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首页> 外文期刊>Journal of Mathematical Biology >The role of mode switching in a population of actin polymers with constraints
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The role of mode switching in a population of actin polymers with constraints

机译：模式切换在肌动蛋白聚合物群中的作用与约束

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In this paper, we introduce a stochastic model for the dynamics of actin polymers and their interactions with other proteins in the cellular envelop. Each polymer elongates and shortens, and can switch between several modes depending on whether it is bound to accessory proteins that modulate its behaviour as, for example, elongation-promoting factors. Our main aim is to understand the dynamics of a large population of polymers, assuming that the only limiting quantity is the total amount of monomers, set to be constant to some large N. We first focus on the evolution of a very long polymer, of size O(N), with a rapid switch between modes (compared to the timescale over which the macroscopic fluctuations in the polymer size appear). Letting N tend to infinity, we obtain a fluid limit in which the effect of the switching appears only through the fraction of time spent in each mode at equilibrium. We show in particular that, in our situation where the number of monomers is limiting, a rapid binding-unbinding dynamics may lead to an increased elongation rate compared to the case where the polymer is trapped in any of the modes. Next, we consider a large population of polymers and complexes, represented by a random measure on some appropriate type space. We show that as N tends to infinity, the stochastic system converges to a deterministic limit in which the switching appears as a flow between two categories of polymers. We exhibit some numerical examples in which the limiting behaviour of a single polymer differs from that of a population of competing (shorter) polymers for equivalent model parameters. Taken together, our results demonstrate that under conditions where the total number of monomers is limiting, the study of a single polymer is not sufficient to understand the behaviour of an ensemble of competing polymers.
机译：在本文中，我们介绍了肌动蛋白聚合物及其与细胞膜中其他蛋白质相互作用动力学的随机模型。每种聚合物都会拉长和缩短，并且可以在几种模式之间切换，这取决于它是否与调节其行为的辅助蛋白质结合，例如，促进伸长的因素。我们的主要目标是了解大量聚合物的动力学，假设唯一的限制量是单体总量，设置为常数，以某个大N。我们首先关注尺寸为O（N）的超长聚合物的演化，以及模式之间的快速切换（与聚合物尺寸出现宏观波动的时间尺度相比）。让N趋于无穷大，我们就得到了一个流体极限，在这个极限下，切换的效果只通过在平衡状态下每种模式所花费的时间的分数出现。我们特别表明，在单体数量有限的情况下，与聚合物被困在任何一种模式下的情况相比，快速结合-解封动力学可能导致伸长率增加。接下来，我们考虑了大量的聚合物和复合物，由一些适当的类型空间上的随机测度表示。我们证明，当N趋于无穷大时，随机系统收敛到一个确定性极限，在该极限下，切换表现为两类聚合物之间的流动。我们展示了一些数值例子，其中单个聚合物的极限行为不同于竞争（较短）聚合物群体在等效模型参数下的极限行为。综上所述，我们的结果表明，在单体总数有限的情况下，对单个聚合物的研究不足以理解相互竞争的聚合物整体的行为。

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