  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.
