Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges.

To understand the macroscopic function of the human heart based on sub-cellular microscopic events, multiscale analysis is indispensable. Our heart simulator uses the so-called homogenization method, where both the human heart and the myocardial cells are modeled and solved simultaneously by the finite element method. Because the contraction and deformation of each finite element in the heart model are governed by their respective cell model, the NDOF of all the cells becomes prohibitively large. Furthermore, the phenomena are highly nonlinear and transient. This challenging problem has been tackled by our group for many years, and a novel algorithm to accelerate the computation was implemented in the code. We have recently tested its performance using the T2K Open Supercomputer (Tokyo). A pulsation of the heart with a total NDOF of 160 million was successfully simulated using 6144 CPU cores in ten hours. Scalability and other computational performances were measured and are discussed.