title: Minimum action transition paths connecting minima on an energy surface.
abstract: Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.
authors.affiliation: Department of Computer Science and Genome Center, University of California, Davis, California 95616, USA.
authors.forename: Patrice
authors.initials: P
authors.lastname: Koehl
mesh_terms: D004548:Elasticity; D008958:Models, Molecular; D011487:Protein Conformation; D013816:Thermodynamics