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bilayer geometry [283, 284]. Specifically, each lipid is characterized by its cross-sectional area 𝑎𝑎_𝑖𝑖 at the polar–apolar interface, its cross-sectional area 𝑎𝑎_ℎ at the headgroup region (measured at fixed distance 𝑙𝑙_ℎ away from the polar–apolar interface), and the effective hydrocarbon chain extension 𝑏𝑏; see Figure 4.5A. The lipid free-energy model (see Methods for details) features “opposing forces” due to the presence of repulsive interactions between lipid headgroups and a chain- stretching penalty, which are both counterbalanced by a surface tension that acts at the polar– apolar interface.

For any membrane curvature, the conformation of the membrane can be energetically optimized, subject to conservation of the hydrophobic lipid volume 𝜈𝜈_𝐿𝐿. This allows calculation of the Gaussian modulus 𝜅𝜅. Note that negative 𝜅𝜅 implies a stable bilayer. When 𝜅𝜅 becomes positive, the membrane tends to spontaneously adopt saddle-like conformations that are characterized by NGC. We chose model parameters of our molecular free energy that are typical for a lipid bilayer with 20 mol% charged lipids (𝜙𝜙 = 0.2), obtaining a Gaussian modulus 𝜅𝜅 = −3.1𝑘𝑘_B𝑇𝑇 .

Inserting metaphilic peptides into the lipid bilayer with a peptide-to-lipid ratio P/L will perturb the host lipid bilayer and thus alter 𝜅𝜅. Within our mean-field framework, we account for two different types of perturbation. The first originates from insertion of the hydrophobic moieties of the peptide into the hydrocarbon core of the lipid bilayer, and the second relates to the electrostatic interactions of the charged terminal groups of the peptide side chains with the anionic lipid headgroups. Our model describes the former as an effective increase of the hydrophobic lipid volume 𝜈𝜈_𝐿𝐿→ 𝜈𝜈_𝐿𝐿+ 𝜈𝜈_𝑃𝑃𝑃𝑃 𝐿𝐿⁄ where 𝜈𝜈𝑃𝑃 is the hydrophobic volume of the peptide. The latter is quantified based on the Poisson–Boltzmann model, which describes free energies of charged surfaces in an electrolyte solution as a function of their effective surface charge density.

We used model parameters that reflect a typical experimental situation, with 𝜙𝜙 = 0.2, a hydrophobic peptide volume 𝜈𝜈_𝑃𝑃 = 10 nm3_{, and 𝑧𝑧}

𝑐𝑐 = +35 charges per peptide. Figure 4.5B shows the Gaussian modulus 𝜅𝜅 as a function of P/L from P/L = 0 to P/L = 1/175. The maximal value P/L = 𝜙𝜙 𝑧𝑧⁄ _𝑐𝑐 = 1/175 reflects electroneutrality of the membrane. Membrane destabilization is absent when the hydrophobic volume of the peptide is assumed to vanish (dash-dotted line) or when electrostatic interactions are ignored (dashed line). However, when both perturbation modes are accounted for (solid line), the Gaussian modulus adopts a positive sign.

Figure 4.5 | Membrane insertion of a metaphilic peptide results in a less negative Gaussian modulus. (A) We characterize a lipid molecule in terms of the cross-sectional area 𝑎𝑎𝑖𝑖 at the hydrocarbon chain–

headgroup interface, the cross-sectional headgroup area 𝑎𝑎ℎ (measured at a surface parallel to the

hydrocarbon chain–headgroup interface at distance 𝑙𝑙ℎ away), and the effective thickness 𝑏𝑏 of the

hydrocarbon chain region. The volume 𝜈𝜈𝐿𝐿 occupied by the lipid’s two hydrocarbon chains is conserved.

The polar headgroup is represented by a light-shaded circle. (B) The Gaussian modulus (measured in units of the thermal energy unit 𝑘𝑘B𝑇𝑇 ) as a function of the peptide-to-lipid ratio P/L. The full molecular model

(solid line) accounts for both the increase in the hydrophobic volume of the membrane core upon peptide insertion and electrostatic interactions of the anionic lipid headgroups with the cationic terminal groups of the metaphilic peptide side chains. This is contrasted with ignoring either the hydrophobic peptide volume (𝜈𝜈𝑃𝑃 = 0, dash-dotted line) or electrostatic interactions (dashed line).

Deep insertion of the peptide into the hydrocarbon core of the membrane tends to not only increase the membrane thickness, but also increase the cross-sectional area per lipid. Yet, a larger cross-sectional lipid area implies weaker mutual headgroup repulsion and an increased surface tension energy at the polar–apolar interface. Hence, we expect the membrane to seek a deformation mode that decreases 𝑎𝑎_𝑖𝑖 even if at the same time 𝑎𝑎_ℎ increases. This is accomplished by a saddle

of the metaphilic peptide side chains further lowers the headgroup repulsion strength and, therefore, even more so enhances the tendency of the membrane to minimize its free energy by adopting NGC.

In our mean-field description above, we found that their facially amphiphilic structural organization allows metaphilic peptides to penetrate deeply into the membrane and render the Gaussian modulus less negative. In addition, peptides with cationic charges also shift the Gaussian modulus to less negative values. Both of these changes in the membrane Gaussian modulus are destabilizing and promote NGC generation, which is necessary for membrane permeation. These mean-field trends are in agreement with SAXS measurements and cell uptake results. In fact, these trends are strikingly similar to those observed for AMPs [7, 116, 199, 202, 285, 286]. Here we see that these metaphilic peptides give us a valuable perspective: It is not possible to vary hydrophobicity and charge of many AMPs and CPPs over a large range due to solubility and stability issues [142, 249–252]. However, the adaptable architecture of metaphilic peptides can accommodate greater cationic charge and hydrophobicity. As a result, these are ideal systems for testing how physicochemical properties impact membrane activity, as the above comparison shows. Further details on the molecular model can be found in Methods.

4.3 Conclusions

Membrane-permeating peptides such as AMPs and CPPs are usually composed of linear sequences of amino acids and have simple architectures. By using a class of peptides with a chemically adaptive metaphilic architecture, which have quasi-liquid surfaces and highly deformable shapes, we showed that it is possible to interact with the membrane in unexpected

peptides. The root causes of this enhancement are explored using a combination of computer simulations, X-ray diffraction, and mean-field theory. Since the metaphilic architecture allows for permeation and translocation mechanisms not available for most peptides, these results here suggest that it may be possible to engineer nanoscopic molecular architectures optimized for applications such as antimicrobial agents for multidrug-resistant bacteria and drug delivery systems.

4.4 Methods