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Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

(RECEIVED August 4, 2005; FINAL REVISION November 25, 2005; ACCEPTED November 25, 2005)

In order to improve our understanding of the physical bases of protein folding, there is a compelling need for better connections between experimental and computational approaches. This work addresses the role of unfolded state conformational heterogeneity and en-route intermediates, as an aid for planning and interpreting protein folding experiments. The expected kinetics were modeled for different types of energy landscapes, including multiple parallel folding routes, preferential paths dominated by one primary folding route, and distributed paths with a wide spectrum of microscopic folding rate constants. In the presence of one or more preferential routes, conformational exchange among unfolded state populations slows down the observed rates for native protein formation. We find this to be a general phenomenon, taking place even when unfolded conformations interconvert much faster than the "escape" rate constants to folding. Dramatic kinetic deceleration is expected in the presence of an increasing number of folding-incompetent unfolded conformations. This argues for the existence of parallel folding paths involving several folding-competent unfolded conformations, during the early stages of protein folding. Deviations from single-exponential behavior are observed for unfolded conformations exchanging at comparable rates or more slowly than folding events. Analysis of the effect of en-route (on-path) intermediate formation and landscape ruggedness on folding kinetics leads to the following unexpected conclusions: (1) intermediates, which often retard native state formation, may in some cases accelerate folding, and (2) rugged landscapes, usually associated with stretched exponentials, display single-exponential behavior in the presence of late high-friction paths.

Keywords: protein folding; single-exponential; stretched-exponential; landscapes; pathways; kinetics

Abbreviations: N, native state • U, unfolded state • I, intermediate state • k_inter-U, rate constant for exchange among different unfolded state conformations • k_inter-I, rate constant for exchange among different intermediate conformations • k_i, folding rate starting from the ith unfolded state conformation • k_UI, rate constant for the transition from a U to an I • k_IU, rate constant for the transition from an I to a U • k_IN, rate constant for the transition from an I to an N • K_i, equilibrium constant for the interconversion among different unfolded state conformations • P_N(t), time-dependent population of native state P_U0,i • initial population of ith unfolded conformation • LSODA, Livermore solver of ordinary differential equations

Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.051758206.

Reprint requests to: Silvia Cavagnero, Department of Chemistry, University of Wisconsin-Madison, 1101 University Ave., Madison, WI 53706, USA; e-mail: cavagnero{at}chem.wisc.edu; fax: (608) 262-9918.

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