Coarsely resolved topography along protein folding pathways

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Abstract
The kinetic data from the coarse representation of polypeptide torsional dynamics described in the preceding paper [Fernandez and Berry, J. Chem. Phys. 112, 5212 (2000), preceding paper] is inverted by using detailed balance to obtain a topographic description of the potential-energy surface (PES) along the dominant folding pathway of the bovine pancreatic trypsin inhibitor (BPTI). The topography is represented as a sequence of minima and effective saddle points. The dominant folding pathway displays an overall monotonic decrease in energy with a large number of staircaselike steps, a clear signature of a good structure-seeker. The diversity and availability of alternative folding pathways is analyzed in terms of the Shannon entropy σ(t) associated with the time-dependent probability distribution over the kinetic ensemble of contact patterns. Several stages in the folding process are evident. Initially misfolded states form and dismantle revealing no definite pattern in the topography and exhibiting high Shannon entropy. Passage down a sequence of staircase steps then leads to the formation of a nativelike intermediate, for which σ(t) is much lower and fairly constant. Finally, the structure of the intermediate is refined to produce the native state of BPTI. We also examine how different levels of tolerance to mismatches of side chain contacts influence the folding kinetics, the topography of the dominant folding pathway, and the Shannon entropy. This analysis yields upper and lower bounds of the frustration tolerance required for the expeditious and robust folding of BPTI.