LIMEcoli {LIM}

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 <[e-mail]>

References

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")