  The adhesion of biological membranes is mediated by the binding of
membrane-anchored receptor and ligand proteins. Central questions are how the
binding kinetics of these proteins is affected by the membranes and by the
membrane anchoring of the proteins. In this article, we (i) present detailed
data for the binding of membrane-anchored proteins from coarse-grained
molecular dynamics simulations, and (ii) provide a theory that describes how
the binding kinetics depends on the average separation and thermal roughness of
the adhering membranes, and on the anchoring, lengths, and length variations of
the proteins. An important element of our theory is the tilt of bound
receptor-ligand complexes and transition-state complexes relative to the
membrane normals. This tilt results from an interplay of the anchoring energy
and rotational entropy of the complexes and facilitates the formation of
receptor-ligand bonds at membrane separations smaller than the preferred
separation for binding. In our simulations, we have considered both
lipid-anchored and transmembrane receptor and ligand proteins. We find that the
binding equilibrium constant and binding on-rate constant of lipid-anchored
proteins are considerably smaller than the binding constant and on-rate
constant of rigid transmembrane proteins with identical binding domains.
