Mishchenko Artem M, Dotsenko Olga I, Taradina Galina V
Biophysical Department, "Vasyl' Stus" Donetsk National University, Vinnitsa, Ukraine.
Gen Physiol Biophys. 2018 Jul;37(4):363-374. doi: 10.4149/gpb_2018005. Epub 2018 Jun 29.
One of commonly used approaches of biophysical modeling of muscle contractile apparatus is spatially explicit discrete lattice models in Monte Carlo simulation. Such models allow to reproduce structural features and actin-myosin interaction in the muscle contractile system more accurately. Limitation of such models is their low computational efficiency and stochasticity under certain circumstances. This work introduces deterministic approximation of stochastic model that considers a pair of rigid contractile filaments interaction. Approximation background is discreetness of spacing between cross-bridges and binding sites. Due to this property cross-bridges can be divided into discrete groups with the same strain, and considered statistically using the set of ordinary differential equations. Deterministic model is more computationally efficient, operates with average values. Within the given approach isotonic contraction was simulated. A comparison with Monte Carlo simulation demonstrates that approximation reproduces results for stochastic model with large number of cross-bridges. Also within the deterministic model a mechanism and essential conditions for oscillations appearance in isotonic transient response, relations of their parameters with geometrical ones of filaments lattice were examined, theoretical and experimental results were compared. The proposed approach can also be applied to approximation of continuous Huxley-based models solutions. Advantage over existing numerical methods is their greater numerical stability.
肌肉收缩装置生物物理建模常用的方法之一是蒙特卡罗模拟中的空间显式离散晶格模型。这类模型能够更准确地再现肌肉收缩系统中的结构特征以及肌动蛋白与肌球蛋白的相互作用。此类模型的局限性在于其计算效率较低，且在某些情况下具有随机性。这项工作引入了一种随机模型的确定性近似方法，该方法考虑了一对刚性收缩细丝的相互作用。近似的背景是横桥与结合位点之间间距的离散性。由于这一特性，横桥可被划分为具有相同应变的离散组，并使用一组常微分方程进行统计考虑。确定性模型的计算效率更高，以平均值进行运算。在给定的方法中对等张收缩进行了模拟。与蒙特卡罗模拟的比较表明，该近似方法能够再现具有大量横桥的随机模型的结果。此外，在确定性模型中，对等张瞬态响应中振荡出现的机制和必要条件、其参数与细丝晶格几何参数的关系进行了研究，并对理论和实验结果进行了比较。所提出的方法也可应用于基于赫胥黎连续模型解的近似。与现有数值方法相比，其优势在于具有更高的数值稳定性。
