Conformational Entropy as Collective Variable for Proteins

Abstract

Many enhanced sampling methods, such as Umbrella Sampling, Metadynamics or Variationally Enhanced Sampling, rely on the identification of appropriate collective variables. For proteins, even small ones, finding appropriate collective variables has proven challenging. Here we suggest that the NMR $S^2$ order parameter can be used to this effect. We trace the validity of this statement to the suggested relation between $S^2$ and entropy. Using the $S^2$ order parameter and a surrogate for the protein enthalpy in conjunction with Metadynamics or Variationally Enhanced Sampling we are able to reversibly fold and unfold a small protein and draw its free energy at a fraction of the time that is needed in unbiased simulations. From a more conceptual point of view this implies describing folding as a resulting from a trade off between entropy and enthalpy. We also use $S^2$ in combination with the free energy flooding method to compute the unfolding rate of this peptide. We repeat this calculation at different temperatures to obtain the unfolding activation energy.

4 pages, 3 figures

References in corpus (6)

• Canonical sampling through velocity-rescaling
• Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
• A Variational Approach to Enhanced Sampling and Free Energy Calculations
• Metadynamics with adaptive Gaussians
• Enhancing entropy and enthalpy fluctuations to drive crystallization in atomistic simulations
• Free Energy Landscape of GAGA and UUCG RNA Tetraloops

Cited by in corpus (3)

• Enhanced sampling methods for molecular dynamics simulations
• Rare Event Kinetics from Adaptive Bias Enhanced Sampling
• Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations