Lipid bilayer adhesion on sparse DNA carpets: Theoretical analysis of membrane deformations induced by single-end-grafted polymers

We consider a single-end-grafted polymer chain covered by a membrane in contact with a flat and rigid surface in the context of supported membrane adhesion on surfaces carrying dilute polymer brushes. The fluid membrane adheres to the surface due to attractive interactions; the presence of a macromolecule locally hinders the membrane-surface contact and creates a protuberant membrane bulge. We study both the size and elevation of such membrane deformations as a function of curvature modulus, surface tension, adhesion energy, and chain size. Scaling results are derived, valid for both ideal and nonideal chain statistics, leading to complex diagrams of states depending on curvature modulus, tension, and adhesion values. We also compute quantitatively the membrane deformation profile for shallow bulges and make predictions for realistic systems involving DNA grafted chains covered by lipid membranes.