(377b) Reaction Coordinates And Transition Pathways Of Rare Events Via Forward Flux Sampling

Path sampling methods based on importance sampling of dynamical trajectories have become powerful simulation tools for understanding dynamics in complex systems. However, the challenges of applying these path sampling algorithms, such as Forward Flux Sampling (FFS), to rare events include: (i) determination of an adequate order parameter (or combination of variables) that allows the description of multiple transition state regions of a process; (ii) assessing efficiency and completeness of sampling; and (iii) estimation of the free energy profile and barriers. These challenges arise, in large part, because the efficiency of these sampling schemes is sensitive to an improper choice of order parameter. To address these limitations, we present a new approach for identifying suitable reaction coordinates to describe the progression of rare events in complex systems. The method is based on a FFS-type sampling technique and standard least square estimation (LSE) and it is therefore denoted as FFS-LSE. The algorithm generates trajectories for the transition between stable states as chains of partially connected paths, which can be then used to obtain ?on-the-fly? estimates for the committor probability to the final region ?p_B?. These p_B data are then used to screen a set of candidate collective properties for an optimal order parameter (i.e., reaction coordinate) that depends on a few relevant variables. LSE is then used to find the coefficients of the proposed reaction coordinate model, and an analysis of variance is used to determine the significant terms in the model. We also introduce a new method to evaluate simultaneously the kinetics and the free energy profile in one single FFS simulation series. The approach computes free energies using the Monte Carlo ensemble of trajectories generated by the FFS-type sampling scheme combined with a reweighing procedure that resembles an umbrella sampling between interfaces. These approaches are demonstrated for several problems including protein folding of both simple lattice models as well as atomistic models like that for the ß-sheet Forming Binding Protein (FBP28) WW domain. We showed that a simple approximation to pB as order parameter in terms of collective variables is sufficient for describe the intrinsic dynamics of the complex system and ensure a complete and efficient sampling. Furthermore, since the p_B surface found from the FFS-LSE approach leads to the identification of the free energy profile in terms of the estimated reaction coordinate, the ensemble of transition states and mechanistic details of the transition can be readily obtained without the need of additional simulations.