Klobusicky Joseph J, Fricks John, Kramer Peter R
The University of Scranton, Department of Mathematics, Scranton, PA, USA.
Arizona State University, School of Mathematical and Statistical Sciences, Tempe, AZ, USA.
Res Math Sci. 2020 Dec;7(4). doi: 10.1007/s40687-020-00230-7. Epub 2020 Sep 21.
Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load.
针对一种细胞内运输系统，推导出了有效漂移、扩散系数、运行时间和运行长度的解析公式。该系统由附着在两个协同但不相同的分子马达（例如，驱动蛋白-1和驱动蛋白-2）上的货物组成，每个分子马达都可以与微管附着和分离。每个阶段中马达和货物的动力学由随机微分方程控制，切换速率取决于马达和货物的空间配置。在一种极限情况下对该系统进行了分析，即分离的马达的动力学比货物快，而货物的动力学又比附着的马达快。附着和分离速率相对于空间动力学也被视为缓慢的。通过对该系统应用迭代随机平均，并使用更新奖励理论将每个切换阶段内的进展拼接在一起，我们得到了马达-货物系统有效漂移、扩散系数和持续运动能力的明确解析表达式。我们的方法特别考虑了在附着和分离事件期间马达-货物位置的跳跃，因为由于平均快速尺度，货物跟踪变量会进行快速调整。对于基于驱动蛋白-1和驱动蛋白-2在各种配对下的实验参数，在辅助、阻碍或无负载情况下的详细模型的直接随机模拟，渐近公式总体上与之吻合良好。
