  Although the importance of protein dynamics in protein function is generally
recognized, the role of protein fluctuations in allosteric effects scarcely has
been considered. To address this gap, the Kullback-Leibler divergence (Dx)
between protein conformational distributions before and after ligand binding
was proposed as a means of quantifying allosteric effects in proteins. Here,
previous applications of Dx to methods for analysis and simulation of proteins
are first reviewed, and their implications for understanding aspects of protein
function and protein evolution are discussed. Next, equations for Dx suggest
that k_{B}TDx should be interpreted as an allosteric free energy -- the free
energy associated with changing the ligand-free protein conformational
distribution to the ligand-bound conformational distribution. This
interpretation leads to a thermodynamic model of allosteric transitions that
unifies existing perspectives on the relation between ligand binding and
changes in protein conformational distributions. The definition of Dx is used
to explore some interesting mathematical relations among commonly recognized
thermodynamic and biophysical quantities, such as the total free energy change
upon ligand binding, and ligand-binding affinities for individual protein
conformations. These results represent the beginnings of a theoretical
framework for considering the full protein conformational distribution in
modeling allosteric transitions. Early applications of the framework have
produced results with implications both for methods for coarsed-grained
modeling of proteins, and for understanding the relation between ligand binding
and protein dynamics.
