Comparison of networks in cell biology

1
Comparison of networksin cell biology
4th SFB-Workshop "Gene regulatory networks",
07.12.2006

• Jörn Behre,
• Dept. of Bioinformatics,
• Friedrich-Schiller-University Jena

2
Structure of the talk

• Metabolic pathway analysis
• properties of metabolic networks
• concept of elementary modes
• Regulatory networks
• properties of regulatory networks
• differences to metabolic networks
• Boolean networks
• some basic properties of Boolean networks
• modelling regulatory networks with Boolean
  networks
• Application of elementary modes
• Structural robustness of metabolic networks

3
Metabolic networks

• Properties of metabolic networks
• mass flow
• steady state
• Enzymes have only catalyzing effect, they are not
  necessarily modified.

4
Metabolic pathway analysis

• Decomposition of a network in smallest functional
  entities (metabolic pathways)
• Knowledge about kinetic parameters is not
  necessary!
• Just stoichiometric coefficients and
  reversibilities / irreversibilities of reactions
  must be known.
• Two possible approaches
• Elementary modes
• Petri nets ? minimal T-invariants

5
Elementary modes

• An elementary flux mode (EM) is a minimal set of
  enzymes that can operate at steady state with all
  irreversible reactions used in the appropriate
  direction
• The enzymes are weighted by the relative flux
  they carry.
• The elementary modes are unique up to scaling.
• All flux distributions in the living cell are
  non-negative linear combinations of elementary
  modes
• Elementarity entails that no elementary mode is a
  subset of any other flux mode.
• Elementary modes are usually starting and ending
  at external metabolites.

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Elementary modes

• Examples

1
2
? 4 elementary modes E1, E2, E1, E3, E5,
E4, E3, E2 and E4, E5 ? NO elementary
modes E1, E3, E1, E3, E4
Q1
S1
P1
3
4
5
Q2
S3
P2
1
2
Q1
S1
P1
3
4
5
Q2
S3
P2
7
Elementary modes
non-elementary flux mode
elementary flux modes
S. Schuster et al. J. Biol. Syst. 2 (1994)
165-182 Trends Biotechnol. 17 (1999) 53-60
Nature Biotechnol. 18 (2000) 326-332
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Software for calculating elementary modes

• EMPATH - J. Woods
• METATOOL - Th. Pfeiffer, F. Moldenhauer, A. von
  Kamp
• GEPASI - P. Mendes
• COPASI - P. Mendes, U. Kummer
• JARNAC - H. Sauro
• In-Silico-DiscoveryTM - K. Mauch
• CellNetAnalyzer (in MATLAB) - S. Klamt
• ScrumPy - M. Poolman
• Alternative algorithm in MATLAB C. Wagner
• PySCeS B. Olivier et al.
• On-line computation
• pHpMetatool - H. Höpfner, M. Lange
• http//pgrc-03.ipk-gatersleben.de/tools/phpMetat
  ool/index.php

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Structural Analysis of regulatory networks

• Regulatory networks are field of current
  interest.
• Knowledge about kinetic parameters is even more
  limited than for metabolic systems
• Superpositions of activations and inhibitions can
  occur.

10
Structural Analysis of regulatory networks
Example from KEGG Insulin signalling pathway
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Properties of regulatory networks
Network motif enzyme cascades Calculation of
elementary modes gives trivial result Every
cycle is a separate mode. Flow of information is
not reflected.
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Properties of regulatory networks
Signal
Network motiv enzyme cascades Calculation of
elementary modes gives trivial result Every
cycle is its own mode. Flow of information is
not reflected.
E1
E1
E2
E2
E3
E3
Target
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Properties of regulatory networks

• Dashed lines do not correspond to mass flow.
• Enzymes or proteins (yellow) can also be modified.

14
2nd motiv binding reactions
Properties of regulatory networks
Here mass flow is relevant!
15
Differences between metabolic and regulatory
networks

• In addition to mass flow we have flow of
  information. Just to analyze mass flow is not
  sufficient.
• Regulatory networks do not usually have a steady
  state (in terms of constant concentrations).
  Temporal dynamics like pulses or oscillations are
  important (e.g. calcium oscillations).
• Participating "players" have low concentrations.
  Thus discrete events and stochastic effects may
  become important.
• Enzymes do not only have catalytic functions.
  They can also be modified themselves.

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EMs for regulatory systems ?

• Nevertheless elementary modes (or Extreme
  pathways or minimal T-invariants in Petri-Nets)
  are also calculated for regulatory systems (if
  those systems can be described by pseudo-mass
  flow).
• Xiong et al., Bioinformatics, 2004
• Papin, Palsson, Journal of Theoretical Biology,
  2004
• Heiner, Koch et al., Biosystems, 2004
• Results are of biological interest.

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EMs for regulatory systems ?

• Reasons for using that concept
• If averaged over a longer time period also
  regulatory systems must be in a stationary state,
  because after a signalling process the system
  must be "recharged" for the next event.
• It is useful to search for elementary routes
  through regulatory networks.
• These routes don't need to be mass balanced. But
  one condition must be fulfilled
• Every node of the network must have at least one
  input and one output

Zevedei-Oancea, Schuster A theoretical framework
for detecting signal transfer routes in
signalling networks, Comput. Chem. Eng. 29
(2005) 597-617.
18
Here only the activated components of the enzyme
cascade are displayed
EMs for regulatory systems ?
19
EMs for regulatory systems ?
This system has2 elementary routes.
20
Boolean networks

• based on Boolean algebra
• just 2 states are defined 0 (off) and 1 (on)
• Example genes can have approximately 2 states
• inactive (0)
• active (1)
• In Boolean networks usually discrete time steps
  are considered.
• Logical steady states can be defined.

21
Boolean networks

• Example 1 Rule table

The system has 3 logical steady states, (0,0),
(0,1) and (1,0).
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Boolean networks

• Example 2 Rule table

The system has 2 logical steady states, (0,0) and
(1,1). Starting at (0,1) or (1,0) ? oscillation.
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Boolean networks

• Small example network from CellNetAnalyzer

S. Klamt et al. BMC Bioinformatics (2006)
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Boolean networks

• Signaling paths linking input layer and output
  layer (1)

S. Klamt et al. BMC Bioinformatics (2006)
25
Boolean networks

• Signaling paths linking input layer and output
  layer (2)

S. Klamt et al. BMC Bioinformatics (2006)
26
Boolean networks

• Shortcomings of interaction graphs

• AND connections are not possible!
• ? hypergraphical representation necessary

S. Klamt et al. BMC Bioinformatics (2006)
27
Boolean networks

• The network as logical interaction hypergraph

S. Klamt et al. BMC Bioinformatics (2006)
28
Application of elementary modes

• Structural robustness of metabolic networks
• How can structural robustness be measured?
• Just taking the number of elementary modes in the
  network as a measure of robustness.
• The network fragility coefficient, based on the
  concept of minimal cut sets (MCS (Steffen Klamt,
  2004), calculated with CellNetAnalyzer) can be
  correlated with the robustness of the network.
• Calculating the average percentage of remaining
  elementary modes after a knockout of enzyme
  (Wilhelm et al., 2004).

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Structural robustness of metabolic networks
A)
B)
2
1
P1
2
P1
S
S1
1
Q1
S1
Q1
P2
P2
S2
3
3
4

• Both networks have 2 elementary modes.
• A knockout of enzyme 1 deletes both elementary
  modes in network A but only one in network B.
• ? Network A is less robust than network B.

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A few mathematical details

• normalised sum of all ratios between the number
  of remaining EMs after knockout and the number of
  EMs in the unperturbed network

r Total number of reactions in the
system z Number of elementary flux modes in
unperturbed network z(i) Number of elementary
modes remaining after knockout
Wilhelm, T., Behre, J., Schuster, S. Analysis of
structural robustness of metabolic networks. IEE
Proceedings Systems Biology, 2004, 1, 114-120.
31
Simple example

• Small example network for explaining the
  calculation
• The network contains 4 EMsE1, E2, E4, E3,
  E4, E5, E6 and E5, E7
• The average robustness R1 is calculated to 0.679
  as shown below

32
Application to central metabolisms ofhuman
erythrocyte and E. coli
Wilhelm et al., IEE Proceedings Systems Biology,
2004
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Outlook

• We are currently generalizing the analysis to
  multiple knockouts
• Calculation can also be based on double
  knockouts, triple knockouts
• Application to new metabolic pathways
• Comparison of animo acid synthesis in E. coli and
  human is currently processed.
• Applying our concept for structural robustness to
  regulatory networks is possible.
• Instead of "classical" EMs from metabolic
  pathways also the pathways through regulatory
  networks can be used for calculating the
  structural robustness.
• Application to the insulin signalling pathway is
  planned.

34
Summary

• Metabolic pathway analysis
• structural analysis of networks without knowledge
  of kinetics
• Regulatory networks
• contain also interactions without mass flow
• "Classical" EMs (or T-invariants in Petri-Nets)
  can not always be computed.
• Boolean networks
• Structural modelling of regulatory networks with
  Boolean networks is possible.
• Elementary routes through a network can be
  computed.
• Structural robustness of networks
• Structural robustness of metabolic networks can
  be calculated on the basis of elementary modes.
• This concept can also be applied to regulatory
  networks.

35
Acknowledgements

• Thank you for your attention ...
• and to
• Prof. Dr. Stefan Schuster (FSU, Jena)
• Dr. Thomas Wilhelm (FLI, Jena)
• Dr. Steffen Klamt (MPI, Magdeburg)