  A coarse-grained variational model is used to investigate the polymer
dynamics of barrier crossing for a diverse set of two-state folding proteins.
The model gives reliable folding rate predictions provided excluded volume
terms that induce minor structural cooperativity are included in the
interaction potential. In general, the cooperative folding routes have sharper
interfaces between folded and unfolded regions of the folding nucleus and
higher free energy barriers. The calculated free energy barriers are strongly
correlated with native topology as characterized by contact order. Increasing
the rigidity of the folding nucleus changes the local structure of the
transition state ensemble non-uniformly across the set of protein studied.
Neverthless, the calculated prefactors k0 are found to be relatively uniform
across the protein set, with variation in 1/k0 less than a factor of five. This
direct calculation justifies the common assumption that the prefactor is
roughly the same for all small two-state folding proteins. Using the barrier
heights obtained from the model and the best fit monomer relaxation time 30ns,
we find that 1/k0 (1-5)us (with average 1/k0 4us). This model can be extended
to study subtle aspects of folding such as the variation of the folding rate
with stability or solvent viscosity, and the onset of downhill folding.
