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Camostat / FOY-251 TMPRSS2 PK/PD against SARS-CoV-2 (Kosinsky 2022)

Source: vignettes/articles/Kosinsky_2022_camostat.Rmd
Kosinsky_2022_camostat.Rmd

Model and source

Kosinsky et al. (2022) built a semi-mechanistic PK/PD model for the oral serine protease inhibitor camostat mesylate and its active metabolite FOY-251, to predict inhibition of host TMPRSS2 and, through it, of SARS-CoV-2 cell entry. The paper contributes two packaged models:

  • Kosinsky_2022_camostat_invitro – the in-vitro PD model fit to cell-free recombinant TMPRSS2 activity and SARS-2-S pseudovirus entry (Hoffmann et al. 2020 data). It estimates the inhibition constant ki, the half-maximal activity ki50, and the Hill coefficient.
  • Kosinsky_2022_camostat_pkpd – the in-vivo semi-mechanistic PK/PD model: one-compartment FOY-251 PK driving a TMPRSS2 covalent-inhibition turnover model, with the PD parameters carried from the in-vitro fit. It is used for the dose-regimen simulations.
inv <- readModelDb("Kosinsky_2022_camostat_invitro")
pkpd <- readModelDb("Kosinsky_2022_camostat_pkpd")
  • Citation: Kosinsky Y, Peskov K, Stanski DR, Wetmore D, Vinetz J. Semi-Mechanistic Pharmacokinetic-Pharmacodynamic Model of Camostat Mesylate-Predicted Efficacy against SARS-CoV-2 in COVID-19. Microbiol Spectr. 2022;10(2):e02167-21. doi:10.1128/spectrum.02167-21. PK parameters in Table 1; PD parameters in Table 2; the in-vivo PK/PD ODEs are Equations 1 and 5 of Materials and Methods.
  • Article: https://doi.org/10.1128/spectrum.02167-21 (open access, CC BY 4.0)
  • Supplement: publisher supplementary PDF (ELF-compartment extension, Figures S1-S4).

Population

The PK model was fit to digitised human FOY-251 plasma profiles: a 12-h intravenous infusion of camostat (Midgley et al. 1994, Xenobiotica 24:79-92) and a single oral dose from the FOIPAN package insert (Kosinsky 2022 Results, Figure S1). Because camostat is hydrolysed by plasma esterases too rapidly to quantify, FOY-251 is the only measured analyte. The FOY-251 volume of distribution (22.4 L) approximates the extracellular water space and the terminal half-life is about 0.6 h.

The PD parameters come from in-vitro experiments of Hoffmann et al. (2020): recombinant TMPRSS2 enzymatic activity after 1 h incubation with FOY-251, and SARS-2-S-driven pseudovirus entry after 2 h incubation. No subject-level cohort or between-subject variability was reported; the model is deterministic and used for dose-regimen simulations.

Both models expose this provenance through their population metadata, e.g. readModelDb("Kosinsky_2022_camostat_pkpd")()$population.

Source trace

In-vivo PK/PD model (Kosinsky_2022_camostat_pkpd):

Equation / parameter Value Source location
lka (ka) 0.67 1/h Table 1 (RSE 5.78%)
lfdepot (F) 0.051 Table 1 (RSE 4.66%)
lvc (Vd) 22.36 L Table 1 (RSE 7.07%)
lkel (kel) 1.22 1/h Table 1 (RSE 4.70%)
propSd 0.14 Table 1 (RSE 17.3%)
lki (ki) 45638.51 nM Table 2 (RSE 7.46%)
kcat (fixed) 400 1/h Table 2 (fixed)
kdis (fixed) 0.049 1/h Table 2 (fixed; 14 h complex half-life)
kdeg (fixed) 0.0575 1/h Methods = log(2)/12 h (assumed enzyme half-life)
lki50 (Ksp) 0.047 Table 2 (RSE 42.4%)
hill (h) 0.59 Table 2 (RSE 16.6%)
d/dt(depot), d/dt(central) n/a Equation 1
d/dt(target), d/dt(complex) n/a Equation 5
viralentry (Hill) n/a Equation 4

In-vitro model (Kosinsky_2022_camostat_invitro): the same ki (estimated), kcat/kdis (fixed), ki50, and hill, with additive residual error addSd_tmprss2 = 0.0346 (Table 2 a1 = 3.46%) and addSd_viralentry = 0.0758 (Table 2 a2 = 7.58%); in-vitro ODEs are Equation 3 and the viral-entry link is Equation 4.

In-vitro model: TMPRSS2 inhibition and viral entry

The in-vitro model integrates the covalent-inhibition ODEs at a fixed applied FOY-251 concentration (CONC_FOY251_NM), reading TMPRSS2 activity at 1 h and viral entry at 2 h. We sweep the applied concentration to reproduce the dose-response relationships of Figure 2.

conc_grid <- 10^seq(1, 6, length.out = 80) # nM
obs_times <- c(0, 0.5, 1, 1.5, 2)
# This model has two `~` residual endpoints (TMPRSS2 activity and viral entry),
# so observation rows carry `cmt = "target"` (a real ODE state) with an explicit
# `dvid`, and `useLinCmt = FALSE` keeps the dvid mapping intact. rxSolve returns
# both `tmprss2` and `viralentry` as columns regardless. No dose is needed --
# the model sets target(0) = 1 internally.
ev_inv <- lapply(seq_along(conc_grid), function(i) {
  data.frame(
    id = i, time = obs_times, amt = NA_real_, cmt = "target",
    evid = 0L, dvid = 1L, CONC_FOY251_NM = conc_grid[i]
  )
}) |>
  dplyr::bind_rows()

sim_inv <- rxode2::rxSolve(inv, ev_inv, keep = "CONC_FOY251_NM", useLinCmt = FALSE) |>
  as.data.frame()
#> Warning: multi-subject simulation without without 'omega'

act_1h <- sim_inv |>
  dplyr::filter(abs(time - 1) < 1e-6) |>
  dplyr::transmute(conc = CONC_FOY251_NM, tmprss2_activity = tmprss2)
ve_2h <- sim_inv |>
  dplyr::filter(abs(time - 2) < 1e-6) |>
  dplyr::transmute(conc = CONC_FOY251_NM, viral_entry = viralentry)
# Replicates Figure 2A of Kosinsky 2022: recombinant TMPRSS2 activity (relative
# to control) versus FOY-251 concentration after 1 h incubation.
ggplot(act_1h, aes(conc, tmprss2_activity)) +
  geom_line() +
  scale_x_log10() +
  labs(
    x = "FOY-251 (nM)", y = "Relative TMPRSS2 activity",
    title = "Figure 2A - TMPRSS2 activity vs FOY-251 (1 h)",
    caption = "Replicates Figure 2A of Kosinsky 2022."
  )

# Replicates Figure 2C of Kosinsky 2022: viral entry rate as a function of the
# model-predicted remaining TMPRSS2 activity (Hill-Langmuir link, Equation 4).
act_grid <- tibble::tibble(sp = 10^seq(-3, 0, length.out = 200))
ksp <- 0.047
h <- 0.59
act_grid$viral_entry <- act_grid$sp^h / (act_grid$sp^h + ksp^h)
ggplot(act_grid, aes(sp, viral_entry)) +
  geom_line() +
  geom_vline(xintercept = ksp, linetype = "dashed") +
  scale_x_log10() +
  labs(
    x = "Relative TMPRSS2 activity", y = "Relative viral entry rate",
    title = "Figure 2C - viral entry vs TMPRSS2 activity",
    caption = "Dashed line: activity = ki50 = 0.047 (50% viral entry)."
  )

The key published claim is that about 95% inhibition of TMPRSS2 is required for 50% inhibition of the viral entry rate. By construction of the Hill-Langmuir half-maximum, viral entry equals 50% exactly when remaining TMPRSS2 activity equals ki50 = 0.047 (i.e. 95.3% TMPRSS2 inhibition).

ve_at_ki50 <- ksp^h / (ksp^h + ksp^h)
tmprss2_inhibition_at_half_entry <- 1 - ksp
stopifnot(
  # Half-maximal viral entry is at activity = ki50 (structural identity).
  abs(ve_at_ki50 - 0.5) < 1e-8,
  # which corresponds to ~95% TMPRSS2 inhibition.
  abs(tmprss2_inhibition_at_half_entry - 0.953) < 1e-3
)
ve_at_ki50
#> [1] 0.5
tmprss2_inhibition_at_half_entry
#> [1] 0.953

In-vivo PK/PD: dose-regimen simulations

The in-vivo model is simulated to steady state for each camostat dosing regimen. Camostat mesylate doses in mg are converted to FOY-251-equimolar nmol using the camostat mesylate molecular weight (494.52 g/mol; see Assumptions).

mw_camostat_mesylate <- 494.52 # g/mol (camostat mesylate salt, PubChem CID 5284360)
to_nmol <- function(mg) mg / mw_camostat_mesylate * 1e6

regimens <- tibble::tribble(
  ~regimen,    ~mg,  ~tau,
  "200 q8h",   200,  8,
  "200 q6h",   200,  6,
  "400 q6h",   400,  6,
  "600 q6h",   600,  6
)

sim_one <- function(mg, tau) {
  horizon <- 24 * 10
  t0 <- horizon - tau
  ev <- rxode2::et() |>
    rxode2::et(amt = to_nmol(mg), ii = tau, until = horizon, cmt = "depot") |>
    rxode2::et(seq(t0, horizon, length.out = 400))
  s <- rxode2::rxSolve(pkpd, ev, atol = 1e-10, rtol = 1e-8, maxsteps = 1e6)
  s[s$time >= t0, ]
}

time_avg <- function(x, t) {
  sum(diff(t) * (head(x, -1) + tail(x, -1)) / 2) / (max(t) - min(t))
}

ss_tab <- regimens |>
  rowwise() |>
  mutate(
    .sim = list(sim_one(mg, tau)),
    Cc_avg = time_avg(.sim$Cc, .sim$time),
    TMPRSS2_pct = time_avg(.sim$tmprss2, .sim$time),
    ViralEntry_pct = time_avg(.sim$viralentry, .sim$time)
  ) |>
  ungroup() |>
  select(regimen, Cc_avg, TMPRSS2_pct, ViralEntry_pct)
# Table 3 of Kosinsky 2022 (time-averaged model outcomes at steady state).
published3 <- tibble::tribble(
  ~regimen,  ~Cc_avg_pub, ~TMPRSS2_pub, ~ViralEntry_pub,
  "200 q8h",  96.6,        14.9,         64.2,
  "200 q6h",  129,         10.3,         59.9,
  "400 q6h",  258,         6.06,         51.5,
  "600 q6h",  386,         4.38,         46.4
)

cmp3 <- ss_tab |>
  left_join(published3, by = "regimen") |>
  mutate(
    Cc_pct_diff = 100 * (Cc_avg - Cc_avg_pub) / Cc_avg_pub,
    TMPRSS2_abs_diff = TMPRSS2_pct - TMPRSS2_pub,
    VE_abs_diff = ViralEntry_pct - ViralEntry_pub
  )

cmp3 |>
  transmute(
    Regimen = regimen,
    `Cc_avg sim (nM)` = round(Cc_avg, 1),
    `Cc_avg pub (nM)` = Cc_avg_pub,
    `TMPRSS2% sim` = round(TMPRSS2_pct, 2),
    `TMPRSS2% pub` = TMPRSS2_pub,
    `ViralEntry% sim` = round(ViralEntry_pct, 1),
    `ViralEntry% pub` = ViralEntry_pub
  ) |>
  knitr::kable(caption = "Table 3 reproduction: time-averaged steady-state outcomes.")
Table 3 reproduction: time-averaged steady-state outcomes.
Regimen Cc_avg sim (nM) Cc_avg pub (nM) TMPRSS2% sim TMPRSS2% pub ViralEntry% sim ViralEntry% pub
200 q8h 94.5 96.6 15.17 14.90 64.4 64.2
200 q6h 126.0 129.0 10.43 10.30 60.2 59.9
400 q6h 252.0 258.0 6.18 6.06 51.8 51.5
600 q6h 378.0 386.0 4.48 4.38 46.7 46.4 
# Deterministic model (no IIV): TMPRSS2 activity and viral entry reproduce the
# published values to within a fraction of a percentage point; Cc_avg is within
# a few percent (the residual is absorption-phase averaging detail not in the
# closed form). These are numerical bounds on a deterministic solve, so they
# are tight on purpose.
stopifnot(
  max(abs(cmp3$TMPRSS2_abs_diff)) < 0.5,
  max(abs(cmp3$VE_abs_diff)) < 0.5,
  max(abs(cmp3$Cc_pct_diff)) < 5
)
# Replicates Figure 3 of Kosinsky 2022: FOY-251 concentration, TMPRSS2 activity
# and viral entry rate over one steady-state dosing interval for 200 mg q6h.
prof <- sim_one(200, 6)
prof$t_rel <- prof$time - min(prof$time)
prof |>
  select(t_rel, Cc, tmprss2, viralentry) |>
  tidyr::pivot_longer(c(Cc, tmprss2, viralentry)) |>
  mutate(name = recode(name,
    Cc = "FOY-251 (nM)",
    tmprss2 = "TMPRSS2 activity (%)",
    viralentry = "Viral entry rate (%)"
  )) |>
  ggplot(aes(t_rel, value)) +
  geom_line() +
  facet_wrap(~name, scales = "free_y", ncol = 1) +
  labs(
    x = "Time within dosing interval (h)", y = NULL,
    title = "Figure 3 - 200 mg q6h steady-state profiles",
    caption = "Replicates Figure 3 of Kosinsky 2022 (200 mg q6h panel)."
  )

PKNCA validation (FOY-251 PK)

The published FOY-251 terminal elimination half-life of about 0.6 h is the kel-governed disposition half-life derived from the intravenous data. Because absorption is slower than elimination (ka = 0.67 < kel = 1.22 1/h), an oral profile shows flip-flop kinetics and its apparent terminal slope reflects ka, not kel; so NCA is run here on an intravenous bolus, which exposes the true elimination half-life.

ev_iv <- rxode2::et() |>
  rxode2::et(amt = to_nmol(200), cmt = "central") |>
  rxode2::et(seq(0, 8, length.out = 300))
sim_iv <- rxode2::rxSolve(pkpd, ev_iv)

sim_nca <- as.data.frame(sim_iv) |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::mutate(id = 1L, treatment = "200 mg IV bolus") |>
  dplyr::select(id, time, Cc, treatment)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)
dose_df <- data.frame(id = 1L, time = 0, amt = to_nmol(200), treatment = "200 mg IV bolus")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)
intervals <- data.frame(
  start = 0, end = Inf,
  cmax = TRUE, tmax = TRUE, aucinf.obs = TRUE, half.life = TRUE
)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
nca_wide <- tidyr::pivot_wider(
  as.data.frame(nca_res$result),
  id_cols = treatment, names_from = PPTESTCD, values_from = PPORRES
)
nca_wide |>
  dplyr::rename(
    "Treatment" = treatment,
    "Cmax (nM)" = cmax,
    "Tmax (h)" = tmax,
    "AUCinf (nM*h)" = aucinf.obs,
    "t1/2 (h)" = half.life
  ) |>
  knitr::kable(caption = "PKNCA summary for a single 200 mg intravenous bolus.")
PKNCA summary for a single 200 mg intravenous bolus.
Treatment Cmax (nM) Tmax (h) tlast clast.obs lambda.z r.squared adj.r.squared lambda.z.time.first lambda.z.time.last lambda.z.n.points clast.pred t1/2 (h) span.ratio AUCinf (nM*h)
200 mg IV bolus 18087.32 0 8 1.043906 1.22 1 1 0.0267559 8 299 1.043906 0.5681535 14.03361 14825.69 
thalf <- nca_wide$half.life[nca_wide$treatment == "200 mg IV bolus"]
# Published elimination half-life "about 0.6 h" (= log(2)/kel = log(2)/1.22).
stopifnot(abs(thalf - log(2) / 1.22) < 0.05)
thalf
#> [1] 0.5681535

Assumptions and deviations

  • Camostat mesylate molecular weight (494.52 g/mol). The paper treats the camostat dose as equimolar to FOY-251 (Methods) but reports only the FOY-251 molecular weight (313 g/mol). To convert clinical mg doses of camostat mesylate to the model’s nmol dose, the maintainers used the camostat mesylate (salt) molecular weight of 494.52 g/mol (a standard chemical constant, PubChem CID 5284360). This value reproduces the published Table 3 Cc_avg to within a few percent across all simulated regimens, confirming the salt (rather than free-base) molecular weight is the correct one.
  • In-vitro residual error scale. Table 2 reports the constant residual error parameters a1 (3.46%) and a2 (7.58%) as percentages. The maintainers encoded them as additive error on the fraction-of-baseline scale (0.0346 and 0.0758), matching the in-vitro readouts, which are relative activities.
  • TMPRSS2 enzyme half-life (12 h). The in-vivo degradation rate kdeg = 0.0575 1/h was computed by the authors from an assumed 12 h enzyme half-life (no literature estimate was available); ksynt = kdeg follows from the baseline activity being 1 (Equation 5).
  • PD parameters shared across the two models. ki, kcat, kdis, ki50, and hill were estimated (or fixed) in the in-vitro model and reused as fixed inputs in the in-vivo PK/PD model, exactly as the authors did.
  • No between-subject variability. The model was fit to digitised literature profiles and used for deterministic simulations; no IIV or subject cohort was reported, so none was introduced.
  • ELF-compartment extension excluded. The supplement adds an epithelial lining fluid compartment (parameters ktr_elf, kel_elf) explored over four hypothetical scenarios (Figures S2-S4) rather than estimated from data. As a sensitivity exploration with no fitted parameters, it is not part of the packaged models.
  • No correction notice for this article was found as of 2026-10-01.