Computational Systems Biochemistry Group

Semi-quantitative analysis of large metabolic networks - Why?

All cellular functions are ultimately linked to the presence of metabolites (such as proteins, nucleotides, fatty acids, phospholipids etc.) produced by the so-called metabolic network comprising thousands of enzyme-catalyzed chemical reactions and carrier-mediated transport processes. The rate (herein called flux) through a given process, i.e. the amount of material chemically converted or transported per time unit, is controlled by various regulatory mechanisms. The set of all fluxes in a metabolic network is called flux distribution. The flux distribution may dramatically change with changing functional status of the cell (e.g. turning on the glycolytic flux when switching from the resting to the working muscle).

It is an important goal of quantitative biochemistry to determine the flux distribution that determines the functionality of the cell. Such studies may help to reveal the relative importance of a specific enzyme and to predict the impact on the flux distribution if the enzyme is not active, e.g. due to a mutation or due to the administration of an enzyme inhibitor. The latter aspect is of central importance for the development of novel drugs interfering with the cellular metabolism. Since experimental determination of metabolic flux rates by means of tracer studies is time-consuming and tedious, various mathematical concepts have been developed to analyze the full spectrum of flux modes possible in a metabolic network (structural analysis) or to predict flux distributions (semi-quantitative analysis). We are focussing on large network systems (consisting of at least 500 reactions). Due to the lack of sufficient information on enzyme kinetics for all enzymes involved in such a metabolic network model, we apply non-kinetic semi-quantitative concepts, namely flux balance analysis a widely used method to estimate unknown fluxes in metabolic networks (Cornish-Bowden, Nature 2002).

Fluxminimization - An alternative flux balance objective allowing to simultaneously optimize for a multitude of cellular functions

Flux balance analysis (FBA) postulates an objective function relating the flux distribution to a specific physiological function of the cell and to determine a flux distribution that optimizes this objective function. The idea behind this approach is that cells are capable of setting up an optimal flux distribution to produce a functionally relevant metabolic output. Most applications of FBA have used an objective function that considers only a single cardinal function of the cell as, for example, the accumulation of cell material (biomass) during the S-phase of the cell cycle. However, even primitive cells have to generate a metabolic output that simultaneously meets several functional demands. To overcome the restriction of FBA to monofunctional objective functions we have recently proposed the principle of flux minimization . According to this principle, functionally relevant target fluxes, i.e. fluxes generating metabolites that are either used as building blocks for the synthesis of complex biomolecules or exported, should be accomplished with a minimal sum of internal network fluxes.

One step further: Investigating flux distributions by decomposition into fundamental modes

Using structural analyses (for example elementary mode analysis) one may explore the full set of flux modes that may exist in a stoichiometric network. Simply speaking, these methods provide an overview of the many routes along which a given metabolite can be converted into another metabolite. Various algebraic concepts have been developed to define a basic set of "fundamental" flux modes which linearly combine to all possible flux modes in the network (Clarke, Cell Biophys. 1988). The two most prominent "fundamental" sets of flux modes are the so-called elementary modes (Schuster, J Math Biol. 2002) and the extremal pathways (Schilling, J Theor Biol. 2000). Due to the combinatorial explosion the number of such fundamental modes for larger networks quickly exceeds a manageable size. The decomposition of physiological meaningful flux distributions into fundamental flux modes is one possibility to distinguish relevant flux modes from irrelevant ones and thus to reduce the size of the calculated mode set. However, the decomposition of a flux distribution into fundamental flux modes is also of high interest for the relation between a given flux distribution and the functional status of a cell because it may elucidate which metabolic capabilities are used under a certain conditions.

The concept of minimal flux modes (MinModes)

We could show that only very few elementary modes are actually needed to decompose flux distributions calculated by flux-balance methods. However, the decomposition of the FBA solution into elementary modes is not unique and not all of the fundamental modes used in this decomposition allow for a clear physiological interpretation. Therefore, we proposed a new type of fundamental modes which we call minimal flux modes (or short: MinModes) . They are defined as minimal flux modes required to maintain a unit flux through a single target reaction of the network. According to this definition, there are only as many /MinModes/ as there are functionally relevant target fluxes. Although MinModes do not form a basis in strict mathematical sense our results suggest that they can be linearly combined to provide a good approximation of a given flux distribution ). The striking advantage of such a representation in terms of MinModes is that the coefficients used for the linear combination have a clear physiological meaning: they represent the metabolic output of the network in a given steady state and thus can be used as a measure for the functionality of the cell. We are currently working to improve this concept by including as much physiological information as available into the approach of fluxminimization.

Note

The computation of MinModes is implemented in FASIMU (Hoppe et al., 2011 , FASIMU website).

Researchers

Sabrina Hoffmann
Dr. Andreas Hoppe

References

Clarke, Clarke BL. (1988) Stoichiometric network analysis. Cell Biophys. 12:237-53. [PubMed]

Cornish-Bowden A, Cárdenas ML. (2002) Metabolic balance sheets. Nature., 420(6912):129-30. [PubMed]

Schilling CH, Letscher D, Palsson BO. (2000) Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J Theor Biol., 203(3):229-48. [PubMed]

Schuster S, Hilgetag C, Woods JH, Fell DA. (2002) Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism. J Math Biol., 45(2):153-81. [PubMed]

Hoppe A, Hoffmann S, Gerasch A, Gille C, Holzhütter HG. (2011) FASIMU: flexible software for flux-balance computation series in large metabolic networks. BMC Bioinformatics., 12(1):28. [PubMed]

		Minimal Flux Modes (MinModes)
Home Research VirtualLiver People Publications Software Positions Events Contact		Semi-quantitative analysis of large metabolic networks - Why? All cellular functions are ultimately linked to the presence of metabolites (such as proteins, nucleotides, fatty acids, phospholipids etc.) produced by the so-called metabolic network comprising thousands of enzyme-catalyzed chemical reactions and carrier-mediated transport processes. The rate (herein called flux) through a given process, i.e. the amount of material chemically converted or transported per time unit, is controlled by various regulatory mechanisms. The set of all fluxes in a metabolic network is called flux distribution. The flux distribution may dramatically change with changing functional status of the cell (e.g. turning on the glycolytic flux when switching from the resting to the working muscle). It is an important goal of quantitative biochemistry to determine the flux distribution that determines the functionality of the cell. Such studies may help to reveal the relative importance of a specific enzyme and to predict the impact on the flux distribution if the enzyme is not active, e.g. due to a mutation or due to the administration of an enzyme inhibitor. The latter aspect is of central importance for the development of novel drugs interfering with the cellular metabolism. Since experimental determination of metabolic flux rates by means of tracer studies is time-consuming and tedious, various mathematical concepts have been developed to analyze the full spectrum of flux modes possible in a metabolic network (structural analysis) or to predict flux distributions (semi-quantitative analysis). We are focussing on large network systems (consisting of at least 500 reactions). Due to the lack of sufficient information on enzyme kinetics for all enzymes involved in such a metabolic network model, we apply non-kinetic semi-quantitative concepts, namely flux balance analysis a widely used method to estimate unknown fluxes in metabolic networks (Cornish-Bowden, Nature 2002). Fluxminimization - An alternative flux balance objective allowing to simultaneously optimize for a multitude of cellular functions Flux balance analysis (FBA) postulates an objective function relating the flux distribution to a specific physiological function of the cell and to determine a flux distribution that optimizes this objective function. The idea behind this approach is that cells are capable of setting up an optimal flux distribution to produce a functionally relevant metabolic output. Most applications of FBA have used an objective function that considers only a single cardinal function of the cell as, for example, the accumulation of cell material (biomass) during the S-phase of the cell cycle. However, even primitive cells have to generate a metabolic output that simultaneously meets several functional demands. To overcome the restriction of FBA to monofunctional objective functions we have recently proposed the principle of flux minimization . According to this principle, functionally relevant target fluxes, i.e. fluxes generating metabolites that are either used as building blocks for the synthesis of complex biomolecules or exported, should be accomplished with a minimal sum of internal network fluxes. One step further: Investigating flux distributions by decomposition into fundamental modes Using structural analyses (for example elementary mode analysis) one may explore the full set of flux modes that may exist in a stoichiometric network. Simply speaking, these methods provide an overview of the many routes along which a given metabolite can be converted into another metabolite. Various algebraic concepts have been developed to define a basic set of "fundamental" flux modes which linearly combine to all possible flux modes in the network (Clarke, Cell Biophys. 1988). The two most prominent "fundamental" sets of flux modes are the so-called elementary modes (Schuster, J Math Biol. 2002) and the extremal pathways (Schilling, J Theor Biol. 2000). Due to the combinatorial explosion the number of such fundamental modes for larger networks quickly exceeds a manageable size. The decomposition of physiological meaningful flux distributions into fundamental flux modes is one possibility to distinguish relevant flux modes from irrelevant ones and thus to reduce the size of the calculated mode set. However, the decomposition of a flux distribution into fundamental flux modes is also of high interest for the relation between a given flux distribution and the functional status of a cell because it may elucidate which metabolic capabilities are used under a certain conditions. The concept of minimal flux modes (MinModes) We could show that only very few elementary modes are actually needed to decompose flux distributions calculated by flux-balance methods. However, the decomposition of the FBA solution into elementary modes is not unique and not all of the fundamental modes used in this decomposition allow for a clear physiological interpretation. Therefore, we proposed a new type of fundamental modes which we call minimal flux modes (or short: MinModes) . They are defined as minimal flux modes required to maintain a unit flux through a single target reaction of the network. According to this definition, there are only as many /MinModes/ as there are functionally relevant target fluxes. Although MinModes do not form a basis in strict mathematical sense our results suggest that they can be linearly combined to provide a good approximation of a given flux distribution ). The striking advantage of such a representation in terms of MinModes is that the coefficients used for the linear combination have a clear physiological meaning: they represent the metabolic output of the network in a given steady state and thus can be used as a measure for the functionality of the cell. We are currently working to improve this concept by including as much physiological information as available into the approach of fluxminimization. Note The computation of MinModes is implemented in FASIMU (Hoppe et al., 2011 , FASIMU website). Researchers Sabrina Hoffmann Dr. Andreas Hoppe References Clarke, Clarke BL. (1988) Stoichiometric network analysis. Cell Biophys. 12:237-53. [PubMed] Cornish-Bowden A, Cárdenas ML. (2002) Metabolic balance sheets. Nature., 420(6912):129-30. [PubMed] Schilling CH, Letscher D, Palsson BO. (2000) Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J Theor Biol., 203(3):229-48. [PubMed] Schuster S, Hilgetag C, Woods JH, Fell DA. (2002) Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism. J Math Biol., 45(2):153-81. [PubMed] Hoppe A, Hoffmann S, Gerasch A, Gille C, Holzhütter HG. (2011) FASIMU: flexible software for flux-balance computation series in large metabolic networks. BMC Bioinformatics., 12(1):28. [PubMed]