Laboratoire de Modélisation et Simulation Multi-Echelle - UMR 8208, Université Paris Est - CNRS, 61 Avenue du Général de Gaulle, 94010, Créteil, France.
Inria - Université Paris-Saclay, 1 rue d'Estienne d'Orves, 91120, Palaiseau, France.
Biomech Model Mechanobiol. 2019 Jun;18(3):563-587. doi: 10.1007/s10237-018-1102-z. Epub 2019 Jan 3.
We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs)-one of which associated with the so-called power stroke-and two possible chemical states, i.e., bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model and (2) to thus account-at the macroscopic scale-for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data-taken here for skeletal muscles-and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.
我们提出了肌球蛋白头在肌节中的化学-机械模型，该模型基于刚性滑动丝的经典描述。在我们的模型中，肌球蛋白头有两个力学自由度（自由度）-其中一个与所谓的动力冲程有关-和两个可能的化学状态，即结合到肌动蛋白位点或不结合。我们的主要动机有两个：（1）推导出多尺度耦合的化学-机械模型，（2）从而在宏观尺度上解释经典肌肉模型无法解释的力学现象。该模型首先以朗之万随机方程的形式编写，然后我们能够获得与力学自由度和化学状态相关的概率密度函数的相应福克-普朗克偏微分方程。这种第二种形式很重要，因为它允许监测肌肉能量学，并且还可以将我们的模型与经典模型进行比较，例如 Huxley'57 模型，我们的方程在两种不同类型的简化假设下可以简化为 Huxley'57 模型。这提供了深入的了解，并为 Huxley'57 提供了朗之万形式。然后，我们展示了如何根据实验数据（这里为骨骼肌）对模型进行校准，数值模拟表明该模型能够很好地代表复杂的生理现象，特别是快速等长瞬变，动力冲程被认为在其中起关键作用，从而避免了许多经典模型的局限性。
