  The study of gene regulation and expression is often discussed in
quantitative terms. In particular, the expression of genes is regularly
characterized with respect to how much, how fast, when and where. Whether
discussing the level of gene expression in a bacterium or its precise location
within a developing embryo, the natural language for these experiments is that
of numbers. Such quantitative data demands quantitative models. We review a
class of models ("thermodynamic models") which exploit statistical mechanics to
compute the probability that RNA polymerase is at the appropriate promoter.
This provides a mathematically precise elaboration of the idea that activators
are agents of recruitment which increase the probability that RNA polymerase
will be found at the promoter of interest. We discuss a framework which
describes the interactions of repressors, activators, helper molecules and RNA
polymerase using the concept of effective concentrations, expressed in terms of
a function we call 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. In a
companion paper [1], these ideas are applied to several case studies which
illustrate the use of the general formalism.
