Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK.
Department of Structural Engineering, University of Tabriz, P.O. Box 51666-16471, Tabriz, Iran.
Biomech Model Mechanobiol. 2018 Dec;17(6):1631-1662. doi: 10.1007/s10237-018-1048-1. Epub 2018 Jul 10.
Cells are quintessential examples of out-of-equilibrium systems, but they maintain a homeostatic state over a timescale of hours to days. As a consequence, the statistics of all observables is remarkably consistent. Here, we develop a statistical mechanics framework for living cells by including the homeostatic constraint that exists over the interphase period of the cell cycle. The consequence is the introduction of the concept of a homeostatic ensemble and an associated homeostatic temperature, along with a formalism for the (dynamic) homeostatic equilibrium that intervenes to allow living cells to evade thermodynamic decay. As a first application, the framework is shown to accurately predict the observed effect of the mechanical environment on the in vitro response of smooth muscle cells. This includes predictions that both the mean values and diversity/variability in the measured values of observables such as cell area, shape and tractions decrease with decreasing stiffness of the environment. Thus, we argue that the observed variabilities are inherent to the entropic nature of the homeostatic equilibrium of cells and not a result of in vitro experimental errors.
细胞是典型的非平衡系统，但它们可以在数小时到数天的时间尺度内维持稳态。因此，所有可观察量的统计数据都非常一致。在这里，我们通过包括细胞周期的间期间存在的稳态约束，为活细胞开发了一个统计力学框架。其结果是引入了稳态系综的概念和相关的稳态温度，以及一种形式主义，用于（动态）稳态平衡，以允许活细胞逃避热力学衰减。作为第一个应用，该框架被证明可以准确预测机械环境对平滑肌细胞体外反应的观察到的影响。这包括预测可观察量（如细胞面积、形状和牵引力）的平均值和多样性/可变性随着环境刚度的降低而降低。因此，我们认为观察到的可变性是细胞稳态平衡的熵性质所固有的，而不是体外实验误差的结果。
