Guo Kunkun, Shillcock Julian, Lipowsky Reinhard
Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany.
J Chem Phys. 2009 Jul 7;131(1):015102. doi: 10.1063/1.3159003.
Brownian dynamics simulations are used to study the dynamical process of self-assembly of actin monomers into long filaments containing up to 1000 actin protomers. In order to overcome the large separation of time scales between the diffusive motion of the free monomers and the relatively slow attachment and detachment processes at the two ends of the filaments, we introduce a novel rescaling procedure by which we speed all dynamical processes related to actin polymerization and depolymerization up by the same factor. In general, the actin protomers within a filament can attain three different states corresponding to a bound adenosine triphosphate (ATP), adenosine diphosphate with inorganic phosphate (ADP/P), and ADP molecule. The simplest situation that has been studied experimentally is provided by the polymerization of ADP-actin, for which all protomers are identical. This case is used to unravel certain relations between the filament's physical properties and the model parameters such as the attachment rate constant and the size of the capture zone, the detachment rate and the probability of the detached event, as well as the growth rate and waiting times between two successive attachment/detachment events. When a single filament is allowed to grow in a bath of constant concentration of free ADP-actin monomers, its growth rate increases linearly with the free monomer concentration in quantitative agreement with in vitro experiments. The results also show that the waiting time is governed by exponential distributions and that the two ends of a filament undergo biased random walks. The filament length fluctuations are described by a length diffusion constant that is found to attain a constant value at low ADP-actin concentration and to increase linearly with this concentration. It is straightforward to apply our simulation code to more complex processes such as polymerization of ATP-actin coupled to ATP hydrolysis, force generation by filaments, formation of filament bundles, and filament-membrane interactions.
布朗动力学模拟用于研究肌动蛋白单体自组装成长达1000个肌动蛋白原体的长丝的动力学过程。为了克服自由单体扩散运动与长丝两端相对较慢的附着和脱离过程之间的时间尺度大分离问题，我们引入了一种新颖的重新缩放程序，通过该程序我们将与肌动蛋白聚合和解聚相关的所有动力学过程加速相同的因子。一般来说，长丝内的肌动蛋白原体可以达到三种不同的状态，分别对应结合的三磷酸腺苷（ATP）、二磷酸腺苷与无机磷酸（ADP/P）以及ADP分子。实验研究的最简单情况是由ADP - 肌动蛋白的聚合提供的，其中所有原体都是相同的。这种情况用于揭示长丝的物理性质与模型参数之间的某些关系，例如附着速率常数和捕获区大小、脱离速率和脱离事件的概率，以及生长速率和两个连续附着/脱离事件之间的等待时间。当允许单根长丝在游离ADP - 肌动蛋白单体浓度恒定的浴中生长时，其生长速率与游离单体浓度呈线性增加，这与体外实验定量一致。结果还表明，等待时间由指数分布控制，并且长丝的两端经历有偏随机游走。长丝长度波动由长度扩散常数描述，发现在低ADP - 肌动蛋白浓度下该常数达到恒定值，并随该浓度线性增加。将我们的模拟代码应用于更复杂的过程，如与ATP水解耦合的ATP - 肌动蛋白聚合、长丝产生力、长丝束的形成以及长丝 - 膜相互作用，是很直接的。
