Modeling actin-myosin interaction: beyond the Huxley–Hill framework
Louis-Pierre Chaintron1 ; Matthieu Caruel2 ; François Kimmig3
1 DMA, École normale supérieure, Université PSL, CNRS, 75005 Paris, France and Inria, France; LMS, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France
2 Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, 94010 Créteil, France
3 Inria, France; LMS, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France
MathematicS In Action, Tome 12 (2023) no. 1, pp. 191-226.

Contractile force in muscle tissue is produced by myosin molecular motors that bind and pull on specific sites located on surrounding actin filaments. The classical framework to model this active system was set by the landmark works of A.F. Huxley and T.L. Hill. This framework is built on the central assumption that the relevant quantity for the model parametrization is the myosin head reference position. In this paper, we present an alternative formulation that allows to take into account the current position of the myosin head as the main model parameter.

The actin-myosin system is described as a Markov process combining Langevin drift-diffusion 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.

Publié le :
DOI : 10.5802/msia.38
Classification : 00X99
Mots clés : Applied mathematics, Applied probability, Muscle contraction, Thermodynamics, Molecular motors, Jump-diffusion process, Poisson random measures
Louis-Pierre Chaintron 1 ; Matthieu Caruel 2 ; François Kimmig 3

1 DMA, École normale supérieure, Université PSL, CNRS, 75005 Paris, France and Inria, France; LMS, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France
2 Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, 94010 Créteil, France
3 Inria, France; LMS, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Louis-Pierre Chaintron; Matthieu Caruel; François Kimmig. Modeling actin-myosin interaction: beyond the Huxley–Hill framework. MathematicS In Action, Tome 12 (2023) no. 1, pp. 191-226. doi : 10.5802/msia.38. https://msia.centre-mersenne.org/articles/10.5802/msia.38/

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