Humboldt-Universität zu Berlin – Theoretische Biophysik

Metabolic networks

Wolfram Liebermeister

ASIM-Workshop Trends in Computational Science and Engineering: Foundations of Modeling and Simulation

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

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

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

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 ?

Metabolic networks

Genome-scale network models of E. coli metabolism

http://www.genome.jp/kegg/pathway/map/map01100.html

Biochemical pathways wall chart

Threonine synthesis pathway

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

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

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

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

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

Multi-omics data show metabolism as a dynamic system

Measured uptake rates and concentrationsin B. subtilis central metabolismafter adding malate to a glucose medium.

Kinetic models

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?

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

A CHomoserine ThreoninePhospho-

homoserine

B

Kinetic models describe the dynamics of biochemical reactions

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

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

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

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

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

Michaelis-Menten kinetics (simple enzymatic law)

Mass-action kinetics (non-enzymatic reactions)

The big problem in kinetic modelling: each enzyme is different !!

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

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

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

1. Wegscheider conditions

Equilibrium constants

Mass-action ratios

Reaction affinities

Fluxes have to satisfy thermodynamic constraints

1. Wegscheider conditions

2. Flux directions and affinities (positive entropy production !)

Equilibrium constants

Mass-action ratios

Reaction affinities

Fluxes have to satisfy thermodynamic constraints

Parameter changehigher substrate supply?

Metabolic change altered concentrations?redirected fluxes?

Metabolic control analysis traces the global effects of local changes

Response coefficients

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

Summary: Modelling formalisms for biochemical systems

stoichiometryconcentration

parameters

reaction rate

A B CKinetic models

enzyme enzyme

Summary: Modelling formalisms for biochemical systems

stoichiometryconcentration

parameters

reaction rate

A B CKinetic models

enzyme enzyme

Constraint-based models(e.g., flux balance analysis)

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)

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)

Technical resources for modelling

Model 1

Model 3

Model 2

Model composition

Playing with biochemical models ?

Model composition

Model merging

Playing with biochemical models ?

Model 1

Model 3

Model 2

“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

Systems Biology Markup Language (SBML)

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

Systems Biology Graphical Notation (SBGN)

http://sbgn.org/

Process description diagram

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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