Based on the complete ensemble of hairpin conformations, a statistical mechanical model that combines the eigenvalue solutions of the rate matrix and the free-energy landscapes has been able to predict the temperature-dependent folding rate, kinetic intermediates, and folding pathways for hairpin-forming RNA sequences. At temperatures higher than a “glass transition” temperature, Tg, the eigenvalues show a distinct time separation, and the rate-limiting step is a two-state single exponential process determined by the slowest eigenmode. At temperatures lower than Tg, no distinct time separation exists for the eigenvalues, hence multiple (slow) eigenmodes contribute to the rate-determining processes, and the folding involves the trapping and detrapping of kinetic intermediates. For a 21-nt sequence we studied, Tg is lower than the transition temperature, Tm, for thermodynamic equilibrium folding. For T > Tm, starting from the native state, the chain undergoes a biphasic unfolding transition: a preequilibrated quasi-equilibrium macrostate is formed followed by a rate-limiting two-state transition from the macrostate to the unfolded state. For Tg < T < Tm, the chain undergoes a two-state on-pathway folding transition, at which a nucleus is formed by the base stacks close to the loop region before a rapid assembly of the whole hairpin structure. For T < Tg, the multistate kinetics involve kinetic trapping, causing the roll-over behavior in the rate-temperature Arrhenius plot. The complex kinetic behaviors of RNA hairpins may be a paradigm for the folding kinetics of large RNAs
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