Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.

肌肉感知内部产生的力和外部施加的力，在不同的时间尺度上以协调的等级方式对这些力作出反应。肌肉基本单位的中心，即肌节 M 带，位置完美，可以感知肌肉所承受的不同类型的负荷。特别是，位于 M 带的肌动蛋白 (TK) 激酶结构域是机械信号传导的已知候选者。在这里，我们开发了一个定量数学模型，该模型描述了基于 TK 的机械敏感信号的动力学，并预测了响应运动和康复方案的营养变化。首先，我们建立了力作用下 TK 构象变化的动力学模型：开放、磷酸化、信号传导和自抑制。我们发现 TK 作为亚稳态机械敏感开关打开，与同样耗能高昂的耐力运动相比，在高负荷阻力运动后自然会产生更大的信号。接下来，为了使模型稳定并给出连贯的预测，特别是对于运动方案开始后的滞后，我们必须考虑磷酸盐的相关动力学（由 ATP 携带）和蛋白质合成速率的非线性依赖性关于肌纤维大小。我们认为后一种效应可能是通过对核糖体扩散通过筛状肌丝晶格的空间抑制而发生的。完整的模型产生了肌肉横截面积和张力的稳态解决方案（稳态），以及对训练的定量合理的肥大反应，以及张力长期降低后的萎缩。