Theoretical Analysis of the Stochastic Behaviour of Skeletal Actomyosin Complex

Abstract

The skeletal muscle models are usually based on the hypotheses proposed by AF Huxley [1,2], but only recently an experimental evidence of them has been obtained: in [3] a single Myosin II shows several 5.5 nm steps on an actin filament in one preferred direction per ATP cycle, in [4] the probability for the actomyosin complex to switch from a weakly to a strongly attached state increases when the myosin is stretched (SS).We have computed the steady state solution of 2D Fokker-Plank equation associated to a system of a motor bound to a needle in the presence of an actin filament. We show how the dwell time of the stable states of the actomyosin complex is affected by the drag coefficient of the needle and use the data in [3] to estimate the bias of the energy toward the direction of the motion.Based on this analysis, we have developed a mathematical model to analyse quantitatively the feasibility of the hypothesis proposed in [3]. The stepping behaviour is view as a diffusive process in a locally tilted but globally flat potential, while the SS affects the jump probability in the attachment-detachment process. The response of the model is analysed by a stochastic simulation of the associated Langevin equations and succeeds to reproduce the behaviour of the muscle in its short time scale, related to the power stroke, and in its long time scale, related to the actin-myosin attachment detachment cycle.[1] Huxley. Prog Biophys Biophys Chem (1957)[2] Huxley, Simmons Nature (1971)[3] Kitamura et al. Biophysics (2005)[4] Iwaki et al. Nat Chem Biol (2009)