A Data-Driven Evolutionary Algorithm for Mapping Multibasin Protein Energy Landscapes

Abstract

Evidence is emerging that many proteins involved in proteinopathies are dynamic molecules switching between stable and semistable structures to modulate their function. A detailed understanding of the relationship between structure and function in such molecules demands a comprehensive characterization of their conformation space. Currently, only stochastic optimization methods are capable of exploring conformation spaces to obtain sample-based representations of associated energy surfaces. These methods have to address the fundamental but challenging issue of balancing computational resources between exploration (obtaining a broad view of the space) and exploitation (going deep in the energy surface). We propose a novel algorithm that strikes an effective balance by employing concepts from evolutionary computation. The algorithm leverages deposited crystal structures of wildtype and variant sequences of a protein to define a reduced, low-dimensional search space from where to rapidly draw samples. A multiscale technique maps samples to local minima of the all-atom energy surface of a protein under investigation. Several novel algorithmic strategies are employed to avoid premature convergence to particular minima and obtain a broad view of a possibly multibasin energy surface. Analysis of applications on different proteins demonstrates the broad utility of the algorithm to map multibasin energy landscapes and advance modeling of multibasin proteins. In particular, applications on wildtype and variant sequences of proteins involved in proteinopathies demonstrate that the algorithm makes an important first step toward understanding the impact of sequence mutations on misfunction by providing the energy landscape as the intermediate explanatory link between protein sequence and function.

Computing energy landscape maps and structural excursions of proteins

“…Work in [28] shows this to be the case for many multi-state proteins with multi-basin landscapes; with the top two PCs one captures more than 45 % of the variance (which means they can be employed for data visualization) and anywhere between 10−25 PCs allow capturing more than 90 % of the variance. The latter is a reduction by more than ten-fold, as the original structures are of proteins with more than 100 amino acids; stripping them down to their CAs prior to PCA exposes more than 300 Cartesian coordinates on which PCA operates to reveal no more than 25 PCs/coordinates that still capture more than 90 % of the variance.…”

Using subpopulation EAs to map molecular structure landscapes

“…Work in [27,28] links the presence of multiple minima in protein energy landscapes to competing objectives in energy functions and demonstrates the utility of multi-objective optimization EAs. Work in [7][8][9] additionally debuts decentralized selection operators to retain diversity. Work in [26,29] pursues various recombination strategies to promote generation of diverse candidates, hybridization for better exploitation, and non-local optimization operators to balance between exploration and exploitation.…”

An Energy Landscape Treatment of Decoy Selection in Template-Free Protein Structure Prediction

“…Specifically, for the evaluation presented in this paper, the method utilizes Principal Component Analysis (PCA) [75] to extract collective, variance-preserving coordinates from decoy structures. PCA and other linear dimensionality reduction techniques are shown effective for analysis of protein structures in various applications of interest in computational biology [16,76,77].…”