Recognizing Local and Global Structural Motifs at the Atomic Scale

Most
of the current understanding of structure–property
relations at the molecular and the supramolecular scales can be formulated
in terms of the stability of and the interactions between a limited
number of recurring structural motifs (e.g., H-bonds, coordination
polyhedra, and protein secondary structure). Here we demonstrate an
algorithm to automatically recognize such patterns, based on the identification
of local maxima in the probability distributions observed in atomistic
computer simulations, which is robust to the dimensionality and the
sparsity of the reference atomistic data. We first discuss its main
features, demonstrating some on artificial data sets, and then show
how it can be applied to identify coordination environments in Lennard-Jones
clusters and to recognize secondary-structure patterns in the simulation
of an oligopeptide. To assess the applicability of this algorithm
for motifs that involve several interdependent degrees of freedom,
we also employ it to identify groups of conformers of the cluster
and the polypeptide, considered in their entirety. The motifs identified
by analyzing atomistic simulations can be used to interpret and rationalize
the stability and behavior of the system at hand, and also as a tool
to accelerate sampling, in association with biased molecular dynamics
schemes.