Free energy profile of the interaction between a monomer or a dimer of protegrin-1 in a specific binding orientation and a model lipid bilayer

Abstract

The free energies of adsorption of the monomer or dimer of the cationic beta-hairpin antimicrobial peptide protegrin-1 (PG1) in a specific binding orientation on a lipid bilayer are determined using molecular dynamics (MD) simulations and Poisson-Boltzmann calculations. The bilayer is composed of anionic palmitoyl-oleoyl-phosphatidylglycerol (POPG) and palmitoyl-oleoyl-phosphatidylethanolamine (POPE) with ratio 1:3 (POPG/POPE). PG1 is believed to kill bacteria by binding on their membranes. There, it forms pores that lyse the bacteria. Herein we focus on the thermodynamics of binding. In particular, we explore the role of counterion release from the lipid bilayer upon adsorption of either the monomeric or the dimeric form of PG1. Twenty-two 4-ns-long MD trajectories of equilibrated systems are generated to determine the free energy profiles for the monomer and dimer as a function of the distance between the peptide(s) and the membrane surface. The MD simulations are conducted at 11 different separations from the membrane for each of the two systems, one with PG1, the second with a PG1 dimer of only a specific orientation of the monomer and dimer without taking into account the change of entropy for the peptide. To calculate the potential of mean force for each peptide/membrane system, a variant of constrained MD and thermodynamic integration is used. We observed that PG1 dimer binds more favorably to the POPG/POPE membrane. A simple method for relating the free energy profile to the PG1-membrane binding constant is employed to predict a free energy of adsorption of -2.4 +/- 0.8 kcal/mol. A corresponding PG1-dimer-membrane binding constant is calculated as -3.5 +/- 1.1 kcal/mol. Free energy profiles from MD simulation were extensively analyzed and compared with results of Poisson-Boltzmann theory. We find the peptide-membrane attraction to be dominated by the entropy increase due to the release of counterions in a POPG/POPE lipid bilayer.

Figure 1

(Color online) Structure of the PG1 dimer in the parallel β-sheet arrangement and in an NCCN packing mode at the membrane surface (N and C stand for the peptide’s N- and C- termini). The peptide residues Cys (i.e. 4 Cys (in yellow)) are also indicated.

Figure 2

(Color online) Schematic binding geometry of the peptide PG1 at the membrane surface, and simplified geometry for Poisson-Boltzmann (PB) analysis. The peptide configuration is defined by a center of mass z-coordinate z. There are N = N_F + N_B peptides in volume V ≃ LA = V_F +V_B, where z = l divides the free (F) and bound (B) volumes. The thickness of the lipid head group region is 2b ≈ 8 Å. The peptide PG1 can be represented by spheres with “effective” radius a ≈ 8.9 Å. The P-P distance d ≈ 36 Å is the mean distance between the headgroup phosphorus atoms in the two membrane leaflets. For the PB analysis a simplify a plane-plane geometry, representing two oppositely charged planar surfaces, with charge densities σ₊ and σ₋, separated by distance D with counterions between them is used. z^* is the running coordinate between the two surfaces for the reduced electrical potential ϕ(z^*), will be explained below in the text. The origin z = 0 (z^* = 0) is chosen at the membrane surface (average position of the upper leaflet phosphorus atoms). The lipid phosphorus atoms are shown as gold spheres. The peptide residues Arg and Cys (i.e. 6 Arg (in blue) and 4 Cys (in yellow)) are also indicated.

Figure 3

Distribution of the average number of Na⁺ counterions involved in the formation of Na⁺-lipid complexes, known as “ion bonds” in the (1:3) mixed POPG:POPE membrane, averaged over a 4 ns simulation without peptide. SSSP state is the solvent-separated solute pair state, where a water molecule is shared between counterion and any lipid head group oxygen and CSP is the contact solute pairs state. For our system we define the existence of an “ion bond” when any lipid head group oxygen is found within 3.5 Å of a Na⁺ ion (the CSP state) or within 6.0 Å of Na⁺ (the SSSP state).

Figure 4

The average number < N_B > of sodium counterions binding to the upper leaflet of the 1:3 mixture of POPG:POPE lipid bilayer averaged over a 4 ns simulation for the peptide PG1 and for the PG1 dimer. D is the separation distance between the PG1 or PG1 dimer surface and the phosphate plane of the upper leaflet of the membrane.

Figure 5

The total free energy profile (PMF) W(D) for PG1 peptide and PG1 dimer obtained from MD simulation. Each data point for W(D) represents the mean of eight 0.5 ns simulations, and the error bar represent the standard deviation obtained from the dispersion among the eight. D is the separation distance between the PG1 surface and the phosphate plane of the upper leaflet of the membrane.

Figure 6

The total free energy profile (PMF) W(D) for PG1 peptide interacting with a (1:3) POPG:POPE lipid bilayer and decomposition of W(D) into entropy −T ΔS(D) and enthalpy ΔH(D) contributions obtained from three different series of MD simulation using (5), (6) at the temperature 310 K and Δ T =15 K. For comparison purposes, the free energy profile at the temperature 325 K W(D,325K), are shown. D is the separation distance between the PG1 surface and the phosphate plane of the upper leaflet of the membrane.

Figure 7

The total free energy profile (PMF) W(D) for PG1 peptide obtained from MD simulation and the theoretical electrostatic free energy profile from Poisson-Boltzmann theory, W_pb(D), are shown. W_pb(D) is calculated numerically from PB theory using (7), (10), (11). Decomposition of W_pb(D) into entropy −T ΔS_pb(D) and enthalpy ΔH_pb(D) contributions for the 1:3 mixture of POPG:POPE lipid bilayer interacting with a charged sphere representing the PG1 peptide we obtained from three different series of numerical solutions for W_pb(z), as explained in the text.

Figure 8

The total free energy profile (PMF) W(D) for PG1 dimer obtained from MD simulation and the theoretical electrostatic free energy profile from Poisson-Boltzmann theory, W_pb(D), are shown. Each data point for W(D) represents the mean of eight 0.5 ns simulations, and the error bar represent the standard deviation obtained from the dispersion among the eight. W_pb(D) is calculated numerically from PB theory using (7), (10), (11). Decomposition of W_pb(D) into entropy −TΔS_pb(D) and enthalpy ΔH_pb(D) contributions for the 1:3 mixture of POPG:POPE lipid bilayer interacting with a charged sphere representing the PG1 dimer we obtained from three different series of numerical solutions for W_pb(z).