Constraint theory and hierarchical protein dynamics
Abstract
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 stressfree 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 Ndimensional 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.
 Publication:

Journal of Physics Condensed Matter
 Pub Date:
 November 2004
 DOI:
 10.1088/09538984/16/44/004
 Bibcode:
 2004JPCM...16S5065P