ORIGINAL PAPER Continuous metadynamics in essential coordinates as a tool for free energy modelling of conformational changes Vojtěch Spiwok & Blanka Králová & Igor Tvaroška Received: 27 February 2008 / Accepted: 19 June 2008 / Published online: 17 July 2008 # Springer-Verlag 2008 Abstract Modelling of conformational changes in bio- polymers is one of the greatest challenges of molecular biophysics. Metadynamics is a recently introduced free energy modelling technique that enhances sampling of configurational (e.g. conformational) space within a molecular dynamics simulation. This enhancement is achieved by the addition of a history-dependent bias potential, which drives the system from previously visited regions. Discontinuous metadynamics in the space of essential dynamics eigenvectors (collective motions) has been proposed and tested in conformation- al change modelling. Here, we present an implementa- tion of two continuous formulations of metadynamics in the essential subspace. The method was performed in a modified version of the molecular dynamics package GROMACS. These implementations were tested on conformational changes in cyclohexane, alanine dipep- tide (terminally blocked alanine, Ace-Ala-Nme) and SH3 domain. The results illustrate that metadynamics in the space of essential coordinates can accurately model free energy surfaces associated with conforma- tional changes. Keywords Conformational change . Essential dynamics . Free energy surface . Metadynamics . Molecular dynamics Introduction One of the most important features of biopolymers is their ability to adopt different conformations to fulfil their catalytic, signalling, memory or mechanical roles. In addition, protein folding, unfolding, and misfolding can all be viewed as conformational changes. Accurate model- ling of conformational changes using molecular modelling methods is one of the greatest challenges in this field. However, conformational families of a molecule are often separated by high free energy barriers. These barriers cause conformational changes to be slow and that the probability of overcoming these barriers in a short (e.g. nanosecond) molecular dynamics simulation is low or even negligible. Solving this problem by using the brute force of supercomputer power is not always applicable. The idea of enhancement the sampling of configurational space is not new in molecular simulations [1]. Metadynamics [2, 3] is a recently introduced molecular dynamics-based technique, which enhances sampling and quantitatively evaluates a free energy surface. The initial step of metadynamics involves the choice of a few (typically two) collective variables. Collective variables are geometric parameters that are supposed to describe the progress of the studied process. Inter-atomic distances, valence and dihedral angles and coordination numbers have often been used as collective variables in recent applications of metadynamics [4–8]. In metadynamics, the system is simulated by a standard molecular dynamics simulation to which a history-dependent bias potential is added. The bias potential is usually formulated as the sum of Gaussian hills J Mol Model (2008) 14:995–1002 DOI 10.1007/s00894-008-0343-7 V. Spiwok (*) : I. Tvaroška Department of Structure and Function of Saccharides, Institute of Chemistry, Center for Glycomics, Slovak Academy of Sciences, Dúbravska cesta 9, 84538 Bratislava, Slovak Republic e-mail: chemspiw@savba.sk V. Spiwok : B. Králová Department of Biochemistry and Microbiology, Institute of Chemical Technology in Prague, Technická 3, 166 28 Prague 6, Czech Republic