Microcanonical versus Canonical Analysis of Protein Folding

The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the $\mathsf{S}$-bend pattern in the caloric curve, which gives rise to negative microcanonical specific heats, and the bimodality of the energy distribution function at the transition temperatures. Models for a good folder are shown to be quite robust against perturbations in the interaction potential parameters.

Figure 1

Canonical heat capacities for the polymer models HMP (a), RHTP (b), and DHTP (c).

Figure 2

Caloric curves for the polymer models HMP (a), RHTP (b), and DHTP (c). Results are for the canonical (dotted line) and microcanonical (full line) ensembles.

Figure 3

Energy distribution functions. HMP (a), RHTP (b) and DHTP (c). Numbers within the panels are the $k_{B}T$ values.

Figure 4

Minimum values of the canonical (dotted line) and microcanonical (full line) caloric curve derivatives as a function of $x$ (see text for details).