Mast cells display IgE antibodies bound to high-affinity Fcε receptors (FcεRI). A single allergen molecule binding one receptor does nothing — degranulation needs a multivalent allergen to physically bridge two IgE-occupied receptors, cross-linking them:
Receptor + IgE-Ag -> mono-bound receptor (one arm free)
mono-bound + free receptor -> cross-linked pair (bridge closed)
ρ = (cross-linked pairs) / (total receptors)
P(degranulate) = ρ^n / (ρ^n + Kd^n), n = 3
Each frame the simulator rolls this Hill-function probability against the live cross-link density ρ. Once enough bridges accumulate, the threshold is crossed, calcium influx is triggered, and the granule payload — histamine, tryptase, leukotrienes — is dumped in one burst (the flash of particles), after which every receptor and antigen resets to free.
- Allergen dose — how many allergen molecules are circulating near the cell. Counter-intuitively, cranking this to maximum does not always degranulate fastest: at very high dose, most receptors get grabbed singly by different allergen molecules before either arm finds a second free receptor, so cross-linking is starved of partners — a real phenomenon called the prozone / high-dose hook effect. Watch the amber (mono-bound) population balloon while red (cross-linked) stays low at extreme dose.
- Receptor density — more FcεRI sites per cell makes finding a second partner easier at a given dose, lowering the effective threshold dose.
- Kd threshold — the cross-link density needed for a 50% chance of firing; this stands in for individual sensitivity (a highly sensitized, anaphylaxis-prone cell has a low Kd).
- Inject Allergen Pulse — simulates a sting or food exposure: a burst of allergen molecules appears near the membrane immediately.