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