Zeitz Maria, Kierfeld Jan
Physics Department, TU Dortmund University, Dortmund, Germany.
Physics Department, TU Dortmund University, Dortmund, Germany.
Biophys J. 2014 Dec 16;107(12):2860-2871. doi: 10.1016/j.bpj.2014.10.056.
We formulate and analyze a theoretical model for the regulation of microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin, which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell edge, which closes a positive feedback loop. We investigate both tubulin sequestering and catastrophe promotion as mechanisms for MT growth inhibition by stathmin. For a homogeneous stathmin concentration in the absence of Rac1, we find a switchlike regulation of the MT mean length by stathmin. For constitutively active Rac1 at the cell edge, stathmin is deactivated locally, which establishes a spatial gradient of active stathmin. In this gradient, we find a stationary bimodal MT-length distribution for both mechanisms of MT growth inhibition by stathmin. One subpopulation of the bimodal length distribution can be identified with fast-growing and long pioneering MTs in the region near the cell edge, which have been observed experimentally. The feedback loop is closed through Rac1 activation by MTs. For tubulin sequestering by stathmin, this establishes a bistable switch with two stable states: one stable state corresponds to upregulated MT mean length and bimodal MT length distributions, i.e., pioneering MTs; the other stable state corresponds to an interrupted feedback with short MTs. Stochastic effects as well as external perturbations can trigger switching events. For catastrophe-promoting stathmin, we do not find bistability.
我们构建并分析了一个理论模型，用于研究信号蛋白Rac1和stathmin对微管（MT）聚合动力学的调控。在细胞中，胞质中的stathmin会抑制MT的生长速率，而Rac1会使stathmin失活。生长中的MT在细胞边缘激活Rac1，从而形成一个正反馈回路。我们研究了stathmin通过微管蛋白隔离和促进微管解聚这两种机制来抑制MT生长的情况。在没有Rac1的情况下，对于均匀的stathmin浓度，我们发现stathmin对MT平均长度具有类似开关的调控作用。对于细胞边缘持续激活的Rac1，stathmin会在局部失活，从而建立起活性stathmin的空间梯度。在这个梯度中，我们发现对于stathmin抑制MT生长的两种机制，MT长度分布都呈现出稳定的双峰分布。双峰长度分布中的一个亚群可以被确定为细胞边缘附近区域中快速生长且较长的先锋MT，这已在实验中观察到。通过MT对Rac1的激活，反馈回路得以闭合。对于stathmin的微管蛋白隔离作用，这建立了一个具有两个稳定状态的双稳态开关：一个稳定状态对应于上调的MT平均长度和双峰MT长度分布，即先锋MT；另一个稳定状态对应于短MT的中断反馈。随机效应以及外部扰动都可以触发开关事件。对于促进微管解聚的stathmin，我们没有发现双稳态。
