metabolic networks · humboldt-universität zu berlin – theoretische biophysik metabolic networks...
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![Page 1: Metabolic networks · Humboldt-Universität zu Berlin – Theoretische Biophysik Metabolic networks Wolfram Liebermeister ASIM-Workshop Trends in Computational Science and Engineering:](https://reader033.vdocuments.us/reader033/viewer/2022060702/606f532905d29c1dc30fb7cb/html5/thumbnails/1.jpg)
Humboldt-Universität zu Berlin – Theoretische Biophysik
Metabolic networks
Wolfram Liebermeister
ASIM-Workshop Trends in Computational Science and Engineering: Foundations of Modeling and Simulation
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How can a living being emerge just from sugar, water, and a couple of salts?
Glucose 5 g/l Na
2HPO
4 6 g/l
KH2PO
4 3 g/l
NH4Cl 1 g/l
NaCl 0.5 g/l MgSO
4 0.12 g/l
CaCl2 0.01 g/l
Minimal Medium for E. coli
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L'essentiel est invisible pour les yeux.
How can a living being emerge just from sugar, water, and a couple of salts?
Glucose 5 g/l Na
2HPO
4 6 g/l
KH2PO
4 3 g/l
NH4Cl 1 g/l
NaCl 0.5 g/l MgSO
4 0.12 g/l
CaCl2 0.01 g/l
Minimal Medium for E. coli
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Metabolic networks produce materials and energy for the cell
Nutrients Small molecules
BIOMASS
Waste products
Macromolecules
catabolismanabolism
Glucose 5 g/l Na
2HPO
4 6 g/l
KH2PO
4 3 g/l
NH4Cl 1 g/l
NaCl 0.5 g/l MgSO
4 0.12 g/l
CaCl2 0.01 g/l
Minimal Medium for E. coli
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Overview
What are metabolic networks and how do they work ?
How can we use models to understand their dynamics ?
How can we predict fluxes in large networks ?
How do metabolic systems respond to perturbations ?
What standards, resources, and software are available ?
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Metabolic networks
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Genome-scale network models of E. coli metabolism
http://www.genome.jp/kegg/pathway/map/map01100.html
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Biochemical pathways wall chart
Threonine synthesis pathway
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Aspartate
Aspartyl-P
Asp semiald
Homoserine
P-Homoserine
Threonine
Metabolites Reactions
ATPADP
NADPH
NADP+,P
P
ATPADP
NADPH
NADP+
Metabolic networks have several levels of regulation
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Aspartate
Aspartyl-P
Asp semiald
Homoserine
P-Homoserine
Threonine
1.2.1.11
2.7.2.4
1.1.1.3
2.7.1.39
4.2.3.1
Metabolites Reactions
ATP
ADP
NADPH
NADP+,P
P
ATP
ADP
NADPH
NADP+
Enzymes
Metabolic networks have several levels of regulation
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Aspartate
Aspartyl-P
Asp semiald
Homoserine
P-Homoserine
Threonine
1.2.1.11
2.7.2.4
1.1.1.3
2.7.1.39
4.2.3.1
Lysine
Metabolites Reactions Metabolicregulation
ATP
ADP
NADPH
NADP+,P
P
ATP
ADP
NADPH
NADP+
Enzymes
Metabolic networks have several levels of regulation
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Aspartate
Aspartyl-P
Asp semiald
Homoserine
P-Homoserine
Threonine
1.2.1.11
2.7.2.4
1.1.1.3
2.7.1.39
4.2.3.1
thrA
thrB
thrC
asd
Lysine
Metabolites Reactions Metabolicregulation
Transcriptional regulation
ATP
ADP
NADPH
NADP+,P
P
ATP
ADP
NADPH
NADP+
Enzymes
Metabolic networks have several levels of regulation
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Aspartate
Aspartyl-P
Asp semiald
Homoserine
P-Homoserine
Threonine
1.2.1.11
2.7.2.4
1.1.1.3
2.7.1.39
4.2.3.1
thrA
thrB
thrC
asd
Transcriptionfactors
Lysine
Metabolites Reactions Metabolicregulation
Transcriptional regulation
ATP
ADP
NADPH
NADP+,P
P
ATP
ADP
NADPH
NADP+
Enzymes
Metabolic networks have several levels of regulation
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Multi-omics data show metabolism as a dynamic system
Measured uptake rates and concentrationsin B. subtilis central metabolismafter adding malate to a glucose medium.
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Kinetic models
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How do metabolic networks work?
● What compounds can the cell produce?
● On which nutrient media can the cell survive?
● What do the metabolic fluxes look like ?
● How do they respond to varying conditions?
● How is all this regulated?
● What conclusions can we draw from limited data?
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0vNS =⋅=
dt
d
321 vvv =+
Mod
el S
ize
Dyn
am
ics
Topological Analysis Flux Balance Analysis Kinetic modeling
Sv1
v3
v2
( )pS,vNS ⋅=
dt
d
S0 S2S1
S
t
Modelling approaches for different complexity
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A CHomoserine ThreoninePhospho-
homoserine
B
Kinetic models describe the dynamics of biochemical reactions
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A C
Reaction rate (“kinetic equations”)How often does the reaction occur per time ?
Homoserine ThreoninePhospho-homoserine
B
Kinetic models describe the dynamics of biochemical reactions
kinetic constant
concentrationreaction rate
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A C
Reaction rate (“kinetic equations”)How often does the reaction occur per time ?
System equationsHow do the concentrations change over time?
Homoserine ThreoninePhospho-homoserine
B
Kinetic models describe the dynamics of biochemical reactions
kinetic constant
concentrationreaction rate
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stoichiometric coefficient
A C
concentration change
kinetic parameters and enzyme concentrations
concentrations
kinetic law forreaction velocity
Reaction rate (“kinetic equations”)How often does the reaction occur per time ?
System equationsHow do the concentrations change over time?
Homoserine ThreoninePhospho-homoserine
B
Kinetic models describe the dynamics of biochemical reactions
kinetic constant
concentrationreaction rate
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S1
S2
S3
S4
S =
v1
v2
v3
v4
v5
v = N =
S1
S2
S3
S4
1 −1 0 0 0
0 0 1 −1 0
0 0 0 0 1
0 0 −1 1 0
Stoichiometric Matrix
v1 v2 v3 v4 v5S1
S2S4
S3
v1 v2
v3
v4
v5
MetaboliteConcentrations
Reaction rates
System equations – an example
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ODEs
d[S1]/dt = v1 − v2
d[S2]/dt = v3 − v4
d[S3]/dt = v5
d[S4]/dt = − v3 + v4
S1
S2
S3
S4
S =
v1
v2
v3
v4
v5
v = N =
S1
S2
S3
S4
1 −1 0 0 0
0 0 1 −1 0
0 0 0 0 1
0 0 −1 1 0
Stoichiometric Matrix
v1 v2 v3 v4 v5
1 −1 0 0 0
0 0 1 −1 0
0 0 0 0 1
0 0 −1 1 0
X
v1
v2
v3
v4
v5
=
v1 −v2 +0 +0 +0
0 +0 +v3 −v4 +0
0 +0 +0 +0 v5
0 +0 −v3 +v4 +0
N v d[S]/dt X =
S1
S2S4
S3
v1 v2
v3
v4
v5
MetaboliteConcentrations
Reaction rates
System equations – an example
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Michaelis-Menten kinetics (simple enzymatic law)
Mass-action kinetics (non-enzymatic reactions)
The big problem in kinetic modelling: each enzyme is different !!
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Haldane relation
Michaelis-Menten kinetics (simple enzymatic law)
Chemical equilibrium
Mass-action kinetics (non-enzymatic reactions)
The big problem in kinetic modelling: each enzyme is different !!
Thermodynamics helps to reduce unknown parameters
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Constraint-based models predict metabolic fluxes in large networks
Stationary (=steady) stateA state in which all variables remain constant in time
Stationarity condition in kinetic models
Condition on the flux vectorKinetic rate laws do not play a role!
Intracellular metabolites (dynamic)Concentration changes due to chemical reactions
External metabolites (e.g. extracellular or buffered)Treated as fixed parameters
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Constraint-based models predict metabolic fluxes in large networks
Stationary (=steady) stateA state in which all variables remain constant in time
Stationarity condition in kinetic models
Condition on the flux vectorKinetic rate laws do not play a role!
Intracellular metabolites (dynamic)Concentration changes due to chemical reactions
External metabolites (e.g. extracellular or buffered)Treated as fixed parameters
Flux balance analysis predicts flux distributions for large networks
Stationarity + Upper and lower bounds on fluxes→ Convex set in flux space
Linear optimisation (e.g. maximal product yield)→ Linear programming problem
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1. Wegscheider conditions
Equilibrium constants
Mass-action ratios
Reaction affinities
Fluxes have to satisfy thermodynamic constraints
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1. Wegscheider conditions
2. Flux directions and affinities (positive entropy production !)
Equilibrium constants
Mass-action ratios
Reaction affinities
Fluxes have to satisfy thermodynamic constraints
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Parameter changehigher substrate supply?
Metabolic change altered concentrations?redirected fluxes?
Metabolic control analysis traces the global effects of local changes
Response coefficients
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Parameter changehigher substrate supply?
Metabolic change altered concentrations?redirected fluxes?
1. Stationary concentrations s(p)
2. Response coefficients
Metabolic control analysis traces the global effects of local changes
Local cause:e.g., single enzyme level
Systemic effect: flux or concentration
Slope at standard state = “response coefficient”
Response curve
Response coefficients
Solution of
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Summary: Modelling formalisms for biochemical systems
stoichiometryconcentration
parameters
reaction rate
A B CKinetic models
enzyme enzyme
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Summary: Modelling formalisms for biochemical systems
stoichiometryconcentration
parameters
reaction rate
A B CKinetic models
enzyme enzyme
Constraint-based models(e.g., flux balance analysis)
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Summary: Modelling formalisms for biochemical systems
stoichiometryconcentration
parameters
reaction rate
A B CKinetic models
enzyme enzyme
Metabolic control theory
Local cause:e.g., single enzyme level
Systemic effect: flux or concentration
Slope at standard state = “control coefficient”
Response curve
Constraint-based models(e.g., flux balance analysis)
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Summary: Modelling formalisms for biochemical systems
Thermodynamic analysis
stoichiometryconcentration
parameters
reaction rate
A B CKinetic models
enzyme enzyme
Metabolic control theory
Local cause:e.g., single enzyme level
Systemic effect: flux or concentration
Slope at standard state = “control coefficient”
Response curve
Constraint-based models(e.g., flux balance analysis)
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Technical resources for modelling
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Model 1
Model 3
Model 2
Model composition
Playing with biochemical models ?
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Model composition
Model merging
Playing with biochemical models ?
Model 1
Model 3
Model 2
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“Most of the published quantitative models in biology are lost for the community because they are either not made available or they are insufficiently characterized to allow them to be reused.”
Le Novere et al, (2005)
Models should be reusable
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Systems Biology Markup Language (SBML)
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SBML main site http://sbml.org/
<?xml version="1.0" encoding="UTF-8"?><sbml xmlns="http://www.sbml.org/sbml/level2/version3" level="2" version="3"> <model id="model" name="model"> <listOfCompartments> <compartment id="c" name="c" size="1"/> <compartment id="ext" name="ext" size="1"/> </listOfCompartments> <listOfSpecies> <species id="C00022_c" name="Pyruvate" compartment="c"> </species> … … ... <reaction id="reaction_8"> <listOfReactants> <speciesReference species="C00022_c" stoichiometry="0.03"/> .... <speciesReference species="O2_c" stoichiometry="0.01"/> </listOfReactants> <listOfProducts> <speciesReference species="C00008_c" stoichiometry="0.81"/> ... </listOfProducts> <listOfModifiers> <modifierSpeciesReference species="enzyme_reaction_8_c"/> </listOfModifiers> </reaction> </listOfReactions> </model></sbml>
Systems Biology Markup Language (SBML)
One exchange format - about 170 tools that understand each other
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Systems Biology Graphical Notation (SBGN)
http://sbgn.org/
Process description diagram
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Data, modelling software, and models are available on the web
www.sbos.eu
SB.OS – Live DVD with free modelling software
Network reconstructions Databases for biological numbers
Modelling software
Database of curated annotated modelshttp://biomodels.org/
JWS online: database of curated modelshttp://jjj.biochem.sun.ac.za/
Model repositories
http://sbml.org/
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Thank you !