The companion 3D sim tracks every CD28, CTLA-4 and B7 molecule individually as a per-molecule stochastic process. This 2D version deliberately trades that away for a completely different numerical method — the same Langmuir competitive-binding law, but integrated as coupled mean-field rate equations (well-mixed, deterministic), the way pharmacologists actually solve competitive receptor-occupancy problems in closed form:
d[CD28·B7]/dt = k_on·[CD28]_free·[B7]_free/N − k_off,CD28·[CD28·B7]
d[CTLA4·B7]/dt = k_on·[CTLA4]_free·[B7]_free/N − k_off,CTLA4·[CTLA4·B7]
[CD28]_free, [CTLA4]_free and [B7]_free are each the total pool minus whatever is currently bound — so the two receptor types are coupled only through the shared B7 pool, exactly like the 3D synapse, but every "molecule" here is really a smooth population fraction advanced with 4th-order Runge–Kutta rather than sampled bond-by-bond. The rate constants are identical to the 3D engine's own: k_on = 0.9 s⁻¹ for both receptors, k_off,CD28 = 1.1 s⁻¹, k_off,CTLA4 = 0.12 s⁻¹ — a ≈9.2× lower K_d (= k_off/k_on) for CTLA-4, so it still wins a disproportionate share of B7 purely by holding on longer, not by binding faster.
- CTLA-4 density — total inhibitory receptor pool competing for B7; CD28 is held fixed at 40 (matching the 3D engine) so only the competitor's supply changes.
- B7 ligand density — total shared ligand pool presented by the APC.
- Anti-CTLA-4 checkpoint inhibitor — removes a fraction of CTLA-4 from the competing pool entirely (sterically blocked, can't bind), shrinking both its bound population and its share of the reported inhibitory signal — watch the top strip chart bend upward and the CTLA-4 curve collapse toward zero as the slider approaches 100%.
- Reset to t=0 — restarts both differential equations from zero bound complexes so you can watch the approach to equilibrium again under the current sliders.
The strip chart never "jitters" the way the 3D per-molecule scatter does — it traces the exact deterministic trajectory the underlying rate law predicts, settling into a true steady state where both derivatives go to zero. The activation index uses the same convention as the 3D readout: 50% = CD28 and CTLA-4 signalling roughly offset; above 50% = costimulation dominates.