Modeling acto-myosin interaction: beyond the Huxley–Hill framework

Louis-Pierre Chaintron (1, 2) , Matthieu Caruel (2) , François Kimmig (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine

Contractile force in muscle tissue is produced by the interaction of myosin molecular motors that bind and pull on specific sites located on surrounding actin filaments. The classical framework set by the landmark works of A.F. Huxley and T.L. Hill to model this active system is build on the central assumption that thermal fluctuations of a given myosin motor are sufficiently small so that it cannot interact with more than one binding site at any time. In this paper we present the physiological and mathematical limitations of this approach to motivate a new formulation that circumvent them without resorting to the more complex multi-site model paradigm. The acto-myosin system is now described as a Markov process combining Langevin driftdiffusion and Poisson jumps dynamics. We show that the corresponding system of Stochastic Differential Equation is well-posed and derive its Partial Differential Equation analog in order to obtain the thermodynamic balance laws. We finally show that by applying standard elimination procedures, a modified version of the original Huxley-Hill framework can be obtained as a reduced version of our model. Theoretical results are supported by numerical simulations where the model outputs are compared to benchmark experimental data.

Mots clés: Applied mathematics; Applied probability; Muscle contraction; Thermodynamics; Molecular motors; Jump-diffusion process; Poisson random measures

Domaines: Modélisation et simulation; Physique mathématique [math-ph]; Biomécanique [physics.med-ph]

Louis-Pierre Chaintron, Matthieu Caruel, François Kimmig. Modeling acto-myosin interaction: beyond the Huxley–Hill framework. 2022. ⟨hal-03699263v1⟩