Target-mediated drug disposition and biologics PK

The full TMDD model

When a drug binds its target with high affinity and the target is present at a concentration comparable to the drug's, binding is not just pharmacology — it is a clearance pathway.

dL/dt  = In - kel*L - kon*L*R + koff*RL          free drug
dR/dt  = ksyn - kdeg*R - kon*L*R + koff*RL       free target
dRL/dt = kon*L*R - (koff + kint)*RL              complex

The characteristic profile has four phases: a rapid initial drop as the target is bound, a slower linear phase while the target is saturated, a steep terminal drop as drug falls below target capacity and target-mediated clearance resumes, and a final linear phase. Dose-normalised profiles that do not superimpose, with the low dose disappearing faster, is the signature.

The model is stiff by construction — kon is typically 10³ to 10⁶ times kel — which is why _models.simulate_tmdd() uses LSODA rather than a fixed-step explicit method.

Approximations, in order of increasing assumption

QSS is the usual practical choice. The full model is rarely identifiable from plasma drug concentrations alone: kon and koff appear almost exclusively as their ratio, and estimating them separately requires target or complex measurements. Pharmpy 2.1.1 exposes exactly this hierarchy — set_tmdd(model, type=...) accepts 'full', 'ib', 'cr', 'crib', 'qss', 'wagner' and 'mmapp', with dv_types to map observations to drug, total drug, target, total target, or complex.

Which quantity was measured is a first-order question. A ligand-binding assay typically reports total drug (free + complex), while the model's natural state is free drug. Fitting a total-drug observation to a free-drug prediction produces a badly wrong Kd, and nothing in the fit statistics reveals it. _models.simulate_tmdd() returns free drug, free target, complex and total drug separately for this reason.

Monoclonal antibody pharmacokinetics

Typical IgG behaviour, useful as a sanity check on any fitted mAb model:

Mechanisms that matter:

• FcRn recycling is what gives IgG its long half-life. Antibodies engineered for higher FcRn affinity at endosomal pH (YTE, LS mutations) extend half-life several-fold.
• Catabolism is nonspecific proteolysis, not renal or hepatic clearance. Renal impairment does not meaningfully change mAb clearance; molecules below ~60 kDa are a different story.
• Target-mediated clearance dominates at low doses; the drug looks nonlinear until the target is saturated.
• Subcutaneous absorption is via the lymphatics, slow and incomplete, and produces flip-flop kinetics: the apparent terminal slope after SC dosing can reflect absorption.

Allometric exponents for mAbs are often closer to 0.85-0.9 for clearance and near 1.0 for volume rather than the small-molecule 0.75.

Immunogenicity

Anti-drug antibodies increase clearance, sometimes by an order of magnitude, and typically appear after weeks. Handling in a model:

• Treat ADA status as a time-varying covariate, not a baseline one. A subject who seroconverts at week 8 has two different clearances in one profile.
• ADA-positive subjects often show a bimodal concentration distribution rather than a shifted one; a covariate on clearance may fit poorly where a mixture model fits well.
• Neutralising versus binding ADA, and titre, matter more than the binary status.
• Assay drug tolerance limits ADA detection when drug is present, so ADA-negative at trough is not the same as ADA-negative.

Antibody-drug conjugates

An ADC needs at least three analytes modelled, and they answer different questions:

• ADC (conjugated antibody) — the dosed entity
• Total antibody (conjugated + unconjugated) — the deconjugation rate is the difference
• Unconjugated payload — usually drives systemic toxicity

Drug-to-antibody ratio changes over time as the conjugate deconjugates, so "the ADC" is a distribution of species, not one molecule. Payload exposure is generally the safety-relevant metric.

Bispecifics and cell engagers

Ternary complex formation (drug + target + effector) is not captured by standard TMDD. The concentration-effect relationship is typically bell-shaped: at high concentrations the drug saturates both arms separately and forms fewer ternary complexes ("hook effect"). A monotone Emax model fitted to such data will mislead about the optimal dose in exactly the region that matters.

Practical guidance

• Do not fit a full TMDD model to plasma drug data alone. Start with QSS; move up only if target or complex measurements exist.
• Check dose-normalised profiles first. If they superimpose across the clinical dose range, TMDD is saturated throughout and a linear model is adequate for that range — but it will not extrapolate to lower doses.
• Baseline target concentration R0 = ksyn/kdeg is often measurable and should be fixed to the measurement rather than estimated.
• Report which analyte each observation is. This single piece of metadata resolves more confused biologics models than any structural change.