Antibody Avidity (2D): Bivalent Antigen Binding

A top-down view of a biosensor surface coated with antigen holds a population of antibodies, each rendered as a hinge with one or two Fab arms that reach out to bind neighbouring antigen sites. Every antibody follows a real continuous-time Markov process with association rate k_on[Ag] and per-arm dissociation rate k_off; once one Fab arm is bound, the second can locally re-engage a neighbouring antigen molecule at rate k_reb before the first arm lets go. Running alongside the particle population, a continuum ordinary differential equation for the same kinetics is integrated every frame with 4th-order Runge–Kutta, and both the noisy particle curve and the smooth ODE curve are plotted together so you can watch them converge on the same measured effective off-rate -- confirming the closed-form eigenvalue prediction for how avidity turns a weak per-arm bond into a functionally tight interaction.