Constraint theory and hierarchical protein dynamics

Abstract

The complexity and functionality of proteins requires that theyoccupy an exponentially small fraction of configuration space (perhaps10−300). How did evolution manage to create such unlikely objects? Thorpe has solved the static halfof this problem (known in protein chemistry as Levinthal’s paradox) by observing that forstress-free chain segments the complexity of optimally constrained elastic networks scales not withexpN (where –1000 is the number of amino acids in a protein), but only withN. Newman’s resultsfor diffusion in N-dimensional spaces provide suggestive insights into the dynamical half of the problem. Heshowed that the distribution of residence (or pausing) time between sign reversals changesqualitatively at . The overall sign of a protein can be defined in terms of a product of curvature andhydrophobic(philic) character over all amino acid residues. This construction agrees withthe sizes of the smallest known proteins and prions, and it suggests a universal clock forprotein molecular dynamics simulations.