Energy landscapes and persistent minima
Résumé
We consider a coarse-graining of high-dimensional potential energy landscapes based
upon persistences, which correspond to lowest barrier heights to lower-energy min-
ima. Persistences can be calculated efficiently for local minima in kinetic transition
networks that are based on stationary points of the prevailing energy landscape. The
networks studied here represent peptides, proteins, nucleic acids, an atomic cluster,
and a glassy system. Minima with high persistence values are likely to represent
some form of alternative structural morphology, which, if appreciably populated at
the prevailing temperature, could compete with the global minimum (defined as in-
finitely persistent). Threshold values on persistences (and in some cases equilibrium
occupation probabilities) have therefore been used in this work to select subsets of
minima, which were then analysed to see how well they can represent features of
the full network. Simplified disconnectivity graphs showing only the selected minima
can convey the funnelling (including any multiple-funnel) characteristics of the corre-
sponding full graphs. The effect of the choice of persistence threshold on the reduced
disconnectivity graphs was considered for a system with a hierarchical, glassy land-
scape. Sets of persistent minima were also found to be useful in comparing networks
for the same system sampled under different conditions, using minimum oriented
spanning forests.