  We consider two- and three-dimensional lattice models of proteins which were
characterized previously. We coarse grain their folding dynamics by reducing it
to transitions between effective states. We consider two methods of selection
of the effective states. The first method is based on the steepest descent
mapping of states to underlying local energy minima and the other involves an
additional projection to maximally compact conformations. Both methods generate
connectivity patterns that allow to distinguish between the good and bad
folders. Connectivity graphs corresponding to the folding funnel have few loops
and are thus tree-like. The Arrhenius law for the median folding time of a
16-monomer sequence is established and the corresponding barrier is related to
easily identifiable kinetic trap states.
