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

*Ontology highlight*

**ABSTRACT**: 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.

**SUBMITTER: **Zarai Y

**PROVIDER: **S-EPMC5552133 | BioStudies | 2017-01-01

**SECONDARY ACCESSION(S): **10.1371/journal.pone.0182074

**REPOSITORIES: ** biostudies

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