Laboratoire J. A. Dieudonné

Reconstructing the free-energy landscape of protein with biased MD simulations: Metadynamics and dihedral Principal Component Analysis

Since the late 1980s emerges the idea that a global overview of the protein's energy surface is of paramount importance for a quantitative understanding of the relationships between structure, dynamics, stability, and functional behavior of proteins. Thanks to continuous increase of the computing power and of the reliability of empirical force fields, all-atom molecular dynamics (MD) simulations become a widely employed computational technique to simulate the dynamics of complex systems such as proteins through discrete integration of the Newtons's equations of motions of each atom. However in several cases all-atom MD simulations are still not competitive to describe the protein conformational dynamics, due to the fact that using an atomistic model is computationally expensive, as sufficiently realistic potential energy functions are intrinsically complex. Moreover, most phenomena of interest take place on times scales that are orders of magnitude larger than the accessible time that can be currently simulated with classical all-atom MD. This issue can be addressed by accelerating the exploration of the conformational space in (all-atom) MD simulations. In this case, a large variety of methods referred to as enhanced sampling techniques have been proposed. They exploit a methodology aimed at accelerating rare events and based on constrained MD. Metadynamics (metaD) belongs to this class of methods: it enhances the sampling of the conformational space of a system along a few selected degrees of freedom, named collective variables (CVs) and reconstructs the probability distribution as a function of these CVs. However, the succes of metaD depends on the critical choice of a reasonable number of relevant CVs. All the relevant slow varying degrees of freedom must be catched by the CVs. In addition, the number of CVs must be small enough to avoid exceedingly long computational time, while being able to distinguish among the different conformational states of the system. Consequently, identifying a set of CVs appropriate for describing complex processes involves a right understanding of the physics and chemistry of the process under study. Choosing a correct set of CVs thus remains a challenge, as a whole, independently of the enhanced sampling technique one could consider.

I will present that coupling Well-Tempered Metadynamics, i.e. the most recent variant of the method, with a set of CVs generated from a dihedral Principal Component Analysis on the Ramachandran dihedral angles (describing the backbone structure of the protein) provides an efficient reconstruction of the free-energy landscape of the small and very diffusive Met-enkephalin pentapeptide.