A multiscale hybrid evolutionary algorithm to obtain sample-based representations of multi-basin protein energy landscapes

Abstract

The emerging picture of proteins as dynamic systems switching between structures to modulate function demands a comprehensive structural characterization only possible through an energy landscape treatment. Only sample-based representations of a protein energy landscape are viable in silico, and sampling-based exploration algorithms have to address the fundamental but challenging issue of balancing between exploration (broad view) and exploitation (going deep). We propose here a novel algorithm that achieves this balance by combining concepts from evolutionary computation and protein modeling research. The algorithm draws samples from a reduced space obtained via principal component analysis of known experimental structures. Samples are lifted from the reduced to an all-atom structure space where they are then mapped to nearby local minima in the all-atom energy landscape. From an algorithmic point of view, this paper makes several contributions, including the design of a local selection operator that is crucial to avoiding premature convergence. From an application point of view, this paper demonstrates the utility of the proposed evolutionary algorithm to advance understanding of multi-basin proteins. In particular, the proposed algorithm makes the first steps to answering the question of how sequence mutations affect function in proteins at the center of proteinopathies by providing the energy landscape as the intermediate explanatory link between protein sequence and function.

Mapping Multiple Minima in Protein Energy Landscapes with Evolutionary Algorithms

“…Similarity is determined fast and coarsely, on a neighborhood-structure in a 2d embedding along the top two PCs. Further details can be found in [3,1].…”

“…However, to maintain feasibility, the de novo setting has been discarded. Instead, known experimental structures of wildtype and variant sequences of such proteins are employed to either define the dimensionality, shape, and bounds of the underlying variable space for a CMA-ES algorithm [2] or in addition to seed the initial population of a population-based memetic cellular EA [3,1].…”

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.…”

A stochastic roadmap method to model protein structural transitions

“…EAs are investigated in detail in our lab in diverse protein modeling scenarios, including de novo structure prediction 72,73 and protein-protein docking. 74,75 The EA we employ here has been recently proposed 9 to further populate the structure space of a protein for which many experimental structures already exist in the Protein Data Bank (PDB). 76 Briefly, the EA leverages the abundance of experimentally-available structures to define the struc- It is this procedure that makes structures generated by the EA specific to a protein sequence under investigation.…”

“…It is worth noting that searching in a PC-based embedding and making use of multiscaling have been previously analyzed in detail in the context of a robotics-inspired (tree-based) search algorithm, 78 and these components are integrated in the recently proposed EA 9 we employ in the sampling stage here. The ensemble Ω of structures fed to stage II of the SRS-based method in this paper consists of all the populations of local minima obtained by the EA across all its g generations for a protein sequence at hand.…”