Modeling actin-myosin interaction: beyond the Huxley–Hill framework
Abstract
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.
Main contribution of the publication
This article presents, for the first time, the conditions for the well-posedness of the classical Huxley-Hill framework for modeling the actin-myosin interaction, a framework that has been widely used since the 1950s.
It introduces a new modeling approach based on an Eulerian parametrization of the molecular motor that accounts for a broader class of physiological configurations compared to existing models, without the need for a more complex multi-site framework.
The compatibility of the newly introduced model with thermodynamic principles is rigorously established.
The model’s formulation leverages the concept of a Poisson random measure, introducing a novel mathematical tool for modeling molecular motors. It depicts them as a continuous-time stochastic Markov process, involving a continuous overdamped Langevin dynamics for the position of the head, and a discrete Poisson dynamics for the state (whether attached or detached).
Reference
@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/}
}