New perspectives on protein flexibility: Monte Carlo Markov Chain algorithms for structural and thermodynamic studies on proteins

A central problem in computational structural biology is to design effective algorithms dealing with high dimensional conformational
spaces, also shedding light on the intrinsic complexity of the problems tackled (identifying meta-stable states, computing free energies, computing kinetic constants).

In this talk, I will review recent work on Monte Carlo Markov chains (MCMC) algorithms of the Hit-and-Run type, for two seemingly unrelated problems: computing the volume of high dimensional polytopes, and sampling the conformational space of long flexible molecules.  I will also discuss the connexion with densities of states (DoS) calculations,  to reliably estimate thermodynamic properties of biomolecular systems with hundreds of degrees of freedom.

[1] Geometric constraints within tripeptides and the existence of tripeptide reconstructions
T. O'Donnell, and F. Cazals
https://www.biorxiv.org/content/10.1101/2022.06.21.497005v2

[2] Enhanced conformational exploration of protein loops using a global parameterization of the backbone geometry
T. O'Donnell, and F. Cazals
https://www.biorxiv.org/content/10.1101/2022.06.21.497022v2

[3] Efficient computation of the the volume of a polytope in high-dimensions using Piecewise Deterministic Markov Processes
A. Chevallier, and F. Cazals, and P. Fearnhead
AISTATS, 2022

[4] Improved polytope volume calculations based on Hamiltonian Monte Carlo with boundary reflections and sweet arithmetics
A. Chevallier, and S. Pion, and F. Cazals
J. of Computational Geometry, 13 (1), 2022

[5] Wang-Landau algorithm: an adapted random walk to boost convergence
A. Chevallier and F. Cazals
J. of Computational Physics, 410(1), 2020