Computing best transition pathways in high-dimensional dynamical systems:: Application to the αL ⇆ β ⇆ αR transitions in octaalanine

The direct computation of rare transitions in high-dimensional dynamical systems such as biomolecules via numerical integration or Monte Carlo is limited by the sampling problem. Alternatively, the dynamics of these systems can be modeled by transition networks (TNs) which are weighted graphs whose edges represent transitions between stable states of the system. The computation of the globally best transition paths connecting two selected stable states is straightforward with available graph-theoretical methods. However, these methods require that the energy barriers of all TN edges be determined, which is often computationally infeasible for large systems. Here, we introduce energy-bounded TNs, in which the transition barriers are specified in terms of lower and upper bounds. We present algorithms permitting the determination of the globally best paths on these TNs while requiring the computation of only a small subset of the true transition barriers. Several variants of the algorithm are given which achieve improved performance, including a parallel version. The effectiveness of the approach is demonstrated by various benchmarks on random TNs and by computing the refolding pathways of a polypeptide: the best transition pathways between the alpha(L) helix, alpha(R) helix, and beta-hairpin conformations of the octaalanine (Ala(8)) molecule in aqueous solution.