The Asymmetric Simple Exclusion Process and The Ribosome Flow Model

Abstract

The asymmetric simple exclusion process (ASEP) is the simplest possible stochastic transport model and has been called the ‘mother of all traffic mod- els’. The key problem in such models is identifying the steady state flow, such as those that have been used to represent biological movement and traffic flow. In this dissertation the mean field approach to the asymmetric simple ex- clusion process is first described before this is extended to the Ribosome Flow Model (RFM) and more specifically the Ribosome Flow Model with input and output (RFMIO), which is used to examine the biological movement of ribo- somes during messenger RNA (mRNA) translation. The RFM can be thought of as a set of coupled mean-field ASEPs. The simple ASEP itself has been used to study ribosome flow among the mRNA strand but the RFMIO gives a more tractible framework for examining the flow of ribosomes during mRNA translation. The RFMIO’s initiation rate is controlled by its input, while the ribosome exit rate is represented by its output. We finish by describing our key findings and use a simple numerical example to demonstrate them.