Cell membranes interact via anchored receptor and ligand molecules. Central questions on cell adhesion concern the binding affinity of these membrane-anchored molecules, the mechanisms leading to the receptor–ligand domains observed during adhesion, and the role of cytoskeletal and other active processes. In this review, these questions are addressed from a theoretical perspective. We focus on models in which the membranes are described as elastic sheets, and the receptors and ligands as anchored molecules. In these models, the thermal membrane roughness on the nanometre scale leads to a cooperative binding of anchored receptor and ligand molecules, since the receptor–ligand binding smoothens out the membranes and facilitates the formation of additional bonds. Patterns of receptor domains observed in Monte Carlo simulations point towards a joint role of spontaneous and active processes in cell adhesion. The interactions mediated by the receptors and ligand molecules can be characterized by effective membrane adhesion potentials that depend on the concentrations and binding energies of the molecules.

The adhesion of cells is mediated by receptors and ligands anchored in apposing membranes. A central question is how to characterize the binding affinity of these membrane-anchored molecules. For soluble molecules, the binding affinity is typically quantified by the binding equilibrium constant K_3D in the linear relation [RL] = K_3D[R][L] between the volume concentration [RL] of bound complexes and the volume concentrations [R] and [L] of unbound molecules. For membrane-anchored molecules, it is often assumed by analogy that the area concentration of bound complexes [RL] is proportional to the product [R][L] of the area concentrations for the unbound receptor and ligand molecules. We show here (i) that this analogy is only valid for two planar membranes immobilized on rigid surfaces, and (ii) that the thermal roughness of flexible membranes leads to cooperative binding of receptors and ligands. In the case of flexible membranes, the area concentration [RL] of receptor–ligand bonds is proportional to [R]²[L]² for typical lengths and concentrations of receptors and ligands in cell adhesion zones. The cooperative binding helps to understand why different experimental methods for measuring the binding affinity of membrane-anchored molecules have led to values differing by several orders of magnitude.

The adhesion of cells is mediated by membrane receptors that bind to complementary ligands in apposing cell membranes. It is generally assumed that the lateral diffusion of mobile receptor-ligand bonds in membrane-membrane adhesion zones is slower than the diffusion of unbound receptors and ligands. We find that this slowing down is not only caused by the larger size of the bound receptor-ligand complexes, but also by thermal fluctuations of the membrane shape. We model two adhering membranes as elastic sheets pinned together by receptor-ligand bonds and study the diffusion of the bonds using Monte Carlo simulations. In our model, the fluctuations reduce the bond diffusion constant in planar membranes by a factor close to 2 in the biologically relevant regime of small bond concentrations.

A major component of ex vivo amyloid plaques of patients with dialysis-related amyloidosis (DRA) is a cleaved variant of β₂-microglobulin (ΔN6) lacking the first six N-terminal residues. Here we perform a computational study on ΔN6, which provides clues to understand the amyloidogenicity of the full-length β₂-microglobulin. Contrary to the wild-type form, ΔN6 is able to efficiently nucleate fibrillogenesis in vitro at physiological pH. This behavior is enhanced by a mild acidification of the medium such as that occurring in the synovial fluid of DRA patients. Results reported in this work, based on molecular simulations, indicate that deletion of the N-terminal hexapeptide triggers the formation of an intermediate state for folding and aggregation with an unstructured strand A and a native-like core. Strand A plays a pivotal role in aggregation by acting as a sticky hook in dimer assembly. This study further predicts that the detachment of strand A from the core is maximized at pH 6.2 resulting into higher aggregation efficiency. The structural mapping of the dimerization interface suggests that Tyr10, His13, Phe30 and His84 are hot-spot residues in ΔN6 amyloidogenesis. Dialysis-related amyloidosis (DRA) is a conformational disease that affects individuals undergoing long-term haemodialysis. In DRA the progressive accumulation of protein human β₂-microglobulin (Hβ₂m) in the osteoarticular system, followed by its assembly into amyloid fibrils, eventually leads to tissue erosion and destruction. Disclosing the aggregation mechanism of Hβ₂m under physiologically relevant conditions represents a major challenge due to the inability of the protein to efficiently nucleate fibrillogenesis in vitro at physiological pH. On the other hand, ΔN6, a truncated variant of Hβ₂m, which is also a major component of ex vivo amyloid deposits extracted from DRA patients, is able to efficiently form amyloid fibrils de novo in physiological conditions. This amyloidogenic behavior is dramatically enhanced in a slightly more acidic pH (6.2) compatible with the mild acidification that occurs in the synovial fluid of DRA patients. In this work, an innovative three-stage methodological approach, relying on an array of molecular simulations, spanning different levels of resolution is used to investigate the initial stage of the de novo aggregation mechanism of ΔN6 in a physiologically relevant pH range. We identify an intermediate state for folding and aggregation, whose potential to dimerize is enhanced at pH 6.2. Our results provide rationalizations for previous experimental observations and new insights into the molecular basis of DRA.