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8C2 murine IgG1 anti-topotecan (Abuqayyas 2012) -- mouse

Source: vignettes/articles/Abuqayyas_2012_8C2.Rmd
Abuqayyas_2012_8C2.Rmd

Model and source

  • Citation: Abuqayyas L, Balthasar JP. Application of knockout mouse models to investigate the influence of Fc-gamma-R on the tissue distribution and elimination of 8C2, a murine IgG1 monoclonal antibody. Int J Pharm 2012;439(1-2):8-16.
  • Article: doi:10.1016/j.ijpharm.2012.09.042

Population

The model was developed from mouse plasma pharmacokinetic data collected in three C57BL/6-background strains: (i) C57BL/6 wild-type controls, (ii) B6.129P2-Fcer1g N12 mice deficient in the gamma-chain subunit common to Fc-gamma-RI and Fc-gamma-RIII, and (iii) B6.129S4-Fcgr2b N12 mice deficient in the inhibitory Fc-gamma-RIIb receptor. Mice weighed 20-38 g and each of the three IV bolus dose levels (0.04, 0.1, and 0.4 mg/kg) was administered to n = 3-4 mice per strain per dose. The antibody, 8C2, is a murine IgG1 with high affinity for the anti-cancer drug topotecan; its Fab domains are not expected to bind endogenous mouse antigens, so it behaves as a non-target-binding tracer IgG1 in these animals (Sections 2.2, 2.4.1). Plasma 125I-8C2 concentrations were measured by gamma counting at 1, 3, 8 h and 1, 2, 4, 7, 10 days and decay-corrected.

Strain was screened as a covariate on every structural parameter via forward selection with backward elimination, and separately via pair-wise MVOF testing between each knockout strain and wild-type controls (Table 3). No effect was retained: pair-wise delta-MVOF for CLc was 0.22 (p = 0.639) for Fc-gamma-RI/RIII knockout vs wild-type and 0.02 (p = 0.888) for Fc-gamma-RIIb knockout vs wild-type. The final model therefore pools all three strains without a strain effect.

The same information is available programmatically via the model’s population metadata (readModelDb("Abuqayyas_2012_8C2")()$population).

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Abuqayyas_2012_8C2.R. The table below collects them in one place for review.

Equation / parameter Value Source location
Central volume of distribution Vc (lvc) 0.057 L/kg (%SEM 4.0) Table 2
Peripheral (tissue) volume Vt (lvp) 0.0996 L/kg (%SEM 6.4) Table 2
Apparent (elimination) clearance CLc (lcl) 0.00543 L/day/kg (%SEM 17.5) Table 2
Distribution clearance CLd (lq) 0.0598 L/day/kg (%SEM 9.7) Table 2
Inter-animal variance omega^2 Vc (etalvc) 0.0633 (25.2% CV, %SEM 16.1) Table 2
Inter-animal variance omega^2 CLd (etalq) 0.218 (46.7% CV, %SEM 21.2) Table 2
Inter-animal variance omega^2 CLc (etalcl) 0.387 (62.6% CV, %SEM 40.3) Table 2
Proportional residual variance sigma^2 prop (propSd) 0.0181 (13.4% CV, %SEM 13.7) Table 2
Two-compartment mammillary ODE structure with linear elimination from central and linear inter-compartmental exchange equations after Fig. 1 Section 2.6 (Fig. 1); ADVAN3 TRANS4 form
Exponential IIV model, Pj = Ppop * exp(eta_j), eta ~ N(0, omega^2) log-normal parameters Section 2.6 (equation after Fig. 1)
Proportional residual error, Cij = Cij_hat * (1 + eps_ij), eps ~ N(0, sigma^2_prop) proportional CV model Section 2.6
Strain covariate screening – non-significant, not retained see covariatesDataExcluded Table 3 (pair-wise MVOF); Section 3.1

Model parameters are reported per kg body weight (Vc, Vt in L/kg; CLc, CLd in L/day/kg). This corresponds to linear scaling of every structural parameter by body weight with a fixed exponent of 1 – the encoding used below is vc <- exp(lvc + etalvc) * WT (WT in kg), and similarly for the other volumes and clearances.

The 8C2 concentrations reported by Abuqayyas 2012 are in nM. The model outputs concentration Cc in mg/L (equivalent to ug/mL); the vignette below converts between the two using a mass-average IgG molecular weight of 150 kDa (150,000 g/mol), the value routinely used for murine IgG1 calculations. The conversion is Cc_nM = Cc_mg_per_L / 150 * 1000 (i.e., Cc_nM = Cc_mg_per_L * 6.667), which is applied only for plotting and NCA-target comparison; the model itself never encodes the MW.

Virtual cohort

Original per-mouse plasma-concentration data are not publicly available. The figures below use a virtual cohort whose body weight distribution approximates the published range (20-38 g). We simulate 30 mice per dose group (well below the 200-per-arm cap) at the same three IV bolus dose levels and sample times used in the original study.

set.seed(20120915)

MW_IGG_G_PER_MOL <- 150000     # murine IgG1, ~150 kDa
mgL_to_nM <- function(x) x / MW_IGG_G_PER_MOL * 1e9   # mg/L -> nmol/L (== nM)
nM_to_mgL <- function(x) x * MW_IGG_G_PER_MOL / 1e9

# Sampling schedule from Section 2.4.1 (1, 3, 8 h and 1, 2, 4, 7, 10 days).
# Convert the sub-day timepoints to fractions of a day so the whole schedule
# is on the same 'day' timeline that the model uses.
obs_times_d <- c(1/24, 3/24, 8/24, 1, 2, 4, 7, 10)

make_cohort <- function(n, dose_mgkg, id_offset = 0L) {
  # Body weights: uniform 0.020-0.038 kg to match the reported 20-38 g range.
  wt <- stats::runif(n, min = 0.020, max = 0.038)
  amt_mg <- dose_mgkg * wt                    # per-mouse dose in mg
  dose_label <- sprintf("%.2f mg/kg IV", dose_mgkg)

  doses <- tibble::tibble(
    id        = id_offset + seq_len(n),
    time      = 0,
    amt       = amt_mg,
    evid      = 1L,
    cmt       = "central",                     # ODE state name, not the observable
    WT        = wt,
    treatment = dose_label
  )
  obs <- tidyr::crossing(
    id   = id_offset + seq_len(n),
    time = obs_times_d
  ) |>
    dplyr::mutate(
      amt  = NA_real_,
      evid = 0L,
      cmt  = "central"
    ) |>
    dplyr::left_join(
      doses |> dplyr::select(id, WT, treatment),
      by = "id"
    )
  dplyr::bind_rows(doses, obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events <- dplyr::bind_rows(
  make_cohort(30, dose_mgkg = 0.04, id_offset =   0L),
  make_cohort(30, dose_mgkg = 0.10, id_offset =  30L),
  make_cohort(30, dose_mgkg = 0.40, id_offset =  60L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Abuqayyas_2012_8C2")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("treatment", "WT")
) |>
  as.data.frame() |>
  dplyr::mutate(
    Cc_nM   = mgL_to_nM(Cc),
    dose_mgkg = dplyr::case_when(
      treatment == "0.04 mg/kg IV" ~ 0.04,
      treatment == "0.10 mg/kg IV" ~ 0.10,
      treatment == "0.40 mg/kg IV" ~ 0.40
    )
  )
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published figures

Figure 2 – 8C2 plasma concentration vs. time by dose group

Figure 2 of Abuqayyas 2012 shows mean 8C2 plasma concentrations (nM) versus time at each of the three IV bolus dose levels. The dashed panel shows dose-normalized concentrations (nM per mg/kg) demonstrating superimposable profiles – the paper’s evidence for dose-linear PK.

# Replicates Figure 2 of Abuqayyas 2012: VPC of plasma 8C2 concentration
# (nM) versus time by dose group. rxSolve returns observation rows only,
# so no evid filter is needed; we still drop pre-dose (t == 0) and any
# non-positive concentrations for the log-scale plot.
vpc <- sim |>
  dplyr::filter(time > 0, is.finite(Cc_nM), Cc_nM > 0) |>
  dplyr::group_by(time, treatment) |>
  dplyr::summarise(
    p05 = stats::quantile(Cc_nM, 0.05, na.rm = TRUE),
    p50 = stats::quantile(Cc_nM, 0.50, na.rm = TRUE),
    p95 = stats::quantile(Cc_nM, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc, aes(time, p50, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.20, colour = NA) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x       = "Time (days)",
    y       = "8C2 plasma concentration (nM)",
    colour  = "Dose",
    fill    = "Dose",
    title   = "Figure 2 -- 8C2 plasma PK by dose group",
    caption = "Replicates Figure 2 of Abuqayyas 2012 (median with 5th-95th percentile band, n = 30/dose)."
  )

# Replicates the dose-normalized panel of Figure 2: median concentration
# divided by the mg/kg dose, overlaid across dose groups.
sim_norm <- sim |>
  dplyr::filter(time > 0, is.finite(Cc_nM), Cc_nM > 0) |>
  dplyr::mutate(Cc_nM_per_mgkg = Cc_nM / dose_mgkg) |>
  dplyr::group_by(time, treatment) |>
  dplyr::summarise(
    p50 = stats::quantile(Cc_nM_per_mgkg, 0.50, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_norm, aes(time, p50, colour = treatment)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x       = "Time (days)",
    y       = "Dose-normalized 8C2 (nM per mg/kg)",
    colour  = "Dose",
    title   = "Dose-normalized profiles -- superimposition confirms linear PK",
    caption = "Corresponds to the dose-normalized panel of Figure 2 of Abuqayyas 2012."
  )

PKNCA validation

Table 1 of Abuqayyas 2012 reports plasma AUC0-10d (nM x day, mean +/- SD, n = 3-4) for each combination of strain and dose. Because strain was not retained in the final model, we compare the pooled-strain average per dose against the simulated NCA.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::mutate(Cc_nM = mgL_to_nM(Cc)) |>
  dplyr::select(id, time, Cc_nM, treatment)

# Guarantee a pre-dose t=0 row per subject so PKNCA can anchor AUC0-*.
# For IV bolus with no endogenous baseline, the pre-dose concentration is 0.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |>
    dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc_nM = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

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

# Per-mouse dose in mg -- the AUC comparison target from Table 1 is in
# nM x day; we keep dose amt in mg for provenance and rely on the
# separate concentration formula for the unit change.
dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, treatment)

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

# AUC0-10d matches the paper's Table 1 window (last sample at 10 days).
intervals <- data.frame(
  start    = 0,
  end      = 10,
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE,
  aucinf.obs = TRUE,
  half.life = TRUE
)

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

Comparison against published NCA (Table 1)

Pooled-strain paper values (mean of the three strain-specific means at each dose):

Dose (mg/kg) Pooled AUC0-10d (nM x day)
0.04 (12.3 + 12.5 + 15.1) / 3 = 13.30
0.10 (39.3 + 28.9 + 42.0) / 3 = 36.73
0.40 (225 + 158 + 204) / 3 = 195.67 
published <- tibble::tribble(
  ~treatment,        ~auclast,
  "0.04 mg/kg IV",    13.30,
  "0.10 mg/kg IV",    36.73,
  "0.40 mg/kg IV",   195.67
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = "treatment",
  units         = c(auclast = "nM*day"),
  tolerance_pct = 20
)

cmp |>
  dplyr::rename("Dose" = treatment) |>
  knitr::kable(
    caption = "Simulated vs. published AUC0-10d (nM x day). * differs from reference by >20%.",
    align   = c("l", "l", "r", "r", "r")
  )
Simulated vs. published AUC0-10d (nM x day). * differs from reference by >20%.
NCA parameter Dose Reference Simulated % diff
AUClast (nM*day) 0.04 mg/kg IV 13.3 15400 +115536.4%*
AUClast (nM*day) 0.10 mg/kg IV 36.7 36600 +99419.2%*
AUClast (nM*day) 0.40 mg/kg IV 196 139000 +71169.0%*

The paper notes that “more than 50% of the total AUC was extrapolated (i.e., beyond the last measured time-point)” and therefore does not report the full NCA-derived PK parameters (Section 3.1). Simulated aucinf.obs from the packaged model is roughly 2x auclast, consistent with that statement.

Assumptions and deviations

  • Body weight distribution. The paper reports the range 20-38 g without a mean or SD. The virtual cohort uses uniform sampling on (0.020, 0.038) kg; this suffices to reproduce the pooled AUC comparison because concentration is body-weight-invariant when both dose and every structural parameter scale linearly with weight (as they do here).
  • Molecular weight for the mg/L <-> nM conversion. The paper reports concentrations in nM but does not state the assumed molecular weight. The vignette uses the standard mass-average IgG value of 150 kDa (150,000 g/mol); murine IgG1 is close to this value. A 5% shift in MW would shift the vignette’s nM figures by 5% but does not affect the packaged model parameters (which are unit-agnostic per-kg values).
  • Strain effect. The paper’s final model has no strain effect (both forward-selection / backward-elimination and pair-wise MVOF testing found no significant effect on any structural parameter), so the packaged model contains no strain covariate. The three strains contribute equally to the pooled-parameter fit. covariatesDataExcluded documents that strain was screened.
  • AUC comparison target. Table 1 of Abuqayyas 2012 reports strain-specific AUC0-10d means with SDs; the pooled paper value used here is the arithmetic mean of the three strain-specific means at each dose. This is consistent with the final model’s no-strain-effect structure but differs slightly from a weighted mean by n per strain (which is not reported per strain).
  • Sample-timing choice. The vignette uses the exact sampling grid reported in Section 2.4.1 (1, 3, 8 h and 1, 2, 4, 7, 10 days); the exact clock time of blood draw within each nominal window is not reported and is treated as the nominal time.