Metatool and bindings for use with PySCeS - adds elementary mode analysis. The MetaTool source code has been slightly altered to allow building under Linux and for use with PySCeS
Brett G. Olivier, Amsterdam 2017.
The official code repository (http://github.com/PySCeS) of The Python Simulator for Cellular Systems: PySCeS project.
Copyright (c) 2004 - 2017, Brett G. Olivier, Johann M. Rohwer and Jan-Hendrik S. Hofmeyr All rights reserved.
METATOOL is a C program developed from 1998 to 2000 by Thomas Pfeiffer (Berlin) in cooperation with Stefan Schuster and Ferdinand Moldenhauer (Berlin) and Juan Carlos Nuno (Madrid). It serves to derive conclusions about the pathway structure of metabolic networks from the stoichiometric reaction equations and information about reversibility and irreversibility of enzymes. It should preferably be compiled with the GNU compiler. For DOS and Win32 console applications, comment out the two lines #include<conio.h> and #include<malloc.h>. The program requires the two names of the input and output files at the command line. To explain the format of the input file, we give an example file (Example.dat), which codifies a reaction scheme comprising the tricarboxylic acid cycle, glyoxylate shunt and adjacent reactions of amino acid synthesis in E. coli (cf. Ref. 1).
-ENZREV Eno Acn SucCD Sdh Fum Mdh AspC Gdh IlvEAvtA
-ENZIRREV Pyk AceEF GltA Icd SucAB Icl Mas AspCon AspA Pck Ppc Pps GluCon AlaCon SucCoACon
-METINT Ala Asp Glu Gly Mal Fum Succ SucCoA OG IsoCit Cit OAA AcCoA CoA Pyr PEP
-METEXT Sucex Alaex Gluex ADP ATP AMP NH3 Aspex FADH2 FAD GTP GDP NADPH NADP NADH CO2 NAD PG
-CAT Eno : PG = PEP . Pyk : PEP + ADP = Pyr + ATP . AceEF : Pyr + NAD + CoA = AcCoA + CO2 + NADH . GltA : OAA + AcCoA = Cit + CoA . Acn : Cit = IsoCit . Icd : IsoCit + NADP = OG + CO2 + NADPH . SucAB : OG + NAD + CoA = SucCoA + CO2 + NADH . SucCD : SucCoA + ADP = Succ + ATP + CoA . Sdh : Succ + FAD = Fum + FADH2 . Fum : Fum = Mal . Mdh : Mal + NAD = OAA + NADH . Icl : IsoCit = Succ + Gly . Mas : Gly + AcCoA = Mal + CoA . AspC : OAA + Glu = Asp + OG . AspCon : Asp = Aspex . AspA : Asp = Fum + NH3 . Gdh : OG + NH3 + NADPH = Glu + NADP . Pck : OAA + ATP = PEP + ADP + CO2 . Ppc : PEP + CO2 = OAA . Pps : Pyr + ATP = PEP + AMP . GluCon : Glu = Gluex . IlvEAvtA : Pyr + Glu = Ala + OG . AlaCon : Ala = Alaex . SucCoACon : SucCoA = Sucex + CoA .
[Explanation: -ENZREV, -ENZIRREV After the key words -ENZREV and -ENZIRREV, names or abbreviations of the reversible and irreversible enzymes, respectively, have to be written. -METINT, -METEXT After the key word -METINT, names or abbreviations of the internal metabolites have to be written. These are the substances which have to fulfil a steady-state condition (production = consumption). After the key word -METEXT names or abbreviations of the external metabolites have to be written. External metabolites (sources and sinks) need not be balanced in the scheme under consideration. The order of these four fields is important. All internal and external metabolites must have an underscore or a letter (no number) as the first character and must not include a white space. -CAT After the key word -CAT, the reaction equations are listed in any order. The raction name is written first just as after the key words -ENZREV and -ENZREV. The reaction name is followed by a white space (space or tab), a colon and a white space. Then the stoichiometric reaction equation follows. Stoichiometric coefficients are integers separated by a white space from the metabolites. After the metabolites, a white space and a plus or a white space and an equal sign follow. The end of each reaction is formed by a white space and a full stop. Metabolites are written in the same way as after the key words -METINT and -METEXT. The order of metabolites in the reaction equations makes no difference. However, the sides of the reaction equations are exchangeable only in the reversible reactions. The metabolites that are formed by the irreversible reactions have to be written on the right side of the reaction equations.]
The program writes the results in an output file. For our example, this file reads as follows:
METATOOL OUTPUT Version 2.0 [your path to]\meta2.exe
INPUT FILE: Example.dat
INTERNAL METABOLITES: 19 REACTIONS: 24
STOICHIOMETRIC MATRIX:
matrix dimension 16 x 24 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 -1 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 0 -1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 following line indicates reversible (0) and irreversible reactions (1) 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[Explanation: The program gives the numbers of internal metabolites and reactions. It also parses the reaction equations and translates them into a stoichiometric matrix. This matrix includes the stoichiometric coefficients (molecularities) of the internal metabolites in all the reaction equations, with the rows corresponding to internal metabolites and the columns corresponding to reactions. The line following the stoichiometric matrix indicates the reversible and irreversible reactions in the same order as after the key words -ENZREV and -ENZIRREV.]
KERNEL
matrix dimension 9 x 24 -1 -1 -1 -1 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 -2 -1 0 -1 -1 -2 -1 -1 0 -2 -2 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 -1 0 -1 -1 -2 0 0 0 -2 -2 -1 0 0 -1 -1 0 0 -1 0 0 0 0 0 1 1 0 1 1 2 0 0 0 2 2 1 0 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -3 -2 0 -1 -1 -2 0 -1 0 -3 -3 -2 -1 0 -1 -1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 -1 0 0 1 0 0 0 2 2 1 0 0 1 1 0 0 0 0 0 0 0 1
[Explanation: The kernel or nullspace is the subspace of all flux vectors V that satisfy the equation Stoich. matrix times V = 0 (see Ref. 2). The rows of the above matrix span this subspace.]
enzymes
1: -Eno -Acn -SucCD -Sdh -Fum -Mdh -Pyk -AceEF -GltA -Icd -SucAB irreversible 2: (-2 Eno) -Acn -Sdh -Fum (-2 Mdh) -AspC -Gdh (-2 Pyk) (-2 AceEF) -GltA -Icl -Mas -AspCon irreversible 3: -Fum -Mdh -AspC -Gdh -AspA irreversible 4: -Eno -Acn -Sdh -Fum (-2 Mdh) (-2 Pyk) (-2 AceEF) -GltA -Icl -Mas -Pck irreversible 5: Eno Acn Sdh Fum (2 Mdh) (2 Pyk) (2 AceEF) GltA Icl Mas -Ppc irreversible 6: Pyk Pps irreversible 7: (-3 Eno) (-2 Acn) -Sdh -Fum (-2 Mdh) -Gdh (-3 Pyk) (-3 AceEF) (-2 GltA) -Icd -Icl -Mas -GluCon irreversible 8: Eno Gdh IlvEAvtA Pyk AlaCon irreversible 9: (2 Eno) Acn -SucCD Mdh (2 Pyk) (2 AceEF) GltA Icl Mas SucCoACon irreversible
[Explanation: This list contains the enzymes that correspond to the rows of the kernel matrix. The coefficients indicate relative fluxes carried by the enzymes. A minus sign before an enzyme name stands for -1. The following nine lines contain the sum of metabolites which are involved in these enzyme reactions. E.g. in reaction 6, Pyk and Pps catalyse PEP + ADP = Pyr + ATP and Pyr + ATP = PEP + AMP, respectively, which gives, as the overall reaction: ADP = AMP]
overall reaction
1: 2 ATP + FADH2 + NADPH + 3 NADH + 3 CO2 = 2 ADP + FAD + NADP + 3 NAD
- PG 2: 2 ATP + Aspex + FADH2 + NADP + 4 NADH + 2 CO2 = 2 ADP + NH3 + FAD + NADPH + 4 NAD + 2 PG 3: NADP + NADH = NADPH + NAD 4: ATP + FADH2 + 4 NADH + 3 CO2 = ADP + FAD + 4 NAD + PG 5: 2 ADP + FAD + 4 NAD + PG = 2 ATP + FADH2 + 4 NADH + 3 CO2 6: ADP = AMP 7: Gluex + 3 ATP + FADH2 + 5 NADH + 4 CO2 = 3 ADP + NH3 + FAD + 5 NAD + 3 PG 8: ADP + NH3 + NADPH + PG = Alaex + ATP + NADP 9: ADP + 3 NAD + 2 PG = Sucex + ATP + 3 NADH + 2 CO2
SUBSETS of reactions (21 rows)
matrix dimension 21 x 24 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
[Explanation: Enzyme subsets are sets of enzymes that always operate together in fixed flux ratios. For example, if aconitase (Acn) is operative, then also citrate synthase (GltA) is operative. This information can be written in the form of a matrix (see above). For example, the second row contains ones at positions 2 and 12, which correspond to Acn and GltA. Below, this information is given in more detailed form, together with the overall reactions of the subsets.]
enzymes
1: -Eno reversible 2: Acn GltA irreversible 3: -SucCD reversible 4: -Sdh reversible 5: -Fum reversible 6: -Mdh reversible 7: -AspC reversible 8: -Gdh reversible 9: IlvEAvtA AlaCon irreversible 10: Pyk irreversible 11: AceEF irreversible 12: Icd irreversible 13: SucAB irreversible 14: Icl Mas irreversible 15: AspCon irreversible 16: AspA irreversible 17: Pck irreversible 18: Ppc irreversible 19: Pps irreversible 20: GluCon irreversible 21: SucCoACon irreversible
overall reaction
1: PEP = PG 2: OAA + AcCoA = IsoCit + CoA 3: Succ + CoA + ATP = SucCoA + ADP 4: Fum + FADH2 = Succ + FAD 5: Mal = Fum 6: OAA + NADH = Mal + NAD 7: Asp + OG = Glu + OAA 8: Glu + NADP = OG + NH3 + NADPH 9: Glu + Pyr = OG + Alaex 10: PEP + ADP = Pyr + ATP 11: CoA + Pyr + NAD = AcCoA + NADH + CO2 12: IsoCit + NADP = OG + NADPH + CO2 13: OG + CoA + NAD = SucCoA + NADH + CO2 14: IsoCit + AcCoA = Mal + Succ + CoA 15: Asp = Aspex 16: Asp = Fum + NH3 17: OAA + ATP = PEP + ADP + CO2 18: PEP + CO2 = OAA 19: Pyr + ATP = PEP + AMP 20: Glu = Gluex 21: SucCoA = CoA + Sucex
[Explanation: Enzymes belonging to the same subset can be lumped. This gives rise to the following reduced reaction system.]
REDUCED SYSTEM with 13 branch point metabolites in 21 reactions (columns)
matrix dimension 13 x 21 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 1 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 -1 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 -1 1 0 0 following line indicates reversible (0) and irreversible reactions (1) 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
[Explanation: "The simplified system is a kind of skeleton model of the original system. It contains only metabolites at branch points. Skeleton models are often used in metabolic modeling to reduce the number of variables" (see Refs. 5-7).
CONVEX BASIS
matrix dimension 12 x 21 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 -1 -1 -1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 -2 1 0 0 0 0 0 -1 0 1 1 1 0 0 0 0 0 1 0 1 0 -1 1 0 -1 -1 -2 0 0 0 2 2 0 0 1 0 0 1 0 0 0 0 -2 1 0 -1 -1 -2 -1 -1 0 2 2 0 0 1 1 0 0 0 0 0 0 -2 1 1 0 0 -1 0 0 0 2 2 0 0 1 0 0 0 0 0 0 1 -3 2 0 -1 -1 -2 0 -1 0 3 3 1 0 1 0 0 0 0 0 1 0
enzymes
1: Fum Mdh AspC Gdh AspA irreversible 2: Pck Ppc irreversible 3: Pyk Pps irreversible 4: Eno AspC Gdh AspCon Ppc irreversible 5: Eno -SucCD -Sdh -Fum -Mdh Ppc SucCoACon irreversible 6: Eno Gdh IlvEAvtA Pyk AlaCon irreversible 7: Eno Acn SucCD Sdh Fum Mdh Pyk AceEF GltA Icd SucAB irreversible 8: (2 Eno) Acn Gdh Pyk AceEF GltA Icd Ppc GluCon irreversible 9: Eno Acn Sdh Fum (2 Mdh) (2 Pyk) (2 AceEF) GltA Icl Mas Pck irreversible 10: (2 Eno) Acn Sdh Fum (2 Mdh) AspC Gdh (2 Pyk) (2 AceEF) GltA Icl Mas AspCon irreversible 11: (2 Eno) Acn -SucCD Mdh (2 Pyk) (2 AceEF) GltA Icl Mas SucCoACon irreversible 12: (3 Eno) (2 Acn) Sdh Fum (2 Mdh) Gdh (3 Pyk) (3 AceEF) (2 GltA) Icd Icl Mas GluCon irreversible
overall reaction
1: NADPH + NAD = NADP + NADH 2: ATP = ADP 3: ADP = AMP 4: NH3 + NADPH + CO2 + PG = Aspex + NADP 5: ATP + FADH2 + NADH + CO2 + PG = Sucex + ADP + FAD + NAD 6: ADP + NH3 + NADPH + PG = Alaex + ATP + NADP 7: 2 ADP + FAD + NADP + 3 NAD + PG = 2 ATP + FADH2 + NADPH + 3 NADH + 3 CO2 8: ADP + NH3 + NAD + 2 PG = Gluex + ATP + NADH + CO2 9: ADP + FAD + 4 NAD + PG = ATP + FADH2 + 4 NADH + 3 CO2 10: 2 ADP + NH3 + FAD + NADPH + 4 NAD + 2 PG = 2 ATP + Aspex + FADH2 + NADP + 4 NADH + 2 CO2 11: ADP + 3 NAD + 2 PG = Sucex + ATP + 3 NADH + 2 CO2 12: 3 ADP + NH3 + FAD + 5 NAD + 3 PG = Gluex + 3 ATP + FADH2 + 5 NADH + 4 CO2
[Explanation: The convex basis is the minimum number of elementary modes to reconstruct the whole reaction system. Any admissible flux distribution in the system (i.e. any distribution that is compatible with the steady-state condition and the directionality of the irreversible reactions) can be written as a non-negative linear combination of the vectors forming the convex basis (Ref. 5). These vectors form the rows of the above matrix. These rows are then translated into lists of enzymes in the same way as have been translated above the rows of the null-space matrix. A basis vector is reversible if its negative is an admissible flux distribution as well, otherwise it is irreversible.]
CONSERVATON RELATIONS
matrix dimension 1 x 16 0 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 0 0
[Explanation - Conservation relations indicate that linear combinations (e.g. the sum) of several internal metabolites are constant. The metabolites are in the same order as after the keyword -METINT. The above row means that SucCoA + AcCoA + CoA = const. (The minus sign in the above row is irrelevant because we can multiply the equation by -1).]
ELEMENTARY MODES
matrix dimension 16 x 21 0 0 0 0 -1 -1 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 -1 0 1 1 0 0 -1 -1 0 0 0 0 0 0 0 1 0 1 0 0 1 -1 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 -2 1 1 0 0 -1 0 0 0 2 2 0 0 1 0 0 0 0 0 0 1 -1 1 -1 -1 -1 -1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 -3 1 2 1 1 0 0 0 0 2 2 0 0 1 0 0 0 1 0 0 2 -2 1 0 0 0 0 0 -1 0 1 1 1 0 0 0 0 0 1 0 1 0 -2 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 -1 1 0 -1 -1 -2 0 0 0 2 2 0 0 1 0 0 1 0 0 0 0 -2 1 0 -1 -1 -2 -1 -1 0 2 2 0 0 1 1 0 0 0 0 0 0 -3 2 0 -1 -1 -2 0 -1 0 3 3 1 0 1 0 0 0 0 0 1 0 -3 2 0 -1 -1 -2 0 0 0 3 3 1 1 1 0 0 0 0 0 0 1
[Explanation: The choice of the basis vectors of the kernel (or nullspace) is not unique. Therefore, it was proposed (Refs. 1,3-5,7) to take a complete set of the simplest basis vectors compatible with the directionality of the irreversible reactions. These are called elementary modes. There may be more of them then actually needed to span the admissible region in flux space, but they have the favourable property to be uniquely determined (up to scalar multiples). These modes can be brought in relation with the biochemical pathways in the system. The rows of the elementary modes matrix give the elementary modes for our example system.]
[Explanation: Below goes the verbal listing of the elementary modes and of the overall reactions in terms of the external metabolites:]
enzymes
1: Fum Mdh AspC Gdh AspA irreversible 2: Pck Ppc irreversible 3: Pyk Pps irreversible 4: Eno AspC Gdh AspCon Ppc irreversible 5: Eno -SucCD -Sdh -Fum -Mdh Ppc SucCoACon irreversible 6: Eno -SucCD -Sdh AspC Gdh AspA Ppc SucCoACon irreversible 7: Eno Gdh IlvEAvtA Pyk AlaCon irreversible 8: (2 Eno) Acn -SucCD Mdh (2 Pyk) (2 AceEF) GltA Icl Mas SucCoACon irreversible 9: Eno Acn SucCD Sdh Fum Mdh Pyk AceEF GltA Icd SucAB irreversible 10: (3 Eno) Acn (-2 SucCD) -Sdh -Fum (2 Pyk) (2 AceEF) GltA Icl Mas Ppc (2 SucCoACon) irreversible 11: (2 Eno) Acn Gdh Pyk AceEF GltA Icd Ppc GluCon irreversible 12: (2 Eno) Acn Pyk AceEF GltA Icd SucAB Ppc SucCoACon irreversible 13: Eno Acn Sdh Fum (2 Mdh) (2 Pyk) (2 AceEF) GltA Icl Mas Pck irreversible 14: (2 Eno) Acn Sdh Fum (2 Mdh) AspC Gdh (2 Pyk) (2 AceEF) GltA Icl Mas AspCon irreversible 15: (3 Eno) (2 Acn) Sdh Fum (2 Mdh) Gdh (3 Pyk) (3 AceEF) (2 GltA) Icd Icl Mas GluCon irreversible 16: (3 Eno) (2 Acn) Sdh Fum (2 Mdh) (3 Pyk) (3 AceEF) (2 GltA) Icd SucAB Icl Mas SucCoACon irreversible
overall reaction
1: NADPH + NAD = NADP + NADH 2: ATP = ADP 3: ADP = AMP 4: NH3 + NADPH + CO2 + PG = Aspex + NADP 5: ATP + FADH2 + NADH + CO2 + PG = Sucex + ADP + FAD + NAD 6: ATP + FADH2 + NADPH + CO2 + PG = Sucex + ADP + FAD + NADP 7: ADP + NH3 + NADPH + PG = Alaex + ATP + NADP 8: ADP + 3 NAD + 2 PG = Sucex + ATP + 3 NADH + 2 CO2 9: 2 ADP + FAD + NADP + 3 NAD + PG = 2 ATP + FADH2 + NADPH + 3 NADH + 3 CO2 10: FADH2 + 2 NAD + 3 PG = 2 Sucex + FAD + 2 NADH + CO2 11: ADP + NH3 + NAD + 2 PG = Gluex + ATP + NADH + CO2 12: ADP + NADP + 2 NAD + 2 PG = Sucex + ATP + NADPH + 2 NADH + 2 CO2 13: ADP + FAD + 4 NAD + PG = ATP + FADH2 + 4 NADH + 3 CO2 14: 2 ADP + NH3 + FAD + NADPH + 4 NAD + 2 PG = 2 ATP + Aspex + FADH2 + NADP + 4 NADH + 2 CO2 15: 3 ADP + NH3 + FAD + 5 NAD + 3 PG = Gluex + 3 ATP + FADH2 + 5 NADH + 4 CO2 16: 3 ADP + FAD + NADP + 6 NAD + 3 PG = Sucex + 3 ATP + FADH2 + NADPH + 6 NADH + 5 CO2
References
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Schuster, S., Dandekar, T and Fell, D. (1999) Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering, TIBTECH, 17, 53-60.
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Reder, C. (1988) Metabolic control theory: a structural approach. J. theor. Biol. 135, 175-201.
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Schuster, S. and Hilgetag, C. (1994) On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165-182.
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Schuster, S., Hilgetag, C., Woods, J. H. and Fell, D. A. (1996) Elementary modes of functioning in biochemical networks. In: Computation in Cellular and Molecular Biological Systems (Cuthbertson, R., Holcombe, M. and Paton, R., eds), pp. 151-165, World Scientific, Singapore.
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T. Pfeiffer, I. Sanchez-Valdenebro, J. C. Nuno, F. Montero and S. Schuster: METATOOL: For Studying Metabolic Networks, Bioinformatics 15 (1999) 251-257.
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R. Heinrich, H.-G. Holzhuetter and S. Schuster (1987) A theoretical approach to the evolution and structural design of enzymatic networks; linear enzymatic chains, branched pathways and glycolysis of erythrocytes, Bull. Math. Biol. 49, 539-595.
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R. Heinrich and S. Schuster (1996) The Regulation of Cellular Systems, Chapman & Hall, New York.
See also http://www.biologie.hu-berlin.de/biophysics/Theory/tpfeiffer/metatool.html.