Induced potential model of muscular contraction mechanism and myosin molecular structure

The proposed model is characterized by the constant r (Eq. 2-1), the induced potential (Fig. 1), two attached states of a myosin head (Fig. 1), the nonlinear elastic property of the crossbridge (Eq. 2-7), and the expression of $\text{U}{}^{\mathrm{\ast }}$ (Eqs. 3-8 and 3-9), which led us to the following conclusions.

• 1.

  1. The following various magnitudes of myosin head motion are compatible with each other: about 2 nm of the quantity called power stroke by Irving (27), which is the mean moving distance of myosin head in the isometric tension in our model, 4–5 nm of the displacement of a single myosin head during one ATP hydrolysis cycle (Molloy et al. (20)) or a few tens of nm when the actin and myosin filaments are set parallel (Tanaka et al. (21) and Kitamura et al. (42)), and more than 200 nm of the myosin head displacement in a multi-myosin head system below 22 °C (Harada et al. (19)).

• 2.

  2. There is one-to-one coupling between the ATP hydrolysis cycle and the attachment-detachment cycle of a myosin head in accordance with the generally accepted concept of chemical reactions, since the head is trapped in the spatially shifting wide potential well (Fig. 1) until ε_ATP is exhausted. Here, an actin filament interacts with a myosin head like a single molecule.

• 3.

  3. The calculated tension dependence of muscle stiffness agrees well with the observations by Ford et al. (12), as shown in Fig. 9.

• 4.

  4. The calculated shortening velocity V of muscle as a function of $\text{P}\text{P}{}_0$ agreed very well with experimental results as shown in Fig. 13. The deviation from the Hill equation (34) observed by Edman (32) is related with $\text{U}{}^{\mathrm{\ast }}$ being effectively infinite for f_J < κ_by_c0 (Fig. 10).

• 5.

  5. Calculated energy liberation rate W + H as a function of $\text{P}\text{P}{}_0$ has characteristics almost the same as the Hill equation (33), and agrees well with the experimental results as shown in Fig. 14.

• 6.

  6. The time course of tension recovery after a quick length change is determined by four parameters: κ_f, κ_b, a, and Z₀. Among them, κ_f, κ_b (Eq. 2–22) and a (Eq. 4-21) are readily determined by analysis of the steady filament sliding and p₀. Calculations of $\text{T}{}_1\text{T}{}_0$ and $\text{T}{}_2\text{T}{}_0$ with these three parameters are in very good agreement with experimental data (Fig. 21). Calculated tension variations by assigning the value in Eq. 4-23 to Z₀ agree with the observation (Fig. 17).

• 7.

  7. The model suggests that large fluctuations exist in relative positions between the actin and myosin filaments even when the load on a muscle is kept constant (Fig. 23). Taking this fluctuation into account, the time course of the isotonic velocity transient shown in Fig. 22 becomes understandable referring to Fig. 24.

• 8.

  8. The experimental data of the δy_hs vs. $\text{ΔP}\text{P}{}_0$ relationship (Fig. 25) is explained. The δy_hs value at $\text{ΔP}\text{P}{}_0\text{= 0}$ (about 5 nm) supports the two-attached-state model and thus indicates that the incremental unit step of a myosin head motion along an actin filament is close to L (5.46 nm).