Sample-Based Models of Protein Energy Landscapes and Slow Structural Rearrangements

Abstract

Proteins often undergo slow structural rearrangements that involve several angstroms and surpass the nanosecond timescale. These spatiotemporal scales challenge physics-based simulations and open the way to sample-based models of structural dynamics. This article improves an understanding of current capabilities and limitations of sample-based models of dynamics. Borrowing from widely used concepts in evolutionary computation, this article introduces two conflicting aspects of sampling capability and quantifies them via statistical (and graphical) analysis tools. This allows not only conducting a principled comparison of different sample-based algorithms but also understanding which algorithmic ingredients to use as knobs via which to control sampling and, in turn, the accuracy and detail of modeled structural rearrangements. We demonstrate the latter by proposing two powerful variants of a recently published sample-based algorithm. We believe that this work will advance the adoption of sample-based models as reliable tools for modeling slow protein structural rearrangements.

From mutations to mechanisms and dysfunction via computation and mining of protein energy landscapes

“…In principle, one can utilize all coordinates (typical numbers range from 10 to 25 PCs), but the dimensionality adds to the computational cost of the analysis. It is worth noting that in cases where SoPriMp can be employed to obtain sample-based representations of energy landscapes, the top two PCs capture more than 50% of the conformation variance, and the top three capture more than 70% of the variance [ 11 – 14 , 17 , 18 ]. The emphasis on reasonable computational costs is due to the objective to apply BDR or SDR in comparative analysis settings that screen numerous variants of a protein in search of landscape features to learn the impact of mutations on dysfunction.…”

“…The ability to do so relies on recent methodological advances that are making it possible to obtain detailed, sample-based representations of energy landscapes for proteins with sufficient, wet-laboratory, conformational data (the “ Related work ” section summarizes these advances). Specifically, these methods are able to feasibly compute detailed, sample-based representations of energy landscapes for different variants of a protein of interest [ 11 – 14 ].…”

“…In particular, since 2015, various stochastic optimization algorithms have been proposed and refined that delay premature convergence and so obtain detailed, sample-based representations of energy landscapes of various medium-size proteins with reasonable computational budgets) [ 11 – 14 , 16 – 18 ]. Sampling of conformations takes place over a carefully-selected variable space.…”

“…Specifically, the data we utilize here are obtained with the SoPriMp algorithm [ 17 ]. The SoPriM algorithm [ 17 ] and its faster version, SoPriMp [ 11 ] do not directly operate in the conformation space of a protein, so as to circumvent the dimensionality issue, but instead compute samples that represent conformations in a low-dimensional variable space of principal components (PCs). Fast transformations between the variable space and the all-atom conformation space allow the algorithms to obtain low-energy, all-atom conformations of a protein sequence of interest.…”

“…The interested reader can learn more about these algorithms and their evaluation in Ref. [ 11 ]. In this paper, the samples analyzed by the proposed landscape analysis methods are generated by SoPriMp (due to its higher exploration capability [ 17 ]) and correspond to computed, all-atom conformations evaluated with the Amber ff14SB forcefield.…”