Refining Collective Coordinates and Improving Free Energy Representation in Variational Enhanced Sampling

Collective variables are used often in many enhanced sampling methods, and their choice is a crucial factor in determining sampling efficiency. However, at times, searching for good collective variables can be challenging. In a recent paper, we combined time-lagged independent component analysis with well-tempered metadynamics in order to obtain improved collective variables from metadynamics runs that use lower quality collective variables [McCarty, J.; Parrinello, M. J. Chem. Phys. 2017, 147, 204109 ]. In this work, we extend these ideas to variationally enhanced sampling. This leads to an efficient scheme that is able to make use of the many advantages of the variational scheme. We apply the method to alanine-3 in water. From an alanine-3 variationally enhanced sampling trajectory in which all the six dihedral angles are biased, we extract much better collective variables able to describe in exquisite detail the protein complex free energy surface in a low dimensional representation. The success of this investigation is helped by a more accurate way of calculating the correlation functions needed in the time-lagged independent component analysis and from the introduction of a new basis set to describe the dihedral angles arrangement.