Kinetics of the Wako-Saitô-Muñoz-Eaton Model of Protein Folding

We consider a simplified model of protein folding, with binary degrees of freedom, whose equilibrium thermodynamics is exactly solvable. Based on this exact solution, the kinetics is studied in the framework of a local equilibrium approach, for which we prove that (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, and (iii) the equilibration rate is an upper bound of the exact one. The kinetics is compared to the exact one for a small peptide and to Monte Carlo simulations for a longer protein; then rates are studied for a real protein and a model structure.

Figure 1

Probability of $\beta$-hairpin bond $i$ being native versus time. Solid lines: Our results; dashed lines: exact results.

Figure 2

Probability of $\alpha$-helix structures in headpiece subdomain being native versus time. Dashed lines: Our results; solid lines: Monte Carlo simulations.

Figure 3

PIN1 equilibration rate versus inverse temperature. Solid line: Metropolis kinetics; dashed line: Glauber kinetics.

Figure 4

Equilibration rate for a $\beta$ sheet of four strands versus absolute contact order. Dots: Our results; line: exponential fit.