Constraint theory and hierarchical protein dynamics

The complexity and functionality of proteins requires that they occupy an exponentially small fraction of configuration space (perhaps 10^-300). How did evolution manage to create such unlikely objects? Thorpe has solved the static half of this problem (known in protein chemistry as Levinthal's paradox) by observing that for stress-free chain segments the complexity of optimally constrained elastic networks scales not with expN (where N \sim 100 -1000 is the number of amino acids in a protein), but only with N. Newman's results for diffusion in N-dimensional spaces provide suggestive insights into the dynamical half of the problem. He showed that the distribution of residence (or pausing) time between sign reversals changes qualitatively at N \sim 40 . The overall sign of a protein can be defined in terms of a product of curvature and hydrophobic(philic) character over all amino acid residues. This construction agrees with the sizes of the smallest known proteins and prions, and it suggests a universal clock for protein molecular dynamics simulations.