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In recent work, we have illustrated the construction of an exploration geometry on free energy surfaces: the adaptive computer-assisted discovery of an approximate low-dimensional manifold on which the effective dynamics of the system evolves. Constructing such an exploration geometry involves geometry-biased sampling (through both appropriately-initialized unbiased molecular dynamics and through restraining potentials) and, machine learning techniques to organize the intrinsic geometry of the data resulting from the sampling (in particular, diffusion maps, possibly enhanced through the appropriate Mahalanobis-type metric). In this contribution, we detail a method for exploring the conformational space of a stochastic gradient system whose effective free energy surface depends on a smaller number of degrees of freedom than the dimension of the phase space. Our approach comprises two steps. First, we study the local geometry of the free energy landscape using diffusion maps on samples computed through stochastic dynamics. This allows us to automatically identify the relevant coarse variables. Next, we use the information garnered in the previous step to construct a new set of initial conditions for subsequent trajectories. These initial conditions are computed so as to explore the accessible conformational space more efficiently than by continuing the previous, unbiased simulations. We showcase this method on a representative test system. [ABSTRACT FROM AUTHOR]

Reaction coordinates are vital tools for qualitative and quantitative analysis of molecular processes. They provide a simple picture of reaction progress and essential input for calculations of free energies and rates. Iso-committor surfaces are considered the optimal reaction coordinate. We present an algorithm to compute efficiently a sequence of isocommittor surfaces. These surfaces are considered an optimal reaction coordinate. The algorithm analyzes Milestoning results to determine the committor function. It requires only the transition probabilities between the milestones, and not transition times. We discuss the following numerical examples: (i) a transition in the Mueller potential; (ii) a conformational change of a solvated peptide; and (iii) cholesterol aggregation in membranes. [ABSTRACT FROM AUTHOR]