch. The lines are the calculated regressions, significant (P < 0.05) only for the control data (continuous lines). Despite the scatter, the rates with added ADP are, on average, lower particularly with length releases.
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Figure 5B is a plot of the pooled rate-constant data (reciprocal time constants) for phase 2a (squares) and phase 2b (circles), isolated by curve fitting to the initial tension recovery after a length step as shown in Fig. 4; the data are plotted on a logarithmic ordinate against the length step amplitude. The data are from five fibres, in three of which data were available in both control and added MgADP conditions, whereas, in the other two fibres, data were obtained only in control or with MgADP (n= 16 for control (filled symbols); n= 10 with 4 mM added MgADP (open symbols)); each fibre contributes data to length release and stretch. There is considerable scatter, but the control data do show the general trends expected (see Fig. 2 of Ranatunga et al. 2002), and also that the tension recovery is slower in the presence of MgADP, particularly with releases. Paired comparison of the control versus MgADP data from three fibres, where data were available under both conditions and with the same length steps, showed significant difference (P < 0.05) for phase 2a (from release) and phase 2b (from release and stretch).
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Isometric force at different temperatures. In a number of experiments at 5, 10, 20, 25 and 30°C, the active tension was measured in fibres that were activated in control conditions and in the presence of different [MgADP] forming a series, followed by a final control contraction. Quantitative analyses, however, were difficult (and probably not meaningful) since the exact [MgADP] in contracting fibres remained unknown (see Methods). Nevertheless, the data showed that the MgADP/control tension ratio increased (and saturated) as the [MgADP] increased up to 4 mM, basically as in Fig. 2. Additionally, the tension ratio at the high MgADP level (4 mM) was larger at the lower temperatures. To examine this further, control and with 4 mM MgADP contractions were recorded in individual fibres at different temperatures.
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Figure 6 shows superimposed tension traces from a muscle fibre that was activated in control solution and in solution containing 4 mM added MgADP at 5, 10 and 20°C. As reported in previous studies (Coupland et al. 2001 and references therein), the control tension (the lower tension trace in each frame) is markedly larger at the higher temperatures. The records also show that the tension is potentiated in the presence of MgADP (upper trace) as reported in previous studies (see Introduction), and it is seen at all the temperatures. In this particular experiment, the potentiation of the steady active tension with 4 mM added MgADP is 22% at 5°C whereas it is decreased to 6% at 20°C, which is indeed lower than in the pooled data (see below) showing the variability among fibres. The decrease in relative potentiation is largely due to the increase of control tension when the temperature is raised (i.e. endothermic nature of muscle force).
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Three pairs of tension traces from the same fibre show activations at 5, 10 and 20°C in control solution (lower trace in each panel) and with 4 mm added ADP (upper trace). The tension traces in each pair have been aligned so that the onset of activation is superimposed. Control steady tension is higher and the tension rise is faster at the higher temperatures. Tension in the presence of 4 mm added MgADP is greater compared with control at all temperatures; the potentiating effect of MgADP however, becomes less marked as temperature is increased. The horizontal time bar beneath the tension records is 2 s.
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Figure 7 shows the pooled data from experiments on a total of 18 fibres in which tension was measured in control conditions and with 4 mM added MgADP. Figure 7A shows mean (±S.E.M.) tension normalized to fibre cross-sectional area plotted against the reciprocal absolute temperature. The tension versus reciprocal temperature (1/T) relation in control solutions (open symbols and continuous curve) is sigmoidal with a half-maximal tension at 12°C, in basic agreement with our previous findings. In the presence of 4 mM MgADP (filled symbols and dashed curve), a sigmoidal plot is obtained but it is shifted upward along the tension axis and to the right (to lower temperatures; half-maximal at 10°C). Figure 7B shows data from the same experiments where the tension measured in solutions containing 4 mM MgADP has been expressed as a ratio of control tension at each temperature and mean (±S.E.M.) shown as histograms against the reciprocal absolute temperature. Compared with the controls, the tension with increased [MgADP] was significantly higher (P < 0.01, paired sample t test) at all temperatures except 30°C. Thus, the potentiating effect of 4 mM MgADP was most marked at 5°C, where mean (±S.E.M.) MgADP/control tension ratio was 1.25 (±0.05) and it decreased to 1.10 at 30°C. The differences in tension ratios between 5 and 20°C, and between 5 and 30°C, were significant (P < 0.05, one-way ANOVA).
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Pooled data from a total of 18 different fibres where tension was measured in control solution and with 4 mm added MgADP at one or more temperatures. At the end of the experiment, mean (±S.E.M.) control tension in these fibres was 0.96 (±0.01) of the initial control tension. A, active tensions measured in control (open symbols) and with added 4 mm MgADP (filled symbols) solutions are plotted as mean (±S.E.M.) specific tension (in kN m–2) against reciprocal absolute temperature (as 103 K/T), also labelled in degrees Celsius. The sigmoidal curve fitted to the control data corresponds to half-maximal tension at 12°C, but the curve is shifted to a slightly lower temperature with MgADP; half-maximal tension from the curve occurs at 10°C. The tension with 4 mm MgADP was significantly greater (P < 0.01) than the controls at 5, 10 and 20°C. B, the data shown in A were normalized, so that tension measured in solutions containing 4 mm MgADP is shown as a ratio of control tension (indicated by the horizontal dashed line) in each fibre and plotted against reciprocal absolute temperature. Data were obtained from 4 different fibres at 5°C, 13 fibres at 10°C, 8 fibres at 20°C and 3 fibres at 30°C. Note that, although there was considerable variability in the ratio, the MgADP/control tension ratio obtained at 5°C is significantly greater than the ratios at 20 and 30°C.
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Shortening velocity and rate of tension redevelopment. In order to obtain shortening velocity data from the same fibre at different [MgADP], the tension response to a large length release of constant amplitude was examined and the length step amplitude divided by the duration of unloaded shortening was taken as a measure of the maximum shortening velocity; this is clearly not an accurate estimate of the Vu since the method ignores the intercept on the length axis. Typical tension records from a fibre activated at 10°C in control and with a series of different levels of added MgADP are shown in Fig. 8A. The traces show that as [MgADP] was increased, so the duration of unloaded shortening increased and the rate of tension redevelopment decreased. This is also shown in the data from different fibres at other temperatures in Fig 8B and C. Figure 8B shows that the control shortening velocity (with no added MgADP) increases markedly with increase of temperature, as obtained in intact rat muscle experiments (Ranatunga, 1984). Although quantitative analysis is difficult since the exact [MgADP] within the fibres is unknown, the data also show that the shortening velocity decreases with increased [MgADP] at all the temperatures; the (4 mM MgADP)/control velocity ratios ranged from 0.41 to 0.6 at 20–30°C and from 0.44 to 0.72 at 5–10°C. Figure 8C shows data for the rate of tension redevelopment (reciprocal of the half-time of tension redevelopment to steady level) following a length release at different temperatures; the control rate of tension rise is markedly increased at higher temperatures, as found in intact muscle experiments (Ranatunga, 1984) and, like shortening velocity, it is decreased with increased [MgADP] at all the temperatures.
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A, superimposed tension records (upper panel) from a maximally activated single fibre in solutions containing 0, 0.5, 1, 2 and 4 mM added MgADP at 10°C. The initial part of the traces shows that isometric tension is higher with higher [MgADP] and, following a length release (amplitude 14%L0) is a slack period and tension redevelopment. For clarity, only a single length record is shown in the lower panel. Note that the slack period (duration of unloaded shortening) increases with increasing [MgADP] and the force redevelopment becomes slower. Length step amplitude/duration of unloaded shortening was taken as shortening velocity. B, data from 4 different fibres (two of which were tested at two different temperatures) are shown where shortening velocity (as L0 s–1) is plotted against added [MgADP] for 30°C (stars), 20°C (triangles), 10°C (filled circles, representing fibre shown in A) and 5°C (diamonds). C, data for rate of tension redevelopment (reciprocal half-time for tension rise) from experiments at 20, 10 and 5°C from the same fibres presented in B. For clarity, the data obtained at 30°C are not shown as the data points were overlaying data at 20°C. Note that the shortening velocity and the rate of tension rise in control conditions (plotted at zero [MgADP]) are markedly increased at the higher temperatures, as found in intact rat muscle experiments (Ranatunga, 1984).
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Simulations of temperature and [MgADP] effects on muscle force
Temperature-dependent changes in occupancy and steady force. Scheme 1 (see Methods) was used in the simulations and, as shown in Fig. 9A, temperature increase was simulated by a marked increase of the rate constant k+1 (force generation, Q10 of 4) and a small increase in step k+4 (Q10 of 1.32), since there is evidence that ADP release itself is temperature sensitive (Siemankowski et al. 1985); increase of k+4, however, was not absolutely necessary to obtain the main findings. Figure 9B shows the steady-state (1 s) occupancy of the five states in the scheme as the temperature is simulated to rise from 0 to 35°C. The calculated fractional occupancy of each of the five states, for control conditions (10 μM[MgADP] and 0.5 mM Pi) and for a selected number of temperatures, is plotted against reciprocal absolute temperature; note that the sum of fractional occupancies of all five states for any temperature is one. Open circles represent occupancy of state V, labelled as [AM] in the scheme so as to discretely identify the ADP-release/ATP-binding step; with millimolar levels of MgATP, however, AM dissociation would be fast and, hence this represents M.ATP + M.ADP.Pi (and AM) states that are not separately identified in the model. Open squares represent state I, i.e. the pre-force generating AM.ADP.Pi state and it predominates at the low temperatures (e.g. 10°C) but its occupancy decreases markedly with warming. Filled symbols represent states II, III and IV (AM*.ADP.Pi, AM*.ADP and AM*'.ADP) in the scheme, each assumed to bear equal force, and the plots show a marked increase in the occupancies of AM.ADP (post-power stroke) states as the temperature is raised.
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The sum of the occupancies of states II, III and IV at 1 s was taken as steady tension (force). Figure 9C (filled circles) shows the simulated control steady-state tension plotted against reciprocal absolute temperature. Tension distribution approximates sigmoidal relation with half-maximal at 10–12°C, as found experimentally. The results obtained from modelling the effects of 4 mM MgADP on steady-state tension at different temperatures are shown by the open symbols in Fig. 9B. Within a temperature range of 0–40°C, the approximate sigmoidal relation is shifted upwards along the tension axis and slightly to the right with 4 mM added ADP – as found in the experiments (Fig. 7A). With added Pi, simulation showed that the relation is shifted to the left (to higher temperatures – not shown) as found in our previous study (Coupland et al. 2001). The dotted curve in Fig. 9C shows (under control conditions) that, if tension measurements were made early after large T-jumps from low starting temperature, the apparent ‘steady’ tension continues to rise at higher temperatures (see below). It is interesting to note that the simulated tension responses (Fig. 11A) with T-jumps reaching high temperatures (e.g. 30, 35°C) indicate slow tension decay after the initial rapid rise.
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T-jumps were simulated under control conditions and the tension rise determined basically as in Fig. 10 (i.e. change with time of the sum of the fractional occupancies of states II, III and IV in Scheme 1 represents the tension rise). A, T-jumps of different amplitudes (as labelled), increasing up to 35°C, were modelled from the same starting temperature of 0°C; both the amplitude and the rate of the T-jump-induced tension rise increase with increase of post-T-jump temperature. Note the qualitative similarity of the transients to those in the experiments of Bershitsky & Tsaturyan (2002) who used large T-jumps from low starting temperatures. The modelled tension responses at high temperatures (e.g. 30 and 35°C), however, showed that the tension decreases slowly after the initial rapid rise so that, if tension is measured at 50–100 ms after large T-jumps, the tension versus temperature relation may not be sigmoidal, nor would it show saturation at high temperatures (see Fig. 9C). B, T-jumps of constant amplitude (5°C) from different starting temperatures of 0–30°C (post-T-jump temperature is labelled); the system was allowed to reach steady state at each temperature before a T-jump was simulated. The rate of rise of the simulated tension response increases with (pre- or post-T-jump) temperature, but its amplitude initially increases and then decreases as the starting temperature is increased (>15°C); since the pre-T-jump tension (the tension at zero time for each trace) increases with warming, the tension amplitude per 5°C T-jump decreases with increase of starting temperature (see Goldman et al. 1987). Note the qualitative similarity of these simulated tension responses to the experimental responses of Coupland et al. (2001) where the traces in Fig. 1A were obtained by adopting a similar methodology.
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Simulated T-jump tension responses; effects of MgADP and Pi. Figure 10A shows simulated tension responses induced by a standard T-jump at 9°C under control conditions (continuous trace) and with 4 mM[MgADP] (dashed trace). The two traces are vertically shifted for superimposition to show that they have similar amplitudes, but the tension rise was slower with 4 mM MgADP, as found experimentally (see Fig. 1). Two component rates (one fast and two combined slow) characterize the tension rise. Examination of these data showed that the MgADP-induced decrease of the rate of tension rise after a T-jump is due to an increase in the amplitude of the combined slower component coupled with a concomitant decrease in the amplitude of the fast component as [MgADP] is increased; analyses by curve fitting (as in Fig. 1) probably cannot distinguish between the two cases when the underlying rates are not very different (10 s–1 compared with 20–40 s–1, see Fig. 3). Figure 10B shows the steady tension before (crosses) and after (circles) T-jumps at a range of [MgADP], where [MgADP] is plotted on a logarithmic axis; the tension is potentiated by 20% at 4 mM[MgADP], with a half-maximal effect at <1 mM[MgADP], as in the experiments.
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A, superimposed tension transients induced by a 3°C standard T-jump at a starting temperature of 9°C, in control activation (continuous curve) and in the presence of 4 mM MgADP (dashed curve). A T-jump was simulated by re-setting k+1 and k+4 to higher values (Q10 values of 4 and 1.3, respectively) and [MgADP] changed by altering k–4: change with time of the sum of the fractional occupancies of states II, III and IV (see Scheme 1) represent the tension rise. The tension records have been shifted vertically for superimposition. Note that the tension rise is slower but amplitudes are similar with added MgADP, as found experimentally (see Fig. 1). B, the pre-T-jump (crosses) and the post-T-jump (circles) tensions calculated for a number of [MgADP] levels (on a logarithmic abscissa) are shown by the symbols; they are normalized to the pre-T-jump control (dashed line). Note the qualitative resemblance to the experimental data shown in Fig. 2. C, since previous simulations of Pi effects did not use a model having MgADP release steps, simulated T-jump-induced tension transients in control (continuous curve) and in the presence of 30 mM Pi (dashed curve) from the present model are shown; [Pi] is changed by altering k–2. Note that tension rise is faster with increased Pi (as previously reported: Davis & Rogers, 1995; Ranatunga, 1999a). D, [Pi] dependence of pre- and post-T-jump tensions from simulations – the presentation is similar to B; the half-maximal effect is at 5–10 mM[Pi].
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Since previous simulations did not consider the slow MgADP release steps, we re-examined simulation of Pi effects with the current model and they are shown in Fig. 10C and D. The analysis showed occurrence of two phases (a slow phase was not seen previously, see Ranatunga, 1999a), a higher rate (40 s–1, endothermic force generation) that increased and saturated at higher [Pi] and a combined lower rate (<10 s–1) that decreased with increased [Pi], essentially as found experimentally (see Ranatunga, 1999a). Figure 10D shows the steady tension before (crosses) and after (circles) T-jumps at a range of [Pi]; the tension is depressed markedly with increased [Pi] with a half-maximal effect at 5–10 mM[Pi].
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Simulated T-jumps of different amplitudes and at different temperatures. Figure 11A shows a number of simulated tension responses (under control conditions) induced by T-jumps of different amplitudes that reached the final temperatures as labelled. The simulated tension responses become faster and larger in amplitude with temperature, and they show qualitative similarity to those in the experiments of Bershitsky & Tsaturyan (1992, 2002) who used large T-jumps from a low starting temperature. In laser T-jump experiments, small T-jumps are induced and, to cover a large temperature range, they are made at different starting temperatures. Figure 11B shows simulations of such an experiment, where 5°C T-jumps were simulated at staring temperatures ranging from 0 to 30°C. The tension rise became faster with increase of temperature, but the tension amplitudes were small and they decreased at the high temperature range (>20°C); these bear resemblance to the actual tension traces reported from an experiment by Coupland et al. (2001, see their Fig. 1A).
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The matrix method (see Gutfreund & Ranatunga, 1999) gives the rate constants and amplitudes for the sum of the exponentials representing the time course of the formation and decay of each state of the system after a perturbation, i.e. the tension rise after a T-jump. The simulated tension responses shown in Fig. 11A and B consisted of three components (one fast and two slow; see Methods and figure legend) but, since the two slow component rates were similar, the number of components could be reduced to two by averaging the two slow rates. Figure 12A illustrates temperature dependence of the fast and the (averaged) slow rate constants; the fast rate increases markedly whereas the slow rate shows only a modest increase with temperature (= post-T-jump temperature). Figure 12B shows that with large T-jumps the amplitude of the fast component (filled circles) shows a rapid rise with temperature; the sum of the amplitudes of the two slow components (open circles) was significant below 25°C but decreased at higher temperatures (indeed becomes negative contributing to tension decline at 35°C). With small 5°C T-jumps from different starting temperatures (as in laser T-jump experiments), the rate-constant data were identical to those in Fig. 12A, but the amplitudes were small (<0.15 of total) as shown in Fig. 12C; both amplitudes showed a bell-shape distribution over the temperature range. Also, the amplitudes normalized to tension at pre- or post-T-jump temperature decreased with increased temperature (as found experimentally, Goldman et al. 1987; Davis & Harrington, 1993; Ranatunga, 1996).
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The tension rise induced by T-jumps, as shown in Fig. 11, consisted of three exponential components (see Methods), one fast and two slow, but could be reduced to two by combining the two slow components whose rates were similar; these were available directly from the matrix method used in the simulations (see Gutfreund & Ranatunga, 1999). Their rates and amplitudes (fractional occupancy) were calculated for 5°C intervals and are plotted against reciprocal post-T-jump temperature. A, the rate of the fast component (filled symbols) increases markedly with temperature; the rates of the two slow components, which had similar values (<10 s–1), were averaged and the average slow rate (open symbols) shows only a modest increase with temperature. B, with simulated large T-jumps, the amplitude of the fast component (filled circles) increases sharply with temperature. The sum of the amplitudes of the two slow components (open circles) is prominent at temperatures <25°C, but decreases at higher temperatures (indeed it becomes negative and contributes to a slow tension decline after T-jump to 30–35°C). C, it should be clear that with small T-jumps (5°C) from different starting temperatures (as in Fig. 11B, and in the experimental studies of Goldman et al. 1987; Davis & Rodgers, 1995; Ranatunga, 1996), the rate constant data in A are identical, but the absolute fractional amplitudes would be small. The filled circles (fast) and the open circles (combined slow) show the amplitude data from simulation of such an experiment. In general, the data show that a T-jump-induced tension rise would contain two components, but the biphasic nature of the tension rise would be less clear when large T-jumps from low starting temperatures are examined because of the rapid growth with increased temperature of the fast component. Also, note that the sum of the amplitudes (T-jump-induced change in the fractional occupancies of the three force-bearing states) plus their sum at the pre-T-jump temperature gives the steady force at a given temperature and, hence, the sigmoidal force versus reciprocal temperature relation as shown by the filled symbols in Fig. 9C.
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Discussion
T-jump-induced tension rise: endothermic force generation
At 10°C, a small rapid T-jump (3°C in 0.2 ms) induced a tension rise to a new steady state (Fig. 1); analysis showed that a T-jump-induced tension rise consists of two exponential components, labelled phase 2b (fast) and phase 3 (slow), where phase 2b represents endothermic force generation in attached crossbridges (see Introduction and Methods). The steady active tension was potentiated by 20% when [MgADP] was increased to a level similar to [MgATP], 4–5 mM in our experiments; the binding of MgADP to nucleotide-free crossbridges (AM) leading to accumulation of force-bearing AM-ADP states (Cooke & Pate, 1985; Dantzig et al. 1991; Lu et al. 1993, 2001), in general, may underlie the tension increase. When [MgADP] was increased, the tension rise induced by a T-jump was slower (Figs 1 and 2) indicating that the approach to the new steady state at the post-T-jump temperature was slower. Although a direct comparison is difficult, our data seem comparable to those of Zhao & Kawai (1994) on the effect of MgADP on the exponential process (C) that they identify from sinusoidal length perturbation technique.
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These effects of increased [MgADP] contrast sharply with those produced by increased Pi that is released earlier in the crossbridge cycle; the steady force was decreased with added Pi (Hibberd et al. 1985), but the kinetics of the approach to the new steady state were enhanced – the tension change was faster after a perturbation (e.g. hydrostatic pressure-jump, Fortune et al. 1991; sinusoidal length oscillation, Kawai & Halvorson, 1991; Pi-jump, Dantzig et al. 1992; T-jump, Ranatunga, 1999a). The unified thesis that arose from such different studies was that, kinetically, the force generation precedes rapid release of Pi and both steps are reversible.
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The aforementioned observations validate the identification of two components (labelled phase 2b and phase 3) in a T-jump-induced tension rise obtained experimentally. For example, at 10–12°C, phase 2b was 40–60 s–1 under control conditions and it became faster (120 s–1) with increased Pi (Ranatunga, 1999a), whereas it became slower with increased [MgADP]. On the other hand, the phase 3 was 10 s–1 and had quite different characteristics, being largely insensitive to MgADP and Pi (in simulations it consists of two slow rates that could be combined – see below). Our thesis is that a T-jump-induced tension response effectively consists of two components, where phase 2b represents crossbridge force generation, and the phase 3 relates to subsequent slow step(s) in the cycle (see Davis & Rodgers, 1995; Ranatunga, 1999a). This conclusion is at variance with the findings of Bershitsky & Tsaturyan (2002) (see Introduction) that suggested that a T-jump tension response represents one process. It is noteworthy, though, that our laser T-jumps are small (<5°C) and made on fibres bathed in buffer solution where the post-T-jump temperature decayed very slowly (Ranatunga, 1996), whereas Bershitsky & Tsaturyan (2002) used large T-jumps induced on fibres held in air. Such differences between the T-jump methods and other uncertainties, as also discussed by Bershitsky & Tsaturyan (2002), may have contributed to the observed differences (also see below).
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Tension responses to length steps and stiffness
The limited observations made on the tension responses induced by small, rapid, length steps at 10°C show (Figs 4 and 5) that the increase of force with 4 mM added MgADP is not accompanied by a corresponding increase of stiffness; there was, however, an indication of a small stiffness increase with added MgADP (see Fig. 5A). This compares with the observation that, although the stiffness is reduced by increased [Pi], its reduction is less than the extent of force depression by Pi (Dantzig et al. 1992; also, see Fig. 4A of Ranatunga et al. 2002). A control stiffness of 163 (±17.8) T0/L0 represents the slope of the T1versus length step amplitude plot in Huxley & Simmons (1971) type of analysis, and its reciprocal corresponds to a fibre compliance of 0.61%L0/T0; this would equate to 7.7 nm per half-sarcomere, but it is important to note that we did not directly measure sarcomere length changes and use these only for comparative purposes. Due to the effect of fibre end-compliance, the above value is indeed higher than that (5–6 nm per half-sarcomere) obtained in studies at 6–16°C on several mammalian species under more control conditions (Galler et al. 1996, rat fibres; Tsaturyan et al. 1999, rabbit fibres, Linari et al. 2004, human fibres). Since tension is increased 20% in the presence of 4 mM MgADP, but the stiffness (slope) remains approximately similar, the corresponding compliance value would be higher, 9 nm per half-sarcomere. A change in the opposite direction was observed when active force was depressed with 25 mM Pi, although the actual values were different (see Fig. 2B of Ranatunga et al. 2002). These findings indicate that, to a considerable extent, the force changes induced by increased MgADP and Pi result from redistribution of attached crossbridge states, thus changing the average force per crossbridge. Similar considerations and analyses have shown that the increase of active force by increased temperature is also due to an increase of average force per crossbridge without a significant increase in the fraction of attached heads: indeed, this has been carefully examined and confirmed in several studies on frog (Bershitsky et al. 1997; Tsaturyan et al. 1999; Piazzesi et al. 2003) and rabbit muscle fibres (Bershitsky & Tsaturyan, 1995, 2002). The general validity of these findings is assumed and encompassed in our model (see Scheme 1).
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Phase 2 tension recovery and endothermic force generation
Analyses of the quick tension recovery after a length step (Huxley–Simmons phase 2 or T1–T2 recovery) showed that the tension recovery is slower with increased MgADP; this was particularly so with length releases where both phase 2a and phase 2b rates were significantly lower with 4 mM MgADP (Fig. 5B); phase 2b with MgADP was slower than control both in stretch and in length release. In previous experiments, we noted that both T-jump force generation (Ranatunga, 1999a) and phase 2b tension recovery from stretch (Ranatunga et al. 2002) become faster to a similar extent with increased Pi; it may be argued that the rather fast recovery rates obtained from length releases and scatter in our data prevented us from observing Pi sensitivity of phase 2 tension recovery after length releases (see Fig. 3B of Ranatunga et al. 2002). Thus, although exact experimental proof is lacking, the effects of MgADP and of Pi may be taken to be similar on T-jump force generation and on phase 2 tension recovery (particularly, its phase 2b component) from length steps, both of which are thought to represent the crossbridge force generation process. This notion gains support from the finding that the rate of phase 2 tension recovery from length step is temperature sensitive (Q10 of 2–3, Piazzesi et al. 2003), the temperature sensitivity being greater in phase 2b than in phase 2a component of recovery (Davis & Harrington, 1993; Davis & Epstein, 2003). Thus, like the T-jump force rise, phase 2b tension recovery represents an endothermic process. It is known that the T-jump force generation is much slower than phase 2 tension recovery from length release. However, in the same preparation and at similar temperature, it is faster than phase 2b recovery from stretches (see Table 1 of Ranatunga et al. 2002), indicating that T-jump force rise monitors force generation in crossbridges unstrained by filament sliding (length steps); its rate (phase 2b recovery) would be enhanced in length release and decreased following stretch, due to particular strain dependence of the underlying rate constants (Huxley & Simmons, 1971). Indeed, by extrapolation, the phase 2b recovery rate that corresponds to the isometric point in a length step versus rate of tension recovery plot in experiments on rabbit psoas fibres at 10°C (e.g. Fig. 3B in Ranatunga et al. 2002; and Fig. 5B here) is 40–60 s–1, which is comparable to the rate of endothermic force generation in our T-jump experiments; despite the scatter in them, the data also indicate that this extrapolated ‘isometric phase 2b recovery’ is enhanced with Pi and depressed with MgADP as is T-jump force generation. In general, these observations support the thesis that phase 2 tension recovery after a length step contains a component (phase 2b) that is homologous to the endothermic force generation observed after a rapid T-jump, as originally proposed by Davis & Harrington (1993; see also Davis, 1998).
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Despite the above considerations, however, the data presented from some careful fibre mechanics experiments by Bershitsky & Tsaturyan (2002 and references therein) show absence of interaction between the tension transients induced by large T-jumps and those induced by length steps when one is applied at different times after the other; this indicates that different processes underlie tension responses to T-jump and length steps. In a recent study by Ferenczi et al. (2005), however, a correspondence between the mechanical (and structural) responses to length steps and to T-jumps has been found, and the apparent strain independence of the responses to T-jumps has been attributed to the presence of a preceding temperature-dependent rate-limiting step. Further work is required to resolve these issues.
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The sigmoidal relation between force and temperature
The control isometric force versus reciprocal temperature is sigmoidal (see Fig. 7A) with half-maximal level at 10–12°C, as found in our previous studies on skinned fibres (Coupland et al. 2001) and on intact fibres (Coupland & Ranatunga, 2003). Although the exact concentration effects remain uncertain, our results also show that the tension potentiation with increased [MgADP] is seen at all the temperatures including high physiological temperatures. In so far that the control tension is markedly increased at high temperature, however, the relative potentiation of tension is lower at the higher temperatures (see Fig. 7B). Consequently, the sigmoidal relation between force and reciprocal temperature was shifted to the right (Fig. 7A) with increased MgADP. A shift of the sigmoidal relation to the left (higher temperatures) was observed with increased [Pi] level and was modelled (see Coupland et al. 2001); these indicate that the position of the relation on the temperature axis could vary depending on the concentration of these products.
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Shortening velocity
Biochemical studies on myosin isoforms from a range of muscle types indicate that differences in ADP release rates underlie the differences in their shortening velocities (Weiss et al. 2001; Nyitrai & Geeves, 2004). Thus, ADP release rate may define the increased rate of detachment of crossbridges and velocity during shortening, as suggested from modelling and other studies (see Smith & Geeves, 1995; He et al. 2000). Interestingly, different temperature sensitivities of the rate of ADP release from AM and the rate of ATP induced dissociation of AM (Bottinelli, 2004) indicate that the former may limit maximum shortening velocity at high temperatures (>20°C), whereas the latter process may be limiting at lower temperatures (unpublished data of Professor M. A. Geeves, personal communication). Indeed, the shortening velocity of intact muscles showed a change in temperature sensitivity at high and low temperature ranges (Ranatunga, 1984), which would be consistent with that finding. Our data showed that the shortening velocity was decreased with increased [MgADP] at all the temperatures. Although quantitative analyses are difficult, we calculated the (4 mM MgADP)/control velocity ratios, but the analysis does not clearly indicate a difference between high and low temperatures with respect to MgADP sensitivity of shortening velocity. However, this may be due to the limited number of data (four fibres) and/or because the estimation of shortening velocity was based on measurements using a single length step amplitude; more detailed work would be required to investigate this further.
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Model simulations
As given above, the unified thesis that arose from several different studies was that, kinetically, the crossbridge force generation occurs in a reversible step before rapid release of Pi (a transition between two AM.ADP.Pi states). The simulations we carried out retaining those features but incorporating a subsequent slow two-step MgADP release (see Dantzig et al. 1991; Kawai, 2003) in an otherwise minimal crossbridge/AM-ATPase scheme (Scheme 1), can qualitatively account for our experimental findings. The findings and predictions from the model may be summarized as follows.
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Firstly, the sigmoidal relation between force and reciprocal temperature is qualitatively modelled by making the pre-Pi-release force-generating step highly temperature sensitive (Q10 of 4); although a low temperature sensitivity of MgADP release (Q10 of 1.3) was also used here (see Fig. 9A), it is not essential to model the main findings. The model predicts that pre-force-generating AM.ADP.Pi state is the predominant species at low temperatures (<10°C); this is in general agreement with the findings of Lionne et al. (2002) that showed that such states (e.g. M/AM.ADP.Pi) become significantly populated in myofibrils under a variety of conditions, including low temperature. Its occupancy decreases with increase of temperature so that the force bearing, AM.ADP states predominate at high temperatures (see Fig. 9B). Thus, the underlying basis of the sigmoidal relation is a shift in the distribution of attached crossbridge states from the pre-force to the force-bearing crossbridge states when the temperature is raised (Davis, 1998; Kawai, 2003). As is evident from previous studies (see Bershitsky & Tsaturyan, 1995, 2002; Bershitsky et al. 1997; Piazzesi et al. 2003; Kawai, 2003), the increased isometric force on heating is not due to a concomitant increase in the number of attachments or to a given crossbridge state developing a larger force at high temperatures. Secondly, the exact position of the sigmoidal relation is predicted to be sensitive to the concentrations of the products of ATP hydrolysis; it is shifted to lower temperatures with increased [MgADP] (see Fig. 9C) and to higher temperatures with increased [Pi] (see Coupland et al. 2001). Thirdly, simulation of a small T-jump at 10°C predicts a force rise to a new steady state as found in the experiments. The pre- and post-T-jump force are potentiated and the T-jump-induced tension rise is slower with increased [MgADP]; the pre- and post-T-jump force are decreased and tension rise becomes faster with increased Pi (see Fig. 10). Finally, simulations further showed that a T-jump-induced tension response has three components that could be reduced to two, a fast and a (combined) slow component (see Figs 11 and 12) as obtained in the experiments; their relative amplitudes, however, are temperature dependent, with the slow component being relatively more prominent at the low temperatures. This and the large increase of the fast component may account for not observing a clear biphasic tension response with large T-jumps to high temperatures, as in the experiments of Bershitsky & Tsaturyan (2002); somewhat similar views were expressed also by Davis & Harrington (1993) and Kawai (2003) with respect to large amplitude T-jumps. Our simulated tension responses also indicate that force measurement early after large T-jumps, from low to high temperatures, may not represent the steady-state force (see Fig. 11A), and may lead to a more linear distribution of force against temperature as found experimentally (Bershitsky & Tsaturyan, 1992, 2002).
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It is relevant to note that other studies have indicated (see Zhao & Kawai, 1994) an irreversible forward step between attached crossbridge states after Pi release (step 3 in our scheme above); in our modelling, step 3 was indeed forward biased with k3 of 15 s–1/5 s–1 (but k3 of 5 s–1/0.5 s–1 was adequate). Also, an irreversible step 3 was compatible with modelling temperature effects on control tensions and Pi effects on tension (as found previously, Ranatunga, 1999a); however, making step 3 irreversible failed to account for the temperature-sensitivity of ADP effects in our experiments. It is noteworthy that He et al. (2000) modelled temperature effects on ATP consumption and efficiency in muscle without having such a rate-limiting irreversible step between attached states; reversibility among attached states in the crossbridge cycle, of course, will increase the efficiency in the system (see Davis & Epstein, 2003).
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Muscle performance at physiological temperatures
Accumulation of the products of ATP hydrolysis in active muscle can be an underlying cause of the changes in muscle contraction during fatigue (Dawson et al. 1978). Therefore, it is of some interest to consider the relative magnitude of the effects of MgADP and Pi in muscle fibres at high physiological temperatures. Our previous results (Coupland et al. 2001) showed that, compared with the effects seen at low temperatures at which most fibre studies are made, the effect of Pi on force is considerably reduced at physiological temperatures; the effect of decreased pH was also less marked at physiological temperatures (Ranatunga, 1987; Pate et al. 1989). The present results lead to a similar conclusion with respect to the effect of increased [MgADP] on tension (see Fig. 7B). One reason for this temperature-dependent change in their effects on active muscle force is the finding that the crossbridge force generation is endothermic and it is not directly linked to the release of products of ATP hydrolysis, as suggested by Davis & Rodgers (1995) when they defined ‘de-novo tension generation in muscle’. Thus, the increase of control tension by increase of temperature results in a relative lessening of the effects of the product accumulation on muscle force at the higher temperatures – as compared with low temperatures.
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It is important to note that force is increased 10% with increased [MgADP] at 30°C, but the velocity is decreased 50% (see Figs 7B and 8B) so that, assuming that the curvature of the force–velocity relation is not much altered, the mechanical power (force X velocity) would be reduced to about 55% compared with the control. With increased Pi, the force is decreased (20% with 25 mM Pi at 30°C, Coupland et al. 2001) but the velocity is unaffected (Cooke & Pate, 1985; Pate & Cooke, 1989a,b), which also leads to a reduction in power output to about 80% of the control. It may be argued that the mechanical power (the rate of doing external work) is a better physiological index of a muscle's performance (see He et al. 1999) than isometric force and, the approximate considerations made above suggest, that accumulation of MgADP or Pi would contribute to muscle fatigue due to a reduction in a muscle's power output; such effects of course would be evident in more dynamic muscular exercise rather than in maximal isometric force production – as commonly used in studies on muscle fatigue.
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Conclusion – unresolved issues
The present study addressed the endothermic characteristics of active muscle force and used a kinetic model with a minimal AM-ATPase pathway that qualitatively accounted for the main findings; the model was simplistic and did not have strain-sensitive features necessary to account for shortening velocity, length step transients, etc. According to current thinking, the closed–open conformation change of the actin-attached myosin head (crossbridge), leading to lever arm movement, underlies muscle force generation Geeves & Holmes (1999). Our data suggest that this occurs in an early step, between two AM.ADP.Pi states; it is particularly temperature sensitive and endothermic. According to the model proposed by Davis & Rodgers (1995), however, the endothermic force generation step is a transition between two AM.ADP states, i.e. after the release of Pi. In a recent study on structure–function correlation of the crossbridge (myosin motor) in muscle, Ferenczi et al. (2005) indeed propose a more complex model where (endothermic) force generation involves two steps: a change in actin-binding characteristics that leads to the lever arm movement. Resolution of these different ideas would require further study.
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Wang & Kawai (2001) have discussed how endothermic (+entropic) events in the crossbridge leading to force generation may be produced on the basis of the known crystallographic structures of myosin and actin. However, studies on myosin-ATPase in solution (see Millar et al. 1987 and references therein) have shown, in particular, that the ATP cleavage step (i.e. in detached crossbridges in fibres) is endothermic (H=+65 kJ mol–1). If a step between detached crossbridge states (only) is particularly temperature sensitive, a latency would be expected before the tension rise induced by a T-jump in active muscle fibres, but no such latency has been observed. Moreover, more recent studies of Werner et al. (1999) and Malnasi-Csizmadia et al. (2000) have provided evidence of temperature-dependent conformational change(s) in myosin in solution, where open–closed transition has been found to be endothermic (H=+94 kJ mol–1, Malnasi-Csizmadia et al. (2000). Additionally, the helical order of myosin filament has been shown to be temperature sensitive, with low temperatures favouring a disordered (open) conformation and high temperatures favouring ordered (closed) conformation together with a second disordered conformation (Xu et al. 2003). If open–closed transition in myosin is endothermic, whether and how the reverse process, the closed–open transition, also can be endothermic on its attachment to actin (i.e. in crossbridges in muscle fibres) is a fundamental issue that remains to be resolved. Therefore, how the above findings from myosin, myosin filaments and myosin-ATPase cycle, and temperature-sensitive steps other than force generation (see Millar et al. 1987; He et al. 1997; Ferenczi et al. 2005), may be accommodated in the AM cycle in muscle fibres remain unclear and have not been duly addressed in our study.
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Zhao Y & Kawai M (1994). Kinetic and thermodynamic studies of the cross-bridge cycle in rabbit psoas muscle fibers. Biophys J 67, 1655–1668., 百拇医药(M. E. Coupland, G. J. Pin)
Abstract
We studied, by experiment and by kinetic modelling, the characteristics of the force increase on heating (endothermic force) in muscle. Experiments were done on maximally Ca2+-activated, permeabilized, single fibres (length 2 mm; sarcomere length, 2.5 μm) from rabbit psoas muscle; [MgATP] was 4.6 mM, pH 7.1 and ionic strength was 200 mM. A small-amplitude (3°C) rapid laser temperature-jump (0.2 ms T-jump) at 8–9°C induced a tension rise to a new steady state and it consisted of two (fast and slow) exponential components. The T-jump-induced tension rise became slower as [MgADP] was increased, with half-maximal effect at 0.5 mM[MgADP]; the pre- and post-T-jump tension increased 20% with 4 mM added [MgADP]. As determined by the tension change to small, rapid length steps (<1.4%L0 complete in <0.5 ms), the increase of force by [MgADP] was not associated with a concomitant increase of stiffness; the quick tension recovery after length steps (Huxley–Simmons phase 2) was slower with added MgADP. In steady-state experiments, the tension was larger at higher temperatures and the plot of tension versus reciprocal absolute temperature was sigmoidal, with a half-maximal tension at 10–12°C; the relation with added 4 mM MgADP was shifted upwards on the tension axis and towards lower temperatures. The potentiation of tension with 4 mM added MgADP was 20–25% at low temperatures (5–10°C), but 10% at the physiological temperatures (30°C). The shortening velocity was decreased with increased [MgADP] at low and high temperatures. The sigmoidal relation between tension and reciprocal temperature, and the basic effects of increased [MgADP] on endothermic force, can be qualitatively simulated using a five-step kinetic scheme for the crossbridge/A-MATPase cycle where the force generating conformational change occurs in a reversible step before the release of inorganic phosphate (Pi), it is temperature sensitive (Q10 of 4) and the release of MgADP occurs by a subsequent, slower, two-step mechanism. Modelling shows that the sigmoidal relation between force and reciprocal temperature arises from conversion of preforce-generating (A-M.ADP.Pi) states to force-bearing (A-M.ADP) states as the temperature is raised. A tension response to a simulated T-jump consists of three (one fast and two slow) components, but, by combining the two slow components, they could be reduced to two; their relative amplitudes vary with temperature. The model can qualitatively simulate features of the tension responses induced by large-T-jumps from low starting temperatures, and those induced by small-T-jumps from different starting temperatures and, also, the interactive effects of Pi and temperature on force in muscle fibres.
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Introduction
It has been known for over half a century (Hadju, 1951) that active force in mammalian skeletal muscle increases as the temperature is raised. Subsequent studies have confirmed and extended this finding to different muscles (e.g. fast and slow muscles, Ranatunga & Wylie, 1983), species (including peripheral muscles of the human body, see references in Ranatunga et al. 1987) and to different types of preparations (e.g. Ca2+-activated skinned fibres, Stephenson & Williams, 1981, 1985). The finding indicated the endothermic nature of active muscle force, i.e. force increases as heat is absorbed. This fundamental characteristic has received considerable attention in a number of studies (see references in Davis, 1998; Kawai, 2003; Ranatunga & Coupland, 2003b), and the basic findings and conclusions that have emerged from mammalian muscle fibre studies, and uncertainties and unknowns that remain, may be briefly summarized as follows. (1) Whereas the rigor force (when crossbridges are strongly attached but not cycling) decreases linearly, the active isometric force (when crossbridges are cycling) increases twofold when the temperature is raised from 10°C to high physiological (>30°C) temperatures (Ranatunga, 1994). The active force versus reciprocal absolute temperature (1/T) is sigmoidal (Davis, 1998; Kawai, 2003; also, see references in Coupland & Ranatunga, 2003) with indication of saturation at physiological temperatures; the latter feature, however, has not been observed in the experiments of Bershitsky & Tsaturyan (1992, 2002) who used force measurements after large temperature-jumps (T-jumps) to high temperatures. Interestingly, a sigmoidal relation between maximum force and temperature is seen also in frog fibres but with a low temperature for the half-maximal tension, 2°C (i.e. 8–10°C lower than for mammalian fibres, see Piazzesi et al. 2003). (2) Increase of active muscle force on heating is not accompanied by a concomitant increase of stiffness (Goldman et al. 1987), indicating that it is not due to a significant increase in the fraction of attached crossbridges, but due to an increase of average force per crossbridge; this has been examined and confirmed in studies on rabbit (Bershitsky & Tsaturyan, 1995, 2002) and frog muscle fibres (Bershitsky et al. 1997; Tsaturyan et al. 1999; Piazzesi et al. 2003). (3) A rapid T-jump induces a bi-exponential (labelled phase 2b and phase 3) rise in force to a level as expected from steady-state experiments; the (faster) phase 2b is identified as ‘endothermic force generation’ in attached crossbridges (Davis & Harrington, 1987; Goldman et al. 1987; Bershitsky & Tsaturyan, 1989, 1992; Ranatunga, 1996). From more recent experiments, however, Bershitsky & Tsaturyan (2002) challenged the validity of identification of two (or more) phases in a T-jump-induced force response, and they analysed the entire tension response as a ‘single process’. (4) Phase 2b has been compared with a slow component of the phase 2 or T1–T2 tension recovery (Huxley & Simmons, 1971) obtained in length-release experiments (Davis & Harrington, 1993; Davis & Rodgers, 1995). However, exact quantitative comparison of the T-jump force response with the T1–T2 transition has proved difficult; on the basis of a number of observations; Bershitsky & Tsaturyan (2002) indeed concluded that tension transients induced by T-jumps and length steps are caused by different processes in crossbridges (see, however, Piazzesi et al. 2003 and Ferenczi et al. 2005). (5) In so far that it is not directly coupled to the release of inorganic phosphate (Pi) in the actomyosin (AM) ATPase cycle that underlies muscle contraction, the phase 2b (after T-jumps) is considered to represent a ‘de novo force generation’ in attached crossbridges (Davis & Rodgers, 1995; Davis, 1998). Subsequent T-jump studies identified this endothermic force generation step as a molecular step before the rapid Pi release (i.e. a transition between two AM.ADP.Pi states) in isometric muscle fibres (Ranatunga, 1999a). This is in agreement with the conclusion reached using other perturbations on muscle fibres (Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992) and on myofibrils (Tesi et al. 2000) that the force generation occurs prior to Pi release by cycling crossbridges. However, whether this unified thesis would be sustained when the ATPase cycle is perturbed in other ways (e.g. increased [MgADP]) remains unknown.
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It is known that MgADP is a product released later in the AM-ATPase cycle; it binds to nucleotide-free (AM) crossbridges, potentiates active force (Cooke & Pate, 1985; Fortune et al. 1989; Dantzig et al. 1991; Lu et al. 1993), decreases maximum shortening velocity and ATPase rate in muscle fibres (Cooke & Pate, 1985; Pate & Cooke, 1989a,b; He et al. 1997; Seow & Ford, 1997; Morris et al. 2003) and in myofibrils (Tesi et al. 1999). However, MgADP effects on endothermic force generation are not known, although such data would be essential for the development of a more complete kinetic model. These were the aims of our study, and they also enable us to address some discrepancies (see above) that remain unresolved among the different T-jump studies.
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Thus, we have examined in single psoas fibres: the force generation induced by a small rapid (0.2 ms) T-jump, force responses to small rapid length steps, and active force and shortening velocity at different temperatures (range 5–30°C) when the [MgADP] was increased, and used a five-step kinetic model to qualitatively simulate some of the findings. Preliminary data from this study have been reported in abstract form (Ranatunga & Coupland, 2003a; Coupland & Ranatunga, 2004).
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Methods
Fibre preparation and solutions
Adult male rabbits were killed by an intravenous injection of an overdose of sodium pentobarbitone, and other tissues were harvested for different experiments by other researchers. Fibre bundles from the psoas muscle were prepared and chemically skinned using 0.5% Brij 58, as previously described (Fortune et al. 1989). Control buffer solutions (with no MgADP) contained 10 mM glycerol 2-phosphate (a temperature-insensitive pH buffer; pH 7.1), 4.6 mM MgATP, 12 mM creatine phosphate, 15 mM EGTA (relaxing solution), CaEGTA (activating solution) or HDTA (preactivating solution), 9 mM glutathione and 50 mM potassium acetate. The MgADP buffer solutions additionally contained 4 mM MgADP with a reduced potassium acetate concentration (12 mM). The compositions of solutions were calculated using a computer program for solving multiequilibria, maintaining ionic strength (200 mM) and a free [Ca2+] in the activating solutions of 0.032 mM. Solutions with MgADP concentrations lower than 4 mM were obtained by mixing 4 mM ADP buffer solution with the control solution. Adenosine pentaphosphate (100 μM) was added to the solutions containing 0.5 mM MgADP; adenosine pentaphosphate inhibits the myofibrillar adenylate kinase reaction that catalyses ADP to AMP and ATP (Cooke & Pate, 1985; see Dantzig et al. 1991). However, we did not notice significant differences in these experiments when tension was measured with and without adenosine pentaphosphate. Creatine kinase (1–2 mg ml–1) (300 units mg–1; Sigma) was added to control buffer solutions before use to decrease [MgADP], and [MgADP] was assumed to be reduced to 10 μM. All solutions also contained 4% dextran (molecular mass 500 kDa) in order to compress the filament lattice spacing to normal dimensions (Maughan & Godt, 1979).
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Apparatus and laser T-jump technique
Details of the trough assembly, design of the force transducer (natural resonant frequency, 14 kHz), and other aspects of the experimental apparatus have been previously described (Ranatunga, 1996, 1999a; Coupland et al. 2001). Briefly, the trough assembly was mounted on the stage of an optical microscope and, by means of a mechanical lever mechanism, the fibre could be moved and immersed in the different trough solutions. The solution temperature in the front experimental trough was clamped at the desired temperature (5–30°C) using thermo-electric modules (Peltier units) with feedback from a small thermistor and monitored with a thermocouple. In order to maintain fibre stability, the temperature in the other troughs containing relaxing and preactivating solutions was kept at 5°C by cooling fluid circulating through the assembly.
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The principle of the laser T-jump technique is similar to that used by Davis & Harrington (1987), and its details have been previously described (Ranatunga, 1996, 1999a). The temperature of the front (glass) experimental trough was clamped at 8–9°C and the T-jump was induced by a 0.2 ms laser pulse radiation of a standard energy (the maximum pulse energy available was 2 J). The laser pulse, of 6 mm in diameter and circular in cross-section, from a Nd-YAG laser (Schwartz Electro-Optics) passed through a long-focal-length (300 mm) cylindrical lens and entered the experimental trough through the front glass window. The pulse cross-section at the level of the fibre was a horizontal ellipse of 6 mm x 2.5 mm; to prevent extraneous thermal expansion effects, the transducer hooks were shadowed from the laser radiation by Al-flags placed outside the trough window. A laser pulse heated the buffer solution in the trough and the muscle fibre bathed in it; the fibre/heated fluid volume ratio was >2500. The wavelength of the radiation was 1.32 μm, similar to that of the iodine laser used by Davis & Harrington (1987): the water extinction length at this wavelength is 10 mm, so that the pulse radiation passed across the trough solution (3 mm) and was reflected back through the solution by platinum foil that lined the trough back-wall; the characteristics of absorption of laser radiation were such that temperature gradients in the trough solution were small. A small thermocouple placed near the fibre showed that after a laser pulse the elevated solution temperature remained constant for at least 500 ms and decreased only slowly (half-time longer than 5 s) afterwards (see Fig. 1 in Ranatunga, 1996).
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A, a fibre was maximally Ca2+-activated in control solution (no added MgADP) at 9°C and, during the steady tension plateau (pre-T-jump tension), a T-jump of 3°C was induced by a laser pulse (indicated by the arrow). The elevated temperature remained constant for at least 500 ms and decreased slowly afterwards (half-time of decrease >5 s; see Fig. 1 of Ranatunga, 1996). The T-jump induced a tension rise to a new steady level (post-T-jump tension) and the tension rise was fitted with a bi-exponential curve extracting two components, phase 2b and phase 3 (see Methods). B, an identical T-jump was induced when the same fibre was activated in the presence of 4 mM added MgADP. For easy comparison with the control, only the initial 500 ms of a 5 s sweep is shown; the tension reached at 500 ms was >99% of that at 700 ms when the temperature had decreased by 0.1°C. Note that compared with the control, the pre-T-jump tension is higher, but the T-jump-induced tension rise is slower in the presence of 4 mM MgADP, whereas the actual amplitude of the tension rise is similar.
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The outputs of the force transducer, the thermocouple and the motor were monitored on digital cathode ray oscilloscopes and digital voltmeters, and recorded using a PC with a CED 1401 (plus) laboratory interface (Cambridge Design Ltd, UK). In some length step experiments, the position of the first-order He–Ne laser diffraction was also monitored by means of a position detector, and the output of this diffractometer was used only as an index of sarcomere length change during length steps (see Ranatunga et al. 2002). A continuous record of the tension was also made on a chart recorder.
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Experimental protocols and data analysis
Using dark-field illumination on the stage of a binocular microscope, single fibres were dissected under paraffin oil. A short fibre segment was attached using nitrocellulose glue between two metal hooks, one connected to the force transducer and the other to the motor. The sarcomere length was set to 2.5 μm using He–Ne laser diffraction, and the fibre width and length were measured under light microscope; fibre length (L0) was 2 mm in most experiments. Several types of experiment were carried out on a total of 24 fibres, and in a given protocol the final control tension was within 12% of the initial control. The different experimental protocols used are summarized below.
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Laser T-jump experiments. The force transients induced by a standard laser T-jump of 3°C and from an initial temperature of 8–9°C were recorded in each fibre after activation to steady state in control conditions, with different added [MgADP], and finally in control conditions. The force rose to a new steady level after a T-jump, and each tension response was fitted with a double exponential function (FigP, Biosoft), and the rate and the amplitude of the two components were determined. For comparability with previous nomenclature, the two components will be referred to as phase 2b (fast, endothermic force generation) and phase 3 (slow). A very fast tension recovery component (phase 2a) was not clearly discernible in this study; it is observed following length release (see below) and after T-jump – if there is a large thermal expansion producing an apparent length-release effect (see Davis & Harrington, 1993; Ranatunga, 1999b).
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Tension responses to length steps. Some observations were also made in the above experiments on the tension transients induced by small rapid length steps, as in Huxley & Simmons, (1971) type of experiments. These were done at the pre-T-jump temperature (8–9°C) with control activation and with activation in the presence of 4 mM added MgADP. In a given fibre, a length step complete in <0.5 ms and of the same amplitude (0.3–1.4%L0, in different fibres) was applied to one end of the fibre under both conditions and the tension transients were recorded. The tension change at the end of length step (T1) was measured and the quick tension recovery afterwards (T2 or phase 2 recovery, Huxley & Simmons, 1971) was characterized by fitting a bi-exponential function isolating two components, phase 2a (very fast) and phase 2b as in our previous study (see Ranatunga et al. 2002).
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[MgADP] on isometric tension at different temperatures. This was examined at a range of added [MgADP]. Many experiments were done at 10°C, but data were also obtained at other temperatures, particularly with and without 4 mM added MgADP. After at least 5 min in relaxing solution, the fibre was transferred to preactivating solution (5 min) before being activated and, soon after maximal tension was reached, the fibre was transferred back to the relaxing solution. The relaxing, preactivating and activating solutions all contained the same added [MgADP].
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[MgADP] on shortening velocity. In a few control experiments, the ‘slack test’ method (Edman, 1979) was used to determine the unloaded shortening velocity (Vu) in fibres that were activated in control solutions and in the presence of 4 mM MgADP. The fibre was shortened using length releases (90% step complete in <1 ms) that were sufficiently large to reduce the fibre tension to zero when applied on the plateau of steady maximal tension. The duration of unloaded shortening from the start of the length release until tension redevelopment was measured, and Vu was estimated from the slope of plot of length change versus duration of unloaded shortening. The Vu determined from three fibres in control solutions and three fibres in the presence of 4 mM MgADP clearly showed that Vu was decreased with added [MgADP], as reported in previous studies (see Introduction).
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Based on the aforementioned experiments, and in order to obtain data from the same fibre at different MgADP levels, we examined the duration of unloaded shortening following a standard length release (5–10%L0 in different fibres) applied on the tension plateau. In each fibre, measurements were made in control solutions and in the presence of different concentrations of added MgADP using the same length step amplitude, and the length step amplitude divided by the duration of the slack period was taken as the Vu. This measurement from a single length step would overestimate the shortening velocity since the intercept on the length axis is not allowed for; nevertheless, it was considered adequate for comparative purposes.
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Some general considerations and uncertainties
(1) During an experiment, a muscle fibre was regularly examined under the microscope and data discarded if there was evidence of development of fibre damage. However, routine continuous monitoring of sarcomere length or its clamping was not made in the present experiments, and hence there is uncertainty, particularly at high temperatures, as to what extent our data were affected by the development of sarcomere nonuniformities. (2) As emphasized in previous studies (see Cooke & Pate, 1985, Pate & Cooke, 1989a), there are difficulties involved in quantitative analyses in muscle fibres of the effects of products (MgADP and Pi) of AM-ATPase cycle due to their generation after activation and accumulation from diffusion-limited equilibration with the bathing solution. We assumed that, under control conditions (i.e. with creatine phosphokinase plus creatine phosphate present), [MgADP] is low (10 μM) and [MgATP] remains constant at 4 mM. Using the principles of the calculations made by Pate & Cooke(1989a), we previously noted that the [Pi] within an active fibre at 10°C would rise to 0.5–0.7 mM at steady state under control conditions and to higher values as the temperature is raised (Coupland et al. 2001). With increased [MgADP] (i.e. with no creatine phosphokinase present), [MgADP] would rise and [MgATP] would fall after activation (Cooke & Pate, 1985); Cooke & Pate (1985) noted that 0.9 mM[MgADP] would be generated at steady state at 10°C, and it is likely to be higher at raised temperatures. However, three further observations are noteworthy. Firstly, comparison with data from intact fibres, in which contractions are brief and electrically evoked, provides some validity of the control observations. Secondly, experiments of He et al. (1997) show that 50–70% of isometric force is developed in the first turnover of the cycle (i.e. before any MgADP is released), and hence [MgADP] as calculated for steady-state accumulation may overestimate its increase when steady force is measured briefly after activation. Thirdly, important meaningful and detailed data have been obtained in muscle fibre studies using similar procedures to ours (see Zhao & Kawai, 1994). Nevertheless, the uncertainties regarding the [MgADP] level within fibres under different conditions restrict our discussions to the differences seen between the control and 4 mM added [MgADP] rather than the quantitative concentration dependence of the effects.
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Simulating T-jump transients and isometric tension behaviour
To qualitatively model our findings, we used a minimal five-step scheme for the crossbridge/AM-ATPase cycle (Scheme 1) which is an extension of the three-step scheme used previously. A number of previous studies by different groups, and using different techniques, proposed that the crossbridge force generation occurs prior to rapid Pi release by cycling crossbridges in muscle (Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992; He et al. 1997). By making the rate of (pre-Pi-release) force generation temperature sensitive (endothermic), the scheme could also account for the Pi effects on T-jump-induced tension transients (Ranatunga, 1999a) and Pi effects on steady force at different temperatures (Coupland et al. 2001). In a detailed examination of mechanokinetic models, Smith & Sleep (2004) indeed ruled out the alternative possibility that force generation follows Pi release, although they preferred a case where a fast force generation step is followed by a slow Pi release. In so far that they did not identify a specific temperature-sensitive step, however, we have retained the original case where the force generation step is followed by a rapid Pi release.
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Thus, the forward rate constant of step 1 (k+1) is a moderately fast (20 s–1 at 10–15°C) temperature-sensitive (endothermic) force generation, whereas the reverse rate constant (k–1, 120 s–1) is not temperature sensitive. Increasing the forward rate constant k+1 with a Q10 of 4, corresponding to an activation enthalpy of 100 kJ K–1, simulates temperature effects. Step 2 is rapid Pi release, where k+2 is set as 0.8 x 103 s–1 and altering k–2 simulates [Pi] changes; the range of k–2 values corresponds to a second-order rate constant of 1.4 x 105M–1 s–1 for Pi binding in step 2 (similar to Dantzig et al. 1992 and Gutfreund & Ranatunga, 1999). Steps 3 and 4 represent the slow two-step ADP release: k+3/k–3 was forward biased and set at 15 s–1/5 s–1 to fit the data distribution in the present study (see discussion). k+4 was set low (2 s–1), and changing k–4 simulates [MgADP] changes; the values of k–4 used for control correspond to a second-order rate constant for ADP binding of 2 x 105M–1 s–1 which is similar to the values used in other studies (Dantzig et al. 1991). Step 5 is irreversible and includes all the steps after ADP release that are necessary to reprime a crossbridge for the next cycle. The overall rate in this route is low (k+5, 10 s–1), probably limited by the M.ATP M.ADP.Pi cleavage step after detachment (see He et al. 2000) which is not separately identified in our scheme, but the initial AM-dissociation step per se would be fast in the presence of millimolar levels of MgATP (>1000 s–1, see Goldman et al. 1984; He et al. 2000). Thus, although AM is a strongly bound state, [AM] as such was considered small, and hence its occupancy was not included for the calculation of force; moreover, He et al. (2000) considered the force per AM state to be small. Also, the effect of inclusion of this state can be inferred from its occupancy changes shown in Fig. 9B. According to the scheme, states II, III and IV (AM*.ADP.Pi, AM*ADP and AM*'.ADP) are equal-force-bearing states (F) and the sum of their fractional occupancy is taken as force.
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A, Arrhenius plots of the two rate constants of the model (see Scheme 1) that were increased to simulate temperature effects. The rate of the force generation step (k+1) increased markedly (see Zhao & Kawai, 1994; Q104) and that of ADP-release step (k+4) slightly (Q10 of 1.3). The symbols show values for a selected number of temperatures. Note that the marked temperature sensitivity of k+1 implies that it would not be very much slower than inorganic phosphate (Pi) release (see Methods) at high temperatures. B, the fractional occupancy of the five states under control conditions (low [MgADP]10 μM and 0.5 mM Pi) calculated for a selected number of temperatures, and plotted against reciprocal absolute temperature. Open symbols show states (V and I) that do not contribute to force (, AM + M.ATP + M.ADP.Pi that are not separately identified in the model; and , AM.ADP.Pi, the pre-force-generating state). Note the dominance of pre-force-generating state (AM.ADP.Pi) at the low temperatures (e.g. 10°C), and the decrease of its occupancy with warming. Filled symbols represent force-bearing states (, AM*.ADP.Pi; , AM*.ADP; and , AM*'.ADP); note the increased occupancy of AM.ADP (post-power stroke) states as the temperature is raised. For any temperature, the sum of the occupancies of the five states is 1. C, filled circles show simulated, steady-state (at 1–2 s) tension (as the sum of the fractional occupancies of states II, III and IV) under control conditions (0.5 mM Pi and 10 μM ADP) at 5°C intervals. Note the approximate sigmoidal relation with half-maximal at 10–12°C, as found experimentally; force at 0°C is 20%. If force is determined at short intervals after large T-jumps to a high temperature, the apparent saturation of force at high temperature is reduced (crosses and dotted line). Open diamonds with dashed curve show that with simulated 4 mM[MgADP] (k–4 set to a higher value), the sigmoidal relation is shifted to the right (compare with Fig. 7A).
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The linear kinetic Scheme 1 was solved by the matrix method using Mathcad 2000 software (Mathsoft), as previously described (Gutfreund & Ranatunga, 1999); it gives results in the form of apparent rate constants (reciprocal relaxation times) and amplitudes for the sum of exponentials representing the formation and decay of each of the states in the system. After a steady state is reached, the method can be used to simulate a relaxation phenomenon by changing the rate constant of the step(s) appropriately (e.g. increasing k+1 with a Q10 of 4 and k+4 with a Q10 of 1.3 for a T-jump in the present study) and the approach to the new steady state obtained. Although a perturbation of a five-step system yields five rate constants, their values were such that only three were practically useful, with values ranging from >10–2 s–1 to <103 s–1. Of these three, two rate constants were small (slow), similar and could be combined, so that a T-jump-induced tension rise is effectively characterized by two rates: a fast rate and a (combined) slow rate as in the experiments. For calculation of the steady tensions at a new steady state, the occupancies of the states were determined 1–2 s after a perturbation.
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For clarity in the presentation, the first section in the Results presents the experimental data, where tension or force in Figs 1–8 refers to the measured values from muscle fibres. The second section in the Results, with Figs 9–12, contains the model simulations where tension or force refers to the sum of the fractional occupancies of the three force-bearing states without normalization to any experimental measurement.
Results
, http://www.100md.com Experimental data
T-jump induced (endothermic) force generation. In experiments on five muscle fibres, we examined the effect of [MgADP] on the force generation induced by a standard laser T-jump of 3°C applied during the tension plateau after maximal Ca2+ activation at 8–9°C; Fig. 1A shows the tension response induced by a T-jump in control activation (no added MgADP); as found in previous studies, the tension rose to a new steady level following a T-jump, and the tension trace could be fitted with a bi-exponential function (drawn through the trace). Figure 1B shows from the same fibre the tension response after activation in the presence of 4 mM added MgADP and it is qualitatively similar to the control. It is seen, however, that compared to the control, the tension before the T-jump is higher but the T-jump-induced tension rise to a new level is slower with increased [MgADP].
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In each fibre experiment, a tension transient to the same T-jump was recorded with control activation and with separate activations in the presence of different levels of MgADP and finally with a control activation. Figure 2 shows the pooled data (mean ±S.E.M.) for the steady active tension measured before the T-jump (8–9°C, open symbols) and after the T-jump (11–12°C, filled symbols) plotted against added [MgADP], where the tensions are normalized to the first pre-T-jump control tension in each fibre. The data show that the both pre- and post-T-jump tension is potentiated by 20% with increase of [MgADP] to 4 mM MgADP.
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Pooled (means ±S.E.M.) tension data are shown for different [MgADP] from five fibres that were maximally Ca2+-activated at 8–9°C () and a T-jump induced; a full data set was obtained from each fibre. The new steady tension data at the elevated temperature of 11–12°C (post-T-jump) are shown by . Tensions are given as ratios of the pre-T-jump tension of the first control (i.e. with no added MgADP) in each fibre. A hyperbolic curve was fitted to each pooled data set. Note that the active tension is increased by about 20% with 4 mM MgADP at both pre- and post-T-jump temperatures. The T-jump increased force by 6% per degree Celsius.
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In Fig. 3, the rates and the amplitudes of the two exponential components derived by curve fitting to the T-jump-induced tension responses (as in Fig. 1) are plotted against added [MgADP]. The rate of endothermic force generation (phase 2b, filled symbols in Fig. 3A) decreased towards a lower level as [MgADP] was increased; a hyperbolic curve was fitted to the pooled individual data for phase 2b rate and it gave a maximum rate of 40 s–1, a minimum of 16 s–1 and 50% decrease at [MgADP] of 0.5 mM. The rate of the slower phase (phase 3) was relatively insensitive to or only slightly decreased with increased [MgADP]. As shown in Fig. 3B, the amplitudes of the two components (normalized to post-T-jump tension) remained similar at different [MgADP] and showed no significant correlation with increased [MgADP] (P > 0.05).
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The tension responses induced by standard T-jumps in control conditions (no added MgADP) and at a range of added [MgADP] were analysed by curve fitting as shown in Fig. 1. A, the mean (±S.E.M.) rate constants (reciprocal time constant) from five fibres are plotted against different [MgADP]. Filled symbols show data for endothermic force generation (phase 2b). A hyperbolic curve was fitted to the pooled individual data for phase 2b gives a maximum rate of 40 s–1, a minimum of 16 s–1 and half-maximal effect at 0.5 mM[MgADP]. Open symbols represent data for the slow phase 3, and show relative insensitivity (or slight decrease) to [MgADP]. B, the amplitudes of the two exponential components (fast phase 2b, filled symbols; slow phase 3, open symbols) are plotted against [MgADP]; the amplitudes of phase 2b and 3 show minimal sensitivity to [MgADP].
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Tension responses to length steps and stiffness estimates. In the aforementioned experiments, the tension responses to 2–4 small length steps per fibre (<1.4%L0 complete in <0.5 ms) were also recorded at 8–10°C, and they were analysed to obtain estimates of fibre stiffness. Figure 4A shows, from a fibre in control activation, the tension responses (top panel) that were elicited when two length steps (bottom panel) were applied to one end of the fibre. As is well known (Huxley & Simmons, 1971), the tension reaches a peak at the end of a length step (T1), but then recovers quickly to T2, which is only partial recovery towards the pre-length step tension level (T0); the tension change (i.e. T1–T0 from a stretch and T0–T1 from a release) divided by the length step amplitude (L) was taken as stiffness. In order to pool the data from different fibres, this ratio was normalized to L0 and control T0. Figure 4B shows records from a fibre activated in the presence of 4 mM MgADP; it can be seen that the initial quick tension recovery is slower than under control conditions, even though the length step amplitude is larger. The quick tension recovery (T1 to T2 phase of the tension transient) was fitted with a double exponential function isolating phase 2a (very fast) and phase 2b; such fitted curves are drawn through the tension traces in Fig. 4.
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A, a fibre was activated to steady state in control solution and a length-release and a length-stretch step of the same amplitude (0.25%L0) was applied; the resultant tension responses are shown on the top panel. A length step was complete in <0.5 ms; the position of the first-order He–Ne laser diffraction for release only, shown in the middle panel (in arbitrary units), indicates sarcomere length shortening induced by the fibre-length release. Temperature 9°C. B, sample traces from an experiment on another fibre, activated in the presence of 4 mM added MgADP, where the length step amplitude was 0.9%L0. The diffractometer signals in the middle panel indicate sarcomere length changes, but the slow oscillations in them are probably artefacts. Note that the tension recovery is slower with MgADP. Temperature 10°C. In each tension response, the tension reaches a peak (T1) at the end of a length step and then quickly but partially recovers to a level referred to as T2 (Huxley & Simmons, 1971). The peak tension change (T) due to a length step (L) was measured as T1–T0 for stretch and T0–T1 for release (T0, steady tension before length step) and stiffness calculated as (T/L); in order to pool the data from different fibres, L was normalized to L0 and T normalized to control T0. The initial rapid tension recovery after length-step (Huxley–Simmons phase 2 or T1–T2 recovery; Huxley & Simmons, 1971) was characterized by fitting a bi-exponential curve isolating two components referred to as phase 2a (very fast) and phase 2b; a curve is drawn through each trace.
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Figure 5A shows, in the form of histograms, the pooled data from three fibres in each of which stiffness estimates were made using the same lengthstep amplitude both in the control and in the presence of 4 mM added MgADP; the length step amplitudes used, however, were different in different fibres. The histograms on the left show that, compared with the control (open column), the steady tension was potentiated 20% with MgADP. Histograms on the right show the mean (±S.E.M.) stiffness ratios (calculated as above): the ratio is 163 (±17.8, n= 8) for the control and it is higher, 171 (±15.5, n= 8), with MgADP, but the difference is not significant (paired t test, P > 0.05). Thus, the increase of force by 4 mM MgADP is not due to a concomitant increase of stiffness.
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A, data from three fibres in each of which the tension responses to 2–4 stretch and release steps of the same amplitude (0.3–1.3%L0, in different fibres) were examined under control conditions (open columns) and in the presence of added 4 mM MgADP (double hatched columns). The columns on the left show (MgADP/control) percentage tension ratios; tension in the presence of ADP is 20% higher. The columns on the right show the mean (±S.E.M., n= 8) stiffness from the fibres (see Fig. 4 legend), normalized to L0 and control T0 of each fibre; the slightly higher stiffness with ADP (178 ± 15.5 T0/L0) is not significantly different (paired t test, P > 0.05) from control stiffness (163 ± 17.8 T0/L0). Thus, the tension potentiation by MgADP is not associated with a corresponding increase of stiffness. B, pooled data for the reciprocal time constants of the two exponential components (phase 2a, squares; phase 2b, circles) isolated by curve fitting to the initial tension recovery after a length step; they are plotted on a logarithmic ordinate against the length step amplitude as percentage L0. Data are from five fibres in three of which data were obtained both in control (filled symbols) and with 4 mM added MgADP (open symbols); each fibre contributed data for release and stretch. The lines are the calculated regressions, significant (P < 0.05) only for the control data (continuous lines). Despite the scatter, the rates with added ADP are, on average, lower particularly with length releases.
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Figure 5B is a plot of the pooled rate-constant data (reciprocal time constants) for phase 2a (squares) and phase 2b (circles), isolated by curve fitting to the initial tension recovery after a length step as shown in Fig. 4; the data are plotted on a logarithmic ordinate against the length step amplitude. The data are from five fibres, in three of which data were available in both control and added MgADP conditions, whereas, in the other two fibres, data were obtained only in control or with MgADP (n= 16 for control (filled symbols); n= 10 with 4 mM added MgADP (open symbols)); each fibre contributes data to length release and stretch. There is considerable scatter, but the control data do show the general trends expected (see Fig. 2 of Ranatunga et al. 2002), and also that the tension recovery is slower in the presence of MgADP, particularly with releases. Paired comparison of the control versus MgADP data from three fibres, where data were available under both conditions and with the same length steps, showed significant difference (P < 0.05) for phase 2a (from release) and phase 2b (from release and stretch).
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Isometric force at different temperatures. In a number of experiments at 5, 10, 20, 25 and 30°C, the active tension was measured in fibres that were activated in control conditions and in the presence of different [MgADP] forming a series, followed by a final control contraction. Quantitative analyses, however, were difficult (and probably not meaningful) since the exact [MgADP] in contracting fibres remained unknown (see Methods). Nevertheless, the data showed that the MgADP/control tension ratio increased (and saturated) as the [MgADP] increased up to 4 mM, basically as in Fig. 2. Additionally, the tension ratio at the high MgADP level (4 mM) was larger at the lower temperatures. To examine this further, control and with 4 mM MgADP contractions were recorded in individual fibres at different temperatures.
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Figure 6 shows superimposed tension traces from a muscle fibre that was activated in control solution and in solution containing 4 mM added MgADP at 5, 10 and 20°C. As reported in previous studies (Coupland et al. 2001 and references therein), the control tension (the lower tension trace in each frame) is markedly larger at the higher temperatures. The records also show that the tension is potentiated in the presence of MgADP (upper trace) as reported in previous studies (see Introduction), and it is seen at all the temperatures. In this particular experiment, the potentiation of the steady active tension with 4 mM added MgADP is 22% at 5°C whereas it is decreased to 6% at 20°C, which is indeed lower than in the pooled data (see below) showing the variability among fibres. The decrease in relative potentiation is largely due to the increase of control tension when the temperature is raised (i.e. endothermic nature of muscle force).
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Three pairs of tension traces from the same fibre show activations at 5, 10 and 20°C in control solution (lower trace in each panel) and with 4 mm added ADP (upper trace). The tension traces in each pair have been aligned so that the onset of activation is superimposed. Control steady tension is higher and the tension rise is faster at the higher temperatures. Tension in the presence of 4 mm added MgADP is greater compared with control at all temperatures; the potentiating effect of MgADP however, becomes less marked as temperature is increased. The horizontal time bar beneath the tension records is 2 s.
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Figure 7 shows the pooled data from experiments on a total of 18 fibres in which tension was measured in control conditions and with 4 mM added MgADP. Figure 7A shows mean (±S.E.M.) tension normalized to fibre cross-sectional area plotted against the reciprocal absolute temperature. The tension versus reciprocal temperature (1/T) relation in control solutions (open symbols and continuous curve) is sigmoidal with a half-maximal tension at 12°C, in basic agreement with our previous findings. In the presence of 4 mM MgADP (filled symbols and dashed curve), a sigmoidal plot is obtained but it is shifted upward along the tension axis and to the right (to lower temperatures; half-maximal at 10°C). Figure 7B shows data from the same experiments where the tension measured in solutions containing 4 mM MgADP has been expressed as a ratio of control tension at each temperature and mean (±S.E.M.) shown as histograms against the reciprocal absolute temperature. Compared with the controls, the tension with increased [MgADP] was significantly higher (P < 0.01, paired sample t test) at all temperatures except 30°C. Thus, the potentiating effect of 4 mM MgADP was most marked at 5°C, where mean (±S.E.M.) MgADP/control tension ratio was 1.25 (±0.05) and it decreased to 1.10 at 30°C. The differences in tension ratios between 5 and 20°C, and between 5 and 30°C, were significant (P < 0.05, one-way ANOVA).
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Pooled data from a total of 18 different fibres where tension was measured in control solution and with 4 mm added MgADP at one or more temperatures. At the end of the experiment, mean (±S.E.M.) control tension in these fibres was 0.96 (±0.01) of the initial control tension. A, active tensions measured in control (open symbols) and with added 4 mm MgADP (filled symbols) solutions are plotted as mean (±S.E.M.) specific tension (in kN m–2) against reciprocal absolute temperature (as 103 K/T), also labelled in degrees Celsius. The sigmoidal curve fitted to the control data corresponds to half-maximal tension at 12°C, but the curve is shifted to a slightly lower temperature with MgADP; half-maximal tension from the curve occurs at 10°C. The tension with 4 mm MgADP was significantly greater (P < 0.01) than the controls at 5, 10 and 20°C. B, the data shown in A were normalized, so that tension measured in solutions containing 4 mm MgADP is shown as a ratio of control tension (indicated by the horizontal dashed line) in each fibre and plotted against reciprocal absolute temperature. Data were obtained from 4 different fibres at 5°C, 13 fibres at 10°C, 8 fibres at 20°C and 3 fibres at 30°C. Note that, although there was considerable variability in the ratio, the MgADP/control tension ratio obtained at 5°C is significantly greater than the ratios at 20 and 30°C.
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Shortening velocity and rate of tension redevelopment. In order to obtain shortening velocity data from the same fibre at different [MgADP], the tension response to a large length release of constant amplitude was examined and the length step amplitude divided by the duration of unloaded shortening was taken as a measure of the maximum shortening velocity; this is clearly not an accurate estimate of the Vu since the method ignores the intercept on the length axis. Typical tension records from a fibre activated at 10°C in control and with a series of different levels of added MgADP are shown in Fig. 8A. The traces show that as [MgADP] was increased, so the duration of unloaded shortening increased and the rate of tension redevelopment decreased. This is also shown in the data from different fibres at other temperatures in Fig 8B and C. Figure 8B shows that the control shortening velocity (with no added MgADP) increases markedly with increase of temperature, as obtained in intact rat muscle experiments (Ranatunga, 1984). Although quantitative analysis is difficult since the exact [MgADP] within the fibres is unknown, the data also show that the shortening velocity decreases with increased [MgADP] at all the temperatures; the (4 mM MgADP)/control velocity ratios ranged from 0.41 to 0.6 at 20–30°C and from 0.44 to 0.72 at 5–10°C. Figure 8C shows data for the rate of tension redevelopment (reciprocal of the half-time of tension redevelopment to steady level) following a length release at different temperatures; the control rate of tension rise is markedly increased at higher temperatures, as found in intact muscle experiments (Ranatunga, 1984) and, like shortening velocity, it is decreased with increased [MgADP] at all the temperatures.
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A, superimposed tension records (upper panel) from a maximally activated single fibre in solutions containing 0, 0.5, 1, 2 and 4 mM added MgADP at 10°C. The initial part of the traces shows that isometric tension is higher with higher [MgADP] and, following a length release (amplitude 14%L0) is a slack period and tension redevelopment. For clarity, only a single length record is shown in the lower panel. Note that the slack period (duration of unloaded shortening) increases with increasing [MgADP] and the force redevelopment becomes slower. Length step amplitude/duration of unloaded shortening was taken as shortening velocity. B, data from 4 different fibres (two of which were tested at two different temperatures) are shown where shortening velocity (as L0 s–1) is plotted against added [MgADP] for 30°C (stars), 20°C (triangles), 10°C (filled circles, representing fibre shown in A) and 5°C (diamonds). C, data for rate of tension redevelopment (reciprocal half-time for tension rise) from experiments at 20, 10 and 5°C from the same fibres presented in B. For clarity, the data obtained at 30°C are not shown as the data points were overlaying data at 20°C. Note that the shortening velocity and the rate of tension rise in control conditions (plotted at zero [MgADP]) are markedly increased at the higher temperatures, as found in intact rat muscle experiments (Ranatunga, 1984).
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Simulations of temperature and [MgADP] effects on muscle force
Temperature-dependent changes in occupancy and steady force. Scheme 1 (see Methods) was used in the simulations and, as shown in Fig. 9A, temperature increase was simulated by a marked increase of the rate constant k+1 (force generation, Q10 of 4) and a small increase in step k+4 (Q10 of 1.32), since there is evidence that ADP release itself is temperature sensitive (Siemankowski et al. 1985); increase of k+4, however, was not absolutely necessary to obtain the main findings. Figure 9B shows the steady-state (1 s) occupancy of the five states in the scheme as the temperature is simulated to rise from 0 to 35°C. The calculated fractional occupancy of each of the five states, for control conditions (10 μM[MgADP] and 0.5 mM Pi) and for a selected number of temperatures, is plotted against reciprocal absolute temperature; note that the sum of fractional occupancies of all five states for any temperature is one. Open circles represent occupancy of state V, labelled as [AM] in the scheme so as to discretely identify the ADP-release/ATP-binding step; with millimolar levels of MgATP, however, AM dissociation would be fast and, hence this represents M.ATP + M.ADP.Pi (and AM) states that are not separately identified in the model. Open squares represent state I, i.e. the pre-force generating AM.ADP.Pi state and it predominates at the low temperatures (e.g. 10°C) but its occupancy decreases markedly with warming. Filled symbols represent states II, III and IV (AM*.ADP.Pi, AM*.ADP and AM*'.ADP) in the scheme, each assumed to bear equal force, and the plots show a marked increase in the occupancies of AM.ADP (post-power stroke) states as the temperature is raised.
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The sum of the occupancies of states II, III and IV at 1 s was taken as steady tension (force). Figure 9C (filled circles) shows the simulated control steady-state tension plotted against reciprocal absolute temperature. Tension distribution approximates sigmoidal relation with half-maximal at 10–12°C, as found experimentally. The results obtained from modelling the effects of 4 mM MgADP on steady-state tension at different temperatures are shown by the open symbols in Fig. 9B. Within a temperature range of 0–40°C, the approximate sigmoidal relation is shifted upwards along the tension axis and slightly to the right with 4 mM added ADP – as found in the experiments (Fig. 7A). With added Pi, simulation showed that the relation is shifted to the left (to higher temperatures – not shown) as found in our previous study (Coupland et al. 2001). The dotted curve in Fig. 9C shows (under control conditions) that, if tension measurements were made early after large T-jumps from low starting temperature, the apparent ‘steady’ tension continues to rise at higher temperatures (see below). It is interesting to note that the simulated tension responses (Fig. 11A) with T-jumps reaching high temperatures (e.g. 30, 35°C) indicate slow tension decay after the initial rapid rise.
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T-jumps were simulated under control conditions and the tension rise determined basically as in Fig. 10 (i.e. change with time of the sum of the fractional occupancies of states II, III and IV in Scheme 1 represents the tension rise). A, T-jumps of different amplitudes (as labelled), increasing up to 35°C, were modelled from the same starting temperature of 0°C; both the amplitude and the rate of the T-jump-induced tension rise increase with increase of post-T-jump temperature. Note the qualitative similarity of the transients to those in the experiments of Bershitsky & Tsaturyan (2002) who used large T-jumps from low starting temperatures. The modelled tension responses at high temperatures (e.g. 30 and 35°C), however, showed that the tension decreases slowly after the initial rapid rise so that, if tension is measured at 50–100 ms after large T-jumps, the tension versus temperature relation may not be sigmoidal, nor would it show saturation at high temperatures (see Fig. 9C). B, T-jumps of constant amplitude (5°C) from different starting temperatures of 0–30°C (post-T-jump temperature is labelled); the system was allowed to reach steady state at each temperature before a T-jump was simulated. The rate of rise of the simulated tension response increases with (pre- or post-T-jump) temperature, but its amplitude initially increases and then decreases as the starting temperature is increased (>15°C); since the pre-T-jump tension (the tension at zero time for each trace) increases with warming, the tension amplitude per 5°C T-jump decreases with increase of starting temperature (see Goldman et al. 1987). Note the qualitative similarity of these simulated tension responses to the experimental responses of Coupland et al. (2001) where the traces in Fig. 1A were obtained by adopting a similar methodology.
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Simulated T-jump tension responses; effects of MgADP and Pi. Figure 10A shows simulated tension responses induced by a standard T-jump at 9°C under control conditions (continuous trace) and with 4 mM[MgADP] (dashed trace). The two traces are vertically shifted for superimposition to show that they have similar amplitudes, but the tension rise was slower with 4 mM MgADP, as found experimentally (see Fig. 1). Two component rates (one fast and two combined slow) characterize the tension rise. Examination of these data showed that the MgADP-induced decrease of the rate of tension rise after a T-jump is due to an increase in the amplitude of the combined slower component coupled with a concomitant decrease in the amplitude of the fast component as [MgADP] is increased; analyses by curve fitting (as in Fig. 1) probably cannot distinguish between the two cases when the underlying rates are not very different (10 s–1 compared with 20–40 s–1, see Fig. 3). Figure 10B shows the steady tension before (crosses) and after (circles) T-jumps at a range of [MgADP], where [MgADP] is plotted on a logarithmic axis; the tension is potentiated by 20% at 4 mM[MgADP], with a half-maximal effect at <1 mM[MgADP], as in the experiments.
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A, superimposed tension transients induced by a 3°C standard T-jump at a starting temperature of 9°C, in control activation (continuous curve) and in the presence of 4 mM MgADP (dashed curve). A T-jump was simulated by re-setting k+1 and k+4 to higher values (Q10 values of 4 and 1.3, respectively) and [MgADP] changed by altering k–4: change with time of the sum of the fractional occupancies of states II, III and IV (see Scheme 1) represent the tension rise. The tension records have been shifted vertically for superimposition. Note that the tension rise is slower but amplitudes are similar with added MgADP, as found experimentally (see Fig. 1). B, the pre-T-jump (crosses) and the post-T-jump (circles) tensions calculated for a number of [MgADP] levels (on a logarithmic abscissa) are shown by the symbols; they are normalized to the pre-T-jump control (dashed line). Note the qualitative resemblance to the experimental data shown in Fig. 2. C, since previous simulations of Pi effects did not use a model having MgADP release steps, simulated T-jump-induced tension transients in control (continuous curve) and in the presence of 30 mM Pi (dashed curve) from the present model are shown; [Pi] is changed by altering k–2. Note that tension rise is faster with increased Pi (as previously reported: Davis & Rogers, 1995; Ranatunga, 1999a). D, [Pi] dependence of pre- and post-T-jump tensions from simulations – the presentation is similar to B; the half-maximal effect is at 5–10 mM[Pi].
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Since previous simulations did not consider the slow MgADP release steps, we re-examined simulation of Pi effects with the current model and they are shown in Fig. 10C and D. The analysis showed occurrence of two phases (a slow phase was not seen previously, see Ranatunga, 1999a), a higher rate (40 s–1, endothermic force generation) that increased and saturated at higher [Pi] and a combined lower rate (<10 s–1) that decreased with increased [Pi], essentially as found experimentally (see Ranatunga, 1999a). Figure 10D shows the steady tension before (crosses) and after (circles) T-jumps at a range of [Pi]; the tension is depressed markedly with increased [Pi] with a half-maximal effect at 5–10 mM[Pi].
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Simulated T-jumps of different amplitudes and at different temperatures. Figure 11A shows a number of simulated tension responses (under control conditions) induced by T-jumps of different amplitudes that reached the final temperatures as labelled. The simulated tension responses become faster and larger in amplitude with temperature, and they show qualitative similarity to those in the experiments of Bershitsky & Tsaturyan (1992, 2002) who used large T-jumps from a low starting temperature. In laser T-jump experiments, small T-jumps are induced and, to cover a large temperature range, they are made at different starting temperatures. Figure 11B shows simulations of such an experiment, where 5°C T-jumps were simulated at staring temperatures ranging from 0 to 30°C. The tension rise became faster with increase of temperature, but the tension amplitudes were small and they decreased at the high temperature range (>20°C); these bear resemblance to the actual tension traces reported from an experiment by Coupland et al. (2001, see their Fig. 1A).
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The matrix method (see Gutfreund & Ranatunga, 1999) gives the rate constants and amplitudes for the sum of the exponentials representing the time course of the formation and decay of each state of the system after a perturbation, i.e. the tension rise after a T-jump. The simulated tension responses shown in Fig. 11A and B consisted of three components (one fast and two slow; see Methods and figure legend) but, since the two slow component rates were similar, the number of components could be reduced to two by averaging the two slow rates. Figure 12A illustrates temperature dependence of the fast and the (averaged) slow rate constants; the fast rate increases markedly whereas the slow rate shows only a modest increase with temperature (= post-T-jump temperature). Figure 12B shows that with large T-jumps the amplitude of the fast component (filled circles) shows a rapid rise with temperature; the sum of the amplitudes of the two slow components (open circles) was significant below 25°C but decreased at higher temperatures (indeed becomes negative contributing to tension decline at 35°C). With small 5°C T-jumps from different starting temperatures (as in laser T-jump experiments), the rate-constant data were identical to those in Fig. 12A, but the amplitudes were small (<0.15 of total) as shown in Fig. 12C; both amplitudes showed a bell-shape distribution over the temperature range. Also, the amplitudes normalized to tension at pre- or post-T-jump temperature decreased with increased temperature (as found experimentally, Goldman et al. 1987; Davis & Harrington, 1993; Ranatunga, 1996).
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The tension rise induced by T-jumps, as shown in Fig. 11, consisted of three exponential components (see Methods), one fast and two slow, but could be reduced to two by combining the two slow components whose rates were similar; these were available directly from the matrix method used in the simulations (see Gutfreund & Ranatunga, 1999). Their rates and amplitudes (fractional occupancy) were calculated for 5°C intervals and are plotted against reciprocal post-T-jump temperature. A, the rate of the fast component (filled symbols) increases markedly with temperature; the rates of the two slow components, which had similar values (<10 s–1), were averaged and the average slow rate (open symbols) shows only a modest increase with temperature. B, with simulated large T-jumps, the amplitude of the fast component (filled circles) increases sharply with temperature. The sum of the amplitudes of the two slow components (open circles) is prominent at temperatures <25°C, but decreases at higher temperatures (indeed it becomes negative and contributes to a slow tension decline after T-jump to 30–35°C). C, it should be clear that with small T-jumps (5°C) from different starting temperatures (as in Fig. 11B, and in the experimental studies of Goldman et al. 1987; Davis & Rodgers, 1995; Ranatunga, 1996), the rate constant data in A are identical, but the absolute fractional amplitudes would be small. The filled circles (fast) and the open circles (combined slow) show the amplitude data from simulation of such an experiment. In general, the data show that a T-jump-induced tension rise would contain two components, but the biphasic nature of the tension rise would be less clear when large T-jumps from low starting temperatures are examined because of the rapid growth with increased temperature of the fast component. Also, note that the sum of the amplitudes (T-jump-induced change in the fractional occupancies of the three force-bearing states) plus their sum at the pre-T-jump temperature gives the steady force at a given temperature and, hence, the sigmoidal force versus reciprocal temperature relation as shown by the filled symbols in Fig. 9C.
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Discussion
T-jump-induced tension rise: endothermic force generation
At 10°C, a small rapid T-jump (3°C in 0.2 ms) induced a tension rise to a new steady state (Fig. 1); analysis showed that a T-jump-induced tension rise consists of two exponential components, labelled phase 2b (fast) and phase 3 (slow), where phase 2b represents endothermic force generation in attached crossbridges (see Introduction and Methods). The steady active tension was potentiated by 20% when [MgADP] was increased to a level similar to [MgATP], 4–5 mM in our experiments; the binding of MgADP to nucleotide-free crossbridges (AM) leading to accumulation of force-bearing AM-ADP states (Cooke & Pate, 1985; Dantzig et al. 1991; Lu et al. 1993, 2001), in general, may underlie the tension increase. When [MgADP] was increased, the tension rise induced by a T-jump was slower (Figs 1 and 2) indicating that the approach to the new steady state at the post-T-jump temperature was slower. Although a direct comparison is difficult, our data seem comparable to those of Zhao & Kawai (1994) on the effect of MgADP on the exponential process (C) that they identify from sinusoidal length perturbation technique.
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These effects of increased [MgADP] contrast sharply with those produced by increased Pi that is released earlier in the crossbridge cycle; the steady force was decreased with added Pi (Hibberd et al. 1985), but the kinetics of the approach to the new steady state were enhanced – the tension change was faster after a perturbation (e.g. hydrostatic pressure-jump, Fortune et al. 1991; sinusoidal length oscillation, Kawai & Halvorson, 1991; Pi-jump, Dantzig et al. 1992; T-jump, Ranatunga, 1999a). The unified thesis that arose from such different studies was that, kinetically, the force generation precedes rapid release of Pi and both steps are reversible.
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The aforementioned observations validate the identification of two components (labelled phase 2b and phase 3) in a T-jump-induced tension rise obtained experimentally. For example, at 10–12°C, phase 2b was 40–60 s–1 under control conditions and it became faster (120 s–1) with increased Pi (Ranatunga, 1999a), whereas it became slower with increased [MgADP]. On the other hand, the phase 3 was 10 s–1 and had quite different characteristics, being largely insensitive to MgADP and Pi (in simulations it consists of two slow rates that could be combined – see below). Our thesis is that a T-jump-induced tension response effectively consists of two components, where phase 2b represents crossbridge force generation, and the phase 3 relates to subsequent slow step(s) in the cycle (see Davis & Rodgers, 1995; Ranatunga, 1999a). This conclusion is at variance with the findings of Bershitsky & Tsaturyan (2002) (see Introduction) that suggested that a T-jump tension response represents one process. It is noteworthy, though, that our laser T-jumps are small (<5°C) and made on fibres bathed in buffer solution where the post-T-jump temperature decayed very slowly (Ranatunga, 1996), whereas Bershitsky & Tsaturyan (2002) used large T-jumps induced on fibres held in air. Such differences between the T-jump methods and other uncertainties, as also discussed by Bershitsky & Tsaturyan (2002), may have contributed to the observed differences (also see below).
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Tension responses to length steps and stiffness
The limited observations made on the tension responses induced by small, rapid, length steps at 10°C show (Figs 4 and 5) that the increase of force with 4 mM added MgADP is not accompanied by a corresponding increase of stiffness; there was, however, an indication of a small stiffness increase with added MgADP (see Fig. 5A). This compares with the observation that, although the stiffness is reduced by increased [Pi], its reduction is less than the extent of force depression by Pi (Dantzig et al. 1992; also, see Fig. 4A of Ranatunga et al. 2002). A control stiffness of 163 (±17.8) T0/L0 represents the slope of the T1versus length step amplitude plot in Huxley & Simmons (1971) type of analysis, and its reciprocal corresponds to a fibre compliance of 0.61%L0/T0; this would equate to 7.7 nm per half-sarcomere, but it is important to note that we did not directly measure sarcomere length changes and use these only for comparative purposes. Due to the effect of fibre end-compliance, the above value is indeed higher than that (5–6 nm per half-sarcomere) obtained in studies at 6–16°C on several mammalian species under more control conditions (Galler et al. 1996, rat fibres; Tsaturyan et al. 1999, rabbit fibres, Linari et al. 2004, human fibres). Since tension is increased 20% in the presence of 4 mM MgADP, but the stiffness (slope) remains approximately similar, the corresponding compliance value would be higher, 9 nm per half-sarcomere. A change in the opposite direction was observed when active force was depressed with 25 mM Pi, although the actual values were different (see Fig. 2B of Ranatunga et al. 2002). These findings indicate that, to a considerable extent, the force changes induced by increased MgADP and Pi result from redistribution of attached crossbridge states, thus changing the average force per crossbridge. Similar considerations and analyses have shown that the increase of active force by increased temperature is also due to an increase of average force per crossbridge without a significant increase in the fraction of attached heads: indeed, this has been carefully examined and confirmed in several studies on frog (Bershitsky et al. 1997; Tsaturyan et al. 1999; Piazzesi et al. 2003) and rabbit muscle fibres (Bershitsky & Tsaturyan, 1995, 2002). The general validity of these findings is assumed and encompassed in our model (see Scheme 1).
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Phase 2 tension recovery and endothermic force generation
Analyses of the quick tension recovery after a length step (Huxley–Simmons phase 2 or T1–T2 recovery) showed that the tension recovery is slower with increased MgADP; this was particularly so with length releases where both phase 2a and phase 2b rates were significantly lower with 4 mM MgADP (Fig. 5B); phase 2b with MgADP was slower than control both in stretch and in length release. In previous experiments, we noted that both T-jump force generation (Ranatunga, 1999a) and phase 2b tension recovery from stretch (Ranatunga et al. 2002) become faster to a similar extent with increased Pi; it may be argued that the rather fast recovery rates obtained from length releases and scatter in our data prevented us from observing Pi sensitivity of phase 2 tension recovery after length releases (see Fig. 3B of Ranatunga et al. 2002). Thus, although exact experimental proof is lacking, the effects of MgADP and of Pi may be taken to be similar on T-jump force generation and on phase 2 tension recovery (particularly, its phase 2b component) from length steps, both of which are thought to represent the crossbridge force generation process. This notion gains support from the finding that the rate of phase 2 tension recovery from length step is temperature sensitive (Q10 of 2–3, Piazzesi et al. 2003), the temperature sensitivity being greater in phase 2b than in phase 2a component of recovery (Davis & Harrington, 1993; Davis & Epstein, 2003). Thus, like the T-jump force rise, phase 2b tension recovery represents an endothermic process. It is known that the T-jump force generation is much slower than phase 2 tension recovery from length release. However, in the same preparation and at similar temperature, it is faster than phase 2b recovery from stretches (see Table 1 of Ranatunga et al. 2002), indicating that T-jump force rise monitors force generation in crossbridges unstrained by filament sliding (length steps); its rate (phase 2b recovery) would be enhanced in length release and decreased following stretch, due to particular strain dependence of the underlying rate constants (Huxley & Simmons, 1971). Indeed, by extrapolation, the phase 2b recovery rate that corresponds to the isometric point in a length step versus rate of tension recovery plot in experiments on rabbit psoas fibres at 10°C (e.g. Fig. 3B in Ranatunga et al. 2002; and Fig. 5B here) is 40–60 s–1, which is comparable to the rate of endothermic force generation in our T-jump experiments; despite the scatter in them, the data also indicate that this extrapolated ‘isometric phase 2b recovery’ is enhanced with Pi and depressed with MgADP as is T-jump force generation. In general, these observations support the thesis that phase 2 tension recovery after a length step contains a component (phase 2b) that is homologous to the endothermic force generation observed after a rapid T-jump, as originally proposed by Davis & Harrington (1993; see also Davis, 1998).
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Despite the above considerations, however, the data presented from some careful fibre mechanics experiments by Bershitsky & Tsaturyan (2002 and references therein) show absence of interaction between the tension transients induced by large T-jumps and those induced by length steps when one is applied at different times after the other; this indicates that different processes underlie tension responses to T-jump and length steps. In a recent study by Ferenczi et al. (2005), however, a correspondence between the mechanical (and structural) responses to length steps and to T-jumps has been found, and the apparent strain independence of the responses to T-jumps has been attributed to the presence of a preceding temperature-dependent rate-limiting step. Further work is required to resolve these issues.
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The sigmoidal relation between force and temperature
The control isometric force versus reciprocal temperature is sigmoidal (see Fig. 7A) with half-maximal level at 10–12°C, as found in our previous studies on skinned fibres (Coupland et al. 2001) and on intact fibres (Coupland & Ranatunga, 2003). Although the exact concentration effects remain uncertain, our results also show that the tension potentiation with increased [MgADP] is seen at all the temperatures including high physiological temperatures. In so far that the control tension is markedly increased at high temperature, however, the relative potentiation of tension is lower at the higher temperatures (see Fig. 7B). Consequently, the sigmoidal relation between force and reciprocal temperature was shifted to the right (Fig. 7A) with increased MgADP. A shift of the sigmoidal relation to the left (higher temperatures) was observed with increased [Pi] level and was modelled (see Coupland et al. 2001); these indicate that the position of the relation on the temperature axis could vary depending on the concentration of these products.
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Shortening velocity
Biochemical studies on myosin isoforms from a range of muscle types indicate that differences in ADP release rates underlie the differences in their shortening velocities (Weiss et al. 2001; Nyitrai & Geeves, 2004). Thus, ADP release rate may define the increased rate of detachment of crossbridges and velocity during shortening, as suggested from modelling and other studies (see Smith & Geeves, 1995; He et al. 2000). Interestingly, different temperature sensitivities of the rate of ADP release from AM and the rate of ATP induced dissociation of AM (Bottinelli, 2004) indicate that the former may limit maximum shortening velocity at high temperatures (>20°C), whereas the latter process may be limiting at lower temperatures (unpublished data of Professor M. A. Geeves, personal communication). Indeed, the shortening velocity of intact muscles showed a change in temperature sensitivity at high and low temperature ranges (Ranatunga, 1984), which would be consistent with that finding. Our data showed that the shortening velocity was decreased with increased [MgADP] at all the temperatures. Although quantitative analyses are difficult, we calculated the (4 mM MgADP)/control velocity ratios, but the analysis does not clearly indicate a difference between high and low temperatures with respect to MgADP sensitivity of shortening velocity. However, this may be due to the limited number of data (four fibres) and/or because the estimation of shortening velocity was based on measurements using a single length step amplitude; more detailed work would be required to investigate this further.
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Model simulations
As given above, the unified thesis that arose from several different studies was that, kinetically, the crossbridge force generation occurs in a reversible step before rapid release of Pi (a transition between two AM.ADP.Pi states). The simulations we carried out retaining those features but incorporating a subsequent slow two-step MgADP release (see Dantzig et al. 1991; Kawai, 2003) in an otherwise minimal crossbridge/AM-ATPase scheme (Scheme 1), can qualitatively account for our experimental findings. The findings and predictions from the model may be summarized as follows.
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Firstly, the sigmoidal relation between force and reciprocal temperature is qualitatively modelled by making the pre-Pi-release force-generating step highly temperature sensitive (Q10 of 4); although a low temperature sensitivity of MgADP release (Q10 of 1.3) was also used here (see Fig. 9A), it is not essential to model the main findings. The model predicts that pre-force-generating AM.ADP.Pi state is the predominant species at low temperatures (<10°C); this is in general agreement with the findings of Lionne et al. (2002) that showed that such states (e.g. M/AM.ADP.Pi) become significantly populated in myofibrils under a variety of conditions, including low temperature. Its occupancy decreases with increase of temperature so that the force bearing, AM.ADP states predominate at high temperatures (see Fig. 9B). Thus, the underlying basis of the sigmoidal relation is a shift in the distribution of attached crossbridge states from the pre-force to the force-bearing crossbridge states when the temperature is raised (Davis, 1998; Kawai, 2003). As is evident from previous studies (see Bershitsky & Tsaturyan, 1995, 2002; Bershitsky et al. 1997; Piazzesi et al. 2003; Kawai, 2003), the increased isometric force on heating is not due to a concomitant increase in the number of attachments or to a given crossbridge state developing a larger force at high temperatures. Secondly, the exact position of the sigmoidal relation is predicted to be sensitive to the concentrations of the products of ATP hydrolysis; it is shifted to lower temperatures with increased [MgADP] (see Fig. 9C) and to higher temperatures with increased [Pi] (see Coupland et al. 2001). Thirdly, simulation of a small T-jump at 10°C predicts a force rise to a new steady state as found in the experiments. The pre- and post-T-jump force are potentiated and the T-jump-induced tension rise is slower with increased [MgADP]; the pre- and post-T-jump force are decreased and tension rise becomes faster with increased Pi (see Fig. 10). Finally, simulations further showed that a T-jump-induced tension response has three components that could be reduced to two, a fast and a (combined) slow component (see Figs 11 and 12) as obtained in the experiments; their relative amplitudes, however, are temperature dependent, with the slow component being relatively more prominent at the low temperatures. This and the large increase of the fast component may account for not observing a clear biphasic tension response with large T-jumps to high temperatures, as in the experiments of Bershitsky & Tsaturyan (2002); somewhat similar views were expressed also by Davis & Harrington (1993) and Kawai (2003) with respect to large amplitude T-jumps. Our simulated tension responses also indicate that force measurement early after large T-jumps, from low to high temperatures, may not represent the steady-state force (see Fig. 11A), and may lead to a more linear distribution of force against temperature as found experimentally (Bershitsky & Tsaturyan, 1992, 2002).
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It is relevant to note that other studies have indicated (see Zhao & Kawai, 1994) an irreversible forward step between attached crossbridge states after Pi release (step 3 in our scheme above); in our modelling, step 3 was indeed forward biased with k3 of 15 s–1/5 s–1 (but k3 of 5 s–1/0.5 s–1 was adequate). Also, an irreversible step 3 was compatible with modelling temperature effects on control tensions and Pi effects on tension (as found previously, Ranatunga, 1999a); however, making step 3 irreversible failed to account for the temperature-sensitivity of ADP effects in our experiments. It is noteworthy that He et al. (2000) modelled temperature effects on ATP consumption and efficiency in muscle without having such a rate-limiting irreversible step between attached states; reversibility among attached states in the crossbridge cycle, of course, will increase the efficiency in the system (see Davis & Epstein, 2003).
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Muscle performance at physiological temperatures
Accumulation of the products of ATP hydrolysis in active muscle can be an underlying cause of the changes in muscle contraction during fatigue (Dawson et al. 1978). Therefore, it is of some interest to consider the relative magnitude of the effects of MgADP and Pi in muscle fibres at high physiological temperatures. Our previous results (Coupland et al. 2001) showed that, compared with the effects seen at low temperatures at which most fibre studies are made, the effect of Pi on force is considerably reduced at physiological temperatures; the effect of decreased pH was also less marked at physiological temperatures (Ranatunga, 1987; Pate et al. 1989). The present results lead to a similar conclusion with respect to the effect of increased [MgADP] on tension (see Fig. 7B). One reason for this temperature-dependent change in their effects on active muscle force is the finding that the crossbridge force generation is endothermic and it is not directly linked to the release of products of ATP hydrolysis, as suggested by Davis & Rodgers (1995) when they defined ‘de-novo tension generation in muscle’. Thus, the increase of control tension by increase of temperature results in a relative lessening of the effects of the product accumulation on muscle force at the higher temperatures – as compared with low temperatures.
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It is important to note that force is increased 10% with increased [MgADP] at 30°C, but the velocity is decreased 50% (see Figs 7B and 8B) so that, assuming that the curvature of the force–velocity relation is not much altered, the mechanical power (force X velocity) would be reduced to about 55% compared with the control. With increased Pi, the force is decreased (20% with 25 mM Pi at 30°C, Coupland et al. 2001) but the velocity is unaffected (Cooke & Pate, 1985; Pate & Cooke, 1989a,b), which also leads to a reduction in power output to about 80% of the control. It may be argued that the mechanical power (the rate of doing external work) is a better physiological index of a muscle's performance (see He et al. 1999) than isometric force and, the approximate considerations made above suggest, that accumulation of MgADP or Pi would contribute to muscle fatigue due to a reduction in a muscle's power output; such effects of course would be evident in more dynamic muscular exercise rather than in maximal isometric force production – as commonly used in studies on muscle fatigue.
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Conclusion – unresolved issues
The present study addressed the endothermic characteristics of active muscle force and used a kinetic model with a minimal AM-ATPase pathway that qualitatively accounted for the main findings; the model was simplistic and did not have strain-sensitive features necessary to account for shortening velocity, length step transients, etc. According to current thinking, the closed–open conformation change of the actin-attached myosin head (crossbridge), leading to lever arm movement, underlies muscle force generation Geeves & Holmes (1999). Our data suggest that this occurs in an early step, between two AM.ADP.Pi states; it is particularly temperature sensitive and endothermic. According to the model proposed by Davis & Rodgers (1995), however, the endothermic force generation step is a transition between two AM.ADP states, i.e. after the release of Pi. In a recent study on structure–function correlation of the crossbridge (myosin motor) in muscle, Ferenczi et al. (2005) indeed propose a more complex model where (endothermic) force generation involves two steps: a change in actin-binding characteristics that leads to the lever arm movement. Resolution of these different ideas would require further study.
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Wang & Kawai (2001) have discussed how endothermic (+entropic) events in the crossbridge leading to force generation may be produced on the basis of the known crystallographic structures of myosin and actin. However, studies on myosin-ATPase in solution (see Millar et al. 1987 and references therein) have shown, in particular, that the ATP cleavage step (i.e. in detached crossbridges in fibres) is endothermic (H=+65 kJ mol–1). If a step between detached crossbridge states (only) is particularly temperature sensitive, a latency would be expected before the tension rise induced by a T-jump in active muscle fibres, but no such latency has been observed. Moreover, more recent studies of Werner et al. (1999) and Malnasi-Csizmadia et al. (2000) have provided evidence of temperature-dependent conformational change(s) in myosin in solution, where open–closed transition has been found to be endothermic (H=+94 kJ mol–1, Malnasi-Csizmadia et al. (2000). Additionally, the helical order of myosin filament has been shown to be temperature sensitive, with low temperatures favouring a disordered (open) conformation and high temperatures favouring ordered (closed) conformation together with a second disordered conformation (Xu et al. 2003). If open–closed transition in myosin is endothermic, whether and how the reverse process, the closed–open transition, also can be endothermic on its attachment to actin (i.e. in crossbridges in muscle fibres) is a fundamental issue that remains to be resolved. Therefore, how the above findings from myosin, myosin filaments and myosin-ATPase cycle, and temperature-sensitive steps other than force generation (see Millar et al. 1987; He et al. 1997; Ferenczi et al. 2005), may be accommodated in the AM cycle in muscle fibres remain unclear and have not been duly addressed in our study.
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