This study proposes a three‑state power‑stroke model to elucidate the SPontaneous Oscillatory Contractions (SPOC) generated by myosin motor proteins during muscle contraction, and conducts a linear stability analysis of the system. The authors couple a molecular‑scale model—“pre‑stroke → post‑stroke → detached” states—to a mesoscale equation of motion for myofibrillar dynamics, reformulating the combined system as a rank‑1 update problem. Within this new mathematical framework they analytically derive the eigenmodes of the Jacobian near the steady state and, for the first time, explicitly state the eigenvalue conditions required for SPOC.
Key findings:
Two positive real eigenvalues dominate the oscillatory dynamics.
The larger eigenvalue corresponds to the rapid sarcomere‑length extension caused by a collective reverse stroke from the post‑stroke state.
The smaller eigenvalue governs the subsequent slow contraction phase.
By tracking how these eigenvalues depend on parameters such as stroke distance, elastic stiffness, and viscous damping, the study systematically evaluates how oscillation frequency and waveform change after crossing a Hopf bifurcation. This mechanistically explains waveforms that combine fast relaxation with slow contraction—patterns difficult to reproduce with previous two‑state models.
Beyond providing a theoretical basis for natural oscillations observed in cardiac and insect asynchronous muscles, the model is valuable for assessing energy efficiency and relaxation mechanisms when many molecular motors work cooperatively. Incorporating this framework into the group’s heart simulations on post‑K supercomputers opens a path to molecular‑level predictions of beat‑to‑beat pressure decay and energy expenditure. Iterating between analytic theory and numerical simulation is expected to refine universal laws underlying SPOC’s nonlinear phenomena.
Article information & citation
Takumi Washio, Toshiaki Hisada, Seine A. Shintani, Hideo Higuchi. Analysis of spontaneous oscillations for a three‑state power‑stroke model. Physical Review E 95, 022411 (2017).