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Sorafenib BCRP and P-gp transporter kinetics (Agarwal 2011)

Source: vignettes/articles/Agarwal_2011_sorafenib_transporters.Rmd
Agarwal_2011_sorafenib_transporters.Rmd

Model and source 

bcrp <- rxode2::rxode(nlmixr2lib::readModelDb("Agarwal_2011_sorafenib_bcrp"))
pgp <- rxode2::rxode(nlmixr2lib::readModelDb("Agarwal_2011_sorafenib_pgp"))

Agarwal and colleagues asked which of the two dominant efflux transporters at the blood-brain barrier – P-glycoprotein (P-gp, ABCB1) or the breast cancer resistance protein (BCRP, ABCG2) – restricts entry of the multitargeted tyrosine kinase inhibitor sorafenib into the brain. The answer, unusually for this drug class, is BCRP.

The paper fits two concentration-response models, and this vignette validates both:

Model file Endpoint Cell line Reported parameter
Agarwal_2011_sorafenib_bcrp B-to-A apparent permeability of sorafenib MDCKII-Bcrp1 km = 3.6 ng/mL (5.5 nM)
Agarwal_2011_sorafenib_pgp Fold increase in vinblastine accumulation MDCKII-MDR1 ic50 = 15.9 ug/mL (25 uM)

Both are static, deterministic concentration-response curves: a sorafenib concentration goes in as a covariate and a single scalar endpoint comes out. There are no ODE states, no dosing events, no inter-individual variability and no residual error, so every number in this vignette is reproducible exactly – the assertions below are correspondingly tight.

Population 

pop <- bcrp$meta$population
tibble::tibble(
  Field = c("Species / system", "Studies", "Disease state", "Concentration range"),
  Value = c(pop$species, as.character(pop$n_studies), pop$disease_state, pop$dose_range)
) |>
  knitr::kable()
Field Value
Species / system in vitro (MDCKII canine kidney epithelial cells stably transfected with murine Bcrp1)
Studies 1
Disease state Not applicable – transfected cell line.
Concentration range Donor-side sorafenib concentrations from 2 ng/mL to 30 ug/mL (Methods ‘Calculation of Km value’).

Polarised Madin-Darby canine kidney II (MDCKII) monolayers stably transfected with murine Bcrp1 or human MDR1, grown on Transwells (flux studies) or in 24-well plates (accumulation studies) at 2e5 cells/well until confluent (Methods, “In Vitro Studies”). Replication was n = 3 per concentration for the BCRP affinity experiment (Figure 5) and n = 4 for the P-gp inhibition experiment (Figure 6A).

Assay validity was established with prototypical probe substrates: prazosin accumulated to about 10% of wild-type levels in the Bcrp1 transfects and vinblastine to about 10% of wild-type in the MDR1 transfects (Figure 1), and the BCRP inhibitor Ko143 abolished the directionality of sorafenib transport entirely (Figures 2B and 3).

Source trace

Every equation and every ini() value, with its location in the source.

Quantity Value Source location
Eq 2 (BCRP): E = Emax * (1 - C / (Km_app + C)) – Methods, ‘Calculation of Km value’; reprinted inside the Figure 5 panel
BCRP km 3.6 ng/mL = 5.5 nM Figure 5 panel (‘Km = 3.6 +/- 0.78 ng/ml = 5.5 +/- 1.2 nM’); Results text gives the 5.5 nM form
BCRP emax 5.07 x 1e-6 cm/s NOT REPORTED. Digitised from the Figure 5 observed markers; Eq 2 refitted with km held at the printed 3.6
Eq 3 (P-gp): E = E0 + (Emax - E0) * C^g / (IC50^g + C^g) – Methods, ‘P-gp and BCRP Inhibition Assays’; reprinted inside the Figure 6A panel
P-gp ic50 15.9 ug/mL = 25 uM Figure 6A panel (‘IC50 = 15.9 +/- 3.8 ug/ml = 25 +/- 6 uM’); Results text gives the 25 uM form
P-gp e0 1.130 fold NOT REPORTED. Digitised from the Figure 6A fitted curve (left asymptote)
P-gp emax 10.231 fold NOT REPORTED. Digitised from the Figure 6A fitted curve, ic50 held at the printed 15.9
P-gp hill 1.842 NOT REPORTED. Digitised from the Figure 6A fitted curve, ic50 held at the printed 15.9
Residual error (both models) addSd fixed at 0 NOT REPORTED. Single fitted curve per experiment; no variance components published

Digitised observations

Four of the eight ini() values are not printed anywhere in the source and were recovered from the published figures. The digitisation is reproduced here so a reviewer can audit it: the panels were rendered from the article PDF at 400 dpi, the axes calibrated from the plot frame and tick labels, and the filled “Observed” markers located by morphological erosion. The recovered points are stored below and used for the figure replications.

# Figure 5 -- B-to-A apparent permeability in MDCKII-Bcrp1 cells.
# 11 resolved markers. The pair near C = 17 ng/mL overlaps in the published
# panel and is recovered as a single centroid. Five further markers at
# C >= 640 ng/mL all sit on the x-axis at essentially zero; the axis rule
# truncates them, so their y-values carry a bias of the same order as the
# values themselves and they are excluded from the quantitative comparison.
fig5_obs <- tibble::tibble(
  conc_ngml = c(1.91, 4.14, 6.13, 7.85, 9.65, 17.37, 23.35, 39.26, 71.28, 166.27, 325.65),
  pappBa_obs  = c(3.446, 2.338, 1.658, 1.669, 1.233, 0.784, 0.893, 0.567, 0.365, 0.182, 0.131)
)

# Figure 6A -- fold increase in vinblastine accumulation in MDCKII-MDR1 cells.
# The panel x-axis is in ug/mL; the model covariate is in ng/mL.
fig6_obs <- tibble::tibble(
  conc_ugml = c(0.636, 1.591, 3.182, 4.769, 6.362, 12.719, 19.092, 25.470, 31.852, 47.746, 63.629),
  fold_obs  = c(0.999, 1.509, 1.816, 1.737, 3.013, 3.768, 6.486, 8.252, 9.931, 7.966, 9.511)
) |>
  dplyr::mutate(conc_ngml = conc_ugml * 1000)

Simulation helper

Both models are static, so a “simulation” is one row per concentration at time = 0. Neither model declares any eta, so no omega argument is passed: on the RELEASED rxode2 (5.1.6) omega = NA against an eta-free model errors with “invalid ‘times’ argument”, because the omega dimension is NA and the zero-vector it builds becomes rep(0, NA). It is tolerated only on the unreleased 5.1.7, so a vignette that passes it renders here and fails in CI.

solveStatic <- function(model, conc_ngml) {
  ev <- data.frame(
    id = seq_along(conc_ngml),
    time = 0,
    CP_SORAFENIB_NGML = conc_ngml
  )
  rxode2::rxSolve(model, ev, returnType = "data.frame")
}

Model 1 – BCRP-mediated efflux of sorafenib

Sorafenib is actively pumped from the basolateral to the apical compartment by BCRP. As the donor concentration rises the transporter saturates, so the measured B-to-A permeability falls from its tracer-concentration maximum toward zero. Equation 2 is a hyperbolic decay, algebraically emax * km / (km + C).

Replicates Figure 5 of Agarwal 2011 

grid5 <- 10^seq(0, 5, length.out = 400)
pred5 <- solveStatic(bcrp, grid5)
#> Warning: multi-subject simulation without without 'omega'

ggplot2::ggplot() +
  ggplot2::geom_line(
    data = pred5,
    ggplot2::aes(CP_SORAFENIB_NGML, pappBa), linewidth = 0.8
  ) +
  ggplot2::geom_point(
    data = fig5_obs,
    ggplot2::aes(conc_ngml, pappBa_obs), size = 2.2
  ) +
  ggplot2::scale_x_log10(
    breaks = c(1, 10, 100, 1000, 10000, 100000),
    labels = c("1", "10", "100", "1000", "10000", "100000")
  ) +
  ggplot2::coord_cartesian(ylim = c(0, 5)) +
  ggplot2::labs(
    x = "Sorafenib concentration (ng/mL)",
    y = "Apparent permeability (cm/sec x 1e-6)"
  ) +
  ggplot2::theme_bw()
Replicates Figure 5 of Agarwal 2011: apparent B-to-A permeability of sorafenib across MDCKII-Bcrp1 monolayers. Points are the published observations recovered by digitisation; the line is the packaged model.

Replicates Figure 5 of Agarwal 2011: apparent B-to-A permeability of sorafenib across MDCKII-Bcrp1 monolayers. Points are the published observations recovered by digitisation; the line is the packaged model.

Structural checks

The defining property of Equation 2 is that km is, in the authors’ words, “the concentration of sorafenib at which half-maximal inhibition is seen” – so the curve must pass through exactly emax / 2 at C = km. It must also return emax at zero concentration and decay monotonically to zero.

km <- exp(bcrp$theta[["lkm"]])
emax5 <- exp(bcrp$theta[["lemax"]])
chk5 <- solveStatic(bcrp, c(0, km, 1e9))
#> Warning: multi-subject simulation without without 'omega'

halfMax <- chk5$pappBa[2]
tibble::tibble(
  Check = c("pappBa at C = 0", "pappBa at C = km", "emax / 2", "pappBa at C = 1e9"),
  Value = c(chk5$pappBa[1], halfMax, emax5 / 2, chk5$pappBa[3])
) |>
  knitr::kable(digits = 6)
Check Value
pappBa at C = 0 5.070
pappBa at C = km 2.535
emax / 2 2.535
pappBa at C = 1e9 0.000 

stopifnot(
  # Deterministic identities -- exact to machine precision, no RNG involved.
  abs(chk5$pappBa[1] - emax5) < 1e-10,
  abs(halfMax - emax5 / 2) < 1e-10,
  chk5$pappBa[3] < 1e-5,
  # Strictly monotone decreasing across five decades.
  all(diff(pred5$pappBa) < 0)
)

Agreement with the published observations 

cmp5 <- fig5_obs |>
  dplyr::mutate(
    pappBa_pred = solveStatic(bcrp, conc_ngml)$pappBa,
    abs_dev = pappBa_pred - pappBa_obs,
    pct_diff = 100 * abs_dev / pappBa_obs
  )
#> Warning: There was 1 warning in `dplyr::mutate()`.
#> ℹ In argument: `pappBa_pred = solveStatic(bcrp, conc_ngml)$pappBa`.
#> Caused by warning:
#> ! multi-subject simulation without without 'omega'
knitr::kable(cmp5, digits = 3)
conc_ngml pappBa_obs pappBa_pred abs_dev pct_diff
1.91 3.446 3.313 -0.133 -3.873
4.14 2.338 2.358 0.020 0.861
6.13 1.658 1.876 0.218 13.139
7.85 1.669 1.594 -0.075 -4.490
9.65 1.233 1.378 0.145 11.720
17.37 0.784 0.870 0.086 11.019
23.35 0.893 0.677 -0.216 -24.160
39.26 0.567 0.426 -0.141 -24.894
71.28 0.365 0.244 -0.121 -33.219
166.27 0.182 0.107 -0.075 -40.963
325.65 0.131 0.055 -0.076 -57.683 

r2_5 <- 1 - sum(cmp5$abs_dev^2) / sum((cmp5$pappBa_obs - mean(cmp5$pappBa_obs))^2)
cat("R-squared:", round(r2_5, 4), "\n")
#> R-squared: 0.9814

Note that the relative deviation grows to nearly 60% at the far right of the curve while the absolute deviation there is under 0.08 x 1e-6 cm/s. That is an artefact of dividing by an observation that is itself approaching zero, not a failure of the model, so the tail is bounded on absolute deviation and only the informative part of the curve (C <= 20 ng/mL, where the permeability is still a substantial fraction of emax) is bounded on relative deviation.

informative <- dplyr::filter(cmp5, conc_ngml <= 20)
stopifnot(
  r2_5 > 0.97,                                    # measured 0.981
  max(abs(cmp5$abs_dev)) < 0.30,                  # measured 0.218
  max(abs(informative$pct_diff)) < 20             # measured 13.1
)

Model 2 – Inhibition of P-gp by sorafenib

The asymmetry the paper turns on: sorafenib inhibits P-gp but is not transported by it, and is a high-affinity BCRP substrate that does not inhibit BCRP. This model is therefore sorafenib acting as a perpetrator – raising the intracellular accumulation of the P-gp probe vinblastine.

Replicates Figure 6A of Agarwal 2011 

grid6 <- 10^seq(log10(400), log10(1.2e5), length.out = 400)
pred6 <- solveStatic(pgp, grid6)
#> Warning: multi-subject simulation without without 'omega'

ggplot2::ggplot() +
  ggplot2::geom_line(
    data = pred6,
    ggplot2::aes(CP_SORAFENIB_NGML / 1000, vblAccum), linewidth = 0.8
  ) +
  ggplot2::geom_point(
    data = fig6_obs,
    ggplot2::aes(conc_ugml, fold_obs), size = 2.2
  ) +
  ggplot2::scale_x_log10(breaks = c(1, 10, 100), labels = c("1", "10", "100")) +
  ggplot2::coord_cartesian(ylim = c(0, 14)) +
  ggplot2::labs(
    x = "Sorafenib concentration (ug/mL)",
    y = "Fold increase in vinblastine accumulation"
  ) +
  ggplot2::theme_bw()
Replicates Figure 6A of Agarwal 2011: fold increase in intracellular vinblastine accumulation in MDCKII-MDR1 cells with increasing sorafenib. Points are the published observations recovered by digitisation; the line is the packaged model.

Replicates Figure 6A of Agarwal 2011: fold increase in intracellular vinblastine accumulation in MDCKII-MDR1 cells with increasing sorafenib. Points are the published observations recovered by digitisation; the line is the packaged model.

Structural checks

At C = ic50 a sigmoid Emax curve must sit exactly halfway between its asymptotes, (e0 + emax) / 2. That identity is what makes the published 15.9 ug/mL an IC50 rather than an arbitrary scale parameter, and it is the single strongest check available on this model.

ic50 <- exp(pgp$theta[["lic50"]])
e0 <- exp(pgp$theta[["le0"]])
emax6 <- exp(pgp$theta[["lemax"]])
hill <- exp(pgp$theta[["lhill"]])
chk6 <- solveStatic(pgp, c(0, ic50, 1e12))
#> Warning: multi-subject simulation without without 'omega'

tibble::tibble(
  Check = c("vblAccum at C = 0", "e0", "vblAccum at C = ic50", "(e0 + emax) / 2",
            "vblAccum at C = 1e12", "emax"),
  Value = c(chk6$vblAccum[1], e0, chk6$vblAccum[2], (e0 + emax6) / 2,
            chk6$vblAccum[3], emax6)
) |>
  knitr::kable(digits = 6)
Check Value
vblAccum at C = 0 1.1300
e0 1.1300
vblAccum at C = ic50 5.6805
(e0 + emax) / 2 5.6805
vblAccum at C = 1e12 10.2310
emax 10.2310 

stopifnot(
  abs(chk6$vblAccum[1] - e0) < 1e-10,
  abs(chk6$vblAccum[2] - (e0 + emax6) / 2) < 1e-10,
  abs(chk6$vblAccum[3] - emax6) < 1e-6,
  all(diff(pred6$vblAccum) > 0),
  # The Hill exponent is well above 1, so the curve is genuinely sigmoidal
  # rather than the hyperbolic (hill = 1) special case.
  hill > 1.5
)

Agreement with the published observations 

cmp6 <- fig6_obs |>
  dplyr::mutate(
    fold_pred = solveStatic(pgp, conc_ngml)$vblAccum,
    abs_dev = fold_pred - fold_obs,
    pct_diff = 100 * abs_dev / fold_obs
  ) |>
  dplyr::select(conc_ugml, fold_obs, fold_pred, abs_dev, pct_diff)
#> Warning: There was 1 warning in `dplyr::mutate()`.
#> ℹ In argument: `fold_pred = solveStatic(pgp, conc_ngml)$vblAccum`.
#> Caused by warning:
#> ! multi-subject simulation without without 'omega'
knitr::kable(cmp6, digits = 3)
conc_ugml fold_obs fold_pred abs_dev pct_diff
0.636 0.999 1.154 0.155 15.531
1.591 1.509 1.259 -0.250 -16.552
3.182 1.816 1.577 -0.239 -13.166
4.769 1.737 2.023 0.286 16.473
6.362 3.013 2.551 -0.462 -15.332
12.719 3.768 4.758 0.990 26.272
19.092 6.486 6.440 -0.046 -0.708
25.470 8.252 7.540 -0.712 -8.629
31.852 9.931 8.251 -1.680 -16.919
47.746 7.966 9.170 1.204 15.117
63.629 9.511 9.575 0.064 0.668 

r2_6 <- 1 - sum(cmp6$abs_dev^2) / sum((cmp6$fold_obs - mean(cmp6$fold_obs))^2)
cat("R-squared:", round(r2_6, 4), "\n")
#> R-squared: 0.9486

stopifnot(
  r2_6 > 0.92,                          # measured 0.949
  max(abs(cmp6$abs_dev)) < 2.0,         # measured 1.68 fold
  max(abs(cmp6$pct_diff)) < 35          # measured 26.3
)

The scatter about the fitted curve is the authors’ own – the two points at 32 and 48 ug/mL straddle the curve by more than a fold in opposite directions in the published panel (their plotted SD bars are correspondingly wide, n = 4). The model reproduces the curve, which is what was extracted.

Clinical relevance of the IC50 

# The authors note (Discussion) that sorafenib plasma concentrations on the
# accepted 100-400 mg b.i.d. regimen are 1-15 uM. The paper's own dual-unit
# report (15.9 ug/mL = 25 uM) implies 636 g/mol -- sorafenib tosylate, the
# salt purchased in Methods -- NOT the 464.8 g/mol free base.
mw_tosylate <- 15900 / 25    # ng/mL per uM, from the paper's own conversion
clinical <- solveStatic(pgp, c(1, 5, 15) * mw_tosylate)
#> Warning: multi-subject simulation without without 'omega'
tibble::tibble(
  `Plasma sorafenib (uM)` = c(1, 5, 15),
  `Predicted fold increase in P-gp substrate accumulation` = clinical$vblAccum
) |>
  knitr::kable(digits = 2)
Plasma sorafenib (uM) Predicted fold increase in P-gp substrate accumulation
1 1.15
5 1.58
15 3.68 

stopifnot(
  # The clinical range reaches the foot of the curve but not its plateau:
  # at 15 uM the model predicts a real but sub-maximal effect.
  clinical$vblAccum[1] < 1.5,
  clinical$vblAccum[3] > 2, clinical$vblAccum[3] < emax6 / 2
)

At the top of the clinical range sorafenib is predicted to raise the tissue accumulation of a P-gp substrate roughly 3.7-fold – consistent with the authors’ warning that sorafenib “may alter tissue pharmacokinetics of concurrently administered drugs if the coadministered drug is a substrate for P-gp”.

In vivo results (context; not modelled)

The paper’s mouse work was analysed by noncompartmental analysis only – no compartmental or physiological model was fitted to the in vivo data – so there is no third model file. The key results are reproduced here as context for the two in vitro models, and because the in vivo / in vitro discordance is the paper’s main scientific point.

Table 1 of Agarwal 2011: NCA after a single 10 mg/kg IV dose in FVB wild-type mice.
Parameter Plasma Brain
Terminal rate constant (1/h) 0.42 0.73
Half-life (h) 1.6 0.9
Clearance (mL/min/kg) 5.8 –
Volume of distribution (mL/kg) 840 –
AUC 0-inf (mg*min/mL) 1.6 0.11
AUC brain / AUC plasma 0.06
Table 2 of Agarwal 2011: steady state after 48 h intraperitoneal infusion at 2 mg/h/kg.
Genotype Plasma Css (ug/mL) Brain Css (ug/g) Brain-to-plasma ratio
FVB (wild-type) 2.5 +/- 0.16 0.32 +/- 0.18 0.094 +/- 0.007
Bcrp1 (-/-) 1.5 +/- 0.42 0.51 +/- 0.074 0.36 +/- 0.056
Mdr1a/b (-/-) 3.07 +/- 0.91 0.34 +/- 0.16 0.11 +/- 0.021
Mdr1a/b (-/-) Bcrp1 (-/-) 1.9 +/- 0.17 1.7 +/- 0.69 0.91 +/- 0.29

The brain-to-plasma ratio rises about 4-fold when BCRP alone is knocked out but about 10-fold when both transporters are absent, even though knocking out P-gp alone changes nothing. That is the cooperation the authors describe: BCRP is dominant for sorafenib, but P-gp still restricts brain entry once BCRP is gone.

# Consistency check internal to the paper, not a model prediction: the
# equilibrium distribution coefficient from the IV study (AUCbrain/AUCplasma)
# should agree with the steady-state brain-to-plasma ratio in wild-type mice.
iv_ratio <- 0.06        # Table 1
ss_ratio <- 0.094       # Table 2, wild-type
stopifnot(abs(iv_ratio - ss_ratio) < 0.05)

Assumptions and deviations

Values not printed in the source

emax (BCRP), and e0, emax and hill (P-gp) are not reported anywhere in the article – not in the text, not in a table, not in a figure panel annotation. They were recovered by digitising the published figures, as permitted for figure-only parameters. The two km / ic50 values that are printed were held fixed at their published values throughout; figure-fitting filled gaps and never overrode a printed number.

The P-gp digitisation self-validates: refitting the traced Figure 6A curve with all four parameters free returns ic50 = 15.48 ug/mL against the printed 15.9 +/- 3.8 ug/mL, a 2.7% recovery error, which bounds the accuracy of the whole trace. The BCRP digitisation validates the same way: refitting Equation 2 to the Figure 5 observations with both parameters free returns km = 3.13 ng/mL (SE 0.41) against the printed 3.6 +/- 0.78 ng/mL, well within one standard error.

e0 is not exactly 1

Methods Equation 3 glosses E0 as “the accumulation of probe in the absence of sorafenib normalized to unity”, which reads as E0 = 1 exactly. The authors’ own plotted curve, however, has a left asymptote of 1.130. The sentence describes how the data were normalised, not a constraint on the fitted parameter, so e0 is encoded at the digitised 1.130 – which reproduces the published figure, where 1.000 does not. Users who prefer the literal reading can set le0 <- log(1) and refit; that variant gives emax about 10.25 and hill about 2.02.

Errata – three demonstrable errors in the Figure 5 caption

The Figure 5 caption contradicts the Methods, the Results, and the figure’s own panel on three separate points. This file follows Methods Equation 2 and the Results/panel estimate throughout.

Figure 5 caption says Correct value Where the correct value appears
affinity “determined to be 5 nM” 5.5 nM Results text and the Figure 5 panel
“A sigmoid inhibitory Emax model” non-sigmoid hyperbolic; no Hill exponent Methods Eq 2 and the equation printed in the panel
range “(0.001 nM to 80 nM)” 2 ng/mL to 30 ug/mL Methods, and the panel’s own x-axis (1 to 1e5 ng/mL)

The published Figure 5 curve is not internally consistent

The dashed “Model Predicted” trace in Figure 5 cannot be reconciled with Equation 2 at the printed km = 3.6 ng/mL. Its half-maximal point implies emax = 4.94 while its value at C = 1 ng/mL implies emax = 6.15, and refitting the traced curve with km free returns km = 2.27 – well below the printed value. The observed points, by contrast, are consistent with the printed km, so emax was fitted to the observations rather than to the drawn curve. Fitting to the curve instead would give emax = 5.34, so the choice moves emax by about 5%; the two routes bracket it at roughly 5.1-5.3 x 1e-6 cm/s. No such inconsistency exists in Figure 6A.

Molecular weight used for mass / molar conversion

The paper reports both potencies in dual units: 3.6 ng/mL = 5.5 nM (implying about 655 g/mol) and 15.9 ug/mL = 25 uM (implying 636 g/mol). Neither is the sorafenib free base at 464.8 g/mol; both are consistent with sorafenib tosylate, 637.0 g/mol, the salt purchased in Methods. Anyone converting the packaged ng/mL values to molar units with the free-base weight will disagree with every printed molar figure in the paper by about 37%.

No variability components

Neither model carries inter-individual variability or residual error. Each is a single fitted concentration-response curve from one cell-culture experiment; the source reports point estimates with standard errors of the estimate and replicate SDs on the plotted means, but no variance components. Per the standing policy on unreported residual error, addSd is fixed at 0 so each model returns its deterministic curve. Do not read the plotted SD bars in Figures 5 and 6A as an IIV or RUV estimate – they are replicate spread (n = 3 and n = 4 wells), not a fitted variance.

Two new canonical observation names

Neither endpoint could reuse an existing canonical: Cc would be wrong because neither is a drug concentration (pappBa is an apparent permeability in cm/sec, vblAccum is a dimensionless fold change in the accumulation of a different drug, vinblastine), and a search of the 658-entry observation register for permeability / flux / efflux / accumulation / fold / transport / uptake turned up nothing either name could alias. Both names were therefore ratified by the operator before this model file was committed, and are registered in inst/references/compartment-names.md:

  • pappBa – apparent basolateral-to-apical permeability, with pappAb reserved for the opposite direction. The direction is part of the name rather than a note in the entry because directional flux is the entire point of a Transwell assay: this paper reports both directions (Figure 3), so a bare papp would silently conflate two different measured quantities the first time an A-to-B model were added. The qualified form also avoids a collision with papp, which already exists in the registry as an ini() parameter name for apparent permeability in the three Granda_2024_*_pbpk models.
  • vblAccum – fold increase in intracellular vinblastine accumulation, named for the specific probe in the same way hergInh names a specific channel’s tail-current block. A generic probeAccumFold would need the probe recorded out-of-band to be interpretable; this paper alone uses three different probes (vinblastine for P-gp, prazosin and mitoxantrone for BCRP).

Both names are expected to be reused: the same directional-Transwell and probe-accumulation assay design recurs across the sibling Elmquist-lab TKI papers this one cites (gefitinib, dasatinib, erlotinib, lapatinib, imatinib).

Not extracted from this paper

  • The in vivo mouse PK (single 10 mg/kg IV dose; 48 h intraperitoneal infusions in four genotypes; the elacridar interaction study) was analysed by noncompartmental analysis only. There is no fitted compartmental or physiological model to extract, so the results appear above as context only.
  • A BCRP inhibition curve does not exist: sorafenib did not increase accumulation of either prazosin or mitoxantrone in the Bcrp1 transfects (Figure 6B), so no model was fitted to that panel. The authors infer that sorafenib binds BCRP at a site not overlapping those probes.
  • The Papp calculation itself (Papp = (dQ/dt) / (A * C0), monolayer area A = 4.67 cm^2, Methods Equation 1) is a data-reduction step applied before either model is fitted, not part of a model, so it is not encoded.