Wang Xinxin, Carlsson Anders E
Department of Physics, Washington University, One Brookings Drive, Campus Box 1105, USA.
Phys Biol. 2014 Oct 14;11(6):066002. doi: 10.1088/1478-3975/11/6/066002.
Directed cell migration requires a spatially polarized distribution of polymerized actin. We develop and treat a mechanical model of cell polarization based on polymerization and depolymerization of actin filaments at the two ends of a cell, modulated by forces at either end that are coupled by the cell membrane. We solve this model using both a simulation approach that treats filament nucleation, polymerization, and depolymerization stochastically, and a rate-equation approach based on key properties such as the number of filaments N and the number of polymerized subunits F at either end of the cell. The rate-equation approach agrees closely with the stochastic approach at steady state and, when appropriately generalized, also predicts the dynamic behavior accurately. The calculated transitions from symmetric to polarized states show that polarization is enhanced by a high free-actin concentration, a large pointed-end off-rate, a small barbed-end off-rate, and a small spontaneous nucleation rate. The rate-equation approach allows us to perform a linear-stability analysis to pin down the key interactions that drive the polarization. The polarization is driven by a positive-feedback loop having two interactions. First, an increase in F at one side of the cell lengthens the filaments and thus reduces the decay rate of N (increasing N); second, increasing N enhances F because the force per growing filament tip is reduced. We find that the transitions induced by changing system properties result from supercritical pitchfork bifurcations. The filament lifetime depends strongly on the average filament length, and this effect is crucial for obtaining polarization correctly.
定向细胞迁移需要聚合肌动蛋白在空间上呈极化分布。我们基于细胞两端肌动蛋白丝的聚合和解聚，开发并处理了一个细胞极化的力学模型，该过程由细胞膜耦合的两端力进行调节。我们使用两种方法求解该模型：一种是随机处理细丝成核、聚合和解聚的模拟方法，另一种是基于诸如细胞两端细丝数量N和聚合亚基数量F等关键特性的速率方程方法。速率方程方法在稳态时与随机方法密切吻合，并且在适当推广时，也能准确预测动态行为。计算得到的从对称态到极化态的转变表明，高游离肌动蛋白浓度、大的尖端解聚速率、小的带刺端解聚速率和小的自发成核速率会增强极化。速率方程方法使我们能够进行线性稳定性分析，以确定驱动极化的关键相互作用。极化由具有两种相互作用的正反馈回路驱动。首先，细胞一侧F的增加会使细丝变长，从而降低N的衰减速率（增加N）；其次，增加N会增强F，因为每个生长细丝末端的力会减小。我们发现，系统特性变化引起的转变是由超临界叉形分岔导致的。细丝寿命强烈依赖于平均细丝长度，这种效应对于正确获得极化至关重要。
