Computer Science Division, University of California, Berkeley, California 94720, USA.
Department of Mathematics, University of Pennsylvania, Pennsylvania 19104, USA.
Phys Rev E. 2018 Jan;97(1-1):012106. doi: 10.1103/PhysRevE.97.012106.
The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the messenger ribonucleic acid (mRNA) during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the matrix ansatz. We then employ a refined mean-field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from Saccharomyces cerevisiae suggests a potential bias against the detection of nearby ribosomes with a gap distance of less than approximately three codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated and show that approximately 1% of the translating ribosomes get obstructed.
完全非对称排斥过程（TASEP）是一种用于描述相互作用粒子输运的经典随机模型，例如在翻译过程中核糖体沿着信使核糖核酸（mRNA）移动。尽管这个模型在过去已经得到了广泛的研究，但粒子之间的碰撞程度和粒子到其最近邻的平均距离尚未明确量化。我们通过孤立粒子的分布提供了对此类数量的理论分析。在模型的经典形式中，每个粒子仅占据一个单一的位置，我们使用矩阵假设获得了精确的解析解。然后，我们采用精细的平均场方法将分析扩展到具有任意大小粒子的广义 TASEP。我们的理论研究在 mRNA 翻译和解释核糖体蛋白组学实验数据方面具有直接的应用。特别是，我们对酿酒酵母数据的分析表明，对于距离小于约三个密码子的附近核糖体的检测可能存在潜在的偏差，这导致在相当一部分基因中估算起始速率和蛋白质产生通量存在一些不确定性。然而，尽管存在这种不确定性，我们理论上证明了与碰撞相关的干扰率可以被稳健地估计，并表明大约 1%的翻译核糖体受到阻碍。
