Comparison of networks in cell biology Jörn Behre, Dept. of Bioinformatics,...

Comparison of networksComparison of networksin cell biologyin cell biology

Jörn Behre,Jörn Behre,

Dept. of Bioinformatics,Dept. of Bioinformatics,

Friedrich-Schiller-University JenaFriedrich-Schiller-University Jena

4th SFB-Workshop "Gene regulatory 4th SFB-Workshop "Gene regulatory networks", 07.12.2006networks", 07.12.2006

22

Structure of the talkStructure of the talk

Metabolic pathway analysisMetabolic pathway analysis properties of metabolic networksproperties of metabolic networks concept of elementary modesconcept of elementary modes

Regulatory networksRegulatory networks properties of regulatory networksproperties of regulatory networks differences to metabolic networksdifferences to metabolic networks

Boolean networksBoolean networks some basic properties of Boolean networkssome basic properties of Boolean networks modelling regulatory networks with Boolean networksmodelling regulatory networks with Boolean networks

Application of elementary modesApplication of elementary modes Structural robustness of metabolic networksStructural robustness of metabolic networks

33

Metabolic networksMetabolic networks

Properties of Properties of metabolic networks:metabolic networks:

mass flowmass flow

steady statesteady state

Enzymes have only Enzymes have only catalyzing effect, they catalyzing effect, they are not necessarily are not necessarily modified.modified.

G6P

F6P

FDP

GAPDHAP

D13PG

NAD

NADH

Pi

Pi

PFK

PGI

FBPase

ALD

TPI

GAPDH

44

Metabolic pathway analysisMetabolic pathway analysis

Decomposition of a network in smallest Decomposition of a network in smallest functional entities (metabolic pathways)functional entities (metabolic pathways)

Knowledge about kinetic parameters is not Knowledge about kinetic parameters is not necessary!necessary!

Just stoichiometric coefficients and reversibilities Just stoichiometric coefficients and reversibilities / irreversibilities of reactions must be known./ irreversibilities of reactions must be known.

Two possible approaches:Two possible approaches: Elementary modesElementary modes Petri nets Petri nets →→ minimal T-invariants minimal T-invariants

55

Elementary modesElementary modes

An An elementary flux modeelementary flux mode (EM) is a (EM) is a minimal set of minimal set of enzymesenzymes that can operate at that can operate at steady statesteady state with with all all irreversible reactions used in the appropriate directionirreversible reactions used in the appropriate direction

The The enzymesenzymes are are weightedweighted by the relative flux they by the relative flux they carry.carry.

The elementary modes are The elementary modes are unique unique up to scaling.up to scaling.

All flux distributions in the living cell are All flux distributions in the living cell are non-negative non-negative linear combinationslinear combinations of elementary modes of elementary modes

Elementarity entails that Elementarity entails that no elementary mode is a subset no elementary mode is a subset of any other flux modeof any other flux mode..

Elementary modes are usually starting and ending at Elementary modes are usually starting and ending at external metabolitesexternal metabolites..

66


Examples:Examples:

Q1 S1 P11

3

Q24

S3 P25

2 4 elementary modes:4 elementary modes:

{E{E11, E, E22}, {E}, {E11, E, E33, E, E55}, },

{E{E44, E, E33, E, E22} and {E} and {E44, E, E55}}

NO elementary modes:NO elementary modes:

{E{E11, E, E33}, },

{E{E11, E, E33, E, E44}}

Q1 S1 P11

3

Q24

S3 P25

2

77


S. Schuster et al.: J. Biol. Syst. 2 (1994) 165-182;Trends Biotechnol. 17 (1999) 53-60; Nature Biotechnol. 18 (2000) 326-332

non-elementary flux mode

elementary flux modes

88

Software for calculating elementary modesSoftware for calculating elementary modes

EMPATH - EMPATH - J. WoodsJ. Woods

METATOOL - METATOOL - Th. Pfeiffer, F. Moldenhauer, A. von KampTh. Pfeiffer, F. Moldenhauer, A. von Kamp

GEPASI - GEPASI - P. MendesP. Mendes

COPASI - COPASI - P. Mendes, U. KummerP. Mendes, U. Kummer

JARNAC - JARNAC - H. SauroH. Sauro

In-Silico-DiscoveryIn-Silico-DiscoveryTMTM - - K. MauchK. Mauch

CellNetAnalyzer (in MATLAB) - CellNetAnalyzer (in MATLAB) - S. KlamtS. Klamt

ScrumPy - ScrumPy - M. PoolmanM. Poolman

Alternative algorithm in MATLAB – Alternative algorithm in MATLAB – C. WagnerC. Wagner

PySCeS – PySCeS – B. Olivier et al.B. Olivier et al.

On-line computation:On-line computation:

pHpMetatool - pHpMetatool - H. Höpfner, M. LangeH. Höpfner, M. Lange

http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/index.phpindex.php

99

Structural Analysis of regulatory networksStructural Analysis of regulatory networks

Regulatory networks are field of current interest.Regulatory networks are field of current interest.

Knowledge about kinetic parameters is even Knowledge about kinetic parameters is even more limited than for metabolic systemsmore limited than for metabolic systems

Superpositions of activations and inhibitions can Superpositions of activations and inhibitions can occur.occur.

1010

Structural Analysis of regulatory networksStructural Analysis of regulatory networks

Example from KEGG: Insulin signalling pathwayExample from KEGG: Insulin signalling pathway

1111

E1 E1*

E2 E2*

E3 E3*

Target

Signal

Network motif: enzyme cascades

Calculation of elementary modesgives trivial result:

Every cycle is a separate mode.

Flow of information is not reflected.

Properties of regulatory networksProperties of regulatory networks

1212

E1 E1*

E2 E2*

E3 E3*

Target

Signal

Network motiv: enzyme cascades

Calculation of elementary modesgives trivial result:

Every cycle is its own mode.

Flow of information is not reflected.


1313


Dashed lines do not Dashed lines do not correspond to mass correspond to mass flow.flow.

Enzymes or proteins Enzymes or proteins ((yellowyellow) can also be ) can also be modified.modified.

E1

E2 E2-P

ATP ATP

E3 E3-P

ATP ATPPi

Pi

1414

22ndnd motiv: binding reactions: motiv: binding reactions:

Protein 1 Protein 2

Protein complex 1.2 Protein 3

Protein complex 1.2.3

Here mass flow is relevant!


1515

In addition to mass flow we have In addition to mass flow we have flow of informationflow of information. Just to analyze . Just to analyze mass flow is not sufficient.mass flow is not sufficient.

Regulatory networks do Regulatory networks do not not usually usually have a steady statehave a steady state (in terms of (in terms of constant concentrations). Temporal dynamics like pulses or constant concentrations). Temporal dynamics like pulses or oscillations are important (e.g. calcium oscillations).oscillations are important (e.g. calcium oscillations).

Participating "players" have Participating "players" have low concentrationslow concentrations. Thus discrete . Thus discrete events and stochastic effects may become important.events and stochastic effects may become important.

Enzymes do not only have catalytic functions. Enzymes do not only have catalytic functions. They can also be They can also be modifiedmodified themselves. themselves.

Differences between metabolic and regulatory Differences between metabolic and regulatory networksnetworks

1616

Nevertheless elementary modes (or Nevertheless elementary modes (or Extreme Extreme pathwayspathways or minimal T-invariants in Petri-Nets) are or minimal T-invariants in Petri-Nets) are also calculated for regulatory systems (if those also calculated for regulatory systems (if those systems can be described by „pseudo-mass flow“).systems can be described by „pseudo-mass flow“).

Xiong et al., Bioinformatics, 2004Xiong et al., Bioinformatics, 2004 Papin, Palsson, Journal of Theoretical Biology, 2004Papin, Palsson, Journal of Theoretical Biology, 2004 Heiner, Koch et al., Biosystems, 2004Heiner, Koch et al., Biosystems, 2004

Results are of biological interest.Results are of biological interest.

EMs for regulatory systems ?EMs for regulatory systems ?

1717

Reasons for using that concept:Reasons for using that concept:

If If averaged over a longer timeaveraged over a longer time period also period also regulatoryregulatory systems must systems must be in a be in a stationary statestationary state, because after a signalling process the , because after a signalling process the system must be "recharged" for the next event.system must be "recharged" for the next event.

It is useful to search for It is useful to search for elementary routes through regulatory elementary routes through regulatory networksnetworks..

These routes These routes don't need to be mass balanceddon't need to be mass balanced. But one condition . But one condition must be fulfilled:must be fulfilled:

Every node of the network must have at least Every node of the network must have at least one inputone input and and one one outputoutput

Zevedei-Oancea, Schuster: A theoretical framework forZevedei-Oancea, Schuster: A theoretical framework fordetecting signal transfer routes in signalling networks, detecting signal transfer routes in signalling networks, Comput. Comput. Chem. EngChem. Eng. 29 (2005) 597-617. 29 (2005) 597-617..


1818

Here only the activated Here only the activated components of the enzyme components of the enzyme cascade are displayed:cascade are displayed:

Signal

E1*

E2*

E4*

Target 2Target 1

E3*


1919

Signal

E1*

E2*

E4*

Target 2Target 1

E3*


This system hasThis system has2 elementary routes2 elementary routes..

2020

Boolean networksBoolean networks

based on based on Boolean algebraBoolean algebra

just 2 states are defined: just 2 states are defined: 0 (off)0 (off) and and 1 (on)1 (on)

Example: genes can have approximately 2 states:Example: genes can have approximately 2 states:inactiveinactive (0)(0)

activeactive (1)(1)

In Boolean networks usually In Boolean networks usually discrete time stepsdiscrete time steps are are considered.considered.

Logical steady statesLogical steady states can be defined. can be defined.

2121


Example 1:Example 1: Rule table: Rule table:

tt t+1t+1

Gene 1Gene 1 Gene 2Gene 2 Gene 1Gene 1 Gene 2Gene 2

00 00 00 00

00 11 00 11

11 00 11 00

11 11 00 00

0,0 0,1

1,0 1,1

The system has The system has 3 logical steady states3 logical steady states,,

(0,0), (0,1) and (1,0).(0,0), (0,1) and (1,0).

2222


Example 2:Example 2: Rule table: Rule table:

tt t+1t+1

Gene 1Gene 1 Gene 2Gene 2 Gene 1Gene 1 Gene 2Gene 2

00 00 00 00

00 11 11 00

11 00 00 11

11 11 11 11

The system has The system has 2 logical steady states2 logical steady states, (0,0) and (1,1)., (0,0) and (1,1).

Starting at (0,1) or (1,0) Starting at (0,1) or (1,0) →→ oscillationoscillation..

0,0 0,1

1,0 1,1

2323


S. Klamt et al.: BMC Bioinformatics (2006)

Small example network from CellNetAnalyzer:Small example network from CellNetAnalyzer:

2424


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


2525


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


2626



Shortcomings of interaction graphs:Shortcomings of interaction graphs:

AND connectionsAND connections are not possible! are not possible!

→ → hypergraphical representationhypergraphical representation necessary necessary

2727



The network as The network as logical interaction hypergraphlogical interaction hypergraph::

2828

Application of elementary modesApplication of elementary modes

Structural robustness of metabolic networksStructural robustness of metabolic networks

How can structural robustness be measured?How can structural robustness be measured?

Just taking the Just taking the number of elementary modesnumber of elementary modes in the in the network as a measure of robustness.network as a measure of robustness.

The The network fragility coefficientnetwork fragility coefficient, based on the concept , based on the concept of of mminimal inimal ccut ut ssets (MCS (Steffen Klamt, 2004), ets (MCS (Steffen Klamt, 2004), calculated with CellNetAnalyzer) can be calculated with CellNetAnalyzer) can be correlated correlated with the robustness of the networkwith the robustness of the network..

Calculating the Calculating the average percentage of remaining average percentage of remaining elementary modes after a knockout of enzyme elementary modes after a knockout of enzyme (Wilhelm et al., 2004)(Wilhelm et al., 2004)..

2929

Structural robustness of metabolic networksStructural robustness of metabolic networks

Both networks have 2 elementary modes.Both networks have 2 elementary modes.

A knockout of enzyme 1 deletes both elementary A knockout of enzyme 1 deletes both elementary modes in network A but only one in network B.modes in network A but only one in network B.

Network A is less robust than network B.Network A is less robust than network B.

A)

Q1 S1P11 2

P23

B)

Q1P23 S2 4

1 2S P1S1

3030

A few mathematical detailsA few mathematical details

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

zr

zR

r

i

i

1

1

Wilhelm, T., Behre, J., Schuster, S.Wilhelm, T., Behre, J., Schuster, S.Analysis of structural robustness of metabolic networks.Analysis of structural robustness of metabolic networks.IEE Proceedings Systems BiologyIEE Proceedings Systems Biology, 2004, 1, 114-120., 2004, 1, 114-120.

3131

Simple exampleSimple example

Small example network for explaining the Small example network for explaining the calculation:calculation:

The network contains 4 EMs:The network contains 4 EMs:{E{E11, E, E22, E, E44}, {E}, {E33, E, E44}, {E}, {E55, E, E66} and {E} and {E55, E, E77}}

The average robustness The average robustness RR11 is calculated to 0.679 as is calculated to 0.679 as

shown below:shown below: 679,0

47

35221

R

S1Q1Q2 S3

P1P2

1 23 4

5 6

P37

S2

3232

Metabolic networkMetabolic network Number ofNumber of

elementary flux modeselementary flux modes

RR11

Human erythrocyteHuman erythrocyte

ATP, hypoxanthine, NADPH, ATP, hypoxanthine, NADPH, 2,3DPG2,3DPG

667667 0.3830.383

E. coliE. coli

Ala, Arg, Asn, HisAla, Arg, Asn, His 667667 0.5080.508

Arg, Asn, His, IleArg, Asn, His, Ile 656656 0.5210.521

Arg, Asn, Ile, LeuArg, Asn, Ile, Leu 567567 0.5480.548

Arg, Asn, Leu, ProArg, Asn, Leu, Pro 540540 0.5360.536

His, Ile, Leu, LysHis, Ile, Leu, Lys 802802 0.5110.511

Ile, Leu, Pro, ValIle, Leu, Pro, Val 597597 0.5490.549

Application to central metabolisms ofApplication to central metabolisms ofhuman erythrocyte and human erythrocyte and E. coliE. coli

Wilhelm et al., IEE Proceedings Systems Biology, 2004

3333

OutlookOutlook

We are currently generalizing the analysis to multiple We are currently generalizing the analysis to multiple knockoutsknockouts

Calculation can also be based on double knockouts, triple Calculation can also be based on double knockouts, triple knockouts …knockouts …

Application to new metabolic pathwaysApplication to new metabolic pathwaysComparison of animo acid synthesis in E. coli and human is Comparison of animo acid synthesis in E. coli and human is currently processed.currently processed.

Applying our concept for structural robustness to Applying our concept for structural robustness to regulatory networks is possible.regulatory networks is possible.

Instead of "classical" EMs from metabolic pathways also the Instead of "classical" EMs from metabolic pathways also the pathways through regulatory networks can be used for pathways through regulatory networks can be used for calculating the structural robustness.calculating the structural robustness.

Application to the insulin signalling pathway is planned.Application to the insulin signalling pathway is planned.

3434

SummarySummary

Metabolic pathway analysisMetabolic pathway analysis structural analysis of networks without knowledge of kineticsstructural analysis of networks without knowledge of kinetics

Regulatory networksRegulatory networks contain also interactions without mass flowcontain also interactions without mass flow "Classical" EMs (or T-invariants in Petri-Nets) can not always be "Classical" EMs (or T-invariants in Petri-Nets) can not always be

computed.computed.

Boolean networksBoolean networks Structural modelling of regulatory networks with Boolean Structural modelling of regulatory networks with Boolean

networks is possible.networks is possible. Elementary routes through a network can be computed.Elementary routes through a network can be computed.

Structural robustness of networksStructural robustness of networks Structural robustness of metabolic networks can be calculated Structural robustness of metabolic networks can be calculated

on the basis of elementary modes.on the basis of elementary modes. This concept can also be applied to regulatory networks.This concept can also be applied to regulatory networks.

3535

AcknowledgementsAcknowledgements

Thank you for your attention ...Thank you for your attention ...

and toand to

Prof. Dr. Stefan Schuster (FSU, Jena)Prof. Dr. Stefan Schuster (FSU, Jena)

Dr. Thomas Wilhelm (FLI, Jena)Dr. Thomas Wilhelm (FLI, Jena)

Dr. Steffen Klamt (MPI, Magdeburg)Dr. Steffen Klamt (MPI, Magdeburg)

Comparison of networks in cell biology Jörn Behre, Dept. of Bioinformatics,...

Documents

Transcript of Comparison of networks in cell biology Jörn Behre, Dept. of Bioinformatics,...