CD28 and CTLA-4 are two receptors on a T cell that both bind the same ligand pool — B7-1/B7-2 (CD80/CD86) presented on an antigen-presenting cell (APC). CD28 delivers a "go" (costimulatory) signal; CTLA-4 delivers a "stop" (inhibitory) checkpoint signal. Each ligand-receptor pair follows standard Langmuir binding kinetics, simulated per-molecule here rather than as a mean-field average:
d[R·B7]/dt = k_on·[R]_free·[B7]_free − k_off·[R·B7]
K_d = k_off / k_on (lower K_d = higher affinity)
CTLA-4 and CD28 have similar on-rates, but CTLA-4 dissociates from B7 far more slowly (bivalent, high-avidity binding), giving it a substantially lower K_d. Over time CTLA-4 wins a disproportionate share of the shared ligand pool even though it isn't "faster" — it just doesn't let go. This simulator uses k_off(CTLA-4) ≈ k_off(CD28)/9 to reproduce that real kinetic asymmetry.
- CTLA-4 density — more inhibitory receptors on the T-cell surface competing for the same B7 pool.
- B7 ligand density — how much shared ligand the APC is presenting.
- Anti-CTLA-4 checkpoint inhibitor — an antibody (e.g. the ipilimumab class) that sterically occupies CTLA-4's binding site. Blocked receptors (grey) are removed from competition entirely, freeing B7 for CD28 and tipping the net signal toward T-cell activation — the actual mechanism by which checkpoint-inhibitor immunotherapy unleashes an anti-tumor T-cell response.
The activation index is a simplified readout of net signal balance: 50% = CD28 and CTLA-4 signaling roughly offset; above 50% = costimulation dominates.