Exploring the Free Energy Landscape: From Dynamics to Networks and Back

Abstract

Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.

Author Summary

A complete description of complex polymers, such as proteins, includes information about their structure and their dynamics. In particular it is of utmost importance to answer the following questions: What are the structural conformations possible? Is there any relevant hierarchy among these conformers? What are the transition paths between them? These and other questions can be addressed by analyzing in an efficient way the Free Energy Landscape of the system. With this knowledge, several problems about biomolecular reactions (such as enzymatic activity, protein folding, protein deposition diseases, etc.) can be tackled. In this article we show how to efficiently describe the Free Energy Landscape for small and large peptides. By mapping the trajectories of molecular dynamics simulations into a graph (the Conformational Markov Network) and unveiling its structural organization, we obtain a coarse grained description of the protein dynamics across the Free Energy Landscape in terms of the relevant kinetic magnitudes of the system. Therefore, we show the way to bridge the gap between the microscopic dynamics and the macroscopic kinetics by means of a mesoscopic description of the associated Conformational Markov Network. Along this path the compromise between the physical nature of the process and the magnitudes that characterize the network is carefully kept to assure the reliability of the results shown.