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A Markov chain-based model for actomyosin dynamics. (English) Zbl 1180.60075

The paper develops a continuous time discrete Markov-chain with \(k+3\) states to describe the dynamics of actomyosin system during the chemical cycle of an ATP molecule. Two of the states are reflecting states and correspond to the phase either when myosin is rigidly attached to the action filament or when the power stroke takes place. The proposed model incorporates the observations of experimental results on the siding of myosin heads along action filament. Steady-state probabilities are derived using standard techniques. A diffusive approximation of the process describing the myosin rising phase is also proposed and it provides a quantitative description of the phenomenon. The approximation of the process is shown to be a Weiner-type diffusion process with jumps between two reflecting barriers.

MSC:

60J85 Applications of branching processes
92C40 Biochemistry, molecular biology