Each antibody cycles through three states with per-arm rate constants: unbound U, singly bound S1 (one Fab arm engaged), and doubly bound S2 (both arms engaged, only possible for bivalent IgG). Antigen is fixed on the sensor surface, so a released arm sitting right next to its still-attached partner has a locally high effective concentration and can rebind before the whole molecule diffuses away:
U --kon[Ag]--> S1 S1 --koff--> U
S1 --k_reb--> S2 S2 --2·koff--> S1
During the Wash phase (kon[Ag] = 0, no re-injection), the bound population decays according to dS1/dt = -(koff+k_reb)S1 + 2koff·S2 and dS2/dt = k_reb·S1 - 2koff·S2. Diagonalizing this 2x2 system gives the slow eigenvalue that governs the long-time decay of the total bound fraction S1+S2:
k_eff = [ (3koff + k_reb) - sqrt((3koff + k_reb)^2 - 8koff^2) ] / 2
When k_reb is large compared to koff (strong avidity), k_eff collapses far below the intrinsic koff -- the antibody behaves as if it almost never lets go, even though each individual Fab-antigen bond is weak on its own. Switch off "Bivalent IgG" to simulate a monovalent Fab fragment: with no second arm to rebind, k_eff reduces exactly to koff. This is why polyclonal/IgG avidity assays report a "functional affinity" that can be orders of magnitude tighter than any single Fab's intrinsic KD, and it is the same rebinding effect SPR and BLI biosensor operators correct for when estimating a true monovalent affinity from a bivalent sensorgram.
- Inject / Wash — toggles whether free antigen is available to bind (Inject) or removed so only dissociation and rebinding continue (Wash, used to measure keff).
- Measured keff — a live least-squares fit of ln(bound fraction) vs. time over the last few seconds of Wash, i.e. the actual simulated decay rate.
- Reset — clears every antibody back to the unbound state and restarts the decay history.