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Cell membranes interact via anchored receptor and ligand molecules. Centralquestions on cell adhesion concern the binding affinity of thesemembrane-anchored molecules, the mechanisms leading to the receptor-liganddomains observed during adhesion, and the role of cytoskeletal and other activeprocesses. In this review, these questions are addressed from a theoreticalperspective. We focus on models in which the membranes are described as elasticsheets, and the receptors and ligands as anchored molecules. In these models,the thermal membrane roughness on the nanometer scale leads to a cooperativebinding of anchored receptor and ligand molecules, since the receptor-ligandbinding smoothens out the membranes and facilitates the formation of additionalbonds. Patterns of receptor domains observed in Monte Carlo simulations pointtowards a joint role of spontaneous and active processes in cell adhesion. Theinteractions mediated by the receptors and ligand molecules can becharacterized by effective membrane adhesion potentials that depend on theconcentrations and binding energies of the molecules.

Adhesion of membranes via receptor-ligand complexes: Domain formation, binding cooperativity, and active processes