Application of New Multiresolution Methods for the Comparison of Biomolecular Electrostatic Properties in the Absence of Global Structural Similarity

Abstract

In this paper we present a method for the multi-resolution comparison of biomolecular electrostatic potentials without the need for global structural alignment of the biomolecules. The underlying computational geometry algorithm uses multi-resolution attributed contour trees (MACTs) to compare the topological features of volumetric scalar fields. We apply the MACTs to compute electrostatic similarity metrics for a large set of protein chains with varying degrees of sequence, structure, and function similarity. For calibration, we also compute similarity metrics for these chains by a more traditional approach based upon 3D structural alignment and analysis of Carbo similarity indices. Moreover, because the MACT approach does not rely upon pairwise structural alignment, its accuracy and efficiency promises to perform well on future large-scale classification efforts across groups of structurally-diverse proteins. The MACT method discriminates between protein chains at a level comparable to the Carbo similarity index method; i.e., it is able to accurately cluster proteins into functionally-relevant groups which demonstrate strong dependence on ligand binding sites. The results of the analyses are available from the linked web databases

Symmetry in Scalar Field Topology

“…While this method studies different scalar fields defined on a common domain, we focus on the detection of repeating patterns within a single scalar field. Several methods for shape matching compare scalar fields using a multi-resolution discrete version of the contour tree and estimate a measure of similarity using geometric, topological, and functional attributes [18,50,51,52]. Though these methods analyse similarity between scalar fields, their goal is to identify the overall similarity between two domains, which is different from our goal of identifying symmetry within a single scalar field.…”

Extraction, Quantification and Visualization of Protein Pockets

“…Those shape properties of protein pockets may be used for building a database of the proteins pocket structures, and applied to the problem of ligand binding [31]. An affine-invariant method of comparing protein structures is described in [47] by using multi-resolution dual contour trees (MDCT) of the molecular shape functions, e.g. solvent accessibility, combined with geometric, topological, and electrostatic potential properties.…”

“…A DCT studies properties of interval volumes within a specific range of a scalar function and is constructed by partitioning arcs of a CT into sets of connected segments, each of which corresponds to a connected interval volume of the function domain [47]. These interval volumes represent connected regions whose function values are within a specific range.…”

“…For each node of the DCT, geometric and topolog- ical properties of the corresponding interval volume are computed. We refer to [46,47] for details of constructing DCT and computing the volume and other attributes of the DCT nodes. Because protein surfaces are highly complicated, they usually contain many small pockets and voids.…”

“…Another way of simplification is to construct a simplified data structure for the volumetric function, e.g. the dual contour tree (DCT) introduced in [46,47].…”