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1 Imperial College London, Division of Biomedical Sciences, Biological Nanoscience Section, SAF Building, London SW7 2AZ, UK
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Abstract |
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(Received 22 March 2005;
accepted after revision 14 July 2005;
first published online 21 July 2005)
Corresponding author T. West: Division of Biomedical Sciences, Biological Nanoscience, Sir Alexander Fleming Building, Imperial College London, London SW7 2AZ, UK. Email: t.west{at}imperial.ac.uk
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Introduction |
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Experiments with mammalian fibres have shown that at subphysiological temperatures (0–20°C) force is strongly depressed as ionic strength is increased beyond the physiological value of 200 mmol l–1 (Kawai et al. 1990; Godt et al. 1993; Seow & Ford, 1993; Iwamoto, 2000). This effect of IS is not simply due to a reduction in the number of cross-bridges attached because stiffness and force do not remain proportional when IS is changed. Stiffness increases relative to force in studies at very low temperatures (1–5°C; Seow & Ford, 1993; Iwamoto, 2000), but decreases in proportion to force near 20°C (Kawai et al. 1990; Godt et al. 1993). Thus it seems that the relative importance of ionic interactions and hydrophobic interactions in determining force varies with temperature. Since all investigations of the effect of IS in mammalian muscle were done at temperatures well below their physiological temperature, it is uncertain whether the observations are relevant to the cross-bridge cycle as it occurs in vivo.
Our aims were to measure the effects of IS changes in the physiological range on the time courses of force and Pi release in permeabilized dogfish white fibres contracting at physiological temperature. The results were used to test the validity of a kinetic scheme that describes force development, Pi release and energetics of these fibres (West et al. 2004). The scheme was developed to interpret observations from both permeabilized and intact fibres, and it takes account of the transition from rest (intact) or rigor (permeabilized) to the contracting state, shortening and the consequent work against series elasticity, reaction heats and changes in ionic strength. Increasing IS depressed the rate of force development and Pi release during force development, but did not affect the maximum force or the steady-state rate of Pi release at physiological temperature. We found that these effects could be simulated when only those steps involving binding of contractile proteins with ATP, ADP or Pi were made sensitive to IS. Effects on attached states of actomyosin were not required to account for the behaviour of the cross-bridge cycle at physiological temperature, suggesting that actin–myosin interactions are non-ionic.
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Methods |
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Bundles of 5–20 fibres, with segments of myosepta at each end, were dissected from the muscle slices (West et al. 2004). The fibre bundles were permeabilized in 2% Triton X-100 (30 min) made up in an ice-cold relaxing solution (Table 1). The myosepta were dissected away under chilled (5°C) relaxing solution and single fibres were pulled gently from the bundle. Aluminium foil T-clips were placed on the fibre ends and the ends were then treated with 0.5% glutaraldehyde in Mg2+-rigor solution (Table 1) as previously described (Thirlwell et al. 1994). Fibres were either used immediately or stored overnight (–20°C) in relaxing solution made up in 50% glycerol. The solutions used for permeabilization, dissection and overnight storage were all at standard IS.
MDCC-PBP assay of Pi release
Assays of Pi release at the standard IS are described in detail elsewhere (He et al. 1997, 1999, 2000; West et al. 2004). Briefly, single fibres were mounted in relaxing solution between a force transducer (AE 801; Sensonor, Horten, Norway) and a fixed hook. After a further treatment with Triton X-100 (1% in relaxing solution for 30 min), the fibre was washed in relaxing solution and taken through a standard sequence of solution changes on a purpose-built temperature-controlled (12°C, physiological temperature for dogfish muscle) stage for a Zeiss ACM upright microscope. While in relaxing solution, the laser diffraction pattern was used to set sarcomere length (SL0) at 2.4 µm; tetanic contraction force of intact white fibres from dogfish is maximal at this sarcomere length (Lou et al. 1997). The fibre was then transferred into Ca2+-free rigor solution, which contained Pi-mop (Brune et al. 1999) made with MEG and PNPase (see Table 1 for definitions). This solution also contained BDM (defined in table 1), an inhibitor of AM-ATPase activity, to minimize the amount of rigor force (Bershitsky et al. 1996). Rigor-tension developed (4–8% of peak isometric force) and stabilized within 5 min. Next, the fibre was treated with Ca2+-rigor solution in which [Ca2+]free was 32 µmol l–1. The fibre was then immersed in loading solution (5 min), which contained NPE-caged ATP and the phosphate binding protein, MDCC-PBP (Brune et al. 1994, 1998).
The fibre was transferred into silicone oil (Dow Corning, 10 centistokes) and then activated with a laser pulse (30 ns) of 100–150 mJ (QSR 2; Lumonics Ltd, Rugby, UK) that released 1.5 mmol l–1 ATP from NPE-caged ATP. Signals for MDCC-PBP fluorescence and force were collected at 2 kHz (R.C. Electronics EGAA Computerscope; Goletta, CA, USA). Details of the epifluorescence microscope are provided by He et al. (1997). Fluorescence time courses were corrected for the inner filter effect that arises from light absorption by the photochemically-generated aci-nitro intermediate formed from NPE-caged ATP. The nature of this aci-nitro intermediate and its absorbance properties have been discussed elsewhere (Walker et al. 1988) and the correction for inner filtering was as described previously (He et al. 1998). Then the concentration of total Pi ([Pi,total]) released, which is equivalent to the sum of free Pi and that bound to the active MDCC-PBP, was calculated from the fluorescence signal (West et al. 2004) using the equation:
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| (1) |
fluorescence/maximum fluorescence), D is the ratio apparent –Kd/1.2 and 1.2 is the concentration of active MDCC-PBP in a fibre. The apparent dissociation constant (Kd) was 0.0158 mmol l–1 (Curtin et al. 2003). The maximum fluorescence change was the difference between background and plateau fluorescence values, with the latter indicating saturation of the active MDCC-PBP with Pi. The first 0.5 s of each fluorescence record was converted to Pi,total using eqn (1).
The rate of Pi release (mmol l–1 s–1) was determined from the differentials of equations fitted to the experimental data; Excel Solver was used to fit total Pi released at time t (Pi,t) to the equation
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| (2) |
Pi release at high ionic strength
Fibres that were to be activated at high IS (400 mmol l–1) were first treated with 1% Triton X-100 (30 min), washed in relaxing solution, and had sarcomere length set to 2.4 µm (as described earlier) in solution at the standard IS (200 mmol l–1). The fibre was then immersed in high IS relaxing solution for 20 min, treated with the high IS solution series and activated as described above (see Table 1 for solutions). The solution constituents were calculated using a computer program (Ferenczi et al. 1984) which took account of the effect of IS on binding constants and thus allowed adjustment of IS while holding the free concentrations of Mg2+ and Ca2+ constant.
Fibre dimensions and normalization of muscle force
Relaxed fibre length (FL0) at SL0 was measured prior to contraction. The fibres were collected after each experiment, dried and weighed. Average fibre length and dry weight were not significantly different for the fibres activated in standard and high IS (Table 2). Dry weight gives an estimate of the total contractile material in the fibre, and is assumed to be proportional to the number of myosin heads. Assuming muscle density is 1 kg l–1 and the concentration of myosin heads is 1.5 x 10–4 mol l–1 (He et al. 1997), we estimate that there are 9.03 x 1019 molecules of myosin heads per kilogram wet weight of muscle. Since each half-sarcomere along the fibre length bears the entire force, we have related force to the estimated number of myosin heads per half-sarcomere to give force in piconewtons per myosin head. The value for the number of myosin heads used in this calculation would not be affected by IS, in contrast to the cross-sectional area.
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| (3) |
Measurements of fibre depth and width were made on a group (n = 5) of fibres that were transferred between standard IS (200 mmol l–1) and high IS (400 mmol l–1) relaxing solutions and cross-sectional areas calculated assuming elliptical shape. The change in cross-sectional area indicates fibre swelling or shrinking in response to changes in IS. Depth and width measurements were made first in the standard IS relaxing solution by microscopic inspection at four or five positions along the fibre length. Each fibre was then transferred to high IS relaxing solution and the measurements were repeated after 20 min. Measurements of fibre depth and width on this subset of fibres showed that relaxed fibre cross-sectional area increased by 18.6 ± 4.8% (mean ± S.E.M., n = 5) when fibres were shifted from standard IS to high IS.
Kinetics of force development and Pi release
We recently developed a kinetic scheme of the cross-bridge cycle that simulated the time courses of force and Pi release during isometric contraction in permeabilized and intact dogfish white fibres (West et al. 2004). Here we used the new results to test whether the scheme could also accurately simulate the effects of increased IS in permeabilized fibres, and also live fibres using our estimate (see Discussion) of intracellular IS 300 mmol l–1. The kinetic scheme (Fig. 1, Table 3) is the same as we have presented previously (West et al. 2004) and is based on other kinetic approaches that have sought to account for the biochemical steps and relative force development during contraction (Pate & Cooke, 1989b; He et al. 1998, 2000; Wang & Kawai, 2001). In brief, simulations in permeabilized fibres are initiated with all sites in the rigor (AM) state. The simulation of contraction is started by the release of NPE-caged ATP through reaction 6. The concentrations of ATP and ADP change during contraction because of the action of actomyosin ATPase; Pi concentration, however, is held at zero to model the tight MDCC-PBP binding of the Pi released as the contraction progresses. The simulation for intact fibres starts from an initial state with all myosin sites in the equilibrium mixture of MATP and MADPPi. The contraction is started by allowing the forward rate constant for reaction 3(k+3) to increase exponentially to its set value with a rate constant of kact. All ADP released in reaction 5 is assumed to be converted immediately to ATP by the action of creatine phosphokinase (CPK), so neither the concentration of ATP (set at 3 mmol l–1) nor that of ADP (0.025 mmol l–1) changes during contraction.
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| (4) |
In this work we made the following additional assumptions: (1) increasing IS from the standard to the high level decreases the rate constants k+1, k–4 and k–5 by the same factor, R; (2) in the intact fibres the values of these rate constants was the geometric mean, 
(kstd
khigh), where kstd is the rate constant at standard IS and khigh is the rate constant at high IS (3) the rate constant k+3 was proportional to the force in the system; and (4) the cycle is driven by the hydrolysis of ATP and thus the free energy change in each complete AM cycle is equal to the free energy of ATP hydrolysis. Therefore, the product of the equilibrium constants of the five steps in the cycle is equal to e83/kT, where 83 represents the free energy of ATP hydrolysis in piconano joules per molecule and kT (3.826 in piconano joules per molecule) is the product of Boltzmann's constant and the absolute temperature.
The kinetic scheme was implemented in MathCad (Simulink) with time intervals of 0.2 ms. Optimum values for the adjustable constants were found using the Simplex method with multiple starting points.
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Results |
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Average records of force for the two IS treatments are shown in Fig. 2 on two different time scales. Mean rigor tension immediately prior to photolysis of NPE-caged ATP was not affected significantly by IS (P = 0.08). After photolysis, force declined initially at both IS, but the delay before the onset of force development was longer in high IS than in standard IS. The peak rate of rise of force (dP/dt), calculated as the change in average force over consecutive 3 ms intervals, was significantly lower, and the time to reach peak dP/dt was longer in high IS. However, the maximal isometric force was not affected significantly by IS (Fig. 2A, see also Table 2).
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A single set of parameters (Table 3) was found that gave the best fit to the time courses of the following sets of experimental data, weighted equally: (1) force and (2) Pi release during 500 ms of contraction by permeabilized fibres at standard IS; (3) force and (4) Pi release at high IS; and (5) force and (6) actomyosin heat + work production during 3.5 s of isometric contraction of intact fibres (this data set for live fibres is shown in detail in West et al. 2004). For intact fibres the intracellular IS was taken to be 300 mmol l–1 (see Discussion for evidence).
Figure 4A and B compares the predicted results from the model with the observed time courses for force production and Pi release in permeabilized fibres. The predicted time courses match the experimental observations well, showing in particular the delayed force production and reduced Pi release by permeabilized fibres at high IS. Our previous simulations (West et al. 2004) incorporated parameters allowing us to predict time courses for force and energetics in both permeabilized and intact fibres. The model as modified here accounts for IS effects in permeabilized fibres and also predicts the time courses of force (Fig. 4C) and heat + work (Fig. 4D) that we have observed previously for intact fibres (West et al. 2004).
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AMADP) becomes significant as the ADP concentration increases, and the forward flux through reaction 1 (AM
+ ATP
MATP +
A) falls as ATP concentration decreases. The competition between ADP and ATP for AM is responsible for the decline in the cycle turnover and ATP hydrolysis rate as contraction progresses. This competition is IS dependent (see k+1 and k–5, Table 3) and is the basis of the IS effects on the cycle rate in permeabilized fibres (Fig. 4B).
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AMADPPi), towards its final high value. During the transition towards the steady state, AMADPPi largely replaces the equilibrium mixture of MATP and MADPPi. After the initial transient there is a marked difference in the occupancy of AMADP state between the intact and the permeabilized fibres. For example, at 0.5 s the values are 22% for intact fibres and 87% for permeabilized fibres. In the intact fibres the Pi concentration increases as the steady state is approached. The net flux through the ATPase cycle decreases because Pi concentration increases and drives a significant reverse flux through reaction 4 (AMADP + Pi
AMADPPi). Note that, in contrast to permeabilized fibres, the concentrations of ATP and ADP remained essentially constant in intact fibres due to the activity of creatine phosphokinase. |
Discussion |
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Comparison with earlier work
These effects of IS are much smaller than those reported for permeabilized mammalian fibres (Kawai et al. 1990; Godt et al. 1993; Seow & Ford, 1993; Iwamoto, 2000). Isometric force produced by rabbit fibres is diminished considerably by raising the IS with potassium propionate over a range similar to that used here; for example, Kawai et al. (1990) reported a reduction of 50% in force when IS was increased from 200 to 300 mmol l–1. Steady-state ATPase of mammalian muscle is also reduced by raising the IS, but by less than the force reduction (Kawai et al. 1990; Godt et al. 1993).
Two possible reasons for this difference can be suggested: temperature, and difference in intrinsic actomyosin properties between species.
Temperature. The mammalian experiments were done in the range 0–20°C. They showed that at very low temperature (0–5°C) and at 20°C, IS had opposite effects on force per cross-bridge, based on measurements of force/stiffness. This evidence indicates that temperature affects the cross-bridge cycle, altering the relative importance of ionic interactions and hydrophobic interactions in determining force per cross-bridge and the proportion of attached bridges. There are steps in the cross-bridge cycle, for example the Pi release step (Zhao & Kawai, 1994; Piazzesi et al. 2003), that produce large enthalpy changes, and therefore their equilibrium constants are altered considerably by temperature. As a result the occupancy of the cross-bridge states is different at different temperatures. Thus ionic strength effects can be enhanced by populating states that participate in ionic interactions.
All the IS experiments on mammalian muscle fibres were done at temperatures well below their physiological range. At temperatures closer to 37°C the cross-bridge cycle may be operating more like that in dogfish fibres at their physiological temperature; that is, at increased IS the cycle is slower to get started, but rather insensitive to IS in the steady state.
Species difference in sensitivity to IS. Godt et al. (1993) reported results showing that isometric force in permeabilized rabbit fibres was more sensitive than permeabilized lobster fibres to IS in the range 150–315 mmol l–1 produced by increasing the concentration of either potassium chloride or potassium methanesulphonate. Lobster fibres retained close to 80% of their maximal force even when IS was raised above 500 mmol l–1 with the sulphonate solution. Intact muscle fibres from freshwater crustaceans and frogs appear to behave like mammalian fibres in the sense that isometric force was depressed when fibres were stimulated in hypertonic external bathing solutions (April et al. 1968; Gordon & Godt, 1970). The suppression of force in these experiments was attributed largely to direct effects of increased intracellular IS on contractile proteins, with relatively minor effects due to perturbed excitation–contraction coupling or fibre volume. The fact that our dogfish muscles show little or no effect of increasing IS to 400 mmol l–1 may reflect the fact that their proteins, in common with other marine animals, are designed to tolerate variations in IS in life. This would be consistent with the variation in tissue solute composition and concentration seen during adaptation to different environmental salinity by dogfish (Bedford, 1983; Sulikowski & Maginniss, 2001).
Alternatively, the dogfish muscle may be less sensitive than mammalian muscle to increases in IS in this range because normal IS in dogfish muscle is within the range 200–400 mmol l–1, whereas IS is 
200 mmol l–1 in mammalian fibres. Estimates of the intracellular K+ and Na+ concentrations can be made from measured values of the resting potential and action potential, assuming that they represent the equilibrium potentials for K+ and Na+, respectively. In white fibres of dogfish the resting membrane potential, –85.2 ± 0.4 mV, and the peak of the action potential, +54.1 ± 3.4 mV (Stanfield, 1972), correspond to intracellular concentrations of 120 mmol l–1 K+ and 36 mmol l–1 Na+. With an equivalent concentration of singly charged anion, this gives an intracellular IS of 313 mmol l–1 due to these ions alone. Similar resting and action potential values were found by Hagiwara & Takahashi (1967) for other elasmobranchs.
Skeletal muscles of marine elasmobranchs have a high solute content, which maintains the cytosol isosmotic with the extracellular fluid (osmolarity about 1000 mosmol l–1). Many of the solutes are organic molecules which are either uncharged, such as urea, or have net charge close to zero at physiological pH (Ballantyne, 1997; Hochachka & Somero, 2002), and therefore contribute little to the cytosolic IS. However, organic zwitterions like glycine betaine and trimethyl-amine-N-oxide (TMAO) are present in significant concentrations, and these solutes are important for counteracting the detrimental effects that high levels of organic and inorganic ions and certain uncharged solutes can have on protein structure and function. Naturally occurring TMAO in dogfish muscle counterbalances the suppressive effect of urea on force production (Altringham & Johnston, 1982). Godt et al. (1993) also demonstrated that TMAO protects the function of contractile proteins in lobster fibres at IS values in excess of 500 mmol l–1. It is remarkable that even in the absence of a counterbalancing solute, a doubling of IS in dogfish permeabilized fibres had no effect on plateau force and steady-state Pi release rate.
Increasing IS causes swelling of relaxed permeabilized fibres and an increase in the lattice spacing. The effect is less pronounced after rigor induction and during contraction (Kawai et al. 1990). It seems from our results that such changes in lattice spacing are not sufficient to affect actomyosin interactions in permeabilized dogfish fibres upon activation from the rigor state.
Effects of IS on the cross-bridge cycle
We proposed that IS affects the rate constants for the binding of anionic species (MgATP, MgADP and Pi) to myosin, K+1, K–5, K–4, respectively, and that all these rate constants are equally diminished by raising IS from 200 to 400 mmol l–1. This is equivalent to a reduction in the activity coefficients of these species, as would be expected from Debye-Hückel theory. Figure 4 shows that with IS reducing these rate constants only, we could accurately account for all the effects of IS on force and ATPase activity that we observed in dogfish fibres at physiological temperature. There is no need to assume that IS influences any other steps in the actomyosin cycle, particularly the actin–myosin interactions. It therefore appears that actin–myosin interactions are largely non-ionic. Greater understanding of the interactions between temperature, ionic strength and the occupancy of myosin states in permeabilized fibres can be gained in future experiments by using, for example, an ADP-sensitive fluorophore (Brune et al. 2001) to complement assays using MDCC-PBP.
The success of the calculations in explaining these new results with permeabilized fibres caused us to examine again the explanation given previously for the results from intact fibres (West et al. 2004). As indicated above, the physiological intracellular IS in dogfish is likely to be in the range 200–400 mmol l–1. Considering that the physiological intracellular IS of the intact fibres is 300 mmol l–1, midway between the standard and high IS, we set the rate constants K+1, k–4 and k–5 midway between the values for standard and high IS (Table 3). The reaction scheme accurately describes force and energy output by actomyosin in intact fibres when these values are used (Fig 4C and D). Note that in intact fibres the concentration of Pi increases during contraction while ADP does not (in contrast to permeabilized fibres); the simulation accounts for force and ATP turnover for both conditions.
The scheme consisted of the minimum number of steps needed to describe the results of our experiments. Although there is evidence from other studies for a preforce AMADPPi state, our results could be simulated without this state. The rate constants k+3 and k–3 are therefore a composite of the rapid transition of myosin heads from detached (MADPPi) to preforce attached (AMADPPi) states together with the slower isomerization to a force producing (AMADPPi) state. The kinetic scheme presented recently by Sleep et al. (2005) shows that simulation of force generation in rabbit psoas fibres can be similarly achieved by incorporating rapid equilibration between the MADPPi and preforce AMADPPi states. In our simulation, like that of Sleep et al. (2005), myosin attachment to actin and subsequent formation of the force producing AMADPPi state is faster than the ATP hydrolysis step. It is a feature of our conditions that either Pi or ADP is always maintained at a very low level while the level of the other product changes significantly; Pi was low in the permeabilized experiments and ADP was low in the intact fibre observations (West et al. 2004). Sleep & Hutton (1980) showed that an additional step is needed to explain what happens when both Pi and ADP levels are raised: an irreversible isomerization of AMADP prior to the release of ADP. We have found that the reaction scheme still gives a good description of our experimental results when this extra step is inserted.
Effects of Pi concentration in permeabilized and intact fibres
The fact that the total rate of ATP use by muscle diminishes during the first few seconds of an isometric contraction while force remains constant has been well known for at least 50 years (Abbott, 1951). Our results on intact and permeabilized fibres show that much of this effect is due to slowing of actomyosin ATPase.
The reaction scheme provides for the first time an explanation of the mechanism of this effect in intact fibres: the flux through reaction 4, Pi release from AMADPPi, is diminished by the build up of Pi from its resting level of about 0.5 mmol l–1 (Curtin et al. 1997) to about 6.5 mmol l–1 after 3.5 s of contraction (West et al. 2004). The effects of Pi in our intact fibres are a reduction of actomyosin ATPase to 20% of its initial value, while force is only diminished to 97.5%. These results contrast with those from many observations of permeabilized fibres studied in the steady state in which increased Pi strongly depresses force and depresses ATPase rather less (Altringham & Johnston, 1985; Kawai et al. 1987; Bowater & Sleep, 1988; Kawai & Halvorson, 1989; Pate & Cooke, 1989a; Millar & Homsher, 1990; Dantzig et al. 1992; Martyn & Gordon, 1992; Pate et al. 1998). Most of these studies were done at subphysiological temperature. The effects of Pi and temperature (5–30°C) have been systematically investigated in permeabilized fibres from rabbits (Coupland et al. 2001) and from rats where the myosin heavy chain type was characterized in each fibre (Debold et al. 2004). These recent studies showed that Pi had much less effect on force as temperature approached the physiological value. Our present results suggest that at physiological temperature raising Pi may have minimal effect on force. Alternatively fibres may lose a factor during permeabilization that acts in intact fibres to prevent or counteract the depression of force by Pi. To make progress on this question, a comparison of Pi effects should be made between intact and permeabilized fibres from the same muscle type.
Conclusion
Force development during contraction of dogfish fibres is slowed by increasing IS, but as the isometric force plateau is approached during contraction the effects of IS diminish. By 0.5 s of contraction, the force and the rate of Pi release were not significantly different at IS of 200 and 400 mmol l–1. Thus dogfish fibres at physiological temperature are less affected by IS than mammalian fibres during contraction at subphysiological temperature. The time courses of force and Pi release by permeabilized and intact dogfish fibres were accurately simulated by a kinetic model of the actomyosin cycle in which IS uniformly affected the rate constants for reactions of ATP, ADP and Pi with the contractile proteins.
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