Max Planck Institute of Colloids and Interfaces, 14476 Potsdam, Germany.
Soft Matter. 2017 Jan 4;13(2):328-344. doi: 10.1039/c6sm01853j.
Intracellular transport is performed by molecular motors that pull cargos along cytoskeletal filaments. Many cellular cargos are observed to move bidirectionally, with fast transport in both directions. This behaviour can be understood as a stochastic tug-of-war between two teams of antagonistic motors. The first theoretical model for such a tug-of-war, the Müller-Klumpp-Lipowsky (MKL) model, was based on two simplifying assumptions: (i) both motor teams move with the same velocity in the direction of the stronger team, and (ii) this velocity matching and the associated force balance arise immediately after the rebinding of an unbound motor to the filament. In this study, we extend the MKL model by including an elastic coupling between the antagonistic motors, and by allowing the motors to perform discrete motor steps. Each motor step changes the elastic interaction forces experienced by the motors. In order to elucidate the basic concepts of force balance and force fluctuations, we focus on the simplest case of two antagonistic motors, one kinesin against one dynein. We calculate the probability distribution for the spatial separation of the motors and the dependence of this distribution on the motors' unbinding rate. We also compute the probability distribution for the elastic interaction forces experienced by the motors, which determines the average elastic force 〈F〉 and the standard deviation of the force fluctuations around this average value. The average force 〈F〉 is found to decrease monotonically with increasing unbinding rate ε. The behaviour of the MKL model is recovered in the limit of small ε. In the opposite limit of large ε, 〈F〉 is found to decay to zero as 1/ε. Finally, we study the limiting case with ε = 0 for which we determine both the force statistics and the time needed to attain the steady state. Our theoretical predictions are accessible to experimental studies of in vitro systems consisting of two antagonistic motors attached to a synthetic scaffold or crosslinked via DNA hybridization.
细胞内运输是由分子马达完成的，这些马达沿着细胞骨架丝拉动货物。许多细胞货物被观察到双向移动，两个方向都有快速运输。这种行为可以理解为两个拮抗马达团队之间的随机拔河比赛。第一个这样的拔河比赛的理论模型，即 Müller-Klumpp-Lipowsky（MKL）模型，基于两个简化假设：（i）两个马达团队在较强团队的方向上以相同的速度移动，（ii）这种速度匹配和相关的力平衡在未绑定的马达重新结合到丝上后立即出现。在这项研究中，我们通过在拮抗马达之间引入弹性耦合，并允许马达进行离散的马达步骤，扩展了 MKL 模型。每个马达步骤都会改变马达所经历的弹性相互作用力。为了阐明力平衡和力波动的基本概念，我们专注于两个拮抗马达最简单的情况，一个是驱动蛋白，另一个是动力蛋白。我们计算了马达之间的空间分离概率分布以及该分布对马达解缚率的依赖性。我们还计算了马达所经历的弹性相互作用力的概率分布，这决定了平均弹性力〈F〉和围绕该平均值的力波动的标准偏差。发现平均力〈F〉随解缚率ε的增加而单调减小。在小ε的极限下，恢复了 MKL 模型的行为。在大ε的相反极限下，发现〈F〉随着 1/ε 衰减到零。最后，我们研究了ε=0 的极限情况，对于这种情况，我们确定了力统计和达到稳态所需的时间。我们的理论预测可以通过体外系统的实验研究来验证，该系统由两个附着在合成支架上或通过 DNA 杂交交联的拮抗马达组成。
