Power series solution of the inhomogeneous exclusion process

Abstract

We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modelling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.

14 pages, 6 figures, mean-field solution included

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Cited by in corpus (9)

• Driven transport on a flexible polymer with particle recycling: a model inspired by transcription and translation
• Power series method for solving TASEP-based models of mRNA translation
• Dynamics of ribosomes in mRNA translation under steady and non-steady state conditions
• Current-density relation in the exclusion process with dynamic obstacles
• Transport in exclusion processes with one-step memory: density dependence and optimal acceleration
• EGGTART: A computational tool to visualize the dynamics of biophysical transport processes under the inhomogeneous $\ell$-TASEP
• On the phase transition in the sublattice TASEP with stochastic blockage
• The fitness landscapes of translation
• Correlations and transport in exclusion processes with general finite memory