  The adhesion of cell membranes is mediated by the binding of
membrane-anchored receptor and ligand proteins. In this article, we review
recent results from simulations and theory that lead to novel insights on how
the binding equilibrium and kinetics of these proteins is affected by the
membranes and by the membrane anchoring and molecular properties of the
proteins. Simulations and theory both indicate that the binding equilibrium
constant K2D and the on- and off-rate constants of anchored receptors and
ligands in their 'two-dimensional' (2D) membrane environment strongly depend on
the membrane roughness from thermally excited shape fluctuations on nanoscales.
Recent theory corroborated by simulations provides a general relation between
K2D} and the binding constant K3D of soluble variants of the receptors and
ligands that lack the membrane anchors and are free to diffuse in three
dimensions (3D).
