A deterministic model for one-dimensional excluded flow with local interactions.

• Main Authors: Yoram Zarai, Michael Margaliot, Anatoly B Kolomeisky
• Format: Article
• Language: English
• Published: Public Library of Science (PLoS) 2017-01-01
• Series: PLoS ONE
• Online Access: http://europepmc.org/articles/PMC5552133?pdf=render

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.