proteins STRUCTURE O FUNCTION O BIOINFORMATICS An NMA-guided path planning approach for computing large-amplitude conformational changes in proteins Svetlana Kirillova, Juan Corte ´s,* Alin Stefaniu, and Thierry Sime ´on LAAS-CNRS, Toulouse, France INTRODUCTION The study of conformational changes in macromolecules such as proteins or DNA is of key importance for understanding their biological functions. Furthermore, accurately predicting molecular interactions with computational methods requires taking into account molecular flexibility. 1–5 Therefore, the development of techni- ques to compute macromolecular motions is currently the subject of much research. The most rigorous method to simulate molecular motions is molecular dynamics (MD), 6,7 which calculates the trajectories of atoms using Newton’s Second Law and potential energy functions of atom–atom interactions. However, the computational cost of MD prohibits routine simulations of large-amplitude motions of macromole- cules. As an alternative to MD methods, stochastic search methods compute low- energy paths by randomly exploring a given molecular force field. Most of the stochastic approaches to compute molecular motions are based on Monte Carlo (MC) algorithms. 6,7 A recently proposed stochastic exploration method based on robotic path planning techniques 8 outperforms classical MC-based algorithms by simultane- ously examining multiple pathways. Despite efforts to develop efficient techniques, the ability of energy-based search methods to compute large-amplitude motions of macro- molecular models is limited by the complexity of the search-space. Indeed, the molec- ular energy landscape is a very high-dimensional manifold with many local minima. The complexity of molecular energy landscapes led us to develop a two-stage approach for computing large-amplitude motions. 9 The first and main stage is purely geometric. A geometric treatment of the strongest molecular constraints, combined with efficient path planning algorithms, permits our method to consider large-amplitude motions with low computational cost. In the second stage, paths computed using the geometric approach are refined by fast energy minimization. We obtained encouraging results when applying this method to compute protein loop motions 10 and ligand–protein access pathways. 9 Recently, a similar approach has been used to compute motions of pairs of a-helices in transmembrane pro- teins. 11 However, despite the efficiency of such geometry-based conformational ex- ploration, it remains difficult to directly handle fully flexible molecular models with this approach because of the very high dimension of the conformational space. This paper presents a new method to compute global macromolecular motions such as open-closed conformational transitions in proteins. It combines the above mentioned geometric approach with normal mode analysis (NMA). 12 A number of works 13–16 have shown that large-amplitude motions in macromolecules (e.g. The Supplementary Material referred to in this article can be found online at http://www.interscience.wiley.com/jpages/ 0887-3585/suppmat/ *Correspondence to: Juan Corte ´s, LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse, France. E-mail: juan.cortes@laas.fr Received 10 November 2006; Revised 19 March 2007; Accepted 16 April 2007 Published online 19 July 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/prot.21570 ABSTRACT This paper presents a new method for computing macromolecular mo- tions based on the combination of path planning algorithms, originat- ing from robotics research, and elas- tic network normal mode analysis. The low-frequency normal modes are regarded as the collective degrees of freedom of the molecule. Geometric path planning algorithms are used to explore these collective degrees of freedom in order to find possi- ble large-amplitude conformational changes. To overcome the limits of the harmonic approximation, which is valid in the vicinity of the mini- mum energy structure, and to get larger conformational changes, nor- mal mode calculations are iterated during the exploration. Initial results show the efficiency of our method, which requires a small number of normal mode calculations to com- pute large-amplitude conformational transitions in proteins. A detailed analysis is presented for the com- puted transition between the open and closed structures of adenylate ki- nase. This transition, important for its biological function, involves large- amplitude domain motions. The obtained motion correlates well with results presented in related works. Proteins 2008; 70:131–143. V V C 2007 Wiley-Liss, Inc. Key words: protein flexibility; large- amplitude conformational transi- tions; elastic network normal mode analysis; path planning algorithms; adenylate kinase open-closed transi- tion pathway. V V C 2007 WILEY-LISS, INC. PROTEINS 131