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Graph-theoretical identification of dissociation pathways on free energy landscapes of biomolecular interaction



Biomolecular association and dissociation reactions take place on complicated interaction free energy landscapes that are still very hard to characterize computationally. For large enough distances, though, it often suffices to consider the six relative translational and rotational degrees of freedom of the two particles treated as rigid bodies. Here, we computed the six-dimensional free energy surface of a dimer of water-soluble alpha-helices by scanning these six degrees of freedom in about one million grid points. In each point, the relative free energy difference was computed as the sum of the polar and nonpolar solvation free energies of the helix dimer and of the intermolecular coulombic interaction energy. The Dijkstra graph algorithm was then applied to search for the lowest cost dissociation pathways based on a weighted, directed graph, where the vertices represent the grid points, the edges connect the grid points and their neighbors, and the weights are the reaction costs between adjacent pairs of grid points. As an example, the configuration of the bound state was chosen as the source node, and the eight corners of the translational cube were chosen as the destination nodes. With the strong electrostatic interaction of the two helices giving rise to a clearly funnel-shaped energy landscape, the eight lowest-energy cost pathways coming from different orientations converge into a well-defined pathway for association. We believe that the methodology presented here will prove useful for identifying low-energy association and dissociation pathways in future studies of complicated free energy landscapes for biomolecular interaction. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010