Last data update: 2014.03.03
R: The Escherichia Coli Core Metabolism: Reaction network model...
The Escherichia Coli Core Metabolism: Reaction network model specificiation
Description
Linear inverse model specification for performing Flux Balance Analysis
of the E.coli metabolism
(as from http://gcrg.ucsd.edu/Downloads/Flux_Balance_Analysis ).
The original input file can be found in the package subdirectory
/examples/Reactions/E_coli.lim
There are 53 substances:
GLC, G6P, F6P, FDP, T3P2, T3P1, 13PDG, 3PG, 2PG, PEP,
PYR, ACCOA, CIT, ICIT, AKG, SUCCOA, SUCC, FUM, MAL, OA,
ACTP, ETH, AC, LAC, FOR, D6PGL, D6PGC, RL5P, X5P,
R5P, S7P, E4P, RIB, GLX, NAD, NADH, NADP, NADPH, HEXT,
Q, FAD, FADH, AMP, ADP,
ATP, GL3P, CO2, PI, PPI, O2, COA, GL, QH2
and 13 externals:
Biomass, GLCxt, GLxt, RIBxt, ACxt, LACxt, FORxt, ETHxt, SUCCxt,
PYRxt, PIxt, O2xt, CO2xt
There are 70 unknown reactions (named by the gene encoding for it):
GLK1, PGI1, PFKA, FBP, FBA, TPIA, GAPA, PGK, GPMA, ENO,
PPSA, PYKA, ACEE, ZWF, PGL, GND,
RPIA, RPE, TKTA1, TKTA2, TALA, GLTA, ACNA, ICDA, SUCA,
SUCC1, SDHA1, FRDA, FUMA, MDH,
DLD1, ADHE2, PFLA, PTA, ACKA, ACS, PCKA, PPC, MAEB, SFCA,
ACEA, ACEB, PPA, GLPK, GPSA1,
RBSK, NUOA, FDOH, GLPD, CYOA, SDHA2, PNT1A, PNT2A, ATPA,
GLCUP, GLCPTS, GLUP, RIBUP,
ACUP, LACUP, FORUP, ETHUP, SUCCUP, PYRUP, PIUP, O2TX,
CO2TX, ATPM, ADK, Growth
The model contains:
54 equalities (Ax=B): the 53 mass balances
(one for each substance) and one equation that sets the ATP
drain flux for constant maintenance requirements to a fixed value (5.87)
70 unknowns (x), the reaction rates
62 inequalities (Gx>h). The first 28 inequalities impose
bounds on some reactions. The last 34 inequalities impose that
the reaction rates have to be positive (for unidirectional reactions
only).
2 functions that have to be maximised, the biomass production
(growth).
Usage
LIMEcoli
Format
LIMEcoli is of type lim
, which is a list of matrices, vectors,
names and values that specify the linear inverse model problem.
see the return value of Setup
for more information
about this list
A more complete description of this structures is in vignette("LIM")
Author(s)
Karline Soetaert <karline.soetaert@nioz.nl>
References
http://gcrg.ucsd.edu/Downloads/Flux_Balance_Analysis
Edwards,J.S., Covert, M., and Palsson, B.., (2002)
Metabolic Modeling of Microbes: the Flux Balance Approach,
Environmental Microbiology, 4(3): pp. 133-140.
See Also
browseURL(paste(system.file(package="LIM"), "/doc/examples/Reactions/", sep=""))
contains "E_coli.lim", the input file; read this with Setup
Examples
# 1. parsimonious (simplest) solution
pars <- Ldei(LIMEcoli)
# 2. the ranges of each reaction
xr <- Xranges(LIMEcoli, central = TRUE, full = TRUE)
# 3. the optimal solution - solved with linear programming
LP <- Linp(LIMEcoli)
Optimal <- t(LP$X)
# show the results
data.frame(pars = pars$X, Optimal, xr[ ,1:3])
# The central value of linear programming problem is a valid solution
# the central point is a valid solution:
X <- xr[ ,"central"]
max(abs(LIMEcoli$A%*%X - LIMEcoli$B))
min(LIMEcoli$G%*%X - LIMEcoli$H)
# 4. Sample solution space - this takes a while - note that iter is not enough
print(system.time(
xs <- Xsample(LIMEcoli, iter = 200, type = "mirror", test = TRUE) ))
pairs(xs[ ,1:10], pch = ".", cex = 2)
# Print results:
data.frame(pars = pars$X, Optimal = Optimal, xr[ ,1:2],
Mean = colMeans(xs), sd = apply(xs,2,sd))
# Plot results
par(mfrow = c(1, 2))
nr <- LIMEcoli$NUnknowns
ii <- 1:(nr/2)
dotchart(Optimal[ii, 1], xlim = range(xr), pch = 16, cex = 0.8)
segments(xr[ii, 1], 1:nr, xr[ii, 2], 1:nr)
ii <- (nr/2+1):nr
dotchart(Optimal[ii, 1], xlim = range(xr), pch = 16, cex = 0.8)
segments(xr[ii, 1], 1:nr, xr[ii, 2], 1:nr)
mtext(side = 3, cex = 1.5, outer = TRUE, line = -1.5,
"E coli Core Metabolism, optimal solution and ranges")
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(LIM)
Loading required package: limSolve
Loading required package: diagram
Loading required package: shape
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LIM/LIMEcoli.Rd_%03d_medium.png", width=480, height=480)
> ### Name: LIMEcoli
> ### Title: The Escherichia Coli Core Metabolism: Reaction network model
> ### specificiation
> ### Aliases: LIMEcoli
> ### Keywords: datasets
>
> ### ** Examples
>
>
>
> # 1. parsimonious (simplest) solution
> pars <- Ldei(LIMEcoli)
>
> # 2. the ranges of each reaction
> xr <- Xranges(LIMEcoli, central = TRUE, full = TRUE)
>
> # 3. the optimal solution - solved with linear programming
> LP <- Linp(LIMEcoli)
> Optimal <- t(LP$X)
>
> # show the results
> data.frame(pars = pars$X, Optimal, xr[ ,1:3])
pars X1 X2 min max
GLK1 1.0000335 0.000000 5.66169049 0.0000000 10.000000
PGI1 4.2838919 807.532745 5.63978625 -15.8333333 807.532745
PFKA 4.4703252 781.590686 5.55399466 0.8333333 2229.130000
FBP 0.1864334 0.000000 0.00000000 0.0000000 1604.130000
FBA 4.2838919 781.590686 5.55399466 0.8333333 781.590686
TPIA 4.2838919 781.590686 5.55399466 0.8333333 781.590686
GAPA 8.5677837 1541.434199 11.03607040 5.0000000 1541.434199
PGK 8.5677837 1541.434199 11.03607040 5.0000000 1541.434199
GPMA 8.5677837 1492.089090 10.87288384 5.0000000 1492.089090
ENO 8.5677837 1492.089090 10.87288384 5.0000000 1492.089090
PPSA 0.3810706 0.000000 0.00000000 0.0000000 1604.130000
PYKA 3.0394798 466.657964 10.50489266 0.0000000 2136.630000
ACEE 0.0000000 1149.295284 0.19494771 0.0000000 1158.949190
ZWF 0.0000000 0.000000 0.00000000 0.0000000 75.000000
PGL 0.0000000 0.000000 0.00000000 0.0000000 75.000000
GND 0.0000000 0.000000 0.00000000 0.0000000 75.000000
RPIA 0.0000000 23.623833 0.07812511 0.0000000 28.202015
RPE 0.0000000 -23.623833 -0.07812511 -23.6238328 50.000000
TKTA1 0.0000000 -5.850762 -0.01934874 -5.8507623 25.000000
TKTA2 0.0000000 -17.773070 -0.05877637 -17.7730705 25.000000
TALA 0.0000000 -5.850762 -0.01934874 -5.8507623 25.000000
GLTA 1.4322163 35.435749 0.11718767 0.0000000 40.847149
ACNA 1.4322163 35.435749 0.11718767 0.0000000 40.847149
ICDA 0.0000000 35.435749 0.11718767 0.0000000 40.847149
SUCA 0.0000000 0.000000 0.00000000 0.0000000 30.000000
SUCC1 0.0000000 0.000000 0.00000000 0.0000000 30.000000
SDHA1 1.4322163 0.000000 0.00000000 0.0000000 100.000000
FRDA 0.0000000 100.000000 0.00000000 0.0000000 100.000000
FUMA 1.4322163 -100.000000 0.00000000 -100.0000000 8.333333
MDH -1.1932998 -100.000000 0.00000000 -1168.3150000 16.666667
DLD1 4.2144864 0.000000 9.59586683 0.0000000 10.000000
ADHE2 2.9210810 1000.000000 0.07228398 0.0000000 1000.000000
PFLA 5.7855136 10.000000 0.40413317 0.0000000 150.000000
PTA 0.8551376 0.000000 0.00000000 0.0000000 1660.380000
ACKA 0.8551376 0.000000 0.00000000 0.0000000 1660.380000
ACS 0.8551376 0.000000 0.00000000 0.0000000 1604.130000
PCKA 1.0156212 0.000000 0.00000000 0.0000000 1604.130000
PPC 3.6411373 194.384939 0.31213537 0.0000000 1704.130000
MAEB 1.1959311 0.000000 0.00000000 0.0000000 1068.315000
SFCA 2.8618012 0.000000 0.00000000 0.0000000 1068.315000
ACEA 1.4322163 0.000000 0.00000000 0.0000000 30.000000
ACEB 1.4322163 0.000000 0.00000000 0.0000000 30.000000
PPA 0.8551376 0.000000 0.00000000 0.0000000 1604.130000
GLPK 0.0000000 0.000000 0.00000000 0.0000000 0.000000
GPSA1 -1.3755677 0.000000 0.00000000 -140.0000000 0.000000
RBSK 0.0000000 0.000000 0.00000000 0.0000000 0.000000
NUOA 0.0000000 140.000000 0.00000000 0.0000000 140.000000
FDOH 0.0000000 0.000000 0.00000000 0.0000000 140.000000
GLPD 1.3755677 0.000000 0.00000000 0.0000000 140.000000
CYOA 2.8077840 40.000000 0.00000000 0.0000000 40.000000
SDHA2 1.4322163 -100.000000 0.00000000 -100.0000000 8.333333
PNT1A 1.6658701 0.000000 0.00000000 0.0000000 3208.260000
PNT2A 1.8455067 567.965512 1.87828831 0.0000000 3208.260000
ATPA -2.3659951 -145.466329 -0.06247093 -460.0000000 1144.130000
GLCUP 1.0000335 0.000000 5.66169049 0.0000000 10.000000
GLCPTS 3.2838584 814.156250 0.00000000 0.0000000 814.156250
GLUP 0.0000000 0.000000 0.00000000 0.0000000 0.000000
RIBUP 0.0000000 0.000000 0.00000000 0.0000000 0.000000
ACUP 0.0000000 0.000000 0.00000000 -75.0000000 0.000000
LACUP -4.2144864 0.000000 -9.59586683 -10.0000000 0.000000
FORUP -5.7855136 -10.000000 -0.40413317 -10.0000000 0.000000
ETHUP -2.9210810 -1000.000000 -0.07228398 -1000.0000000 0.000000
SUCCUP 0.0000000 -100.000000 0.00000000 -130.0000000 0.000000
PYRUP 0.0000000 -27.796342 0.00000000 -150.0000000 0.000000
PIUP 0.0000000 120.547782 0.39865711 0.0000000 120.547782
O2TX 1.4038920 20.000000 0.00000000 0.0000000 20.000000
CO2TX -1.4322163 -990.346093 0.00000000 -1000.0000000 0.000000
ATPM 5.8700000 5.870000 5.87000000 5.8700000 5.870000
ADK 1.2362082 0.000000 0.00000000 0.0000000 1604.130000
Growth 0.0000000 33.117523 0.10952118 0.0000000 33.117523
central
GLK1 5.2217621
PGI1 216.5697207
PFKA 238.7778727
FBP 22.9161429
FBA 215.8617298
TPIA 215.8617298
GAPA 430.0614321
PGK 430.0614321
GPMA 422.7068367
ENO 422.7068367
PPSA 50.9755288
PYKA 162.1156839
ACEE 315.0391553
ZWF 4.7377785
PGL 4.7377785
GND 4.7377785
RPIA 5.1002515
RPE -0.3624730
TKTA1 0.7072381
TKTA2 -1.0697111
TALA 0.7072381
GLTA 8.0839604
ACNA 8.0839604
ICDA 6.3683952
SUCA 1.0869072
SUCC1 1.0869072
SDHA1 1.8617943
FRDA 43.4000979
FUMA -41.5383036
MDH -75.1064185
DLD1 6.0611808
ADHE2 293.8147256
PFLA 9.5011072
PTA 72.0346497
ACKA 72.0346497
ACS 69.5691667
PCKA 36.7907143
PPC 128.7671200
MAEB 27.6528586
SFCA 7.6308214
ACEA 1.7155652
ACEB 1.7155652
PPA 69.5691667
GLPK 0.0000000
GPSA1 -8.7841492
RBSK 0.0000000
NUOA 47.2738862
FDOH 5.5622880
GLPD 8.7841492
CYOA 20.0820198
SDHA2 -41.5383036
PNT1A 106.2471989
PNT2A 161.4679124
ATPA -66.0598334
GLCUP 5.2217621
GLCPTS 217.0729311
GLUP 0.0000000
RIBUP 0.0000000
ACUP -2.4654831
LACUP -6.0611808
FORUP -3.9388192
ETHUP -293.8147256
SUCCUP -44.3407761
PYRUP -18.9265277
PIUP 17.9669311
O2TX 10.0410099
CO2TX -276.1017986
ATPM 5.8700000
ADK 120.5446954
Growth 4.9359701
>
> # The central value of linear programming problem is a valid solution
> # the central point is a valid solution:
> X <- xr[ ,"central"]
> max(abs(LIMEcoli$A%*%X - LIMEcoli$B))
[1] 3.979039e-13
> min(LIMEcoli$G%*%X - LIMEcoli$H)
[1] 0
>
> # 4. Sample solution space - this takes a while - note that iter is not enough
> print(system.time(
+ xs <- Xsample(LIMEcoli, iter = 200, type = "mirror", test = TRUE) ))
user system elapsed
1.380 0.028 1.409
Warning message:
In lsei(E = E, F = F, G = G, H = H) : No equalities - setting type = 2
>
> pairs(xs[ ,1:10], pch = ".", cex = 2)
>
> # Print results:
> data.frame(pars = pars$X, Optimal = Optimal, xr[ ,1:2],
+ Mean = colMeans(xs), sd = apply(xs,2,sd))
pars Optimal.1 Optimal.2 min max
GLK1 1.0000335 0.000000 5.66169049 0.0000000 10.000000
PGI1 4.2838919 807.532745 5.63978625 -15.8333333 807.532745
PFKA 4.4703252 781.590686 5.55399466 0.8333333 2229.130000
FBP 0.1864334 0.000000 0.00000000 0.0000000 1604.130000
FBA 4.2838919 781.590686 5.55399466 0.8333333 781.590686
TPIA 4.2838919 781.590686 5.55399466 0.8333333 781.590686
GAPA 8.5677837 1541.434199 11.03607040 5.0000000 1541.434199
PGK 8.5677837 1541.434199 11.03607040 5.0000000 1541.434199
GPMA 8.5677837 1492.089090 10.87288384 5.0000000 1492.089090
ENO 8.5677837 1492.089090 10.87288384 5.0000000 1492.089090
PPSA 0.3810706 0.000000 0.00000000 0.0000000 1604.130000
PYKA 3.0394798 466.657964 10.50489266 0.0000000 2136.630000
ACEE 0.0000000 1149.295284 0.19494771 0.0000000 1158.949190
ZWF 0.0000000 0.000000 0.00000000 0.0000000 75.000000
PGL 0.0000000 0.000000 0.00000000 0.0000000 75.000000
GND 0.0000000 0.000000 0.00000000 0.0000000 75.000000
RPIA 0.0000000 23.623833 0.07812511 0.0000000 28.202015
RPE 0.0000000 -23.623833 -0.07812511 -23.6238328 50.000000
TKTA1 0.0000000 -5.850762 -0.01934874 -5.8507623 25.000000
TKTA2 0.0000000 -17.773070 -0.05877637 -17.7730705 25.000000
TALA 0.0000000 -5.850762 -0.01934874 -5.8507623 25.000000
GLTA 1.4322163 35.435749 0.11718767 0.0000000 40.847149
ACNA 1.4322163 35.435749 0.11718767 0.0000000 40.847149
ICDA 0.0000000 35.435749 0.11718767 0.0000000 40.847149
SUCA 0.0000000 0.000000 0.00000000 0.0000000 30.000000
SUCC1 0.0000000 0.000000 0.00000000 0.0000000 30.000000
SDHA1 1.4322163 0.000000 0.00000000 0.0000000 100.000000
FRDA 0.0000000 100.000000 0.00000000 0.0000000 100.000000
FUMA 1.4322163 -100.000000 0.00000000 -100.0000000 8.333333
MDH -1.1932998 -100.000000 0.00000000 -1168.3150000 16.666667
DLD1 4.2144864 0.000000 9.59586683 0.0000000 10.000000
ADHE2 2.9210810 1000.000000 0.07228398 0.0000000 1000.000000
PFLA 5.7855136 10.000000 0.40413317 0.0000000 150.000000
PTA 0.8551376 0.000000 0.00000000 0.0000000 1660.380000
ACKA 0.8551376 0.000000 0.00000000 0.0000000 1660.380000
ACS 0.8551376 0.000000 0.00000000 0.0000000 1604.130000
PCKA 1.0156212 0.000000 0.00000000 0.0000000 1604.130000
PPC 3.6411373 194.384939 0.31213537 0.0000000 1704.130000
MAEB 1.1959311 0.000000 0.00000000 0.0000000 1068.315000
SFCA 2.8618012 0.000000 0.00000000 0.0000000 1068.315000
ACEA 1.4322163 0.000000 0.00000000 0.0000000 30.000000
ACEB 1.4322163 0.000000 0.00000000 0.0000000 30.000000
PPA 0.8551376 0.000000 0.00000000 0.0000000 1604.130000
GLPK 0.0000000 0.000000 0.00000000 0.0000000 0.000000
GPSA1 -1.3755677 0.000000 0.00000000 -140.0000000 0.000000
RBSK 0.0000000 0.000000 0.00000000 0.0000000 0.000000
NUOA 0.0000000 140.000000 0.00000000 0.0000000 140.000000
FDOH 0.0000000 0.000000 0.00000000 0.0000000 140.000000
GLPD 1.3755677 0.000000 0.00000000 0.0000000 140.000000
CYOA 2.8077840 40.000000 0.00000000 0.0000000 40.000000
SDHA2 1.4322163 -100.000000 0.00000000 -100.0000000 8.333333
PNT1A 1.6658701 0.000000 0.00000000 0.0000000 3208.260000
PNT2A 1.8455067 567.965512 1.87828831 0.0000000 3208.260000
ATPA -2.3659951 -145.466329 -0.06247093 -460.0000000 1144.130000
GLCUP 1.0000335 0.000000 5.66169049 0.0000000 10.000000
GLCPTS 3.2838584 814.156250 0.00000000 0.0000000 814.156250
GLUP 0.0000000 0.000000 0.00000000 0.0000000 0.000000
RIBUP 0.0000000 0.000000 0.00000000 0.0000000 0.000000
ACUP 0.0000000 0.000000 0.00000000 -75.0000000 0.000000
LACUP -4.2144864 0.000000 -9.59586683 -10.0000000 0.000000
FORUP -5.7855136 -10.000000 -0.40413317 -10.0000000 0.000000
ETHUP -2.9210810 -1000.000000 -0.07228398 -1000.0000000 0.000000
SUCCUP 0.0000000 -100.000000 0.00000000 -130.0000000 0.000000
PYRUP 0.0000000 -27.796342 0.00000000 -150.0000000 0.000000
PIUP 0.0000000 120.547782 0.39865711 0.0000000 120.547782
O2TX 1.4038920 20.000000 0.00000000 0.0000000 20.000000
CO2TX -1.4322163 -990.346093 0.00000000 -1000.0000000 0.000000
ATPM 5.8700000 5.870000 5.87000000 5.8700000 5.870000
ADK 1.2362082 0.000000 0.00000000 0.0000000 1604.130000
Growth 0.0000000 33.117523 0.10952118 0.0000000 33.117523
Mean sd
GLK1 5.383570 2.957629
PGI1 499.824050 86.573131
PFKA 674.894666 187.037241
FBP 171.030694 150.846768
FBA 503.863972 86.289267
TPIA 503.863972 86.289267
GAPA 1009.196079 172.412354
PGK 1009.196079 172.412354
GPMA 1006.093364 171.752924
ENO 1006.093364 171.752924
PPSA 135.822696 123.040973
PYKA 299.846173 184.157629
ACEE 842.617205 164.346761
ZWF 8.506655 7.451535
PGL 8.506655 7.451535
GND 8.506655 7.451535
RPIA 4.320968 2.815135
RPE 4.185687 5.159968
TKTA1 2.467668 2.509367
TKTA2 1.718019 2.692102
TALA 2.467668 2.509367
GLTA 10.661805 4.748595
ACNA 10.661805 4.748595
ICDA 6.528516 3.980254
SUCA 4.300392 3.534375
SUCC1 4.300392 3.534375
SDHA1 12.196778 10.645321
FRDA 87.046794 11.887012
FUMA -74.850016 15.623049
MDH -323.275874 135.664449
DLD1 4.577249 2.732855
ADHE2 853.523085 162.459546
PFLA 43.318177 26.829693
PTA 142.343586 118.870458
ACKA 142.343586 118.870458
ACS 132.514405 117.499635
PCKA 156.115946 151.650165
PPC 493.760224 197.152522
MAEB 140.291090 119.139474
SFCA 112.268056 99.666325
ACEA 4.133288 3.590485
ACEB 4.133288 3.590485
PPA 132.514405 117.499635
GLPK 0.000000 0.000000
GPSA1 -31.770162 23.134791
RBSK 0.000000 0.000000
NUOA 34.976164 23.675260
FDOH 37.895425 26.537944
GLPD 31.770162 23.134791
CYOA 29.791734 9.409149
SDHA2 -74.850016 15.623049
PNT1A 696.851707 502.203200
PNT2A 602.729535 500.365131
ATPA -9.149463 236.270588
GLCUP 5.383570 2.957629
GLCPTS 503.363606 86.665513
GLUP 0.000000 0.000000
RIBUP 0.000000 0.000000
ACUP -9.829181 8.449412
LACUP -4.577249 2.732855
FORUP -5.422751 2.732855
ETHUP -853.523085 162.459546
SUCCUP -83.283697 17.202926
PYRUP -23.540523 21.650282
PIUP 7.579787 6.883000
O2TX 14.895867 4.704574
CO2TX -814.763062 162.938172
ATPM 5.870000 0.000000
ADK 268.337101 171.673516
Growth 2.082359 1.890934
>
> # Plot results
> par(mfrow = c(1, 2))
> nr <- LIMEcoli$NUnknowns
> ii <- 1:(nr/2)
> dotchart(Optimal[ii, 1], xlim = range(xr), pch = 16, cex = 0.8)
> segments(xr[ii, 1], 1:nr, xr[ii, 2], 1:nr)
> ii <- (nr/2+1):nr
> dotchart(Optimal[ii, 1], xlim = range(xr), pch = 16, cex = 0.8)
> segments(xr[ii, 1], 1:nr, xr[ii, 2], 1:nr)
> mtext(side = 3, cex = 1.5, outer = TRUE, line = -1.5,
+ "E coli Core Metabolism, optimal solution and ranges")
>
>
>
>
>
> dev.off()
null device
1
>