Energetic and entropic contributions to the interactions between like-charged groups in cationic peptides: A molecular dynamics simulation study

Abstract

The interaction between like-charged amino acid residues has been proposed to stabilize the folded state of peptides and proteins, and to modulate the substrate binding and the action mechanism of enzymes. We have used an alanine- and lysine-based peptide as a model system to study the interaction between like charges, and we have performed a 16-nsec molecular dynamics simulation in solution. The calculated potential of mean force for the approach of the lysine's Nzeta atoms showed a minimum at a distance of 0.7 nm, in agreement with the separation probabilities obtained from analysis of protein crystal structures. The analysis of the individual energy components showed that the solvent polarization pays for the approach of the like charges and that the van der Waals energies do not contribute significantly. The entropic contributions have been divided in conformational and desolvation terms. Both terms favor the formation of the charge pair. A 10-fold increase in counterion concentration was observed-with respect to its bulk concentration-next to the peptide charges, which helps to stabilize the peptide charges at a close distance.

Fig. 1.

Potentials of mean force for the interaction between the Nζ atoms of Lys₂ and Lys₆ of the peptide Ac-AKAAAK-NMe in α-helix conformation, corresponding to simulations in solution and in vacuum.

Fig. 2.

Distance between lysine Nζ atoms (upper panels), and the distance between Nζ atoms and Cl⁻ ions (lower panels), for two different portions of the simulation in solution. Color code for the lower panels: Nζ2–Cl⁻_a black; Nζ2–Cl⁻_b green; Nζ6–Cl⁻_a red; Nζ6–Cl⁻_b blue. (A) From 4000 to 5500 psec. (B) From 8750 to 10,000 psec.

Fig. 3.

Potential of mean force for the interaction between the Nζ atoms of Lys₂ and Lys₆ of the peptide Ac-AKAAAK-NMe in the α-helix conformation, corresponding to the portions in panels A and B shown in Figure 2 ▶.

Fig. 4.

The average electrostatic energy components of the total energy as a function of the Nζ–Nζ distance. E_culPep–Pep, E_culPep–SoL, E_culPep–Cl⁻, E_culSol–Sol, E_culSol–Cl⁻, and E_culCl⁻–Cl⁻ correspond to the electrostatic interactions within the peptide, between the peptide and the solvent, between the peptide and Cl⁻ ions, between the solvent molecules, between the solvent and the Cl⁻ ions, and between the Cl⁻ ions, respectively. The displayed values are the average energies calculated over five equally long portions of the trajectory. The error bars represent ± 1 SD from the five determinations.

Fig. 5.

The average van der Waals energy components of the total energy as a function of the Nζ–Nζ distance. E_vdwPep–Pep, E_vdwPep–Sol, correspond to the van der Waals interactions within the peptide, and between the peptide and the solvent molecules, respectively. The displayed values are the average calculated on five equally long portions of the trajectory. The error bars represent ± 1 SD from the five determinations.

Fig. 6.

The entropic contributions to the free energy along the reaction coordinate. Sconf is the conformational entropy calculated according to equation 6. Ssolv is the desolvation entropy calculated from the changes in hydrophobic-accessible surface area with equation 7. Ssol + Sconf is the sum of the conformational and desolvation terms. The results are reported as −TΔS. The values at 0.7 nm are taken as reference and the temperature is 300 K.

Fig. 7.

The three most populated conformers in solutions for the peptide Ac-AKAAAK-NMe in the α-helix conformation.

Fig. 8.

Atomic isodensity surfaces. The color code and the density values are as follows: blue for the Nζ atoms, density = 5 M; green for the Cl⁻ ions, density = 1 M; red for the water oxygens, density = 440 M; and white for water hydrogens, density = 440 M. The densities were determined by direct counting of the corresponding atoms within cubic cells of 0.05 nm per side. The bulk density of Cl⁻ ions is 0.075 M. The figure was prepared with gOpenMol (Laaksonen 1992).