(190ad) A Comparative Study On the Enhanced Sampling of Small Peptides

Molecular dynamics (MD) provides a useful way to investigate the underlying thermodynamics of a system that are difficult to resolve by experiment alone. However, MD as it stands is insufficient when the subject of interest involves large-scale conformational changes in soft-matter systems (e.g., proteins or polymers). Such events tend to occur on the order of microseconds or longer, a timescale far beyond the range of MD. In response to this, numerous enhanced sampling algorithms have been developed to effectively explore conformational space in a reasonable amount of time. Two common classes of methods for overcoming energy barriers are: 1) those that manipulate a system’s energy by adding an external bias (e.g., umbrella sampling or metadynamics) and 2) those that periodically expose a system to temperatures above the melting point (e.g., parallel tempering).

The work we present focuses on the convergence of conformational sampling and thermodynamic energy landscapes of an explicitly solvated 20-residue tryptophan-cage protein (Trp-cage). Three types of simulations are compared: classical parallel tempering (PT) [1], parallel tempering and well-tempered metadynamics (PT-WTM) [2], and a new method that uses metadynamics within the well-tempered ensemble of Bonomi and Parrinello [3]. This new method allows for a broad temperature range to be sampled using many fewer replicas than PT or PT-WTM. Dubbed Well-Tempered Exchange (WTEx), not only does this approach significantly reduce computational cost – compared to the aforementioned methods – but it also enables the possibility of scaling to systems larger than what was previously considered practical for PT simulations.

As a proof of concept, initial simulations of an N-methylalanylacetamide (alanine dipeptide) toy system are presented. The underlying free-energy surface (FES) agrees well with umbrella sampling calculations and previous estimates. Following subsequent optimizations of the WTEx parameter space, we extend the method to larger systems of practical interest. The overall convergence and efficiencies of obtaining the FES for PT (100 replica), PT-WTM (100 replica), and WTEx (10 replica) are presented. Finally, the approach is used to examine the folding of a more complicated structure – bovine pancreatic trypsin inhibitor.

[1] Sugita & Okamoto, Chem. Phys. Let. 314, 141-151 (1999)

[2] Barducci et al., Biophys. Jour. 98, L44 (2010)

[3] Bonomi & Parrinello, Phys. Rev. Let. 104, 190601 (2010)