Ligand Binding, Protein Fluctuations, and Allosteric Free Energy

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.Comment: 18 pages; 7 figures; Second International Congress of the Biocomputing and Physics of Complex Systems Research Institute, Zaragoza, Spain, 8-11 Feb 2006; increase breadth of review of methods for analysis of allosteric mechanisms; Add AIP in press; fix missing kTs in equation

Quantum crystallographic charge density of urea

Standard X-ray crystallography methods use free-atom models to calculate mean unit cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared to models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the data is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. The results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra high-resolution X-ray crystallographic model building and refinement.Comment: 40 pages, 4 figures, 6 table