Navigating molecular worms inside chemical labyrinths

Predicting whether a molecule can traverse chemical labyrinths of channels, tunnels, and buried cavities usually requires performing computationally intensive molecular dynamics simulations. Often one wants to screen molecules to identify ones that can pass through a given chemical labyrinth or screen chemical labyrinths to identify those that allow a given molecule to pass. Because it is impractical to test each molecule/labyrinth pair using computationally expensive methods, faster, approximate methods are used to prune possibilities, “triaging” the ability of a proposed molecule to pass through the given chemical labyrinth. Most pruning methods estimate chemical accessibility solely on geometry, treating atoms or groups of atoms as hard spheres with appropriate radii. Here, we explore geometric configurations for a moving “molecular worm,” which replaces spherical probes and is assembled from solid blocks connected by flexible links. The key is to extend the fast marching method, which is an ordered upwind one-pass Dijkstra-like method to compute optimal paths by efficiently solving an associated Eikonal equation for the cost function. First, we build a suitable cost function associated with each possible configuration, and second, we construct an algorithm that works in ensuing high-dimensional configuration space: at least seven dimensions are required to account for translational, rotational, and internal degrees of freedom. We demonstrate the algorithm to study shortest paths, compute accessible volume, and derive information on topology of the accessible part of a chemical labyrinth. As a model example, we consider an alkane molecule in a porous material, which is relevant to designing catalysts for oil processing.