Mechanochemical Energy Landscapes Under Force: Catch–Slip Bonds in T-Cell Activation

Traditional theories explain T-cell activation by antigen concentration, binding affinity, and dissociation rate, but they fail to account for its extraordinary sensitivity. Recent cryo-electron microscopy and molecular-dynamics studies show that mechanical force transmitted through the T-cell receptor, the peptide–major histocompatibility complex, and the CD3 signaling module can enhance this sensitivity and thereby promote T-cell activation. We present a minimal energy-landscape model showing how force transmission reshapes the activation barrier and bond lifetime. Mathematically, we prove a sharp force cutoff F _c = D ₀ /(2 d ₀ ) (maximum binding depth D ₀ , optimal distance d ₀ ) above which no bound state exists. At or below F _c , the system admits at most two stationary points: a bound minimum and a saddle that coalesce in a fold (saddle-node) at the bond-breaking point. Stable binding occurs only on the near-separation branch d < d ₀ ln 2 (smaller receptor-ligand separation). Numerically, we tracked these stationary points as the force varied, computed the force-dependent barrier Δ V _f , and mapped bond lifetimes using Kramers/Langer theory. We found that agonists and weak agonists follow a catch–slip pattern; barriers and lifetimes peak at intermediate forces, whereas antagonists exhibit slip, with barriers and lifetimes decreasing as force increases. Our framework provides a testable mechanochemical link between force, barriers, and lifetimes in TCR signaling, as well as a path to refine predictions with targeted measurements for T-cell activation under force.