多头绒泡菌原生质滴机械化学模式的主动孔隙弹性模型
An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum
摘要：
基于最近的实验研究，我们推导并分析了多头绒泡菌原生质液滴中观察到的收缩模式的二维模型。该模型耦合一个模型的一个积极的多孔弹性两相介质与方程描述的细胞内游离钙浓度的时空动态。多孔弹性介质被认为是由一个积极的粘弹性固体代表的细胞骨架和描述的细胞溶质的粘性流体。多孔弹性介质的模型方程是从连续的力平衡方程，其中包括相关的机械领域和不可压缩性关系的两相介质。本文用平流运输法对绒泡菌原生质中钙动力学的反应扩散方程进行了推广，平流运输是由机械应力引起的胞质液流动引起的。此外，我们假设在固体细胞骨架的主动张力调节的钙浓度在流体相在同一位置，这引入了化学机械反馈。没有变形和胞质流的均匀状态的线性稳定性分析表现出振荡的图灵不稳定性足够大的机械化学耦合强度。模型方程的数值模拟再现了各种各样的波模式，包括行波和驻波，湍流模式，旋转螺旋线和反相振荡与实验观察的原生质液滴中的收缩模式。
英文摘要：
Motivated by recent experimental studies, we derive and analyze a twodimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a model of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The model equations for the poroelastic medium are obtained from continuum force-balance equations that include the relevant mechanical fields and an incompressibility relation for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stresses. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a chemomechanical feedback. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.
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