Emmanuel Sapin

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

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 proteins 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.

A Novel EA-based Memetic Approach for Efficiently Mapping Complex Fitness Landscapes

Recent work in computational structural biology focuses on modeling intrinsically dynamic proteins important to human biology and health. The energy landscapes of these proteins are rich in minima that correspond to alternative structures with which a dynamic protein binds to molecular partners in the cell. On such landscapes, evolutionary algorithms that switch their objective from classic optimization to mapping are more informative of protein structure function relationships. While techniques for mapping energy landscapes have been developed in computational chemistry and physics, protein landscapes are more difficult for mapping due to their high dimensionality and multimodality. In this paper, we describe a memetic evolutionary algorithm that is capable of efficiently mapping complex landscapes. In conjunction with a hall of fame mechanism, the algorithm makes use of a novel, lineage- and neighborhood-aware local search procedure or better exploration and mapping of complex landscapes. We evaluate the algorithm on several benchmark problems and demonstrate the superiority of the novel local search mechanism. In addition, we illustrate its effectiveness in mapping the complex multimodal landscape of an intrinsically dynamic protein important to human health.

Mapping Multiple Minima in Protein Energy Landscapes with Evolutionary Algorithms

Many proteins involved in human proteinopathies exhibit complex energy landscapes with multiple thermodynamically-stable and semi-stable structural states. Landscape reconstruction is crucial to understanding functional modulations, but one is confronted with the multiple minima problem. While traditionally the objective for evolutionary algorithms (EAs) is to find the global minimum, here we present work on an EA that maps the various minima in a proteins energy landscape. Specifically, we investigate the role of initialization of the initial population in the rate of convergence and solution diversity. Results are presented on two key proteins, H-Ras and SOD1, related to human cancers and familial Amyotrophic lateral sclerosis (ALS).

Evolutionary search strategies for efficient sample-based representations of multiple-basin protein energy landscapes

Protein function is the result of a complex yet precise relationship between protein structure and dynamics. The ability of a protein to assume different structural states is key to biomolecular recognition and function modulation. Protein modeling research is driven by the need to complement experimental techniques in obtaining a comprehensive and detailed characterization of protein equilibrium dynamics. This is a non-trivial task, as it requires mapping the structure space (and underlying energy landscape) available to a protein under physiological conditions. Existing algorithms invariably adopt a stochastic optimization approach to explore the non-linear and multimodal protein energy landscapes. At the present, such algorithms suffer from limited sampling, particularly in high-dimensional and non-linear variable spaces rich in local minima. In this paper, we equip a recently published evolutionary algorithm with novel evolutionary search strategies to enhance the sampling capability for mapping multi-basin protein energy landscapes. We investigate initialization strategies to delay premature convergence and techniques to maintain and update on-the-fly a sample-based representation that serves as a map of the energy landscape. Applications on three proteins central to human disease show that the novel strategies are effective at locating basins in complex energy landscapes with a practical computational budget.

Evolution Strategies for Exploring Protein Energy Landscapes

The focus on important diseases of our time has prompted many experimental labs to resolve and deposit functional structures of disease-causing or disease-participating proteins. At this point, many functional structures of wildtype and disease-involved variants of a protein exist in structural databases. The objective for computational approaches is to employ such information to discover features of the underlying energy landscape on which functional structures reside. Important questions about which subset of structures are most thermodynamically-stable remain unanswered. The challenge is how to transform an essentially discrete problem into one where continuous optimization is suitable and effective. In this paper, we present such a transformation, which allows adapting and applying evolution strategies to explore an underlying continuous variable space and locate the global optimum of a multimodal fitness landscape. The paper presents results on wildtype and mutant sequences of proteins implicated in human disorders, such as cancer and Amyotrophic lateral sclerosis. More generally, the paper offers a methodology for transforming a discrete problem into a continuous optimization one as a way to possibly address outstanding discrete problems in the evolutionary computation community.

Evolving Conformation Paths to Model Protein Structural Transitions

Proteins are dynamic biomolecules. A structure-by-structure characterization of a proteins transition between two different functional structures is central to elucidating the role of dynamics in modulating protein function and designing therapeutic drugs. Characterizing transitions challenges both dry and wet laboratories. Some computational methods compute discrete representations of the energy landscape that organizes structures of a protein by their potential energies. The representations support queries for paths (series of structures) connecting start and goal structures of interest. Here we address the problem of modeling protein structural transitions under the umbrella of stochastic optimization and propose a novel evolutionary algorithm (EA). The EA evolves paths without reconstructing the energy landscape, addressing two competing optimization objectives, energetic cost and structural resolution. Rather than seek one path, the EA yields an ensemble of paths to represent a transition. Preliminary applications suggest the EA is effective while operating under a reasonable computational budget.

Evolutionary search for paths on protein energy landscapes

Proteins are in perpetual motion, switching between structures to regulate interactions with molecular partners. These motions correspond to hops in an energy landscape that organizes the structures available to a protein by their potential energies. Here we introduce an evolutionary algorithm (EA) that computes structural excursions of a protein without the need to reconstruct its energy landscape a priori. The preliminary results are promising and suggest further directions of research.

An evolutionary algorithm to model structural excursions of a protein

Excursions of a protein between different structures at equilibrium are key to its ability to modulate its biological function. The energy landscape, which organizes structures available to a protein by their energetics, contains all the information needed to characterize and simulate structural excursions. Computational research aims to uncover such excursions to complement wet-laboratory studies in characterizing protein equilibrium dynamics. Popular strategies adapt the robot motion planning framework and construct full or partial, structured representations of the energy landscape. In this paper, we present a novel, complementary approach based on evolutionary computation. We propose an evolutionary algorithm that evolves path representations of a specific structural excursion without a priori construction of the energy landscape. Preliminary applications on healthy and pathogenic variants of a protein central to human health are promising and warranting further investigation of evolutionary search techniques for modeling protein structural excursions.

Modeling protein structural transitions as a multiobjective optimization problem

Proteins of importance to human biology can populate significantly different three-dimensional (3d) structures at equilibrium. By doing so, a protein is able to interface with different molecules in the cell and so modulate its function. A structure-by-structure characterization of a proteins transition between two structures is central to elucidate the role of structural dynamics in regulating molecular interactions, understand the impact of sequence mutations on function, and design molecular therapeutics. Much wet- and dry-laboratory research is devoted to characterizing structural transitions. Computational approaches rely on constructing a full or partial, structured representation of the energy landscape that organizes structures by potential energy. The representation readily yields one or more paths that consist of series of structures connecting start and goal structures of interest. In this paper, we propose instead to cast the problem of computing transition paths as a multiobjective optimization one. We identify two desired characteristics of computed paths, energetic cost and structural resolution, and propose a novel evolutionary algorithm (EA) to compute low-cost and highresolution paths. The EA evolves paths representing a specific structural excursion without a priori constructing the energy landscape. Preliminary applications suggest the EA is effective while operating under a reasonable computational budget.

Path-based Guidance of an Evolutionary Algorithm in Mapping a Fitness Landscape and its Connectivity

Understanding function regulation in proteins that switch between different structural states at equilibrium requires both finding the basins that correspond to such states and computing the sequence of intermediate structures employed (i.e., the path taken) in basin-to-basin switching. Recent worksuggests that evolutionary strategies can be used to map protein energy landscapes effectively. Further work has shown that the constructed maps can be additionally equipped with connectivity information to help identify basin-switching paths. Here we highlight a potential issue when the problems of mapping and path finding are considered separately. We conduct a simple, proof-of principle study that demonstrates the ability of an EA to allow extracting better paths from an EA-built map when the EA is supplied with the right information. The study is conducted on two key, multi-state proteins of importance to human biology and disease. The results presented here suggest that further research efforts to guide an EA with path-based information are warranted and feasible.