Zarai Yoram, Margaliot Michael, Kolomeisky Anatoly B
School of Electrical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel.
School of Electrical Engineering and the Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv 69978, Israel.
PLoS One. 2017 Aug 10;12(8):e0182074. doi: 10.1371/journal.pone.0182074. eCollection 2017.
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a "soft" simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.
自然现象常常涉及大量相互作用的分子在有限的空间区域内移动。由驱动蛋白介导的细胞运输就是这种集体行为的一个例子。我们推导了一个确定性的隔室模型，用于描述粒子沿一维晶格位点的单向流动，粒子之间存在最近邻相互作用。相邻位点之间的流动由“软”简单排除原理以及相邻粒子之间的吸引或排斥力控制。利用收缩理论的工具，我们证明该模型存在唯一的稳态，并且每条轨迹都收敛于该稳态。对吸引和排斥力对该稳态影响的分析和模拟突出了这些力在增加稳态流量中可能发挥的关键作用，并揭示这种增加源于晶格沿线交通堵塞的缓解。我们的理论分析阐明了复杂多粒子动态过程的微观方面。
