- Open Access
FASIMU: flexible software for flux-balance computation series in large metabolic networks
BMC Bioinformatics volume 12, Article number: 28 (2011)
Flux-balance analysis based on linear optimization is widely used to compute metabolic fluxes in large metabolic networks and gains increasingly importance in network curation and structural analysis. Thus, a computational tool flexible enough to realize a wide variety of FBA algorithms and able to handle batch series of flux-balance optimizations is of great benefit.
We present FASIMU, a command line oriented software for the computation of flux distributions using a variety of the most common FBA algorithms, including the first available implementation of (i) weighted flux minimization, (ii) fitness maximization for partially inhibited enzymes, and (iii) of the concentration-based thermodynamic feasibility constraint. It allows batch computation with varying objectives and constraints suited for network pruning, leak analysis, flux-variability analysis, and systematic probing of metabolic objectives for network curation. Input and output supports SBML. FASIMU can work with free (lp_solve and GLPK) or commercial solvers (CPLEX, LINDO). A new plugin (faBiNA) for BiNA allows to conveniently visualize calculated flux distributions. The platform-independent program is an open-source project, freely available under GNU public license at http://www.bioinformatics.org/fasimu including manual, tutorial, and plugins.
We present a flux-balance optimization program whose main merits are the implementation of thermodynamics as a constraint, batch series of computations, free availability of sources, choice on various external solvers, and the flexibility on metabolic objectives and constraints.
The distribution of fluxes (i.e. reactions rates of enzymes and transporters) in large metabolic networks is commonly calculated by means of constraint-based optimization methods, usually referred to as flux-balance analysis (FBA). The first FBA applications relied on the steady-state assumption and biomass maximization only . However, recently the scope of FBA has widened: (i) alternative objective functions are necessary to adapt FBA to different environments, metabolic excretion and growth patterns, and cell types [2, 3], (ii) thermodynamic principles have to be considered in the calculation , (iii) mRNA, protein and metabolite profiles are available as an additional information source , (iv) metabolic networks are curated using on the fly verification , and (iv) FBA is used for structural network analysis avoiding the combinatorial explosion that topological algorithms suffer from. Thus, the quality of FBA software must now be measured on (i) the flexibility in the definition of objectives and constraints and (ii) the ability to perform batch series of calculations with varying objectives and constraints whose results are automatically evaluated.
Several software solutions for FBA are currently available. The freely available software COBRA  covers a considerable variety of FBA algorithms and is conceptually similar to FASIMU. It is a MATLAB  toolbox using a variety of free and commercial solvers including CPLEX via the TOMLAB® Optimization Environment  as the recommended choice. OptFlux  covers an even larger range of flux optimization methods accessible through a graphical user interface. It is an easy-to-use solution well suited for biotechnologists with lesser interest in the algorithmic details. Systems Biology Research Tool (SBRT)  is a conceptually very powerful framework for the analysis of stoichiometric networks. A number of algorithms based on flux-balance optimizations is implemented and the addition of further "processes" is possible. The BioSPICE  framework includes two modules performing flux balance optimization: Fluxor  computes biomass maximization and MOMA  is the original implementation of the method with the same name. The open source program PathwayAnalyser  is a simple command-line program implementing FBA and MOMA. See Table 1 for a feature comparison of the cited packages.
For all of the above programs, the use of thermodynamic feasibility as a direct constraint is currently missing. AnNET  is the only available tool so far that tests a given flux distribution on thermodynamic feasibility but only as a post-check and not as a constraint for FBA. A number of FBA-based algorithms such as pruning , thermodynamic realizability , inferring active subnetworks from expression profiles [18, 19] are not yet available as an easy-to-use implementation. Batch processing of easily definable simulation series required for on-the-fly testing of network functions in a network curation process are not included in the above software solutions. This prompted us to develop a new software.
We have developed FASIMU - a comprehensive, flexible and user-friendly computation environment for FBA. Its command-line interface allows to tackle difficult problems in an interactive approach which can later be transferred into an executable computation script. FASIMU is "open" in two aspects: (i) the source code is open and written in widely known scripting languages which makes it easy to adapt and to implement new functions and (ii) intermediate results are stored in human-readable files rendering the calculation process traceable.
For the computational effort, FASIMU is divided in two parts. The computationally expensive part, the solution of the optimization problem, is left to specialized and highly optimized software: the commercials programs CPLEX  (currently freely available for academic purposes) or LINDO , alternatively the open source programs GLPK  or lp_solve . The computationally easy but semantically complex part is written in a combination of scripting languages which are easy to understand and modify: the parser language gawk (GNU AWK)  and the script language bash . bash is the default command-line shell in LINUX, MacOS, and many UNIX systems, so many computer users are familiar with it already. In FASIMU it is used to start and iterate gawk calls, define command-line functions, and to call the solver. gawk allows to program data processing in an extremely terse form. In FASIMU it is used to transform raw data into intermediate files, to prepare the input files for the solver, to interpret the solver output, and to generate result files. It is preinstalled on every LINUX and MacOS system and available for Windows and UNIX.
FASIMU is structured in two layers: functions of basic layer, FABASE, deal with a single FBA problem, whereas functions of the upper layer, FASIMU, generate a series of FBA solutions by running FABASE functions iteratively (See Figure 1). The instructions for the iterative calls are listed in a user-editable file comprising (i) the simulation identifiers, (ii) metabolic target functions, (iii) constraints, and (iv) expressions for the automatic evaluation of the flux distribution. Therefore, in one such simulation series different metabolic objectives, enzyme knock-outs, and media composition can be considered. Upon a function call the simulations are performed and (i) an evaluation file as a short report on succeeded and failed computations and (ii) a detailed solution file are created. The latter can be further processed to provide the input files for BiNA , Cytoscape , or CellNetAnalyzer  visualization.
Algorithms implemented in FASIMU comprise biomass maximization , the principle of flux minimization , the fitness maximization at enzyme deficiencies , the minimization of metabolic adjustment (MOMA)  and the similar ROOM , inferring active subnetworks from expression profiles , also in combination with flux minimization , flux variability analysis [32–34], metabolic flux analysis , leak analysis , and pruning to the functional subnetwork . It can be combined with constraints on flux values, metabolite exchange rates, and the thermodynamic feasibility constraint based on variable metabolite concentrations .
Crucial to the evaluation of a large number of flux distributions is their visualization. Here, we developed the plugin faBiNA for BiNA  showing a computed flux distribution where the thickness and color of reaction arrows visualize the flux rate. The compartment of the metabolite is either shown as a color of the metabolite node or all metabolites of a compartment are displayed in a separate box. The particular strength of BiNA is the customizable automatic generation of a graph layout using yFiles algorithms  which provide coherent graphs for up to 300 reactions. It can also be used to scroll through a set of precomputed flux distributions and show them in the context of the whole network or alternatively only the nonzero fluxes. The definition of reaction subsets (e.g. textbook pathways) will show the flux distribution in a hierarchical layout. Additional network information like gene expression can be mapped to node color or line thickness. Finally, flux modes can be exported by vector or scalar images. FASIMU also prepares the input files needed by CellNetAnalyzer  and FluxViz , a plugin for Cytoscape , especially suited to visualize the flux in the full network context.
In a network curation process the batch processing of defined simulations is required to verify metabolic functions on the fly. As an application example we show how FASIMU has successfully aided the curation of the genome-scale model of the human hepatocyte  (see tutorial chapter 3). The raw network as the output of the curation tool METANNOGEN  at the final stage comprised of 3369 reactions and 997 metabolites in 9 compartments (2458 localized metabolites). To assert the functional parts of the network the pruning algorithm  is applied yielding 2539 reactions and 777 metabolites (1420 localized). On a 64-bit LINUX PC (3 GHz processor) using CPLEX 10.1 the running time of this process was 27:37 min. As the process included 6411 single optimizations, that averages 0.26 s for a single optimization. On the reduced model we performed 442 simulations (defining the metabolic functions of the hepatocyte) which required 4:26 min by simple flux minimization, 0.6 s for a single optimization. The full computation including the thermodynamic feasibility constraint (can only be realized as a MILP problem) and a check on the computed solutions (a further optimization) required 10 h:43 min:44 s, 87 s for a single simulation. The protocol for these computations using (Additional file 1 saved as FASIMU_complete.zip) is:
cp MIMES.txt MIPES.txt PIPES.txt sub
FASIMU can run on LINUX, Windows (from 98 or NT V ≥ 4 to the most recent Windows versions), MacOS, AIX, HP-UX and possibly many other operating systems since its minimal requirements, GNU bash , GNU awk  and GLPK  are open source and ported to many systems. FASIMU requires the alternative use of one of the solvers: the external solver lp_solve , GLPK , LINDO , CPLEX . For Microsoft Windows, using Cygwin (Linux-like environment for Windows, http://www.cygwin.com) is recommended providing bash, gawk, GLPK for almost any Windows version available.
FASIMU's input is a stoichiometric model given in SBML , level 2 version 1-4, CellNetAnalyzer , or plain text format and additional text files specifying FBA objectives and constraints. FASIMU's computed flux distribution are returned in SBML level 2 version 4 or val files (plain text format compatible with CellNetAnalyzer  and FluxViz ).
With other powerful flux-balance optimization programs at hand, the question arises why another product is necessary. The fact that important published methods have not been available as an executable program has already been mentioned. An alternative to a new software would have been to implement the required algorithms in one of the more open programming frameworks COBRA , SBRT , BioSPICE  or even as direct plugins to Cytoscape , CellDesigner , SBW  or BiNA . However, we found that the important preconditions could not be met in one of the solutions: (i) integration of powerful commercial solvers and free solvers, (ii) independence on the MATLAB framework, (iii) description language of simulations and the integration in scripts, (iv) easy implementation of new algorithmic ideas.
COBRA  has a comprehensive coverage of flux-balance methods, however, being a MATLAB  toolbox somewhat hampers its applicability. It is necessary to purchase a license of MATLAB for every machine COBRA should run. To use the best available LP solver, CPLEX , additionally a license of TOMLAB® is required. The modification and integration of COBRA into a workflow is confined to the MATLAB language and its API. In contrast, FASIMU can be integrated directly on the level of the operating system. In SBRT  the development of the mentioned algorithms as new processes is not as straightforward and it lacks the integration with a network visualization program. OptFlux  has quite a number of algorithms already implemented but lacks the flexibility of tools which are designed in a more open framework. The analysis of large networks is hampered by the fact that only GLPK  is used as the solver. In our comparison of the solvers in FASIMU we found that CPLEX is numerically stable for considerably larger MILP problems compared with GLPK. For BioSPICE , the development of flux-balance optimization is not the main focus in the BioSPICE development and only two algorithms are implemented. PathwayAnalyser  also covers only two FBA variants and its installation is not straightforward, it requires the solvers GLPK and OOQP http://pages.cs.wisc.edu/~swright/ooqp, the latter requiring BLAS and software from HSL  only available after registration and a FORTRAN 77 (not supported by recent gcc) compile process.
The main difference between FASIMU and all other comparable software is the concept of a concise description file for flux-balance simulations. Its development has been driven by the necessity of a clearly defined protocol for network testing. The main objective was that the description file contained the minimal necessary information but allows considerable flexibility to define heterogeneous network tasks, beside (i) the simple test on the producibility or degradability of metabolites, also (ii) simulations of enzymopathies, (iii) tests on the non-existence of solutions, and (iv) tests on side conditions in the flux distributions. For instance the 442 simulations to test HepatoNet1  are contained in a text file of only 57 k characters (additionally 3 interface description files of 1227 characters). This is extremely condensed given that it even contains some documentation.
A freely available software based on free and widely available software has large advantages for a first test as the program can immediately be tested. Aside from the consideration whether the fee for a commercial product such as MATLAB or CPLEX is worth the investment free software such as GNU bash, gawk, and GLPK is available for the maximum of possible computer architectures and operating systems.
Basing FASIMU on free software is a practical consideration rather than a decision on principle. We found out that for problems such as a feasible MILP implementation for a large metabolic system, the available free software is not yet sufficient. Thus, to integrate CPLEX or LINDO is a logical consequence of common sense: free software where possible, commercial where necessary. The same is true for the use of BiNA which uses powerful algorithms to draw network graphs. BiNA is freely available but not open source since it uses the commercial software yFiles licensed for free of charge use in conjunction with BiNA.
For FASIMU a compilable language such as JAVA or C++ was not used to support easy modification. FASIMU is also designed as a testing environment for newly developed algorithms, thus, development time is critical. Furthermore, the majority of the computation time is used by the external solver program. Therefore, to decrease the running time of the software which merely controls and transforms the input and output of the solver program would not have a great effect.
Graphical user interfaces (GUI) allow an easy access to the possible options and require minimal learning time. However, users who want to combine and modify the given algorithms rely on a scripting language. Programs allowing both the control by a graphical user interface and by a command-line interface require considerably more software development time. For FASIMU the focus is clearly the command-line usability. Powerful network visualization products such as BiNA, Cytoscape, CellDesigner, SBW  have already been developed. Thus, the integration of FASIMU with the programs mentioned appeared to be the better solution than the development of a separate visualization component in FASIMU. This integration is simplified by the SBML standard . FASIMU solutions can be converted to SBML. However, to increase the usability in connection with FASIMU computations, faBiNA and FluxViz have been developed to allow an even better control of BiNA and Cytoscape.
We present a Flux Analysis SIMUlation framework which (i) offers the first available implementation of thermodynamic feasibility as a quickly computable MILP, (ii) is flexible in the choice of objective functions and constraints, (iii) allows for batch processing of heterogeneous computations and automatic evaluation of the solutions, (iv) facilitate visualization of the computed fluxes with plugins for BiNA and Cytoscape, and (v) can completely be based on free software.
Availability and requirements
Project name FASIMU
Project home page http://www.bioinformatics.org/fasimu
Operating system(s) Platform independent.
Programming language(s) bash version 3.0.0 or higher, version 4.0.0 or higher recommended. gawk version 3.0.0 or higher.
Other requirements Any of CPLEX (version 9-12 tested), GLPK (version 4.42 tested), lp_solve (version 5.5 tested), LINDO (version 220.127.116.117 tested).
License GNU GPL
Any restrictions to use by non-academics none.
Edwards JS, Ibarra RU, Palsson BO: In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol 2001, 19(2):125–130. 10.1038/84379
Schuster S, Pfeiffer T, Fell DA: Is maximization of molar yield in metabolic networks favoured by evolution? J Theor Biol 2008, 252(3):497–504. 10.1016/j.jtbi.2007.12.008
Schuetz R, Kuepfer L, Sauer U: Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Mol Syst Biol 2007, 3: 119. 10.1038/msb4100162
Kümmel A, Panke S, Heinemann M: Systematic assignment of thermodynamic constraints in metabolic network models. BMC Bioinformatics 2006, 7: 512.
Milne CB, Kim PJ, Eddy JA, Price ND: Accomplishments in genome-scale in silico modeling for industrial and medical biotechnology. Biotechnol J 2009, 4(12):1653–1670. 10.1002/biot.200900234
Feist AM, Herrgård MJ, Thiele I, Reed JL, Palsson BØ: Reconstruction of biochemical networks in microorganisms. Nat Rev Microbiol 2009, 7(2):129–143.
Becker SA, Feist AM, Mo ML, Hannum G, Palsson BØ, Herrgård MJ: Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox. Nat Protoc 2007, 2(3):727–738. 10.1038/nprot.2007.99
MATLAB - The Language Of Technical Computing[http://www.mathworks.com/products/matlab/] [The MathWorks, Inc]
TOMLAB is a general purpose development and modeling environment in Matlab for research, teaching and practical solution of optimization problems[http://tomopt.com/tomlab] [Tomlab support and development. Västerås Technology Park, Trefasgatan 4, SE-721 30 Västerås, Sweden]
Rocha I, Maia P, Evangelista P, Vilaca P, Soares S, Pinto JP, Nielsen J, Patil KR, Ferreira EC, Rocha M: OptFlux: an open-source software platform for in silico metabolic engineering. BMC Syst Biol 2010, 4: 45. 10.1186/1752-0509-4-45
Wright J, Wagner A: The Systems Biology Research Tool: evolvable open-source software. BMC Syst Biol 2008, 2: 55. 10.1186/1752-0509-2-55
Garvey TD, Lincoln P, Pedersen CJ, Martin D, Johnson M: BioSPICE: access to the most current computational tools for biologists. OMICS 2003, 7(4):411–420. 10.1089/153623103322637715
Segrè D, Vitkup D, Church GM: Analysis of optimality in natural and perturbed metabolic networks. Proc Natl Acad Sci USA 2002, 99(23):15112–15117.
Raman K, Chandra N: PathwayAnalyser: A Systems Biology Tool for Flux Analysis of Metabolic Pathways. Poster Presented at: 5th International Conference on Bioinformatics, New Delhi, India, 20 December 2006 2008.
Zamboni N, Kümmel A, Heinemann M: anNET: a tool for network-embedded thermodynamic analysis of quantitative metabolome data. BMC Bioinformatics 2008, 9: 199. 10.1186/1471-2105-9-199
Hoffmann S, Hoppe A, Holzhütter HG: Pruning genome-scale metabolic models to consistent ad functionem networks. Genome Inform 2007, 18: 308–319. full_text
Hoppe A, Hoffmann S, Holzhütter HG: Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks. BMC Syst Biol 2007, 1: 23. 10.1186/1752-0509-1-23
Shlomi T, Cabili MN, Herrgård MJ, Palsson BØ, Ruppin E: Network-based prediction of human tissue-specific metabolism. Nat Biotechnol 2008, 26(9):1003–1010. 10.1038/nbt.1487
Huthmacher C, Hoppe A, Bulik S, Holzhütter HG: Antimalarial drug targets in Plasmodium falciparum predicted by stage-specific metabolic network analysis. BMC Syst Biol 2010., 4(120): [Accepted] [Accepted] 10.1186/1752-0509-4-120
IBM ILOG CPLEX - High-performance mathematical programming engine[http://www.ibm.com/software/integration/optimization/cplex]
LINDO Systems - Optimization Software: Integer Programming, Linear Programming, Nonlinear Programming, Global Optimization[http://www.lindo.com]
GLPK (GNU Linear Programming Kit)[http://www.gnu.org/software/glpk/]
lp_solve - a Mixed Integer Linear Programming (MILP) solver[http://lpsolve.sourceforge.net/]
Bash, the GNU Project's Bourne Again SHell, a complete implementation of the IEEE POSIX and Open Group shell specification[http://www.gnu.org/software/bash/]
Küntzer J, Blum T, Gerasch A, Backes C, Hildebrandt A, Kaufmann M, Kohlbacher O, Lenhof H: BN++ - A Biological Information System. J Integr Bioinformatics 2006, 3(2):34.
Killcoyne S, Carter GW, Smith J, Boyle J: Cytoscape: a community-based framework for network modeling. Methods Mol Biol 2009, 563: 219–239. full_text
Klamt S, Saez-Rodriguez J, Gilles ED: Structural and functional analysis of cellular networks with CellNetAnalyzer. BMC Syst Biol 2007, 1: 2. 10.1186/1752-0509-1-2
Holzhütter HG: The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. Eur J Biochem 2004, 271(14):2905–2922.
Holzhütter HG: The generalized flux-minimization method and its application to metabolic networks affected by enzyme deficiencies. Biosystems 2006, 83(2–3):98–107.
Shlomi T, Berkman O, Ruppin E: Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proc Natl Acad Sci USA 2005, 102(21):7695–7700. 10.1073/pnas.0406346102
Burgard AP, Maranas CD: Probing the performance limits of the Escherichia coli metabolic network subject to gene additions or deletions. Biotechnol Bioeng 2001, 74(5):364–375. 10.1002/bit.1127
Reed JL, Palsson BØ: Genome-scale in silico models of E. coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states. Genome Res 2004, 14(9):1797–1805. 10.1101/gr.2546004
Llaneras F, Picó J: An interval approach for dealing with flux distributions and elementary modes activity patterns. J Theor Biol 2007, 246(2):290–308. 10.1016/j.jtbi.2006.12.029
Lee K, Berthiaume F, Stephanopoulos GN, Yarmush ML: Metabolic flux analysis: a powerful tool for monitoring tissue function. Tissue Eng 1999, 5(4):347–368. 10.1089/ten.1999.5.347
Gevorgyan A, Poolman MG, Fell DA: Detection of stoichiometric inconsistencies in biomolecular models. Bioinformatics 2008, 24(19):2245–2251. 10.1093/bioinformatics/btn425
Wiese R, Eiglsperger M, Kaufmann M: yFiles: Visualization and Automatic Layout of Graphs. In 11th Symposium on Graph Drawing (GD01), Volume 2265/2002. Springer; 2002:588–590. [Lecture Notes in Computer Science] [Lecture Notes in Computer Science]
König M, Holzhütter HG: FluxViz - Cytoscape Plug-in for Vizualisation of Flux Distributions in Networks. Genome Informatics 2010, 24: 96–103. [http://sourceforge.net/projects/fluxvizplugin]
Gille C, Bölling C, Hoppe A, Bulik S, Hoffmann S, Hübner K, Karlstädt A, Ganeshan R, König M, Rother K, Weidlich M, Behre J, Holzhütter HG: HepatoNet1: a comprehensive metabolic reconstruction of the human hepatocyte for the analysis of liver physiology. Mol Syst Biol 2010, 6: 411. 10.1038/msb.2010.62
Gille C, Hoffmann S, Holzhütter HG: METANNOGEN: compiling features of biochemical reactions needed for the reconstruction of metabolic networks. BMC Syst Biol 2007, 1: 5. 10.1186/1752-0509-1-5
Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H, Arkin AP, Bornstein BJ, Bray D, Cornish-Bowden A, Cuellar AA, Dronov S, Gilles ED, Ginkel M, Gor V, Goryanin II, Hedley WJ, Hodgman TC, Hofmeyr JH, Hunter PJ, Juty NS, Kasberger JL, Kremling A, Kummer U, Novère NL, Loew LM, Lucio D, Mendes P, Minch E, Mjolsness ED, Nelson MR, Nielsen PF, Sakurada T, Schaff JC, Shapiro BE, Shimizu TS, Spence HD, Stelling J, Takahashi K, Tomita M, Wagner J, Wang J, Forum SBML: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 2003, 19(4):524–531. [http://sbml.org] 10.1093/bioinformatics/btg015
Funahashi A, Tanimura N, Morohashi M, Kitano H: CellDesigner: a process diagram editor for gene-regulatory and biochemical networks. BIOSILICO 2003, 1(5):159–162. 10.1016/S1478-5382(03)02370-9
Sauro HM, Hucka M, Finney A, Wellock C, Bolouri H, Doyle J, Kitano H: Next generation simulation tools: the Systems Biology Workbench and BioSPICE integration. OMICS 2003, 7(4):355–372. 10.1089/153623103322637670
Numerical Analysis Group, Science & Facilities Council:The HSL Mathematical Software Library. [http://www.hsl.rl.ac.uk/]
Bell SL, Palsson BØ: expa: a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 2005, 21(8):1739–1740. 10.1093/bioinformatics/bti228
Pfeiffer T, Sanchez-Valdenebro I, Nuño JC, Montero F, Schuster S: METATOOL: for studying metabolic networks. Bioinformatics 1999, 15(3):251–257. 10.1093/bioinformatics/15.3.251
von Kamp A, Schuster S: Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 2006, 22(15):1930–1931. 10.1093/bioinformatics/btl267
Acknowledgements and Funding
The work of AH has been funded by HepatoSys, the Network Systems Biology, funded by Bundesministerium für Bildung und Forschung, Germany.
AH developed FASIMU; SH, AG, and AH wrote faBiNA. AH and CG wrote the manual/tutorial. AH, SH, HH, and CG drafted the manuscript, approved by all authors.
Electronic supplementary material
Additional file 1:FASIMU 2.2.1 release archive. This archive contains the complete FASIMU distributions and unzips in five directories: FASIMU contains the programs, FASIMU - Doc contains the documentation (manual and tutorial), FASIMU - Ery - Example contains a small example of the human erythrocyte, FASIM - Ecoli - Example a large example of the E. coli, FASIMU - Liver - Example another large example of the human hepatocyte. (ZIP 1 MB)
Authors’ original submitted files for images
Below are the links to the authors’ original submitted files for images.
About this article
Cite this article
Hoppe, A., Hoffmann, S., Gerasch, A. et al. FASIMU: flexible software for flux-balance computation series in large metabolic networks. BMC Bioinformatics 12, 28 (2011). https://doi.org/10.1186/1471-2105-12-28
- Flux Distribution
- Commercial Solver
- Description File
- Open Source Program
- Flux Variability Analysis