1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
|
# Was Id: mkinmod.R 71 2010-09-12 01:13:36Z jranke
# Some of the CAKE R modules are based on mkin
# Portions Johannes Ranke, 2010
# Contact: mkin-devel@lists.berlios.de
# Modifications developed by Tessella for Syngenta: Copyright (C) 2011-2020 Syngenta
# Tessella Project Reference: 6245, 7247, 8361, 7414, 10091
# The CAKE R modules are free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
CakeModel <- function(..., use_of_ff = "max")
{
# While spec is modified throughout this function, topology is added as-is to the returned model
topology <- list(...)
spec <- list(...)
obs_vars <- names(spec)
if (!use_of_ff %in% c("min", "max")) stop("The use of formation fractions 'use_of_ff' can only be 'min' or 'max'")
# differential equations, parameter names and a mapping from model variables
# to observed variables. If possible, a matrix representation of the
# differential equations is included
parms <- vector()
diffs <- vector()
map <- list()
nlt <- list()
# Establish list of differential equations
for (varname in obs_vars)
{
if(is.null(spec[[varname]]$type)) stop("Every argument to CakeModel must be a list containing a type component")
if(!spec[[varname]]$type %in% c("SFO", "FOMC", "DFOP", "HS", "IORE")) stop("Available types are SFO, FOMC, DFOP, HS and IORE only")
new_parms <- vector()
# New (sub)compartments (boxes) needed for the model type
if (spec[[varname]]$type == "DFOP" && varname != "Parent"){
# If this is a DFOP metabolite, we need to form a system of two differential equations
# (see FOCUS page 137)
new_boxes <- paste(varname, c("1", "2"), sep="_")
} else{
new_boxes <- varname
}
map[[varname]] <- new_boxes
names(map[[varname]]) <- rep(spec[[varname]]$type, length(new_boxes))
# Start a new differential equation for each new box
new_diffs <- paste("d_", new_boxes, " =", sep="")
# Turn on sink if not specified otherwise
if(is.null(spec[[varname]]$sink)) spec[[varname]]$sink <- TRUE
# Construct and add SFO term and add SFO parameters if needed
if(spec[[varname]]$type == "SFO") {
if (use_of_ff == "min") { # Minimum use of formation fractions
if(spec[[varname]]$sink) {
# From p. 53 of the FOCUS kinetics report
k_term <- paste("k", new_boxes[[1]], "sink", sep="_")
nonlinear_term <- paste(k_term, new_boxes[[1]], sep=" * ")
spec[[varname]]$nlt<-nonlinear_term
new_diffs[[1]] <- paste(new_diffs[[1]], "-", nonlinear_term)
new_parms <- k_term
ff <- vector()
decline_term <- paste(nonlinear_term, "*", new_boxes[[1]])
} else { # otherwise no decline term needed here
decline_term <- "0"
}
} else {
k_term <- paste("k", new_boxes[[1]], sep="_")
nonlinear_term <- paste(k_term, new_boxes[[1]], sep=" * ")
spec[[varname]]$nlt<-nonlinear_term
new_diffs[[1]] <- paste(new_diffs[[1]], "-", nonlinear_term)
new_parms <- k_term
ff <- vector()
decline_term <- paste(nonlinear_term, "*", new_boxes[[1]])
}
}
# Construct and add FOMC term and add FOMC parameters if needed
if(spec[[varname]]$type == "FOMC") {
if(match(varname, obs_vars) != 1) {
stop("Type FOMC is only possible for the first compartment, which is assumed to be the source compartment")
}
# From p. 53 of the FOCUS kinetics report
nonlinear_term <- paste("(alpha/beta) * ((time/beta) + 1)^-1 *", new_boxes[[1]])
spec[[varname]]$nlt<-nonlinear_term
new_diffs[[1]] <- paste(new_diffs[[1]], "-", nonlinear_term)
new_parms <- c("alpha", "beta")
ff <- vector()
}
# Construct and add DFOP term and add DFOP parameters if needed
if(spec[[varname]]$type == "DFOP") {
k1_term <- paste("k1", varname, sep="_")
k2_term <- paste("k2", varname, sep="_")
g_term <- paste("g", varname, sep="_")
new_parms <- c(k1_term, k2_term, g_term)
ff <- vector()
if (varname == "Parent"){
# From p. 57 of the FOCUS kinetics report
# Looks like this: paste("((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) *", new_boxes[[1]])
nonlinear_term <- paste("((", k1_term, " * ", g_term, " * exp(-", k1_term, " * time) + ", k2_term, " * (1 - ", g_term, ") * exp(-", k2_term, " * time)) / (", g_term, " * exp(-", k1_term, " * time) + (1 - ", g_term, ") * exp(-", k2_term, " * time))) *", new_boxes[[1]])
spec[[varname]]$nlt<-nonlinear_term
new_diffs[[1]] <- paste(new_diffs[[1]], "-", nonlinear_term)
} else {
# From p. 137 of the FOCUS kinetics report - two sub-compartments with g applied to initial conditions (in ODE pre-processing) and in formation terms.
first_nonlinear_term <- paste(k1_term, new_boxes[[1]], sep=" * ")
second_nonlinear_term <- paste(k2_term, new_boxes[[2]], sep=" * ")
# CU-150: formation has already been accounted for on the formation into the two sub-compartments; it does not need to be factored in again on the way out
overall_term_for_formation <- paste("(", first_nonlinear_term, " + ", second_nonlinear_term, ")")
spec[[varname]]$nlt <- overall_term_for_formation
new_diffs[[1]] <- paste(new_diffs[[1]], "-", first_nonlinear_term)
new_diffs[[2]] <- paste(new_diffs[[2]], "-", second_nonlinear_term)
}
}
# Construct and add HS term and add HS parameters if needed
if(spec[[varname]]$type == "HS") {
if(match(varname, obs_vars) != 1) {
stop("Type HS is only possible for the first compartment, which is assumed to be the source compartment")
}
# From p. 55 of the FOCUS kinetics report: nonlinear_term <- paste("ifelse(time <= tb, k1, k2)", "*", new_boxes[[1]])
# Replaced this with the smoothed version on the next line to ease convergence.
nonlinear_term <- paste("((k1 - k2) / ( 1 + exp( 300*(time - tb)/(tb + 0.00001) ) ) + k2)", "*", new_boxes[[1]])
spec[[varname]]$nlt<-nonlinear_term
new_diffs[[1]] <- paste(new_diffs[[1]], "-", nonlinear_term)
new_parms <- c("k1", "k2", "tb")
ff <- vector()
}
# Construct and add IORE term and add IORE parameters if needed
if(spec[[varname]]$type == "IORE") {
k_term <- paste("k", new_boxes[[1]], sep="_")
nonlinear_term <- paste(k_term, new_boxes[[1]], sep=" * ")
nonlinear_term <- paste(nonlinear_term, "^N")
spec[[varname]]$nlt<-nonlinear_term
new_diffs[[1]] <- paste(new_diffs[[1]], "-", nonlinear_term)
new_parms <- c(k_term, "N")
ff <- vector()
}
# Add observed variable to model
parms <- c(parms, new_parms)
names(new_diffs) <- new_boxes
diffs <- c(diffs, new_diffs)
}
# Transfer between compartments
for (varname in obs_vars) {
to <- spec[[varname]]$to
if(!is.null(to)) {
fraction_left <- NULL
for (target in to) {
target_boxes <- switch(spec[[target]]$type,
SFO = target,
DFOP = paste(target, c("1", "2"), sep="_"))
if(spec[[varname]]$type %in% c("FOMC", "DFOP", "HS", "SFO", "IORE")) {
if ( length(to)==1 && !spec[[varname]]$sink ) {
# There is only one output, so no need for any flow fractions. Just add the whole flow from the parent
formation_term <- spec[[varname]]$nlt
} else {
fraction_to_target <- paste("f", varname, "to", target, sep="_")
fraction_not_to_target <- paste("(1 - ", fraction_to_target, ")", sep="")
if(is.null(fraction_left)) {
fraction_really_to_target <- fraction_to_target
fraction_left <- fraction_not_to_target
} else {
# If this is the last output and there is no sink, it gets what's left
if ( target==tail(to,1) && !spec[[varname]]$sink ) {
fraction_really_to_target <- fraction_left
} else {
fraction_really_to_target <- fraction_to_target
fraction_left <- paste(fraction_left, " - ", fraction_to_target, sep="")
}
}
ff[target] <- fraction_really_to_target
formation_term <- paste(ff[target], "*", spec[[varname]]$nlt)
# Add the flow fraction parameter (if it exists)
if ( target!=tail(to,1) || spec[[varname]]$sink ) {
parms <- c(parms, fraction_to_target)
}
}
if (spec[[target]]$type == "DFOP") {
g_term <- paste("g", target, sep="_")
first_formation_term <- paste(g_term, "*", formation_term)
second_formation_term <- paste("(1 -", g_term, ") *", formation_term)
diffs[[target_boxes[[1]]]] <- paste(diffs[[target_boxes[[1]]]], "+", first_formation_term)
diffs[[target_boxes[[2]]]] <- paste(diffs[[target_boxes[[2]]]], "+", second_formation_term)
} else{
diffs[[target_boxes[[1]]]] <- paste(diffs[[target_boxes[[1]]]], "+", formation_term)
}
}
}
}
}
model <- list(diffs = diffs, parms = parms, map = map, use_of_ff = use_of_ff, topology = topology)
if (exists("ff")) {
model$ff <- ff
}
class(model) <- "mkinmod"
invisible(model)
}
|
