Opposing effects of cationic antimicrobial peptides and divalent cations on bacterial lipopolysaccharides

The permeability of the bacterial outer membrane, enclosing Gram-negative bacteria, depends on the interactions of the outer, lipopolysaccharide (LPS) layer, with surrounding ions and molecules. We present a coarse-grained model for describing how cationic amphiphilic molecules (e.g., antimicrobial peptides) interact with and perturb the LPS layer in a biologically relevant medium, containing monovalent and divalent salt ions (e.g., ${\text{Mg}}^{\text{2+}}$). In our approach, peptide binding is driven by electrostatic and hydrophobic interactions and is assumed to expand the LPS layer, eventually priming it for disruption. Our results suggest that in parameter ranges of biological relevance (e.g., at micromolar concentrations) the antimicrobial peptide magainin 2 effectively disrupts the LPS layer, even though it has to compete with ${\text{Mg}}^{\text{2+}}$ for the layer. They also show how the integrity of LPS is restored with an increasing concentration of ${\text{Mg}}^{\text{2+}}$. Using the approach, we make a number of predictions relevant for optimizing peptide parameters against Gram-negative bacteria and for understanding bacterial strategies to develop resistance against cationic peptides.

Figure 1

Outer membrane (OM) permeability in the presence of cationic AMPs and ${\mathrm{Mg}}^{2+}$, and our modeling strategy. (a) (Upper panel) At a low surface coverage, AMP binding perturbs weakly the outer membrane. Bound peptides reside on the headgroup surface or at the headgroup-tail interface in a parallel orientation. At a sufficiently high coverage, AMPs can disrupt the OM by forming pores, for instance (see Fig. 7 in Ref. [33]). For simplicity, polysaccharides (green dashed lines) are shown for a few LPS molecules. (b) The molecular structure of LPS is shown. Each hexagon represents a sugar molecule: glucosamine in light blue (in lipid A), Kdo in yellow (in the inner core),... The illustration in (b) is adapted from Ref. [34] (see Refs. [1, 2, 3] for more details). Copyrighted by the American Physical Society. (c) This shows a surface-lattice model (i), in which LPS charges are viewed as forming discrete lattice sites, decorated with ions and peptides, as well as “lattice reconstruction” (ii). Parallel insertion of a peptide will perturb the lattice. In our approach, this is taken into account by shifting a few lattice sites; the resulting lattice reconstruction is shown [the right bottom panel labeled as (ii)]. Also shown are ion pairs between two opposite charges (e.g., ${\mathrm{Mg}}^{2+}$ and an LPS charge right below) on the top and area exclusion effects. The dashed line or a short stretch of lattices sites cannot accommodate a peptide in the same orientation. The illustrations in this figure are adapted from Ref. [19] by permission of The Royal Society of Chemistry so as to include pore formation in (a) and hydrophobic insertion, leading to lattice reconstruction in (c).

Figure 2

Theoretical scheme for calculating the lateral electrostatic free energy of the reconstructed LPS lattice decorated with ${\mathrm{Na}}^{+}, {\mathrm{Mg}}^{2+}$, and peptides. Recall that a hydrophobically bound peptide will shift $Q$ lattice sites and create $Q$ sites for its occupation. Except for this, our scheme here is essentially identical to the one used for electrostatically bound peptides [19, 20]. We first rearrange charges on the lattice into an energy-minimizing distribution in which the charges alternate in sign except on neutral ones (${\mathrm{Na}}^{+}$-paired or polycation-paired sites). We then use as a reference a “perfect” lattice shown in (i), where equal numbers of positive and negative charges are alternatively arranged. Since this does not correctly represent the initial energy-minimizing one to the left of (i), we remove some of the charges until the perfect lattice becomes the initial one and calculate the resulting free energy cost. In the limit of $N_0\to \infty$, the irregular shape of the reconstructed lattice becomes irrelevant. (This illustration is modified from Refs. [19, 20] by permission of The Royal Society of Chemistry; it is consistent with our reconstructed lattice model in Fig. 1.)

Figure 3

Competitive binding of ${\mathrm{Mg}}^{2+}$ and AMPs to LPS as well as LPS perturbation. We have chosen $\left[{\mathrm{Na}}^{+}\right]=100\mathrm{mM}$ and $Q=4$, and used a few choices of $\left[{\mathrm{Mg}}^{2+}\right]$ (left) and $\left[\mathrm{AMP}\right]$ (right) as indicated in the legend. (a) The graph shows the fractional area increase of LPS, $\mathrm{\Delta }A/A_0$, and the fractional charge occupancy of ${\mathrm{Mg}}^{2+}$ on the LPS layer, $2N_2/N_0$; for $\mathrm{\Omega }=Q=4$ as for magainin 2, $\mathrm{\Delta }A/A_0=Q{N}_p/N_0=P/L$, i.e., the fractional area increase coincides with the fractional charge occupancy of AMPs. (Left) As $\left[\mathrm{AMP}\right]$, the bulk concentration of AMPs, increases, the occupancy of AMPs on the LPS layer and $\mathrm{\Delta }A/A_0$ increase, reducing the binding of ${\mathrm{Mg}}^{2+}$. This graph suggests that LPS perturbation by AMPs is more effective for a smaller value of $\left[{\mathrm{Mg}}^{2+}\right]$. (Right) As $\left[{\mathrm{Mg}}^{2+}\right]$, the bulk concentration of ${\mathrm{Mg}}^{2+}$, increases, the occupancy of ${\mathrm{Mg}}^{2+}$ on the LPS layer increases, diminishing the binding of AMPs. This graph implies that the LPS stabilizing effects of ${\mathrm{Mg}}^{2+}$ is more pronounced for a smaller value of $\left[\mathrm{AMP}\right]$. (b) These graphs show the excess lateral pressure $\mathrm{\Delta }\mathrm{\Pi }$ of the LPS layer induced by peptide binding. Note that $1k_{\mathrm{B}}T/{\mathrm{nm}}^2\approx 4.1\mathrm{mN}/\mathrm{m}$ at $300\mathrm{K}$. (Left) The increase of $\mathrm{\Delta }\mathrm{\Pi }$ with $\left[\mathrm{AMP}\right]$ is correlated with the $\left[\mathrm{AMP}\right]$ dependence of $\mathrm{\Delta }A/A_0$ in (a). As $\left[\mathrm{AMP}\right]$ increases, more peptides will bind to LPS, increasing $\mathrm{\Delta }\mathrm{\Pi }$. (Right) This shows how $\mathrm{\Delta }\mathrm{\Pi }$ varies with $\left[{\mathrm{Mg}}^{2+}\right]$. Obviously, it decreases as $\left[{\mathrm{Mg}}^{2+}\right]$ increases. This is correlated with the enhanced binding of ${\mathrm{Mg}}^{2+}$ at higher concentrations seen in (a). The trend seen with the curves corresponding to different values of $\left[{\mathrm{Mg}}^{2+}\right]$ on the left is consistent with the ${\mathrm{Mg}}^{2+}$-dependence of the results in the graphs on the right.

Figure 4

Fractional area change, $\mathrm{\Delta }A/A_0$, and fractional charge occupancy of ${\mathrm{Mg}}^{2+}, 2N_2/N_0$ vs. $Q$ (a and c) and $a/a_0$ (b). We have chosen $H=-10k_{\mathrm{B}}T$ and $\mathrm{\Omega }=4$ in both (a) and (b); $Q=1,...,7$ in (a) and $Q=4$ in (b); in (b), the lattice constant is chosen to be $a=1,2,3,4a_0$; in (c), $Q=\mathrm{\Omega }$ and $H=-2.5Q{k}_{\mathrm{B}}T$ ($=10k_{\mathrm{B}}T$ for $\mathrm{\Omega }=4$); in all cases, $\left[{\mathrm{Na}}^{+}\right]=100\mathrm{mM}$. (a) The graph shows the results for $\mathrm{\Delta }A/A_0=\mathrm{\Omega }{N}_p/N_0$ and $2N_2/N_0$. (a) As $Q$ increases, $\mathrm{\Delta }A/A_0$ increases initially and then decreases beyond $Q=4$, for all $\left[{\mathrm{Mg}}^{2+}\right]$ values used. On the other hand, $2N_2/N_0$ decreases monotonically. The non-monotonic dependence of $\mathrm{\Omega }{N}_p/N_0$ on $Q$ can be attributed to the balance between LPS-peptide attractions and peptide-peptide repulsions on the LPS surface, both becoming stronger with increasing $Q$. (b) As the lattice dilates, both $\mathrm{\Delta }A/A_0$ and $2N_2/N_0$ decrease monotonically, as their attraction with LPS diminishes. In all the cases shown, $\mathrm{\Delta }A/A_0=P/L$ (for $\mathrm{\Omega }=Q=4$) becomes smaller than $P/L^{*}\approx 0.1$, as $a$ approaches $2a_0$. (c) The graph here shows $\mathrm{\Delta }A/A_0$ as a function of $Q$, which is chosen to coincide with $\mathrm{\Omega }$, for the two choices of $a$: $a=a_0,2a_0$. It suggests that AMPs become more potent with increasing $Q=\mathrm{\Omega }$ and $\left|H\right|$ (the magnitude of the hydrophobic free energy). For $\mathrm{\Omega }>4, \mathrm{\Omega }{N}_p/N_0>P/L$. The quantity $\mathrm{\Omega }{N}_p/N_0$ is a better measure of LPS perturbation, since it is related to the area expansion of the LPS layer induced by peptide binding. The corresponding threshold value is represented by a horizontal dashed line. For $Q\ge 6$, the curve with squares in magenta obtained for a dilated lattice, is above the threshold value (the dashed line); also included is a curve obtained for the original lattice, which is well above the dashed line. This may offer design principles for combating resistant bacteria with reduced LPS charges.

Figure 5

Fractional area change $\mathrm{\Delta }A/A_0$ obtained using the two choices of the deformation free energy: the original harmonic free energy given in Eq. (8) and the full expression in Eq. (A1) in place of the harmonic one, described by the curves in magenta (dashed) and blue (solid), respectively. We have chosen the parameters as $\left[{\mathrm{Na}}^{+}\right]=100\mathrm{mM}$ and $\left[{\mathrm{Mg}}^{2+}\right]=5\mathrm{mM}$; other parameters are the same as in Fig. 3. The difference between the two cases seems to be minor for the entire range of $\left[\mathrm{AMP}\right]$. Shown in the inset is the free energy in Eq. (A1) (in blue) and its harmonic approximation (in magenta).