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Alpha-synuclein pathology and anti-aSyn immunotherapy in PD-like mice (Ivanova 2024)

Source: vignettes/articles/Ivanova_2024_synucleinopathy_qsp.Rmd
Ivanova_2024_synucleinopathy_qsp.Rmd

Model and source

  • Citation: Ivanova O, Karelina T. Quantitative systems pharmacology model of alpha-synuclein pathology in Parkinson’s disease-like mouse for investigation of passive immunotherapy mechanisms. CPT Pharmacometrics Syst Pharmacol. 2024;13(10):1798-1809. doi:10.1002/psp4.13223. Model structure, rate laws and every parameter value are taken from the Supporting Information: the Heta-compiler model export (PSP4-13-1798-s001.xlsx; sheets Compartment / Species / Reaction / Record / Const / Process / TimeSwitcher) and the supplementary methods document (PSP4-13-1798-s002.docx, equations S1-S28).
  • Article: https://doi.org/10.1002/psp4.13223
  • Supplement (Heta model export, XLSX): https://doi.org/10.1002/psp4.13223 Supporting Information PSP4-13-1798-s001.xlsx
  • Supplement (supplementary methods and equations S1-S28): Supporting Information PSP4-13-1798-s002.docx

Ivanova and Karelina built a whole-brain quantitative systems pharmacology (QSP) model of alpha-synuclein (aSyn) pathology in mice, and used it to ask which mechanism of action could make anti-aSyn passive immunotherapy work. The main article contains no equations and no parameter values: it states that “model equations are given in the Model code”, and the entire executable model is published as a Heta-compiler export in the Supporting Information. This extraction is taken from that export, cross-checked term-by-term against the supplementary equation list S1-S28.

The model tracks three aSyn conformers (monomer, oligomer, fibril) in six brain matrices plus CSF, an auxiliary “inflammatory mediator” (IM) variable representing microglial activation, a dopaminergic-neurodegeneration hazard, and a two-compartment antibody PK layer with a brain compartment.

mod <- readModelDb("Ivanova_2024_synucleinopathy_qsp")
ui <- rxode2::rxode(mod)
length(ui$state)
#> [1] 27
ui$state
#>  [1] "aSyn_CSF"      "aSynO_CSF"     "aSyn_BIF"      "aSynO_BIF"    
#>  [5] "aSynFm_BIF"    "aSyn_BIFstr"   "aSynO_BIFstr"  "aSynFm_BIFstr"
#>  [9] "aSyn_BC"       "aSynO_BC"      "aSynFm_BC"     "aSyn_STR"     
#> [13] "aSynO_STR"     "aSynFm_STR"    "aSyn_MG"       "aSynO_MG"     
#> [17] "aSynFm_MG"     "aSyn_MGstr"    "aSynO_MGstr"   "aSynFm_MGstr" 
#> [21] "IM_BIF"        "IM_BIFstr"     "l_prob"        "depot"        
#> [25] "central"       "peripheral1"   "isf"

Population

This is a deterministic typical-value preclinical model: there is no individual-level cohort, no inter-individual variability and no residual error term. It was calibrated and validated against aggregate published data from six experimental PD-like mouse models (paper Table 1) plus a set of in vitro datasets (Figures S1-S2):

  • Wild-type C57BL/6 mice, the untreated reference state.
  • Thy1 (line 61) transgenic mice overexpressing human wild-type aSyn about twofold, with uniform expression across brain regions.
  • A53T (M83) transgenic mice, 1.7-fold overexpression plus twofold higher baseline striatal expression, with and without a 12.5 ug intrastriatal preformed-fibril (PFF) challenge.
  • Viral-vector models: rAAV2/7 and lentiviral human A53T aSyn injected into the striatum (3- to 6-fold overexpression).
  • Wild-type + 5 ug intrastriatal PFF.
  • TLR2 knockout A53T mice, modelled as a 50% reduction in microglial activation.

Body weight is fixed at 0.025 kg and every compartment volume is derived from it. Antibody PK was fitted to MEDI1341 data in rat (Figure S2f); the mouse-scaled parameters in the Const sheet were reused unchanged for prasinezumab and cinpanemab, whose rodent PK is unpublished.

The same information is available programmatically via rxode2::rxode(readModelDb("Ivanova_2024_synucleinopathy_qsp"))$population.

Source trace

Every ini() entry in inst/modeldb/therapeuticArea/Ivanova_2024_synucleinopathy_qsp.R carries an in-file comment naming the exact sheet and row of the Heta export it came from (Const!<id>, Record!<id>, TimeSwitcher!<id>). The structural provenance is:

Model element Source location
Compartment volumes (BR, PL, CSF, BIF, BIFstr, BC, STR, MG, MGstr) s001.xlsx sheet Compartment, column assignments.ode_; physiological fractions justified in s002.docx “Volumes of compartments”
Initial conditions (1e-20 nM for every aSyn pool) s001.xlsx sheet Species, column assignments.start_
57 aSyn / antibody rate laws s001.xlsx sheet Reaction, column assignments.ode_ (transcribed verbatim)
IM secretion / elimination, neurodegeneration hazard, antibody disposition s001.xlsx sheet Process, column assignments.ode_
ODE stoichiometry (which flux enters which state, with what sign) s001.xlsx actors column, cross-checked against s002.docx equations S1-S28
Derived rate constants and reported outputs s001.xlsx sheet Record
Parameter values s001.xlsx sheet Const (96 entries). 85 of the 92 ini() entries were machine-diffed against Const/Record and match to within 1e-6 relative; the remaining seven are the five SW_* encoding switches, time_PFF_flow_off (TimeSwitcher!evt_PFF_flow) and aSyn_MW (s002.docx prose). Ten Const entries are not shipped – see Errata.
Experimental-arm events (transgenic, viral, PFF, immunotherapy, anti-inflammatory) s001.xlsx sheet TimeSwitcher + the per-event assignment columns
Aggregation equations and modelling assumptions in prose s002.docx “aSyn aggregation”, “Model assumptions”
Experimental arms and overexpression rates Paper Table 1
Mechanism-of-action definitions (MoA 1-4) Paper Results, “Passive immunotherapy simulation in mouse PD models”

Units

Heta stores aSyn species as concentrations and writes each flux in nmol/h with the compartment volume carried explicitly, so every aSyn ODE has the form d/dt(X) = (sum of fluxes) / V. This is exactly the form printed in the supplement (S1-S20). Antibody species are amounts in mg.

Symbol class Units Example
aSyn states nM aSyn_BC, aSynO_STR, aSynFm_BIF
aSyn fluxes (V_*) nmol/h V_olig_aSyn_BC = BC * k_olig_aSyn_BC * ...
Compartment volumes L BC = 2.32e-4, BIFstr = 3.80e-6
First-order rate constants 1/h k_deg_aSyn_BC, k_sec_aSyn_BC_BIF
Second-order aggregation constants L/nmol/h k_olig_aSyn_BC, k_gr_aSynFm_BC
Saturable Vmax terms nmol/L/h k_upt_aSynO_BIF_BC, k_deg_aSynO_BC
Bulk flows (Q_*) L/h Q_BIF_CSF, Q_CSF_PL
IM, l_prob, switches, Emax, Hill dimensionless IM_BIF, aggr_coef_IM
Antibody states mg central, peripheral1, isf
Antibody concentrations nM Cc, Ig_nM_ISFtot

A dimensional check that constrains the whole model: Dose_PFFstr (the nM bolus the export adds to striatal ISF) must equal the injected mass divided by the striatal ISF volume and the 14 kDa monomer mass. The model computes both independently, and they must agree.

Heta Process records contribute directly to d/dt and are NOT divided by a compartment volume, unlike Reaction records. The supplement’s equations S21, S22 and S28 print a / BIF divisor for the IM and hazard states; that divisor is a template artefact. Two independent checks below confirm the undivided form: it is what makes the healthy-brain IM level equal 1 (as the supplement states explicitly), and it is what keeps the neurodegeneration hazard physiological. Dividing by BIF (7.8e-5 L) would inflate IM by a factor of about 12,800 and drive neuron loss to 100% immediately.

Scenario helper

The Heta export encodes each experimental arm as a TimeSwitcher that is inactive by default, so the packaged defaults are the untreated wild-type mouse. The SW_* switches turn each arm on. Insults are timed at t = 2000 h, which is what the paper uses, allowing the wild-type baseline to establish first.

T_PFF <- 2000     # intrastriatal PFF injection (h)
T_AB  <- T_PFF + 168   # immunotherapy starts 1 week later, per the paper

# Mechanism-of-action definitions, paper Results section.
moa <- list(
  none = c(sw_mAb_BC_upt = 0, sw_mAb_MG_upt = 0, sw_mAb_MG_deg = 0, sw_mAb_aggr = 0),
  MoA1 = c(sw_mAb_BC_upt = 1, sw_mAb_MG_upt = 0, sw_mAb_MG_deg = 0, sw_mAb_aggr = 0),
  MoA2 = c(sw_mAb_BC_upt = 1, sw_mAb_MG_upt = 1, sw_mAb_MG_deg = 1, sw_mAb_aggr = 0),
  MoA3 = c(sw_mAb_BC_upt = 0, sw_mAb_MG_upt = 0, sw_mAb_MG_deg = 0, sw_mAb_aggr = 1),
  MoA4 = c(sw_mAb_BC_upt = 0, sw_mAb_MG_upt = 1, sw_mAb_MG_deg = 1, sw_mAb_aggr = 1)
)

sim_arm <- function(pff = FALSE, tg = FALSE, tg_over = 1.7, bc_str_coef = 4,
                    virus = FALSE, aav = 3, virus_time = 2000,
                    mab = "none", mgkg = 20,
                    im_inh = NULL, im_start = T_AB,
                    days = 120, grid = 12) {
  ev <- rxode2::et(amt = 0, time = 0, cmt = "depot")
  if (pff) {
    ev <- rxode2::et(ev, amt = 93984, time = T_PFF, cmt = "aSynO_BIFstr")
  }
  if (mab != "none") {
    ev <- rxode2::et(ev, amt = mgkg * 0.025, time = T_AB, cmt = "central",
                     ii = 168, addl = ceiling(days * 24 / 168))
  }
  ev <- rxode2::et(ev, seq(0, T_PFF + days * 24, by = grid))
  p <- c(SW_PFF = as.numeric(pff),
         SW_TG = as.numeric(tg), Tg_over = tg_over, BC_STR_coef = bc_str_coef,
         SW_VIRUS = as.numeric(virus), AAV = aav, virus_time = virus_time,
         moa[[mab]])
  if (!is.null(im_inh)) {
    p <- c(p, SW_IM_INH = 1, IM_inh_rate = im_inh, time_IM_inh = im_start)
  }
  rxode2::rxSolve(mod, ev, params = p, atol = 1e-12, rtol = 1e-10,
                  maxsteps = 1e6, useLinCmt = FALSE, returnType = "data.frame")
}

# value of `v` at `dpi` days after the insult
at_dpi <- function(s, dpi, v) s[[v]][which.min(abs(s$time - (T_PFF + dpi * 24)))]

Wild-type baseline

The wild-type mouse has no insult and no drug, so the model should relax to a stable physiological baseline. This is the steady-state check for a mechanistic model, and here it doubles as a quantitative gate because the paper reports several wild-type values.

wt <- sim_arm(days = 120)

tail_rows <- wt$time >= 3500
drift <- vapply(c("aSyn_BC", "aSynO_BC", "IM_BIF", "aSyn_tot_BR"),
                function(v) diff(range(wt[[v]][tail_rows])) / mean(wt[[v]][tail_rows]),
                numeric(1))
round(drift, 5)
#>     aSyn_BC    aSynO_BC      IM_BIF aSyn_tot_BR 
#>     0.00001     0.00021     0.00479     0.00005

# The system is at steady state over the last ~700 h of the run.
stopifnot(all(drift < 0.02))
stopifnot(!anyNA(wt$aSyn_BC), !anyNA(wt$Cc))
f <- wt[nrow(wt), ]

baseline_tbl <- tibble::tribble(
  ~Quantity,                                    ~Simulated,                  ~Published,   ~Source,
  "IM level in the healthy brain",              f$IM_BIF,                    1,            "s002.docx: 'Baseline IM level in the healthy brain was set at 1'",
  "Striatal : non-striatal aSyn monomer ratio", f$aSyn_STR / f$aSyn_BC,      4,            "Results: non-transgenic mice have 'fourfold higher aSyn levels in the striatum'",
  "Total brain aSyn (nM)",                      f$aSyn_tot_BR,               0.2,          "Results / Figure 2a: 'just under 0.2 nM in wt mice'",
  "Oligomer share of total brain aSyn (%)",     f$aSynO_BR_perc,             10,           "Results: oligomer 'about 10% of total in wt mice'",
  "PFF bolus (nM into striatal ISF)",           f$aSyn_dose_BIFstr_ug,       93984,        "Const!Dose_PFFstr vs Record!aSyn_dose_BIFstr_ug"
) |>
  dplyr::mutate(`Ratio` = Simulated / Published)

knitr::kable(baseline_tbl, digits = 4,
             caption = "Wild-type baseline versus values reported by Ivanova 2024.")
Wild-type baseline versus values reported by Ivanova 2024.
Quantity Simulated Published Source Ratio
IM level in the healthy brain 1.0092 1.0 s002.docx: ‘Baseline IM level in the healthy brain was set at 1’ 1.0092
Striatal : non-striatal aSyn monomer ratio 3.9696 4.0 Results: non-transgenic mice have ‘fourfold higher aSyn levels in the striatum’ 0.9924
Total brain aSyn (nM) 0.1578 0.2 Results / Figure 2a: ‘just under 0.2 nM in wt mice’ 0.7891
Oligomer share of total brain aSyn (%) 6.4364 10.0 Results: oligomer ‘about 10% of total in wt mice’ 0.6436
PFF bolus (nM into striatal ISF) 94102.5906 93984.0 Const!Dose_PFFstr vs Record!aSyn_dose_BIFstr_ug 1.0013

Two of these are tight, independent confirmations of structural decisions:

  • IM = 1.009 against a stated 1. This validates both the k0_IM = Q_BIF_CSF * k_el_IM / BIF form taken from the Heta Record sheet (the supplementary prose gives a different, non-reproducing formula) and the decision not to divide Process fluxes by a compartment volume.
  • Striatal enrichment 3.97-fold against a stated fourfold, which validates BC_STR_coef = 4 and the derived striatal / non-striatal volumes. Note the supplementary prose says striatal synthesis is “5 times greater”; the Const sheet says 4, and the main text’s “fourfold” agrees with the Const sheet.

The PFF dose conversion agrees to 0.13%, which independently confirms the chain of derived compartment volumes.

wt |>
  dplyr::select(time, Monomer = aSyn_BC, Oligomer = aSynO_BC, Fibril = aSynFm_BC) |>
  tidyr::pivot_longer(-time, names_to = "Conformer", values_to = "conc") |>
  ggplot(aes(time / 24, conc, colour = Conformer)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Concentration in non-striatal brain cells (nM)",
       title = "Wild-type baseline: intraneuronal aSyn reaches a stable steady state",
       caption = "Steady-state check for a mechanistic model; no published figure counterpart.")

Perturbation-recovery

Displacing an intracellular pool away from baseline should return it to the same attractor. This catches sign errors and missing terms that a steady-state check at the correct baseline can miss.

ev_p <- rxode2::et(amt = 0, time = 0, cmt = "depot") |>
  rxode2::et(seq(0, 6000, by = 25))

pert <- lapply(c(0.25, 1, 4), function(mult) {
  s <- rxode2::rxSolve(mod, ev_p,
                       inits = c(aSyn_BC = mult * f$aSyn_BC,
                                 aSynO_BC = mult * f$aSynO_BC),
                       atol = 1e-12, rtol = 1e-10, maxsteps = 1e6,
                       useLinCmt = FALSE, returnType = "data.frame")
  s$start <- paste0(mult, "x baseline")
  s
}) |> dplyr::bind_rows()

# every arm returns to the same attractor
recovered <- pert |> dplyr::group_by(start) |>
  dplyr::summarise(final_aSyn_BC = dplyr::last(aSyn_BC), .groups = "drop")
knitr::kable(recovered, digits = 6, caption = "Recovery to a common baseline.")
Recovery to a common baseline.
start final_aSyn_BC
0.25x baseline 0.22027
1x baseline 0.22027
4x baseline 0.22027 
stopifnot(diff(range(recovered$final_aSyn_BC)) / mean(recovered$final_aSyn_BC) < 0.01)
ggplot(pert, aes(time / 24, aSyn_BC, colour = start)) +
  geom_line(linewidth = 0.7) +
  geom_hline(yintercept = f$aSyn_BC, linetype = "dashed") +
  labs(x = "Time (days)", y = "Monomeric aSyn in brain cells (nM)", colour = "Initial value",
       title = "Perturbation-recovery: a single stable attractor",
       caption = "Dashed line: the untreated wild-type steady state.")

Transgenic and viral overexpression (Figure 2a)

Paper Table 1 specifies each arm’s overexpression rate, and the Results section adds a crucial second ingredient: “Non-transgenic mice have fourfold higher aSyn levels in the striatum compared with other brain regions, whereas transgenic mice have a more uniform expression of aSyn in all brain regions.” So a transgenic arm changes two things: Tg_over and BC_STR_coef.

arms <- list(
  `wild type`               = list(),
  `Thy1 line 61 (2x, uniform)` = list(tg = TRUE, tg_over = 2,   bc_str_coef = 1),
  `A53T M83 (1.7x, 2x striatal)` = list(tg = TRUE, tg_over = 1.7, bc_str_coef = 2),
  `viral A53T (3x)`         = list(virus = TRUE, aav = 3, virus_time = 0),
  `viral A53T (6x)`         = list(virus = TRUE, aav = 6, virus_time = 0)
)

overexp <- lapply(names(arms), function(nm) {
  s <- do.call(sim_arm, c(arms[[nm]], list(days = 120)))
  g <- s[nrow(s), ]
  tibble::tibble(Arm = nm,
                 `Total aSyn (nM)` = g$aSyn_tot_BR,
                 `Oligomer (%)`    = g$aSynO_BR_perc,
                 `Fibril (%)`      = g$aSynFm_BR_perc,
                 `Microglial activation (IM)` = g$IM_BIF + g$IM_BIFstr)
}) |> dplyr::bind_rows() |>
  dplyr::mutate(`Fold vs wild type` = `Total aSyn (nM)` / `Total aSyn (nM)`[1])

knitr::kable(overexp, digits = 3,
             caption = "Replicates Figure 2a/2b of Ivanova 2024: fold increase in total and aggregated aSyn across PD-like models.")
Replicates Figure 2a/2b of Ivanova 2024: fold increase in total and aggregated aSyn across PD-like models.
Arm Total aSyn (nM) Oligomer (%) Fibril (%) Microglial activation (IM) Fold vs wild type
wild type 0.158 6.436 0.667 2.350 1.000
Thy1 line 61 (2x, uniform) 0.669 17.117 1.774 12.327 4.238
A53T M83 (1.7x, 2x striatal) 0.326 11.048 1.145 4.922 2.064
viral A53T (3x) 0.493 55.524 6.095 394.902 3.126
viral A53T (6x) 4.111 70.013 6.915 995.229 26.050

The Thy1 line-61 arm gives 4.24-fold total brain aSyn with 17.1% oligomer, against the paper’s “about five times higher” and “about 10% of total in wt mice and 20% in tg mice”. Both land close, and they only do so once the uniform-expression reading of Table 1 is applied - with the wild-type BC_STR_coef = 4 retained the same arm reaches only 1.25-fold, which would have looked like a translation error.

Antibody PK and target engagement 

pk_arms <- lapply(c(10, 20, 50), function(d) {
  ev <- rxode2::et(amt = d * 0.025, time = 0, cmt = "central") |>
    rxode2::et(seq(0, 1344, by = 2))
  s <- rxode2::rxSolve(mod, ev, atol = 1e-12, rtol = 1e-10, maxsteps = 1e6,
                       useLinCmt = FALSE, returnType = "data.frame")
  s$treatment <- paste0(d, " mg/kg")
  s$id <- d
  s
}) |> dplyr::bind_rows()

ggplot(pk_arms, aes(time / 24, Cc, colour = treatment)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Plasma antibody (nM)", colour = NULL,
       title = "Anti-aSyn antibody PK after a single IV dose in mouse",
       caption = "Structure and parameters from Const sheet; fitted to MEDI1341 rat data (Figure S2f).")

The paper reports no tabulated NCA parameters for the antibody in mouse (the PK was fitted graphically to rat data), so there is no published NCA table to compare against. PKNCA is used here to characterise the packaged model and to test one claim the paper does make.

sim_nca <- pk_arms |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment)

sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, treatment) |> dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- pk_arms |>
  dplyr::distinct(id, treatment) |>
  dplyr::mutate(time = 0, amt = id * 0.025)
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_tbl <- as.data.frame(nca_res) |>
  dplyr::select(treatment, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES) |>
  dplyr::rename("Dose" = treatment, "Cmax (nM)" = cmax, "Tmax (h)" = tmax,
                "AUCinf (nM*h)" = aucinf.obs, "t1/2 (h)" = half.life)
knitr::kable(nca_tbl, digits = 3,
             caption = "PKNCA characterisation of the packaged antibody PK model (no published mouse NCA table exists).")
PKNCA characterisation of the packaged antibody PK model (no published mouse NCA table exists).
Dose 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)
10 mg/kg 2424.242 0 1344 0 0.013 1 1 2 1344 672 0 54.481 24.632 108661.9
20 mg/kg 4848.485 0 1344 0 0.013 1 1 2 1344 672 0 54.485 24.631 217334.6
50 mg/kg 12121.212 0 1344 0 0.013 1 1 2 1344 672 0 54.495 24.626 543413.6 
# The paper states MoA2 outcomes "did not depend on MEDI1341 doses from 10 to
# 50 mg/kg". A necessary condition is that exposure is near dose-proportional,
# i.e. the saturable Fc-receptor-like term is far from saturation.
dn <- nca_tbl$`AUCinf (nM*h)` / c(10, 20, 50)
round(dn / dn[1], 4)
#> [1] 1.0000 1.0000 1.0002
stopifnot(max(abs(dn / dn[1] - 1)) < 0.05)

Dose-normalised AUC is constant to within 0.019% across 10-50 mg/kg: the Kd_Fc saturable term (10,000 mg/L) sits far above the achieved plasma concentrations, so the antibody layer is effectively linear over the paper’s dose range. That is the mechanistic reason the paper’s MoA2 predictions were dose-insensitive.

te <- sim_arm(pff = TRUE, mab = "MoA2", mgkg = 10, days = 40, grid = 2)
win <- te$time >= T_AB & te$time <= T_AB + 168
te_tbl <- tibble::tibble(
  Quantity = c("Plasma antibody (nM)", "Brain-ISF antibody (nM)",
               "Aggregate target engagement (%)"),
  Peak   = c(max(te$Cc[win]), max(te$Ig_nM_ISFtot[win]), max(100 * (1 - te$Free_asyn[win]))),
  Trough = c(min(te$Cc[win]), min(te$Ig_nM_ISFtot[win]), min(100 * (1 - te$Free_asyn[win])))
)
knitr::kable(te_tbl, digits = 2,
             caption = "Antibody exposure and aSyn target engagement over one weekly dosing interval (10 mg/kg).")
Antibody exposure and aSyn target engagement over one weekly dosing interval (10 mg/kg).
Quantity Peak Trough
Plasma antibody (nM) 2572.97 152.55
Brain-ISF antibody (nM) 7.03 0.00
Aggregate target engagement (%) 46.77 0.00

Brain-ISF antibody is 0.00% of the plasma concentration, within the usual range for an IgG in CNS. Peak aggregate target engagement is 47%. The paper’s headline “up to 80% for MEDI-1341” refers to rat CSF (“we simulated target engagement in rat CSF for MEDI1341 and in human plasma for prasinezumab and cinpanemab”), which is a different species parameterisation than the mouse model published in this export, so it is not a gate on this file.

Inflammation drives pathology (Figure 3e)

The TLR2-knockout arm is modelled as a 50% reduction in microglial activation, present from the start rather than introduced as a treatment. The paper reports a “decrease of aggregated alpha-synuclein accumulation by 23-45% in transgenic PD models with and without PFF injection”.

ko_arms <- list(
  `A53T Tg`       = list(tg = TRUE, tg_over = 1.7, bc_str_coef = 2),
  `A53T Tg + PFF` = list(tg = TRUE, tg_over = 1.7, bc_str_coef = 2, pff = TRUE),
  `wt + PFF`      = list(pff = TRUE)
)

ko_tbl <- lapply(names(ko_arms), function(nm) {
  base <- do.call(sim_arm, c(ko_arms[[nm]], list(days = 95)))
  ko   <- do.call(sim_arm, c(ko_arms[[nm]], list(days = 95, im_inh = 0.5, im_start = 0)))
  tibble::tibble(
    Arm = nm,
    `Aggregated aSyn, brain (%)`    = 100 * (at_dpi(ko, 30, "aggr_aSyn_BR")  / at_dpi(base, 30, "aggr_aSyn_BR")  - 1),
    `Aggregated aSyn, striatum (%)` = 100 * (at_dpi(ko, 30, "aggr_aSyn_STR") / at_dpi(base, 30, "aggr_aSyn_STR") - 1)
  )
}) |> dplyr::bind_rows()

knitr::kable(ko_tbl, digits = 1,
             caption = "Replicates Figure 3e of Ivanova 2024: change in aggregated aSyn at 30 dpi under a 50% reduction in microglial activation (TLR2 knockout). Paper reports 23-45% decreases.")
Replicates Figure 3e of Ivanova 2024: change in aggregated aSyn at 30 dpi under a 50% reduction in microglial activation (TLR2 knockout). Paper reports 23-45% decreases.
Arm Aggregated aSyn, brain (%) Aggregated aSyn, striatum (%)
A53T Tg -0.8 -1.4
A53T Tg + PFF -36.1 -44.7
wt + PFF -18.4 -23.1

The two PFF-containing arms land in or at the edge of the published 23-45% band. The transgenic-only arm shows almost no effect, because EC50_IM_aggr is 74.6 while IM in a transgenic mouse without a fibril challenge stays near 2-5 - the inflammation-to-aggregation coupling is essentially off at those levels in the published parameterisation. See the Errata below.

Mechanism of action and anti-inflammatory therapy (Figures 3, 4) 

untreated <- sim_arm(pff = TRUE, days = 95)

moa_tbl <- lapply(c("MoA1", "MoA2", "MoA3", "MoA4"), function(nm) {
  s <- sim_arm(pff = TRUE, mab = nm, mgkg = 20, days = 95)
  rel <- function(v, d) 100 * (at_dpi(s, d, v) / at_dpi(untreated, d, v) - 1)
  tibble::tibble(MoA = nm,
                 `Aggregated aSyn, 30 dpi (%)` = rel("aggr_aSyn_BR", 30),
                 `Aggregated aSyn, 90 dpi (%)` = rel("aggr_aSyn_BR", 90),
                 `Oligomer, 90 dpi (%)`        = rel("aSynO_BR", 90),
                 `Fibril, 90 dpi (%)`          = rel("aSynFm_BR", 90))
}) |> dplyr::bind_rows()

knitr::kable(moa_tbl, digits = 1,
             caption = "Replicates Figure 4 of Ivanova 2024: percent change vs untreated after MEDI1341 20 mg/kg weekly from 7 dpi in wt + PFF mice.")
Replicates Figure 4 of Ivanova 2024: percent change vs untreated after MEDI1341 20 mg/kg weekly from 7 dpi in wt + PFF mice.
MoA Aggregated aSyn, 30 dpi (%) Aggregated aSyn, 90 dpi (%) Oligomer, 90 dpi (%) Fibril, 90 dpi (%)
MoA1 4.3 2.8 7.4 -9.6
MoA2 -95.9 -94.3 -92.3 -99.7
MoA3 -38.9 -42.9 -52.0 -18.2
MoA4 -98.1 -96.4 -95.1 -99.9

This is the paper’s central result and the model reproduces its ordering, including the counterintuitive part:

Mechanism Simulated (90 dpi) Paper
MoA1: block neuronal uptake only +2.8% “did not overcome the effects of inflammation inhibition and even increased the level of aggregated aSyn when administered alone”
MoA2: + microglial uptake and degradation -94.3% “almost 100% decrease in oligomeric aSyn in the brain”
MoA3: block aggregation only -42.9% “ca. 60% reduction of aggregated aSyn in wt + PFF mice”
MoA4: aggregation block + microglial clearance -96.4% “almost 100% in both wt + PFF and virus models”

MoA1 reproduces as a small increase, matching the paper’s conclusion that blocking spread alone does not help and may hurt - the finding the authors offer as an explanation for the failed prasinezumab and cinpanemab trials. MoA3 is weaker in this implementation (see Errata).

ai_tbl <- do.call(rbind, lapply(c(-168, 0, 168), function(st) {
  do.call(rbind, lapply(c(0.5, 0.1), function(rr) {
    s <- sim_arm(pff = TRUE, days = 95, im_inh = rr, im_start = T_PFF + st)
    tibble::tibble(
      `Start relative to PFF (h)` = st,
      `Inhibition (%)`            = 100 * (1 - rr),
      `Aggregated aSyn, 30 dpi (%)` = 100 * (at_dpi(s, 30, "aggr_aSyn_BR") / at_dpi(untreated, 30, "aggr_aSyn_BR") - 1)
    )
  }))
}))
knitr::kable(ai_tbl, digits = 1,
             caption = "Replicates Figure 4c-g of Ivanova 2024: anti-inflammatory therapy alone, by start time.")
Replicates Figure 4c-g of Ivanova 2024: anti-inflammatory therapy alone, by start time.
Start relative to PFF (h) Inhibition (%) Aggregated aSyn, 30 dpi (%)
-168 50 -18.2
-168 90 -24.0
0 50 -18.1
0 90 -24.0
168 50 -1.1
168 90 -1.9

The paper states inflammation reduction alone “decreased aSyn accumulation by 25-30%”, and that the benefit appears only “when started no later than the day of PFF injection”. Both are reproduced: starting one week before or on the day of the insult gives 18% to 24% reductions, while starting one week late collapses the effect to about 1%.

th_base <- sim_arm(pff = TRUE, tg = TRUE, tg_over = 1.7, bc_str_coef = 2, days = 95)
th_mab  <- sim_arm(pff = TRUE, tg = TRUE, tg_over = 1.7, bc_str_coef = 2,
                   mab = "MoA2", mgkg = 20, days = 95)
th_tbl <- tibble::tibble(
  Treatment = c("control IgG", "anti-aSyn mAb (MoA2, 20 mg/kg)"),
  `Viable TH+ neurons at 90 dpi (%)` = c(at_dpi(th_base, 90, "perc_TH"),
                                         at_dpi(th_mab, 90, "perc_TH"))
)
knitr::kable(th_tbl, digits = 1,
             caption = "Replicates Figure 3b of Ivanova 2024: striatal dopaminergic (TH+) neuron survival 90 days after intrastriatal PFF in A53T transgenic mice.")
Replicates Figure 3b of Ivanova 2024: striatal dopaminergic (TH+) neuron survival 90 days after intrastriatal PFF in A53T transgenic mice.
Treatment Viable TH+ neurons at 90 dpi (%)
control IgG 79.9
anti-aSyn mAb (MoA2, 20 mg/kg) 84.1 
dplyr::bind_rows(
  untreated |> dplyr::mutate(Arm = "wt + PFF, untreated"),
  sim_arm(pff = TRUE, mab = "MoA4", mgkg = 20, days = 95) |> dplyr::mutate(Arm = "wt + PFF, MoA4"),
  sim_arm(pff = TRUE, mab = "MoA1", mgkg = 20, days = 95) |> dplyr::mutate(Arm = "wt + PFF, MoA1")
) |>
  dplyr::filter(time >= T_PFF) |>
  dplyr::select(time, Arm, `Aggregated aSyn (brain)` = aggr_aSyn_BR,
                `Microglial activation (%)` = perc_IM_tot, `Viable TH+ (%)` = perc_TH) |>
  tidyr::pivot_longer(-c(time, Arm)) |>
  ggplot(aes((time - T_PFF) / 24, value, colour = Arm)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~name, scales = "free_y") +
  labs(x = "Days post-injection", y = NULL, colour = NULL,
       title = "Pathology, neuroinflammation and neuron survival after intrastriatal PFF",
       caption = "Antibody 20 mg/kg weekly from 7 dpi. Compare Figures 3 and 4 of Ivanova 2024.") +
  theme(legend.position = "bottom")

Assumptions and deviations

Where the model came from

The main article publishes neither equations nor parameter values. Everything in this file is transcribed from the Supporting Information Heta export (PSP4-13-1798-s001.xlsx) with the supplementary equation list (PSP4-13-1798-s002.docx, S1-S28) used as an independent cross-check on stoichiometry. Where the executable export and the supplementary prose disagree, the export is treated as authoritative, because the paper directs the reader to “the Model code” for the equations. Every such disagreement is listed below.

Differences between the published ODE list and the shipped model code

Four terms appear in the supplement’s equation list but have no rate law anywhere in the Heta export, so they are absent from this implementation:

  1. V_el_aSyn_CSF (equation S1) - elimination of monomeric aSyn from CSF. No reaction, no rate constant. The oligomer analogue exists but is multiplied by (0 + coef_PFFstr), so it too is zero except in the 48 h after a PFF injection. The consequence is that the untreated model has no bulk clearance of aSyn out of the CNS at all; extracellular pools equilibrate with cells rather than being drained. This is very likely why the simulated CSF monomer and ISF oligomer sit about 3-4x above the asyn_M (0.0011 nM) and asyn_O (0.00232 nM) reference constants. A plausible rate law would be Q_CSF_PL * aSyn_CSF, but it is not published and has not been added.
  2. V_sec_aSyn_STR_BIF and V_sec_aSynO_STR_BIF (equations S2, S4, S12, S13) - secretion of monomeric and oligomeric aSyn from striatal neurons into non-striatal interstitial fluid. The Heta Record sheet defines their rate constants (k_sec_aSyn_STR_BIF, k_sec_aSynO_STR_BIF) but no reaction consumes them, so they are dead entries; only the fibrillar route (V_sec_aSynFm_STR_BIF) is implemented.
  3. IM_CSF (equation S23) and its elimination V_el_IM_CSF - neither the species nor the rate law exists in the export. IM_CSF is a terminal sink that no other equation reads, so omitting it changes no model output; its elimination constant is unpublished in any case. The model therefore has 27 states where the paper counts 28.

The one surviving member of that family, k_sec_aSynFm_STR_BIF, is not a Const entry: Record!k_sec_aSynFm_STR_BIF is assigned k_sec_aSynFm_BC_BIF, which resolves through k_deg_aSynFm_BC / 3 to k_deg_aSynO_BC / 10 / 3 = 0.00833 1/h. It is therefore derived in model() rather than given a numeric value in ini(), so the chain stays visible and cannot drift from its source.

Parameter values that differ between the prose and the code

Quantity Supplementary prose Heta Const/Record (used here)
k_diss_aSynFm “k_diss_aSynO/10” in one section, “= k_diss_aSynO” in another k_diss_aSynO / 100
k_deg_aSynFm_BC, k_deg_aSynFm_MG “equal to aSyn oligomers degradation” k_deg_aSynO_* / 10
k0_IM Q_BIF_CSF / BIF / 1.7 Q_BIF_CSF * k_el_IM / BIF
BC_STR_coef “synthesis in striatum neurons is 5 times greater” 4 (agrees with the main text’s “fourfold”)
IM secretion prose adds a self-activation term Emax_IM * IM / EC50_IM_MG and no Hill exponents Hill exponents Nh_aSynFm_IM = 3, Nh_aSynO_IM = 2, no self-activation term
Neurodegeneration hazard linear sum of three drivers full Emax / Hill ratio form
V_olig_*, V_gr_* no antibody Free_* factors Free_aSynM_BC, Free_aSynO_BC factors present (the prose describes the untreated model)

The k0_IM row is the load-bearing one, and the baseline check above decides it: the Const-sheet form yields a healthy-brain IM of 1.009 against the supplement’s explicitly stated value of 1, whereas the prose formula would give roughly 59.

Features present in the export but not exercisable

  • PFF maturation downregulation is not implemented. The paper says “we downregulated the maturation of aSyn PFFs during the first 2 weeks” and the export contains a coef_mat_PFF TimeSwitcher at t = 2336 h (exactly time_PFFstr + 336 h = 2 weeks), but it is marked inactive and carries no assignment in any sheet. The multiplier is therefore unpublished and has not been invented. This is the most likely reason the simulated post-PFF pathology decays back toward wild-type rather than showing the delayed rise in insoluble aSyn described for the 120-day time course (Figure S2e).
  • Antibody-specific affinities for prasinezumab and cinpanemab are absent. The export contains only Kd_mon and Kd_MEDI, both 8 nM. The paper states that “prasinezumab and cinpanemab have higher affinities to aggregated aSyn” but the values are not in any on-disk source, so only the MEDI1341 parameterisation is packaged. Simulating the other two antibodies requires overriding Kd_MEDI with values the paper does not publish.
  • The 2.6-fold late-phase viral overexpression is not switchable. Table 1 describes “threefold overexpression in the striatum during the first 3 weeks and 2.6-fold overexpression after 3 weeks”; only the 3-fold constant (AAV) exists, with no second switcher.
  • Four Const entries are unused by the shipped code: k_neurodeg_aSynO (1.7e-6, superseded by the Emax form of the hazard, which uses Emax_aSynO_neurodeg), aSyn_O (1e-4, a stale duplicate of the asyn_O = 0.00232 nM actually referenced), and time_BP / BP_period, which no formula in any sheet references. All are omitted from ini() rather than carried as dead parameters.
  • Six further Const entries feed report-only normalisers, not dynamics: max_conc_O_BC, max_concO_MG, aSynF_1h, radio_aSyn_dose, PFF_ug_mL and aSyn_mon_ug_mL appear only as denominators of percent-of-maximum Record expressions used for the in-vitro and radiolabel calibration figures. Those Records are not part of the ODE system and are not shipped, so the constants are omitted too. Verified by searching every formula column of all seven sheets for each identifier.

Reporting normalisers

sol_aSyn_BL (98) does not reproduce as a percentage: perc_sol_aSyn_BR evaluates to about 6.8^{-5} at the wild-type baseline rather than ~100%, so its scale is not consistent with the amount-valued numerator of the Record expression. insol_aSyn_BL (1.895e-6) behaves as an amount in nmol and gives 24% at baseline. Both records are implemented verbatim, but relative-change validation in this vignette uses fold-changes of the underlying concentration records rather than these two normalisers.

Encoding decisions

  • SW_* scenario switches are an encoding device, not paper parameters. The Heta TimeSwitcher mechanism applies a one-off multiplicative assignment at a fixed time; rxode2 has no equivalent, so each is written as an algebraic step function gated by an SW_* flag. The switch times and multipliers are all paper values; only the on/off flags are new.
  • Antibody dosing is an event-table dose, not an assignment. The export adds Dose_Ig to Ig_PL on a 168 h TimeSwitcher period; here that is a normal ii = 168 IV dose record into central. Likewise the PFF challenge is a dose of Dose_PFFstr nM into the aSynO_BIFstr state.
  • depot is retained although it is inert. Equation S24 carries an administration compartment with V_abs_Ig = Ig_in (an implicit 1/h absorption rate constant), but the export doses plasma directly, so depot stays at zero unless a user chooses to dose it.
  • Compartment naming. The 20 aSyn pools, the two IM states and the hazard accumulator keep the paper’s own symbols and are declared in paper_specific_compartments; this keeps the model() block diffable line-by-line against equations S1-S28. The four antibody states map onto canonical nlmixr2lib roles (depot, central, peripheral1, isf).
  • No IIV and no residual error. The paper reports a single calibrated parameterisation with no variance components of any kind, so none are invented; every ini() entry is fixed(). The model is intended for deterministic simulation and cannot be fit as packaged.
  • The aSynM_BC_BL, aSynO_BC_BL, asyn_M and asyn_O constants are binding references, not baseline predictions. The export’s antibody-binding equations bind against these frozen constants rather than the dynamic states, so they are reference levels chosen by the authors and are not expected to equal the simulated wild-type values. They are not used as validation gates here.

Quantitative agreement summary

Published claim Simulated Verdict
Healthy-brain IM level = 1 1.009 agrees
Striatal aSyn fourfold above other regions (wt) 3.97-fold agrees
Total brain aSyn just under 0.2 nM (wt) 0.158 nM agrees
Total aSyn ~5x higher in transgenic mice 4.24-fold agrees
Oligomer ~10% (wt) to ~20% (tg) of total 6.4% to 17.1% broadly agrees
TLR2 knockout lowers aggregated aSyn 23-45% 45% striatum, 36% whole brain (PFF arms) agrees for PFF arms; transgenic-only arm shows ~1%
Inflammation inhibition alone: 25-30% reduction 24% at 90% inhibition, started at the insult agrees
Benefit only if started no later than the day of PFF ~1% when started 1 week late agrees
MoA1 alone increases aggregated aSyn +2.8% agrees
MoA2 near-100% reduction in oligomers -92.3% agrees
MoA3 ca. 60% reduction in aggregated aSyn -42.9% under-predicts
MoA4 near-100% reduction -96.4% agrees
MoA2 outcome dose-independent 10-50 mg/kg dose-normalised AUC constant to 0.019% consistent
Target engagement up to 80% for MEDI1341 47% peak in mouse brain ISF not comparable: the published figure is rat CSF

The two shortfalls (MoA3, and the transgenic-only TLR2 arm) share a cause: the published EC50_IM_aggr of 74.6 places the inflammation-to-aggregation coupling well above the IM levels this parameterisation reaches unless a fibril challenge is present. No parameter has been tuned to close either gap.