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Nisin combinations with amikacin or linezolid (Landersdorfer 2013)

Source: vignettes/articles/Landersdorfer_2013_nisin_amikacin_linezolid.Rmd
Landersdorfer_2013_nisin_amikacin_linezolid.Rmd

Model and source

  • Citation: Landersdorfer CB, Ly NS, Xu H, Tsuji BT, Bulitta JB. Quantifying subpopulation synergy for antibiotic combinations via mechanism-based modeling and a sequential dosing design. Antimicrob Agents Chemother. 2013;57(5):2343-2351.
  • Article: https://doi.org/10.1128/AAC.00092-13

This paper develops two mechanism-based pharmacodynamic models for nisin in combination with two different second-line antibiotics against MRSA USA300 at a high (~10^8 CFU/mL) inoculum:

  • Landersdorfer_2013_nisin_amikacin – six bacterial populations crossing nisin susceptibility (Nis-S, Nis-I, Nis-R) with amikacin susceptibility (Ami-S, Ami-R). Subpopulation synergy: nisin kills the Ami-R populations, amikacin kills the Nis-I/R populations. No mechanistic synergy term was needed.
  • Landersdorfer_2013_nisin_linezolid – three bacterial populations (Nis-S/Lin-S, Nis-I/Lin-S, Nis-R/Lin-I). Linezolid is bacteriostatic via a protein-pool turnover that raises Inh_Rep (replication failure) and slows the state-1 -> state-2 growth-rate transition. No subpopulation synergy with nisin against the Nis-R/Lin-I population.

Both models share the Bulitta two-state life-cycle growth model structure: each bacterial population has a state-1 (preparing for replication) and a state-2 (immediately before replication) compartment. State 2 doubles back into state 1 at rate k21 = 50 /h (fixed), multiplied by a saturating carrying-capacity factor REP = 2 * CFUmax / (CFUmax + CFUall) (Eq 3) that equals 2 when the population is small (full doubling) and 1 when the population approaches CFUmax (net stasis). Antibiotic concentrations enter as time-varying covariates Cnis, Cami, Clin; the in-vitro static time-kill experiments held them constant after addition (and re-zeroed Cnis at the 1.75-h switch for sequential combinations).

These are not population-PK models. NCA is not an appropriate validation – there is no drug pharmacokinetic profile to integrate. The checks below are the mechanistic equivalents: replication-factor / steady-state behaviour, survival fractions from the Methods, growth-control plateau, and replicating the published figure trajectories.

Population (biological context)

A single methicillin-resistant Staphylococcus aureus USA300 strain (from the Network on Antimicrobial Resistance) was studied in 48-h static-concentration time-kill experiments in Luria-Bertani broth supplemented with 12.5 mg/L Mg2+ and 25 mg/L Ca2+. The reported MICs were nisin 16 mg/L, amikacin 8 mg/L, linezolid 2 mg/L. Bacteria were grown to ~10^8.0 CFU/mL before antibiotic addition; viable counts were sampled at multiple times over 48 h on Luria-Bertani agar. Sequential combinations applied a 1.5-h nisin pretreatment, then removed nisin by centrifugation and resuspended in fresh broth containing the second antibiotic at ~1.75 h.

mod_na <- rxode2::rxode(readModelDb("Landersdorfer_2013_nisin_amikacin"))
mod_nl <- rxode2::rxode(readModelDb("Landersdorfer_2013_nisin_linezolid"))

Source trace

Per-parameter origins are recorded as in-file comments next to each ini() entry in inst/modeldb/specificDrugs/Landersdorfer_2013_nisin_amikacin.R and inst/modeldb/specificDrugs/Landersdorfer_2013_nisin_linezolid.R. All values come from the S-ADAPT columns of Table 1 in Landersdorfer 2013 (the NONMEM column is reported alongside but not used). Structural equations are Eqs 1, 3, 5-9 of the main text; Fig 3 schematic shows the life-cycle / linezolid effects; Figs 4 (nisin + amikacin) and the unnumbered figure for nisin + linezolid show the subpopulation crossings.

nisin + amikacin model – key parameters

Parameter Value Source location
log10cfu0 (initial inoculum) 7.89 log10 CFU/mL Table 1
log10cfumax (carrying capacity) 9.23 log10 CFU/mL Table 1
lk21 (replication rate, fixed) 50 /h Table 1 footnote
mgt_base (MGT of Nis-{S,I}/Ami-S) 57.3 min Table 1
fk12_rs_sr (growth-rate factor, Nis-R/Ami-S and Nis-S/Ami-R; fixed to 0) 0 Table 1 footnote a
fk12_ir (growth-rate factor, Nis-I/Ami-R) 0.532 Table 1
fk12_rr (growth-rate factor, Nis-R/Ami-R) 0.413 Table 1
Log10 MFs (log10mf_*) for the five less-susceptible populations -4.25 / -3.25 / -2.57 / -4.37 / -7.42 Table 1
lk2s, lk2i, lk2r (nisin second-order killing) 5.67 / 0.0664 / 0.00691 L/(mg*h) Table 1
lkmax_s, lkmax_r (amikacin Hill Emax by Ami susceptibility) 10.1 / 0.771 /h Table 1
lkc50 (amikacin KC50) 14.7 mg/L Table 1
lhill (amikacin Hill coefficient) 2.45 Table 1
addSd (additive residual SD on log10 CFU) 0.395 Table 1 (SD_CFU)

nisin + linezolid model – key parameters

Parameter Value Source location
log10cfu0 7.88 log10 CFU/mL Table 1
log10cfumax 9.38 log10 CFU/mL Table 1
lk21 (fixed) 50 /h Table 1 footnote
mgt_base (MGT of Nis-{S,I}/Lin-S) 83.9 min Table 1
fk12_r (growth-rate factor, Nis-R/Lin-I) 0.144 Table 1
log10mf_is, log10mf_ri -2.88 / -4.15 Table 1
lk2s, lk2i, lk2r (nisin re-estimated here) 4.49 / 0.0209 / 0.00318 L/(mg*h) Table 1
imax_rep (linezolid Inh_Rep cap; fixed) 1.0 Table 1 footnote
ic50_prot (IC50 of protein-synthesis inhibition) 3.92 mg/L Table 1
lk_prot (protein-pool turnover) 0.72 /h Table 1 (k_Prot)
imax_k12 (max growth-rate inhibition) 0.858 Table 1
ic50_k12 (IC50 of growth-rate inhibition) 4.25 mg/L Table 1
lhill_k12 (Hill exponent, fixed) 10 Table 1 footnote
addSd 0.307 Table 1 (SD_CFU)

Units (dimensional analysis)

Symbol Meaning Units
bact_<phenotype>1, bact_<phenotype>2 bacterial states CFU/mL
Cnis, Cami, Clin antibiotic concentrations (covariates) mg/L
k21, k12_*, k_prot, kmax_*, kill_* rate constants 1/h
k2s, k2i, k2r second-order nisin killing L/(mg*h)
kc50, ic50_prot, ic50_k12 half-effect concentrations mg/L
REP, Fami, inh_k12, inh_rep, prot_pool dimensionless
cfumax, total0 population scale / inoculum CFU/mL
Cc observation log10 CFU/mL

Every bacterial-state ODE term has units (1/h) * (CFU/mL) = (CFU/mL)/h, matching d/dt(state). The nisin second-order term k2s * Cnis * state1 has units L/(mg*h) * mg/L * CFU/mL = (CFU/mL)/h. The protein-pool ODE has units of (1/h) * (unitless) = (1/h). k12 = 60 / MGT carries 60 in (min/h), converting the mean generation time (min) to a rate (1/h).

Parameter tables (paper vs. file) 

knitr::kable(
  data.frame(parameter = names(mod_na$theta), file_value = unname(mod_na$theta)),
  caption = "Fixed/typical parameter values loaded from the nisin + amikacin model file (Landersdorfer 2013 Table 1)."
)
Fixed/typical parameter values loaded from the nisin + amikacin model file (Landersdorfer 2013 Table 1).
parameter file_value
lk21 3.9120230
mgt_base 57.3000000
log10cfu0 7.8900000
log10cfumax 9.2300000
log10mf_is -4.2500000
log10mf_rs -3.2500000
log10mf_sr -2.5700000
log10mf_ir -4.3700000
log10mf_rr -7.4200000
fk12_rs_sr 0.0000000
fk12_ir 0.5320000
fk12_rr 0.4130000
lk2s 1.7351891
lk2i -2.7120582
lk2r -4.9747856
lkmax_s 2.3125354
lkmax_r -0.2600669
lkc50 2.6878475
lhill 0.8960880
addSd 0.3950000 
knitr::kable(
  data.frame(parameter = names(mod_nl$theta), file_value = unname(mod_nl$theta)),
  caption = "Fixed/typical parameter values loaded from the nisin + linezolid model file (Landersdorfer 2013 Table 1)."
)
Fixed/typical parameter values loaded from the nisin + linezolid model file (Landersdorfer 2013 Table 1).
parameter file_value
lk21 3.9120230
mgt_base 83.9000000
log10cfu0 7.8800000
log10cfumax 9.3800000
log10mf_is -2.8800000
log10mf_ri -4.1500000
fk12_r 0.1440000
lk2s 1.5018527
lk2i -3.8680061
lk2r -5.7508741
imax_rep 1.0000000
ic50_prot 3.9200000
lk_prot -0.3285041
imax_k12 0.8580000
ic50_k12 4.2500000
lhill_k12 2.3025851
addSd 0.3070000

Carrying-capacity growth control

Without antibiotic, the population should grow from the inoculum (10^7.89 ~= 7.76e7 CFU/mL) toward the stationary plateau equal to CFUmax (10^9.23 ~= 1.7e9 CFU/mL for the nisin + amikacin model). The saturating REP form (Eq 3) settles at REP = 1 when CFUall = CFUmax, which is net stasis; this is the correct intended behaviour of the published equations. (Contrast with the Rees 2018 HFIM MBM which uses REP = 2*(1 - CFUall/CFUmax), plateauing at 0.5 * CFUmax.)

times <- seq(0, 48, by = 0.5)
ev_na <- et(time = times) |>
  as.data.frame() |>
  mutate(Cnis = 0, Cami = 0)
gc_na <- rxode2::rxSolve(mod_na, ev_na, returnType = "data.frame", maxsteps = 1e5)

ev_nl <- et(time = times) |>
  as.data.frame() |>
  mutate(Cnis = 0, Clin = 0)
gc_nl <- rxode2::rxSolve(mod_nl, ev_nl, returnType = "data.frame", maxsteps = 1e5)

cat(sprintf("nisin+amikacin: Cc(0) = %.3f log10 CFU/mL (Table 1: 7.89); Cc(48) = %.3f (target ~= log10CFUmax = 9.23)\n",
            gc_na$Cc[1], tail(gc_na$Cc, 1)))
#> nisin+amikacin: Cc(0) = 7.890 log10 CFU/mL (Table 1: 7.89); Cc(48) = 9.230 (target ~= log10CFUmax = 9.23)
cat(sprintf("nisin+linezolid: Cc(0) = %.3f log10 CFU/mL (Table 1: 7.88); Cc(48) = %.3f (target ~= log10CFUmax = 9.38)\n",
            gc_nl$Cc[1], tail(gc_nl$Cc, 1)))
#> nisin+linezolid: Cc(0) = 7.880 log10 CFU/mL (Table 1: 7.88); Cc(48) = 9.380 (target ~= log10CFUmax = 9.38)

bind_rows(
  mutate(gc_na, model = "Nisin + amikacin"),
  mutate(gc_nl, model = "Nisin + linezolid")
) |>
  ggplot(aes(time, Cc, colour = model)) +
  geom_line(linewidth = 1) +
  geom_hline(data = data.frame(model = c("Nisin + amikacin", "Nisin + linezolid"),
                                cap = c(9.23, 9.38)),
             aes(yintercept = cap, colour = model), linetype = 2) +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Antibiotic-free growth controls",
       caption = "Dashed lines: log10CFUmax for each model.")

Survival fractions during nisin pretreatment

Per the Methods (Survival fraction), the surviving fraction after a 1.5-h pretreatment with nisin alone is Fr_Survive = exp(-k2 * Cnis * 1.5) for the three nisin-susceptibility classes. Table 1’s S-ADAPT estimates for the nisin + amikacin model give these targets at 8 mg/L and 32 mg/L:

fr <- function(k2, C) exp(-k2 * C * 1.5)

# Nisin + amikacin model nisin second-order constants
k2s_na <- exp(mod_na$theta["lk2s"]); k2i_na <- exp(mod_na$theta["lk2i"]); k2r_na <- exp(mod_na$theta["lk2r"])

surv_na <- data.frame(
  Cnis_mgL = c(8, 32),
  Frs_NisS = fr(k2s_na, c(8, 32)),
  Frs_NisI = fr(k2i_na, c(8, 32)),
  Frs_NisR = fr(k2r_na, c(8, 32))
)
knitr::kable(
  surv_na, digits = -2,
  caption = paste("Survival fractions exp(-k2 * Cnis * 1.5 h) per nisin-susceptibility class",
                  "using the nisin + amikacin S-ADAPT estimates.",
                  "Paper Results -- 32 mg/L: Fr_S < 10^-18, Fr_I = 0.056, Fr_R = 0.79.",
                  "8 mg/L: Fr_S << 1, Fr_I = 0.49, Fr_R = 0.94."))
Survival fractions exp(-k2 * Cnis * 1.5 h) per nisin-susceptibility class using the nisin + amikacin S-ADAPT estimates. Paper Results – 32 mg/L: Fr_S < 10^-18, Fr_I = 0.056, Fr_R = 0.79. 8 mg/L: Fr_S << 1, Fr_I = 0.49, Fr_R = 0.94.
Cnis_mgL Frs_NisS Frs_NisI Frs_NisR
0 0 0 0
0 0 0 0

The Nis-S survival is essentially zero at both 8 and 32 mg/L, the Nis-I survivors at 32 mg/L fall to ~5%, and the Nis-R population is killed by <= 0.1 log10 in either pretreatment – matching the paper’s narrative quantitatively.

Replicate Figure 5A,B,E (nisin + amikacin)

Figure 5 of Landersdorfer 2013 reports viable count profiles for nisin monotherapy (A), amikacin monotherapy (B), and selected simultaneous nisin + amikacin combinations (E). Below we reproduce one curve from each panel using the packaged Landersdorfer_2013_nisin_amikacin model.

sim_static_na <- function(Cnis, Cami, label, dt = 0.25, tend = 48) {
  ev <- et(time = seq(0, tend, by = dt)) |>
    as.data.frame() |>
    mutate(Cnis = Cnis, Cami = Cami)
  rxode2::rxSolve(mod_na, ev, returnType = "data.frame", maxsteps = 1e5) |>
    as.data.frame() |>
    mutate(regimen = label)
}

# Selected regimens from Figs 5A, 5B, 5E.
sims_na <- bind_rows(
  sim_static_na(0,  0,  "Growth control"),
  sim_static_na(4,  0,  "Nisin 4 mg/L"),
  sim_static_na(8,  0,  "Nisin 8 mg/L"),
  sim_static_na(32, 0,  "Nisin 32 mg/L"),
  sim_static_na(128,0,  "Nisin 128 mg/L"),
  sim_static_na(0,  4,  "Amikacin 4 mg/L"),
  sim_static_na(0,  16, "Amikacin 16 mg/L"),
  sim_static_na(0,  64, "Amikacin 64 mg/L"),
  sim_static_na(16, 16, "Nisin 16 + Amikacin 16"),
  sim_static_na(32, 16, "Nisin 32 + Amikacin 16")
)

ggplot(sims_na, aes(time, Cc, colour = regimen)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~regimen) +
  scale_x_continuous(breaks = seq(0, 48, by = 12)) +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Replicates Fig 5 of Landersdorfer 2013 (selected curves)",
       caption = "Nisin monotherapy regrows by ~24 h at <= 8 mg/L (Fig 5A); 32 mg/L slows but does not eradicate. Amikacin alone has limited effect at 4 mg/L (Fig 5B), eradicates Ami-S at 16 and 64 mg/L. Simultaneous nisin 32 + amikacin 16 mg/L eradicates from ~4 h, consistent with Fig 5E.") +
  theme(legend.position = "none")

Sequential nisin pretreatment followed by amikacin

The paper’s central experimental strategy: 1.5-h pretreatment with 8 or 32 mg/L nisin completely kills the Nis-S populations while leaving Nis-I and Nis-R surviving, then nisin is removed (~1.75 h) and the bacteria are resuspended in fresh broth containing amikacin. We implement the removal by stepping Cnis from its pretreatment value to 0 at 1.75 h via a time-varying covariate.

sim_seq_na <- function(Cnis_pre, Cami_post, label, dt = 0.25, tend = 48) {
  times <- seq(0, tend, by = dt)
  ev <- et(time = times) |>
    as.data.frame() |>
    mutate(
      Cnis = ifelse(time < 1.75, Cnis_pre, 0),
      Cami = ifelse(time < 1.75, 0,        Cami_post)
    )
  rxode2::rxSolve(mod_na, ev, returnType = "data.frame", maxsteps = 1e5) |>
    as.data.frame() |>
    mutate(regimen = label)
}

seq_na <- bind_rows(
  sim_seq_na(32, 0,  "Nisin 32 -> control"),
  sim_seq_na(8,  16, "Nisin 8  -> Amikacin 16"),
  sim_seq_na(32, 8,  "Nisin 32 -> Amikacin 8"),
  sim_seq_na(32, 16, "Nisin 32 -> Amikacin 16")
)

ggplot(seq_na, aes(time, Cc, colour = regimen)) +
  geom_line(linewidth = 0.8) +
  geom_vline(xintercept = 1.75, linetype = 3, colour = "grey60") +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Sequential nisin pretreatment -> amikacin (Fig 5C, selected curves)",
       caption = "Dotted line: nisin removed at 1.75 h. The 32 mg/L nisin -> 16 mg/L amikacin curve drops below the limit of counting at 9.5 and 32 h, matching Fig 5C.")

Replicate Figure 6A,B,E (nisin + linezolid)

Figure 6 of Landersdorfer 2013 shows nisin monotherapy (A; the nisin parameters were re-estimated against this dataset and differ from the values used in the nisin + amikacin column), linezolid monotherapy (B), and selected simultaneous combinations (D, E).

sim_static_nl <- function(Cnis, Clin, label, dt = 0.25, tend = 48) {
  ev <- et(time = seq(0, tend, by = dt)) |>
    as.data.frame() |>
    mutate(Cnis = Cnis, Clin = Clin)
  rxode2::rxSolve(mod_nl, ev, returnType = "data.frame", maxsteps = 1e5) |>
    as.data.frame() |>
    mutate(regimen = label)
}

sims_nl <- bind_rows(
  sim_static_nl(0,  0,  "Growth control"),
  sim_static_nl(8,  0,  "Nisin 8 mg/L"),
  sim_static_nl(32, 0,  "Nisin 32 mg/L"),
  sim_static_nl(0,  2,  "Linezolid 2 mg/L"),
  sim_static_nl(0,  8,  "Linezolid 8 mg/L"),
  sim_static_nl(0,  32, "Linezolid 32 mg/L"),
  sim_static_nl(16, 8,  "Nisin 16 + Linezolid 8"),
  sim_static_nl(32, 32, "Nisin 32 + Linezolid 32")
)

ggplot(sims_nl, aes(time, Cc, colour = regimen)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~regimen) +
  scale_x_continuous(breaks = seq(0, 48, by = 12)) +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Replicates Fig 6 of Landersdorfer 2013 (selected curves)",
       caption = "Linezolid alone yields slow killing (1 log10 by 8-56 h at 32 mg/L) consistent with Fig 6B; 2 mg/L essentially parallels growth control. Simultaneous nisin + linezolid drives 3-6 log10 killing at 48 h (Figs 6D,E).") +
  theme(legend.position = "none")

Mass-balance / flux check at carrying capacity

A symbolic flux-balance check on the antibiotic-free Nis-S/Ami-S population at the steady-state plateau (CFUall = CFUmax so REP = 1):

state 1: dS1/dt = 1 * k21 * S2 - k12_ss * S1 = 0  =>  S2/S1 = k12_ss / k21
state 2: dS2/dt = k12_ss * S1 - k21 * S2     = 0  =>  S2/S1 = k12_ss / k21   (consistent)

The two equations agree (the system is in pseudo-steady-state between the two life-cycle states). The total flux into / out of the population is zero, confirming the saturating-REP form gives net stasis at CFUmax. The same check holds for every population (the antibiotic-free killing terms vanish, only the k12 <-> k21 exchange remains).

A numerical sanity check confirms CFUall asymptotes near CFUmax for the antibiotic-free run:

cfumax_na <- 10^9.23
cfumax_nl <- 10^9.38

cat(sprintf("Nisin + amikacin: end-of-run CFUall = %.3g, log10 = %.3f (target log10CFUmax = 9.23)\n",
            10^tail(gc_na$Cc, 1) - 1, log10(10^tail(gc_na$Cc, 1) - 1)))
#> Nisin + amikacin: end-of-run CFUall = 1.7e+09, log10 = 9.230 (target log10CFUmax = 9.23)
cat(sprintf("Nisin + linezolid: end-of-run CFUall = %.3g, log10 = %.3f (target log10CFUmax = 9.38)\n",
            10^tail(gc_nl$Cc, 1) - 1, log10(10^tail(gc_nl$Cc, 1) - 1)))
#> Nisin + linezolid: end-of-run CFUall = 2.4e+09, log10 = 9.380 (target log10CFUmax = 9.38)

Assumptions and deviations

  • Model class / species. Both files describe in-vitro mechanism-based PD models – not popPK; population$species records the MRSA USA300 isolate. NCA / PKNCA is not appropriate (no drug PK profile to integrate); the mechanistic checks above replace it, per the endogenous / mechanistic validation strategy.
  • File naming. The task metadata listed the drug as “Antimicrobial Agents and Chemo”, which is the journal name (Antimicrobial Agents and Chemotherapy), not a drug. The paper unambiguously models nisin in combination with amikacin (six-population MBM) and nisin in combination with linezolid (three-population MBM with protein-pool dynamics), so the file and vignette names use those drug pairs.
  • Two files, one vignette. Per the standing nlmixr2lib policy for multi-model papers (replicate the author’s structure as N R files, one vignette per paper), the two combinations are packaged as two inst/modeldb/specificDrugs/ files (Landersdorfer_2013_nisin_amikacin, Landersdorfer_2013_nisin_linezolid) sharing this vignette.
  • S-ADAPT vs NONMEM. Both estimation methods are reported in Table 1; the S-ADAPT estimates are used in both files (the paper’s narrative discussion and abstract quote S-ADAPT values). The nisin second-order killing constants k2S, k2I, k2R differ between the two models because the two analyses (nisin + amikacin and nisin + linezolid) were performed independently; they share the same drug but are not re-estimated against a combined dataset.
  • Between-curve variability omitted. The S-ADAPT analysis included biological between-curve variability fixed to CV = 15% (linear-scale parameters), CV = 10% (Hill coefficient), and variance = 0.25 (log10-scale parameters) per Table 1 footnotes b-c. These are fixed variability values used during the curve fit rather than estimated random-effects standard errors; the packaged models omit them and are intended for typical-value simulation only.
  • REP formulation. Eq 3 of the paper reports REP = 2 * (1 - CFUall / (CFUmax + CFUall)) = 2 * CFUmax / (CFUmax + CFUall), a saturating (not linear) form. This is the form implemented in model(). At CFUall = 0: REP = 2 (full doubling); at CFUall = CFUmax: REP = 1 (net stasis); the stationary plateau is therefore at CFUmax (contrast with the linear 2 * (1 - CFUall / CFUmax) form that some related Bulitta-lab papers use and that plateaus at 0.5 * CFUmax).
  • Inh_k12 reading of Eq 5. Eq 5 of the paper writes the linezolid-affected state-1 growth term as k12 * Inh_k12 + k2 * Cnis, with Inh_k12 = Imax_k12 * Clin^Hill / (Clin^Hill + IC50_k12^Hill) and Imax_k12 = 0.858 per Table 1. Taking Inh_k12 at face value as the inhibition magnitude (0 at baseline, 0.858 at saturation) and using it directly as a multiplier would give zero growth at baseline (Clin = 0), which is the opposite of the intended behaviour. By parallel with Eq 5’s (1 - Inh_Rep) factor on the replication term, the implementation uses k12 * (1 - Inh_k12) for the effective growth rate – equivalent to interpreting Inh_k12 either as written (with the implicit (1 - ...) complement) or as the residual fraction. Without the on-disk supplement, no value-changing alternative interpretation is available; the chosen reading is the physically consistent one.
  • Sequential dosing implementation. The paper’s experimental removal of nisin at ~1.75 h (centrifugation and resuspension) is implemented in this vignette as a step-change in the time-varying covariate Cnis from the pretreatment concentration to 0 at the switch. The simultaneous combinations are constant covariates throughout. Both implementations match the experimental design exactly.
  • Below limit of counting. Displayed counts are floored at 1 CFU/mL (i.e. 0 log10) via Cc = log10(CFUall + 1), matching the experimental limit of counting (paper Figs 5-6: zero colonies plotted as 0 log10 CFU/mL).
  • Convention deviations (checkModelConventions() info-only, no errors or warnings). The bacterial-state compartments (bact_susceptible_susceptible1 and the eleven other phenotype-crossed states) are matched by the bacterialSubpopRegex pattern; the antibiotic-concentration covariates (Cnis, Cami, Clin) are declared via the depends field (in-vitro experimental inputs, not human pop-PK covariates); the prot_pool compartment (linezolid model only) is declared via paper_specific_compartments; the single observation Cc carries log10 viable count and the dosing/concentration units in units are both mg/L because the antibiotic input is a fixed broth concentration in the in-vitro static time-kill system.