We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape.

Metadynamics is a powerful technique for enhancing sampling in molecular dynamics simulations and reconstructing the free‐energy surface as a function of few selected degrees of freedom, often referred to as collective variables (CVs). In metadynamics, sampling is accelerated by a history‐dependent bias potential, which is adaptively constructed in the space of the CVs. Since its first appearance, significant improvements have been made to the original algorithm, leading to an efficient, flexible, and accurate method that has found many successful applications in several domains of science. Here, we discuss first the theory underlying metadynamics and its recent developments. In particular, we focus on the crucial issue of choosing an appropriate set of CVs and on the possible strategies to alleviate this difficulty. Later in the second part, we present a few recent representative applications, which we have classified into three main classes: solid‐state physics, chemical reactions, and biomolecules. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 826‐843 DOI: 10.1002/wcms.31This article is categorized under: Molecular and Statistical Mechanics > Free Energy Methods

70-kDa Heat shock proteins are ATP-driven molecular chaperones that perform a myriad of essential cellular tasks. Although structural and biochemical studies have shed some light on their functional mechanism, the fundamental issue of the role of energy consumption, due to ATP-hydrolysis, has remained unaddressed. Here we establish a clear connection between the non-equilibrium nature of Hsp70, due to ATP hydrolysis, and the determining feature of its function, namely its high affinity for its substrates. Energy consumption can indeed decrease the dissociation constant of the chaperone-substrate complex by several orders of magnitude with respect to an equilibrium scenario. We find that the biochemical requirements for observing such ultra-affinity coincide with the physiological conditions in the cell. Our results rationalize several experimental observations and pave the way for further analysis of non-equilibrium effects underlying chaperone functions.

Significance: Molecular chaperones are a group of proteins that are essential for avoiding the aggregation of other proteins in the crowded cellular environment. Chaperones function by interacting with these substrate proteins in different ways. However, it has remained a challenge to measure the changes that occur in the substrate proteins and understand how these changes prevent misfolding or aggregation. Here we investigate a chaperone system that keeps the substrate protein denatured by clamping the polypeptide chain. We observe an expansion of the substrate protein chain up to 30-fold in volume owing to steric repulsion between multiple copies of the chaperone bound to a single substrate protein. In this way, unwanted interactions within or between substrate proteins can be prevented.