title: Analysis and elimination of a bias in targeted molecular dynamics simulations of conformational transitions: application to calmodulin.
abstract: The popular targeted molecular dynamics (TMD) method for generating transition paths in complex biomolecular systems is revisited. In a typical TMD transition path, the large-scale changes occur early and the small-scale changes tend to occur later. As a result, the order of events in the computed paths depends on the direction in which the simulations are performed. To identify the origin of this bias, and to propose a method in which the bias is absent, variants of TMD in the restraint formulation are introduced and applied to the complex open ↔ closed transition in the protein calmodulin. Due to the global best-fit rotation that is typically part of the TMD method, the simulated system is guided implicitly along the lowest-frequency normal modes, until the large spatial scales associated with these modes are near the target conformation. The remaining portion of the transition is described progressively by higher-frequency modes, which correspond to smaller-scale rearrangements. A straightforward modification of TMD that avoids the global best-fit rotation is the locally restrained TMD (LRTMD) method, in which the biasing potential is constructed from a number of TMD potentials, each acting on a small connected portion of the protein sequence. With a uniform distribution of these elements, transition paths that lack the length-scale bias are obtained. Trajectories generated by steered MD in dihedral angle space (DSMD), a method that avoids best-fit rotations altogether, also lack the length-scale bias. To examine the importance of the paths generated by TMD, LRTMD, and DSMD in the actual transition, we use the finite-temperature string method to compute the free energy profile associated with a transition tube around a path generated by each algorithm. The free energy barriers associated with the paths are comparable, suggesting that transitions can occur along each route with similar probabilities. This result indicates that a broad ensemble of paths needs to be calculated to obtain a full description of conformational changes in biomolecules. The breadth of the contributing ensemble suggests that energetic barriers for conformational transitions in proteins are offset by entropic contributions that arise from a large number of possible paths.
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States. ovchinnv@georgetown.edu
authors.forename: Victor
authors.initials: V
authors.lastname: Ovchinnikov
authors.forename: Martin
authors.initials: M
authors.lastname: Karplus
mesh_terms: D000465:Algorithms; D000818:Animals; D002147:Calmodulin / Q000737:chemistry*; D018360:Crystallography, X-Ray; D056004:Molecular Dynamics Simulation; D016805:Paramecium tetraurelia / Q000737:chemistry*; D011487:Protein Conformation; D015800:Protozoan Proteins / Q000737:chemistry*; D013816:Thermodynamics; D029867:Xenopus Proteins / Q000737:chemistry*; D014982:Xenopus laevis / Q000378:metabolism*
chemical_list: D002147:Calmodulin; D015800:Protozoan Proteins; D029867:Xenopus Proteins