Biomechanics and Biorobotics, Stuttgart Centre for Simulation Sciences (SC SimTech), Universität Stuttgart, Allmandring 28, Stuttgart 70569, Germany; Institut für Sportwissenschaft, Friedrich-Schiller-Universität, Seidelstraße 20, Jena 07749, Germany.
Biomechanics and Biorobotics, Stuttgart Centre for Simulation Sciences (SC SimTech), Universität Stuttgart, Allmandring 28, Stuttgart 70569, Germany; Multi-level Modeling in Motor Control and Rehabilitation Robotics, Hertie-Institute for Clinical Brain Research, Eberhard-Karls-Universität, Hoppe-Seyler-Straße 3, Tübingen 72076, Germany.
J Theor Biol. 2018 Nov 7;456:137-167. doi: 10.1016/j.jtbi.2018.07.023. Epub 2018 Jul 23.
Measuring, analysing, and modelling muscle contraction has a long history. In consequence, some signature characteristics of skeletal muscle contraction have been found. On a microscopic level, these are the typical non-steady-state responses of the cross-bridge bindings to steps in force and length. On a macroscopic level, the force-velocity, enthalpy-velocity, and efficiency-velocity relations for concentric steady-state contractions are crucial characteristics. As these characteristics were repeatedly confirmed across animal species and sizes, they are expected to pinpoint basic physical properties of the mechanical structure that embodies the skeletal muscle machinery. The approach presented in this article explains, for the first time, these characteristics at both the microscopic and the macroscopic scale with one model and one set of parameters. According to expectation, this model is solely built on the basic mechanical structure of the muscular, contractile machinery. Its four mechanical elements represent the source of work, the serial elasticity, damping due to mechanical deformation, and damping due to the biochemical ATP hydrolysis in the energy conversion process. For explaining all mentioned non-steady-state and steady-state characteristics at once, the model requires, at maximum, ten parameters of which only three parameters representing damping properties plus one representing muscle-internal steady-state kinematics were free to be chosen. All other parameters were already fixed by literature knowledge of the geometrical structure and force characteristics of one cross-bridge. Amongst other results, we found that (i) the most reduced variant of the model is mathematically equivalent to a former version and (ii) the curvature parameter of the Hill relation can be interpreted as the ratio of strengths of the two modelled damping processes. This model approach not only unifies microscopic and macroscopic experimental findings, but further allows to interpret findings of molecular damping and elasticity and scaling of muscle properties, as discussed in this article.
测量、分析和模拟肌肉收缩已有很长的历史。因此，发现了一些骨骼肌收缩的特征。在微观水平上，这些特征是横桥结合物对力和长度阶跃的典型非稳态响应。在宏观水平上，同心稳态收缩的力-速度、焓-速度和效率-速度关系是至关重要的特征。由于这些特征在不同的动物物种和大小中得到了反复证实，因此它们被认为可以确定体现骨骼肌机械结构的基本物理特性。本文提出的方法首次用一个模型和一组参数解释了微观和宏观尺度上的这些特征。根据预期，该模型仅基于肌肉收缩机械结构的基本力学结构。它的四个力学元件代表了工作的来源、串联弹性、由于机械变形引起的阻尼以及能量转换过程中由于生化 ATP 水解引起的阻尼。为了一次性解释所有提到的非稳态和稳态特征，该模型最多需要十个参数，其中只有三个代表阻尼特性的参数和一个代表肌肉内部稳态运动学的参数可以自由选择。所有其他参数都已经通过一个横桥的几何结构和力特性的文献知识固定。在其他结果中，我们发现(i)模型的最简化变体在数学上等同于以前的版本，(ii)Hill 关系的曲率参数可以解释为两个建模阻尼过程的强度比。这种模型方法不仅统一了微观和宏观实验结果，而且还允许解释分子阻尼和弹性以及肌肉特性的缩放的发现，如本文所讨论的。
