  Quantifying convergence and sufficient sampling of macromolecular molecular
dynamics simulations is more often than not a source of controversy (and of
various ad hoc solutions) in the field. Clearly, the only reasonable,
consistent and satisfying way to infer convergence (or otherwise) of a
molecular dynamics trajectory must be based on probability theory. Ideally, the
question we would wish to answer is the following : "What is the probability
that a molecular configuration important for the analysis in hand has not yet
been observed ?". Here we propose a method for answering a variant of this
question by using the Good-Turing formalism for frequency estimation of
unobserved species in a sample. Although several approaches may be followed in
order to deal with the problem of discretizing the configurational space, for
this work we use the classical RMSD matrix as a means to answering the
following question: "What is the probability that a molecular configuration
with an RMSD (from all other already observed configurations) higher than a
given threshold has not actually been observed ?". We apply the proposed method
to several different trajectories and show that the procedure appears to be
both computationally stable and internally consistent. A free, open-source
program implementing these ideas is immediately available for download via
public repositories.
