Ion-bridges and lipids drive aggregation of same-charge nanoparticles on lipid membranes

The control of the aggregation of biomedical nanoparticles (NP) in physiological conditions is crucial as clustering may change completely the way they interact with the biological environment. Here we show that Au nanoparticles, functionalized by an anionic, amphiphilic shell, spontaneously aggregate in fluid zwitterionic lipid bilayers. We use molecular dynamics and enhanced sampling techniques to disentangle the short-range and long-range driving forces of aggregation. At short inter-particle distances, ion-mediated, charge–charge interactions (ion bridging) stabilize the formation of large NP aggregates, as confirmed by cryo-electron microscopy. Lipid depletion and membrane curvature are the main membrane deformations driving long-range NP-NP attraction. Ion bridging, lipid depletion, and membrane curvature stem from the configurational flexibility of the nanoparticle shell. Our simulations show, more in general, that the aggregation of same-charge membrane inclusions can be expected as a result of intrinsically nanoscale effects taking place at the NP–NP and NP–bilayer soft interfaces.

snorkeled in the membrane and then multiplied it in a 9x9 grid to obtain the entire configuration.
In order to create a membrane patch with an embedded NP, we used the insane tool, 1 placing the NP at a relative distance of 0 nm (fully snorkeled) or 3 nm (semi-snorkeled) compared to the bilayer midplane. We then equilibrated the system freezing the NP core in order to let the membrane-NP system stabilize. The final box (39x39x16 nm 3 ) contained 9 NPs and 4158 DOPC lipids.
Lipid-depletion simulations. We conceived a particular setup to better analyze the lipid depletion auras around NPs and produce the maps of Figure 4. Indeed, these simulations have been performed in the NVT ensemble (after NPT equilibration) and keeping the Au cores of the NPs frozen in the XY plane to reduce the noise coming from the simulation box oscillations and the NP movements (migration/rotation) inside the membrane. The freezing in the XY plane was essential for the dimer simulations to keep the two NPs at a fixed distance. All the ligands were always free to move, and we verified that the same effect (lipid tails depletion), although appearing noisier, was present also in the absence of core freezing.
n-MUS simulations. In these cases, the starting configurations were taken from the respective system's starting configurations with standard NPs. Figure S1 -The NP-bilayer interaction evolves through 3 different metastable states, corresponding to different degrees of embedding of the NP into the membrane: a) adsorbed, b) semi-snorkeled and c) fully snorkeled. These three metastable states are long lived and can be observed experimentally, by cryo-EM. As the NP penetrates the membrane core, it induces different curvatures to the bilayer, as discussed in Lavagna et al. 2 and shown by the sketches on the right.  The data reported in Figure S4 are taken from ref. 8 We recall here the most important details of the experimental procedures.
NP synthesis. Gold nanoparticles were synthesized according to the procedure described in our previous publications 9, 10 . The size distribution of the nanoparticles was determined by transmission electron microscopy (TEM) and the ratio between MUS and OT was determined with nuclear magnetic resonance spectroscopy ( 1 H-NMR), as described in 9,10 .  The NP is represented with a sketch, the yellow circle being the core and the cyan circle the ligand shell. While the membrane bends in the presence of the NP, the deformation is under 15% of the thickness of the bilayer, hence there is no wrapping of the NP. b) NP-NP RDF from the 9 adsorbed NP unbiased simulation. The peak of NP-NP distance is the same of that from the simulations in water, as shown in Figure S1a. c) Flattening process: in the initial configuration, a cluster of 6 NP is adsorbed on the membrane, forming two layers of NPs: 4 NPs in the bottom layer, in direct contact with the membrane, 2 NPs in the top layer. After 2 µs one of the NPs from the upper layer manages to make contact with the membrane, and in this position it remains stable for the rest of the simulation (10 µs).