The thermodynamics and kinetics of protein folding: A lattice model analysis of multiple pathways with intermediates

The kinetics and thermodynamics of folding of a representative sequence of a 125-residue protein model subject to Monte Carlo dynamics on a simple cubic lattice were investigated. The diverse trajectories that lead to the native state can be classified into a relatively small number of average pathways: a "fast track" in which the chain forms a stable core that folds directly to the native state and several "slow tracks" in which particular contacts form before the core is complete and direct the chain to-a misfolded intermediate. Rearrangement from the intermediates to the native state is slow because it requires breaking stable contacts, which involve primarily surface residues. The transition state for folding is identified by activated dynamics simulations and consists of a reduced version of the core in the absence of other (native and nonnative) contacts which slow folding. Each track involves an ensemble of structures that can be characterized by two progress coordinates for the reaction. These coordinates are based on a comparison of folding and nonfolding trajectories: one coordinate monitors the formation of the core and the other monitors whether the chain is trapped in a long-lived intermediate. From Monte Carlo simulations, we obtain an estimate for the density of states and calculate equilibrium averages, including the free energy, energy, and entropy, as functions of the two coordinates. The thermodynamics are in good agreement with the observed kinetics; the transition states correspond to plateaus or barriers in the free energy while the intermediates are energetically stabilized local foe energy minima. The complexities of the folding mechanism bear a striking similarity to those observed experimentally for lysozyme, a well-studied protein of comparable size.