Power series method for solving TASEP-based models of mRNA translation

Abstract: We develop a method for solving mathematical models of messenger RNA (mRNA) translation based on the totally asymmetric simple exclusion process (TASEP). Our main goal is to demonstrate that the method is versatile and applicable to realistic models of translation. To this end we consider the TASEP with codon-dependent elongation rates, premature termination due to ribosome drop-off and translation reinitiation due to circularisation of the mRNA. We apply the method to the model organism {\it Saccharomyces cerevisiae} under physiological conditions and find excellent agreements with the results of stochastic simulations. Our findings suggest that the common view on translation as being rate-limited by initiation is oversimplistic. Instead we find theoretical evidence for ribosome interference and also theoretical support for the ramp hypothesis which argues that codons at the beginning of genes have slower elongation rates in order to reduce ribosome density and jamming.