Computing energy landscape maps and structural excursions of proteins

Abstract

BackgroundStructural excursions of a protein at equilibrium are key to biomolecular recognition and function modulation. Protein modeling research is driven by the need to aid wet laboratories in characterizing equilibrium protein dynamics. In principle, structural excursions of a protein can be directly observed via simulation of its dynamics, but the disparate temporal scales involved in such excursions make this approach computationally impractical. On the other hand, an informative representation of the structure space available to a protein at equilibrium can be obtained efficiently via stochastic optimization, but this approach does not directly yield information on equilibrium dynamics.MethodsWe present here a novel methodology that first builds a multi-dimensional map of the energy landscape that underlies the structure space of a given protein and then queries the computed map for energetically-feasible excursions between structures of interest. An evolutionary algorithm builds such maps with a practical computational budget. Graphical techniques analyze a computed multi-dimensional map and expose interesting features of an energy landscape, such as basins and barriers. A path searching algorithm then queries a nearest-neighbor graph representation of a computed map for energetically-feasible basin-to-basin excursions.ResultsEvaluation is conducted on intrinsically-dynamic proteins of importance in human biology and disease. Visual statistical analysis of the maps of energy landscapes computed by the proposed methodology reveals features already captured in the wet laboratory, as well as new features indicative of interesting, unknown thermodynamically-stable and semi-stable regions of the equilibrium structure space. Comparison of maps and structural excursions computed by the proposed methodology on sequence variants of a protein sheds light on the role of equilibrium structure and dynamics in the sequence-function relationship.ConclusionsApplications show that the proposed methodology is effective at locating basins in complex energy landscapes and computing basin-basin excursions of a protein with a practical computational budget. While the actual temporal scales spanned by a structural excursion cannot be directly obtained due to the foregoing of simulation of dynamics, hypotheses can be formulated regarding the impact of sequence mutations on protein function. These hypotheses are valuable in instigating further research in wet laboratories.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-016-2798-8) contains supplementary material, which is available to authorized users.

Evolutionary search for paths on protein energy landscapes

“…is is comparable to the best path produced by the EA in [3], which has a cost of 266 REUs and a resolution of 0.145Å (rounded to 0.15 in Table 1).…”

“…e EA is run to obtain paths connecting two known structures corresponding to two di erent functional states of H-Ras. e computational budget was xed to 100, 000 tness evaluations, 10 times less than that used in prior work that reconstructs energy landscapes with an EA and then uses graph-based representations to answer path queries [3]. e N = 15 paths obtained in the nal generation with the path-evolving EA with this budget are rendered in Fig.…”

“…e legend lists path costs and resolutions. Table 1 juxtaposes the 10 lowest-cost paths obtained by the pathevolving EA with the 10 lowest-cost paths obtained by the EA in prior work [3]. e comparison is limited to 10 paths, as the resolution of the paths deteriorates a erwards.…”

“…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.…”

“…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].…”