The Adaptive Path Collective Variable: A Versatile Biasing Approach to Compute the Average Transition Path and Free Energy of Molecular Transitions

Abstract

In the past decade, great progress has been made in the development of enhanced sampling methods, aimed at overcoming the time-scale limitations of molecular dynamics (MD) simulations. Many sampling schemes rely on adding an external bias to favor the sampling of transitions and to estimate the underlying free energy landscape. Nevertheless, sampling molecular processes described by many order parameters, or collective variables (CVs), such as complex biomolecular transitions, remains often very challenging. The computational cost has a prohibitive scaling with the dimensionality of the CV-space. Inspiration can be taken from methods that focus on localizing transition pathways: The CV-space can be projected onto a path-CV that connects two stable states, and a bias can be exerted onto a one-dimensional parameter that captures the progress of the transition along the path-CV. In principle, such a sampling scheme can handle an arbitrarily large number of CVs. A standard enhanced sampling technique combined with an adaptive path-CV can then locate the mean transition pathway and obtain the free energy profile along the path. In this chapter, we discuss the adaptive path-CV formalism and its numerical implementation. We apply the path-CV with several enhanced sampling methods—steered MD, metadynamics, and umbrella sampling—to a biologically relevant process: The Watson–Crick to Hoogsteen base-pairing transition in double-stranded DNA. A practical guide is provided on how to recognize and circumvent possible pitfalls during the calculation of a free energy landscape that contains multiple pathways. Examples are presented on how to perform enhanced sampling simulations using PLUMED, a versatile plugin that can work with many popular MD engines.