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...dividualsreactions.s This relates to step 1 of Figure 2.3-1: the stoichiometry and linear algebrasConvex analysis 2.3.6 The next constraints imposed on the network analysis relate to convex analysis =-=[93]-=-.sConvex analysissis an area of mathematics that enables the analysis of inequalities andssystems of linear equations to generate a convex set of vectors that can be used toscharacterize all of the st...

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...wledge of thessystem and the availability of certain metabolites to enter and exit the system.sFor example:sInternal fluxes: if the maximum limit was known, equation 2.11 becomes:smax,0 ii vv +≤≤si = =-=[1,2,3,4]-=- (2.12)sExchange fluxes: let’s say the substrate A is allowed to enter and exit the systemswhilst metabolite B and the byproduct are only allowed to exit, the constraintsswould be:sExchange flux const...

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...ter in Section 5.1.sThe AraCyc database contains a mix of two types of information:si) Pathways of reactions and enzyme information computationally predicted usingsthe multiorganism database, MetaCyc =-=[57, 58]-=-, as a reference database. Thespredicted pathways are then manually reviewed and validated by a curator whosassesses whether their computational prediction is justified, based on a numbersof cues from...

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...itativesmetabolic modelling [80], they do not require any knowledge of the metabolitesconcentrations or the enzyme kinetics of the system, which are not easy to obtain. Thessteady state (homeostasis) =-=[81, 82]-=- assumption in MPA precludes the need forsknowledge of nutrients at any time as long as that quantity remains constant; it alsosremoves the need for specific rate laws since it simply requires that th...

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...h has been done on the biosynthesis [24, 25] and metabolism [26] of flavonoidssand their pathways are one of the best characterized in plants. A review of the history ofstheir research can be seen in =-=[27, 28]-=-. This offers a great platform for furthering oursunderstanding about their metabolic structure and functions. The knowledge would leadsto better utilization of flavonoids as well as improved approach...

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...their chemicalsproperties [23]. Because of their low toxicity, animals, including humans, are able tosingest them and benefit as well from their properties.sResearch has been done on the biosynthesis =-=[24, 25]-=- and metabolism [26] of flavonoidssand their pathways are one of the best characterized in plants. A review of the history ofstheir research can be seen in [27, 28]. This offers a great platform for f...

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...nded convex subset in Figure 2.3-1sdiscussed in iii) under section 2.3.6, can be analysed using MPA. There are two types ofsMPA approaches: extreme pathways (ExPa) [95] and elementary flux modes (EM) =-=[96]-=-.sA comparison of these two approaches is provided in [97]. While they both use convexsanalysis to identify all possible and feasible metabolic routes for a given network atssteady state, their differ...

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... or chemistry, e.g., flux (v) has to be positive; certain metabolite enters but doesn’tsleave system; etc.s19sA review of the history and advances in MPA and FBA can respectively be found in [83]sand =-=[84, 85]-=-.sSolution space and imposed constraintss2.3.1 The solution space contains all possible functions of the reconstructed network or allsallowable phenotypes [17]. Constraints-based modelling (Section 1....

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...earch has been based on the AraCyc database, the development of newsreconstructions of the Arabidopsis network, as discussed in Section 5.2, is noted.s9sAnalysis Tools 1.9 • The CellNetAnalyzer (CNA) =-=[64]-=- is the main software tool used in this researchsfor application of the MPA methods to the Arabidopsis flavonoid subnetwork. Itsis an advanced pathway analysis tool that runs in MatLab and that provid...

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...writing, the AraCyc database was up to version 8.0, and contained 2,825scompounds, 2,689 reactions and 5520 enzymes with 446 pathways. The AraCycsmetabolic pathway tools query page can be accessed at =-=[63]-=-.sIn response to the ongoing updating and curating of the metabolic pathways andsreactions in AraCyc, the flavonoid subnetwork used in this research is correspondinglysupdated when a new version of th...

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...te hypotheses regarding the functions of the networks in the absence of detailedskinetic information. It is now being recognized as a central approach to the structuralsanalysis of metabolic networks =-=[94]-=-. As defined in [95], “Metabolic pathways are thestrue functional units of metabolic systems.” The metabolic pathways defined here aresthe elementary modes (EMs) described in Section 2.4.2, which are ...

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... or chemistry, e.g., flux (v) has to be positive; certain metabolite enters but doesn’tsleave system; etc.s19sA review of the history and advances in MPA and FBA can respectively be found in [83]sand =-=[84, 85]-=-.sSolution space and imposed constraintss2.3.1 The solution space contains all possible functions of the reconstructed network or allsallowable phenotypes [17]. Constraints-based modelling (Section 1....

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...5sOther Definitions 3.2.3 The notion of MCSs does exist in other theories and research areas, particularly insrelation to risk analysis. In developing the algorithm for MCSs, S. Klamt and E.D.sGilles =-=[107]-=- looked at previous similar definitions of MCSs that existed in other areas atsthe time. These included fault trees and graph theory which shall be discussed here;sother similar concepts are looked at...

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...h has been done on the biosynthesis [24, 25] and metabolism [26] of flavonoidssand their pathways are one of the best characterized in plants. A review of the history ofstheir research can be seen in =-=[27, 28]-=-. This offers a great platform for furthering oursunderstanding about their metabolic structure and functions. The knowledge would leadsto better utilization of flavonoids as well as improved approach...

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... of constraints-based modellings(Section 1.5) and how the MPA analysis methods are derived.sConcepts of Importance in Network Analysis 2.3 The structural properties of metabolic networks, as shown in =-=[64, 78, 79]-=-, are closelysrelated to their phenotypic functions. These structural and functional properties are oftenscalled emergent properties [13, 69] because they emerge from the whole network, notsfrom its i...

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...aresFlavNet with the manually curated Poolman model but this would require more timesand work and so could be undertaken separately in future work where other metabolicsreconstruction methods such as =-=[75]-=- could be used to assist in comparing names of thesdifferently reconstructed Arabidopsis metabolic networks.s74sMethod 5.3 There are three different Arabidopsis models representing different levels of...

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... network. ............ 14sFigure 2.2-1: A metabolic network with a subnetwork (grey) ...................................... 16sFigure 2.3-1: Successive application of constraints. Source: Figure 3 of =-=[13]-=- .............. 19sFigure 2.3-2: Example of a metabolic network. ........................................................... 22sFigure 2.3-3: Stoichiometric matrix, S, of Figure 2.3 2 ...................

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...ugh which cells convert thousands of organic compounds intosbiomolecules necessary to support their existence. By doing so, they direct metabolismsalong a map of pathways and networks. These networks =-=[11, 12]-=- can now besreconstructed and the genome-scale metabolic networks of sequenced organisms aresbecoming increasingly available online and accessible for use worldwide. One suchsnetwork that has become a...

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...ary and are denoted by beswhere the subscript e refers to the index of the external fluxes.sLimited thermodynamic information can be used to determine whether a reaction issreversible or irreversible =-=[88, 89]-=-. A reversible internal reaction is considered as twosfluxes occurring irreversibly in opposite directions so all internal fluxes can besconsidered as nonnegative:svi ≥ 0 (for all i ∈ Irreversible) (2...

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...ough this cannotsprecisely predict cellular behaviour (functional states), it leads to the formulation ofssolution spaces where cellular behaviour can be attained.sConstraints-based modelling methods =-=[18, 19]-=- have proved useful for analysingscomplex biological systems. They lead to in silico analysis procedures that are helpfulsin analysing, interpreting, and occasionally predicting the genotype-phenotype...

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....sThis confers a crucial role to networks because they embed these interactions and, asssuch, are responsible for observable cellular behaviour.sExamples of networks used in biology include metabolic =-=[5, 6]-=- (Section 2.1), regulatorys[7, 8] and signalling [9, 10] networks, of which metabolic networks are perhaps the bestscharacterized. Systems biology for metabolic networks involves investigating thesint...

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...ough this cannotsprecisely predict cellular behaviour (functional states), it leads to the formulation ofssolution spaces where cellular behaviour can be attained.sConstraints-based modelling methods =-=[18, 19]-=- have proved useful for analysingscomplex biological systems. They lead to in silico analysis procedures that are helpfulsin analysing, interpreting, and occasionally predicting the genotype-phenotype...

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...networks because they embed these interactions and, asssuch, are responsible for observable cellular behaviour.sExamples of networks used in biology include metabolic [5, 6] (Section 2.1), regulatorys=-=[7, 8]-=- and signalling [9, 10] networks, of which metabolic networks are perhaps the bestscharacterized. Systems biology for metabolic networks involves investigating thesinteraction between the components o...

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...ugh which cells convert thousands of organic compounds intosbiomolecules necessary to support their existence. By doing so, they direct metabolismsalong a map of pathways and networks. These networks =-=[11, 12]-=- can now besreconstructed and the genome-scale metabolic networks of sequenced organisms aresbecoming increasingly available online and accessible for use worldwide. One suchsnetwork that has become a...

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...h physics or chemistry, e.g., flux (v) has to be positive; certain metabolite enters but doesn’tsleave system; etc.s19sA review of the history and advances in MPA and FBA can respectively be found in =-=[83]-=-sand [84, 85].sSolution space and imposed constraintss2.3.1 The solution space contains all possible functions of the reconstructed network or allsallowable phenotypes [17]. Constraints-based modellin...

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...e have reconstructed our flavonoid subnetwork, consists of a collection ofspathways of known reactions and enzymes for Arabidopsis. These pathways are mainlysautomatically predicted using the MetaCyc =-=[53, 166]-=- database and manually validated tosremove pathways considered to be non-Arabidopsis. This manual curation processsincludes correcting pathways and adding missing pathways. The resulting databasescont...

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...s. This research uses EMs for network analysis as it issa superset of ExPas, so ExPas are contained in the set of EMs as described in the briefsoverview below.sExtreme Pathways 2.4.1 Extreme pathways =-=[98, 99]-=- are unique sets of fluxes satisfying the steady-state masssbalance constraints given by equation (2.10) and inequalities such as those in equations(2.11) & (2.12). They are irreducible, non-redundant...

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...t the metabolism of Escherichia coli, which needs to besable to adapt to a changing environment, was more robust than that of the humanserythrocyte.sExample 3: In another study, Van Dien and Lidstrom =-=[105]-=- used EMs as part of theirsstudy on a proposed metabolic network for Methylobacterium extorquenssAM1.sVan Dien and Lidstrom used EMs to explore the flux space of thesreaction network of a biomass synt...

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...etwork.sThe main strengths of constraints-based (Section 1.5) methods like the EMs (Sections2.4.2) and MCSs (Chapter 3) concepts of MPA (Section 2.4) are that, unlike quantitativesmetabolic modelling =-=[80]-=-, they do not require any knowledge of the metabolitesconcentrations or the enzyme kinetics of the system, which are not easy to obtain. Thessteady state (homeostasis) [81, 82] assumption in MPA precl...

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...e mouse and fruit fly (Drosphila) play in human biology. It may currently be thesonly plant in which a comprehensive network of secondary metabolism can bescharacterized within a single plant species =-=[49]-=-.sThe above aspects and the fact that it is very similar to most other plants such thatswhatever properties it contains would most likely exist in all other flowering plants asswell [50], make Arabido...

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... strategies forscoupled product and biomass synthesis, altogether offering great flexibility in definingsand solving knock out problems. Other examples of MCSs in metabolic engineering cansbe seen in =-=[108, 120]-=-, discussed earlier in Section 3.2.s53sSimilar concepts 3.5sBottlenecks 3.5.1 Bottlenecks characterize a point of congestion in a system that happens when workloadssarrive at a given point more quickl...

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...ogys1.4 As discussed by Palsson [13], mathematical model building in biology is faced with thesbasic challenges presented by the complex intracellular chemical environment [14] andsthe dual causality =-=[15]-=- of genetics and natural laws, causing three main problems:s• The first problem is that the complexity of the intracellular environment makessit hard to define and formulate the fundamental kinetic eq...

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...nzymes that aresexpressed or suppressed.sBased on this idea, we could use experimental results of compounds that are found in asparticular tissue, or are conversely absent, to identify the viable EMs =-=[94, 96, 102]-=- andsMCSs [66, 106, 107] for certain tissues and, subsequently, genes that are beingsexpressed in terms of the reactions that are taking place. This would be cheaper andseasier to use than practical e...

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............. 27sFigure 2.4-2: Extreme pathway analysis ...................................................................... 28sFigure 3.2-1: Network layout for an example network (NetEx) discussed in =-=[106]-=-. ...... 33sFigure 3.2-2: EMs for NetEx. ...................................................................................... 34sFigure 3.2-3: Example of a Fault Tree with equivalent Reliability Blo...

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... furthering oursunderstanding about their metabolic structure and functions. The knowledge would leadsto better utilization of flavonoids as well as improved approaches in their metabolicsengineering =-=[21]-=-. A recent review of available research in this area can be found in [29,s30].sTo give an idea of the important role that flavonoids play, two areas they are involved insare given below. This research...

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....sThis confers a crucial role to networks because they embed these interactions and, asssuch, are responsible for observable cellular behaviour.sExamples of networks used in biology include metabolic =-=[5, 6]-=- (Section 2.1), regulatorys[7, 8] and signalling [9, 10] networks, of which metabolic networks are perhaps the bestscharacterized. Systems biology for metabolic networks involves investigating thesint...

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...t plants often produce moresflavonoid compounds within their leaves and flowers, as a response to stress caused bysan increase in UVB- radiation. This involves changes in the expression of many geness=-=[38]-=- and often happens at the cost of the primary productivity [39, 40] of the plant. Itswas found [41] that the light-induced synthesis of UV-protective flavonoids divertsssubstrates from primary metabol...

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...ted in terms of their importance for the differentsmetabolic needs of the cell. They showed that EMs provide a way of detectingsnon-redundant pathways in metabolic networks.sExample 2: Wilhelm et al. =-=[104]-=- used EMs to study the structural robustness ofsmetabolic networks.sWilhelm et al. found that the number of EMs can be used with othersrobust measures to determine structural robustness. They were abl...

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...s. This research uses EMs for network analysis as it issa superset of ExPas, so ExPas are contained in the set of EMs as described in the briefsoverview below.sExtreme Pathways 2.4.1 Extreme pathways =-=[98, 99]-=- are unique sets of fluxes satisfying the steady-state masssbalance constraints given by equation (2.10) and inequalities such as those in equations(2.11) & (2.12). They are irreducible, non-redundant...

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...their chemicalsproperties [23]. Because of their low toxicity, animals, including humans, are able tosingest them and benefit as well from their properties.sResearch has been done on the biosynthesis =-=[24, 25]-=- and metabolism [26] of flavonoidssand their pathways are one of the best characterized in plants. A review of the history ofstheir research can be seen in [27, 28]. This offers a great platform for f...

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... of constraints-based modellings(Section 1.5) and how the MPA analysis methods are derived.sConcepts of Importance in Network Analysis 2.3 The structural properties of metabolic networks, as shown in =-=[64, 78, 79]-=-, are closelysrelated to their phenotypic functions. These structural and functional properties are oftenscalled emergent properties [13, 69] because they emerge from the whole network, notsfrom its i...

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...mic mass balance 2.3.4 All physical systems obey the law of conservation of mass which states that anysdisappearance of mass must be accompanied somewhere by the appearance of an equalsamount of mass =-=[90]-=-. As shown in equation 2.6, the rate at which the concentration of asmetabolite changes (dxi/dt) is the sum of the rates of reactions that produce it minus thessum of those that consume it (multiplied...

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...ts caused by natural selection and evolution. The next sectionsdiscusses constraints-based modelling and how it tackles these challenges.s4sConstraints-based modelling 1.5 Constraints-based modelling =-=[17]-=- tackles the model building challenges by taking intosaccount the fact that cells are subject to governing constraints which are easier tosidentify. The modelling approach imposes the constraints and ...

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...tress caused bysan increase in UVB- radiation. This involves changes in the expression of many geness[38] and often happens at the cost of the primary productivity [39, 40] of the plant. Itswas found =-=[41]-=- that the light-induced synthesis of UV-protective flavonoids divertsssubstrates from primary metabolism to the formation of the secondary product.sUnderstanding the metabolism and cellular processes ...

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...sFigure 2.4-2: Extreme pathway analysissproduces a set of vectors that define the convex solution space where the extreme pathwaysslie at the edges of the bounded null space of the flux cone. Source: =-=[100]-=-sElementary flux modes 2.4.2 Elementary flux modes (EMs) [94, 96, 101, 102], are unique routes, or nondecomposable pathways, that consist of the minimal sets of reactions that allow thesnetwork to ope...

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...lico model for an individual organism would not apply to other individuals insthe population because of polymorphism in the genes which means thatsindividuals and kinetic parameters are non-identical =-=[16]-=-.sThus, mathematical model building in biology needs to accommodate both challenges:sthe physicochemical constraints under which cells operate, as well as the spatial andsenvironmental constraints cau...

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...traviolet UV-B irradiation [35]; theysconstitute a major subgroup of flavonoids.sFlavonoids also help protect plants from attack by microbes and insects as well as fromsUV light; for example, studies =-=[36, 37]-=- have shown that plants often produce moresflavonoid compounds within their leaves and flowers, as a response to stress caused bysan increase in UVB- radiation. This involves changes in the expression...

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...xsdistribution involving the objective reaction; MCSs are the minimal hitting sets of thestarget EMs [108] or the minimal sets of knockouts that disable the operation of asspecified set of target EMs =-=[109]-=-.sIn terms of the network structure, a continued operation of the objective reaction wouldsnot be physiologically possible because it would lead to the depletion or accumulationsof metabolite pools an...

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...even subclasses. These are:si) anthocyanins; (ii) flavanols; iii) flavanones; iv) flavones; v) flavonols; vi)sleucoanthocyanidin and vii) proanthocyanidins. Details of these flavonoids can be seensin =-=[22, 32, 171]-=-. Four non-flavonoid groups are identified:si) lignin [172]; ii)sbenzenoids [173, 174]; iii) amides; and iv) coumarins [175, 176]. The rest of the nonflavonoid compound products are classified as othe...

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...s [23]. Because of their low toxicity, animals, including humans, are able tosingest them and benefit as well from their properties.sResearch has been done on the biosynthesis [24, 25] and metabolism =-=[26]-=- of flavonoidssand their pathways are one of the best characterized in plants. A review of the history ofstheir research can be seen in [27, 28]. This offers a great platform for furthering oursunders...

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...networks because they embed these interactions and, asssuch, are responsible for observable cellular behaviour.sExamples of networks used in biology include metabolic [5, 6] (Section 2.1), regulatorys=-=[7, 8]-=- and signalling [9, 10] networks, of which metabolic networks are perhaps the bestscharacterized. Systems biology for metabolic networks involves investigating thesinteraction between the components o...

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...te B are exported out across the system boundary.s22sReaction mapsFigure 2.3-2: Example of a metabolic network.sThe amounts of matter that flow through each chemical reaction are the metabolicsfluxes =-=[72, 87]-=- or reaction rates. Internal fluxes occur inside the network and aresdenoted by vi where the subscript i refers to the index of the internal fluxes.sExternal/exchange fluxes occur across the system bo...

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...tions, thussproviding a way to study the structural characteristics of the system by itself, regardlesssof what the environment or the internal states of the system are.sThe stoichiometric matrix, S, =-=[86]-=- consists of the stoichiometric coefficients of thesreactions that comprise a network. Its columns represent the reactions and its rowssrepresent the compounds or metabolites. S transforms the reactio...

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...3234] are easily observed. One example is where flowers have been found to lose theirsanthocyanin colour pigmentation in response to hawkmoths, who preferred palersflowers, being the major pollinator =-=[45]-=-. It is reasonable to expect that such loss-offunction adaptations are relatively unconstrained because they can be achieved in manys80sways. For example, the suppression of any one of the enzymes cat...

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...te B are exported out across the system boundary.s22sReaction mapsFigure 2.3-2: Example of a metabolic network.sThe amounts of matter that flow through each chemical reaction are the metabolicsfluxes =-=[72, 87]-=- or reaction rates. Internal fluxes occur inside the network and aresdenoted by vi where the subscript i refers to the index of the internal fluxes.sExternal/exchange fluxes occur across the system bo...

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...aves and flowers, as a response to stress caused bysan increase in UVB- radiation. This involves changes in the expression of many geness[38] and often happens at the cost of the primary productivity =-=[39, 40]-=- of the plant. Itswas found [41] that the light-induced synthesis of UV-protective flavonoids divertsssubstrates from primary metabolism to the formation of the secondary product.sUnderstanding the me...

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...ct pollinators and seed dispersers. Thesmain compounds involved are called anthocyanins [32-34], which also have antioxidantsproperties and so also protect plants against ultraviolet UV-B irradiation =-=[35]-=-; theysconstitute a major subgroup of flavonoids.sFlavonoids also help protect plants from attack by microbes and insects as well as fromsUV light; for example, studies [36, 37] have shown that plants...

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...ferentstypes of data into genome-scale reconstructions of biochemical reaction networks andsthen creating in silico computational models to compute the functional states of thesreconstructed networks =-=[4]-=-. The ultimate goal of the systems-based approach is tosestablish the relation between the phenotypic characteristics of a biological system andsthe interdependent structure and dynamics of its compon...

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...traviolet UV-B irradiation [35]; theysconstitute a major subgroup of flavonoids.sFlavonoids also help protect plants from attack by microbes and insects as well as fromsUV light; for example, studies =-=[36, 37]-=- have shown that plants often produce moresflavonoid compounds within their leaves and flowers, as a response to stress caused bysan increase in UVB- radiation. This involves changes in the expression...

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...rganicscompounds into biomolecules necessary to support and maintain cells.sIn general, the metabolic network is a directed graph where the nodes representscompounds, and the edges chemical reactions =-=[69, 70]-=-. The boundary nodes are externalsbiochemical inputs (substrates) or outputs (products) while the internal nodes aresintermediate compounds with associated stoichiometric constraints to guarantee mass...

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... essentialsto understand the concept of external compounds.sExternal compounds 2.2.1 There are various reasons why a compound may be taken as external for a subnetworksand not subject to conservation =-=[77]-=-; the reasons relate to the concept of buffering orshaving a reservoir for an external compound. For compounds to be justifiably external,sthey need to be of sufficient supply in the cell or be buffer...

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...n of desired products;s• predicting the effect of enzyme deficiency;s29s• identifying gene targets;s• reducing perturbations to the system; ands• so on.sA review of the history of EMs can be found in =-=[103]-=-.sExamples of work using elementary flux modes 2.4.2.1 Example 1: Schuster et al. [101] used EMs to analyse the interplay between thespentose phosphate pathway and glycolysis.sThe EMs obtained from th...

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...even subclasses. These are:si) anthocyanins; (ii) flavanols; iii) flavanones; iv) flavones; v) flavonols; vi)sleucoanthocyanidin and vii) proanthocyanidins. Details of these flavonoids can be seensin =-=[22, 32, 171]-=-. Four non-flavonoid groups are identified:si) lignin [172]; ii)sbenzenoids [173, 174]; iii) amides; and iv) coumarins [175, 176]. The rest of the nonflavonoid compound products are classified as othe...

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...enes that result in the elimination of most of thesflavonoids, benzenoid production is not affected. This provides a quantified explanationsof experimental observations such as that by Spitzer et al. =-=[44]-=- where they showed thatsthe suppression of the anthocyanin pathway, via CHS silencing, dramatically reducedsflavonoids but did not affect scent (benzenoids) production.sDiscussions and conclusions 7.4...

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...atorial explosion. This is an ongoing process throughout the research, insrelation to the ongoing curation of the AraCyc database.s Initial ideas for the work were presented at the MODSIM conference =-=[67]-=-s Material from Chapter 4, in combination with material from subsequentschapters, have been compiled into an article which has been published in thesBMC Bioinformatics journal [68].siv) Verifying the...

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... MODSIM conference [67]s Material from Chapter 4, in combination with material from subsequentschapters, have been compiled into an article which has been published in thesBMC Bioinformatics journal =-=[68]-=-.siv) Verifying the self-contained flavonoid network extracted from the full Arabidopsissnetwork by comparing the compounds and reactions to those contained in a moresrecently reconstructed and verifi...

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...itativesmetabolic modelling [80], they do not require any knowledge of the metabolitesconcentrations or the enzyme kinetics of the system, which are not easy to obtain. Thessteady state (homeostasis) =-=[81, 82]-=- assumption in MPA precludes the need forsknowledge of nutrients at any time as long as that quantity remains constant; it alsosremoves the need for specific rate laws since it simply requires that th...

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...BsExchange fluxes Chemical reactionssb1 Asb2 Bsb3 bypsSteady state 2.3.5 When the boundary of a system is fixed, the system tends to evolve to some stablesunchanging state called the steady state =-=[91, 92]-=-. At steady state the mass balance in thesnetwork (equation 2.6) can be represented by the flux-balance equation:svS ˆ*0 = (2.10)swhere S is the stoichiometric matrix andsthe reaction fluxes. The path...

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...wledge of thessystem and the availability of certain metabolites to enter and exit the system.sFor example:sInternal fluxes: if the maximum limit was known, equation 2.11 becomes:smax,0 ii vv +≤≤si = =-=[1,2,3,4]-=- (2.12)sExchange fluxes: let’s say the substrate A is allowed to enter and exit the systemswhilst metabolite B and the byproduct are only allowed to exit, the constraintsswould be:sExchange flux const...

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...embed these interactions and, asssuch, are responsible for observable cellular behaviour.sExamples of networks used in biology include metabolic [5, 6] (Section 2.1), regulatorys[7, 8] and signalling =-=[9, 10]-=- networks, of which metabolic networks are perhaps the bestscharacterized. Systems biology for metabolic networks involves investigating thesinteraction between the components of cellular networks, ap...

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...es of Model Building in Biologys1.4 As discussed by Palsson [13], mathematical model building in biology is faced with thesbasic challenges presented by the complex intracellular chemical environment =-=[14]-=- andsthe dual causality [15] of genetics and natural laws, causing three main problems:s• The first problem is that the complexity of the intracellular environment makessit hard to define and formulat...

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... amount of literature availablesfor them. There are over 5000 naturally occurring flavonoids that have beenscharacterized. These have been divided into 6 sub-groups based on their chemicalsproperties =-=[23]-=-. Because of their low toxicity, animals, including humans, are able tosingest them and benefit as well from their properties.sResearch has been done on the biosynthesis [24, 25] and metabolism [26] o...

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...- the role of flavonoids, specificallysanthocyanins, in plants.sFlavonoids in plant reproduction and defense 1.7.1 Flavonoids assist in plant reproduction by producing yellow or red/blue pigmentations=-=[31]-=- in flowers and fruits, which help to attract pollinators and seed dispersers. Thesmain compounds involved are called anthocyanins [32-34], which also have antioxidantsproperties and so also protect p...

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...aves and flowers, as a response to stress caused bysan increase in UVB- radiation. This involves changes in the expression of many geness[38] and often happens at the cost of the primary productivity =-=[39, 40]-=- of the plant. Itswas found [41] that the light-induced synthesis of UV-protective flavonoids divertsssubstrates from primary metabolism to the formation of the secondary product.sUnderstanding the me...

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...ds in the medical field 1.7.2 Flavonoids are also important in the medical field because of their beneficial effects onshuman health. They contain antioxidant properties [23], although recent studies =-=[46]-=-shave found that these antioxidant properties do not apply in the human body. The healthsbenefits that flavonoids provide against cancer disease are the result of mechanismsscaused by the body trying ...

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...Arabidopsis is a small flowering plant related to cabbage andsmustard. It is one of the most studied organisms in plantssciences and genetics and is the first plant to have its genomesfully sequenced =-=[48]-=-. It contains one of the smallest genomessin the plant kingdom which makes it a model organism, notsonly for genetic mapping and sequencing, but also forsfundamental molecular and physiological studie...

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...plant species [49].sThe above aspects and the fact that it is very similar to most other plants such thatswhatever properties it contains would most likely exist in all other flowering plants asswell =-=[50]-=-, make Arabidopsis an ideal organism for the research.sInformation for the research is obtained from the AraCyc database [51], available onlinesand containing the full metabolic network of the Arabido...

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...rted bysthe Pathway Tools software developed by Peter Karp’s group at Stanford ResearchsInstitute (SRI) and is the most highly curated species-specific database present at thesPlant Metabolic Network =-=[54]-=-. In addition, the AraCyc database [51] is one of 6sdatabases classified as Tier 1 curation level in the larger BioCyc database system [55,s56] containing a collection of 2037 Pathway/Genome Databases...

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...which 87% were manuallysvalidated to exist in Arabidopsis and to be correct in relation to evidence from literature.sThe rest were based on computational predictions validated from cues in literature =-=[62]-=-.sAt the time of writing, the AraCyc database was up to version 8.0, and contained 2,825scompounds, 2,689 reactions and 5520 enzymes with 446 pathways. The AraCycsmetabolic pathway tools query page ca...

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...ed to study the functionality of genes in multi-cellular organismss Material from this review work has been published in the specials‘Metabolism and Systems Biology’ issue of the Metabolites journal =-=[66]-=-.siii) Reconstructing the full Arabidopsis network from the AraCyc database, andsextracting a self-contained subnetwork (Chapter 4) to which constraints-basedsmodelling (Section 1.5) analysis methods ...

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...BsExchange fluxes Chemical reactionssb1 Asb2 Bsb3 bypsSteady state 2.3.5 When the boundary of a system is fixed, the system tends to evolve to some stablesunchanging state called the steady state =-=[91, 92]-=-. At steady state the mass balance in thesnetwork (equation 2.6) can be represented by the flux-balance equation:svS ˆ*0 = (2.10)swhere S is the stoichiometric matrix andsthe reaction fluxes. The path...