Structural correlations in protein folding funnels

Abstract

While the overall energy landscape of a foldable protein can be described by means of a few parameters characterizing its statistical topography, specific energetic terms subtly bias the representative structures giving rise to residue pair correlations as in a liquid. We use a free energy functional incorporating an inhomogeneous pair contact energy along with a contact formation entropy and a cooperativity contribution to determine residue-specific contact probabilities in the denatured state and the transition state ensemble. The predicted "hot residues" for the theoretical transition state ensemble reasonably agree with experiment for chymotrypsin inhibitor 2, and generally a strong correlation exists with the measured kinetic effects of mutating residues not involved in highly solvent-exposed regions.

Figure 1

(a) Native contact map (at Q = 1.0) for CI2 shown in the upper left and contact map of calculated contact probabilities (at Q* = 0.2) for the CI2 transition state ensemble without any tertiary or secondary cooperativity in the lower right. (b) Contact map of calculated contact probabilities (at Q* = 0.2) with α_h = 0.45 and α_t = 0.0 shown in the upper left and α_h = 0 and α_t = 0.05 shown in the lower right.

Figure 2

Correlation of the energy-unweighted contact density (S_th) to the molecular dynamics S_tertiary (S_ter). Q* = 0.45 is used to match the simulation’s average value of S_tertiary. There is good agreement for core residues and reasonable agreement for helical and sheet residues. The diagonal line S_ter = S_th is indicated in black along with the separate correlation lines for core (red) and sheet (black) in a and α-helical (green), minicore (black), and turn and coil (red) residues in b.

Figure 3

Correlation of the energy-weighted φ_th to the measured φ_exp for the core and β-sheet residues (a) and the helical, minicore, and turn and coil residues (b), using the same color scheme as Fig. 2. Error bars for a few representative (larger or smaller) experimental values are indicated from data of Fersht and co-workers (4).

Figure 4

The folded structure of CI2 is shown for ensembles at Q* = 0.45 (a) and Q* = 0.2 (b) with residues colored according to the theoretically predicted energy-unweighted S_tertiary in those ensembles. The specific hot sites identified by experiment are indicated by arrows. The experimental and theoretical energy-weighted φ values are as follows: Ala-16 φ_exp = 1.1, φ_th = 0.6; Leu-49 φ_exp = 0.5, φ_th = 0.3; and Ile-57 φ_exp = 0.1, φ_th = 0.2.