Nucleic Acids Research Advance Access published online on June 1, 2007
Nucleic Acids Research, doi:10.1093/nar/gkm342
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Web Server Issue |
MinActionPath: maximum likelihood trajectory for large-scale structural transitions in a coarse-grained locally harmonic energy landscape
1Department of Physics, Reed College, Portland, OR 97202, USA, 2Department of Computer Science and Genome Center, UC Davis, Davis, CA 95616, USA, 3Departments of Physics and Applied Physics, Stanford University, Stanford, CA 94305-4045, USA, and 4Department of Structural Biology and Chemistry and URA 2185 du C.N.R.S., Institut Pasteur, Paris, France
*To whom correspondence should be addressed. Tel: +33-1-45-688605; Fax: +33-1-40-613793; Email: delarue{at}pasteur.fr
Received January 31, 2007. Revised April 19, 2007. Accepted April 22, 2007.
The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using ‘morphing’ techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http://lorentz.dynstr.pasteur.fr/joel/index.php.