Simulation of the folding equilibrium of alpha-helical peptides: a comparison of the generalized Born approximation with explicit solvent

Abstract

We compare simulations using the generalized Born/surface area (GB/SA) implicit solvent model with simulations using explicit solvent (transferable intermolecular potential 3 point, TIP3P) to test the GB/SA algorithm. We use the replica exchange molecular dynamics method to sample the conformational phase space of two alpha-helical peptides, A21 and the Fs, by using two different classical potentials and both water models. We find that when using GB/SA: (i) A21 is predicted to be more helical than the Fs peptide at all temperatures; (ii) the native structure of the Fs peptide is predicted to be a helical bundle instead of a single helix; and (iii) the persistence length and most probable end-to-end distance are too large in the unfolded state when compared against the explicit solvent simulations. We find that the potential of mean force in the phi(psi) plane is markedly different in the two solvents, making the two simulated peptides respond differently when the backbone torsions are perturbed. A fit of the temperature melting curves obtained in these simulations to a Lifson-Roig model finds that the GB/SA model has an unphysically large nucleation parameter, whereas the explicit solvent model produces values similar to experiment.

Fig. 1.

Equilibrium thermal denaturation of A₂₁ and F_s peptides in explicit solvent by using the parm94 and parm-mod force fields. (Upper) The mean number of hydrogen bonds computed as the average number of w residues by using the classification described in Methods. (Lower) The average number of helices computed as the average number of unbroken stretches of w residues. Error bars are 65% confidence limits estimated by block averages. The F_s peptide is clearly more helical than A₂₁ under both force fields.

Fig. 2.

Equilibrium thermal denaturation of A₂₁ and F_s peptides in GB/SA by using the parm94 and parm-mod force fields. (Upper) The mean number of hydrogen bonds. (Lower) The average number of helices. The curves and error bars are computed as in Fig. 1. Unlike in explicit solvent (Fig. 1), at high temperatures the F_s peptide has the same helical content as A₂₁, and at lower temperatures with the parm94 force field it is less helical. The low-temperature behavior is caused by the experimentally incorrect formation of structures with multiple helices.

Fig. 3.

A projection of the 200-K ensemble of the F_s peptide in GB/SA (parm94) onto the two largest principal components; each structure in the ensemble corresponds to a single point in the plane. We show representative structures from the major clusters. The ribbon backbone is colored according to sequence position: red is N-terminal and blue is C-terminal. Fewer than 9% of the structures occur in the leftmost cluster, which corresponds to the physically correct single-helix structures. The 200-K ensemble is shown for clarity. Remnants of these major clusters persist above 350 K.

Fig. 4.

The variation of energetic factors along the largest principal component for the F_s peptide in GB/SA at 200 K. Each point corresponds to a structure in the 200-K ensemble. The principal component is the same as principal component 1 shown in Fig. 3. The leftmost cluster corresponds to structures that have a single helix as seen experimentally. The other clusters contain multiple helices. The red line is an average over structures with similar values for their largest principal component. The multiple helix structures have unfavorable electrostatic plus GB interactions (compared with a single helix) and favorable van der Waals and surface burial interactions.

Fig. 5.

The fractional helicity as a function of residue index for the F_s peptide (parm94) in explicit solvent and in GB/SA. The temperature (375 K) is slightly below the denaturation temperature for both the explicit solvent and GB/SA denaturation temperatures (393 K and 380 K, respectively). The explicit solvent simulations have enhancement of the helicity at residue positions one and two positions toward the N terminus of arginine residues; no enhancement is seen in GB/SA simulations.

Fig. 6.

The potential of mean force in the Φ–Ψ plane averaged over the central seven residues of A₂₁ in the unfolded state with explicit solvent (A) and GB/SA (B). Both are shown at a temperature ≈1.27 times the T_m (456 K and 513 K). Contours are in units of RT at each temperature. Notice that explicit solvent produces a much more diverse distribution of conformations including β, PPII, and left-handed α-helix, but the GB/SA simulation is largely restricted to the α-helical region. This restriction produces a large persistence length and a large mean end-to-end distance with GB/SA compared with explicit solvent. (C) The distribution of end-to-end distances for explicit solvent (red) and GB/SA (black).