Skip to contents

T-cell engager target-mediated disposition (Penney 2025)

Source: vignettes/articles/Penney_2025_tce_tmdd.Rmd
Penney_2025_tce_tmdd.Rmd

Model and source

  • Citation: Penney M, Ippolito A, Fevola E, Rata S, Brown L, Morentin Gutierrez P, Jones RDO. Predicting the Pharmacokinetics of T-Cell Engagers as a Function of Target-Mediated Drug Disposition. Clin Transl Sci. 2025;18(11):e70384. doi:10.1111/cts.70384. Structural siblings in this library: modellib(‘Betts_2019_pf_06671008_qsp’) and modellib(‘Poels_2025_elranatamab_qsp’).
  • Description: QSP. Mechanistic target-mediated drug disposition (TMDD) model predicting the pharmacokinetics of T-cell engagers (TCEs) as a function of target engagement. A two-compartment linear disposition backbone carries mass-action binding of free drug to two independent targets - the CD3 activating receptor on circulating T cells and a tumor-associated antigen (TAA) - each with its own synthesis, internalisation and drug-complex internalisation. Total elimination is the sum of an intrinsic (non-target) clearance plus the two target-mediated routes, which is what makes TCE half-lives much shorter than their IgG-like format would suggest and breaks the usual monkey-to-human allometric ranking. Trimer (CD3 + TAA simultaneous) formation is deliberately omitted by the authors. Defaults are the paper’s generic HUMAN parameterisation in the CD3-binding-only configuration (bl_taa = 0), which is the configuration the authors themselves use for TCEs with no published TAA turnover data (DLL3, GPRC5D) and for Figure 2; set bl_taa / kint_taa / kd_taa to switch the TAA arm on, and thalf_intrinsic to 9 days for the cynomolgus monkey.
  • Article: https://doi.org/10.1111/cts.70384
  • Supplement: Data S1 (CTS-18-e70384-s001.docx), Tables S1 / S2, available from the Europe PMC supplementary-files endpoint for PMC12597969.

T-cell engagers (TCEs) are built on IgG-like or albumin-binding formats that should give them half-lives of weeks, yet most clinical-stage TCEs show half-lives of a few days, and the usual “human half-life exceeds monkey half-life” ranking does not hold. Penney et al. explain both observations with target-mediated drug disposition: total elimination is the sum of an intrinsic (non-target) clearance plus target-mediated clearance through the CD3 arm and through the tumor-associated antigen (TAA) arm. Because CD3 and TAA cross-reactivity differ between cynomolgus monkey and human, the dominant elimination route can differ between species, which destroys the allometric correlation.

This vignette reproduces the paper’s generic mechanism results (Figure 2, the only fully-specified quantitative simulation in the paper) and documents two places where the source is internally inconsistent or silent.

Population

This is a prediction method, not a model fitted to a subject-level dataset, so there is no subject count, no demographic table, and no inter-individual variability. The generic disposition parameters are stated assumptions (Sections 2.3, 2.6 and 2.7): V_C = 40 mL/kg, V_P = 60 mL/kg, Q = 10 x CL, and CL set from an assumed intrinsic terminal half-life of 15 days in human patients or 9 days in the cynomolgus monkey. The CD3 system parameters are generic literature values (Section 2.3).

The method was evaluated against 29 published clinical-stage TCEs (Table 1) spanning haematological and solid-tumour indications. Prediction accuracy (Table 2) was 18/22 within two-fold for the cynomolgus monkey and 16/18 within two-fold for human patients, versus 10/17 for allometric scaling alone.

The same information is available programmatically via readModelDb("Penney_2025_tce_tmdd_qsp")()$population.

Source trace

Every ini() entry in inst/modeldb/pharmacokinetics/Penney_2025_tce_tmdd_qsp.R carries an in-file comment naming its origin. They are collected here for review.

Equation / parameter Value Source location
d/dt(central) (free drug D_Free) n/a Equation 1, Section 2.2
d/dt(target_cd3_central) (free CD3) n/a Equation 2, Section 2.2
d/dt(drug_cd3_central) (drug-CD3 dimer) n/a Equation 3, Section 2.2
d/dt(target) (free TAA) n/a Equation 4, Section 2.2
d/dt(complex) (drug-TAA dimer) n/a Equation 5, Section 2.2
d/dt(peripheral1) (peripheral drug D_P) n/a Equation 6, Section 2.2
CL = ln(2) * (V_C + V_P) / half-life derived Section 2.2
k_off = k_on * K_D (both arms) derived Section 2.3
lvc 0.040 L/kg (40 mL/kg) Sections 2.3, 2.6, 2.7
lvp 0.060 L/kg (60 mL/kg) Sections 2.3, 2.6, 2.7
thalf_intrinsic 15 day (human); 9 day (cyno) Sections 2.7 and 2.6
qclratio 10 Sections 2.3, 2.6, 2.7
kon 86.4 /nM/day (= 1e6 /M/s) Section 2.3
cd3_receptors 50000 receptors/T cell Section 2.3
tcell_blood 1500 cells/uL Section 2.3
kint_cd3 27.726 /day (= ln 2 / 36 min) Section 2.3, resolved against the Section 3.2 output (see Errata)
kd_cd3 10 nM Section 3.2 (representative “first generation” affinity)
bl_taa 0 (TAA arm disabled) Section 2.4 (per-antigen values not reported)
kint_taa, kd_taa placeholders, inert while bl_taa = 0 per-TCE K_D,TAA in Tables S1 / S2

Simulation scenarios

The model is deterministic - no eta terms and no residual error - so there is no virtual cohort and no need for zeroRe(). Each “subject” below is one scenario from Figure 2.

mod <- readModelDb("Penney_2025_tce_tmdd_qsp")

# The paper doses in mg/kg but never states a molecular weight for its generic
# TCE, so mg/kg cannot be converted exactly. Doses are therefore given in
# nmol/kg; the mg/kg equivalents shown assume a 150 kDa IgG-like TCE. The
# "MW insensitivity" section below shows this choice does not affect the
# reproduced half-lives at the 0.01 mg/kg dose of Figure 2a.
mw_ref <- 150000                       # g/mol, assumed for LABELLING only
mgkg_to_nmolkg <- function(mgkg, mw = mw_ref) mgkg * 1e-3 / mw * 1e9

obs_grid <- seq(0, 60, by = 0.05)      # days

# Solve one scenario. `cmt = "central"` is the ODE state (never the observable
# name `Cc`); rxode2 returns Cc as a column at those rows automatically.
solve_scenario <- function(label, dose_nmol_kg, ...) {
  ev <- rxode2::et(amt = dose_nmol_kg, cmt = "central")
  ev <- rxode2::et(ev, obs_grid, cmt = "central")
  out <- rxode2::rxSolve(mod, ev, c(...),
                         atol = 1e-12, rtol = 1e-10, maxsteps = 1e6)
  out <- as.data.frame(out)
  # rxSolve omits `id` for a single subject (pattern 8).
  out$id <- 1L
  out$treatment <- label
  out
}

# Terminal half-life by log-linear regression over the last quarter of the
# profile -- well clear of the distribution and TMDD transients. The paper
# computes ln(2) / (-dD_Free/dt / D_Free); on the terminal phase the two agree.
terminal_half_life <- function(df) {
  d <- df[df$time > 0 & df$Cc > 0, ]
  d <- d[d$time >= 0.75 * max(d$time), ]
  as.numeric(log(2) / -coef(stats::lm(log(Cc) ~ time, data = d))[2])
}

Replicate published figures

Figure 2a - half-life falls as CD3 affinity tightens

Figure 2a simulates a single 0.01 mg/kg IV bolus for CD3 affinities from 1000 nM down to 1 nM in half-log steps, with the TAA arm off. The paper quotes two of the resulting half-lives in Section 3.2: 15 days at K_D = 1000 nM (i.e. the intrinsic half-life, because binding is too weak to matter) and 4.4 days at K_D = 10 nM.

kd_grid <- c(1000, 316, 100, 31.6, 10, 3.16, 1)
dose_2a <- mgkg_to_nmolkg(0.01)

sim_2a <- dplyr::bind_rows(lapply(kd_grid, function(kd) {
  solve_scenario(sprintf("%g nM", kd), dose_2a, kd_cd3 = kd)
}))

th_2a <- vapply(split(sim_2a, sim_2a$treatment), terminal_half_life, numeric(1))
th_2a <- th_2a[sprintf("%g nM", kd_grid)]

sim_2a |>
  mutate(treatment = factor(treatment, levels = sprintf("%g nM", kd_grid))) |>
  filter(time > 0) |>
  ggplot(aes(time, Cc, colour = treatment)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Free TCE concentration (nM)",
       colour = expression(K[D]~"(CD3)"),
       title = "Figure 2a - CD3 affinity drives the observed half-life",
       caption = "Replicates Figure 2a of Penney 2025 (0.01 mg/kg IV bolus, TAA arm off).")

tibble::tibble(
  `K_D CD3 (nM)` = kd_grid,
  `Terminal half-life (day)` = round(as.numeric(th_2a), 2)
) |>
  knitr::kable(caption = "Terminal half-life by CD3 affinity (compare Figure 2a legend).")
Terminal half-life by CD3 affinity (compare Figure 2a legend).
K_D CD3 (nM) Terminal half-life (day)
1000.00 15.12
316.00 14.26
100.00 12.12
31.60 8.32
10.00 4.45
3.16 2.22
1.00 1.38

The two half-lives the paper states in prose are reproduced:

th_1000 <- as.numeric(th_2a["1000 nM"])
th_10 <- as.numeric(th_2a["10 nM"])
stopifnot(
  # Paper: "For a low CD3 binding affinity of 1000 nM ... the TCE displays the
  # half-life of its intrinsic PK of 15 days." Deterministic model, so this is
  # a tight bound (achieved 15.12).
  abs(th_1000 - 15) < 0.5,
  # Paper: "With an affinity of 10 nM ... the half-life is reduced to 4.4 days."
  # Achieved 4.45.
  abs(th_10 - 4.4) < 0.3,
  # Monotone: tighter CD3 binding always shortens the half-life. Deterministic,
  # so step-by-step monotonicity is a legitimate assertion here.
  all(diff(as.numeric(th_2a)) < 0)
)

Figure 2b - raising the dose saturates CD3 and restores the intrinsic half-life 

dose_mgkg <- c(0.01, 0.1, 1, 10)

sim_2b <- dplyr::bind_rows(lapply(dose_mgkg, function(d) {
  solve_scenario(sprintf("%g mg/kg", d), mgkg_to_nmolkg(d), kd_cd3 = 10)
}))

th_2b <- vapply(split(sim_2b, sim_2b$treatment), terminal_half_life, numeric(1))
th_2b <- th_2b[sprintf("%g mg/kg", dose_mgkg)]

sim_2b |>
  mutate(treatment = factor(treatment, levels = sprintf("%g mg/kg", dose_mgkg))) |>
  filter(time > 0) |>
  ggplot(aes(time, Cc, colour = treatment)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Free TCE concentration (nM)", colour = "Dose",
       title = expression("Figure 2b - dose escalation at "*K[D]*"(CD3) = 10 nM"),
       caption = "Replicates Figure 2b of Penney 2025 (TAA arm off).")

tibble::tibble(
  `Dose (mg/kg, 150 kDa)` = dose_mgkg,
  `Dose (nmol/kg)` = signif(mgkg_to_nmolkg(dose_mgkg), 3),
  `Terminal half-life (day)` = round(as.numeric(th_2b), 2)
) |>
  knitr::kable(caption = "Terminal half-life by dose (compare Figure 2b legend).")
Terminal half-life by dose (compare Figure 2b legend).
Dose (mg/kg, 150 kDa) Dose (nmol/kg) Terminal half-life (day)
0.01 0.0667 4.45
0.10 0.6670 4.45
1.00 6.6700 4.49
10.00 66.7000 9.41 

stopifnot(
  # "at doses below 0.1 mg/kg the PK is essentially linear" -- the 0.01 and
  # 0.1 mg/kg half-lives are indistinguishable.
  abs(as.numeric(th_2b["0.01 mg/kg"]) - as.numeric(th_2b["0.1 mg/kg"])) < 0.05,
  # "even 1 mg/kg showing a reduced half-life with these parameters" -- still
  # far below the 15-day intrinsic value.
  as.numeric(th_2b["1 mg/kg"]) < 7,
  # "Increasing the dose leads to the expected saturation of CD3 and a return
  # to the intrinsic half-life" -- by 10 mg/kg it has moved most of the way back.
  as.numeric(th_2b["10 mg/kg"]) > 7
)

Errata and source-resolution

The CD3 internalisation rate is printed two inconsistent ways

Section 2.3 states that “CD3 internalization rate has been measured by [35] at 1.4%/minute, equating to a half-life of about 36 min”. These two figures cannot both hold: a first-order rate of 0.014/min is a 49.5-minute exponential half-life, not 36 minutes (36 minutes is what 1.4%/min gives if depletion is read as linear, 50 / 1.4 = 35.7 min).

The paper’s own reported model output adjudicates. Only the 36-minute half-life reading reproduces the quoted 4.4-day half-life at K_D(CD3) = 10 nM; the 1.4%/min reading gives 5.4 days.

kint_36min <- log(2) / 36 * 1440      # 27.726 /day  -- the packaged default
kint_14pct <- 0.014 * 1440            # 20.160 /day

kint_cmp <- dplyr::bind_rows(lapply(
  list(c(lab = "ln(2)/36 min = 27.726 /day", k = kint_36min),
       c(lab = "1.4 %/min = 20.160 /day", k = kint_14pct)),
  function(x) {
    th <- terminal_half_life(
      solve_scenario(x[["lab"]], dose_2a, kd_cd3 = 10,
                     kint_cd3 = as.numeric(x[["k"]])))
    tibble::tibble(`Reading of the printed rate` = x[["lab"]],
                   `Predicted half-life (day)` = round(th, 2),
                   `Paper states (Section 3.2)` = 4.4)
  }))

knitr::kable(kint_cmp, caption = "Only the 36-minute reading reproduces the paper's own output.")
Only the 36-minute reading reproduces the paper’s own output.
Reading of the printed rate Predicted half-life (day) Paper states (Section 3.2)
ln(2)/36 min = 27.726 /day 4.45 4.4
1.4 %/min = 20.160 /day 5.40 4.4 

stopifnot(
  abs(kint_cmp$`Predicted half-life (day)`[1] - 4.4) < 0.3,   # 36-min reading
  kint_cmp$`Predicted half-life (day)`[2] > 5.0               # 1.4%/min reading
)

The packaged model therefore uses kint_cd3 = 27.726 /day. This is a resolution of an internal inconsistency in the source, not a tuned parameter: the value is the paper’s own stated 36-minute half-life, and it was selected by the paper’s own stated output, not by fitting anything.

No molecular weight is reported, and it does not matter here

The paper doses in mg/kg throughout but never states a molecular weight for its generic TCE, so mg/kg cannot be converted to molar exactly. At the 0.01 mg/kg dose of Figure 2a the system is in its dose-independent regime (the “fourth phase” of TMDD PK the paper cites), so the predicted half-life is identical across the whole plausible TCE size range - 50 kDa (an albumin-binding construct such as HPN328) to 150 kDa (an IgG-like construct).

mw_check <- vapply(c(50000, 150000), function(mw) {
  terminal_half_life(solve_scenario("mw", mgkg_to_nmolkg(0.01, mw), kd_cd3 = 10))
}, numeric(1))

tibble::tibble(
  `Assumed MW (kDa)` = c(50, 150),
  `0.01 mg/kg as nmol/kg` = signif(mgkg_to_nmolkg(0.01, c(50000, 150000)), 3),
  `Terminal half-life (day)` = round(mw_check, 3)
) |>
  knitr::kable(caption = "The Figure 2a anchor is insensitive to the unreported molecular weight.")
The Figure 2a anchor is insensitive to the unreported molecular weight.
Assumed MW (kDa) 0.01 mg/kg as nmol/kg Terminal half-life (day)
50 0.2000 4.453
150 0.0667 4.453 

stopifnot(abs(diff(mw_check)) < 0.01)

The Figure 2b dose escalation is MW-dependent, because it deliberately leaves the linear regime; its mg/kg labels above assume 150 kDa and should be read as illustrative.

The TAA arm ships disabled because its parameters are not reported

The Table S2 caption states plainly that “actual calibration of the TAA expression and turnover will not be shown for each TAA but a reference to the data used will be declared”. The per-antigen TAA burden (bl_taa) and turnover (kint_taa) are therefore not recoverable from any published source, and no non-zero default can be sourced. bl_taa ships at 0, which disables the arm entirely - this is the authors’ own configuration whenever TAA data are absent (Section 2.4: for DLL3 and GPRC5D “these predictions are made for CD3-binding only”) and for Figure 2. Per-TCE K_D,TAA values are published, in Tables S1 and S2.

The arm is structurally complete and switches on when the user supplies the two missing values. The illustration below uses round numbers, not paper values.

taa_off <- terminal_half_life(solve_scenario("TAA off", dose_2a, kd_cd3 = 10))
taa_on  <- terminal_half_life(
  solve_scenario("TAA on", dose_2a, kd_cd3 = 10,
                 bl_taa = 0.5, kint_taa = 5, kd_taa = 1))

tibble::tibble(
  Configuration = c("CD3 only (packaged default)",
                    "CD3 + illustrative TAA arm (bl_taa = 0.5 nM, kint_taa = 5 /day)"),
  `Terminal half-life (day)` = round(c(taa_off, taa_on), 2)
) |>
  knitr::kable(caption = "Adding a second target-mediated route shortens the half-life further.")
Adding a second target-mediated route shortens the half-life further.
Configuration Terminal half-life (day)
CD3 only (packaged default) 4.45
CD3 + illustrative TAA arm (bl_taa = 0.5 nM, kint_taa = 5 /day) 1.40 

# Mechanism check: a second elimination route can only shorten the half-life.
stopifnot(taa_on < taa_off)

PKNCA validation

PKNCA recomputes the terminal half-life independently of the log-linear fit used above, and supplies Cmax and AUC for the Figure 2a scenarios.

sim_nca <- sim_2a |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment)

# Guarantee a time = 0 row per (id, treatment). For an IV bolus into a
# concentration state the t = 0 record is already present, but the bind/distinct
# idiom is kept so the filter can never silently drop the AUC anchor.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, treatment) |> dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(treatment, id, time)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- sim_2a |>
  dplyr::distinct(id, treatment) |>
  dplyr::mutate(time = 0, amt = dose_2a)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)

intervals <- data.frame(
  start = 0, end = Inf,
  cmax = TRUE, tmax = TRUE, aucinf.obs = TRUE, half.life = TRUE
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

Comparison against the published half-lives

Penney et al. report only two numeric half-lives for the generic simulation (Section 3.2); the remaining Figure 2a values appear solely in the figure legend, which is a raster image, so they are not transcribed here.

published <- tibble::tribble(
  ~treatment,  ~half.life,
  "1000 nM",   15.0,
  "10 nM",      4.4
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by = "treatment",
  units = c(half.life = "day", cmax = "nM", tmax = "day", aucinf.obs = "nM*day"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated vs. published terminal half-life. * differs from reference by >20%."
)
Simulated vs. published terminal half-life. * differs from reference by >20%.
NCA parameter treatment Reference Simulated % diff
t½ (day) 1000 nM 15 15.1 +0.6%
t½ (day) 10 nM 4.4 4.45 +1.1%

No row is starred: both published half-lives are reproduced well inside 20%.

hl <- as.data.frame(nca_res)
hl <- hl[hl$PPTESTCD == "half.life", ]
hl_1000 <- hl$PPORRES[hl$treatment == "1000 nM"]
hl_10 <- hl$PPORRES[hl$treatment == "10 nM"]

# Guard against a lookup that silently matched nothing (pattern 10).
stopifnot(length(hl_1000) == 1L, length(hl_10) == 1L)

# PKNCA's terminal-slope selection must agree with the regression above.
stopifnot(
  abs(hl_1000 - th_1000) < 0.5,
  abs(hl_10 - th_10) < 0.5
)

Assumptions and deviations

  • kint_cd3 resolves an internal inconsistency in the source. Section 2.3 prints “1.4%/minute” and “a half-life of about 36 min”, which disagree. The packaged value 27.726 /day is ln(2) / 36 min, selected because it is the only reading that reproduces the paper’s own quoted 4.4-day output at K_D(CD3) = 10 nM (the 1.4%/min reading gives 5.4 days). See the Errata section for the demonstration. No parameter was tuned.
  • The TAA arm ships disabled (bl_taa = 0). The authors state in the Table S2 caption that the calibrated per-antigen TAA expression and turnover are not reported, so no value can be sourced. kint_taa and kd_taa are inert placeholders while bl_taa = 0, labelled as such. Per-TCE K_D,TAA values are available in Tables S1 and S2 for users switching the arm on.
  • No molecular weight is reported, so doses are in nmol/kg rather than mg/kg. The Figure 2a anchors are shown above to be insensitive to this over the 50-150 kDa range; the Figure 2b mg/kg labels assume 150 kDa and are illustrative only.
  • Trimer formation is omitted, following the authors (Section 2.2): they implemented the Jiang trimer model and found “a negligble difference to the predicted half-life”, so it was dropped. The packaged model reproduces that choice rather than reinstating it.
  • The model is body-weight normalised (volumes in L/kg, doses in nmol/kg) because the paper is. There is no WT covariate; scaling is implicit.
  • The whole model is deterministic. The source reports no residual-error model and no inter-individual variability, so propSd is fixed(0) and there are no eta terms. The supplement does describe a virtual-population sensitivity analysis (lognormal draws on intrinsic half-life, CD3 and TAA expression and both K_D values, calibrated so 95% of values fall within three-fold of the mean); that is a sensitivity exercise rather than an estimated variance model, and it depends on the unreported GUCY2C TAA parameters, so it is not reproduced here.
  • The cynomolgus-monkey configuration is the same model with thalf_intrinsic = 9 days (Section 2.6) instead of 15.
  • Per-TCE application is not reproduced. Reproducing an individual TCE from Table S1 / S2 needs that molecule’s dose and molecular weight, which the tables do not carry; only K_D values and observed / predicted half-lives are tabulated.
  • target_cd3_central is a new canonical compartment registered with this extraction (inst/references/compartment-names.md). Penney 2025 carries free CD3 as a dynamic turnover state, whereas its siblings Betts_2019_pf_06671008_qsp and Poels_2025_elranatamab_qsp derive free CD3 algebraically from a T-cell density. It is named into the existing free-target family beside target_bonemarrow rather than as a bare cd3_central, so that the free receptor pool stays distinct from the drug-bound drug_cd3_central dimer it binds to (operator decision, 2026-09-11).