Zhang Yunxin
School of Mathematical Sciences, Fudan University, Shanghai 200433, China and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):061918. doi: 10.1103/PhysRevE.79.061918. Epub 2009 Jun 12.
Molecular motors are essential components for the biophysical functions of the cell. Current quantitative understanding of how multiple motors move along a single track is not complete, even though models and theories for a single motor mechanochemistry abound. Recently, Müller et al. have developed a tug-of-war model to describe the bidirectional movement of the cargo [Proc. Natl. Acad. Sci. U.S.A. 105, 4609 (2008)]. They found that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of single motor parameters, and they suggested that the sensitivity can be used by a cell to regulate its cargo traffic. In the present paper, we will carry out a detailed theoretical analysis of a special case of tug-of-war model: in which the numbers of the two different motor species which bound to the cargo tend to infinite. Through the analysis, all the stable, i.e., biophysically observable, steady states and their stability domains can be obtained. Depending on values of the several parameters, the tug-of-war model exhibits uni-, bi-, or tristability. The steady-state movement of the cargo, which is transported by two different molecular motor species, is determined by the initial numbers of the motors which bound to the track.
分子马达是细胞生物物理功能的重要组成部分。尽管关于单个马达机械化学的模型和理论众多，但目前对多个马达如何沿着单一路径移动的定量理解仍不完整。最近，米勒等人开发了一个拔河模型来描述货物的双向运动[《美国国家科学院院刊》105, 4609 (2008)]。他们发现拔河模型呈现出几种性质不同的运动状态，这取决于单个马达参数的精确值，并且他们认为细胞可以利用这种敏感性来调节其货物运输。在本文中，我们将对拔河模型的一个特殊情况进行详细的理论分析：即与货物结合的两种不同马达种类的数量趋于无穷大。通过分析，可以得到所有稳定的，即生物物理上可观测的稳态及其稳定域。根据几个参数的值，拔河模型呈现出单稳态、双稳态或三稳态。由两种不同分子马达种类运输的货物的稳态运动由与路径结合的马达的初始数量决定。
