Two-State Folding, Folding through Intermediates, and Metastability in a Minimalistic Hydrophobic-Polar Model for Proteins

Within the frame of an effective, coarse-grained hydrophobic-polar protein model, we employ multicanonical Monte Carlo simulations to investigate free-energy landscapes and folding channels of exemplified heteropolymer sequences, which are permutations of each other. Despite the simplicity of the model, the knowledge of the free-energy landscape in dependence of a suitable system order parameter enables us to reveal complex folding characteristics known from real bioproteins and synthetic peptides, such as two-state folding, folding through weakly stable intermediates, and glassy metastability.

Figure 1

Multicanonical histograms $H_{\mathrm{muca}}(E,Q)$ of energy $E$ and angular overlap parameter $Q$ and free-energy landscapes $F(Q)$ at different temperatures for the three sequences (a) $S1$, (b) $S2$, and (c) $S3$. The reference folds reside at $Q=1$ and $E=E_{\min }$. Pseudophases are symbolized by $D$ (denatured states), $N$ (native folds), $I$ (intermediates), and $M$ (metastable states). Representative conformations in intermediate and folded phases are also shown.