Finding Transition Pathways Using the String Method with Swarms of Trajectories

Abstract

An approach to find transition pathways in complex systems is presented. The method, which is related to the string method in collective variables of Maragliano et al. (J. Chem. Phys. 2006, 125, 024106), is conceptually simple and straightforward to implement. It consists of refining a putative transition path in the multidimensional space supported by a set of collective variables using the average dynamic drift of those variables. This drift is estimated on-the-fly via swarms of short unbiased trajectories started at different points along the path. Successive iterations of this algorithm, which can be naturally distributed over many computer nodes with negligible interprocessor communication, refine an initial trial path toward the most probable transition path (MPTP) between two stable basins. The method is first tested by determining the pathway for the C7eq to C7ax transition in an all-atom model of the alanine dipeptide in vacuum, which has been studied previously with the string method in collective variables. A transition path is found with a committor distribution peaked at 1/2 near the free energy maximum, in accord with previous results. Last, the method is applied to the allosteric conformational change in the nitrogen regulatory protein C (NtrC), represented here with a two-state elastic network model. Even though more than 550 collective variables are used to describe the conformational change, the path converges rapidly. Again, the committor distribution is found to be peaked around 1/2 near the free energy maximum between the two stable states, confirming that a genuine transition state has been localized in this complex multidimensional system.

Transition path theory analysis of c-Src kinase activation

“…In practical applications, one is often interested in knowing the probability if a specific microstate is (or is not) along the path of a reactive trajectory (π Constructing Pathways from TPT. The string method, by which a transition pathway is discretized into a chain of states called images, is a powerful technique to study rare event in complex systems (29,30). Once the optimized string has been obtained, thermodynamic and kinetic information can be extracted from milestoning simulations.…”

Explaining why Gleevec is a specific and potent inhibitor of Abl kinase

“…This is carried out by calculating the potential of mean force (PMF) with respect to two pseudodihedral angles controlling the DFG-flip using umbrella sampling MD simulations (details are provided in Methods). The choice of the two pseudodihedral angles for Abl and c-Src, referred to as χ 1 and χ 2 , was suggested from previous studies of the DFG-flip using the string method, a computational technique to determine the pathway of conformational transitions (19). The 1D-PMF of Fig.…”

Calculation of free energy landscapes: A histogram reweighted metadynamics approach

“…5). Alanine dipeptide is one of the most studied model systems over the last years [44,[74][75][76][77][78][79][80]. The corresponding eigenvalues and the cumulative positional fluctuations are shown in Fig.…”