## 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.

*Japanese Society for Bioinformatics*