- - -

Introduction -

+ +

Testing hierarchical pathway kinetics with +residue data on cyantraniliprole

Johannes Ranke

Last change on 13 February 2023, last compiled on 13 +Februar 2025

+ +

+true +

+ +

Introduction

The purpose of this document is to test demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS, with serial formation of two or more metabolites can @@ -117,7 +377,7 @@ be fitted with the mkin package.

173340 (Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data) of the German Environment Agency carried out in 2022 and 2023.

The mkin package is used in version 1.2.6 which is currently under +

The mkin package is used in version 1.2.9 which is currently under development. The newly introduced functionality that is used here is a simplification of excluding random effects for a set of fits based on a related set of fits with a reduced model, and the documentation of the @@ -129,49 +389,47 @@ but is also loaded to make the convergence plot function available.

also provides the kable function that is used to improve the display of tabular data in R markdown documents. For parallel processing, the parallel package is used.

-library(mkin)
-library(knitr)
-library(saemix)
-library(parallel)
-n_cores <- detectCores()
-
-# We need to start a new cluster after defining a compiled model that is
-# saved as a DLL to the user directory, therefore we define a function
-# This is used again after defining the pathway model
-start_cluster <- function(n_cores) {
-  if (Sys.info()["sysname"] == "Windows") {
-    ret <- makePSOCKcluster(n_cores)
-  } else {
-    ret <- makeForkCluster(n_cores)
-  }
-  return(ret)
-}
-cl <- start_cluster(n_cores)

Test data -

library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+n_cores <- detectCores()
+
+# We need to start a new cluster after defining a compiled model that is
+# saved as a DLL to the user directory, therefore we define a function
+# This is used again after defining the pathway model
+start_cluster <- function(n_cores) {
+  if (Sys.info()["sysname"] == "Windows") {
+    ret <- makePSOCKcluster(n_cores)
+  } else {
+    ret <- makeForkCluster(n_cores)
+  }
+  return(ret)
+}
+cl <- start_cluster(n_cores)

Test data

The example data are taken from the final addendum to the DAR from 2014 and are distributed with the mkin package. Residue data and time step normalisation factors are read in using the function read_spreadsheet from the mkin package. This function also performs the time step normalisation.

-data_file <- system.file(
-  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
-  package = "mkin")
-cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)

data_file <- system.file(
+  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
+  package = "mkin")
+cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)

The following tables show the covariate data and the 5 datasets that were read in from the spreadsheet file.

-pH <- attr(cyan_ds, "covariates")
-kable(pH, caption = "Covariate data")

- +

pH <- attr(cyan_ds, "covariates")
+kable(pH, caption = "Covariate data")

- + + - + + @@ -195,24 +453,25 @@ were read in from the spreadsheet file.

Covariate data
	pH
Nambsheim

-for (ds_name in names(cyan_ds)) {
-  print(
-    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
-      caption = paste("Dataset", ds_name),
-      booktabs = TRUE, row.names = FALSE))
-    cat("\n\\clearpage\n")
-}

- +

for (ds_name in names(cyan_ds)) {
+  print(
+    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+    cat("\n\\clearpage\n")
+}

- + + - + + @@ -424,15 +683,17 @@ were read in from the spreadsheet file.

Dataset Nambsheim
time	cyan	JCZ38	J9C38	JSE76	J9Z38
0.000000

- +

- + + - + + @@ -618,15 +879,17 @@ were read in from the spreadsheet file.

Dataset Tama
time	cyan	JCZ38	J9Z38	JSE76
0.000000

- +

- + + - + + @@ -882,15 +1145,17 @@ were read in from the spreadsheet file.

Dataset Gross-Umstadt
time	cyan	JCZ38	J9Z38	JSE76
0.0000000

- +

- + + - + + @@ -1020,15 +1285,17 @@ were read in from the spreadsheet file.

Dataset Sassafras
time	cyan	JCZ38	J9Z38	JSE76
0.000000

- +

- + + - + + @@ -1160,25 +1427,25 @@ were read in from the spreadsheet file.

Dataset Lleida
time	cyan	JCZ38	J9Z38	JSE76
0.000000

Parent only evaluations -

Parent only evaluations

As the pathway fits have very long run times, evaluations of the parent data are performed first, in order to determine for each hierarchical parent degradation model which random effects on the degradation model parameters are ill-defined.

-cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
-  cyan_ds, quiet = TRUE, cores = n_cores)
-cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
-cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
-status(cyan_saem_full) |> kable()

- - +

cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
+  cyan_ds, quiet = TRUE, cores = n_cores)
+cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
+cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
+status(cyan_saem_full) |> kable()

+ + - + + @@ -1208,14 +1475,15 @@ degradation model parameters are ill-defined.

	const	tc
SFO

All fits converged successfully.

-illparms(cyan_saem_full) |> kable()

- - +

illparms(cyan_saem_full) |> kable()

+ + - + + @@ -1248,16 +1516,17 @@ degradation model parameters are ill-defined.

of the parent compound is ill-defined. For the biexponential models DFOP and SFORB, the random effect of one additional parameter is ill-defined when the two-component error model is used.

-anova(cyan_saem_full) |> kable(digits = 1)

	const	tc
SFO

- +

anova(cyan_saem_full) |> kable(digits = 1)

+ + - + + @@ -1335,74 +1604,71 @@ when the two-component error model is used.

two-component error model is preferable for all parent models with the exception of DFOP. The lowest AIC and BIC values are are obtained with the FOMC model, followed by SFORB and DFOP.

-stopCluster(cl)

stopCluster(cl)

Pathway fits -

Evaluations with pathway established previously -

Pathway fits

Evaluations with pathway established previously

To test the technical feasibility of coupling the relevant parent degradation models with different transformation pathway models, a list of mkinmod models is set up below. As in the EU evaluation, parallel formation of metabolites JCZ38 and J9Z38 and secondary formation of metabolite JSE76 from JCZ38 is used.

-if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
-cyan_path_1 <- list(
-  sfo_path_1 = mkinmod(
-    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  fomc_path_1 = mkinmod(
-    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  dfop_path_1 = mkinmod(
-    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  sforb_path_1 = mkinmod(
-    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  hs_path_1 = mkinmod(
-    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
-)
-cl_path_1 <- start_cluster(n_cores)

if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
+cyan_path_1 <- list(
+  sfo_path_1 = mkinmod(
+    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  fomc_path_1 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  dfop_path_1 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  sforb_path_1 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  hs_path_1 = mkinmod(
+    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
+)
+cl_path_1 <- start_cluster(n_cores)

To obtain suitable starting values for the NLHM fits, separate pathway fits are performed for all datasets.

-f_sep_1_const <- mmkin(
-  cyan_path_1,
-  cyan_ds,
-  error_model = "const",
-  cluster = cl_path_1,
-  quiet = TRUE)
-status(f_sep_1_const) |> kable()

	npar	AIC	BIC	Lik
SFO const

- +

f_sep_1_const <- mmkin(
+  cyan_path_1,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_1,
+  quiet = TRUE)
+status(f_sep_1_const) |> kable()

+ + - + + @@ -1446,18 +1712,19 @@ pathway fits are performed for all datasets.

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1

-f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
-status(f_sep_1_tc) |> kable()

- - +

f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
+status(f_sep_1_tc) |> kable()

+ + - + + @@ -1511,18 +1778,18 @@ for the parent only fits is used as an argument no_random_effect to the mhmkin function. The possibility to do so was introduced in mkin version 1.2.2 which is currently under development.

-f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
-  no_random_effect = illparms(cyan_saem_full),
-  cluster = cl_path_1)

-status(f_saem_1) |> kable()

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1

- +

f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
+  no_random_effect = illparms(cyan_saem_full),
+  cluster = cl_path_1)

status(f_saem_1) |> kable()

+ + - + + @@ -1558,19 +1825,20 @@ Fisher Information Matrix could not be inverted for the fixed effects fits, ill-defined parameters cannot be determined using the illparms function, because it relies on the Fisher Information Matrix.

-illparms(f_saem_1) |> kable()

	const	tc
sfo_path_1

illparms(f_saem_1) |> kable()

---+++ - + + - + + @@ -1600,18 +1868,68 @@ sd(f_JCZ38_qlogis)

	const	tc
sfo_path_1

The model comparison below suggests that the pathway fits using DFOP +

The model comparisons below suggest that the pathway fits using DFOP or SFORB for the parent compound provide the best fit.

-anova(f_saem_1) |> kable(digits = 1)

- - +

anova(f_saem_1[, "const"]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
sfo_path_1 const	16	2693.0	2686.8	-1330.5
fomc_path_1 const	18	2427.9	2420.9	-1196.0
dfop_path_1 const	20	2403.2	2395.4	-1181.6
sforb_path_1 const	20	2401.4	2393.6	-1180.7
hs_path_1 const	20	2427.2	2419.4	-1193.6

anova(f_saem_1[1:4, ]) |> kable(digits = 1)

+ + + - + + @@ -1656,20 +1974,13 @@ or SFORB for the parent compound provide the best fit.

- - - - - - - - + @@ -1680,29 +1991,27 @@ or SFORB for the parent compound provide the best fit.

	npar	AIC	BIC	Lik
sfo_path_1 const	-1180.7
hs_path_1 const	20	2427.2	2419.4	-1193.6
dfop_path_1 tc	20	2398.0	2390.1	-1179.0
sforb_path_1 tc	20	2399.9

For these two parent model, successful fits are shown below. Plots of the fits with the other parent models are shown in the Appendix.

-plot(f_saem_1[["dfop_path_1", "tc"]])

plot(f_saem_1[["dfop_path_1", "tc"]])

+ +

DFOP pathway fit with two-component error

-plot(f_saem_1[["sforb_path_1", "tc"]])

plot(f_saem_1[["sforb_path_1", "tc"]])

+ SFORB pathway fit with two-component error +

SFORB pathway fit with two-component error

A closer graphical analysis of these Figures shows that the residues of transformation product JCZ38 in the soils Tama and Nambsheim observed at later time points are strongly and systematically underestimated.

-stopCluster(cl_path_1)

stopCluster(cl_path_1)

Alternative pathway fits -

Alternative pathway fits

To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was introduced in an alternative version of the transformation pathway, in analogy to the back-reaction from K5A78 to K5A77. Both pairs of @@ -1711,55 +2020,56 @@ corresponding amide (Addendum 2014, p. 109). As FOMC provided the best fit for the parent, and the biexponential models DFOP and SFORB provided the best initial pathway fits, these three parent models are used in the alternative pathway fits.

-cyan_path_2 <- list(
-  fomc_path_2 = mkinmod(
-    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "fomc_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  ),
-  dfop_path_2 = mkinmod(
-    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "dfop_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  ),
-  sforb_path_2 = mkinmod(
-    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "sforb_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  )
-)
-
-cl_path_2 <- start_cluster(n_cores)
-f_sep_2_const <- mmkin(
-  cyan_path_2,
-  cyan_ds,
-  error_model = "const",
-  cluster = cl_path_2,
-  quiet = TRUE)
-
-status(f_sep_2_const) |> kable()

- - +

cyan_path_2 <- list(
+  fomc_path_2 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "fomc_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  dfop_path_2 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "dfop_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  sforb_path_2 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "sforb_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  )
+)
+
+cl_path_2 <- start_cluster(n_cores)
+f_sep_2_const <- mmkin(
+  cyan_path_2,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_2,
+  quiet = TRUE)
+
+status(f_sep_2_const) |> kable()

+ + - + + @@ -1789,18 +2099,19 @@ alternative pathway fits.

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2

Using constant variance, separate fits converge with the exception of the fits to the Sassafras soil data.

-f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
-status(f_sep_2_tc) |> kable()

- - +

f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
+status(f_sep_2_tc) |> kable()

+ + - + + @@ -1831,18 +2142,18 @@ the fits to the Sassafras soil data.

Using the two-component error model, all separate fits converge with the exception of the alternative pathway fit with DFOP used for the parent and the Sassafras dataset.

-f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
-  no_random_effect = illparms(cyan_saem_full[2:4, ]),
-  cluster = cl_path_2)

-status(f_saem_2) |> kable()

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2

- +

f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
+  no_random_effect = illparms(cyan_saem_full[2:4, ]),
+  cluster = cl_path_2)

status(f_saem_2) |> kable()

+ + - + + @@ -1862,20 +2173,22 @@ parent and the Sassafras dataset.

	const	tc
fomc_path_2

The hierarchical fits for the alternative pathway completed -successfully.

-illparms(f_saem_2) |> kable()

- +successfully, with the exception of the model using FOMC for the parent +compound and constant variance as the error model.

illparms(f_saem_2) |> kable()

---+++ - + + - + + @@ -1894,19 +2207,21 @@ successfully.

	const	tc
fomc_path_2

In both fits, the random effects for the formation fractions for the -pathways from JCZ38 to JSE76, and for the reverse pathway from JSE76 to -JCZ38 are ill-defined.

-anova(f_saem_2) |> kable(digits = 1)

- - +

In all biphasic fits (DFOP or SFORB for the parent compound), the +random effects for the formation fractions for the pathways from JCZ38 +to JSE76, and for the reverse pathway from JSE76 to JCZ38 are +ill-defined.

anova(f_saem_2[, "tc"]) |> kable(digits = 1)

+ + - + + @@ -1916,27 +2231,55 @@ JCZ38 are ill-defined.

+ + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
fomc_path_2 tc	-1103.5
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2239.7	2231.1	-1097.9

anova(f_saem_2[2:3,]) |> kable(digits = 1)

+ + + + + + + + + + + + - + - + - + @@ -1951,31 +2294,30 @@ and BIC values and are plotted below. Compared with the original pathway, the AIC and BIC values indicate a large improvement. This is confirmed by the plots, which show that the metabolite JCZ38 is fitted much better with this model.

-plot(f_saem_2[["fomc_path_2", "tc"]])

plot(f_saem_2[["fomc_path_2", "tc"]])

+ FOMC pathway fit with two-component error, alternative pathway +

FOMC pathway fit with two-component error, alternative pathway

-plot(f_saem_2[["dfop_path_2", "tc"]])

plot(f_saem_2[["dfop_path_2", "tc"]])

+ DFOP pathway fit with two-component error, alternative pathway +

DFOP pathway fit with two-component error, alternative pathway

-plot(f_saem_2[["sforb_path_2", "tc"]])

plot(f_saem_2[["sforb_path_2", "tc"]])

+ SFORB pathway fit with two-component error, alternative pathway +

SFORB pathway fit with two-component error, alternative pathway

- +

Refinement of alternative pathway fits

All ill-defined random effects that were identified in the parent only fits and in the above pathway fits, are excluded for the final evaluations below. For this purpose, a list of character vectors is @@ -1983,29 +2325,29 @@ created below that can be indexed by row and column indices, and which contains the degradation parameter names for which random effects should be excluded for each of the hierarchical fits contained in f_saem_2.

-no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
-no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
-  "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
-  "f_JCZ38_qlogis", "f_JSE76_qlogis")
-clusterExport(cl_path_2, "no_ranef")
-
-f_saem_3 <- update(f_saem_2,
-  no_random_effect = no_ranef,
-  cluster = cl_path_2)

-status(f_saem_3) |> kable()

	npar	AIC	BIC	Lik
dfop_path_2 const	22	2288.4	2279.8	-1122.2
sforb_path_2 const	22	2283.3	2274.7	-1119.7
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2239.7

- +

no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
+no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+clusterExport(cl_path_2, "no_ranef")
+
+f_saem_3 <- update(f_saem_2,
+  no_random_effect = no_ranef,
+  cluster = cl_path_2)

status(f_saem_3) |> kable()

+ + - + + @@ -2028,14 +2370,15 @@ be excluded for each of the hierarchical fits contained in all updated fits completed successfully. However, the Fisher Information Matrix for the fixed effects (Fth) could not be inverted, so no confidence intervals for the optimised parameters are available.

-illparms(f_saem_3) |> kable()

	const	tc
fomc_path_2

- +

illparms(f_saem_3) |> kable()

+ + - + + @@ -2054,16 +2397,17 @@ confidence intervals for the optimised parameters are available.

	const	tc
fomc_path_2

-anova(f_saem_3) |> kable(digits = 1)

- - +

anova(f_saem_3[, "tc"]) |> kable(digits = 1)

+ + - + + @@ -2073,27 +2417,55 @@ confidence intervals for the optimised parameters are available.

+ + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
fomc_path_2 tc	-1105.5
dfop_path_2 tc	20	2237.3	2229.5	-1098.6
sforb_path_2 tc	20	2241.3	2233.5	-1100.7

anova(f_saem_3[2:3,]) |> kable(digits = 1)

+ + + + + + + + + + + + - + - + - + @@ -2106,13 +2478,11 @@ confidence intervals for the optimised parameters are available.

two-component error) are lower than in the previous fits with the alternative pathway, the practical value of these refined evaluations is limited as no confidence intervals are obtained.

-stopCluster(cl_path_2)

stopCluster(cl_path_2)

Conclusion -

Conclusion

It was demonstrated that a relatively complex transformation pathway with parallel formation of two primary metabolites and one secondary metabolite can be fitted even if the data in the individual datasets are @@ -2122,55 +2492,50 @@ practical feasibility of iterative refinements based on ill-defined parameters and of alternative checks of parameter identifiability based on multistart runs.

Acknowledgements -

Acknowledgements

The helpful comments by Janina Wöltjen of the German Environment Agency are gratefully acknowledged.

Appendix -

Plots of fits that were not refined further -

-plot(f_saem_1[["sfo_path_1", "tc"]])

Appendix

Plots of fits that were not refined further

plot(f_saem_1[["sfo_path_1", "tc"]])

+ SFO pathway fit with two-component error +

SFO pathway fit with two-component error

-plot(f_saem_1[["fomc_path_1", "tc"]])

plot(f_saem_1[["fomc_path_1", "tc"]])

+ FOMC pathway fit with two-component error +

FOMC pathway fit with two-component error

-plot(f_saem_1[["sforb_path_1", "tc"]])

plot(f_saem_1[["sforb_path_1", "tc"]])

+ HS pathway fit with two-component error +

HS pathway fit with two-component error

Hierarchical fit listings -

Pathway 1 -

Hierarchical fit listings

Pathway 1


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:27:41 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:31:33 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - k_cyan * cyan
@@ -2183,7 +2548,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 421.347 s
+Fitted in 480.873 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2288,17 +2653,17 @@ JCZ38  14.46  48.05
 J9Z38 103.86 345.00
 JSE76 143.91 478.04
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:27:55 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:32:28 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - k_cyan * cyan
@@ -2311,7 +2676,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 435.122 s
+Fitted in 534.75 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -2418,17 +2783,17 @@ JCZ38  15.81  52.52
 J9Z38 107.97 358.68
 JSE76 114.20 379.35
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:28:33 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:33:51 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -2443,7 +2808,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 473.357 s
+Fitted in 618.676 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2563,17 +2928,17 @@ JCZ38  20.53   68.19       NA
 J9Z38 140.07  465.32       NA
 JSE76 318.86 1059.22       NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:28:46 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:34:01 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -2588,7 +2953,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 486.031 s
+Fitted in 627.822 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -2701,17 +3066,17 @@ JCZ38  22.01  73.1       NA
 J9Z38 130.09 432.2       NA
 JSE76 210.98 700.9       NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:29:15 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:33:18 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -2730,7 +3095,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 514.477 s
+Fitted in 584.724 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2847,17 +3212,17 @@ JCZ38  22.34  74.22       NA      NA      NA
 J9Z38 119.92 398.36       NA      NA      NA
 JSE76 200.41 665.76       NA      NA      NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:31:58 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:35:43 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -2876,7 +3241,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 677.928 s
+Fitted in 729.575 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -2993,17 +3358,17 @@ JCZ38  22.20  73.75       NA      NA      NA
 J9Z38 108.23 359.53       NA      NA      NA
 JSE76 179.30 595.62       NA      NA      NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:29:33 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:34:05 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -3021,7 +3386,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 532.937 s
+Fitted in 632.71 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3158,17 +3523,17 @@ JCZ38  22.98  76.33       NA           NA           NA
 J9Z38 116.28 386.29       NA           NA           NA
 JSE76 193.42 642.53       NA           NA           NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:31:58 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:37:01 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -3186,7 +3551,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 677.936 s
+Fitted in 807.852 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3323,17 +3688,17 @@ JCZ38  22.34  74.2       NA           NA           NA
 J9Z38 110.14 365.9       NA           NA           NA
 JSE76 177.11 588.3       NA           NA           NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:29:18 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:33:29 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan
@@ -3348,7 +3713,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 518.128 s
+Fitted in 596.235 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3465,21 +3830,20 @@ JCZ38  22.27  73.98       NA      NA      NA
 J9Z38 113.09 375.69       NA      NA      NA
 JSE76 187.01 621.23       NA      NA      NA
 
-

+ +

Pathway 2 -

Pathway 2


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:40:28 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:46:08 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -3494,7 +3858,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 499.317 s
+Fitted in 536.687 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3543,28 +3907,28 @@ Likelihood computed by importance sampling
   2249 2241  -1104
 
 Optimised parameters:
-                       est.      lower      upper
-cyan_0            101.55265  9.920e+01  103.90593
-log_k_JCZ38        -2.32302 -2.832e+00   -1.81416
-log_k_J9Z38        -5.13082 -5.942e+00   -4.31990
-log_k_JSE76        -3.01756 -4.262e+00   -1.77360
-f_cyan_ilr_1        0.70850  3.657e-01    1.05135
-f_cyan_ilr_2        0.95775  2.612e-01    1.65432
-f_JCZ38_qlogis      3.86105  9.248e-01    6.79733
-f_JSE76_qlogis      7.51583 -1.120e+02  127.03921
-log_alpha          -0.15308 -4.508e-01    0.14462
-log_beta            2.99165  2.711e+00    3.27202
-a.1                 2.04034  1.811e+00    2.26968
-b.1                 0.06924  5.745e-02    0.08104
-SD.log_k_JCZ38      0.50818  1.390e-01    0.87736
-SD.log_k_J9Z38      0.86597  2.652e-01    1.46671
-SD.log_k_JSE76      1.38092  4.864e-01    2.27541
-SD.f_cyan_ilr_1     0.38204  1.354e-01    0.62864
-SD.f_cyan_ilr_2     0.55129  7.198e-02    1.03060
-SD.f_JCZ38_qlogis   1.88457  1.710e-02    3.75205
-SD.f_JSE76_qlogis   2.64018 -2.450e+03 2455.27887
-SD.log_alpha        0.31860  1.047e-01    0.53249
-SD.log_beta         0.24195  1.273e-02    0.47117
+                       est.      lower     upper
+cyan_0            101.55265  9.920e+01  103.9059
+log_k_JCZ38        -2.32302 -2.832e+00   -1.8142
+log_k_J9Z38        -5.13082 -5.942e+00   -4.3199
+log_k_JSE76        -3.01756 -4.262e+00   -1.7736
+f_cyan_ilr_1        0.70850  3.657e-01    1.0513
+f_cyan_ilr_2        0.95775  2.612e-01    1.6543
+f_JCZ38_qlogis      3.86105  9.248e-01    6.7973
+f_JSE76_qlogis      7.51583 -1.120e+02  127.0392
+log_alpha          -0.15308 -4.508e-01    0.1446
+log_beta            2.99165  2.711e+00    3.2720
+a.1                 2.04034  1.843e+00    2.2382
+b.1                 0.06924  5.749e-02    0.0810
+SD.log_k_JCZ38      0.50818  1.390e-01    0.8774
+SD.log_k_J9Z38      0.86597  2.652e-01    1.4667
+SD.log_k_JSE76      1.38092  4.864e-01    2.2754
+SD.f_cyan_ilr_1     0.38204  1.354e-01    0.6286
+SD.f_cyan_ilr_2     0.55129  7.198e-02    1.0306
+SD.f_JCZ38_qlogis   1.88457  1.711e-02    3.7520
+SD.f_JSE76_qlogis   2.64018 -2.450e+03 2454.9447
+SD.log_alpha        0.31860  1.047e-01    0.5325
+SD.log_beta         0.24195  1.273e-02    0.4712
 
 Correlation: 
                cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
@@ -3595,15 +3959,15 @@ SD.log_k_J9Z38    0.8660  2.652e-01    1.4667
 SD.log_k_JSE76    1.3809  4.864e-01    2.2754
 SD.f_cyan_ilr_1   0.3820  1.354e-01    0.6286
 SD.f_cyan_ilr_2   0.5513  7.198e-02    1.0306
-SD.f_JCZ38_qlogis 1.8846  1.710e-02    3.7520
-SD.f_JSE76_qlogis 2.6402 -2.450e+03 2455.2789
+SD.f_JCZ38_qlogis 1.8846  1.711e-02    3.7520
+SD.f_JSE76_qlogis 2.6402 -2.450e+03 2454.9447
 SD.log_alpha      0.3186  1.047e-01    0.5325
 SD.log_beta       0.2420  1.273e-02    0.4712
 
 Variance model:
-       est.   lower   upper
-a.1 2.04034 1.81101 2.26968
-b.1 0.06924 0.05745 0.08104
+       est.   lower upper
+a.1 2.04034 1.84252 2.238
+b.1 0.06924 0.05749 0.081
 
 Backtransformed parameters:
                       est.     lower    upper
@@ -3635,17 +3999,17 @@ JCZ38   7.075  23.50       NA
 J9Z38 117.249 389.49       NA
 JSE76  14.169  47.07       NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:41:25 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:47:06 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3665,7 +4029,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 555.724 s
+Fitted in 594.209 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3826,17 +4190,17 @@ JCZ38  12.50  41.53       NA      NA      NA
 J9Z38 118.69 394.27       NA      NA      NA
 JSE76  24.32  80.78       NA      NA      NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:44:08 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:49:43 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3856,7 +4220,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 718.988 s
+Fitted in 751.883 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3933,15 +4297,15 @@ f_JSE76_qlogis      4.54884  -7.25628  16.35395
 log_k1             -2.38201  -2.51639  -2.24763
 log_k2             -4.66741  -4.91865  -4.41617
 g_qlogis           -0.28446  -1.14192   0.57300
-a.1                 2.05925   1.83267   2.28582
-b.1                 0.06172   0.05076   0.07268
+a.1                 2.05925   1.86481   2.25369
+b.1                 0.06172   0.05062   0.07282
 SD.log_k_JCZ38      0.81137   0.25296   1.36977
-SD.log_k_J9Z38      0.83542   0.25396   1.41689
+SD.log_k_J9Z38      0.83542   0.25395   1.41689
 SD.log_k_JSE76      0.97903   0.30100   1.65707
 SD.f_cyan_ilr_1     0.37878   0.13374   0.62382
 SD.f_cyan_ilr_2     0.67274   0.10102   1.24446
-SD.f_JCZ38_qlogis   1.35327  -0.42361   3.13015
-SD.f_JSE76_qlogis   1.43956 -19.15140  22.03052
+SD.f_JCZ38_qlogis   1.35327  -0.42359   3.13012
+SD.f_JSE76_qlogis   1.43956 -19.14972  22.02884
 SD.log_k2           0.25329   0.07521   0.43138
 SD.g_qlogis         0.95167   0.35149   1.55184
 
@@ -3972,19 +4336,19 @@ g_qlogis       -0.1656 -0.0928
 Random effects:
                     est.     lower   upper
 SD.log_k_JCZ38    0.8114   0.25296  1.3698
-SD.log_k_J9Z38    0.8354   0.25396  1.4169
+SD.log_k_J9Z38    0.8354   0.25395  1.4169
 SD.log_k_JSE76    0.9790   0.30100  1.6571
 SD.f_cyan_ilr_1   0.3788   0.13374  0.6238
 SD.f_cyan_ilr_2   0.6727   0.10102  1.2445
-SD.f_JCZ38_qlogis 1.3533  -0.42361  3.1301
-SD.f_JSE76_qlogis 1.4396 -19.15140 22.0305
+SD.f_JCZ38_qlogis 1.3533  -0.42359  3.1301
+SD.f_JSE76_qlogis 1.4396 -19.14972 22.0288
 SD.log_k2         0.2533   0.07521  0.4314
 SD.g_qlogis       0.9517   0.35149  1.5518
 
 Variance model:
        est.   lower   upper
-a.1 2.05925 1.83267 2.28582
-b.1 0.06172 0.05076 0.07268
+a.1 2.05925 1.86481 2.25369
+b.1 0.06172 0.05062 0.07282
 
 Backtransformed parameters:
                       est.     lower     upper
@@ -4017,17 +4381,17 @@ JCZ38   8.93  29.66       NA      NA      NA
 J9Z38 110.45 366.89       NA      NA      NA
 JSE76  17.96  59.66       NA      NA      NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:41:22 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:46:57 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4045,7 +4409,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 553.276 s
+Fitted in 585.771 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -4213,17 +4577,17 @@ JCZ38   7.203  23.93       NA           NA           NA
 J9Z38 131.918 438.22       NA           NA           NA
 JSE76  14.287  47.46       NA           NA           NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:44:02 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:50:00 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4241,7 +4605,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 713.14 s
+Fitted in 767.874 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4320,17 +4684,17 @@ f_cyan_ilr_1               0.70640  3.562e-01  1.057e+00
 f_cyan_ilr_2               1.42704  3.170e-01  2.537e+00
 f_JCZ38_qlogis             2.84779  1.042e+00  4.654e+00
 f_JSE76_qlogis             8.63674 -6.407e+02  6.580e+02
-a.1                        2.07082  1.846e+00  2.296e+00
-b.1                        0.06227  5.120e-02  7.334e-02
+a.1                        2.07082  1.877e+00  2.265e+00
+b.1                        0.06227  5.098e-02  7.355e-02
 SD.log_k_cyan_free         0.49674  1.865e-01  8.069e-01
-SD.log_k_cyan_bound_free   0.28537  6.808e-02  5.027e-01
+SD.log_k_cyan_bound_free   0.28537  6.809e-02  5.027e-01
 SD.log_k_JCZ38             0.74846  2.305e-01  1.266e+00
 SD.log_k_J9Z38             0.86077  2.713e-01  1.450e+00
 SD.log_k_JSE76             0.97613  3.030e-01  1.649e+00
 SD.f_cyan_ilr_1            0.38994  1.382e-01  6.417e-01
 SD.f_cyan_ilr_2            0.82869  3.917e-02  1.618e+00
-SD.f_JCZ38_qlogis          1.05000 -2.809e-02  2.128e+00
-SD.f_JSE76_qlogis          0.44681 -3.986e+05  3.986e+05
+SD.f_JCZ38_qlogis          1.05000 -2.808e-02  2.128e+00
+SD.f_JSE76_qlogis          0.44681 -3.985e+05  3.985e+05
 
 Correlation: 
                       cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
@@ -4359,19 +4723,19 @@ f_JSE76_qlogis         0.0064  0.0345  0.2015 -0.7058
 Random effects:
                            est.      lower     upper
 SD.log_k_cyan_free       0.4967  1.865e-01 8.069e-01
-SD.log_k_cyan_bound_free 0.2854  6.808e-02 5.027e-01
+SD.log_k_cyan_bound_free 0.2854  6.809e-02 5.027e-01
 SD.log_k_JCZ38           0.7485  2.305e-01 1.266e+00
 SD.log_k_J9Z38           0.8608  2.713e-01 1.450e+00
 SD.log_k_JSE76           0.9761  3.030e-01 1.649e+00
 SD.f_cyan_ilr_1          0.3899  1.382e-01 6.417e-01
 SD.f_cyan_ilr_2          0.8287  3.917e-02 1.618e+00
-SD.f_JCZ38_qlogis        1.0500 -2.809e-02 2.128e+00
-SD.f_JSE76_qlogis        0.4468 -3.986e+05 3.986e+05
+SD.f_JCZ38_qlogis        1.0500 -2.808e-02 2.128e+00
+SD.f_JSE76_qlogis        0.4468 -3.985e+05 3.985e+05
 
 Variance model:
-       est.  lower   upper
-a.1 2.07082 1.8458 2.29588
-b.1 0.06227 0.0512 0.07334
+       est.   lower   upper
+a.1 2.07082 1.87680 2.26483
+b.1 0.06227 0.05098 0.07355
 
 Backtransformed parameters:
                           est.      lower     upper
@@ -4409,22 +4773,21 @@ JCZ38   8.535  28.35       NA           NA           NA
 J9Z38 105.517 350.52       NA           NA           NA
 JSE76  17.837  59.25       NA           NA           NA
 
-

+ +

Pathway 2, refined fits -

Pathway 2, refined fits


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:57:07 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:03:52 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -4439,7 +4802,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 776.732 s
+Fitted in 830.375 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4488,26 +4851,26 @@ Likelihood computed by importance sampling
   2249 2242  -1106
 
 Optimised parameters:
-                     est.   lower   upper
-cyan_0          101.24524      NA      NA
-log_k_JCZ38      -2.85375      NA      NA
-log_k_J9Z38      -5.07729      NA      NA
-log_k_JSE76      -3.53511      NA      NA
-f_cyan_ilr_1      0.67478      NA      NA
-f_cyan_ilr_2      0.97152      NA      NA
-f_JCZ38_qlogis  213.48001      NA      NA
-f_JSE76_qlogis    2.02040      NA      NA
-log_alpha        -0.11041      NA      NA
-log_beta          3.06575      NA      NA
-a.1               2.05279 1.82393 2.28166
-b.1               0.07116 0.05910 0.08322
-SD.log_k_JCZ38    1.21713 0.44160 1.99266
-SD.log_k_J9Z38    0.88268 0.27541 1.48995
-SD.log_k_JSE76    0.59452 0.15005 1.03898
-SD.f_cyan_ilr_1   0.35370 0.12409 0.58331
-SD.f_cyan_ilr_2   0.78186 0.18547 1.37824
-SD.log_alpha      0.27781 0.08168 0.47394
-SD.log_beta       0.32608 0.06490 0.58726
+                     est.   lower  upper
+cyan_0          101.24524      NA     NA
+log_k_JCZ38      -2.85375      NA     NA
+log_k_J9Z38      -5.07729      NA     NA
+log_k_JSE76      -3.53511      NA     NA
+f_cyan_ilr_1      0.67478      NA     NA
+f_cyan_ilr_2      0.97152      NA     NA
+f_JCZ38_qlogis  213.48001      NA     NA
+f_JSE76_qlogis    2.02040      NA     NA
+log_alpha        -0.11041      NA     NA
+log_beta          3.06575      NA     NA
+a.1               2.05279 1.85495 2.2506
+b.1               0.07116 0.05912 0.0832
+SD.log_k_JCZ38    1.21713 0.44160 1.9927
+SD.log_k_J9Z38    0.88268 0.27541 1.4900
+SD.log_k_JSE76    0.59452 0.15005 1.0390
+SD.f_cyan_ilr_1   0.35370 0.12409 0.5833
+SD.f_cyan_ilr_2   0.78186 0.18547 1.3782
+SD.log_alpha      0.27781 0.08168 0.4739
+SD.log_beta       0.32608 0.06490 0.5873
 
 Correlation is not available
 
@@ -4522,9 +4885,9 @@ SD.log_alpha    0.2778 0.08168 0.4739
 SD.log_beta     0.3261 0.06490 0.5873
 
 Variance model:
-       est.  lower   upper
-a.1 2.05279 1.8239 2.28166
-b.1 0.07116 0.0591 0.08322
+       est.   lower  upper
+a.1 2.05279 1.85495 2.2506
+b.1 0.07116 0.05912 0.0832
 
 Backtransformed parameters:
                       est. lower upper
@@ -4556,18 +4919,18 @@ JCZ38  12.03  39.96       NA
 J9Z38 111.14 369.19       NA
 JSE76  23.77  78.98       NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:58:51 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:47 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4587,7 +4950,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 880.94 s
+Fitted in 945.728 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -4722,18 +5085,18 @@ JCZ38  13.04  43.33       NA      NA      NA
 J9Z38 120.93 401.73       NA      NA      NA
 JSE76  26.39  87.68       NA      NA      NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:58:58 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:49 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4753,7 +5116,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 887.853 s
+Fitted in 947.743 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4830,13 +5193,13 @@ f_JSE76_qlogis  414.80884      NA      NA
 log_k1           -2.38601      NA      NA
 log_k2           -4.63632      NA      NA
 g_qlogis         -0.33920      NA      NA
-a.1               2.10837 1.88051 2.33623
-b.1               0.06223 0.05108 0.07338
+a.1               2.10837 1.91261 2.30413
+b.1               0.06223 0.05085 0.07361
 SD.log_k_JCZ38    1.30902 0.48128 2.13675
 SD.log_k_J9Z38    0.83882 0.25790 1.41974
 SD.log_k_JSE76    0.58104 0.14201 1.02008
 SD.f_cyan_ilr_1   0.35421 0.12398 0.58443
-SD.f_cyan_ilr_2   0.79373 0.12007 1.46740
+SD.f_cyan_ilr_2   0.79373 0.12007 1.46739
 SD.log_k2         0.27476 0.08557 0.46394
 SD.g_qlogis       0.96170 0.35463 1.56878
 
@@ -4854,8 +5217,8 @@ SD.g_qlogis     0.9617 0.35463 1.5688
 
 Variance model:
        est.   lower   upper
-a.1 2.10837 1.88051 2.33623
-b.1 0.06223 0.05108 0.07338
+a.1 2.10837 1.91261 2.30413
+b.1 0.06223 0.05085 0.07361
 
 Backtransformed parameters:
                       est. lower upper
@@ -4888,18 +5251,18 @@ JCZ38  11.49  38.18       NA      NA      NA
 J9Z38 107.55 357.28       NA      NA      NA
 JSE76  27.20  90.36       NA      NA      NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:58:49 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:38 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4917,7 +5280,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 878.878 s
+Fitted in 936.368 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -5059,18 +5422,18 @@ JCZ38  12.92  42.93       NA           NA           NA
 J9Z38 114.71 381.07       NA           NA           NA
 JSE76  26.04  86.51       NA           NA           NA
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:10 2023 
-Date of summary: Thu Nov 16 04:59:11 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:52 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -5088,7 +5451,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 899.539 s
+Fitted in 950.661 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -5167,8 +5530,8 @@ f_cyan_ilr_1               0.72263      NA      NA
 f_cyan_ilr_2               1.45352      NA      NA
 f_JCZ38_qlogis             2.00778      NA      NA
 f_JSE76_qlogis           941.58570      NA      NA
-a.1                        2.11130 1.88299 2.33960
-b.1                        0.06299 0.05176 0.07421
+a.1                        2.11130 1.91479 2.30780
+b.1                        0.06299 0.05152 0.07445
 SD.log_k_cyan_free         0.50098 0.18805 0.81390
 SD.log_k_cyan_bound_free   0.31671 0.08467 0.54875
 SD.log_k_JCZ38             1.25865 0.45932 2.05798
@@ -5182,7 +5545,7 @@ Correlation is not available
 Random effects:
                            est.   lower  upper
 SD.log_k_cyan_free       0.5010 0.18805 0.8139
-SD.log_k_cyan_bound_free 0.3167 0.08467 0.5488
+SD.log_k_cyan_bound_free 0.3167 0.08467 0.5487
 SD.log_k_JCZ38           1.2587 0.45932 2.0580
 SD.log_k_J9Z38           0.8683 0.27222 1.4644
 SD.log_k_JSE76           0.5933 0.14711 1.0394
@@ -5191,8 +5554,8 @@ SD.f_cyan_ilr_2          0.8854 0.13797 1.6329
 
 Variance model:
        est.   lower   upper
-a.1 2.11130 1.88299 2.33960
-b.1 0.06299 0.05176 0.07421
+a.1 2.11130 1.91479 2.30780
+b.1 0.06299 0.05152 0.07445
 
 Backtransformed parameters:
                           est. lower upper
@@ -5230,15 +5593,14 @@ JCZ38  11.06  36.75       NA           NA           NA
 J9Z38 106.71 354.49       NA           NA           NA
 JSE76  25.44  84.51       NA           NA           NA
 
-

+ +

Session info -

R version 4.3.2 (2023-10-31)
-Platform: x86_64-pc-linux-gnu (64-bit)
+
+Session info
+R version 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
@@ -5261,56 +5623,75 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.2 npde_3.3   knitr_1.42 mkin_1.2.6
+[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
+[5] rmarkdown_2.29  nvimcom_0.9-167
 
 loaded via a namespace (and not attached):
- [1] sass_0.4.6        utf8_1.2.3        generics_0.1.3    stringi_1.7.12   
- [5] lattice_0.21-8    digest_0.6.31     magrittr_2.0.3    evaluate_0.21    
- [9] grid_4.3.2        fastmap_1.1.1     cellranger_1.1.0  rprojroot_2.0.3  
-[13] jsonlite_1.8.4    processx_3.8.1    pkgbuild_1.4.0    deSolve_1.35     
-[17] DBI_1.1.3         mclust_6.0.0      ps_1.7.5          gridExtra_2.3    
-[21] purrr_1.0.1       fansi_1.0.4       scales_1.2.1      codetools_0.2-19 
-[25] textshaping_0.3.6 jquerylib_0.1.4   cli_3.6.1         crayon_1.5.2     
-[29] rlang_1.1.1       munsell_0.5.0     cachem_1.0.8      yaml_2.3.7       
-[33] inline_0.3.19     tools_4.3.2       memoise_2.0.1     dplyr_1.1.2      
-[37] colorspace_2.1-0  ggplot2_3.4.2     vctrs_0.6.2       R6_2.5.1         
-[41] zoo_1.8-12        lifecycle_1.0.3   stringr_1.5.0     fs_1.6.2         
-[45] MASS_7.3-60       ragg_1.2.5        callr_3.7.3       pkgconfig_2.0.3  
-[49] desc_1.4.2        pkgdown_2.0.7     bslib_0.4.2       pillar_1.9.0     
-[53] gtable_0.3.3      glue_1.6.2        systemfonts_1.0.4 highr_0.10       
-[57] xfun_0.39         tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.0 
-[61] htmltools_0.5.5   nlme_3.1-163      rmarkdown_2.21    compiler_4.3.2   
-[65] prettyunits_1.1.1 readxl_1.4.2     
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    processx_3.8.4   
+[13] pkgbuild_1.4.5    deSolve_1.40      mclust_6.1.1      ps_1.8.1         
+[17] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
+[21] jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4       munsell_0.5.1    
+[25] cachem_1.1.0      yaml_2.3.10       inline_0.3.20     tools_4.4.2      
+[29] colorout_1.3-2    dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1    
+[33] vctrs_0.6.5       R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4  
+[37] MASS_7.3-61       pkgconfig_2.0.3   callr_3.7.6       pillar_1.9.0     
+[41] bslib_0.8.0       gtable_0.3.6      glue_1.8.0        xfun_0.49        
+[45] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
+[49] nlme_3.1-166      compiler_4.4.2    readxl_1.4.3

Hardware info -

Hardware info

CPU model: AMD Ryzen 9 7950X 16-Core Processor

MemTotal:       64927712 kB

MemTotal:       64927788 kB

- - - - + + + + + + + - - + + - + -- cgit v1.2.1

Hierarchical SFO path 1 fit with constant variance
	npar	AIC	BIC	Lik
dfop_path_2 const	20	2282.2	2274.4	-1121.1
sforb_path_2 const	20	2279.7	2271.9	-1119.9
dfop_path_2 tc	20	2237.3	2229.5	-1098.6
sforb_path_2 tc	20	2241.3

Testing hierarchical pathway kinetics with residue data on cyantraniliprole

Johannes -Ranke

Last change on 20 April 2023, -last compiled on 16 November 2023

Introduction -

Testing hierarchical pathway kinetics with +residue data on cyantraniliprole

Johannes Ranke

Last change on 13 February 2023, last compiled on 13 +Februar 2025

Introduction

Test data -

Test data

Parent only evaluations -

Parent only evaluations

Pathway fits -

Evaluations with pathway established previously -

Pathway fits

Evaluations with pathway established previously

Alternative pathway fits -

Alternative pathway fits

Refinement of alternative pathway fits -

Refinement of alternative pathway fits

Conclusion -

Conclusion

Acknowledgements -

Acknowledgements

Appendix -

Plots of fits that were not refined further -

Appendix

Plots of fits that were not refined further

Hierarchical fit listings -

Pathway 1 -

Hierarchical fit listings

Pathway 1

Pathway 2 -

Pathway 2

Pathway 2, refined fits -

Pathway 2, refined fits

Session info -

Session info

Hardware info -

Hardware info