CTLA-4 Checkpoint Blockade: Mean-Field Occupancy Kinetics

CD28 and CTLA-4 compete for the same pool of B7 ligand at the T-cell/APC immune synapse — the 3D companion sim shows that competition as individual molecules binding and unbinding. This version solves the identical Langmuir kinetics a different way: as two coupled ordinary differential equations, integrated in real time with 4th-order Runge–Kutta, so the receptor-occupancy curves you see are the exact deterministic solution rather than a noisy per-molecule sample. Because CTLA-4's off-rate is roughly nine times slower than CD28's even though their on-rates match, it captures a disproportionate share of B7 at equilibrium purely by refusing to let go — and dialing in an anti-CTLA-4 checkpoint inhibitor removes receptors from that competition outright, bending the whole system's steady state back toward CD28 costimulation, exactly the mechanism exploited by CTLA-4-targeted cancer immunotherapy.