Web Release Date: March 16,
Statistical Mechanics of Helix Bundles Using a Dynamic Programming Approach
and
Contribution from the Department of Mathematics, Saint Mary's College of California, Moraga, California 94575-3517, Department of Computer & Information Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143-2240
Received October 11, 2006
Abstract:
Despite much study, biomolecule folding cooperativity is not well understood. There are
quantitative models for helix-coil transitions and for coil-to-globule transitions, but no accurate models yet
treat both chain collapse and secondary structure formation together. We develop here a dynamic
programming approach to statistical mechanical partition functions of foldamer chain molecules. We call it
the ascending levels model. We apply it to helix-coil and helix-bundle folding and cooperativity. For 14- to
50-mer Baldwin peptides, the model gives good predictions for the heat capacity and helicity versus
temperature and urea. The model also gives good fits for the denaturation of Oas's three-helix bundle B
domain of protein A (F13W*) and synthetic protein 
3C by temperature and guanidine. The model predicts
the conformational distributions. It shows that these proteins fold with transitions that are two-state, although
the transitions in the Baldwin helices are nearly higher order. The model shows that the recently developed
three-helix bundle polypeptoids of Lee et al. fold anti-cooperatively, with a predicted value of 
HvH/Hcal =
0.72. The model also predicts that two-helix bundles are unstable in proteins but stable in peptoids. Our
dynamic programming approach provides a general way to explore cooperativity in complex foldable
polymers.
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