Extracting Biochemical Parameters for Cellular Modeling: A Mean-Field Approach

Abstract

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.