The elementary step that generates force and sinusoidal analysis in striated muscle fibers

Figures

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  Fig. 1. A Two-state model (apparent rate constant: Eq. A19), and B three-state model (apparent rate constant: Eq. 1) involving phosphate (Pi) release. C Three-state model with each molecular constituent identified, where M myosin and A actin. X4, X5, and X6 represent CB states, and T4, T5, and T6 represent force supported by the respective state. r4 and r−4 are the intrinsic rate constants of Step 4, and K5 is the Pi association constant. Note that K5 is defined for the X6 → X5 (backward) direction, hence K5 is written under the arrows. The slow Step 6 shown with a broken arrow (r6) appears not to occur while faster Steps 4 and 5 are observed, hence Step 6 can be eliminated from theoretical analysis. Step 6 becomes important when the rate-limiting step is considered

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  Fig. 2. Experiments on rabbit soleus slow-twitch fibers, activated at pCa 4.40 and 5 mM MgATP at 20°C. The average over nine experiments, with SEM, are shown. A Apparent rate constant 2πb is plotted against [Pi] and fitted to Eq. 1. From this fitting, three kinetic constants (r4 = 5.7 ± 0.5 s−1, r−4 = 4.5 ± 0.5 s−1, and K5 = 0.18 ± 0.01 mM.−1) were deduced. B Changes in CB occupancy X4 (Eq. 2), X5 (Eq. 3), and X6 (Eq. 4) as functions of [Pi], calculated by using K4 (≡r4/r−4 = 1.37 ± 0.13) and K5 obtained from A. Also plotted is X5 + X6 (labelled). C Isometric force (normalized to first control force Tc) is plotted against [Pi] and fitted to Eq. 6 by using K4 and K5 deduced from A. From this fitting, T5 = T6 = 1.29 ± 0.05 Tc (N = 9) was obtained, where Tc = 142 ± 15 kPa (N = 24). In A and C, the curved lines are the best fit results; reproduced from Wang and Kawai (1997)

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  Fig. 3. Temperature jump study in rabbit psoas fibers. A Data from Bershitsky and Tsaturyan (2002), reproduced and relettered with permission from Journal of Physiology (John Wiley & Sons). B Simulation from Kawai (2003) based on kinetic constants observed by Zhao and Kawai (1994). The abscissa has been shrunken, and the ordinate has been expanded to match A

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  Fig. 4. Secondary Pi binding site in Pi release tunnel. Pi at the center (4 oxygen arms in the tetrahedral arrangement are seen) is coordinated by four aa residues (S153, T197, S203 and E461) and one salt link (R205) helped by E242. aa residue numbers are based on myosin VI sequence. Red spheres are O atoms of H2O molecules. Reproduced from Llinas et al. (2015) with permission from Developmental Cell (Cell Press)

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  Fig. 5. Complete cross-bridge cycle. Abbreviations are the same as those in Fig. 1. A “+” indicates the direction of the barbed end, “−" indicates the direction of the pointed end, and “Z” indicates the direction of the Z-line (barbed end). Monomeric actin is drawn to show its polarity, with individual actin molecules identified by numbers. Elementary step numbers are indicated in (), which are common to many authors. Force generation occurs at Step 4, which accompanies a closure of actin binding cleft, as predicted by Murphy et al. (1996) and as shown from crystallographic studies (Holmes et al. 2004; Málnási-Csizmadia and Kovács 2010). The dark areas (on myosin) indicate stereospecific and hydrophobic interactions between actin and myosin. The step that generates force is called the “power/working stroke” to emphasize a swing of the lever arm, which stretches series elasticity. This applies force to the external load. Actual linear work is carried out in Step 6, which transfers momentum to the load (Sect. 6.3), and the free energy stored in series elasticity is transferred to the external load as kinetic energy. Step 6 is unidirectional and is the slowest step under the isometric…

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  Fig. 6. CB scheme approximation of Fig. 5 while oscillatory work (process B) is observed. X3c combines states 1, 2, 3, and 3a in Fig. 5 (X3c≡X1 + X2 + X3 + X3a). Because Steps 1–3a are faster than Step 4 (Process B), they can be approximated by an equilibrium in Step 3c. K3c is the equilibrium constant of X3c ↔ X4 interconversion. Because Step 6 is much slower than Step 4, it can be approximated that it does not happen (r6 ≈ 0) while Process B is observed

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  Fig. 7. Force supported by each CB state. Rabbit psoas (fast-twitch type IID fibers) (Kawai and Zhao 1993) and rabbit soleus (slow-twitch type I fibers) (Wang and Kawai 1997). Data were taken from original publications and replotted. Data were normalized to the first control force. Det detached states that include M.ATP and M.ADP.Pi

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  Fig. 8. A Isometric tension on rabbit psoas fibers during standard activation (pCa 4.40, MgATP 5 mM, Pi 8 mM, ionic strength 200 mM, pH 7.00). B Equilibrium constant K4, fitted to modified Van’t Hoff equation (solid curve is based on Eq. 21 with best fit values). Replotted from Murphy et al. (1996) and Kawai (2003), original data from Zhao and Kawai (1994). Average and SEM are shown