13,629 research outputs found
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
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