Role of side-chain interactions on the formation of $\alpha$-helices in model peptides

The role played by side-chain interactions on the formation of $\alpha$-helices is studied using extensive all-atom molecular dynamics simulations of polyalanine-like peptides in explicit TIP4P water. The peptide is described by the OPLS-AA force field except for the Lennard-Jones interaction between $C_{\beta }-C_{\beta }$ atoms, which is modified systematically. We identify values of the Lennard-Jones parameter that promote $\alpha$-helix formation. To rationalize these results, potentials of mean force (PMF) between methane-like molecules that mimic side chains in our polyalanine-like peptides are computed. These PMF exhibit a complex distance dependence where global and local minima are separated by an energy barrier. We show that $\alpha$-helix propensity correlates with values of these PMF at distances corresponding to $C_{\beta }\text{–}{C}_{\beta }$ of $i-i+3$ and other nearest neighbors in the $\alpha$-helix. In particular, the set of Lennard-Jones parameters that promote $\alpha$-helices is characterized by PMF that exhibit a global minimum at distances corresponding to $i-i+3$ neighbors in $\alpha$-helices. Implications of these results are discussed.

Figure 1

Time evolution of secondary structure content for $\epsilon =1$ kJ/mol, N = 9, and $\sigma$ values of (a) 0.27 nm, (b) 0.37 nm, (c) 0.47 nm, and (d) 0.57 nm. $N_{\mathrm{residue}}$ is the number of residues assuming coil in black, $\beta$-sheet in red (medium gray), turn in yellow (light gray), and $\alpha$-helix in blue (dark gray) structures.

Figure 2

Content of various secondary structure elements as a function of $\sigma$ for several values of $\epsilon$. All plots are for the nine-residue-long peptides $\left(N=9\right)$ averaged over the entire 400 ns trajectory. Helices are depicted in blue (open circles), turns in orange (triangles), and $\beta$-sheets in red (square).

Figure 3

Time evolution of secondary structure content along the amino acid sequence ($y$ axis) for $\epsilon =1$ kJ/mol. Panels (a) and (b) correspond to $\sigma =0.37$ nm and 0.47 nm, respectively.

Figure 4

Potential of mean force between methane-like particles and ${\mathrm{C}}_{\beta }$–${\mathrm{C}}_{\beta }$ LJ interaction using $\epsilon =1.0$ kJ/mol and $\sigma =0.47$ nm.

Figure 5

Top: (a) The potential of mean force between two methane-like molecules with different values of the $C_{\beta }\text{−}{C}_{\beta }$ LJ $\sigma$ parameter (${\epsilon }_{C_{\beta }\text{–}{C}_{\beta }}=1.0$ kJ/mol), solvated in aqueous solution, as a function of the distance between these two central atoms. (b) The normalized distribution of the distance between the $C_{\beta }$ atoms in $\alpha$-helical conformations in 9-mer ($\sigma =0.47$ nm and $\epsilon =2.0$ kJ/mol) and 12-mer ($\sigma =0.47$ nm and $\epsilon =1.0$ kJ/mol) peptides. The frames of the trajectories in an $\alpha$-helical conformation were determined by a RMSD (with respect to a perfect helix) cutoff value of 0.12 nm which corresponds to the location of the first minimum of the RMSD histogram. Bottom: Representation of an ideal $\alpha$-helical structure viewed from (c) the side, (d) C-terminal, and (e) N-terminal (c).

Figure 6

Correlation between side-chain–side-chain (SC-SC) energy and the fraction of $\alpha$-helix for 9-mer and 12-mer peptides. Lines are a guide to the eye.