T-cell engagers and target-mediated drug disposition

Why the sharp drop is not there, and what the published models actually estimated

Index of the TCE-TMDD project: the working specification on why target-mediated drug disposition is rarely visible in T-cell engager pharmacokinetics, a parameter survey across the published population models, and the references.

A T-cell engager (TCE) binds CD3 with nanomolar affinity, CD3 internalizes within the hour, and the priming doses are smaller than the circulating receptor pool. Textbook target-mediated drug disposition (TMDD) should follow, and the published concentration-time profiles do not show it: half-lives across the approved hematology TCEs run from 6 to 22 days, which is what an ordinary IgG does. This project works out where the TMDD went, and compiles the pharmacokinetic parameters needed to work it out.

The answer, in one table

Where each explanation stands after Section 9’s simulations

Explanation	Verdict
The priming dose never puts the concentration above the Michaelis constant, so the elbow is compressed into the first hours	✅ Holds, simulated. Odronextamab’s \(k_m\) is 1.95 mg/L and its 0.7 mg priming dose peaks at 0.14 mg/L. The apparent half-life is 0.39 d over the first day against 2.9 d from week three
The target is destroyed within a day or two, so by the therapeutic dose there is no sink left to bend the curve	✅ Holds, simulated. 80% of the antigen pool is gone one day after a saturating dose
The target is mostly peripheral, so the elbow is spread across the distribution phase instead of happening in the first hours	✅ Holds, simulated, and it decides the answer. Moving the antigen pool from central to peripheral takes the curvature ratio at a priming dose from 7.5 to 0.8, and changes nothing at a saturating dose
The CD3 arm is what makes T-cell engagers different	❌ Falsified. A B-cell depleting antibody with no CD3 arm, same target and same dose, gives a curvature ratio of 7.0 against the engager’s 7.5
The published models report a small time-dependent clearance because the clinical schedule hides a large one	❌ Falsified. A round-trip through the clinical schedule recovers 25-fold against a 40-fold truth
Slow subcutaneous absorption rate-limits the terminal slope	⚠️ Narrow. True for teclistamab early in treatment, false for elranatamab, inapplicable to the intravenous drugs

First contact with data. The structure has now been fitted to digitized observed medians for one drug. It reproduces DLBCL with a residual standard deviation of 0.22 on the log scale and fails follicular lymphoma at 0.83, needing more B cells than a person has. The target pool it implies for DLBCL runs from 3.0 to 27.8 mg depending on where the target is placed, with no change in fit, so the quantity the project has been trying to infer is not identifiable from concentrations at all. Identifying it needs a B-cell or tumor-burden time course.

How much of this is established. The arithmetic is certain and the mechanism is untested. One structure reproduces the published clearance changes across three drugs by moving a single parameter, and nothing in this project has yet met an observed concentration-time profile. Two hypotheses that looked sound before they were simulated have already been falsified. Section 5 of the model document states the confidence claim by claim; Section 6 is the digitization plan that would replace it with evidence.

The finding underneath: nothing about this is specific to T-cell engagers. The same antibody, same target, same affinity, dosed at 0.7 mg rather than 1000 mg, behaves the same way. What a T-cell engager has is a dose three orders of magnitude below a conventional antibody’s, and at that dose the target-mediated phase is over within a day at concentrations near the assay floor.

Scope. Molecules with an intact Fc domain. Blinatumomab, tebentafusp and the albumin-binding formats clear in hours on molecular size alone and are here only as a contrast.

Documents

• Working specification. The question, four explanations and a falsifier for each, the simulations that test them, and the order of work. Its In brief section is one screen and says what the rest argues. Sections 3 and 4 carry the argument; Section 7 is the back-of-envelope on how much drug the CD3 pool can consume.
• One structural model for the class. A PK-only model with no CD3 arm, target in central and tissue, quasi-steady-state binding and drug-driven target killing. Calibrated to the published clearance changes for three drugs by moving one parameter, with the identifiability problem that follows, an explicit statement of how much confidence any of it supports, and the digitization sequence that would settle it.
• One model across the class. The current state of the work. A five-state model with no CD3 arm, shared parameters fixed at biologically argued values, fitted to three drug-and-disease settings by the accessible target burden alone. Residual standard deviations of 0.26, 0.45 and 0.32 on the log scale, and target burdens ordered the way the diseases are.
• The model against digitized data. Figure 4A of the odronextamab paper digitized and fitted. DLBCL is reproduced, follicular lymphoma falsifies the structure, and the target pool turns out to be unidentifiable within a factor of nine.
• PK parameters. The reference table: structure, fixed effects, interindividual variability, residual error and covariates for eight T-cell engagers, each in the same six slots. Section 4 is the nlmixr2lib gap analysis and the note to Bill Denney.
• References. What to read and in what order, and a status marker on every source recording whether the claim drawn from it has been checked.

Code

Both documents compute their figures and tables in R chunks with freeze: auto, so a rendered page carries the output of the last run rather than a number typed into prose. The odronextamab simulations use rxode2.