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Enhanced, targeted sampling of high-dimensional free-energy landscapes using variationally enhanced sampling, with an application to chignolin

Significance The problem of sampling complex systems characterized by metastable states separated by kinetic bottlenecks is a universal one that has received much attention. Popular strategies involve applying a bias to a small number of collective variables. This strategy fails when the choice of collective variable is not clear or when the system’s free energy cannot be projected meaningfully on a low-dimensional manifold. We use a variational principle that allows one to construct approximate but effective multidimensional biases. We show in a practical case that the method is much more efficient than alternative methods. We expect this method to be useful for a wide variety of sampling problems in chemistry, biology, and materials science. The capabilities of molecular simulations have been greatly extended by a number of widely used enhanced sampling methods that facilitate escaping from metastable states and crossing large barriers. Despite these developments there are still many problems which remain out of reach for these methods which has led to a vigorous effort in this area. One of the most important problems that remains unsolved is sampling high-dimensional free-energy landscapes and systems that are not easily described by a small number of collective variables. In this work we demonstrate a new way to compute free-energy landscapes of high dimensionality based on the previously introduced variationally enhanced sampling, and we apply it to the miniprotein chignolin.