Membrane-mediated interaction of intercellular cylindrical nanoparticles

Nanoparticles in intercellular gaps, junctions, or seals could have close contact with neighboring cells simultaneously. Understanding the interaction between intercellular nanoparticles and confining cell membranes is of fundamental importance, not only to the unravelling of endocytic mechanisms but also to implications such as controlled drug delivery in tumor tissues. Here we theoretically examine the mechanical behaviors of adhesive cylindrical nanoparticles confined between two lipid membrane patches of finite size. As the size of the particle-membrane contact region or wrapping degree increases, neighboring cylindrical nanoparticles become separated and the nanoparticle distance increases first and then decreases until the particles are fully trapped by adjacent membrane patches. Depending on the nanoparticle size, adhesion energy, membrane bending rigidity and tension, and intermembrane distance, three characteristic particle-membrane interaction phases are determined as no wrapping, partial trapping, and full trapping, and the corresponding interaction phase diagram is established. Further energy comparison indicates that multiple nanoparticles undergoing the two-membrane trapping process do not exhibit cooperative effects. Analytical estimations on the system energy and configurations at equilibrium are performed based on the force balance of the membranes at small deformation and match well with numerical solutions. The results shed light on the mechanical behaviors of multiple nanoparticles in cell junctions or gaps and may have implications for drug delivery in tumor tissues.