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.
Keywords: Applied mathematics, Applied probability, Muscle contraction, Thermodynamics, Molecular motors, Jump-diffusion process, Poisson random measures
@article{MSIA_2023__12_1_191_0, author = {Louis-Pierre Chaintron and Matthieu Caruel and Fran\c{c}ois Kimmig}, title = {Modeling actin-myosin interaction: beyond the {Huxley{\textendash}Hill} framework}, journal = {MathematicS In Action}, pages = {191--226}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {12}, number = {1}, year = {2023}, doi = {10.5802/msia.38}, language = {en}, url = {https://msia.centre-mersenne.org/articles/10.5802/msia.38/} }
TY - JOUR AU - Louis-Pierre Chaintron AU - Matthieu Caruel AU - François Kimmig TI - Modeling actin-myosin interaction: beyond the Huxley–Hill framework JO - MathematicS In Action PY - 2023 SP - 191 EP - 226 VL - 12 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - https://msia.centre-mersenne.org/articles/10.5802/msia.38/ DO - 10.5802/msia.38 LA - en ID - MSIA_2023__12_1_191_0 ER -
%0 Journal Article %A Louis-Pierre Chaintron %A Matthieu Caruel %A François Kimmig %T Modeling actin-myosin interaction: beyond the Huxley–Hill framework %J MathematicS In Action %D 2023 %P 191-226 %V 12 %N 1 %I Société de Mathématiques Appliquées et Industrielles %U https://msia.centre-mersenne.org/articles/10.5802/msia.38/ %R 10.5802/msia.38 %G en %F MSIA_2023__12_1_191_0
Louis-Pierre Chaintron; Matthieu Caruel; François Kimmig. Modeling actin-myosin interaction: beyond the Huxley–Hill framework. MathematicS In Action, Maths Bio, Volume 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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