  The adhesion of biomembranes is mediated by the binding of membrane-anchored
receptor and ligand proteins. The proteins can only bind if the separation
between apposing membranes is sufficiently close to the length of the protein
complexes, which leads to an interplay between protein binding and membrane
shape. In this article, we review current models of biomembrane adhesion and
novel insights obtained from the models. Theory and simulations with
elastic-membrane and coarse-grained molecular models of biomembrane adhesion
indicate that the binding of proteins in membrane adhesion strongly depends on
nanoscale shape fluctuations of the apposing membranes, which results in
binding cooperativity. A length mismatch between protein complexes leads to
repulsive interactions that are caused by membrane bending and act as a driving
force for the length-based segregation of proteins during membrane adhesion.
