FLUX BALANCE ANALYSIS OVERVIEW Learning Objectives Each student should be able to:
Explain flux balance analysis (FBA). Explain the stoichiometric reactions and metabolites. Explain mass balanced linear equations. Explain the biomass reaction. Explain how to create a stoichiometric matrix from reactions and metabolites. Explain gene-protein-reaction associations. Explain the constraint-based modeling. Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox FLUX BALANCE ANALYSIS Orth, J. D. , I. Thiele, et al. (2010)
FLUX BALANCE ANALYSIS Orth, J. D., I. Thiele, et al. (2010). "What is flux balance analysis?" Nature biotechnology 28(3): Through the use of genome-scale metabolic network reconstructions, Flux BalanceAnalysis (FBA) can be used to calculate the flow of metabolites through a metabolicnetwork. This capability makes it possible to predict the growth rate of an organismand/or the rate of production of a given metabolite. FBA has limitations! It does not use kinetic parameters, thus it cannot predictmetabolite concentrations. It is also only capable of determining fluxes at steadystate. Typically, FBA does not account for regulatory effects such as activation ofenzymes by protein kinases or regulation of gene expression. Therefore, itspredictions may not always be accurate. Becker, S. A., A. M. Feist, et al. (2007). "Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox." Nature protocols 2(3): The manner in which microorganisms utilize their metabolic processes can be predicted using constraint-based analysis of genome-scale metabolic networks. Herein, we present the constraint-based reconstruction and analysis toolbox, a software package running in the Matlab environment, which allows for quantitative prediction of cellular behavior using a constraint-based approach. Specifically, this software allows predictive computations of both steady-state and dynamic optimal growth behavior, the effects of gene deletions, comprehensive robustness analyses, sampling the range of possible cellular metabolic states and the determination of network modules. Functions enabling these calculations are included in the toolbox, allowing a user to input a genome-scale metabolic model distributed in Systems Biology Markup Language format and perform these calculations with just a few lines of code. The results are predictions of cellular behavior that have been verified as accurate in a growing body of research. After software installation, calculation time is minimal, allowing the user to focus on the interpretation of the computational results. Formulation of Flux Balance Analysis
Figure 2 Formulation of an FBA problem. (a) A metabolic network reconstruction consists of a list of stoichiometrically balanced biochemical reactions. (b) This reconstruction is converted into a mathematical model by forming a matrix (labeled S), in which each row represents a metabolite and each column represents a reaction. Growth is incorporated into the reconstruction with a biomass reaction (yellow column), which simulates metabolites consumed during biomass production. Exchange reactions (green columns) are used to represent the flow of metabolites, such as glucose and oxygen, in and out of the cell. (c) At steady state, the flux through each reaction is given by Sv = 0, which defines a system of linear equations. As large models contain more reactions than metabolites, there is more than one possible solution to these equations. (d) Solving the equations to predict the maximum growth rate requires defining an objective function Z = cTv (c is a vector of weights indicating how much each reaction (v) contributes to the objective). In practice, when only one reaction, such as biomass production, is desired for maximization or minimization, c is a vector of zeros with a value of 1 at the position of the reaction of interest. In the growth example, the objective function is Z = vbiomass (that is, c has a value of 1 at the position of the biomass reaction). (e) Linear programming is used to identify a flux distribution that maximizes or minimizes the objective function within the space of allowable fluxes (blue region) defined by the constraints imposed by the mass balance equations and reaction bounds. The thick red arrow indicates the direction of increasing Z. As the optimal solution point lies as far in this direction as possible, the thin red arrows depict the process of linear programming, which identifies an optimal point at an edge or corner of the solution space. Orth, J. D., I. Thiele, et al. (2010). "What is fluxbalance analysis?" Nature biotechnology 28(3): Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox Identifying Metabolic Reactions and Metabolites (Gene-Protein-Reactions)
Objective: Create A biochemically, genetically and genomically (BiGG) structured knowledge base. Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010) Desired Reaction Information
Reaction Name* Reaction Description* Reaction Formula* Gene-reaction Association* Genes (Gene Locus) * Proteins Cellular Subsystem *(e.g. Glycolysis) Reaction Direction* Flux Lower Bound* Flux Upper Bound* Confidence Score (1-5) EC Number Notes References * Required Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide by Orth, Fleming, and Palsson (2010) Genome-scale Reconstruction Reactions Desired Metabolite Information
Metabolite Name* Metabolite Description* Metabolite Neutral Formula Metabolite Charged Formula* Metabolite Charge* Metabolite Compartment* Metabolite KEGGID Metabolite PubChemID Metabolite CheBI ID Metabolite Inchi String Metabolite Smile * Required Thiele, I. and B. O. Palsson (2010). "A protocol for generating a high-quality genome-scale metabolic reconstruction." Nature protocols 5(1): Genome-scale Reconstruction Metabolites Metabolic Pathway D-Glucose Exchange Reaction (mmol/gDW-hr-1)
hexokinase Metabolites (mmol) Reactions (mmol/gDW-hr-1) D-Glucose 6-phosphate Metabolic Pathway glucose-6-phosphate isomerase D-Fructose 6-phosphate fructose-bisphosphatase Phosphofructokinase D-Fructose 1,6-bisphosphate Figure 2 | Stoichiometric representation of metabolic networks. (a) The first few reactions of glycolysis in a graphical form. (b) The stoichiometric matrix (S) corresponding to a. As indicated, each column corresponds to a particular reaction and each row to a particular metabolite. The last column, labeled EX_glc, is an exchange reaction for glucose that allows glucose to enter and leave the system. (c) The upper (UB) and lower bounds (LB) for each reaction. The three reversible reactions (PGI, FBA and TPI) have lower bounds of N. The irreversible reactions have lower bounds of zero because they are not to proceed in the reverse direction. The exchange reaction in the last column has a lower bound of 2 indicating a potential glucose uptake rate of 2 mmol gDW1 h1. All reactions are effectively unconstrained in the forward direction. fructose-bisphosphate aldolase Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate triose-phosphate isomerase Becker, S. A., et al. (2007). "Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox." Nature protocols 2(3): System Boundaries: Exchange & Transport Reactions
Periplasm [p] Cytoplasm [c] Exchange Reactions Extracellular [e] Thiele, I. and B. O. Palsson (2010). "A protocol for generating a high-qualitygenome-scale metabolic reconstruction." Nature protocols 5(1): GENOME-SCALE METABOLIC RECONSTRUCTIONS
Overview Draft Reconstruction Refinement of Reconstruction Conversion of Reconstruction into Computable Format Network Evaluation Data Assembly and Dissemination Draft Reconstruction Conversion of Reconstruction Refinement of Reconstruction Network Evaluation Data Assembly and Dissemination Thiele, I. and B. O. Palsson (2010). "A protocol for generating a high-quality genome-scale metabolic reconstruction." Nature protocols 5(1): Reconstruction Process: 96 Step Protocol Thiele, I. and B. O
Reconstruction Process: 96 Step Protocol Thiele, I. and B. O. Palsson (2010). "A protocol for generating a high-quality genome-scale metabolic reconstruction." Nature protocols 5(1): Figure 1. Overview of the procedure to iteratively reconstruct metabolic networks. In particular stages 2 to 4 are continuously iterated until model predictions are similar to the phenotypic characteristics of the target organism and/or all experimental data for comparison are exhausted. E.coli Core Model Pentose Phosphate Shunt
Ana TCA OxP PPP Glyc Ferm N E.coli Core Model Oxidative Phosphorylation and Transfer of Reducing Equivalents Glycolysis Tricarbonoxylic Acid Cycle (TCA) Glycoxylate Cycle, Gluconeogenesis, and Anapleurotic Reactions Supplementary Figure 1 Map of the core E. coli metabolic network. Orange circles represent cytosolic metabolites, yellow circles represent extracellular metabolites, and the blue arrows represent reactions. Reaction name abbreviations are uppercase and metabolite name abbreviations are lowercase. The metabolic pathways shown in these maps are glycolysis (Glyc), pentose phosphate pathway (PPP), TCA cycle (TCA), oxidative phosphorylation (OxP), anaplerotic reactions (Ana) [Anaplerosis is the act of replenishing TCA cycle intermediates that have been extracted for biosynthesis], and fermentation pathways (Ferm). glycolysis (Glyc) - the metabolic pathway that converts glucose into pyruvate pentose phosphate pathway (PPP) process that generates NADPH and pentoses (5-carbon sugars) TCA cycle (TCA) -the citric acid cycle is part of a metabolic pathway involved in the chemical conversion of carbohydrates, fats and proteins into carbon dioxide and water to generate a form of usable energy. Other relevant reactions in the pathway include those in glycolysis and pyruvate oxidation before the citric acid cycle, and oxidative phosphorylation after it. In addition, it provides precursors for many compounds including some amino acids and is therefore functional even in cells performing fermentation. oxidative phosphorylation (OxP) -a metabolic pathway that uses energy released by the oxidation of nutrients to produce adenosine triphosphate (ATP). anaplerotic reactions (Ana) - Anaplerosis is the act of replenishing TCA cycle intermediates that have been extracted for biosynthesis (in what are called cataplerotic reactions fermentation pathways (Ferm) - Fermentation is important in anaerobic conditions when there is no oxidative phosphorylation to maintain the production of ATP (Adenosine triphosphate) by glycolysis. During fermentation, pyruvate is metabolised to various different compounds. Homolactic fermentation is the production of lactic acid from pyruvate; alcoholic fermentation is the conversion of pyruvate into ethanol and carbon dioxide; and heterolactic fermentation is the production of lactic acid as well as other acids and alcohols. Fermentation does not necessarily have to be carried out in an anaerobic environment. Nitrogen Metabolism Fermentation Orth, J. D., I. Thiele, et al. (2010). "What is flux balance analysis?" Nature biotechnology 28(3): Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox Creating A Stoichiometric Matrix
The stoichiometric matrix, S, is the centerpiece of a mathematical representation of genome-scale metabolic networks. This matrix represents each reaction as a column and each metabolite as a row, where each numerical element is the corresponding stoichiometric coefficient. Figure 2 | Stoichiometric representation of metabolic networks. (a) The first few reactions of glycolysis in a graphical form. (b) The stoichiometric matrix (S) corresponding to a. As indicated, each column corresponds to a particular reaction and each row to a particular metabolite. The last column, labeled EX_glc, is an exchange reaction for glucose that allows glucose to enter and leave the system. (c) The upper (UB) and lower bounds (LB) for each reaction. The three reversible reactions (PGI, FBA and TPI) have lower bounds of N. The irreversible reactions have lower bounds of zero because they are not to proceed in the reverse direction. The exchange reaction in the last column has a lower bound of 2 indicating a potential glucose uptake rate of 2 mmol gDW1 h1. All reactions are effectively unconstrained in the forward direction. Note: Flux flows into (positive) and out (negative) of nodes (metabolites) not reactions Becker, S. A., A. M. Feist, et al. (2007). "Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox." Nature protocols 2(3): Genome-scale Metabolic Reconstruction
BIGG Database Metabolic Pathway Stoichiometric Matrix Gene-Protein-Reaction (GPR) Associations Reed, J. L., I. Famili, et al. (2006). "Towards multidimensional genome annotation." Nature reviews. Genetics 7(2): Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox How can we use the Stoichiometric Matrix?
The stoichiometric matrix, S, is a linear transformation of the fluxvector, v to a vector of time derivatives of the concentration vector, x. Reactions The concentration vector, x, represents the concentration of each ofthe metabolites. If we assume that a cell will be in a particular phenotype for a timemuch larger than the changing time of metabolites then we can alsoassume that the concentration pools for the metabolites will be non- changing thus setting dx/dt = 0. This is the steady state assumption offlux balance analysis. Metabolites Since there are normally many more reactions (columns) thanmetabolites (rows), more unknown variables than equations, then thereis no unique solutions (could be a large number of solutions). Need to find a way to constrain the solution space! Dynamic Mass Balance Linear Transformation A simple network A B C e1
v1 v4 v3 v2 Stoichiometric Matrix Linear Differential Equations Dynamic Mass Balance (Steady State) Note: More unknown variables than equations, thus no unique solutions! Need constraints! The Conceptual Basis of Constraint-based Modeling
With no constraints, the flux distribution of a biological network may lie at any point in a solution space. When massbalance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower andupper bounds (ai and bi) (label 2) are applied to a network, it defines an allowable solution space. The network mayacquire any flux distribution within this space, but points outside this space are denied by the constraints. Throughoptimization of an objective function using linear programming, FBA can identify a single optimal flux distribution thatlies on the edge of the allowable solution space. Orth, J. D., I. Thiele, et al. (2010). "What is flux balance analysis?" Nature biotechnology 28(3): Role of Constraints REI601M,Introduction to Systems Biology, Dr. Innes Thiele,2012, https://systemsbiology.hi.is/wiki/REI601M FLUX OPTIMIZATION (Linear Programming or Linear Optimization Problem)
Maximize the objective function The goal is to create and objective function that is biologically meaningful. These could include; Cellular growth (maximization) Particular metabolite engineering (maximization) Energy consumption (minimization) with the following constraints For the case of cellular growth as the objective function (Biomass Function) where It has been shown that under rich growth conditions (i.e. no lack of phosphate and nitrogen), E. coli grows in a stoichiometrically optimal manner. (Schilling 2001, Edwards 1994) It is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performance. (Segre, 2002.) x = concentration vector v = flux vector c = objective function weights S = Stoichiometric matrix j = Lower bound of flux j = upper bound of flux Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox Biomass Precursors The biomass reaction accounts forall the fractional contributionsfrom biosynthetic precursors andkey cofactors to create 1g ofbiomass. These factional contributionsneed to be determinedexperimentally for cells growing inlog phase. It may not be possible to obtain adetailed biomass composition forthe target organism. In this case,one can estimate the relativefraction of each precursor fromexisting databases. Thiele, I. and B. O. Palsson (2010). "A protocol for generating a high-quality genome-scale metabolic reconstruction." Nature protocols 5(1): E.coli Precursor Metabolites
Sugar nucleotides Amino sugars Nicotinamide coenzymes Glycerol-3-phosphate -> Phospholipids Vitamins and cofactors Folates Riboflavin Coenzyme A Adenosylcobalamine Nicotinamide Purine nucleotides Pyrimidine nucleotides Phosphoribosyl pyrophosphate Histidine Tryptophan Serine Family Serine -> Tryptophan -> Ethanolamine -> 1-C units Glycine -> Purine nucleotides Cysteine Aromatic Family Tyrosine Tryptophan Phenylalanine Chorismate Vitamins and cofactors Ubiquinone Menaquinone Folates 2-Keto-3-deoxyoctanate Heptose in LPS Orth, J. D., I. Thiele, et al. (2010). "What is flux balance analysis?" Nature biotechnology 28(3): Pharkya, P., A. P. Burgard, et al. (2003). "Exploring the overproduction of amino acids using the bilevel optimization framework OptKnock." Biotechnology and bioengineering 84(7): Schaechter, M., Ingraham, J.L., Neidhardt, F. C., Microbe, ASM Press, 2005, p. 116. Heme Pyruvate family Alanine Valine Leucine Isoleucine Isoprenoids Aspartate family Asparagine Threonine Methionine -> Spermidine Aspartate -> Nicotinamide coenzymes -> Pyrimidine nucleotides Lysine Glutamate family Glutamate -> Hemes Glutamine Arginine -> Polyamines Proline Fatty Acids Murein Leucine Maintenance Energy Requirements
To simulate growth, the energy required to maintain the cell growth mustbe accounted for. Two forms of energy are required; growth associated maintenance (GAM)energy and nongrowth associated maintenance (NGAM) energy (e.g. turgorpressure). GAM reaction accounts for the energy (ATP) necessary to replicate a cell.It is represented in the model by x ATP +x H20 -> x ADP +x Pi + x H+ Where x is the number of required phosphate bonds (59.81 in core model).This will be included in the biomass reaction The NGAM reaction (ATPM) is given by ATP + 1H2O -> 1 ADP + 1 Pi + 1 H+where the flux through this reaction is constrained by experimental datato 8.39 mmol gDW-1h-1 Thiele, I. and B. O. Palsson (2010). "A protocol for generating a high-quality genome-scale metabolic reconstruction." Nature protocols 5(1): Biomass Reaction For E.coli Core Model
(1.496) 3pg + (3.7478) accoa + ( ) atp + (0.3610)e4p + (0.0709) f6p + (0.1290) g3p + (0.2050) g6p +(0.2557) gln-L + (4.9414) glu-L + ( ) h2o + (3.5470)nad + ( ) nadph + (1.7867) oaa + (0.5191) pep +(2.8328) pyr + (0.8977) r5p --> ( ) adp + (4.1182)akg + (3.7478) coa + ( ) h + (3.5470) nadh +( ) nadp + ( ) pi * Key Cofactors ecoli_core_models.xls iaf1260 BIOMASS OBJECTIVE FUNCTION (Ec_biomass_iAF1260_core_59p81M)
Z = fthf[c] ohph[c] ala-L[c] amet[c] arg-L[c] asn-L[c] asp-L[c] atp[c] ca2[c] cl[c] coa[c] cobalt2[c] ctp[c] cu2[c] cys-L[c] datp[c] dctp[c] dgtp[c] dttp[c] fad[c] fe2[c] fe3[c] gln-L[c] glu-L[c] gly[c] gtp[c] h2o[c] his-L[c] ile-L[c] k[c] kdo2lipid4[e] leu-L[c] lys-L[c] met-L[c] mg2[c] mlthf[c] mn2[c] mobd[c] murein5px4p[p] nad[c] nadp[c] nh4[c] pe160[c] pe160[p] pe161[c] pe161[p] phe-L[c] pheme[c] pro-L[c] pydx5p[c] ribflv[c] ser-L[c] sheme[c] so4[c] thf[c] thmpp[c] thr-L[c] trp-L[c] tyr-L[c] + 5.5e-005 udcpdp[c] utp[c] val-L[c] zn2[c]-> adp[c] h[c] pi[c] ppi[c] Formulation of Flux Balance Analysis
Figure 2 Formulation of an FBA problem. (a) A metabolic network reconstruction consists of a list of stoichiometrically balanced biochemical reactions. (b) This reconstruction is converted into a mathematical model by forming a matrix (labeled S), in which each row represents a metabolite and each column represents a reaction. Growth is incorporated into the reconstruction with a biomass reaction (yellow column), which simulates metabolites consumed during biomass production. Exchange reactions (green columns) are used to represent the flow of metabolites, such as glucose and oxygen, in and out of the cell. (c) At steady state, the flux through each reaction is given by Sv = 0, which defines a system of linear equations. As large models contain more reactions than metabolites, there is more than one possible solution to these equations. (d) Solving the equations to predict the maximum growth rate requires defining an objective function Z = cTv (c is a vector of weights indicating how much each reaction (v) contributes to the objective). In practice, when only one reaction, such as biomass production, is desired for maximization or minimization, c is a vector of zeros with a value of 1 at the position of the reaction of interest. In the growth example, the objective function is Z = vbiomass (that is, c has a value of 1 at the position of the biomass reaction). (e) Linear programming is used to identify a flux distribution that maximizes or minimizes the objective function within the space of allowable fluxes (blue region) defined by the constraints imposed by the mass balance equations and reaction bounds. The thick red arrow indicates the direction of increasing Z. As the optimal solution point lies as far in this direction as possible, the thin red arrows depict the process of linear programming, which identifies an optimal point at an edge or corner of the solution space. Orth, J. D., I. Thiele, et al. (2010). "What is fluxbalance analysis?" Nature biotechnology 28(3): E.coli Core Model PPP OxP Glyc TCA Ana Ferm
Supplementary Figure 1 Map of the core E. coli metabolic network. Orange circles represent cytosolic metabolites, yellow circles represent extracellular metabolites, and the blue arrows represent reactions. Reaction name abbreviations are uppercase and metabolite name abbreviations are lowercase. The metabolic pathways shown in these maps are glycolysis (Glyc), pentose phosphate pathway (PPP), TCA cycle (TCA), oxidative phosphorylation (OxP), anaplerotic reactions (Ana) [Anaplerosis is the act of replenishing TCA cycle intermediates that have been extracted for biosynthesis], and fermentation pathways (Ferm). glycolysis (Glyc) - the metabolic pathway that converts glucose into pyruvate pentose phosphate pathway (PPP) process that generates NADPH and pentoses (5-carbon sugars) TCA cycle (TCA) -the citric acid cycle is part of a metabolic pathway involved in the chemical conversion of carbohydrates, fats and proteins into carbon dioxide and water to generate a form of usable energy. Other relevant reactions in the pathway include those in glycolysis and pyruvate oxidation before the citric acid cycle, and oxidative phosphorylation after it. In addition, it provides precursors for many compounds including some amino acids and is therefore functional even in cells performing fermentation. oxidative phosphorylation (OxP) -a metabolic pathway that uses energy released by the oxidation of nutrients to produce adenosine triphosphate (ATP). anaplerotic reactions (Ana) - Anaplerosis is the act of replenishing TCA cycle intermediates that have been extracted for biosynthesis (in what are called cataplerotic reactions fermentation pathways (Ferm) - Fermentation is important in anaerobic conditions when there is no oxidative phosphorylation to maintain the production of ATP (Adenosine triphosphate) by glycolysis. During fermentation, pyruvate is metabolised to various different compounds. Homolactic fermentation is the production of lactic acid from pyruvate; alcoholic fermentation is the conversion of pyruvate into ethanol and carbon dioxide; and heterolactic fermentation is the production of lactic acid as well as other acids and alcohols. Fermentation does not necessarily have to be carried out in an anaerobic environment. Orth, J. D., I. Thiele, et al. (2010). "What is flux balance analysis?" Nature biotechnology 28(3): Ferm Genome-Scale Reconstructions
E.coli K-12 MG1655 Genome-Scale Reconstructions iAF1260 6.Feist, A. M., C. S. Henry, et al. (2007). "A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information." Molecular Systems Biology 3: 121. iJO Orth, J. D. and B. O. Palsson (2012). "Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions." BMC systems biology 6(1): 30. BIGG E.coli model ecoli_iaf1260.xml The Iterative Reconstruction and History of the E
The Iterative Reconstruction andHistory of the E. Coli Metabolic Network Figure 2 The iterative reconstruction and history of the E. coli metabolic network. Six milestone efforts are shown that contributed to the reconstruction of the E. coli metabolic network. For each of the six reconstructions1219, the number of included reactions (blue diamonds), genes (green triangles) and metabolites (purple squares) are displayed. Also listed are noteworthy expansions that each successive reconstruction provided over previous efforts. For example, Varma & Palsson13,14 included amino acid and nucleotide biosynthesis pathways in addition to the content that Majewski & Domach12 characterized. The start of the genomic era92 (1997) marked a significant increase in included reconstruction components for each successive iteration. The reaction, gene and metabolite values for pregenomic-era reconstructions were estimated from the content outlined in each publication and in some cases, encoding genes for reactions were unclear. Feist, A. M. and B. O. Palsson (2008). "The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli." Nature biotechnology 26(6): E.coli Genome-scale Reconstructions
Escherichia coli 042 Escherichia coli 536 Escherichia coli 55989 Escherichia coli ABU 83972 Escherichia coli APEC O1 Escherichia coli ATCC 8739 Escherichia coli B str. REL606 Escherichia coli BL21(DE3) AM946981 Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG Escherichia coli BL21(DE3) CP001509 Escherichia coli BW2952 Escherichia coli CFT073 Escherichia coli DH1 Escherichia coli DH1 ME8569 Escherichia coli E24377A Escherichia coli ED1a Escherichia coli ETEC H10407 Escherichia coli HS Escherichia coli IAI1 Escherichia coli IAI39 Escherichia coli IHE3034 Escherichia coli KO11FL Escherichia coli LF82 Escherichia coli NA114 Escherichia coli O103:H2 str Escherichia coli O111:H- str Escherichia coli O127:H6 str. E2348/69 Escherichia coli O157:H7 EDL933 Escherichia coli O157:H7 str. EC4115 Escherichia coli O157:H7 str. Sakai Escherichia coli O157:H7 str. TW14359 Escherichia coli O26:H11 str Escherichia coli O55:H7 str. CB9615 Escherichia coli O83:H1 str. NRG 857C Escherichia coli S88 Escherichia coli SE11 Escherichia coli SE15 Escherichia coli SMS-3-5 Escherichia coli str. K-12 substr. DH10B Escherichia coli str. K-12 substr. MG1655 Escherichia coli str. K-12 substr. W3110 Escherichia coli UM146 Escherichia coli UMN026 Escherichia coli UMNK88 Escherichia coli UTI89 Escherichia coli W Escherichia coli W CP002185 Escherichia coli K-12 MG1655 Monk, J. M., P. Charusanti, et al. (2013). Proceedings of the National Academy of Sciences of the United States of America 110(50): Phylogenetic Coverage of Genome-scale Network Reconstructions
Figure 3 Phylogenetic coverage of GENREs. Distribution of GENREs across the phylogenetic tree of life for 78 species with existing GENREs (as of February 2013). The Bacteria domain has the most organisms with reconstructed GENREs. Within Bacteria the Proteobacteria phylum has the most organisms (32) with reconstructed GENREs. There are many phyla for which no GENREs have been reconstructed (red). See the SBRG website (http://sbrg.ucsd.edu/ optimizing-genres/) for an up-to-date representation of reconstructed species and their location in the tree of life. Monk, J., J. Nogales, et al. (2014). "Optimizing genome-scale networkreconstructions." Nature biotechnology 32(5): Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox COBRA TOOLBOX Matlab Cobra Toolbox Flux Optimization
Flux Variability Analysis Robustness Analysis Phenotype Phase Plane Analysis Parsimonious FBA Visualization Tools Gene Additions & Knockouts Production Envelopes Load Models SBML, Excel Graphical Output Output Maps Numerical Output Save Models Matlab Code M-Files Links for installing COBRA toolbox for MATLAB Matlab Interface DRAWING FLUX VALUES ONTO A MAP Print Flux Values ACONTa ACONTb AKGDH ATPM 8.39 ATPS4r Biomass_ CO2t CS CYTBD ENO EX_co2(e) EX_glc(e) -10 EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e) EX_pi(e) FBA FUM G6PDH2r GAPD GLCpts10 GLNS GLUDy GND H2Ot ICDHyr MDH NADH NH4t O2t PDH PFK PGI PGK PGL PGM PIt2r PPC PYK RPE RPI SUCDi SUCOAS TALA TKT TKT TPI Growth Rate Inputs & Outputs (Exchange Reactions) Aerobic Growth on Glucose
EX_glc(e) Aerobic Growth on Glucose Exchange Reactions EX_o2(e) EX_h(e) EX_co2(e) EX_glc(e) EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e) EX_pi(e) EX_pi(e) EX_h2o(e) EX_co2(e) EX_nh4(e) Close-up of TCA Cycle Anaerobic Growth on Glucose
Exchange Reactions Biomass EX_ac(e) EX_co2(e) EX_etoh(e) EX_for(e) EX_glc(e)-18.5 EX_h2o(e) EX_h(e) EX_nh4(e) EX_pi(e) AEROBIC vs. ANAEROBIC GROWTH Orth, J. D. , I. Thiele, et al. (2010)
AEROBIC vs. ANAEROBIC GROWTH Orth, J. D., I. Thiele, et al. (2010). "What is flux balance analysis?" Nature biotechnology 28(3): Supplementary Figure 2 Flux distributions computed by FBA can be visualized on network maps. In these two examples, the thick blue arrows represent reactions carrying flux, and the thin black arrows represent unused reactions. These maps show the state of the E. coli core model with maximum growth rate as the objective (Z) under aerobic (a) and anaerobic (b) conditions. Reactions that are in use have thick blue arrows, while reactions that carry 0 flux have thin black arrows. The metabolic pathways shown in these maps are glycolysis (Glyc), pentose phosphate pathway (PPP), TCA cycle (TCA), oxidative phosphorylation (OxP), anaplerotic reactions (Ana), and fermentation pathways (Ferm). These flux maps were drawn using SimPheny and edited for clarity with Adobe Illustrator. a. b. Aerobic Growth Anaerobic Growth Substrate Maximum Growth Rate
Aerobic (hr-1) Anaerobic (hr-1) acetate 0.3893 acetaldehyde 0.6073 2-oxoglutarate 1.0982 ethanol 0.6996 D-fructose 1.7906 0.5163 fumarate 0.7865 D-glucose L-glutamine 1.1636 L-glutamate 1.2425 D-lactate 0.7403 L-malate pyruvate 0.6221 0.0655 succinate 0.8401 The core E. coli modelcontains exchange reactionsfor 13 different organiccompounds, each of whichcan be used as the solecarbon source under aerobicor anaerobic conditions. Supplementary Table 1 The maximum growth rate of the core E. coli model on its 13 different organic substrates, computed by FBA. Growth rate was calculated for both aerobic and anaerobic conditions for each substrate, and the maximum substrate uptake rate was set to 20 mmol gDW-1 hr-1 for every substrate. ("What is flux balanceanalysis? - Supplementary tutorial) Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox A Growing Toolbox for Constraint-based Analysis
Figure 1 | A growing toolbox for constraint-based analysis. The two steps that are used to form a solution space reconstruction and the imposition of governing constraints are illustrated in the centre of the figure1,20,37,111 . As indicated, several methods are being developed at various laboratories to analyse the solution space. The primary references for the methods indicated are: 1, REF. 40; 2, REFS 41, 61; 3, REFS 50, 99; 4, REFS 70, 71; 5, REFS 45, 49; 6, REFS 45, 62, 112; 7, REF. 55; 8, REF. 97; 9, REF. 23; 10, REF. 59; 11, REF. 58; 12, REF. 83; 13, REF. 35; 14, REF. 64; 15, REF. 85; 16, REF. 29. Ci, concentration of compound i; Cj, concentration of compound j; EP, extreme pathway;vi, flux through reaction i; vj, flux through reaction j; v1, flux through reaction 1; v2, flux through reaction 2; v3, flux through reaction 3; vnet, net flux through loop. Price, N. D., J. L. Reed, et al. (2004). "Genome-scale models of microbial cells: evaluating the consequences of constraints." Nature reviews. Microbiology 2(11): Methods in Constraint-based Reconstruction and Analysis
Flux Balance Analysis Overview
Stoichiometric Reactions & Metabolites Mathematical Representation of Reactions & Constraints Mass Balanced Linear Equations Biomass Reaction Calculating Fluxes Flux Balance Analysis Toolbox