Abstract
We examine the adhesion of biomembranes to substrates topographically patterned with concave nanopits and identify several universal features in the adhesion process. We find three distinct states, depending on whether the membrane remains flat above the nanopit, partially enters it, or completely adheres to it, and derive analytical conditions for the stability of these states valid for a very general class of nanopit shapes. Surprisingly, completely adhered states are always (meta)stable. We also show that the presence of many nanopits can increase or decrease the effective adhesiveness of a substrate, depending on the tension of the membrane and the strength of the membrane-substrate attraction. Our results have implications regarding several experimental methods, which involve the formation of supported lipid bilayers on substrates patterned with nanopits, as well as observations of decreased spreading of cells and migration of cells toward regions of lower nanopit density on topographically patterned substrates. Furthermore, our predictions can also be directly tested in experiments exploring the adhesion of micropipette-aspirated giant vesicles to such substrates.