Correlation between rate of folding, energy landscape, and topology in the folding of a model protein HP-36

We explore the correlation between the energy landscape and topology in the folding of a model protein (chicken villin headpiece HP-36) by using a force-field which incorporates the effects of water through a hydropathy scale and the role of helical propensity of amino acids through a nonlocal harmonic potential. Each amino acid is represented by one side chain atom which is attached to the backbone C\alpha atom. Sizes and interactions of all the side chain residues are different and depend on the hydrophobicity of a particular amino acid, whereas helical propensities are incorporated in the interaction of C\alpha atoms. Simulations have been carried out by quenching from a fixed high temperature to two different low temperatures for many initial random configurations. The simulated structures resemble the real native state rather closely, with the root mean square deviation of the best structure being 4.5 Å. Moreover, the structure shows both the helices and bends at the appropriate positions of the model protein. The simplified model allows the study of energy landscape and also of the correlation between energy landscape with the dynamics of folding and topology. The initial part of folding is very fast, followed by two distinct slow stages, with the last stage being certainly the rate determining of the folding process. The initial fast dynamics is primarily due to hydrophobic collapse. The very slow last stage of folding is accompanied by a significant and sharp increase in the relative contact order parameter but relatively small decrease in energy. Analysis of the time dependence of the formation of the individual contact pairs show rich and complicated dynamics, where some contacts wait for a long time to form. This seems to suggest that the slow late stage folding is due to long range contact formation and also that the free energy barrier is entropic in origin. Results have been correlated with the theories of protein folding