Sampling conformations in high dimensions using low-dimensional distribution functions.
We present an approximation to a molecule's N-dimensional conformational probability density function (pdf) in terms of marginal pdfs of highest order l, where l is much less than N. The approximation is constructed as a product of conditional pdfs derived by recursive application of the generalized Kirkwood superposition approximation. Furthermore, an algorithm is presented to sample conformations from the approximate full-dimensional pdf based upon all input marginal pdfs. The sampling algorithm is tested for three small molecule systems by using the algorithm to sample conformations at levels l=1, 2, or 3 and comparing the distributions of sampled conformations with those from the molecular dynamics (MD) simulations. The distributions of conformations sampled at third (l=3) order resemble the MD distributions rather well and significantly better than those sampled at second (l=2) or first (l=1) order. In addition to highlighting the importance of correlations among internal degrees of freedom, these results suggest that low-order correlations suffice to describe most of the conformational fluctuations of molecules in a thermal environment.
Somani
Sandeep
S
Center for Advanced Research in Biotechnology, UMBI, 9600 Gudelsky Drive, Rockville, Maryland 20850, USA.
Killian
Benjamin J
BJ
Gilson
Michael K
MK
D000465:Algorithms; D003198:Computer Simulation; D008958:Models, Molecular; D015233:Models, Statistical; D008962:Models, Theoretical; D008968:Molecular Conformation; D013816:Thermodynamics