(168d) Parallel Tempering Metadynamics in the Well Tempered Ensemble: Getting More and Spending Less

The task of quickly and accurately exploring large regions of phase space (i.e., conformational sampling) continues to be a pressing challenge in biomolecular simulations, especially for large systems.  Schemes that address this challenge, frequently referred to as “enhanced sampling” methods, typically fall into two broad categories. In one class of methods, specific degrees of freedom, or collective variables (CVs), are biased in order to traverse conformational space efficiently. A prominent example of this class is the metadynamics method, which has become increasingly popular over the past decade (1, 2).  The method is based on the introduction of a bias potential to accelerate sampling and reconstruct the free-energy profile along a set of CVs. Metadynamics suffers from a general problem, however: hidden degrees of freedom, which may not be accurately described by the chosen CVs, can frustrate exploration of phase space, sometimes limiting the extent of convergence and accuracy of results.  This challenge has been partially overcome by coupling metadynamics with parallel tempering, however this can limit the accessible system size due to well-known scaling challenges. 

Herein we report significant reduction in the cost of combined parallel tempering and metadynamics simulations (PTMetaD).  The efficiency boost is achieved using the recently proposed well-tempered ensemble (WTE) algorithm.  We studied the convergence of PTMetaD-WTE conformational sampling and free energy reconstruction of an explicitly solvated 20-residue tryptophan-cage protein (trp-cage).  By exploiting the properties of the recently introduced WTE, we were able to maintain amplified potential energy fluctuations in a system containing an explicitly solvated tryptophan-cage protein while actively biasing two additional CVs.  The convergence properties of PTMetaD-WTE depend both on the total simulation time and the RTT.  Without any significant tuning of the adjustable parameter γ, we observed that the trp-cage simulations can be reduced to 10 total replicas and achieve a similar RTT (and thus equal total computational cost) to 100-replica PTMetaD and PTMetaD-WTE simulations.  This is significant in that the 10 replica simulations have no energy overlap (and therefore an infinite RTT) without the WTE framework. A reduction of the overall computational cost can also be achieved by further increasing the value of the WTE parameter gamma, thus reducing the RTT. The agreement found in our simulations shows that PTMetaD-WTE in all-atom simulations of biomolecules is a robust improvement to current sampling schemes. Finally, this technique presents a bridge toward the enhanced sampling of systems that are far larger than what has previously been considered, thus greatly extending the applicability of the metadynamics method. 

1.         Laio, A., and M. Parrinello. 2002. Escaping free-energy minima. Proc. Natl. Acad. Sci. USA 99:12562-12566.

2.         Barducci, A., M. Bonomi, and M. Parrinello. 2011. Metadynamics. Wiley Interdisciplinary Reviews: Computational Molecular Science 1:826-843.