Jumping low, jumping high: Controlling hopping in the protein energy surface

Abstract

Corrcsponding AuthorKeywords-basin hopping; local minima; greedy local search; fragment-based assembly; protein native state.The protein conformational space is characterized as a multi-dimensional funnel-like energy surface with conformations corresponding to the native state around the energy basin [1]. The dimensionally and ruggedness of this energy surface are primary why computationally determining the biologically active or native state of a protein remains a difficult challenge. A common template among structure prediction protocols begins by sampling many local minima in the energy surface. Basin Hopping (BH) has emerged as a suitable framework for effectively sampling these coarsegrained local minima [2], [3]. BH consists of a series structural perturbations followed by minimizations, forming a trajectory of local minima with the Metropolis criterion biasing it towards increasingly low-energy minima.We conduct a detailed investigation of the perturbation and minimization components of our recently proposed BH framework [3]. We show that biasing the perturbation distance effectively controls the mean distance between consecutively sampled local minima. We then investigate the effect of controlling this minima distance on the ability of the BH framework to effectively capture near-native minima. In cases where unbiased perturbation leads to few small hops, biasing perturbation to create smaller hops in the energy surface leads to greater sampling of near-native minima. We compare a greedy local search to employing a MMC search with different effective temperatures for the minimization component. Employing a low non-zero temperature allows an MMC search to jump over small energy barriers and probe down to lower local minima. Analysis shows, however, that despite reaching lower energy levels, the longer MMC search is no more effective than simple greedy search at exploring near-native conformations.We investigate a novel multi-objective approach for filtering the resulting ensemble of sampled local minima to obtain a subset of interesting conformations for further refinement. Energy functions are computed as the weighted sum of multiple distinct energy terms and the selection of weights 978-1-4673-2747-3/12/$31.00 ©2012 IEEE 946 Figure 1: Energy vs. IRMSD to the native structure is shown for each conformation in the full ensemble and Pareto front.for these energy terms is a significant source of error for the energy function. We eliminate this source of error by taking the more nuanced approach of considering each energy term individually. As shown in Figure 1, the resulting Pareto front of non-dominated conformations represents at least a 94% reduction in ensemble size but still retains more "interesting" local minima suitable for further refinement as compared to a naive cutoff based only on total energy. ACKNOWLEDGMENTS