From Optimization to Mapping: An Evolutionary Algorithm for Protein Energy Landscapes

Abstract

Stochastic search is often the only viable option to address complex optimization problems. Recently, evolutionary algorithms have been shown to handle challenging continuous optimization problems related to protein structure modeling. Building on recent work in our laboratories, we propose an evolutionary algorithm for efficiently mapping the multi-basin energy landscapes of dynamic proteins that switch between thermodynamically stable or semi-stable structural states to regulate their biological activity in the cell. The proposed algorithm balances computational resources between exploration and exploitation of the nonlinear, multimodal landscapes that characterize multi-state proteins via a novel combination of global and local search to generate a dynamically-updated, information-rich map of a protein's energy landscape. This new mapping-oriented EA is applied to several dynamic proteins and their disease-implicated variants to illustrate its ability to map complex energy landscapes in a computationally feasible manner. We further show that, given the availability of such maps, comparison between the maps of wildtype and variants of a protein allows for the formulation of a structural and thermodynamic basis for the impact of sequence mutations on dysfunction that may prove useful in guiding further wet-laboratory investigations of dysfunction and molecular interventions.

An evolutionary algorithm to model structural excursions of a protein

“…e EA presented here evolves a population of paths directly, exploits experimentally-known structures of a protein in its initialization, and makes use of novel selection and crossover operators. Key building blocks in the proposed path-evolving EA have been developed and analyzed in prior work [18][19][20]. ey include exploiting known structures of a protein (of healthy and diseased sequence variants) to extract a lower-dimensional variable space for exploration.…”

“…A recent roadmap-based approach, which is the subject of our comparative analysis in Section 3 rst reconstructs the energy landscape of a protein with a powerful memetic EA (making use of several building blocks developed over the years [4,5,19,20]) and then exploits a graph-based representation of the landscape to answer path queries corresponding to structural excursions of interest [18].…”

Evolutionary search for paths on protein energy landscapes

“…Key building blocks in the path-evolving EA have been developed and analyzed in prior work [3][4][5]. ey include exploiting known structures of a protein (of healthy and diseased sequence variants) to extract a lower-dimensional variable space for exploration.…”

“…Protein modeling research aims to uncover the functionally-relevant structural excursions that a protein employs to tune its biological function. One direction of in-silico work involves rst reconstructing energy landscapes (o en with powerful memetic EAs [4,5]) and then exploiting graph-based representations of such landscapes to answer path queries corresponding to structural excursions of interest. is direction has revealed key insights on many proteins [3] but has a large computational footprint due to the need to construct comprehensive and detailed representations of energy landscapes that are vast and high-dimensional [1,2].…”

Approximating landscape insensitivity regions in solving ill-conditioned inverse problems

“…Such regions are considered in the general study of optimization landscapes in both, discrete and con-tinuous problems (see e.g. [2]), and they are often called plateaus.…”