Mechanochemical energy landscapes under force support catch–slip bonds in T-cell activation

Traditional theories explain T-cell activation using antigen concentration, binding affinity and dissociation rate, but they fail to account for its extraordinary sensitivity. Recent developments in structural biology, biophysics and modelling have motivated the view that mechanical force can influence T-cell receptor–peptide–major histocompatibility complex (MHC) interactions and reshape receptor–ligand binding under load. We formulate a minimal two-dimensional TCR–pMHC mechanochemical energy-landscape model in which peptide-dependent allosteric binding geometry, hinge elasticity, receptor extension, binding-site separation and applied force jointly determine the activation barrier and bond lifetime. Mathematically, we prove a sharp model-internal force cut-off Fc=D0/(2d0)—where D0 is the maximum binding depth and d0 is the effective interaction-range parameter—above which no bound state exists. At or below this cut-off, the system admits at most two stationary points—a bound minimum and a saddle—which coalesce at the bond-breaking point. Stable binding occurs only on the near-separation branch d