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.
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BibTeX
@misc{battaglia2026kinetics,
title = {{Kinetics, Proofreading, and the Lifetime of Multivalent Contacts}},
author = {Giuseppe Battaglia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38394},
eprint = {2610.38394},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38394},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Kinetics, Proofreading, and the Lifetime of Multivalent Contacts
AU - Giuseppe Battaglia
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38394
UR - https://arxiv.org/abs/2610.38394
AB - 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.
ER -