Simplified and improved string method for computing the minimum energy paths in barrier-crossing events

Abstract

We present a simplified and improved version of the string method, originally proposed by E et al. [Phys. Rev. B 66, 052301 (2002)] for identifying the minimum energy paths in barrier-crossing events. In this new version, the step of projecting the potential force to the direction normal to the string is eliminated and the full potential force is used in the evolution of the string. This not only simplifies the numerical procedure, but also makes the method more stable and accurate. We discuss the algorithmic details of the improved string method, analyze its stability, accuracy and efficiency, and illustrate it via numerical examples. We also show how the string method can be combined with the climbing image technique for the accurate calculation of saddle points and we present another algorithm for the accurate calculation of the unstable directions at the saddle points.

Free energy of conformational transition paths in biomolecules: The string method and its application to myosin VI

“…3,20 The essence of the method is to evolve a curve-the stringusing −M(θ)∇G(θ ) as a force while maintaining a prescribed parametrization of the curve. If we parametrize the string as θ (α) with α ∈ [0, 1], this evolution can be written as…”

“…Initial values for the these collective variables (initial "string" of replicas) are determined from a minimum energy path (MEP) calculated between the endpoint structures using the zero-temperature string method in the full space of Cartesian atom positions. 3,20 With the string method in collective variables 5 and starting from the initial string, the replicas are allowed to "relax" in the direction of the negative gradient of the free energy, with the arc-length between adjacent replicas kept approximately constant. The final converged string corresponds to an MFEP between the endpoint states in the collective variable space.…”

“…5 that the errors due to the use of a restraint instead of a constraint in the approximation, Eq. (20), are of the order (βk i ) −1 (see also Sec. III D 3).…”

“…In the present application, we found that convergence was difficult to achieve using Eq. (20) as written, and Hamiltonian replica exchange was employed with the MD simulations to improve sampling.…”

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

“…One is to make our computation fast by using parallel computing. But a more promising way can be to use a better modeling strategy, such as the string method, [84][85][86] to efficiently connect different hydration states in the fluctuating relaxing motion of solute-solvent interface.…”