Analysis and Elimination of a Bias in Targeted Molecular Dynamics Simulations of Conformational Transitions: Application to Calmodulin

Abstract:

The popular targeted mol. dynamics (TMD) method for generating transition paths in complex biomol. 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 assocd. 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 no. 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-​temp. string method to compute the free energy profile assocd. with a transition tube around a path generated by each algorithm. The free energy barriers assocd. 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 calcd. to obtain a full description of conformational changes in biomols. 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 no. of possible paths.