Biologic drugs (monoclonal antibodies) don't cross cell membranes — they act by binding a surface receptor from outside the cell. Two coupled processes decide how much effect a dose has at any moment: how fast the drug clears from the blood, and how tightly it occupies its target once it's there.
Pharmacokinetics (1st-order elimination):
C(t) = C0 · e^(−k_el·t), k_el = ln2 / t½
Pharmacodynamics (rapid-equilibrium receptor binding):
RO(t) = C(t) / (C(t) + Kd)
C(t) is the free-drug concentration, C0 the dose you administer, and t½ the elimination half-life (typical for IgG-based biologics: 1–4 weeks, dominated by FcRn recycling). RO is the fraction of target receptors bound at any instant, assuming binding equilibrates fast relative to the drug's clearance — the standard simplifying assumption used to relate dose to target engagement for antibody therapeutics (anti-TNF agents, checkpoint inhibitors, IL-6 receptor blockers, etc.).
- Dose — sets C0, the peak free-drug concentration right after administration.
- Kd — the dissociation constant: a lower Kd means higher affinity, so the same dose occupies more receptors and occupancy stays high longer as the drug clears.
- Half-life — how fast C(t) decays; a longer half-life keeps occupancy near-saturating for more of the dosing interval, which is why antibody engineering (Fc modification) targets longer half-lives.
- Repeat dosing — re-injects C0 every 14 days; if the interval is shorter than a few half-lives, trough occupancy never falls back to zero — the basis for maintenance dosing regimens.
In the scene, green target-cell receptor dots are free; red ones are momentarily bound by an antibody. The fraction lit red at any time tracks RO(t) — free antibody molecules (small triads) drift through the tissue and visibly thin out as C(t) decays.