Transcriptional regulation by the numbers: models

The expression of genes is regularly characterized with respect to how much, how fast, when and where. Such quantitative data demands quantitative models. Thermodynamic models are based on the assumption that the level of gene expression is proportional to the equilibrium probability that RNA polymerase (RNAP) is bound to the promoter of interest. Statistical mechanics provides a framework for computing these probabilities. Within this framework, interactions of activators, repressors, helper molecules and RNAP are described by a single function, the 'regulation factor'. This analysis culminates in an expression for the probability of RNA polymerase binding at the promoter of interest as a function of the number of regulatory proteins in the cell.