核糖体流模型中蛋白质翻译速率的最大化：均匀情况
Maximizing Protein Translation Rate in the Ribosome Flow Model: the Homogeneous Case
摘要：
基因翻译是细胞内的大分子（称为核糖体）将mRNA链中的遗传信息解码成相应蛋白质的过程。基因翻译包括几个步骤。在延伸步骤中，核糖体以顺序的方式沿着mRNA移动，并以相应的顺序将氨基酸连接在一起以产生蛋白质。均质核糖体流动模型（HRFM）是一个确定性的计算模型，假设沿mRNA链的恒定延伸率的限制-延长。HRFM由一组n阶非线性常微分方程描述，其中n表示mRNA链上的位点数。HRFM还包括两个阳性参数：核糖体起始速率和（恒定）延伸速率。在本文中，我们表明，在HRFM的稳态平移速率是其参数的凹函数。这意味着确定使平移速率最大化的参数值的问题相对简单。我们的研究结果可能有助于更好地理解的机制和演变的预缩伸长。我们证明了这一点，通过使用理论结果来估计在M的起始速率。胚胎干细胞基本假设是进化优化了翻译机制。对于无限维的HRFM，我们推导出一个封闭形式的解决方案的问题，确定的起始和过渡率，最大限度地提高蛋白质的翻译速率。我们表明，这些表达式提供了很好的近似的最佳值在n维HRFM已经为相对较小的n值。这些结果可能具有合成生物学的应用，其中一个重要的问题是重新设计基因组系统，以最大限度地提高蛋白质的生产率。
英文摘要：
Gene translation is the process in which intracellular macro-molecules, called ribosomes, decode genetic information in the mRNA chain into the corresponding proteins. Gene translation includes several steps. During the elongation step, ribosomes move along the mRNA in a sequential manner and link amino-acids together in the corresponding order to produce the proteins. The homogeneous ribosome flow model(HRFM) is a deterministic computational model for translation-elongation under the assumption of constant elongation rates along the mRNA chain. The HRFM is described by a set of n first-order nonlinear ordinary differential equations, where n represents the number of sites along the mRNA chain. The HRFM also includes two positive parameters: ribosomal initiation rate and the (constant) elongation rate. In this paper, we show that the steady-state translation rate in the HRFM is a concave function of its parameters. This means that the problem of determining the parameter values that maximize the translation rate is relatively simple. Our results may contribute to a better understanding of the mechanisms and evolution of translation-elongation. We demonstrate this by using the theoretical results to estimate the initiation rate in M. musculus embryonic stem cell. The underlying assumption is that evolution optimized the translation mechanism. For the infinite-dimensional HRFM, we derive a closed-form solution to the problem of determining the initiation and transition rates that maximize the protein translation rate. We show that these expressions provide good approximations for the optimal values in the n-dimensional HRFM already for relatively small values of n. These results may have applications for synthetic biology where an important problem is to re-engineer genomic systems in order to maximize the protein production rate.
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