Shtylla Blerta, Keener James P
Department of Mathematics, Pomona College, Claremont, California 91711, USA.
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042711. doi: 10.1103/PhysRevE.91.042711. Epub 2015 Apr 20.
The generation of directed movement of cellular components frequently requires the rectification of Brownian motion. Molecular motor enzymes that use ATP to walk on filamentous tracks are typically involved in cell transport, however, a track-altering motor can arise when an enzyme interacts with and alters its track. In Caulobacter crescentus and other bacteria, an active DNA partitioning (Par) apparatus is employed to segregate replicated chromosome regions to specific locations in dividing cells. The Par apparatus is composed of two proteins: ParA, an ATPase that can form polymeric structures on the nucleoid, and ParB, a protein that can bind and destabilize ParA structures. It has been proposed that the ParB-mediated alteration of ParA structures could be responsible for generating the directed movement of DNA during bacterial division. How precisely these actions are coordinated and translated into directed movement is not clear. In this paper we consider the C. crescentus segregation apparatus as an example of a track altering motor that operates using a so-called burnt-bridge mechanism. We develop and analyze mathematical models that examine how diffusion and ATP-hydrolysis-mediated monomer removal (or cleaving) can be combined to generate directed movement. Using a mean first passage approach, we analytically calculate the effective ParA track-cleaving velocities, effective diffusion coefficient, and other higher moments for the movement a ParB protein cluster that breaks monomers away at random locations on a single ParA track. Our model results indicate that cleaving velocities and effective diffusion constants are sensitive to ParB-induced ATP hydrolysis rates. Our analytical results are in excellent agreement with stochastic simulation results.
细胞成分的定向运动生成通常需要对布朗运动进行整流。利用ATP在丝状轨道上移动的分子运动酶通常参与细胞运输，然而，当一种酶与它的轨道相互作用并改变轨道时，就可能产生一种改变轨道的运动。在新月柄杆菌和其他细菌中，一种活跃的DNA分配（Par）装置被用来将复制的染色体区域分离到分裂细胞中的特定位置。Par装置由两种蛋白质组成：ParA，一种能在类核上形成聚合结构的ATP酶，以及ParB，一种能结合并破坏ParA结构稳定性的蛋白质。有人提出，ParB介导的ParA结构改变可能是细菌分裂过程中DNA定向运动的原因。这些作用究竟是如何精确协调并转化为定向运动尚不清楚。在本文中，我们以新月柄杆菌分离装置为例，说明一种使用所谓“烧桥”机制运行的改变轨道的运动。我们开发并分析了数学模型，研究扩散和ATP水解介导的单体去除（或裂解）如何结合以产生定向运动。使用平均首次通过方法，我们分析计算了有效ParA轨道裂解速度、有效扩散系数，以及单个ParA轨道上随机位置处ParB蛋白簇裂解单体运动的其他高阶矩。我们的模型结果表明，裂解速度和有效扩散常数对ParB诱导的ATP水解速率敏感。我们的分析结果与随机模拟结果非常吻合。
