A Local Rigid Body Framework for Global Optimization of Biomolecules

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe present a local rigid body framework for simulations of biomolecules. In this framework, arbritrary sets of atoms may be treated as rigid bodies. Such groupings reduce the number of degrees of freedom, which can result in a significant reduction of computational time.As benchmarks, we consider global optimization for the tryptophan zipper (trpzip 1, 1LE0; using the CHARMM force field) and chignolin (1UAO; using the AMBER force field). We use a basin-hopping algorithm to find the global minima and compute the mean first encounter time from random starting configurations with and without the local rigid body framework.Minimal groupings are used, where only peptide bonds, termini and side chain rings are considered rigid. Finding the global minimum is 4.2 and 2.5 times faster, respectively, for trpzip 1 and chignolin, within the local rigid body framework. We further compare O(10 5 ) low-lying local minima to the fully relaxed unconstrained representation for trpzip 1 at different levels of rigidification. The resulting Pearson correlation coefficients, and thus the apparent intrinsic rigidity of the various groups, appear in the following order: side chain rings > termini > trigonal planar centres ≥ peptide bonds side chains. This approach is likely to be even more beneficial for structure prediction in larger biomolecules.

The potential energy landscape for crystallisation of a Lennard-Jones fluid

“…Alignment of endpoints is critically important to obtain pathways via geometry optimisation [66]. The alignment, minimising the Euclidean distance in 3N dimensions, of N distinguishable atoms in two dierent configurations is easily achieved using a quaternion procedure [67].…”

A conformational factorisation approach for estimating the binding free energies of macromolecules

“…The analysis that follows defines quantitative conditions under which this simplification will be valid. Furthermore, our local rigidification procedure 44 provides an ideal framework for implementing this approach, and enables us to determine a minimal set of states for estimating free energies of binding.…”

“…(9) is to sample local minima with the common region constrained in the reference conformation. This sampling is accomplished here using the local rigidification framework 44 . Our strategy for testing Eq.…”

“…Atoms in the 'inner' region, adjacent to the ligand, are unconstrained, while those in the 'intermediate' region are treated using the local rigid body framework. 44 All atoms in the 'outer' layer were grouped as one rigid body, but their contributions to the potential energy of the system are retained. The local rigid body framework is used to reduce the number of degrees of freedom, both in sampling minima and in the calculation of normal mode frequencies.…”

Exploring Energy Landscapes: Metrics, Pathways, and Normal-Mode Analysis for Rigid-Body Molecules

“…1 Applications of such rigid-body representations in computational science are wide-ranging, from crystal structure prediction of small organic molecules, [2][3][4] to local rigidification of secondary structures in proteins and other biomolecules. 5,6 For simulations on longer length scales, coarse-grained descriptions are typically used, which may involve orientation-dependent potentials to describe nonspherical molecules with convex shapes. [7][8][9][10][11][12] To represent an anisotropic molecule or interaction potential, six degrees of freedom are required (unless the molecule is linear): three for the translation of the center of mass, and three for the orientation.…”