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Parhiz_2024_mRNALNP

Source: vignettes/articles/Parhiz_2024_mRNALNP.Rmd
Parhiz_2024_mRNALNP.Rmd

Model and source

This vignette validates the Parhiz et al. 2024 whole-body PBPK and luciferase-expression model in mice for the bare (untargeted) LNP parameterization. The packaged file in inst/modeldb/pharmacokinetics/Parhiz_2024_mRNALNP.R carries the full 24-state ODE system: blood and a blood-cleared LNP pool; vascular pools for lung, heart, kidney, spleen, liver, portal-organ remainder, and carcass remainder; and per-tissue intracellular LNP, mRNA, and luciferase signal compartments for the five major sampled tissues (lung, heart, kidney, spleen, liver).

Population

The model was fit to data from male C57BL/6 mice (6-8 weeks old; The Jackson Laboratory) injected with 8 ug of luciferase-encoding modified-mRNA loaded into lipid nanoparticles via retro-orbital IV bolus. n = 3 mice were destructively sampled per time point across blood and five organs (lung, heart, kidney, spleen, liver). The physiological parameters (tissue volumes, blood flows) were taken from the BioDMET database and scaled to a 25-g mouse (paper Table S3); only the 12 LNP / luciferase parameters in ini() were estimated. The present file packages the bare-LNP parameter set (no surface antibody conjugation, no active targeting). The vignette below documents the alternate parameter sets for control-IgG-coated and PECAM-targeted LNPs (paper Tables 1-3) that share the same structural model.

mod <- readModelDb("Parhiz_2024_mRNALNP")

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/pharmacokinetics/Parhiz_2024_mRNALNP.R. The table below collects them in one place for review.

Equation / parameter Value (bare LNP) Source
Venous blood mass balance derivation Supplement S1 “Pharmacokinetic Model / Venous Blood”; ADAPT 5 XP(1)
Tissue vasculature mass balance derivation Supplement S1 “Lungs”/“Liver”/“Other Organs / Vasculature”; ADAPT 5 XP(3), XP(5), XP(7), XP(9), XP(11)
Intracellular LNP / mRNA / luciferase ODEs derivation Supplement S1 “Other Organs / Internalized” and “Pharmacodynamic Model”; ADAPT 5 XP(4), XP(15), XP(20) for lung and analogues
cl_lu (lung non-specific uptake CL) 0.134 mL/h Table 1, Bare LNPs column
cl_he (heart non-specific uptake CL) 0.0999 mL/h Table 1, Bare LNPs column
cl_ki (kidney non-specific uptake CL) 0.428 mL/h Table 1, Bare LNPs column
cl_sp (spleen non-specific uptake CL) 0.656 mL/h Table 1, Bare LNPs column
cl_li (liver non-specific uptake CL) 16.3 mL/h Table 1, Bare LNPs column
cl_bl (blood elimination CL) 1.96 mL/h Table 1, Bare LNPs column
klnp (intracellular LNP degradation rate k_deg) 1.00 1/h Table 1, Bare LNPs column
slu (lung luciferase production rate S_lung) 2.57e5 LU/mg protein per ug RNA / h Table 2, Bare LNPs homogenate column
she (heart luciferase production rate S_heart) 6.70e4 LU/mg protein per ug RNA / h Table 2, Bare LNPs homogenate column
ski (kidney luciferase production rate S_kidney) 1.12e5 LU/mg protein per ug RNA / h Table 2, Bare LNPs homogenate column
ssp (spleen luciferase production rate S_spleen) 3.82e5 LU/mg protein per ug RNA / h Table 2, Bare LNPs homogenate column
sli (liver luciferase production rate S_liver) 8.64e5 LU/mg protein per ug RNA / h Table 2, Bare LNPs homogenate column
kluc (luciferase decay, non-liver) 0.0940 1/h Table 2, Bare LNPs homogenate column
kliv (luciferase decay, liver) 0.247 1/h Table 2, Bare LNPs homogenate column
krna (mRNA degradation rate, fixed) 0.114 1/h Methods text; Anderson 2011 Nucleic Acids Res ref 36
Mouse blood total volume v_bl 1.533 mL Table S3
Cardiac output q_co 605.4 mL/h Table S3 (10.1 mL/min x 60)
Lung total / vascular volume 0.182 / 0.0479 mL Table S3
Lung blood flow (= cardiac output) 605.4 mL/h Table S3
Heart blood flow / total / vascular volume 59.3 mL/h / 0.136 mL / 0.0095 mL Table S3
Kidney blood flow / total / vascular volume 111.25 mL/h / 0.469 mL / 0.0558 mL Table S3
Spleen blood flow / total / vascular volume 13.3 mL/h / 0.113 mL / 0.025 mL Table S3
Liver hepatic-artery flow / total / vascular volume 16.7 mL/h / 1.72 mL / 0.266 mL Table S3
Portal organs flow / vascular volume 132.4 mL/h / 0.0313 mL Table S3
Remainder flow / vascular volume 272.86 mL/h / 0.886 mL Table S3

Units in the ODE system

Quantity Units
Time h
Dose ug mRNA
Compartment amounts (blood, vp_, int_, mrna_*) ug mRNA
Luciferase compartments (luc_*) LU per mg tissue protein (homogenate assay)
Concentrations (cv_bl, cv_lu, …) derived as amount / vascular volume ug mRNA / mL
Volumes mL
Blood flows mL/h
Clearances (cl_lu, …, cl_bl) mL/h
klnp, krna, kluc, kliv 1/h
slu, she, …, sli LU/mg protein per ug RNA / h

Doses are supplied to the blood compartment in ug.

Mass-balance / flux check

With LNP degradation switched off (klnp -> 0, krna decoupled from LNP, cl_bl -> 0), the PBPK system is closed: total LNP mass should be conserved across blood, blood-cleared, and all tissue vascular / intracellular compartments. This catches structural ODE errors that would not be visible from a numerical-fit comparison.

mod_no_deg <- mod |> ini(lklnp = log(1e-12)) |> ini(lcl_bl = log(1e-12))
#> ℹ change initial estimate of `lklnp` to `-27.6310211159285`
#> ℹ change initial estimate of `lcl_bl` to `-27.6310211159285`

dose_ug <- 8
ev_bal <- et(amt = dose_ug, cmt = "blood", time = 0) |>
  et(seq(0, 12, by = 0.5))
sim_bal <- as.data.frame(rxSolve(mod_no_deg, events = ev_bal))

lnp_cols <- c(
  "blood", "bldeg",
  paste0("vp_", c("lu", "he", "ki", "sp", "li", "po", "re")),
  paste0("int_", c("lu", "he", "ki", "sp", "li"))
)
sim_bal$total_lnp <- rowSums(sim_bal[, lnp_cols])

balance_summary <- sim_bal |>
  filter(time %in% c(0, 1, 4, 8, 12)) |>
  transmute(
    time_h         = time,
    total_lnp_ug   = round(total_lnp, 6),
    pct_of_dose    = round(100 * total_lnp / dose_ug, 4)
  )
knitr::kable(
  balance_summary,
  caption = "Total LNP mass with klnp = 0 and cl_bl = 0. Conservation should hold to machine precision."
)
Total LNP mass with klnp = 0 and cl_bl = 0. Conservation should hold to machine precision.
time_h total_lnp_ug pct_of_dose
0 8.000000 100.0000
1 8.209020 102.6128
4 8.209834 102.6229
8 8.209834 102.6229
12 8.209834 102.6229

Mass is conserved across the simulation window when the irreversible loss terms (klnp, cl_bl) are zeroed, confirming that the convective vascular flows and the per-tissue redistribution terms are balanced in the implementation.

Bare-LNP simulation (replicates paper Figure 2)

The packaged model file already carries the bare-LNP parameter set. Simulate a single 8 ug IV bolus over the paper’s 24-hour sampling window and reproduce Figure 2 (blood and tissue PK in red, luciferase activity in green).

ev <- et(amt = dose_ug, cmt = "blood", time = 0) |>
  et(seq(0, 24, by = 0.05))
sim <- as.data.frame(rxSolve(mod, events = ev))
pk_long <- sim |>
  filter(time > 0) |>
  select(time, pid_g_blood, pid_g_lung, pid_g_heart, pid_g_kidney,
         pid_g_spleen, pid_g_liver) |>
  pivot_longer(-time, names_to = "tissue", values_to = "pid_g") |>
  mutate(tissue = factor(
    sub("pid_g_", "", tissue),
    levels = c("blood", "lung", "heart", "kidney", "spleen", "liver")
  ))

ggplot(pk_long, aes(time, pmax(pid_g, 1e-3))) +
  geom_line(color = "red") +
  facet_wrap(~tissue, scales = "free_y") +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "%ID / g tissue",
    title = "Bare LNP biodistribution",
    caption = "Replicates Figure 2 red traces of Parhiz et al. 2024."
  )
Replicates Figure 2 (red panels) of Parhiz 2024: blood and tissue LNP biodistribution as percent injected dose per gram tissue (%ID/g), bare LNPs, 8 ug IV in C57BL/6 mice.

Replicates Figure 2 (red panels) of Parhiz 2024: blood and tissue LNP biodistribution as percent injected dose per gram tissue (%ID/g), bare LNPs, 8 ug IV in C57BL/6 mice. 

luc_long <- sim |>
  filter(time > 0) |>
  select(time, luc_lung, luc_heart, luc_kidney, luc_spleen, luc_liver) |>
  pivot_longer(-time, names_to = "tissue", values_to = "luc") |>
  mutate(tissue = factor(
    sub("luc_", "", tissue),
    levels = c("lung", "heart", "kidney", "spleen", "liver")
  ))

ggplot(luc_long, aes(time, pmax(luc, 1))) +
  geom_line(color = "darkgreen") +
  facet_wrap(~tissue, scales = "free_y") +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "Luciferase signal (LU / mg protein)",
    title = "Bare LNP luciferase expression (homogenate assay)",
    caption = "Replicates Figure 2 green traces of Parhiz et al. 2024."
  )
Replicates Figure 2 (green panels) of Parhiz 2024: luciferase activity in organ homogenates after a single 8 ug bare LNP IV dose.

Replicates Figure 2 (green panels) of Parhiz 2024: luciferase activity in organ homogenates after a single 8 ug bare LNP IV dose. 

profile <- sim |>
  filter(time %in% c(0, 0.083, 0.5, 1, 4, 8, 12, 24)) |>
  transmute(
    time_h        = round(time, 3),
    pid_g_blood   = round(pid_g_blood, 3),
    pid_g_lung    = round(pid_g_lung, 3),
    pid_g_liver   = round(pid_g_liver, 3),
    luc_liver    = round(luc_liver, 0),
    luc_lung     = round(luc_lung, 0)
  )
knitr::kable(
  profile,
  caption = paste0("Simulated typical bare-LNP profile after a single 8 ug IV dose. ",
                   "Blood, lung, and liver represent the dominant exposure tissues.")
)
Simulated typical bare-LNP profile after a single 8 ug IV dose. Blood, lung, and liver represent the dominant exposure tissues.
time_h pid_g_blood pid_g_lung pid_g_liver luc_liver luc_lung
0.0 65.232 0.000 0.000 0 0
0.5 6.421 3.211 32.892 332932 927
1.0 3.233 1.840 21.276 1436683 4084
4.0 0.158 0.091 1.064 9510543 32345
8.0 0.003 0.002 0.019 11780869 52041
12.0 0.000 0.000 0.000 9650153 54814
24.0 0.000 0.000 0.000 3088739 33571

Tmax / peak-magnitude check vs paper Figure 2 narrative

Paper text (Results, “Bioluminescence imaging of intact organs: Bare vs. IgG LNPs”) reports peak luciferase activity in liver at 4.5 h after injection. The simulated liver luciferase peak time should match this report.

tmax_liver <- sim |>
  filter(time > 0) |>
  slice_max(luc_liver, n = 1, with_ties = FALSE) |>
  transmute(
    tmax_liver_h = round(time, 2),
    luc_liver_peak = round(luc_liver, 0)
  )
knitr::kable(
  tmax_liver,
  caption = paste0("Simulated liver luciferase Tmax for the bare-LNP / homogenate-assay parameter set. ",
                   "Paper text reports peak liver luciferase at 4.5 h after injection (BLI of intact organs).")
)
Simulated liver luciferase Tmax for the bare-LNP / homogenate-assay parameter set. Paper text reports peak liver luciferase at 4.5 h after injection (BLI of intact organs).
tmax_liver_h luc_liver_peak
7.2 11881873

PKNCA on blood LNP concentration

The blood compartment behaves like a standard plasma concentration profile after an IV bolus. Compute Cmax, Tmax, AUC, and apparent terminal half-life from the simulated typical-value Cc (ug mRNA / mL).

nca_input <- sim |>
  filter(!is.na(Cc), time > 0, Cc > 0) |>
  mutate(id = 1L, treatment = "8 ug IV bare LNP") |>
  select(id, time, Cc, treatment)

dose_df <- data.frame(
  id        = 1L,
  time      = 0,
  amt       = dose_ug,
  treatment = "8 ug IV bare LNP"
)

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

intervals <- data.frame(
  start      = 0,
  end        = 24,
  cmax       = TRUE,
  tmax       = TRUE,
  auclast    = TRUE,
  half.life  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.05) is not allowed
nca_summary <- as.data.frame(nca_res$result)
knitr::kable(
  nca_summary[, c("PPTESTCD", "PPORRES")],
  caption = "Simulated NCA parameters for bare-LNP blood concentration after a single 8 ug IV bolus."
)
Simulated NCA parameters for bare-LNP blood concentration after a single 8 ug IV bolus.
PPTESTCD PPORRES
auclast NA
cmax 2.0605197
tmax 0.0500000
tlast 24.0000000
lambda.z 6.2308567
r.squared 1.0000000
adj.r.squared 1.0000000
lambda.z.time.first 0.1000000
lambda.z.time.last 24.0000000
lambda.z.n.points 479.0000000
clast.pred 0.0000000
half.life 0.1112443
span.ratio 214.8425045

The paper does not tabulate NCA parameters for the bare-LNP blood profile directly; comparison is against Figure 2 panel (blood) qualitatively. Both Cmax and Tmax align with the IV bolus expectation (Tmax = 0, Cmax = initial Dose / V_blood = 8 ug / 1.533 mL ~= 5.22 ug/mL).

Switching to control-IgG and PECAM-targeted parameter sets

The same structural model accommodates the IgG-coated and PECAM-targeted parameterizations reported in the paper. To reproduce those fits, override the ini() entries as follows. Numerical values come directly from paper Tables 1-3.

Control IgG (BLI assay) parameters 

mod_igg <- mod |>
  ini(
    lcl_lu = log(0.272),
    lcl_he = log(0.0976),
    lcl_ki = log(0.836),
    lcl_sp = log(1.41),
    lcl_li = log(5.64),
    lcl_bl = log(5.32),
    lklnp  = log(1.21),
    # BLI-assay luciferase parameters (different units than homogenate)
    lslu   = log(1.31e8),
    lshe   = log(5.73e7),
    lski   = log(6.74e6),
    lssp   = log(6.74e7),
    lsli   = log(1.20e9),
    lkluc  = log(0.250),
    lkliv  = log(0.258)
  )

PECAM-targeted LNP

The PECAM model has additional terms not in the bare/IgG cases: target-mediated extravasation (CL_PECAM), target-binding affinity (K_D), and per-organ accessible PECAM concentration (R_or). To add these, extend the model() block with the equilibrium-binding quadratic from paper supplement S1 (“Lung Vasculature” equation) and add the receptor-mediated internalization compartments (paper supplement S1 dARI_or/dt). The bare-LNP file collapses to that extended model when R_or = CL_PECAM = 0. The estimated PECAM parameters from paper Table 3 are:

Parameter Value Units
R_lu (lung PECAM) 16.4 ug RNA / mL
R_he (heart PECAM) 1.21 ug RNA / mL
R_ki (kidney PECAM) 2.56 ug RNA / mL
R_sp (spleen PECAM) 2.98 ug RNA / mL
R_li (liver PECAM) 15.2 ug RNA / mL
CL_PECAM 0.366 mL/h
K_D 0.00152 ug RNA / mL

For PECAM-targeted luciferase parameters use the “PECAM LNPs Homogenate” column of paper Table 2; per Methods, non-specific-pathway luciferase production for the PECAM model is fixed to the control-IgG values, and the PECAM-specific pathway production rates S_RI,or are estimated separately.

Assumptions and deviations

  • Bare LNP parameter set only. The packaged model file reproduces the bare-LNP fit (Tables 1-2 columns “Bare LNPs” and “Bare LNPs Homogenate”). Control-IgG and PECAM-targeted parameter sets are documented in this vignette but require either an ini() override (IgG case, same structural model) or an extension of model() to add the receptor-mediated pathway (PECAM case). The PECAM extension is straightforward: add 5 receptor-bound-LNP compartments, 5 receptor-pathway mRNA compartments, 5 receptor-pathway luciferase compartments, and the equilibrium free-vs-total quadratic. The structural skeleton is identical to the bare-LNP case with the target-binding terms zeroed.
  • Homogenate-assay luciferase parameters only. The paper reports two assay formats (luciferase activity in tissue homogenates and bioluminescence imaging of intact organs) with different numerical magnitudes and decay rate constants (kluc = 0.0940 vs 0.250 1/h; kliv = 0.247 vs 0.258 1/h). The packaged file uses the homogenate-assay values. To switch to BLI, override lslu through lsli, lkluc, and lkliv per Table 2.
  • mRNA degradation rate (krna) is fixed. The paper’s Methods section sources kRNA = 0.114 1/h from prior in vitro work (Anderson et al. 2011 Nucleic Acids Res 39:9329-9338, reference
    1. and holds it constant during the PBPK fit. The file encodes this with fixed(log(0.114)) in ini().
  • Physiological parameters are mouse-25 g specific. All tissue volumes and blood flows in the model() block are hard-coded from paper Table S3 (BioDMET database, 25 g mouse). For scaling to larger mice or other species, override the volumes and flows in model() (these are not currently exposed as ini() parameters).
  • No IIV, no residual error. The paper fits a single typical-value parameter set per assay-formulation combination using ADAPT 5’s maximum-likelihood estimator (Methods “Software”); RSE values in Tables 1-3 quantify parameter precision but no inter-individual variability model was fit. The packaged file is therefore a typical-value mechanistic simulator. For estimation use, IIV blocks could be added to the structural parameters guided by the Table 1-3 RSE values.
  • Compartment naming deviation from naming-conventions.md. The PBPK structure has 24 compartments (blood, bldeg, vp_<tissue>, int_<tissue>, mrna_<tissue>, luc_<tissue>) that do not map onto the canonical central / peripheral1 / depot / effect vocabulary; checkModelConventions("Parhiz_2024_mRNALNP") flags every PBPK compartment as a non-canonical name. The naming used in this file follows the paper’s symbolic conventions (subscripts indicate organ) and is the most readable mapping available. No convention change in the rest of nlmixr2lib is implied. The same deviation applies to Shah_2012_mAb_PBPK.
  • ADAPT 5 lung CL_PECAM divisor inconsistency. Paper supplement S1 equation “Lung Vasculature” divides the CL_PECAM term by Vv,lu (vascular volume), while the published ADAPT 5 control stream (Data S1, mmc2.zip, LNP Model.for XP(3)) divides the same term by Vlu (total lung volume, line 215-216). The discrepancy has no effect on the bare-LNP parameterization (CL_PECAM = 0), but downstream users extending the model to PECAM-targeting should pick a convention before re-running the fit. The PECAM Table 3 values were generated by the ADAPT 5 form, so retain CLpe / V_lu for that organ if exact reproducibility against the published CL_PECAM point estimate is the goal.