# Self-organized system-size oscillation of a stochastic lattice-gas model

## TL;DR

This paper introduces a stochastic lattice-gas model combining TASEP with growth and shrinkage, revealing self-organized size oscillations driven by the interplay of diffusion and shrinkage in confined systems.

## Contribution

It extends the TASEP model to include size dynamics and demonstrates the emergence of robust oscillations in system size due to diffusion and shrinkage interactions.

## Key findings

- Size exhibits quasi-periodic oscillations under certain conditions
- Oscillation frequency depends on growth rate
- Effective theory explains oscillation origin and behavior

## Abstract

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for non-equilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semi-closed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasi-periodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, as for instance the oscillation frequency, on the growth rate.