Kinetics, Proofreading, and the Lifetime of Multivalent Contacts

Abstract

Selective recognition is how a cell finds the right partner in a crowd and how a drug carrier finds the right cell, so getting it wrong means a missed target or a toxic one. It must also be reversible: a cell has to hold its target tightly enough to tell it from everything else, then release it to act again, and equilibrium binding, which weighs only how favorable a contact is, cannot do both. What settles recognition is how long a contact lasts. We make lifetime the control variable, passing from a master equation through a Smoluchowski equation to the Kramers lifetime of a multivalent contact. Lifetimes are exponential in free energy, so a tenfold change in receptor number moves a contact from seconds to months, turning a smooth thermodynamic gradient into a switch. Selectivity then depends on the encounter: under flow a nanoparticle is kept only if its contact outlives the vascular dwell time, which sharpens the density threshold beyond equilibrium binding. Receptor-mediated endocytosis is itself a kinetic-proofreading cascade, so uptake inherits the Kramers exponential raised to the number of driven steps, a double amplification that vanishes without metabolism and gives a testable route to phenotype-selective delivery. The same readout, on a single bond, is how a T cell discriminates antigen, with immune memory lowering the activation threshold while leaving the specificity untouched.