Kein Folientitel

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Transport equations
O2external O2 H2external H2 HO2external HO2
t1 1 0 0
O2 H2 H20
t2 0 1 0
t3 0 0 1
Transport Matrix T
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Elemental Balance
In biosystems, elements (C, H, N, O, P, S) are
always conserved, thus
O 2 0 1
O2 H2 H20
H 0 2 2
Elemental Composition Matrix E
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Reaction equation 1/2 O2 H2 H2O
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BRENDA Threonine dehydratase
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Reaction equation L-Homoserine PyruvateNH3
C4 H9 N O3 C3 H4 O3 NH3
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Elemental Balances May Reveal Inconsistencies in
Biochemical Reaction Systems
Should read L-Homoserine 2-Oxobutyrate NH3
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Pathway (Topological) Analysis Metabolic Flux
Analysis
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Metabolic Network - Regulatory NetworkHierarchica
l Organisation
Metabolic Network
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Pathway Analysis Flux Analysis
Metabolic Network
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Introduction Pathway AnalysisMetabolic Flux
AnalysisExample

• Bioinformatics and Metabolic Engineering
• Structured metabolic models
• Metabolite balancing
• Conserved moieties
• Elementary flux modes
• Estimation of flux distributions
• Observability of metabolic fluxes
• Overdetermined and underdetermined systems
• Metabolic model of Saccharomyces cerevisiae
• Model Analysis

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Chemical entities (atoms, ions, assemblies of
atoms or ions) participating in a reaction system
without loss of integrity and always remaining in
the system (even if it is an open one) are called
conserved moieties. Example of a conservation
relation NADH NAD const.
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r1 Acetaldehyde H2ONAD AcetateNADH2 H r2
1/2 O2 NADHH H2O NAD
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r1 -1 1 0 -1 -1 1 -1
r2 0 0 -1/2 1 2 -1 1
t1 1 0 0 0 0 0 0
t2 0 1 0 0 0 0 0
t3 0 0 1 0 0 0 0
t4 0 0 0 1 0 0 0
Acetaldehyde Acetate O2 H20 H NADH NAD
t5 0 0 0 0 1 0 0
NADH NAD const.
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The presence of conservation relations leads to
linear dependent rows in the balance matrix N.
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r1 -1 1 0 -1 -1 1 -1
r2 0 0 -1/2 1 2 -1 1
t1 1 0 0 0 0 0 0
t2 0 1 0 0 0 0 0
t3 0 0 1 0 0 0 0
t4 0 0 0 1 0 0 0
Acetaldehyde Acetate O2 H20 H NADH NAD
t5 0 0 0 0 1 0 0
N0
N
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Since a metabolic reaction network comprises n
conservation relations (conserved moieties), n
algebraic relations between the balanced
metabolites occur.
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Introduction Pathway AnalysisMetabolic Flux
AnalysisExample

• Bioinformatics and Metabolic Engineering
• Structured metabolic models
• Metabolite balancing
• Conserved moieties
• Elementary flux modes
• Estimation of flux distributions
• Observability of metabolic fluxes
• Overdetermined and underdetermined systems
• Metabolic model of Saccharomyces cerevisiae
• Model Analysis

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Null- Space (Kernel)
N v 0
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-1/2 -1 1
1 0 0
0 1 0
0 0 1
O2 H2 H2O
-1/2 -1 1
1 0 0
0 1 0
0 0 1
O2 H2 H2O
r1 t1 t2 t3
0 0 0

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-1/2 -1 1
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1
1 1/2 1
O2 H2 H2O
r1 t1 t2 t3
0 0 0

Row reduced echelon form of matrix N
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1
1/2
1
1
-1/2 -1 1
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1
1 1/2 1
O2 H2 H2O
1 1/2 1 -1
0 0 0

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1
1
1/2
1
-1/2 -1 1
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1
1 1/2 1
O2 H2 H2O
-1 -1/2 -1 1
0 0 0

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The basis of the kernel of N does NOT
necessarily fulfil reversibility properties.
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Degrees of Freedom
Degrees of Freedom number of fluxes - number of
linear independent rows of balance matrix N
Degrees of Freedom number of fluxes - rank(N)
Degrees of Freedom dim(kernel(N))
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-1/2 -1 1
1 0 0
0 1 0
0 0 1
O2 H2 H2O
-1/2 -1 1
1 0 0
0 1 0
0 0 1
O2 H2 H2O
r1 t1 t2 t3
0 0 0

Degree of Freedom 4-31
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r1 -1 1 0 -1 -1 1 -1
r2 0 0 -1/2 1 2 -1 1
t1 1 0 0 0 0 0 0
t2 0 1 0 0 0 0 0
t3 0 0 1 0 0 0 0
t4 0 0 0 1 0 0 0
Acetaldehyde Acetate O2 H20 H NADH NAD
t5 0 0 0 0 1 0 0
Degree of Freedom 7-6 1
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v1 v2 v3
v1 1
v2 -1
v3 -1
M
0

irreversible
Degrees of Freedom number of fluxes -
rank(N) Degrees of Freedom 3 -1 2 The
Null-Space (kernel) is spanned by 2 base vectors
(flux modes)
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a) Flux vectors spanning the kernel of N
1
1
1
0
0
1
Flux Mode 1 a)
Flux Mode 2 a)
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b) Flux vectors spanning the kernel of N
2
1
1
0
1
1
Flux Mode 1 b)
Flux Mode 2 b)
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The base of the kernel of N is NOT unique.
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Flux Mode 1 b)
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Elementary Flux Modes

• Fulfil steady state condition
• Fulfil reversibilty properties
• Can not be decomposed into smaller modes (i.e.
  modes that involve less enzymes)

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Network Design
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GLUCOSE
RIBU5P
G6P
ATP
XYL5P
RIB5P
F6P
NADP
E4P
F6P
GAP
ADP
3PG
NADPH
Pi
PEP
CO2
PYR
ACCOA
H2O
COA
THREONIN
OAC
ISOCIT
NAD
H
MAL
FADH2
AKG
FAD
NADH
FUM
SUC
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irreversible
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Elementary Flux Mode 1
Y THREONIN / GLUCOSE 4/3
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Elementary Flux Mode 2
Y THREONIN / GLUCOSE 1
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Elementary Flux Mode 3
Y THREONIN / GLUCOSE 2/3
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Elementary Flux Mode 4
Y THREONIN / GLUCOSE 0
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1
Elementary Flux Mode 5
GLUCOSE
3
RIBU5P
G6P
2
Y THREONIN / GLUCOSE 0
XYL5P
RIB5P
F6P
E4P
F6P
GAP
1
3PG
PEP
PYR
ACCOA
1
OAC
ISOCIT
MAL
AKG
FUM
SUC
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1
Elementary Flux Mode 6
GLUCOSE
G6P
Y THREONIN / GLUCOSE 0
F6P
GAP
2
3PG
PEP
PYR
ACCOA
2
OAC
ISOCIT
MAL
AKG
FUM
SUC
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RIBU5P
G6P
6PG
XYL5P
RIB5P
F6P
E4P
F6P
GAP
2PG
FALD
METOH
PEP
PYR
ACCOA
THREONIN
OAC
ISOCIT
GLYO
MAL
AKG
FUM
SUC
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Elementary Flux Modes
Use in Metabolic Engineering

• Optimal and suboptimal yields can be easily
  obtained
• Identification of dispensable enzymes (bypass)
• Medium optimisation

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Elementary Flux Modes
Use in Modelling Tools

• Identification of the complete material flow
  functioning
• Identification of parts of the network without
  any function (dead subnets)
• Identification of futile cycles

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Elementary Flux Modes
Some Properties

• The set of elementary flux modes is unique
• The vector space spanned by elementary flux modes
  exceeds (or equals) the dimension of the kernel

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Introduction Pathway AnalysisMetabolic Flux
AnalysisExample

• Bioinformatics and Metabolic Engineering
• Structured metabolic models
• Metabolite balancing
• Conserved moieties
• Elementary flux modes
• Estimation of flux distributions
• Observability of metabolic fluxes
• Overdetermined and underdetermined systems
• Metabolic model of Saccharomyces cerevisiae
• Model Analysis

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Estimation of Metabolic Fluxes
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Experimental Determination ofNet Conversion Rates
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Estimation of Metabolic Fluxes
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Estimation of Metabolic Fluxes
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Estimation of Metabolic Fluxes
A) Exactly Determined System
B) Overdetermined System
C) Underdetermined System
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Estimation of Metabolic Fluxes
Exactly Determined System without conservation
relations
Observability criterion
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Estimation of Metabolic Fluxes
Underdetermined System
An underdetermined system can never be observed
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Estimation of Metabolic Fluxes
Overdetermined System
Observability criterion
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An overdetermined system isNOT always observable.
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v2
v1
v4
v5
S0
S1
M1
M2
M3
v3
Degrees of freedom 2
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v2
v1
v4
v5
S0
S1
M1
M2
M3
v3
Degrees of freedom 2
Fluxes derived from measurements v1, v4, v5
Not observeable v2, v3
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v2
v1
v4
v5
Vnetv3-v2
S0
S1
M1
M2
M3
v3
Degrees of freedom 2
Fluxes derived from measurements v1, v4, v5
Observeable vnet v3 -v2
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v2
v1
v4
v5
S0
S1
M1
M2
M3
v3
Degrees of freedom 2
Derived from measurements v1, v3, v5
Observeable v2, v4
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Model Validation
Invalid Model / Inconsistent Data
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c2 -Distribution
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Introduction Pathway AnalysisMetabolic Flux
AnalysisExample

• Bioinformatics and Metabolic Engineering
• Structured metabolic models
• Metabolite balancing
• Conserved moieties
• Elementary flux modes
• Estimation of flux distributions
• Observability of metabolic fluxes
• Overdetermined and underdetermined systems
• Metabolic model of Saccharomyces cerevisiae
• Model Analysis

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Metabolic Model of Saccharomyces cerevisiae
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Nutrients
Excreted Products
Biomass
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Macromolecular Composition of Saccharomyces
cerevisiae
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Model Structure
GlucoseAcetateCO2O2EthanolGlycerolHH2OAmm
oniaSulphatePhosphateBiomass
GlycolysisPentose Phosphate PathwayAnabolismSyn
thesis of Macromolecules (Polymerisation)
Cytosol
System boundary
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Introduction Pathway AnalysisMetabolic Flux
AnalysisExample

• Bioinformatics and Metabolic Engineering
• Structured metabolic models
• Metabolite balancing
• Conserved moieties
• Elementary flux modes
• Estimation of flux distributions
• Observability of metabolic fluxes
• Overdetermined and underdetermined systems
• Metabolic model of Saccharomyces cerevisiae
• Model Analysis

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Conservation Relations
nadcytnadhcyt const nadmitnadhmit
const. nadpcytnadphcyt const. accoAcytaccoAmit
coAcytcoAmitsuccoAcytsuccoAmit
const. fadmitfadh2mit const. fthfcytmethfcyt
mythfcytthfcyt const.
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Violated Conservation Relation
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Yields of Amino Acids on Glucose Obtained from
Elementary Flux Modes
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Maximal Theoretical Yields ofAmino Acids on
Glucose
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Maximal Yields ofMacromolecules on Glucose
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Maximal Yield ofBiomass on Glucose
1 composition of macromolecules taken at a growth
rate of m 0.1 h-1 2 same metabolic network but
without compartmentation
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Medium Design Effect of Additives on the Yield
of Biomass on Glucose
D Y (g/g)
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Net Conversion Rates
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Saccharomyces cerevisia CBS 7336 D0.10 h-1
Cytosol
Mitochondrien
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Saccharomyces cerevisia CBS 7336 D0.33 h-1
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Index
Bioinformatics and Metabolic Engineering
Structured metabolic models Metabolite
balancing Conserved moieties Elementary flux
modes Estimation of flux distributions
Observability of metabolic fluxes Overdetermined
and undertetermined systems Metabolic model of
Saccharomyces cerevisiae Model Analysis
Computational Aspects