  Native shortcut networks (SCN0) are sub-graphs of native protein residue
networks (PRN0). In this paper, we propose the Network Dynamics (ND) model,
which reconstructs a PRN0 by adding back its edges according to some recipe,
while its nodes are fixed at native (PDB) locations. A PRN0 reconstruction will
eventually reconstruct its SCN0, but only after exploring several non-native
shortcut network (SCN) configurations. It is these other SCN configurations
that are of interest to us, as they produce the statistics to evaluate the
different recipes. The recipes vary from each other slightly to investigate the
effect of different edge orderings on protein folding. An edge ordering is
deemed more successful if it produces a stronger correlation with experimental
folding rates. Over proteins of different chain fold types, this basic
requirement is best satisfied when a recipe favours earlier restoration of
edges with smaller sequence separation, and earlier restoration of edges
incident on nodes with larger remaining degree within the 1-hop neighborhood of
a previously selected node. Further, this recipe generated more route-like
trajectories over SCN space and a wider range of simulated folding rates, both
of which signal cooperative two-state folding behavior. It also produced better
correspondence between ND calculated phi-values and experimental phi-values
obtained from a set of ten transition state ensembles (TSE). Also introduced is
the local centrality measure which uses centrality of initial fold
substructures to yield calculated phi-values from PRN0s with even better
overall correspondence than ND calculated phi-values. Preliminary investigation
with mixed ND recipes by chain fold type suggests that concocting further
context-sensitive recipes by chain fold type and combining them could improve
ND. This search task may be better undertaken by machine learning.
