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A microscopic theory of the free energy barriers and folding routes forminimally frustrated proteins is presented, greatly expanding on thepresentation of the variational approach outlined previously [J. J. Portman, S.Takada, P. G. Wolynes, Phys. Rev. Lett. {\bf 81}, 5237 (1998)]. We choose the$\lambda$-repressor protein as an illustrative example and focus on how thepolymer chain statistics influence free energy profiles and partially orderedensembles of structures. In particular, we investigate the role of chainstiffness on the free energy profile and folding routes. We evaluate theapplicability of simpler approximations in which the conformations of theprotein molecule along the folding route are restricted to have residues thatare either entirely folded or unfolded in contiguous stretches. We find thatthe folding routes obtained from only one contiguous folded region correspondsto a chain with a much greater persistence length than appropriate for naturalprotein chains, while the folding route obtained from two contiguous foldedregions is able to capture the relatively folded regions calculated within thevariational approach. The free energy profiles obtained from the contiguoussequence approximations have larger barriers than the more microscopicvariational theory which is understood as a consequence of partial ordering.Comment: 16 pages, 11 figure

Microscopic theory of protein folding rates. I. Fine structure of the free energy profile and folding routes from a variational approach