Using metadynamics to explore complex free-energy landscapes

Metadynamics is an atomistic simulation technique that allows, within the same framework, acceleration of rare events and estimation of the free energy of complex molecular systems. It is based on iteratively ‘filling’ the potential energy of the system by a sum of Gaussians centred along the trajectory followed by a suitably chosen set of collective variables (CVs), thereby forcing the system to migrate from one minimum to the next. The power of metadynamics is demonstrated by the large number of extensions and variants that have been developed. The first scope of this Technical Review is to present a critical comparison of these variants, discussing their advantages and disadvantages. The effectiveness of metadynamics, and that of the numerous alternative methods, is strongly influenced by the choice of the CVs. If an important variable is neglected, the resulting estimate of the free energy is unreliable, and predicted transition mechanisms may be qualitatively wrong. The second scope of this Technical Review is to discuss how the CVs should be selected, how to verify whether the chosen CVs are sufficient or redundant, and how to iteratively improve the CVs using machine learning approaches. Metadynamics is a technique to enhance the probability of observing rare events, such as chemical reactions and phase transitions, in molecular dynamics simulations. This Technical Review surveys the technique, addressing the critical issues that are met in practical applications. Metadynamics makes it possible to accelerate conformational transitions between metastable states, broadening the scope of molecular dynamics simulations. Like other enhanced sampling methods, metadynamics requires the introduction of low-dimensional descriptors (collective variables) whose choice affects the rate at which transitions are enhanced. The ideal collective variable should take different values not only in all the relevant metastable states but also in the transition states between them. The appropriate collective variables can be found by trial and error or designed automatically using methods inspired by machine learning. Two variants of metadynamics are commonly used, namely ordinary and well-tempered metadynamics. The former has the advantage of inducing transitions between the metastable states even if the collective variable is not ideal. The latter has the advantage of providing an exact estimator of the free energy. Metadynamics can be used in combination with most molecular dynamics software packages by taking advantage of dedicated software libraries that implement the method and a large number of collective variables.