Bioquant, and Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany.
Proc Natl Acad Sci U S A. 2010 Apr 6;107(14):6304-9. doi: 10.1073/pnas.0913730107. Epub 2010 Mar 22.
The lamellipodium of migrating animal cells protrudes by directed polymerization of a branched actin network. The underlying mechanisms of filament growth, branching, and capping can be studied in in vitro assays. However, conflicting results have been reported for the force-velocity relation of such actin networks, namely both convex and concave shapes as well as history dependencies. Here we model branching as a reaction that is independent of the number of existing filaments, in contrast to capping, which is assumed to be proportional to the number of existing filaments. Using both stochastic network simulations and deterministic rate equations, we show that such a description naturally leads to the stability of two qualitatively different stationary states of the system, namely a +/- 35 degrees and a +70/0/-70 degrees orientation pattern. Changes in network growth velocity induce a transition between these two patterns. For sufficiently different protrusion efficiency of the two network architectures, this leads to hysteresis in the growth velocity of actin networks under force. Dependent on the history of the system, convex and concave regimes are obtained for the force-velocity relation. Thus a simple generic model can explain the experimentally observed anomalies, with far reaching consequences for cell migration.
迁移动物细胞的片状伪足通过分支肌动蛋白网络的定向聚合突出。可以在体外测定中研究细丝生长、分支和盖帽的基础机制。然而，对于这种肌动蛋白网络的力-速度关系，已经报道了相互矛盾的结果，即凸形和凹形以及历史依赖性。在这里，我们将分支建模为一种独立于现有细丝数量的反应，而盖帽则假设与现有细丝的数量成正比。使用随机网络模拟和确定性速率方程，我们表明，这种描述自然导致系统两种定性不同的稳定状态的稳定性，即 +/- 35 度和 +70/0/-70 度取向模式。网络生长速度的变化会诱导这两种模式之间的转变。对于两种网络结构的突起效率足够不同，这会导致在力下肌动蛋白网络的生长速度出现滞后。取决于系统的历史，会得到凸形和凹形区域的力-速度关系。因此，一个简单的通用模型可以解释实验观察到的异常，这对细胞迁移有深远的影响。
