Conformational Entropy of Biomolecules: Beyond the Quasi-Harmonic Approximation

Jorge Numata[1] (numata@chemie.fu-berlin.de)
Michael Wan[1][2] (mwan@fas.harvard.edu)
Ernst-Walter Knapp[1] (knapp@chemie.fu-berlin.de)

[1]Macromolecular Modeling Group, Dept. of Chemistry and Biochemistry, Freie Universitaet Berlin, Takustr. 6, Berlin 14195 Germany
[2]Aspuru-Guzik Research Group, Harvard University, Dept. of Chemistry and Chemical Biology, 12 Oxford Street, Cambridge, MA 02138, USA

Abstract

A method is presented to calculate thermodynamic conformational entropy of a biomolecule from molecular dynamics simulation. Principal component analysis (the quasi-harmonic approximation) provides the first decomposition of the correlations in particle motion. Entropy is calculated analytically as a sum of independent quantum harmonic oscillators. The largest classical eigenvalues tend to be more anharmonic and show statistical dependence beyond correlation. Their entropy is corrected using a numerical method from information theory: the k-nearest neighbor algorithm. The method calculates a tighter upper limit to entropy than the quasi-harmonic approximation and is likewise applicable to large solutes, such as peptides and proteins. Together with an estimate of solute enthalpy and solvent free energy from methods such as MMPB/SA, it can be used to calculate the free energy of protein folding as well as receptor-ligand binding constants.

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