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 Saccharomyces cerevisiae under physiological conditions and find an excellent agreement 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.

中文翻译：

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幂级数方法，用于求解基于TASEP的mRNA翻译模型。

我们开发了一种基于完全不对称简单排除过程（TASEP）解决信使RNA（mRNA）翻译数学模型的方法。我们的主要目标是证明该方法是通用的，适用于现实的翻译模型。为此，我们认为TASEP具有依赖密码子的延伸率，由于核糖体脱落引起的过早终止和由于mRNA环化引起的翻译重新初始化。我们将该方法应用于生理条件下的酿酒酵母模型生物，并发现与随机模拟的结果非常吻合。我们的发现表明，对于翻译的普遍看法是，翻译受翻译速度的限制是过于简单的。