Computational Analysis of Metabolic Networks
Ralf Steuer
Humboldt-University Berlin, Germany
Institute of Theoretical Biology (ITB)
CzechGlobe
Global Change Research Centre, Brno, CZ
Fakulta informatiky MU
pondělí 14. 5. 2012, 14:00
A living cell is a complex dynamic system
involving many hierarchies of regulation:
outline
A living cell is a complex dynamic system
involving many hierarchies of regulation:
(1) Transcriptional regulation: from DNA to protein
DNA
protein
transcription/translation
outline
A living cell is a complex dynamic system
involving many hierarchies of regulation:
(2) Post­transcriptional regulation: (de­)activation of proteins
DNA
protein
protein activity
signaling networks
transcription/translation
outline
A living cell is a complex dynamic system
involving many hierarchies of regulation:
(3) Cellular metabolism: energy and growth
DNA
protein
protein activity
cell metabolism
signaling networks
building “infrastructure”
transcription/translation
outline
A living cell is a complex dynamic system
involving many hierarchies of regulation:
(4) Cellular physiology: division, motility, etc ...
DNA
protein
protein activity
cell metabolism
physiology and
behavior
signaling networks
building “infrastructure”
transcription/translation
outline
A living cell is a complex dynamic system
involving many hierarchies of regulation:
(4) Cellular physiology: division, motility, etc ...
DNA
protein
protein activity
cell metabolism
physiology and
behavior
signaling networks
building “infrastructure”
transcription/translation
outline
A living cell is a complex dynamic system
involving many hierarchies of regulation:
Aim: Computational Modeling of Cellular Processes
DNA
protein
protein activity
cell metabolism
physiology and
behavior
signaling networks
building “infrastructure”
transcription/translation
outline
Computational modeling as a tool to understand
the functioning of cellular interactions? 
Three main issues:
(1) Why should one care about modeling?
(2) How should a (good) model be constructed?
(3) And to what end?
the rationale of mathematical modeling
The rationale of mathematical modelling
Mathematical Models: A method for representation
1.1.
Mathematical Models: A method for deduction
2.2.
the rationale of mathematical modeling
Mathematical Models: A method of representation
Transcription of properties into a formal representation.
Modeling provides a language for representation.
1.1.
An example: The basic Michaelis­Menten Scheme
The rationale of mathematical modelling
the rationale of mathematical modeling
A slightly more complicated example: 
MFPMFP
MNFP2
MNFP1
XYZ1
XYZ2
XYZ3
ABC1ABC1 ABCa2ABCa2?
R2D2
inhibition
Note that 
models do not
need to
be 'true'.
The rationale of mathematical modelling
Mathematical Models: A method of representation
Transcription of properties into a formal representation.
Modeling provides a language for representation.
1.1.
the rationale of mathematical modeling
Mathematical Models: A method for deduction
Translation into emergent properties at the systems level.
Mathematical models organize parts into a coherent whole.
2.2.
Facts often only mean little in isolation, but need to be interpreted
in terms of a theory or model.
Science is built with facts, as a house is with stones. But a collection of facts
is no more a science than a heap of stones is a house. — Henri Poincare
The rationale of mathematical modelling
the rationale of mathematical modeling
Mathematical Models: A method for deduction
Translation into emergent properties at the systems level.
Mathematical models organize parts into a coherent whole.
2.2.
An example: Can this mechanism oscillate? 
Translation into
emergent properties
MFPMFP
MNFP2
MNFP1
XYZ1
XYZ2
XYZ3
ABC1ABC1 ABCa2ABCa2?
R2D2
inhibition
The rationale of mathematical modelling
the rationale of mathematical modeling
The modeling relation according to Casti:
The rationale of mathematical modelling
the rationale of mathematical modeling
“There is a zoo of mathematical models in the literature. Many of these 
appear  to  have  little  purpose  other  than  calculating  numbers  which 
conform  reasonably  to  experimental  data.  This  is,  in  itself,  not  a 
distinguished  endeavor;  it  is  not  particularly  difficult,  and  it  teaches 
little. ... Modeling is relatively meaningless without explicit definition, 
at the outset, of its purpose”
                      
                                                                J. E. Bailey (1944­2001)
                                                                in Biotechnol. Prog. 14:8­20, 1998
The rationale of mathematical modelling
the rationale of mathematical modeling
Computational models of metabolic networks
models of metabolic networks
Computational models of metabolic networks
“food”
protein
carbohydrates
fat
“useful”
energy
building 
blocks
models of metabolic networks
Computational models of metabolic networks
“food”
protein
carbohydrates
fat
“useful”
energy
building 
blocks
Cellular
constituents
maintenance
models of metabolic networks
Computational models of metabolic networks
Copyright 2004 by Alberts, Bray, 
Johnson, Lewis, Raff, Roberts, 
Walter.Garland Publishing: Taylor 
Francis Group.
models of metabolic networks
The “bow­tie” structure of metabolism:
A bow-tie
models of metabolic networks
The “bow­tie” structure of metabolism:
A Complex Network of Interactions:
• Biochemical reactions
• Metabolic compounds
• Regulatory interactions 
Applications of Relevance:
Biotechnology
Diseases and medical applications
A link from genotype to phenotype
models of metabolic networks
The network of enzyme­catalyzed biochemical reactions:
Enzymes  are  biological  molecules  that  catalyze  (i.e.,  increase  the 
rates  of)  chemical  reactions.  Almost  all  chemical  reactions  in  a 
biological cell need enzymes in order to occur at rates sufficient for 
life.  Since  enzymes  are  selective  for  their  substrates and speed  up 
only  a  few  reactions  from  among  many  possibilities,  the  set  of 
enzymes made in a cell determines which metabolic pathways occur 
in that cell.
Like  all  catalysts,  enzymes  work  (only)  by  lowering  the 
activation energy for a reaction, thus dramatically increasing the 
rate of the reaction. 
from: WIKIPEDIA
models of metabolic networks
Enzyme­catalyzed reactions:
Reaction:    A             B             (exergonic ∆G<0)
models of metabolic networks
Enzyme­catalyzed reactions:
Reaction:    A             B             (exergonic ∆G<0)
Reaction:    C             D             (endergonic ∆G>0)
models of metabolic networks
Enzyme­catalyzed reactions:
Reaction:    A             B             (exergonic ∆G<0)
Reaction:    C             D             (endergonic ∆G>0)
Enzymes can couple processes
Reaction:    C             D                                  (∆G>0)
Reaktion:ATP             ADP + “energy”        (∆G<0)
        C + ATP              ADP + D                     (∆G<0)
models of metabolic networks
Enzyme mechanisms:
models of metabolic networks
Enzyme mechanisms and rate equations:
Translation into mathematical model: rate equations
models of metabolic networks
Michaelis­Menten Kinetics:
Translation into mathematical model: rate equations
models of metabolic networks
Michaelis­Menten Kinetics:
Translation into mathematical model: rate equations
Maximal velocity
models of metabolic networks
Translation into mathematical model: rate equations
Michaelis­Menten constant
Maximal velocity
Michaelis­Menten Kinetics:
models of metabolic networks
Michaelis­Menten Kinetics:
Michaelis­Menten constant
Maximal velocity
models of metabolic networks
More complicated enzyme­kinetic mechanisms ...
models of metabolic networks
More complicated enzyme­kinetic mechanisms ...
models of metabolic networks
Building a model of cellular metabolism ...
(1) Assemble the building blocks: reactions and metabolites
models of metabolic networks
Building a model of cellular metabolism ...
(1) Assemble the building blocks: reactions and metabolites
(2) Assign rate equations to each reaction
models of metabolic networks
Building a model of cellular metabolism ...
(1) Assemble the building blocks: reactions and metabolites
(2) Assign rate equations to each reaction
(3) Assign values to all parameters
models of metabolic networks
Building a model of cellular metabolism ...
(1) Assemble the building blocks: reactions and metabolites
(2) Assign rate equations to each reaction
(3) Assign values to all parameters
(4) Solve the system numerically
models of metabolic networks
Building a model of cellular metabolism ...
(1) Assemble the building blocks: reactions and metabolites
(2) Assign rate equations to each reaction
(3) Assign values to all parameters
(4) Solve the system numerically
(5) DONE!
models of metabolic networks
Building a model of cellular metabolism ...
(1) Assemble the building blocks: reactions and metabolites
(2) Assign rate equations to each reaction
(3) Assign values to all parameters
(4) Solve the system numerically
Unfortunately not so easy ...
(1) The 'Building blocks' are often unknown.
(2) Parameters are difficult to estimate
(3) Numerically complex
models of metabolic networks
A few words on nomenclature:
Reaction:
models of metabolic networks
A few words on nomenclature:
Reaction:
Stoichiometry:
Rate equation:
models of metabolic networks
A few words on nomenclature:
Organize the network into a set of differential equations:
models of metabolic networks
A few words on nomenclature:
Organize the network into a set of differential equations:
Stoichiometric coefficients
models of metabolic networks
A few words on nomenclature:
Organize the network into a set of differential equations:
Rate equations
models of metabolic networks
A few words on nomenclature:
Organize the network into a set of differential equations:
In matrix notation:
models of metabolic networks
Organize the network in a set of differential equations: 
models of metabolic networks
Organize the network in a set of differential equations: 
models of metabolic networks
Organize the network in a set of differential equations: 
models of metabolic networks
The stoichiometry is increasingly known:
models of metabolic networks
The stoichiometry is increasingly known:
models of metabolic networks
The stoichiometry is increasingly known:
models of metabolic networks
Other resources:
models of metabolic networks
Modelling metabolic networks
models of metabolic networks
Modelling metabolic networks ... has many facettes:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
● Static description
● No kinetic parameters
● Topological properties
Quantitative Models
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
● Static description
● No kinetic parameters
● Topological properties
Quantitative Models
the substrate 
graph
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
Quantitative Models
An example: The S. cerevisiae metabolic network
M = 810 vertices (metabolites)
R = 843 reactions
E = 3419 edges 
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
Quantitative Models
Typical network properties:
Pathlength and clustering
Degree distribution
Hierarchies and modularity
Robustness and error tolerance
Advantages:
Applicable to large­scale systems
Requires only topological information
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
Quantitative Models
the degree distribution
Typical network properties:
Pathlength and clustering
Degree distribution
Hierarchies and modularity
Robustness and error tolerance
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
Quantitative Models
the degree distribution
highly connected metabolites:
glycolysis, TCA cycle (pyruvate, etc ...) 
cofactors (ATP, NAD, etc ...)
Typical network properties:
Pathlength and clustering
Degree distribution
Hierarchies and modularity
Robustness and error tolerance
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
Quantitative Models
Typical network properties:
Pathlength and clustering
Degree distribution
Hierarchies and modularity
Robustness and error tolerance
highly connected metabolites:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Topological Analysis
Quantitative Models
Typical network properties:
Pathlength and clustering
Degree distribution
Hierarchies and modularity
Robustness and error tolerance
Limitations:
Only qualitative description
No dynamic properties
No specific features of metabolic networks
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Explicit Kinetic Models
● Dynamic description
● Kinetic parameters
● Differential equations
Quantitative Models
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Explicit Kinetic Models
● Dynamic description
● Kinetic parameters
● Differential equations
Quantitative Models
(1) Assemble the “parts list”: reactions and metabolites
(2) Assign rate equations to each reaction
(3) Assign values to all parameters
(4) Solve the system numerically
(5) DONE!
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Explicit Kinetic Models
● Dynamic description
● Kinetic parameters
● Differential equations
Quantitative Models
A simple Example:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Explicit Kinetic Models
● Dynamic description
● Kinetic parameters
● Differential equations
Quantitative Models
A typical rate equation:
Example from Chassagnole (2002)
A simple Example:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Explicit Kinetic Models
● Dynamic description
● Kinetic parameters
● Differential equations
Quantitative Models
Then solve system computationally:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
A more complex example: Identify best (putative) drug
targets in a model of human metabolism. 
By E. Murabito (Manchester)
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
A more complex example: Identify best (putative) drug
targets in a model of human metabolism. 
By E. Murabito (Manchester)
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
A more complex example: Identify best (putative) drug
targets in a model of human metabolism. 
By E. Murabito (Manchester)
Matrix of control coefficients
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
A more complex example: Identify best (putative) drug
targets in a model of human metabolism. 
By E. Murabito (Manchester)
Advantages
A large number od potential targets can be tested quickly
No ethical problems
Fast results
Cheap
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
A more complex example: Identify best (putative) drug
targets in a model of human metabolism. 
Advantages
A large number od potential targets can be tested quickly
No ethical problems
Fast results
Cheap
But: 
Current models not predictive yet
Too many unknown parameters
Too many unknown interactions
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
See repositories for explicit kinetic models:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
See repositories for explicit kinetic models:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
See repositories for explicit kinetic models:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
See repositories for explicit kinetic models:
Advantages
A large number od potential targets can be tested quickly
No ethical problems
Fast results
Cheap
But: 
Current models not predictive yet
Too many unknown parameters
Too many unknown interactions
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
Most research now on the intermediate level!
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Stoichiometric Analysis (Flux Balance Analysis)
● Static description
● No kinetic parameters
● Quantitative predictions
Exploits constraints in flux distribution
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Stoichiometric Analysis (FBA)
● Static description
● No kinetic parameters
● Quantitative predictions
Exploits constraints in flux distribution
A simple Example:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Stoichiometric Analysis (FBA)
● Static description
● No kinetic parameters
● Quantitative predictions
Exploits constraints in flux distribution
In general only a small fraction of fluxes need to be known:
independent = (number fluxes) – (number metabolites)
A simple Example:
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Stoichiometric Analysis (FBA)
● Static description
● No kinetic parameters
● Quantitative predictions
Exploits constraints in flux distribution
The S. cerevisiae metabolic network
M = 810 vertices (metabolites)
R = 843 reaction rates
Optimize according to
an objective function
Probably the best approach to date ...
models of metabolic networks
Qualitative Models
Size of System
Level of Detail
Quantitative Models
Most research now on the intermediate level!
Extend with features of explicit kinetic models
Include quantitative description of dynamics
Include feedback regulation into the description
Keep the advantages of topological analysis
No knowledge of kinetic parameters
Computationally feasible for large networks
No explicit enzyme­kinetic rate equations
models of metabolic networks
Research at HU­Berlin/ITB: Systems Biology
of Cyanobacterial Biofuel Production
Cyanobacterial Biofuel Production
Research at HU­Berlin/ITB: Systems Biology
of Cyanobacterial Biofuel Production
Fossil fuels (mainly petroleum, coal, natural gas) account
for 80%-90% of the current world energy demand.
Fossil fuels account for 95% of transportation fuels.
Cyanobacterial Biofuel Production
Fossil fuels (mainly petroleum, coal, natural gas) account
for 80%-90% of the current world energy demand.
Fossil fuels account for 95% of transportation fuels.
Alternatives are urgently needed!
Wishlist: Renewable, cheap, abundant, 
biodegradable, etc ...
Cyanobacterial Biofuel Production
Biofuel production from biomass
a) vegetable oil/biodiesel (soybean, palm, rapeseed)
b) bioalcohol from sugar cane and starch (corn, maize)
+ some others (charcoal, biogas, etc ...)
maize (wiki)palm plantation (wiki)
Cyanobacterial Biofuel Production
Biofuel production from biomass
a) vegetable oil/biodiesel (soybean, palm, rapeseed)
b) bioalcohol from sugar cane or starch (corn, maize)
Some Issues:
● High energy input in production, low net yield
● Food vs. fuel issues: direct competition with food crops
● Requires food crops (starch, e.g. sugarcane, maize, etc ...)
● Requires large amounts of arable land
● Requires large amounts fresh water
● Little potential for increase in production
So what to do?
Alternatives are needed!
Cyanobacterial Biofuel Production
Biofuel production from cellulosic biomass
Better and cheaper biomass: non-edible parts of plants:
Woodchips (e.g. poplar), fuel crops, grass, corn stover ...
A DIFFICULT AND EXPENSIVE PROCESS (AS YET)
“biomass recalcitrance”: Plant cell walls naturally resist
decomposition from microbes and enzymes
Cyanobacterial Biofuel Production
Biofuel production from cellulosic biomass
Better and cheaper biomass: non-edible parts of plants:
Woodchips (e.g. poplar), fuel crops, grass, corn stover ...
But considerable potential within the next decade(s)!
Switchgrass (wiki):
Possible Improvements:
Manipulate cellusosic content in plants
Enzymatic pretreatment (funghi)
Better conversion of 5-carbon sugars
Higher ethanol resistance
Cyanobacterial Biofuel Production
Alternative: Cyanobacteria as a source of biofuels
Cyanobacterial Biofuel Production
Photosynthetic cyanobacteria: An alternative to fossil fuels
Alternative: Cyanobacteria as a source of biofuels
They live from nothing but sun and air
High yield and fast growth rates (up to 6h division time)
Straightforwardly cultivable (algae farms)
Little arable land required 
Can be cultivated in seawater
An open pond Spirulina farm:
Cyanobacterial Biofuel Production
FORSYS­Partner: Systems Biology of
Cyanobacterial Biofuel Production
Plot courtesy of CYANO BIOFUELS
Cyano Biofuels GmbH
Dan Kramer
Karl Ziegler
Biochemistry (HU-Berlin)
Wolfgang Lockau
Yvonne Zilliges
Genetics (HU-Berlin)
Thomas Boerner
Jan-Christoph Kehr
Modelling (ITB, HU-Berlin)
Ralf Steuer
Henning Knoop
Microbiology (U. Giessen)
Annegret Wilde
and FRISYS (Freiburg)
Wolfgang Hess
Cyanobacterial Biofuel Production
FORSYS­Partner: Systems Biology of
Cyanobacterial Biofuel Production
Plot courtesy of Algenol
Cyanobacterial Biofuel Production
FORSYS­Partner: Systems Biology of
Cyanobacterial Biofuel Production
Plot courtesy of Algenol
Cyanobacterial Biofuel Production
Plot courtesy of http://www.algenolbiofuels.com/
FORSYS­Partner: Systems Biology of
Cyanobacterial Biofuel Production
Cyanobacterial Biofuel Production
The modelling perspective
Progress in strain improvement will depend on the
development of theoretical methods that facilitate the
elucidation of mechanisms and the identification of
genetic targets for modification (*).
(*) from: Exploiting biological complexity for strain improvement through systems biology,
G. Stephanopoulos, H. Alper & J. Moxley, Nature Biotechnology 22, 1261 – 1267, 2004
FORSYS­Partner: Systems Biology of
Cyanobacterial Biofuel Production
Cyanobacterial Biofuel Production
What can be, if anything, achieved by
mathematical modelling?
1. Network reconstruction and FBA
2. Towards large­scale kinetic models
3. Integrative models: The regulation of metabolism
4. Predicting biotechnological modifications
FORSYS­Partner: Systems Biology of
Cyanobacterial Biofuel Production
Cyanobacterial Biofuel Production
Understanding cellular metabolism
1. Network reconstruction and FBA (Henning Knoop)
333 reactions
267 metabolites
Reconstruction mainly by manual curation
Cyanobacterial Biofuel Production
Understanding cellular metabolism
1. Network reconstruction and FBA (Henning Knoop)
333 reactions
267 metabolites
Reconstruction mainly by manual curation
the end
End of Part II
Hands on examples
Hands-on examples
Hands on examples
1. Numerical Integration in matlab
Hands-on examples
Hands on examples
1. Numerical Integration: Runge-Kutta algorithm
Hands-on examples
Hands on examples
1. Numerical Integration: a simple example
Hands-on examples
then:
Hands on examples
1. Numerical Integration: a simple example
Hands-on examples
then:
Hands on examples
1. Numerical Integration: the Lorenz System
Hands-on examples
Hands on examples
1. Numerical Integration: the Lorenz System
Hands-on examples
Hands on examples
1. Numerical Integration: the Lorenz System
Hands-on examples
Hands on examples
1. Numerical Integration: the Lorenz System
Hands-on examples
Hands on examples
1. Numerical Integration: the Lorenz System
Hands-on examples
Hands on examples: a metabolic pathway
Hands-on examples
Hands on examples: a metabolic pathway
Hands-on examples
Hands on examples: a metabolic pathway
Hands-on examples
Hands on examples: signal transduction
Hands-on examples
Hands on examples: a model of the cell cycle
Hands-on examples
Hands on examples: a model of the cell cycle
Hands-on examples
Hands on examples: a model of the cell cycle
Hands-on examples
Hands on examples: a model of the cell cycle
Hands-on examples
Hands on examples: a model of the cell cycle
Hands-on examples
Gene expression as a stochastic process
Hands-on examples
Transcription of a mRNA
Decay of a mRNA
Translation of a protein
Decay of a protein
Gene expression as a stochastic process
Hands-on examples
Gene expression as a stochastic process
Hands-on examples
Gene expression as a stochastic process
Hands-on examples
Gene expression as a stochastic process
Hands-on examples
Gene expression as a stochastic process
Hands-on examples
The end
Hands-on examples