Deconstructing thermodynamic parameters of a coupled system from site-specific observables

Cooperative interactions mediate information transfer between structural domains of a protein molecule and are major determinants of protein function and modulation. The prevalent theories to understand the thermodynamic origins of cooperativity have been developed to reproduce the complex behavior of a global thermodynamic observable such as ligand binding or enzyme activity. However, in most cases the measurement of a single global observable cannot uniquely define all the terms that fully describe the energetics of the system. Here we establish a theoretical groundwork for analyzing protein thermodynamics using site-specific information. Our treatment involves extracting a site-specific parameter (defined as chi value) associated with a structural unit. We demonstrate that, under limiting conditions, the chi value is related to the direct interaction terms associated with the structural unit under observation and its intrinsic activation energy. We also introduce a site-specific interaction energy term (chi(diff)) that is a function of the direct interaction energy of that site with every other site in the system. When combined with site-directed mutagenesis and other molecular level perturbations, analyses of chi values of site-specific observables may provide valuable insights into protein thermodynamics and structure.