Iafolla Marco A J, McMillen David R
Department of Chemical and Physical Sciences and Institute for Optical Sciences, University of Toronto at Mississauga, 3359 Mississauga Road North, Mississauga, Ontario L5L 1C6, Canada.
J Phys Chem B. 2006 Nov 2;110(43):22019-28. doi: 10.1021/jp062739m.
Recent developments in molecular biology have made it feasible to carry out experimental verification of mathematical models for biochemical processes, offering the eventual prospect of creating a detailed, validated picture of gene expression. A persistent difficulty with this long-term goal is the incompleteness of the kinetic information available in the literature: Many rate constants cannot or have not yet been measured. Here, we present a method of filling in missing parameters using an approach conceptually analogous to mean-field approaches in statistical mechanics: When studying a particular gene, we extract key parameters by considering the averaged effect of all other genes in the system, analogously to considering the averaged magnetic field in a physical spin model. This methodology has been applied to account for the effect of the presence of the Escherichia coli genome on the availability of key enzymes involved in gene expression (RNA polymerases and ribosomes), yielding the number of free enzymes as a function of cellular growth rate. These conclusions have been obtained by deriving genome-wide averages and matching them to bulk literature values of E. coli K-12 and B/r. Average rate constants have been found for RNA polymerases and ribosomes binding to promoter and ribosome-binding sites, respectively; these results suggest that cells vary not only their production rates of RNA polymerase and ribosomes under different growth-rate conditions but also change their global level of transcriptional/translational activation and repression, thus altering the average binding rate constants for these enzymes. To test the mean-field method, the results from the genome-wide averages have been applied to the induced lac operon, where our derived on-rate for binding of RNA polymerase to the promoter is in good agreement with previous experimental results.
分子生物学的最新进展使得对生化过程数学模型进行实验验证成为可能，为最终构建基因表达的详细、经过验证的图景提供了前景。实现这一长期目标的一个持续难题是文献中可用动力学信息的不完整性：许多速率常数无法测量或尚未测量。在此，我们提出一种填补缺失参数的方法，该方法在概念上类似于统计力学中的平均场方法：在研究特定基因时，我们通过考虑系统中所有其他基因的平均效应来提取关键参数，类似于在物理自旋模型中考虑平均磁场。这种方法已被用于解释大肠杆菌基因组的存在对基因表达中关键酶（RNA聚合酶和核糖体）可用性的影响，得出游离酶数量作为细胞生长速率的函数。这些结论是通过推导全基因组平均值并将其与大肠杆菌K-12和B/r的大量文献值进行匹配而得出的。分别发现了RNA聚合酶和核糖体与启动子和核糖体结合位点结合的平均速率常数；这些结果表明，细胞不仅在不同生长速率条件下改变RNA聚合酶和核糖体的产生速率，还改变其转录/翻译激活和抑制的全局水平，从而改变这些酶的平均结合速率常数。为了测试平均场方法，全基因组平均值的结果已应用于诱导型乳糖操纵子，我们推导的RNA聚合酶与启动子结合的结合速率与先前的实验结果高度一致。
