Table 3.
Rate constants for the forward (k+x) and backward (k−x) transitions and corresponding equilibrium constants (Kx) for the scheme of Fig. 6.
| Step in the cycle | k+x | k−x | Kx | Justification |
|---|---|---|---|---|
| A, green-highlighted path in Fig. 6 | ||||
| (1) | 1 × 106 M−1s−1 | 1 s−1 | 1 × 106 M−1 | According to refs. 32,38,62,63 |
| (2) | 14 s−1 | 9 s−1 | 1.56 | k2, according to ref. 38; k-2, selected to adjust the distribution of detached myosin motors |
| (3) | 2.2 s−1 | 4.5 s−1 | 0.49 | k+3, adjusted to fit the fraction of attached motors in isometric contraction19 |
| (4) | 11 s−1 | 0.9 × 103 M−1s−1 | 12.2 × 10−3 M | k+4 from refs. 9,15 (assuming Q10 = 2) and K4 adjusted to fit the Pi dependence of the rate of force development assuming these steps are 50 times slower than in psoas muscle32 |
| (5) | 1 s−1 | 1 × 103 M−1 s−1 | 1 × 10−3 M | Adjusted to fit kcat in isometric contraction in the absence of OM64–66 |
| (6) | 0.8 s−1 | 2 × 10−3 s−1 | 0.4 × 103 | Adjusted to fit the Pi dependence of kcat in the absence of OM37 |
| (7) | 50 s−1 | – | – | Rapid and irreversible release of hydrolysis products and ATP binding37 |
| B, pink-highlighted path in Fig. 6 | ||||
| (8) | 400 × 106 M−1 s−1 | 100 s−1 | 4 × 106 M−1 | Adjusted to have the correct proportion of OM-bound myosin motors |
| (9) | 1.2 s−1 | 1 s−1 | 1.2 | k+9 and k−9 adjusted to account for OM-dependent increase of probability of actin attachment by motors (K9 > K3)15 and for the constant total number of attached motors in the presence of OM |
| (10) | 18 s−1 | 1.48 × 103 M−1 s−1 | 12.2 × 10−3 M | k+10 set to 1.64 k+4, to take into account the effect of OM on the rate of Pi release9,15; K10, same value as in step (4) |
| (11) | 1000 s−1 | 1000 s−1 | 1 | Rapid isomerization step; K11 set to 1 to adjust the stoichiometry of the Pi effect |
| (12) | 1.5 s−1 | 2 × 10−3 s−1 | 1 × 103 | Detachment set to fit kcat in the presence of OM |
| (13) | 3 s−1 | – | – | Irreversible release of ADP and OM followed by rapid ATP binding |
| (14) | 3 × 103 M−1 s−1 | 3 × 106 M−1 s−1 | 1 × 10−3 | Adjusted to fit the kinetics of force development and the Pi dependence of T0 and e0 in the presence of OM |
Values for the model in the absence of OM (A, green-highlighted in Fig. 6) and for the branched pathway induced by OM (B, pink-highlighted in Fig. 6). The justification of the kinetic parameters are reported in the last column. Where possible, the parameters are selected according to the relevant information from the literature. The selection of the value of the kinetic parameters concerning OM and OM-Pi actions and the sensitivity of the model fit to the selected value are achieved with an iterative procedure of model simulation by changing one parameter at a time as detailed in “Methods” and in Supplementary Figs. 2 and 3. x represents the step number, as reported in brackets in the first column. For the second-order rate constants, the apparent rate constants are calculated assuming [MgATP] = 5 mM and [ADP] = 20 μM; [Pi] and [OM] according to the experimental conditions.