Investigations of the interactions between nanoparticles and lipid bilayer may yield insight into the understanding of the protein-biomembrane interactions and the cytotoxicity of drugs. Here, we theoretically investigate the membrane-mediated interactions between two nanoparticles supported on a substrate. We examine the effects of the packing density of lipids, the direct nanoparticle-lipid interaction, and the direct substrate-lipid interaction on the effective interactions between the nanoparticles and find the effective interactions between the two nanoparticles are mainly dominated by the competition of the deformations of the different parts of the lipid bilayers as well as the stretching of the lipid chains sandwiched between the nanoparticles. By varying the above-mentioned effects, the effective interactions between the two nanoparticles can be efficiently modulated. The results may provide some theoretical insight into experiments on the membrane-mediated nanoparticle organization on a substrate and organization of the membrane proteins or drug nanoparticles on the surfaces of the cellular membranes.
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