Modeling Random Fluctuations in Molecules

• Activity Number: 22
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Harshinder Singh*+
• Companies: West Virginia University
• Keywords: dihedral angles ; entropy ; molecular dynamic simulations ; von Mises Distribution

Abstract

Probabilistic modeling and the estimation of entropy of random fluctuations in the internal coordinates of molecules is important for studying their properties and functions. The entropy of a molecule depends mainly on random fluctuations in the dihedral angles of the molecule. Large molecules, such as peptides and proteins, have many dihedral angles and entropy estimation for such molecules is a challenging problem. The traditional approach assumes a multivariate Gaussian distribution for the internal coordinates of molecules. However, the assumption of normality is not valid in many situations. We discuss the circular probability modeling approach for modeling the dihedral angles in molecules. Applications of circular distributions are illustrated using data on the dihedral angles of some molecules. In general, the distributions of coordinates can have arbitrary shapes and we also discuss a nonparametric approach to estimation of entropy of molecules based on kth nearest neighbor distances between n sample points, where k (< n) is a fixed positive integer. Applications of the proposed estimators are illustrated by using them for estimation of entropy of some molecules.