Volumes and surface areas: geometries and scaling relationships between coarse- grained and atomic structures.

Computing volumes and surface areas of molecular structures is generally considered to be a solved problem, however, comparisons presented in this review show that different ways of computing surface areas and volumes can yield dramatically different values. Volumes and surface areas are the most basic geometric properties of structures, and estimating these becomes especially important for large scale simulations when individual components are being assembled in protein complexes or drugs being fitted into proteins. Good approximations of volumes and surfaces are derived from Delaunay tessellations, but these values can differ significantly from those from the rolling ball approach of Lee and Richards (3V webserver).

Immunoglobulin Structure Exhibits Control over CDR Motion.

Motions of the IgG structure are evaluated using normal mode analysis of an elastic network model to detect hinges, the dominance of low frequency modes, and the most important internal motions. One question we seek to answer is whether or not IgG hinge motions facilitate antigen binding. We also evaluate the protein crystal and packing effects on the experimental temperature factors and disorder predictions.

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms.

This paper presents an efficient group-theoretic approach for computing the statistics of non-reversal random walks (NRRW) on lattices. These framed walks evolve on proper crystallographic space groups. In a previous paper we introduced a convolution method for computing the statistics of NRRWs in which the convolution product is defined relative to the space-group operation.

Models to Approximate the Motions of Protein Loops.

We approximate the loop motions of various proteins by using a coarse-grained model and the theory of rubberlike elasticity of polymer chains. The loops are considered as chains where only the first and the last residues thereof are tethered by their connections to the main structure; while within the loop, the loop residues are connected only to their sequence neighbors. We applied these approximate models to five proteins.

Chain dimensions and fluctuations in elastomeric networks in which the junctions alternate regularly in their functionality.

A matrix method is used to determine fluctuations of junctions and points along the polymer chains making up a phantom Gaussian network that has the topology of an infinite, symmetrically grown tree. The functionalities of the junctions alternates between phi(1) and phi(2), such that one end of each network chain has functionality phi(1), while the opposite end has functionality phi(2). Quantities calculated include fluctuations of phi(1)-functional and phi(2)-functional junctions, and fluctuations of points along network chains, as well as correlations of these fluctuations.

Position and Orientation Distributions for Locally Self-Avoiding Walks in the Presence of Obstacles.

This paper presents a new approach to study the statistics of lattice random walks in the presence of obstacles and local self-avoidance constraints (excluded volume). By excluding sequentially local interactions within a window that slides along the chain, we obtain an upper bound on the number of self-avoiding walks (SAWs) that terminate at each possible position and orientation. Furthermore we develop a technique to include the effects of obstacles.

Torsional random walk statistics on lattices using convolution on crystallographic motion groups.

This paper presents a new algorithm for generating the conformational statistics of lattice polymer models. The inputs to the algorithm are the distributions of poses (positions and orientations) of reference frames attached to sequentially proximal bonds in the chain as it undergoes all possible torsional motions in the lattice. If z denotes the number of discrete torsional motions allowable around each of the n bonds, our method generates the probability distribution in end-to-end pose corresponding to all of the z(n) independent lattice conformations in O(n(D) (+1)) arithmetic operations for lattices in D-dimensional space.