A high resolution method for determining the complex stiffness of single muscle fibres is described. In this method the length of the fibre is oscillated sinusoidally, and the resulting force amplitude and phase shift are observed and interpreted in terms of chemo-mechanical energy transduction. In activated, fast skeletal muscles of rabbit (psoas), frog (semitendinosus) and crayfish (walking leg flexor), we resolved at least three exponential rate processes. We named these (A), (B), (C) in order of slow to fast. These processes should reflect ATP hydrolysis and concomitant energy transduction since they are absent in muscles that the relaxed, in rigor or fixed. The great similarities in the complex stiffness data from different muscles suggests that there is a common mechanism of chemo-mechanical energy transduction across a broad phylogenetic range.

The elementary steps of contraction in rabbit fast twitch muscle fibers were investigated with particular emphasis on the mechanism of phosphate (Pi) binding/release, the mechanism of force generation, and the relation between them. We monitor the rate constant 2 pi b of a macroscopic exponential process (B) by imposing sinusoidal length oscillations. We find that the plot of 2 pi b vs. Pi concentration is curved. From this observation we infer that Pi released is a two step phenomenon: an isomerization followed by the actual Pi release. Our results fit well to the kinetic scheme: [formula: see text] where A = actin, M = myosin, S = MgATP (substrate), D = MgADP, P = phosphate, and Det is a composite of all the detached and weakly attached states. For our data to be consistent with this scheme, it is also necessary that step 4 (isomerization) is observed in process (B). By fitting this scheme to our data, we obtained the following kinetic constants: k4 = 56 s-1, k-4 = 129 s-1, and K5 = 0.069 mM-1, assuming that K2 = 4.9. Experiments were performed at pCa 4.82, pH 7.00, MgATP 5 mM, free ATP 5 mM, ionic strength 200 mM in K propionate medium, and at 20 degrees C. Based on these kinetic constants, we calculated the probability of each cross-bridge state as a function of Pi, and correlated this with the isometric tension. Our results indicate that all attached cross-bridges support equal amount of tension. From this, we infer that the force is generated at step 4. Detailed balance indicates that 50-65% of the free energy available from ATP hydrolysis is transformed to work at this step. For our data to be consistent with the above scheme, step 6 must be the slowest step of the cross-bridge cycle (the rate limiting step). Further, AM*D is a distinctly different state from the AMD state that is formed by adding D to the bathing solution. From our earlier ATP hydrolysis data, we estimated k6 to be 9 s-1.

The effect of temperature on elementary steps of the cross-bridge cycle was investigated with sinusoidal analysis technique in skinned rabbit psoas fibers. We studied the effect of MgATP on exponential process (C) to characterize the MgATP binding step and cross-bridge detachment step at six different temperatures in the range 5-30 degrees C. Similarly, we studied the effect of MgADP on exponential process (C) to characterize the MgADP binding step. We also studied the effect of phosphate (Pi) on exponential process (B) to characterize the force generation step and Pi-release step. From the results of these studies, we deduced the temperature dependence of the kinetic constants of the elementary steps and their thermodynamic properties. We found that the MgADP association constant (K0) and the MgATP association constant (K1) significantly decreased when the temperature was increased from 5 to 20 degrees C, implying that nucleotide binding became weaker at higher temperatures. K0 and K1 did not change much in the 20-30 degree C range. The association constant of Pi to cross-bridges (K5) did not change much with temperature. We found that Q10 for the cross-bridge detachment step (k2) was 2.6, and for its reversal step (k-2) was 3.0. We found that Q10 for the force generation step (Pi-isomerization step, k4) was 6.8, and its reversal step (k-4) was 1.6. The equilibrium constant of the detachment step (K2) was not affected much by temperature, whereas the equilibrium constant of the force generation step (K4) increased significantly with temperature increase. Thus, the force generation step consists of an endothermic reaction. The rate constant of the rate-limiting step (k6) did not change much with temperature, whereas the ATP hydrolysis rate increased significantly with temperature increase. We found that the force generation step accompanies a large entropy increase and a small free energy change; hence, this step is an entropy-driven reaction. These observations are consistent with the hypothesis that the hydrophobic interaction between residues of actin and myosin underlies the mechanism of force generation. We conclude that the force generation step is the most temperature-sensitive step among elementary steps of the cross-bridge cycle, which explains increased isometric tension at high temperatures in rabbit psoas fibers.

Elementary steps of the crossbridge cycle in chemically skinned ferret myocardium were investigated with sinusoidal analysis. The muscle preparations were activated at pCa 4.82 and an ionic strength of 200 mM, and the effects of the change in the MgATP (S) and phosphate (Pi) concentrations on three exponential processes were studied at 20 degrees C. Results are consistent with the following crossbridge scheme: [formula: see text] where A is actin, M is myosin, D is MgADP, and Det includes all detached states (MS and MDP) and weakly attached states (AMS and AMDP). From our studies, we obtained K1a = 0.99 mM-1 (MgATP association), k1b = 270 s-1 (ATP isomerization), k-1b = 280 s-1 (reverse isomerization), K1b = k1b/k-1b = 0.95, k2 = 48 s-1 (crossbridge detachment), k-2 = 14 s-1 (reverse detachment), K2 = 3.5, k4 = 11 s-1 (crossbridge attachment), k-4 = 107 s-1 (reverse attachment), K4 = 0.11, and K5 = 0.06 mM-1 (Pi association). K6 is the rate-limiting step, and it is the slowest forward reaction in the cycle, which results in the rigor-like AM state. K1a (MgATP binding) is four times that of rabbit psoas, and K5 (Pi binding) is 0.3 times that of psoas, demonstrating that crossbridges in myocardium bind MgATP more and Pi less than psoas. The rate constants of ATP isomerization (k1b, k-1b), crossbridge detachment (k2, k-2), and crossbridge attachment (k4) steps are generally an order of magnitude slower than rabbit psoas. The reverse attachment step (k-4) is similar to that in psoas, indicating that this step may occur irrespective of the myosin type and possibly spontaneously. The above scheme with the deduced kinetic constants predicts the following crossbridge distributions at 5 mM MgATP2- and 8 mM Pi:AM (3%), AM S (15%), AM*S (14%), Det (50%), AM*DP (6%), and AM*D (12%). The actual number of attached crossbridges was measured to be 51 +/- 4% by the stiffness ratio during activation and after rigor induction, and a strong correlation was seen with the prediction. Our results are consistent with the hypothesis that force generation occurs at the Det-->AM*DPi transition, and the same force is maintained after the release of Pi.

The actin-myosin lattice spacing of rabbit psoas fibers was osmotically compressed with a dextran T-500, and its effect on the elementary steps of the cross-bridge cycle was investigated. Experiments were performed at the saturating Ca (pCa 4.5-4.9), 200 mM ionic strength, pH 7.0, and at 20 degrees C, and the results were analyzed by the following cross-bridge scheme: [formula: see text] where A = actin, M = myosin head, S = MgATP, D = MgADP, and P = Pi = phosphate. From MgATP and MgADP studies on exponential process (C) and (D), the association constants of cross-bridges to MgADP (K0), MgATP (K1a), the rate constants of the isomerization of the AM S state (k1b and k-1b), and the rate constants of the cross-bridge detachment step (k2 and k-2) were deduced. From Pi study on process (B), the rate constants of the cross-bridge attachment (power stroke) step (k4- and k-4) and the association constant of Pi ions to cross-bridges (K5) were deduced. From ATP hydrolysis measurement, the rate constant of ADP-isomerization (rate-limiting) step (k6) was deduced. These kinetic constants were studied as functions of dextran concentrations. Our results show that nucleotide binding, the ATP-isomerization, and the cross-bridge detachment steps are minimally affected by the compression. The rate constant of the reverse power stroke step (k-4) decreases with mild compression (0-6.3% dextran), presumably because of the stabilization of the attached cross-bridges in the AM*DP state. The rate constant of the power stroke step (k4) does not change with mild compression, but it decreases with higher compression (> 6.3% dextran), presumably because of an increased difficulty in performing the power stroke. These results are consistent with the observation that isometric tension increases with a low level of compression and decreases with a high level of compression. Our results also show that the association constant K5 of Pi with cross-bridge state AM*D is not changed with compression. Our result further show that the ATP hydrolysis rate decreased with compression, and that the rate constants of the ADP-isomerization step (k6) becomes progressively less with compression. The effect of compression on the power stroke step and rate-limiting step implies that a large-scale molecular rearrangement in the myosin head takes place in these two slow reaction steps.