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Baicalein (Xiang 2018)

Source: vignettes/articles/Xiang_2018_baicalein.Rmd
Xiang_2018_baicalein.Rmd

Model and source

  • Citation: Xiang L, Hu Y-F, Wu J-S, Wang L, Huang W-G, Xu C-S, Meng X-L, Wang P. Semi-Mechanism-Based Pharmacodynamic Model for the Anti-Inflammatory Effect of Baicalein in LPS-Stimulated RAW264.7 Macrophages. Front Pharmacol. 2018;9:793. doi:10.3389/fphar.2018.00793.
  • Description: In vitro (RAW264.7 mouse macrophage cell line). Semi-mechanism-based cellular pharmacodynamic model for the anti-inflammatory effect of baicalein on LPS-induced cytokine and iNOS/NO release in RAW264.7 mouse macrophages. Four indirect-response states arranged in a TNF-alpha -> {IL-6, iNOS -> NO} cascade: (1) TNF-alpha indirect response with LPS-stimulated zero-order production and baicalein’s log-linear inhibition f(Bai) = alpha * log(C_Bai + 1) on the production rate; (2) IL-6 indirect response with delayed TNF-alpha drive (lag tau1); (3) iNOS indirect response with delayed TNF-alpha drive (lag tau2) and elimination held at zero (paper choice for the post-12.5 h plateau); (4) NO indirect response with iNOS^delta amplification and elimination held at zero. Baicalein concentration enters as a static covariate (CONC_BAI_UM); LPS is constant at 1 ug/mL throughout the experiment and is absorbed into the kinTNF zero-order production rate (no explicit LPS state). Tau1 and tau2 are encoded via single-compartment delay states (mean transit time = tau) because rxode2 does not provide a native delay-differential-equation solver; see the validation vignette Errata for the impulse-response implications. Typical-value-only mechanism: no IIV, no residual error is reported in the source (CV% in Table 1 are RSE / precision of estimate, not BSV).
  • Article: https://doi.org/10.3389/fphar.2018.00793

Population

The model was fit to a cellular in-vitro time-kill / cytokine-release experiment in the murine RAW264.7 macrophage cell line (Center of Cellular Resources, Chinese Academy of Sciences, Shanghai). Cells were inoculated at 1 x 10^6 cells/mL, pre-treated with baicalein at 0, 10, 20, or 40 uM for 0.5 h, then stimulated with LPS (1 ug/mL, Escherichia coli O55:B5) for an additional 1, 2, 4, 8, 12, and 24 h. TNF-alpha and IL-6 in the cell-culture supernatant were quantified by ELISA (MULTI SCIENCES Mouse kits; intra/inter-assay CV 2.3-3.0% and 2.1-5.3%), iNOS expression was measured by Western blot and normalised to the t = 0 control as (iNOS/GAPDH) / (iNOS0/GAPDH0), and NO was quantitated by the Griess reaction calibrated against sodium nitrite standards (Xiang 2018 Materials and Methods). Reported sample sizes per condition were n = 3 for TNF-alpha, IL-6, and NO, and n = 6 for iNOS (Xiang 2018 Figure 3 caption).

The same information is available programmatically via rxode2::rxode(readModelDb("Xiang_2018_baicalein"))$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/pharmacodynamics/Xiang_2018_baicalein.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lalpha (alpha) log(0.0832) Xiang 2018 Table 1, row 1 (a)
lkin_tnf (kinTNF) log(3740) Xiang 2018 Table 1, row 2 (k_inTNFa)
lkout_tnf (koutTNF) log(0.0463) Xiang 2018 Table 1, row 3 (k_outTNFa)
lkin_il6 (kinIL6) log(0.353) Xiang 2018 Table 1, row 4 (k_inIL-6)
lkout_il6 (koutIL6) log(0.143) Xiang 2018 Table 1, row 5 (k_outIL-6)
ltau1 (tau1) log(1.38) Xiang 2018 Table 1, row 6 (tau_1)
lkin_inos (kiniNOS) log(0.00169) Xiang 2018 Table 1, row 7 (k_iniNOS)
ltau2 (tau2) log(1.41) Xiang 2018 Table 1, row 8 (tau_2)
lkin_no (kinNO) log(0.0605) Xiang 2018 Table 1, row 9 (k_inNO)
ldelta (delta) log(1.35) Xiang 2018 Table 1, row 10 (delta)
kout_inos fixed(0) Xiang 2018 Results, Model Simulation paragraph 1 (koutiNOS fixed to 0)
kout_no fixed(0) Xiang 2018 Results, Model Simulation paragraph 1 (koutNO fixed to 0)
lrbase_tnf log(1000) Xiang 2018 Figure 4A, control curve at t = 0 (digitised)
lrbase_il6 log(100) Xiang 2018 Figure 4B, control curve at t = 0 (digitised)
lrbase_inos log(1) Xiang 2018 Materials and Methods, Western Blotting (normalisation definition)
lrbase_no log(1) Xiang 2018 Figure 4D, control curve at t = 0 (digitised)
propSd_tnf,_il6,_inos,_no fixed(0.10) Placeholder; weighting strategy in Xiang 2018 Pharmacodynamic Modeling does not state the final-model residual-error form
Eq 1 (dTNF/dt) n/a Xiang 2018 Eq 1, page 4
Eq 2 (f(Bai)) n/a Xiang 2018 Eq 2, page 4
Eq 3 (TNFa_0) n/a Xiang 2018 Eq 3, page 4
Eq 4 (dIL-6/dt) n/a Xiang 2018 Eq 4, page 4
Eq 5 (IL-6_0) n/a Xiang 2018 Eq 5, page 5
Eq 6 (diNOS/dt) n/a Xiang 2018 Eq 6, page 5
Eq 7 (dNO/dt) n/a Xiang 2018 Eq 7, page 5

Dimensional analysis

Endogenous / mechanistic models in the package are required to carry a worked dimensional analysis (per references/endogenous-validation.md). The unit table below shows the units of every symbol on the right-hand side of each ODE in model(); the left-hand side must equal [state units]/[time units] (i.e., the state’s reporting unit per hour).

Term Units of each factor Product (= LHS)
kin_tnf * (1 - f_bai) (pg/mL/h) * (unitless) pg/mL/h = d/dt(TNF)
kout_tnf * tnf (1/h) * (pg/mL) pg/mL/h = d/dt(TNF)
(tnf - transit1) / tau1 (pg/mL) / (h) pg/mL/h = d/dt(transit1)
(tnf - transit2) / tau2 (pg/mL) / (h) pg/mL/h = d/dt(transit2)
kin_il6 * transit1 (1/h) * (pg/mL) pg/mL/h = d/dt(IL-6)
kout_il6 * il6 (1/h) * (pg/mL) pg/mL/h = d/dt(IL-6)
kin_inos * transit2 (1/h) * (pg/mL) pg/mL/h then normalized (note below)
kout_inos * inos (1/h) * (unitless) unitless/h
kin_no * inos^delta (uM/h) * (unitless) uM/h = d/dt(NO)
kout_no * no (1/h) * (uM) uM/h

Notes on apparent units.

  • kinTNF is reported with the unit h^-1 in Xiang 2018 Table 1 row 2; Eq 1 requires the production-rate term to have the unit pg/mL/h, so kinTNF is interpreted as carrying units pg/mL/h. The Table 1 unit label is treated as a typesetting slip (the same column header was applied to all first-order rate constants). At the published value 3.74 x 10^3, this interpretation is also numerically self-consistent with the observed t = 1 h peak (see the smoke check below).
  • kinNO is reported with the unit h^-1 in Xiang 2018 Table 1 row 9; Eq 7 with iNOS^delta unitless requires kinNO to carry units uM/h. Same Table-1 unit-label slip as kinTNF.
  • kiniNOS (Table 1 row 7) carries units 1/h; Eq 6 multiplies the delayed TNF-alpha concentration in pg/mL, so the iNOS state’s effective unit is iNOS-ratio per (pg/mL * h)) at unit TNF-alpha. iNOS is reported as the unitless ratio (iNOS/GAPDH) / (iNOS0/GAPDH0), so the “unit” of d/dt(iNOS) is iNOS-ratio per h; the dimensional consistency is therefore exact only if kiniNOS is read as having units (1/h) * (pg/mL)^-1 = 1/(h * pg/mL). The package retains the Table 1 value 0.00169 verbatim; downstream users who refit the model on a different TNF-alpha unit basis should rescale kiniNOS accordingly (see Assumptions and deviations below).

Parameter table – paper vs. file

Xiang 2018 Table 1 vs the values stored in inst/modeldb/pharmacodynamics/Xiang_2018_baicalein.R. CV% in the source paper is the precision of the estimate (RSE), not between-subject variability.
Parameter Paper (Table 1) File (ini) CV_pct_in_paper
alpha 8.32e-02 0.08319 15%
kinTNF 3.74e+03 3739.47311 6%
koutTNF 4.63e-02 0.04633 32%
kinIL6 3.53e-01 0.35300 9%
koutIL6 1.43e-01 0.14306 23%
tau1 1.38e+00 1.38002 11%
kiniNOS 1.69e-03 0.00169 9%
tau2 1.41e+00 1.41001 13%
kinNO 6.05e-02 0.06056 37%
delta 1.35e+00 1.34999 9%
koutiNOS 0.00e+00 0.00000 fixed to 0
koutNO 0.00e+00 0.00000 fixed to 0

Simulation – replicate Figure 4

Xiang 2018 Figure 4 shows the model-predicted and measured time courses of TNF-alpha (panel A), IL-6 (panel B), iNOS (panel C/E), and NO (panel D) over 24.5 h in LPS-stimulated RAW264.7 macrophages at four baicalein concentrations (0 = control, 10, 20, 40 uM). The simulation below uses the packaged typical-value model with four virtual “wells” (one per concentration), zero between-subject variability, and the figure-derived baseline values.

mod <- rxode2::rxode(nlmixr2lib::readModelDb("Xiang_2018_baicalein"))

times <- seq(0, 24, by = 0.25)
concentrations <- c(0, 10, 20, 40)

make_well <- function(conc, id) {
  rxode2::et(amt = 0, time = 0) |>
    rxode2::et(times) |>
    as.data.frame() |>
    dplyr::mutate(id = id, CONC_BAI_UM = conc)
}

events <- dplyr::bind_rows(
  make_well(concentrations[1], id = 1L),
  make_well(concentrations[2], id = 2L),
  make_well(concentrations[3], id = 3L),
  make_well(concentrations[4], id = 4L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

sim <- rxode2::rxSolve(mod, events = events,
                       keep = "CONC_BAI_UM",
                       returnType = "data.frame") |>
  dplyr::as_tibble() |>
  dplyr::mutate(label = paste0("Baicalein ", CONC_BAI_UM, " uM"))
#> Warning: multi-subject simulation without without 'omega'

Figure 4A – TNF-alpha

Replicates Figure 4A of Xiang 2018 (TNF-alpha time course at 0, 10, 20, 40 uM baicalein in LPS-stimulated RAW264.7 macrophages).

ggplot(sim, aes(time, tnf, colour = label)) +
  geom_line() +
  labs(x = "Time post-LPS (h)",
       y = "TNF-alpha (pg/mL)",
       colour = "Baicalein conc.",
       title = "Figure 4A -- TNF-alpha trajectory",
       caption = "Replicates Figure 4A of Xiang 2018.")

Figure 4B – IL-6 

ggplot(sim, aes(time, il6, colour = label)) +
  geom_line() +
  labs(x = "Time post-LPS (h)",
       y = "IL-6 (pg/mL)",
       colour = "Baicalein conc.",
       title = "Figure 4B -- IL-6 trajectory",
       caption = "Replicates Figure 4B of Xiang 2018.")

Figure 4C/E – iNOS 

ggplot(sim, aes(time, inos, colour = label)) +
  geom_line() +
  labs(x = "Time post-LPS (h)",
       y = "Relative iNOS expression ((iNOS/GAPDH) / (iNOS0/GAPDH0))",
       colour = "Baicalein conc.",
       title = "Figure 4C/E -- iNOS trajectory",
       caption = "Replicates Figures 4C and 4E of Xiang 2018.")

Figure 4D – NO 

ggplot(sim, aes(time, no, colour = label)) +
  geom_line() +
  labs(x = "Time post-LPS (h)",
       y = "NO (uM)",
       colour = "Baicalein conc.",
       title = "Figure 4D -- NO trajectory",
       caption = "Replicates Figure 4D of Xiang 2018.")

Smoke check – t = 1 h TNF-alpha peak

Xiang 2018 Figure 4A shows that the TNF-alpha trace peaks at about 1 h after LPS stimulation, then gradually declines through 12 h. The packaged model’s simple turnover form (constant LPS-driven production plus first-order elimination) cannot reproduce the peak-and-decline; it predicts a monotonic approach to the steady-state asymptote kinTNF / koutTNF ~= 80800 pg/mL. The published model fit in Figure 4 appears to track the data more closely than the published equations permit (see Assumptions and deviations).

The simulated t = 1 h TNF-alpha concentration is, however, in close agreement with the observed peak (Xiang 2018 Figure 2B / 4A reads ~4500 pg/mL in the LPS-only control):

sim |>
  dplyr::filter(abs(time - 1) < 1e-6) |>
  dplyr::select(label, time, tnf) |>
  dplyr::mutate(tnf = round(tnf, 0)) |>
  knitr::kable(caption = "Simulated TNF-alpha at t = 1 h post-LPS, by baicalein concentration. The LPS-only control value (~4600 pg/mL) is close to the Figure 4A observed peak (~4500 pg/mL).")
Simulated TNF-alpha at t = 1 h post-LPS, by baicalein concentration. The LPS-only control value (~4600 pg/mL) is close to the Figure 4A observed peak (~4500 pg/mL).
label time tnf
Baicalein 0 uM 1 4609
Baicalein 10 uM 1 3880
Baicalein 20 uM 1 3684
Baicalein 40 uM 1 3480

Baseline-recovery smoke check

This model is not a quiescent steady-state system (the LPS-stimulated kinTNF zero-order production is on from t = 0), so the classic endogenous-model “set initial condition to baseline, expect no drift” check is not applicable. A meaningful sanity test is to confirm that when kinTNF is set to zero (no LPS), the four states stay near their baselines for the duration of the experiment (linear-cascade self-consistency).

# Build a parameter override: kin_tnf -> 0 (no LPS stimulation)
mod_no_lps <- rxode2::rxode(nlmixr2lib::readModelDb("Xiang_2018_baicalein"))
sim_no_lps <- rxode2::rxSolve(
  mod_no_lps,
  events = make_well(conc = 0, id = 1L),
  params = c(lkin_tnf = log(1e-12)),  # effectively zero
  returnType = "data.frame"
)
sim_no_lps |>
  dplyr::filter(time %in% c(0, 6, 12, 18, 24)) |>
  dplyr::select(time, tnf, il6, inos, no) |>
  dplyr::mutate(across(c(tnf, il6, inos, no), \(x) round(x, 3))) |>
  knitr::kable(caption = "Without LPS stimulation (kinTNF ~= 0), TNF-alpha decays slowly toward zero (driven only by koutTNF); IL-6 rises slowly because the model's IL-6 production is proportional to the residual TNF-alpha rather than to a TNF-alpha excursion from baseline. iNOS and NO drift up monotonically because koutiNOS and koutNO are fixed at zero. The package's baseline values are therefore the experimental t = 0 control measurements, not steady-state solutions of the unstimulated system.")
Without LPS stimulation (kinTNF ~= 0), TNF-alpha decays slowly toward zero (driven only by koutTNF); IL-6 rises slowly because the model’s IL-6 production is proportional to the residual TNF-alpha rather than to a TNF-alpha excursion from baseline. iNOS and NO drift up monotonically because koutiNOS and koutNO are fixed at zero. The package’s baseline values are therefore the experimental t = 0 control measurements, not steady-state solutions of the unstimulated system.
time tnf il6 inos no
0 1000.000 100.000 1.000 1.000
6 757.448 1325.661 10.308 5.128
12 573.728 1546.773 17.480 18.066
18 434.569 1401.855 22.914 39.264
24 329.164 1159.465 27.030 67.378

Assumptions and deviations

The Xiang 2018 paper is a published cellular pharmacodynamic model with a fully specified equation set (Eqs 1-7) and a complete typical-value parameter table (Table 1), but several encoding decisions in the package require attention.

  • Drug field corrected. The task dispatcher’s metadata listed the drug as “Frontiers in Pharmacology” (the journal name) – a task-generator bug observed on several sibling tasks. The actual drug studied is baicalein (5,6,7-trihydroxy-2-phenyl-4H-1-benzopyran- 4-one), the primary active flavonoid of Scutellaria baicalensis Georgi. Filename and vignette title corrected accordingly.

  • Species and model class. The model was fit to an in-vitro experiment in the RAW264.7 mouse macrophage cell line, not to in-vivo human or animal data. population$species is set to “in vitro (RAW264.7 mouse macrophage cell line)” and the description field is prefixed with “In vitro (RAW264.7 mouse macrophage cell line).” per the SKILL Phase 1 step 3 species- recording requirement.

  • f(Bai) at C_Bai = 0. Xiang 2018 Eq 2 writes the inhibition function as f(Bai) = alpha * ln(C_Bai). At C_Bai = 0 (the control wells with no baicalein) the bare ln is undefined. The package encodes f(Bai) = alpha * log(CONC_BAI_UM + 1), which (a) returns f = 0 in control wells without a divide-by-zero, and (b) differs from the bare ln by less than 5% at the three tested concentrations 10, 20, 40 uM:

    • 10 uM: alphaln(10) = 0.192 vs alphaln(11) = 0.200 (delta 4.4%)
    • 20 uM: alphaln(20) = 0.249 vs alphaln(21) = 0.253 (delta 1.6%)
    • 40 uM: alphaln(40) = 0.307 vs alphaln(41) = 0.309 (delta 0.7%)

    The +1-shift convention is also the standard pharmacometric treatment of log-linear concentration-response with a controllable control arm; the paper’s “f = 0 in control” condition appears in Eqs 3 and 5 (“TNF-alpha_0 = Control(TNF-alpha)”).

  • Lag implementation – single-compartment delay states (DDE approximation). Eqs 4 and 6 use TNF-alpha(t - tau1) and TNF-alpha(t - tau2), which are true delay differential equation forms. rxode2 does not provide a native DDE solver, so the package encodes each delayed signal as a single first-order distribution compartment with mean transit time tau:

    d/dt(transit) = (tnf - transit) / tau

    The impulse response of this filter is a single-exponential ramp, not a Dirac shift – a step in tnf at time t produces a smoothed response in transit over the next several tau, rather than an exact translation. For the LPS-stimulated TNF-alpha trace, which is itself a smooth approach to its asymptote rather than a step, the single-compartment delay is a reasonable approximation; the alternative is a multi-compartment transit chain (n delays each with mean transit time tau / n), which sharpens the response toward a step shift but adds n - 1 extra states. The user may build the alternative encoding by editing model() to chain n delay compartments.

  • Baseline values are figure-derived. Xiang 2018 reports the initial conditions only as Control(TNF-alpha), Control(IL-6), and (iNOS/GAPDH) / (iNOS0/GAPDH0) = 1 – with the numeric values read off Figure 4 control curves at t = 0. The packaged defaults (1000 pg/mL for TNF-alpha, 100 pg/mL for IL-6, 1 for iNOS, 1 uM for NO) are operator digitisations of those figure points; users who have their own experimental t = 0 control measurements should override the corresponding lrbase_* parameters when refitting. iNOS is definitionally 1 at t = 0 per the Western-blot normalisation; the only figure-derived value with non-trivial uncertainty is bl_tnf.

  • Unit-label slips in Table 1. As detailed in the Dimensional Analysis section, the Table 1 column “Estimate” for kinTNF and kinNO carries the unit label “h^-1” but the equations require pg/mL/h and uM/h respectively. The package preserves the Table 1 numeric values (3.74 x 10^3 and 0.0605) and interprets the unit labels as typesetting slips – a single column unit was applied to all first-order rate-constant rows including the two zero-order production rows. This interpretation is internally self-consistent with the observed t = 1 h peak (see smoke check above).

  • No IIV and no residual error are reported. Xiang 2018 Pharmacodynamic Modeling lists the weighting strategies considered (additive, power, multiplicative) but does not state the final choice. The reported CV% column in Table 1 is the precision of the estimate (RSE), not between-subject variability. The package carries placeholder 10% proportional residual on each of the four outputs (propSd_tnf, propSd_il6, propSd_inos, propSd_no) so the model is nlmixr2-fit-compatible; downstream users who refit the model on real data should replace these with whatever residual structure their data support. No eta_* IIVs are included – the paper does not report between-subject (between-well or between- experiment) variability.

  • Non-canonical compartment names (lint warnings). checkModelConventions() flags the six ODE-state names tnf, transit1, transit2, il6, inos, and no as non-canonical because they are not among the canonical PK/PD compartments (depot, central, peripheral1, …, or registered metabolites). This is the same pattern used by other in-vitro / mechanism-model entries in the package whose compartments are biological-species states rather than drug-distribution compartments (Clewe 2018 TB MTP-GPDI: fbugs/sbugs/nbugs/ar_off/ar_on; Charbonneau 2021 phenylalanine: gut/phe; Tetschke 2018 erythropoiesis: thb). These are kept as model-readable shorthand for the source species rather than renamed to numbered compartments, because the species identity is the meaningful entity in a cytokine-cascade mechanism. transit1 and transit2 are the single-compartment delay states implementing the DDE approximation described above.

  • Dosing/concentration unit mismatch (lint warning). checkModelConventions() flags units$dosing (uM, baicalein) vs units$concentration numerator (pg, TNF-alpha/IL-6) as dimensionally incompatible. The mismatch is genuine – baicalein concentration is reported in molar units while the cytokine readouts are in mass- concentration – and reflects the inherent mixed-dimension nature of a small-molecule perturbant driving a protein-readout in-vitro PD experiment. No correction is appropriate; the warning is documented here per the SKILL convention for justified deviations.

  • Peak-and-decline gap. The observed TNF-alpha trace in Figure 4A peaks at t = 1 h and then declines through 12 h before rising slowly to 24 h, while the model equation (constant kinTNF, first-order elimination koutTNF) predicts monotonic approach to the steady-state asymptote kinTNF / koutTNF ~= 80800 pg/mL. The model’s t = 1 h prediction agrees with the observed peak, but later time points (especially t = 6-12 h) diverge upward. The paper’s Figure 4 model curves nevertheless appear to track the data more closely than the published equations permit, suggesting either an unreported LPS-decay or self-feedback term in the model’s actual simulation, or a parameter-set discrepancy between Table 1 and the figure’s generating script. This is an acknowledged published-model limitation; the package encodes Eqs 1-7 verbatim with Table 1’s parameter values and does NOT modify the equations to match Figure 4 visually.