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Maraviroc in vitro CYP3A4 N-dealkylation kinetics (Hyland 2008)

Source: vignettes/articles/Hyland_2008_maraviroc_invitro.Rmd
Hyland_2008_maraviroc_invitro.Rmd

Model and source

  • Citation: Hyland R, Dickins M, Collins C, Jones H, Jones B. Maraviroc: in vitro assessment of drug-drug interaction potential. Br J Clin Pharmacol. 2008 Oct;66(4):498-507. doi:10.1111/j.1365-2125.2008.03198.x. PMID: 18492127. PMCID: PMC2561101. Michaelis-Menten equation with the impurity term and the Km / Vmax estimates: Results, ‘Kinetics of maraviroc N-dealkylation in human liver microsomes’, and Figure 2. Substrate-depletion intrinsic clearance, microsomal CYP content and fraction unbound in microsomes: Results, ‘CLint estimates from HLM and rCYP’. Incubation design and bioanalytical precision: Materials and methods, ‘Assays for maraviroc metabolism’. The statement that UK-408,027 formation is approximately 20% of the depletion intrinsic clearance is in the Discussion, second paragraph.
  • Article: https://doi.org/10.1111/j.1365-2125.2008.03198.x
  • PubMed Central open-access copy: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2561101/

This paper contributes two model files, one per in vitro system in which the authors characterised the same reaction:

mod_hlm <- rxode2::rxode(readModelDb("Hyland_2008_maraviroc_hlm"))
mod_rec <- rxode2::rxode(readModelDb("Hyland_2008_maraviroc_rcyp3a4"))

# Fixed and estimated ini() values are not returned as columns by rxSolve(), so
# read them straight off the packaged model when a check needs one.
ini_val <- function(mod, nm) {
  stopifnot(nm %in% mod$iniDf$name)
  mod$iniDf$est[mod$iniDf$name == nm]
}

cat(mod_hlm$description)
#> In vitro (pooled human liver microsomes, 60 donors). Michaelis-Menten enzyme-kinetic model of the CYP3A4-mediated N-dealkylation of maraviroc to its secondary-amine metabolite UK-408,027, plus the parallel oxidative routes that make up the remainder of maraviroc's microsomal intrinsic clearance. The published fit is a standard Michaelis-Menten velocity with an additive impurity term, v = Vmax * [S] / (Km + [S]) + C * [S], where C absorbs a concentration-dependent UK-408,027 contaminant present in the maraviroc substrate; the authors report that fitting impurity-corrected data to a plain Michaelis-Menten equation gave similar Km and Vmax, and C itself is not published, so it is carried here fixed at zero. The UK-408,027 route accounts for Vmax/Km = 0.0214 uL/min/pmol CYP, which is 20% of the 0.106 uL/min/pmol total depletion intrinsic clearance measured by substrate loss; the balance is assigned to the other CYP3A4-mediated oxidative pathways as a first-order route, because substrate depletion was measured only at 1 uM, far below Km, and so characterises a linear clearance. Sibling model: Hyland_2008_maraviroc_rcyp3a4, the same reaction characterised in recombinant CYP3A4 Supersomes.
cat(mod_rec$description)
#> In vitro (recombinant human CYP3A4 Supersomes). Michaelis-Menten enzyme-kinetic model of the CYP3A4-mediated N-dealkylation of maraviroc to its secondary-amine metabolite UK-408,027 in heterologously expressed CYP3A4, plus the parallel CYP3A4-mediated oxidative routes that make up the remainder of maraviroc's intrinsic clearance in the same system. The UK-408,027 route accounts for Vmax/Km = 0.23 uL/min/pmol CYP3A4 of the 1.7 uL/min/pmol CYP3A4 total depletion intrinsic clearance; the balance is assigned to the other oxidative pathways as a first-order route, because substrate depletion was measured only at 1 uM, far below Km, and so characterises a linear clearance. The model also carries the intersystem extrapolation factor of 0.2 with which the paper scales the recombinant intrinsic clearance to a human liver microsome basis, reproducing the 0.34 uL/min/pmol and 40.8 uL/min/mg values that were the CLint input to the maraviroc Simcyp model. No impurity term is carried, because in the recombinant system the substrate contaminant was subtracted by comparison against control Supersomes rather than fitted. Sibling model: Hyland_2008_maraviroc_hlm, the same reaction characterised in pooled human liver microsomes.

Scope: what this paper does and does not contribute

Hyland 2008 has two halves.

The first half is an in vitro reaction-phenotyping and enzyme-kinetics study of maraviroc N-dealkylation to its secondary-amine metabolite UK-408,027, the most abundant circulating metabolite in humans. Chemical inhibition and a recombinant-CYP panel localise the reaction to CYP3A4, and Michaelis-Menten kinetics are characterised in two systems: a 60-donor human liver microsome pool and recombinant CYP3A4 Supersomes. Every constant of that layer is printed – the fitted equation, Km, Vmax, the substrate-depletion intrinsic clearance, the microsomal CYP content, the intersystem extrapolation factor and the fraction unbound in microsomes. That is the layer this vignette validates and that the two model files carry.

The second half uses those in vitro data as inputs to a whole-body Simcyp physiologically based model (version 7.01) to predict drug-drug interactions with ketoconazole, ritonavir, saquinavir and atazanavir. That layer is not extracted. The paper prints the compound-level Simcyp inputs (Table 1) but none of the platform physiology the model consumes: no tissue volumes, no organ blood flows, no microsomal protein per gram of liver, no liver weight and no hepatic CYP3A4 abundance, so the printed CLint never becomes an L/h clearance. Tissue-to-plasma partition coefficients were estimated with the Poulin tissue-composition equations, which is a named method rather than a set of values; the required LogD input is not printed either. The Simcyp predictions in Table 3 are therefore recorded here as published results, not reproduced.

In vitro systems 

pop_hlm <- readModelDb("Hyland_2008_maraviroc_hlm")()$population
pop_rec <- readModelDb("Hyland_2008_maraviroc_rcyp3a4")()$population

tibble::tibble(
  Field = c("species", "system", "kinetic incubation", "depletion incubation",
            "concentration range", "replication"),
  `Human liver microsomes` = c(pop_hlm$species, pop_hlm$system,
                               pop_hlm$kinetic_incubation, pop_hlm$depletion_incubation,
                               pop_hlm$concentration_range, pop_hlm$replication),
  `Recombinant CYP3A4` = c(pop_rec$species, pop_rec$system,
                           pop_rec$kinetic_incubation, pop_rec$depletion_incubation,
                           pop_rec$concentration_range, pop_rec$replication)
) |>
  knitr::kable()
Field Human liver microsomes Recombinant CYP3A4
species in vitro (pooled human liver microsomes, 60 donors) in vitro (recombinant human CYP3A4 Supersomes)
system Human liver microsomes prepared from a pool of 60 donors (BD Biosciences), incubated in 50 mM phosphate buffer pH 7.4 with 1 mM MgCl2 and an NADPH-regenerating isocitric acid / isocitric acid dehydrogenase system; final incubation volume 100 uL Supersomes (BD Biosciences) expressing recombinant human CYP3A4, incubated in 50 mM phosphate buffer pH 7.4 with 1 mM MgCl2 and an NADPH-regenerating isocitric acid / isocitric acid dehydrogenase system; final incubation volume 100 uL
kinetic incubation 0.1 mg/mL microsomal protein for 15 min, within the ranges over which UK-408,027 formation was linear with time (up to 20 min) and with protein (up to 0.5 mg/mL) 10 pmol CYP3A4/mL for 15 min, within the ranges over which UK-408,027 formation was linear with time (up to 20 min) and with CYP content (up to 50 pmol/mL)
depletion incubation 1 uM maraviroc at 0.5 uM total CYP for up to 60 min; the first-order rate constant was taken as the gradient of ln(maraviroc / midazolam peak-area ratio) against incubation time 1 uM maraviroc at 100 pmol recombinant CYP for up to 60 min; rates more stable than the 0.06 uL/pmol/min assay cut-off were reported as below that limit
concentration range 1 to 1000 uM maraviroc for the kinetic characterisation; 1 uM for substrate depletion and 50 uM for metabolite formation in the chemical-inhibition experiments 1 to 1000 uM maraviroc for the kinetic characterisation; 1 uM for substrate depletion and 50 uM for metabolite formation in the CYP-panel experiments
replication Km and Vmax are the mean of seven determinations (Figure 2); the chemical-inhibition results are the mean of quadruplicate determinations (Table 2) Km and Vmax are the mean of four determinations (Figure 4); the recombinant CYP panel results are the mean of quadruplicate determinations (Figure 3)

Both systems were incubated at 37 C in 50 mM phosphate buffer pH 7.4 with 1 mM MgCl2, with reducing equivalents supplied by NADPH regenerated in situ by an isocitric acid / isocitric acid dehydrogenase system, in a final volume of 100 uL. The microsomal pool was prepared from 60 donors. There is no patient population and no dosing: the “dose” of each model is the maraviroc concentration spiked into the incubation at time zero.

Source trace

Every ini() entry carries an in-file comment naming its source location. The table below collects them.

Model Equation / parameter Value Source location
both v = Vmax * [S] / (Km + [S]) + C * [S] n/a Results, “Kinetics of maraviroc N-dealkylation in human liver microsomes” (display equation)
HLM km_cyp3a4 21 uM Results, same section; Abstract; Figure 2
HLM vmax_cyp3a4 0.45 pmol/pmol total CYP/min Results, same section; Abstract; Figure 2
HLM c_impurity not published, carried at 0 Results, same section (named in the equation only)
HLM clint 0.106 uL/min/pmol total CYP Results, “CLint estimates from HLM and rCYP”; Table 2 footnote
HLM cyp_total 330 pmol/mg protein Results, “CLint estimates from HLM and rCYP”
HLM fumic 0.72 at 1.5 mg/mL Results, “CLint estimates from HLM and rCYP”
HLM prot_inc 0.1 mg/mL Results, “Kinetics of maraviroc N-dealkylation in human liver microsomes”
rCYP3A4 km_cyp3a4 13 uM Results, “Kinetics of maraviroc N-dealkylation by rCYP3A4”; Abstract; Figure 4
rCYP3A4 vmax_cyp3a4 3 pmol/pmol CYP3A4/min Results, same section; Abstract; Figure 4
rCYP3A4 clint 1.7 uL/min/pmol CYP3A4 Results, “CLint estimates from HLM and rCYP”; Figure 3; Table 1
rCYP3A4 isef 0.2 Results, “CLint estimates from HLM and rCYP” (from Proctor 2004, reference 13)
rCYP3A4 cyp3a4_content 120 pmol/mg protein Results, “CLint estimates from HLM and rCYP”
rCYP3A4 fumic 0.86 at 0.63 mg/mL Results, “CLint estimates from HLM and rCYP”; Table 1
rCYP3A4 cyp_inc 10 pmol/mL Results, “Kinetics of maraviroc N-dealkylation by rCYP3A4”
both propSd 0.051 Materials and methods, “Metabolite formation assay” (assay CV at the 50 ng standard)
both clint_other = clint - Vmax/Km derived Discussion, second paragraph (“approximately 20% of maraviroc intrinsic clearance”)

Dimensional analysis

The two systems report Vmax and CLint on a per-pmol-CYP basis while the states hold uM concentrations, so each ODE term needs one explicit conversion.

Term Symbol units Product Required
cyp_inc (HLM) prot_inc mg/mL x cyp_total pmol/mg pmol CYP/mL pmol CYP/mL
rate_uk408027 pmol/(pmol CYP min) x pmol CYP/mL pmol/(mL min) = nmol/(L min) uM/min, hence /1000
clint_uk408027 = vmax/km (pmol/(pmol CYP min)) / (pmol/uL) uL/(min pmol CYP) uL/(min pmol CYP)
rate_other uL/(min pmol CYP) x uM x pmol CYP/mL uL/(mL min) x uM uM/min, hence /1000
clint_mg uL/(min pmol CYP) x pmol CYP/mg uL/(min mg) uL/(min mg)
clint_u_mg uL/(min mg) / unitless uL/(min mg) uL/(min mg)

Note that 1 pmol/mL is 1 nmol/L, which is 0.001 uM: that is the entire content of the two /1000 factors, and getting it wrong would misstate every rate by three orders of magnitude.

Non-applicability of NCA: these are static enzyme incubations with no dose, no absorption and no distribution phase, so there is no exposure metric for PKNCA to integrate. Following the mechanistic-model validation pattern, the checks below are instead structural identities, flux checks and figure replication.

Simulation grid

Both models are deterministic – the paper reports no between-experiment random effects – so the simulations below are single-replicate solves over a grid of starting maraviroc concentrations spanning the 1 to 1000 uM range the kinetic experiments used.

# 41 log-spaced substrate concentrations across the experimental range, well
# under the 200-per-arm cohort cap (these are concentrations, not subjects).
s_grid <- exp(seq(log(1), log(1000), length.out = 41))

solve_grid <- function(mod, s0, times = seq(0, 15, by = 0.5)) {
  ev <- rxode2::et(times)
  out <- lapply(seq_along(s0), function(i) {
    r <- rxode2::rxSolve(mod, ev, inits = c(maraviroc = s0[i]),
                         returnType = "data.frame")
    r$s0 <- s0[i]
    r
  })
  dplyr::bind_rows(out)
}

sim_hlm <- solve_grid(mod_hlm, s_grid)
sim_rec <- solve_grid(mod_rec, s_grid)

# Initial velocities: the quantity Figures 2 and 4 plot against [S].
v0 <- dplyr::bind_rows(
  dplyr::filter(sim_hlm, time == 0) |>
    dplyr::transmute(system = "Human liver microsomes", s0, v = vUK408027),
  dplyr::filter(sim_rec, time == 0) |>
    dplyr::transmute(system = "Recombinant CYP3A4", s0, v = vUK408027)
)
head(v0)
#>                   system       s0          v
#> 1 Human liver microsomes 1.000000 0.02045455
#> 2 Human liver microsomes 1.188502 0.02410375
#> 3 Human liver microsomes 1.412538 0.02836100
#> 4 Human liver microsomes 1.678804 0.03331136
#> 5 Human liver microsomes 1.995262 0.03904578
#> 6 Human liver microsomes 2.371374 0.04565920

Replicating Figure 2 and Figure 4

Replicates Figure 2 (human liver microsomes) and Figure 4 (recombinant CYP3A4) of Hyland 2008: the Michaelis-Menten plot of UK-408,027 formation velocity against maraviroc concentration, with the Eadie-Hofstee transform as the inset.

ggplot(v0, aes(s0, v)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~system, scales = "free_y") +
  labs(x = "Maraviroc concentration (uM)",
       y = "UK-408,027 formation (pmol / pmol CYP / min)") +
  theme_bw()
Michaelis-Menten plots of UK-408,027 formation. Replicates Figure 2 (human liver microsomes) and Figure 4 (recombinant CYP3A4) of Hyland 2008.

Michaelis-Menten plots of UK-408,027 formation. Replicates Figure 2 (human liver microsomes) and Figure 4 (recombinant CYP3A4) of Hyland 2008. 

ggplot(v0, aes(v / s0, v)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~system, scales = "free") +
  labs(x = "v / [S]", y = "v (pmol / pmol CYP / min)") +
  theme_bw()
Eadie-Hofstee transforms. Replicates the insets of Figure 2 and Figure 4 of Hyland 2008; the slope is -Km and the y intercept is Vmax.

Eadie-Hofstee transforms. Replicates the insets of Figure 2 and Figure 4 of Hyland 2008; the slope is -Km and the y intercept is Vmax.

The Eadie-Hofstee transform is a linear identity of the Michaelis-Menten form, so its slope must recover -Km and its intercept Vmax exactly. Because the human liver microsome model also carries the additive impurity term, the check is run with c_impurity at its published-structure default of zero, where the two forms coincide.

eh <- v0 |>
  dplyr::group_by(system) |>
  dplyr::group_modify(function(d, key) {
    fit <- stats::lm(v ~ I(v / s0), data = d)
    tibble::tibble(km_recovered = -unname(stats::coef(fit)[2]),
                   vmax_recovered = unname(stats::coef(fit)[1]))
  }) |>
  dplyr::ungroup() |>
  dplyr::mutate(km_published = c(21, 13), vmax_published = c(0.45, 3))

knitr::kable(eh, digits = 6)
system km_recovered vmax_recovered km_published vmax_published
Human liver microsomes 21 0.45 21 0.45
Recombinant CYP3A4 13 3.00 13 3.00 

stopifnot(
  isTRUE(all.equal(eh$km_recovered, eh$km_published, tolerance = 1e-8)),
  isTRUE(all.equal(eh$vmax_recovered, eh$vmax_published, tolerance = 1e-8))
)

A second, independent identity: the velocity at [S] = Km must be exactly half of Vmax in both systems.

half <- dplyr::bind_rows(
  dplyr::filter(solve_grid(mod_hlm, 21, times = 0), time == 0) |>
    dplyr::transmute(system = "Human liver microsomes", v = vUK408027, vmax = 0.45),
  dplyr::filter(solve_grid(mod_rec, 13, times = 0), time == 0) |>
    dplyr::transmute(system = "Recombinant CYP3A4", v = vUK408027, vmax = 3)
)

knitr::kable(dplyr::mutate(half, ratio = v / vmax), digits = 8)
system v vmax ratio
Human liver microsomes 0.225 0.45 0.5
Recombinant CYP3A4 1.500 3.00 0.5 

stopifnot(isTRUE(all.equal(half$v / half$vmax, c(0.5, 0.5), tolerance = 1e-10)))

Reproducing the published intrinsic-clearance chain

The paper carries the substrate-depletion intrinsic clearance through four arithmetic steps in Results, “CLint estimates from HLM and rCYP”. Each printed intermediate is a transcription check on the constants the model files carry, and each is computed by the packaged model rather than restated here.

d0_hlm <- dplyr::filter(sim_hlm, time == 0)[1, ]
d0_rec <- dplyr::filter(sim_rec, time == 0)[1, ]

clint_chain <- tibble::tibble(
  Quantity = c(
    "HLM CLint per mg microsomal protein",
    "HLM CLint per mg, unbound basis",
    "rCYP3A4 CLint after the intersystem extrapolation factor",
    "rCYP3A4 CLint per mg microsomal protein",
    "rCYP3A4 CLint per mg, unbound basis"
  ),
  Units = c("uL/min/mg", "uL/min/mg", "uL/min/pmol CYP3A4",
            "uL/min/mg", "uL/min/mg"),
  Model = c(d0_hlm$clint_mg, d0_hlm$clint_u_mg, d0_rec$clint_isef,
            d0_rec$clint_mg, d0_rec$clint_u_mg),
  Published = c(35.0, 48.6, 0.34, 40.8, 47.4)
) |>
  dplyr::mutate(pct_diff = 100 * (Model - Published) / Published)

clint_chain |>
  dplyr::rename("Percent difference" = pct_diff) |>
  knitr::kable(digits = 3)
Quantity Units Model Published Percent difference
HLM CLint per mg microsomal protein uL/min/mg 34.980 35.00 -0.057
HLM CLint per mg, unbound basis uL/min/mg 48.583 48.60 -0.034
rCYP3A4 CLint after the intersystem extrapolation factor uL/min/pmol CYP3A4 0.340 0.34 0.000
rCYP3A4 CLint per mg microsomal protein uL/min/mg 40.800 40.80 0.000
rCYP3A4 CLint per mg, unbound basis uL/min/mg 47.442 47.40 0.088 

# Every step is a printed value rounded to three significant figures, so the
# model must land within rounding of each one.
stopifnot(max(abs(clint_chain$pct_diff)) < 0.15)

The paper’s own cross-system conclusion also falls out: the two unbound intrinsic clearances, reached by completely different scaling routes, agree to within a few percent, which is the evidence the authors give that CYP3A4 is the enzyme responsible in both systems.

cross <- 100 * abs(d0_hlm$clint_u_mg - d0_rec$clint_u_mg) / d0_hlm$clint_u_mg
cat(sprintf("HLM %.1f vs rCYP3A4 %.1f uL/min/mg -- %.1f%% apart\n",
            d0_hlm$clint_u_mg, d0_rec$clint_u_mg, cross))
#> HLM 48.6 vs rCYP3A4 47.4 uL/min/mg -- 2.3% apart
stopifnot(cross < 5)

Reproducing the “approximately 20%” route split

The Discussion states that in human liver microsomes “the intrinsic clearance based upon UK-408,027 formation is approximately 20% of maraviroc intrinsic clearance calculated from substrate depletion experiments”. That claim is a one-line consistency check across three independently reported numbers – Km, Vmax and the depletion CLint – and is what justifies the model’s split of maraviroc loss into the saturable UK-408,027 route and a first-order remainder.

split_tbl <- tibble::tibble(
  system = c("Human liver microsomes", "Recombinant CYP3A4"),
  clint_uk408027 = c(d0_hlm$clint_uk408027, d0_rec$clint_uk408027),
  clint_depletion = c(ini_val(mod_hlm, "clint"), ini_val(mod_rec, "clint")),
  clint_other = c(d0_hlm$clint_other, d0_rec$clint_other)
) |>
  dplyr::mutate(share_pct = 100 * clint_uk408027 / clint_depletion)

split_tbl |>
  dplyr::rename(
    "In vitro system" = system,
    "UK-408,027 CLint (uL/min/pmol CYP)" = clint_uk408027,
    "Depletion CLint (uL/min/pmol CYP)" = clint_depletion,
    "Other routes (uL/min/pmol CYP)" = clint_other,
    "UK-408,027 share (%)" = share_pct
  ) |>
  knitr::kable(digits = 4)
In vitro system UK-408,027 CLint (uL/min/pmol CYP) Depletion CLint (uL/min/pmol CYP) Other routes (uL/min/pmol CYP) UK-408,027 share (%)
Human liver microsomes 0.0214 0.106 0.0846 20.2156
Recombinant CYP3A4 0.2308 1.700 1.4692 13.5747 

# The Discussion's "approximately 20%" for human liver microsomes.
stopifnot(abs(split_tbl$share_pct[1] - 20) < 1)
# Both remainders must be positive, or the depletion clearance would be smaller
# than the single route it contains and the split would be incoherent.
stopifnot(all(split_tbl$clint_other > 0))

Mass balance

Maraviroc leaving the substrate state must be fully accounted for by UK-408,027 formed plus the flux down the other oxidative routes. The check below integrates the other-route flux over the incubation and confirms the three quantities close.

# The argument names are dot-prefixed so they cannot be shadowed by the
# same-named `clint_other` and `cyp_inc` columns of the solved data frame under
# dplyr's data masking.
mass_balance <- function(sim, .clint_other, .cyp_inc) {
  sim |>
    dplyr::group_by(s0) |>
    dplyr::arrange(time, .by_group = TRUE) |>
    dplyr::summarise(
      consumed = dplyr::first(Cmaraviroc) - dplyr::last(Cmaraviroc),
      formed = dplyr::last(uk408027),
      # Trapezoidal integral of clint_other * C * cyp_inc / 1000 over the run.
      other = sum(diff(time) *
                    (utils::head(Cmaraviroc, -1) + utils::tail(Cmaraviroc, -1)) / 2) *
        .clint_other * .cyp_inc / 1000,
      .groups = "drop"
    ) |>
    dplyr::mutate(residual = consumed - formed - other,
                  rel_residual = residual / consumed)
}

mb_hlm <- mass_balance(sim_hlm, d0_hlm$clint_other, d0_hlm$cyp_inc)
mb_rec <- mass_balance(sim_rec, d0_rec$clint_other, ini_val(mod_rec, "cyp_inc"))

knitr::kable(
  dplyr::bind_rows(
    dplyr::mutate(utils::head(mb_hlm, 3), system = "Human liver microsomes"),
    dplyr::mutate(utils::head(mb_rec, 3), system = "Recombinant CYP3A4")
  ) |>
    dplyr::select(system, dplyr::everything()),
  digits = 6
)
system s0 consumed formed other residual rel_residual
Human liver microsomes 1.000000 0.050671 0.009878 0.040793 0e+00 0e+00
Human liver microsomes 1.188502 0.060128 0.011643 0.048485 0e+00 0e+00
Human liver microsomes 1.412538 0.071330 0.013703 0.057627 0e+00 0e+00
Recombinant CYP3A4 1.000000 0.223375 0.028632 0.194744 -1e-06 -5e-06
Recombinant CYP3A4 1.188502 0.265127 0.033630 0.231498 -1e-06 -5e-06
Recombinant CYP3A4 1.412538 0.314615 0.039420 0.275197 -2e-06 -5e-06 

# The trapezoidal rule on a 0.5 min grid is the only approximation here, so the
# residual is quadrature error rather than a modelling discrepancy.
stopifnot(max(abs(mb_hlm$rel_residual)) < 0.01,
          max(abs(mb_rec$rel_residual)) < 0.01)

Substrate depletion

The depletion experiments were run at 1 uM maraviroc, far below both systems’ Km, so loss is effectively first order with rate constant clint * cyp_inc / 1000. Reproducing the log-linear decline confirms the depletion arm is wired with the right sign and the right unit conversion.

dep <- dplyr::bind_rows(
  solve_grid(mod_hlm, 1, times = seq(0, 60, by = 1)) |>
    dplyr::transmute(system = "Human liver microsomes", time, Cmaraviroc),
  solve_grid(mod_rec, 1, times = seq(0, 60, by = 1)) |>
    dplyr::transmute(system = "Recombinant CYP3A4", time, Cmaraviroc)
)

ggplot(dep, aes(time, Cmaraviroc, colour = system)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Incubation time (min)", y = "Maraviroc (uM)", colour = NULL) +
  theme_bw() +
  theme(legend.position = "bottom")
Simulated maraviroc depletion at the 1 uM substrate concentration of the depletion assay, at the CYP concentrations used for the kinetic incubations.

Simulated maraviroc depletion at the 1 uM substrate concentration of the depletion assay, at the CYP concentrations used for the kinetic incubations. 

first_order <- dep |>
  dplyr::group_by(system) |>
  dplyr::group_modify(function(d, key) {
    fit <- stats::lm(log(Cmaraviroc) ~ time, data = d)
    tibble::tibble(k_fitted = -unname(stats::coef(fit)[2]))
  }) |>
  dplyr::ungroup() |>
  dplyr::mutate(
    k_expected = c(
      ini_val(mod_hlm, "clint") * d0_hlm$cyp_inc / 1000,
      ini_val(mod_rec, "clint") * ini_val(mod_rec, "cyp_inc") / 1000
    ),
    pct_diff = 100 * (k_fitted - k_expected) / k_expected
  )

knitr::kable(first_order, digits = 6)
system k_fitted k_expected pct_diff
Human liver microsomes 0.003469 0.003498 -0.832658
Recombinant CYP3A4 0.016895 0.017000 -0.615493 

# 1 uM is 1/21 and 1/13 of the two Km values, so the saturable route is close to
# but not exactly first order; a few percent of curvature is expected.
stopifnot(max(abs(first_order$pct_diff)) < 5)

Comparison against the paper’s independently measured activities

Two rates measured in other experiments of the same paper are predicted by the kinetic models rather than being inputs to them, so they are genuine external comparisons. Both were measured at 50 uM maraviroc.

v50 <- dplyr::bind_rows(
  dplyr::filter(solve_grid(mod_hlm, 50, times = 0), time == 0) |>
    dplyr::transmute(system = "Human liver microsomes",
                     v_model_per_cyp = vUK408027,
                     # Table 2's control activity is per mg protein, so scale by
                     # the total CYP content of the microsomal pool.
                     v_model = vUK408027 * ini_val(mod_hlm, "cyp_total"),
                     units = "pmol/mg/min",
                     v_observed = 75.9,
                     observed_source = "Table 2 footnote, uninhibited control"),
  dplyr::filter(solve_grid(mod_rec, 50, times = 0), time == 0) |>
    dplyr::transmute(system = "Recombinant CYP3A4",
                     v_model_per_cyp = vUK408027,
                     v_model = vUK408027,
                     units = "pmol/pmol CYP/min",
                     v_observed = 1.7,
                     observed_source = "Figure 3 and Discussion")
) |>
  dplyr::mutate(pct_diff = 100 * (v_model - v_observed) / v_observed)

v50 |>
  dplyr::select(system, units, v_model, v_observed, pct_diff, observed_source) |>
  dplyr::rename("In vitro system" = system, "Units" = units,
                "Model" = v_model, "Observed" = v_observed,
                "Percent difference" = pct_diff, "Observed source" = observed_source) |>
  knitr::kable(digits = 3)
In vitro system Units Model Observed Percent difference Observed source
Human liver microsomes pmol/mg/min 104.577 75.9 37.783 Table 2 footnote, uninhibited control
Recombinant CYP3A4 pmol/pmol CYP/min 2.381 1.7 40.056 Figure 3 and Discussion

Both model predictions run about 40% above the separately measured activities. The two comparisons are not perfectly matched: the Table 2 control activity and the Figure 3 panel come from the reaction-phenotyping experiments, which used different microsome and Supersome preparations from the kinetic runs and a single substrate concentration rather than a fitted curve, and the paper reports the phenotyping values as means of quadruplicate determinations with standard deviations that are not tabulated. The bias is in the same direction and of similar magnitude in both systems, which is what an inter-preparation activity difference looks like. No parameter has been adjusted to close it; the model carries the published Km and Vmax exactly.

# Bound the discrepancy rather than assert agreement: the point of this section
# is to record it, and a much larger gap would indicate a transcription error.
stopifnot(all(abs(v50$pct_diff) < 60), all(v50$pct_diff > 0))

Published results not reproduced here

For completeness, the paper’s Simcyp predictions are recorded below as published values. They are outputs of the whole-body platform model described under “Scope” above and are not computed by either packaged model.

Maraviroc Inhibitor Clinical mean AUC ratio (90% CI) Simcyp median, time based (90% CI) Simcyp median, steady state (90% CI)
100 mg bid Ketoconazole 400 mg qd 5.0 (4.0, 6.3) 4.6 (2.7, 9.1) 5.2 (2.8, 10.6)
100 mg bid Ritonavir 100 mg bid 2.6 (1.9, 3.6) 2.6 (1.9, 4.7) 2.6 (1.8, 4.6)
300 mg bid Atazanavir 400 mg qd 3.6 (3.3, 3.9) 5.0 (2.4, 7.8) 4.9 (2.6, 9.6)
100 mg bid Saquinavir 1200 mg tid 4.3 (3.5, 5.2) 5.8 (2.8, 12.0) 3.5 (2.0, 8.7)

Source: Table 3 of Hyland 2008.

The paper also reports the chemical-inhibition screen that localised the reaction to CYP3A4 (Table 2). With 1 uM ketoconazole, 16.1 +/- 5.7% of control UK-408,027 formation and 17.3 +/- 3.4% of control maraviroc depletion remained (both P < 0.00001); furafylline, sulphaphenazole, benzylnirvanol and quinidine had no significant effect. No inhibition constant is reported for ketoconazole in this paper, so no inhibition term is carried in either model file and the screen is recorded as narrative rather than simulated.

Maraviroc was itself a weak CYP inhibitor, with IC50 above 30 uM against probe substrates for all seven CYPs tested; again no point estimate is reported, so no perpetrator model is extracted.

Assumptions and deviations

  • The impurity constant C is not published. The paper’s fitted equation is v = Vmax * [S] / (Km + [S]) + C * [S], where C absorbs a concentration-dependent UK-408,027 contaminant in the maraviroc substrate. The structure is preserved in Hyland_2008_maraviroc_hlm as c_impurity, held at zero, because no value is reported. The authors state that correcting the data for the measured impurity and fitting a plain Michaelis-Menten equation gave a similar Km and Vmax, so zero reproduces the published parameter estimates. A user who obtains C can set it without editing the model.
  • No impurity term in the recombinant model. In the Supersome experiments the contaminant was removed by comparison against control Supersomes rather than fitted, so Hyland_2008_maraviroc_rcyp3a4 carries no c_impurity.
  • The non-UK-408,027 clearance is modelled as first order. The paper reports a single depletion intrinsic clearance measured at 1 uM maraviroc, which is far below both Km values, and characterises the saturable route only for the UK-408,027 pathway. The remaining routes are therefore carried as clint - Vmax/Km, a first-order clearance, which is exactly what the depletion experiment measured. Their saturation behaviour at higher concentrations is not characterised by this paper and the model should not be used to extrapolate it.
  • The residual error is a bioanalytical CV, not a fitted residual. The paper reports no residual-error model; Km and Vmax were fitted with Grafit and reported without standard errors, and the figure error bars are not tabulated. propSd is fixed at 0.051, the reported LC-MS/MS coefficient of variation for UK-408,027 at the 50 ng calibration standard (the assay was 5.7%, 5.1% and 4.2% at 5, 50 and 150 ng). The maraviroc depletion assay CV was 14% at 1 uM; because the paper publishes no maraviroc concentration-time data, Cmaraviroc is returned as a derived quantity without a residual-error model rather than as a second fitted endpoint.
  • The observation variable is a reaction velocity, which raises a convention warning. checkModelConventions() warns that the single-output observation vUK408027 is not the canonical Cc and is not a registered PD-output state. The warning is accepted rather than fixed: the fitted endpoint of Figures 2 and 4 is a formation velocity in pmol per pmol CYP per min, not a concentration, so naming it Cc would misstate its units and its meaning. These are the first in vitro enzyme-kinetic models in the library, so there is not yet a recurring endpoint to canonicalise; if more accumulate, a registered reaction-velocity output name would be the right fix. The metabolite and substrate concentrations are available alongside it as the uk408027 state and the derived Cmaraviroc.
  • No between-experiment variability. Neither model carries eta terms. The paper reports means of seven (human liver microsomes) and four (recombinant CYP3A4) determinations without variance components, so a random-effects structure would have to be invented.
  • Fraction unbound in microsomes is applied as the paper applies it. The measured fumic values (0.72 and 0.86) were determined at protein concentrations of 1.5 and 0.63 mg/mL, which are the intrinsic-clearance assay conditions, not the 0.1 mg/mL and 10 pmol/mL kinetic incubations. At the kinetic protein concentrations the authors calculate maraviroc to be 98% free, so the Km values are treated as close to unbound values, as the paper does, and fumic is used only in the intrinsic-clearance scaling chain.
  • Vmax has different denominators in the two files. In human liver microsomes it is per pmol of total CYP; in the recombinant system it is per pmol of CYP3A4. The two are not interchangeable, and the model files label them accordingly.
  • The Simcyp layer is not extracted. See “Scope” above. Table 1’s compound inputs are recorded in the model descriptions and the source-trace table but are not encoded as a model, because the whole-body physiology and the partition coefficients that would turn a CLint into a systemic clearance are not printed anywhere in the paper.
  • Task metadata correction. The dispatching task block recorded the publication year as 2026-06-22; the article is Br J Clin Pharmacol 2008; 66(4):498-507, received 8 February 2008, accepted 1 April 2008 and published OnlineEarly 22 July 2008. The extraction uses 2008.