Rockenfeller Robert, Günther Michael, Stutzig Norman, Haeufle Daniel F B, Siebert Tobias, Schmitt Syn, Leichsenring Kay, Böl Markus, Götz Thomas
Mathematical Institute, University of Koblenz-Landau, Koblenz, Germany.
Institute for Modelling and Simulation of Biomechanical Systems, Computational Biophysics and Biorobotics, University of Stuttgart, Stuttgart, Germany.
Front Physiol. 2020 May 5;11:306. doi: 10.3389/fphys.2020.00306. eCollection 2020.
Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit and were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.
由神经冲动和随后的钙释放引发，骨骼肌纤维由于肌动蛋白 - 肌球蛋白横桥的重复动力冲程而收缩（主动产生力）。执行这些横桥循环所需的能量由三磷酸腺苷（ATP）的水解提供。反应产物二磷酸腺苷（ADP）和无机磷酸（P ），然后与其他反应物（如磷酸肌酸）一起用于补充ATP能量储存。然而，类似于因自身废物而死亡的酵母，水解反应产物会降低ATP的化学势，因此随着它们浓度的升高会抑制肌肉的力产生。我们建议使用“耗竭”一词来表示由P 和ADP的累积以及ATP浓度可能降低引起的力降低（疲劳）。基于生化动力学，我们提出了一个基于水解ATP - ADP - P 动力学的肌肉纤维耗竭模型，该动力学被认为与长度和钙活性有关。用微分代数方程表示，新的子模型允许以直接的方式增强现有的希尔型兴奋 - 收缩模型。利用兔等长收缩过程中力衰减的测量时间过程进行模型验证，结果发现我们建议的模型增强非常有前景。我们讨论了我们的模型方法对一般增强肌肉模型的影响，以及磷酸盐动力学作为肌肉疲劳一个因素的重要性的几个方面。
