The potential energy landscape (PEL) of a physical system is graph of the real-valued function associated a potential energy to a given conformation. PELs encode all thermodynamic and kinetic properties, whence their central importance.

Yet, modeling such landscapes is extremely challenging due to their high dimensionality. For example, a protein involving n atoms (say n=10,000) has a PEL defined over a d=3n dimensional space - since each atom has 3 Cartesian coordinates. This talk will revisit three fundamental problems for PEL, in light of recent developments in Computer Science.

First, a hybrid exploration algorithm combining basin hopping and rapidly exploring random trees will be sketched, yielding an enhanced exploration of complex energy landscapes [RDRC16].

Second, a generic algorithm to analyze a height field, stressing in particular its Morse structure (critical points, their connexions, and their stability) will be presented [CDM+ 15]. The algorithm will be used to identify so-called persistent local minima, their attraction basins, and connexions across saddles. The interest of such features will be discussed [CMCW16].

Finally, an algorithm to compare two (sampled) energy landscapes will be outlined [CM16]. The strategy, based on optimal transportation theory, consists of computing a least cost mapping between the basins, compatible with the transition paths known on both landscapes. Illustrations on various systems whose (frustrated) landscapes have been exhaustively studied in the literature will be presented.

The software implementing the algorithms discussed is made available to the community in the Structural bioinformatics Library at http://sbl.inria.fr > Applications > Conformational Analysis.

References

[CDM+15] F. Cazals, T. Dreyfus, D. Mazauric, A. Roth, and C.H. Robert. Conformational ensembles and sampled energy landscapes: Analysis and comparison. Journal of Computational Chemistry, 36(16):1213-1231, 2015.

[CM16] F. Cazals and D. Mazauric. Mass transportation problems with connectivity constraints, with applications to energy landscape comparison. Submitted, 2016. Preprint: Inria tech report 8611.

[CMCW16] J. Carr, D. Mazauric, F. Cazals, and D.J. Wales. Energy landscapes and persistent minima. The Journal of Chemical Physics,144(5), 2016.

[RDRC16] A. Roth, T. Dreyfus, C. Robert, and F. Cazals. Hybridizing rapidly growing random trees and basin hopping yields an improved exploration of energy landscapes. Journal of Computational Chemistry, 37(8), 2016.