  The classical approach to protein folding inspired by statistical mechanics
avoids the high dimensional structure of the conformation space by using
effective coordinates. Here we introduce a network approach to capture the
statistical properties of the structure of conformation spaces. Conformations
are represented as nodes of the network, while links are transitions via
elementary rotations around a chemical bond. Self-avoidance of a polypeptide
chain introduces degree correlations in the conformation network, which in turn
lead to energy landscape correlations. Folding can be interpreted as a biased
random walk on the conformation network. We show that the folding pathways
along energy gradients organize themselves into scale free networks, thus
explaining previous observations made via molecular dynamics simulations. We
also show that these energy landscape correlations are essential for recovering
the observed connectivity exponent, which belongs to a different universality
class than that of random energy models. In addition, we predict that the
exponent and therefore the structure of the folding network fundamentally
changes at high temperatures, as verified by our simulations on the AK peptide.
