Analysis of a mesoscopic stochastic model of microtubule dynamic instability
Analysis of a mesoscopic stochastic model of microtubule dynamic instability
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DOI：
10.1103/physreve.74.041920
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发表时间：
2006-10-01
影响因子：
2.4
通讯作者：
Alber, Mark S.
中科院分区：
文献类型：
--
作者：
Margolin, Gennady;Gregoretti, Ivan V.;Alber, Mark S.
为了研究细胞边缘在体内的作用并分析竞争对有限数量微管蛋白的影响，建立了有界域中线性一维微管系统动态不稳定性的理论模型。该模型与早期模型的不同之处在于，MTS的演变基于单个介观单元(例如，每个原丝的异二聚体)转变的速率，而不是假设的更大规模宏观变化的有效率和频率，例如从MTS的长度历史曲线中提取。假定聚合后GTP以有限速率自发水解，并推导出有效突变频率的理论估计以及表征MT长度分布和帽大小的其他参数。我们实现了一个简单的帽模型，该模型不包括矢量水解。我们证明了我们的理论预测，如自由微管蛋白的稳态浓度和MT长度分布参数，与数值模拟是一致的。本模型在封闭体系中控制MTS动力学的介观参数和MTS的宏观特征之间建立了定量联系。最后，我们对实验中观察到的非指数MT长度分布进行了解释。特别是，我们证明了在实验中出现这种非指数分布可能是因为没有达到真正的稳定状态和/或由于细胞边缘的存在。
A theoretical model of dynamic instability of a system of linear one-dimensional microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single-mesoscopic-unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates and frequencies of larger-scale macroscopic changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady-state concentration of free tubulin and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between mesoscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Last, we provide an explanation for nonexponential MT length distributions observed in experiments. In particular, we show that the appearance of such nonexponential distributions in the experiments can occur because a true steady state has not been reached and/or due to the presence of a cell edge.