Conformational entropy of biomolecules: beyond the quasi-harmonic approximation

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.