Antibody-Antigen Binding Kinetics

Binding kinetics

Association k_on 1.0e5

Dissociation k_off 1.0e-2

Antibody [Ab] 10 nM

K_d (affinity)

–

Bound now

–

Equilibrium

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τ (time constant)

–

How it works

Each of the 140 antigen dots is an independent molecule obeying the law of mass action: in every timestep it binds a free antibody with probability derived from k_on·[Ab] (pseudo-first-order, antibody held in excess) and, once bound, unbinds with probability derived from k_off. No dot "cheats" — the population-level curve you see emerges purely from these per-molecule coin-flips, exactly like a real Markov binding process.

d[AgAb]/dt = kon·[Ab]·[Ag_free] − koff·[AgAb]
Kd = koff / kon
f_eq = [Ab] / ([Ab] + Kd)
f(t) = f_eq·(1 − e^(−(kon·[Ab]+koff)·t))

k_on — association rate constant; higher means antigen gets captured faster once antibody is around.
k_off — dissociation rate constant; higher means bound complexes fall back apart faster, weakening apparent affinity.
[Ab] — antibody concentration; raising it pushes the equilibrium toward full neutralization even with modest affinity.
K_d = k_off/k_on — the dissociation constant, the single number clinicians use to compare antibody affinity: a lower Kd means a tighter-binding, more potent antibody.

Real-world relevance: this exact kon/koff/Kd framework governs how neutralizing antibodies (vaccine-elicited or therapeutic, e.g. monoclonals) clear a pathogen or toxin, and is measured directly in the lab with surface plasmon resonance (SPR) or bio-layer interferometry.

Free antigen Free antibody Bound complex