Touya Clément, Schwalger Tilo, Lindner Benjamin
Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051913. doi: 10.1103/PhysRevE.83.051913. Epub 2011 May 16.
Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.
活性布朗粒子（ABP）遵循具有速度依赖漂移和噪声幅度的非线性朗之万方程，是用于描述生物学中自推进运动的著名模型。在本文中，我们研究了一个描述一组耦合分子马达（CMM）随机动力学的模型。使用两种独立的数值方法，一种基于马达的平稳速度分布，另一种基于速度的局部增量（也称为克莱默斯 - 莫亚尔系数），我们建立了CMM模型与ABP模型之间的联系。通过这两种方法为ABP提取的参数在对称和非对称情况下都显示出良好的一致性，并且与马达数量N无关，前提是N不太小。这表明确实可以用更简单的ABP模型来描述CMM问题。然而，CMM模型中速度涨落的功率谱在有限频率处出现一个峰值，而这个峰值在ABP模型的速度谱中不存在。这意味着CMM模型具有更丰富的动力学特征，而这些特征无法被ABP模型捕捉。
