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Systems theory
The behavior of a system depends on:
(Properties of the) components of the system
The interactions between the components
A system represents a set of components together with the relations
connecting them to form a unity
Defining a system divides reality into the system itself and its
environment
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Systems biology
New? NO and YES
Systems theory and theoretical biology are old
Experimental and computational possibilities are
new
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(publications of von Bartalanffy, 1933-1970)
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Omics-revolution shifts paradigm tolarge systems
- Integrative bioinformatics
- (Network) modeling
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Gene expression networks: based on micro-array data andclustering of genes with similar expression values overdifferent conditions (i.e. correlations).
Protein-protein interaction networks: based on yeast-two-hybrid approaches.
Metabolic networks: network of interacting metabolites
through biochemical reactions.
Reconstruction of networks from ~omicsfor systems analysis
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Genome annotation allows for reconstruction:
If an annotated gene codes for an enzyme it can (in mostcases) be associated to a reaction
How to reconstruct metabolic networks?
genome
transcriptome
proteome
metabolome
Genome-scale
network
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Reconstructed genome-scale networks
Species #Reactions #Genes Reference
Escherichia coli 2077 1260 Feist AM. et al. (2007),Mol. Syst. Biol.
Saccharomyces cerevisiae 1175 708 Frster J. et al. (2003),Genome Res.
Bacillus subtilis 1020 844 Oh YK. et al. (2007), J.Biol. Chem.
Lactobacillus plantarum 643 721 Teusink B. et al., (2006),J. Bio. Chem.
Human 3673 1865 Duarte NC. et al., (2007),PNAS
>30
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Data visualization via Gene-Protein-Reactionrelations (formalized knowledge)
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From network to model
The Modeling Ideal - A complete kinetic description
Flux*Rxn1= f(pH, temp, concentration,regulators,)
Can model fluxes and concentrations overtime
Drawbacks Lots of parameters
Measured in vitro(valid in vivo?)
Can be complex, nasty equations
Nearly impossible to get all parameters at genome-scale
*measure of turnover rate of substrates through a reaction (mmol.h-1.gDW-1)
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Theory vs. Genome-scale modeling
Theory
Complete knowledge
Solution is a single point
Genome-scale
Incomplete knowledge
Solution is a space
Flux A
Flux C
Flux B
Flux A
Flux C
Flux B
AB
C
For genome-scale networks there is no detailed kinetic
description -> too many reactions involved!
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Genome-scale modeling
How to model genome-scale networks?
We need: A metabolic reaction network
Exchange reactions: link between environment andreaction network (systems boundary)
Constraints that limit network function:
Mass balancing (conservation) of metabolites inthe systems
Exchange fluxes with environment
Goal:prediction of growth and reaction fluxes
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From network to constraint-based model
A system represents a set of components together with the relations connecting
them to form a whole unity
Defining a system divides reality into the system itself and its environment
Mass balancing
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Constraint-based modeling - Data structure
Stoichiometric matrix S (Mass balancing):
1: metabolite produced in reaction
-1: metabolite consumed by reaction
0: metabolite not involved in reaction
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Principles of Constraint-Based Analysis
Steady-state assumption: for each metabolite in network, write a
balance equation
XiV1 V2
V3
Flux balance on component Xi:
V1 = V2 + V3 V1 - V2 - V3 = 0
Matrix notation: S.v = 0 S = Stoichiometric matrix (m x n)v = Metabolic reaction fluxes (n)
Result is a system of m equations (number of metabolites) and n
unknowns (reaction fluxes)
Normally, n>m so the system is underdetermined
No unique solution!
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Impose constraints
Flux
C
Flux B
Flux
C
Flux B
BoundedSolution space
UnboundedSolution space
Constraints:(i) Stoichiometry (mass
conservation)(ii) Exchange fluxes (capacity)(iii)
AB
C
Exchange reactions allow nutrients to be taken up from the environmentwith a certain maximum flux
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Interpretation of solution space
Solution space, Convex cone, Flux cone
One allowable functional state (flux
distribution) of network given
constraints
AB
C
AB
C
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Flux balance analysis (FBA)
A
B
C Constraints set bounds on solution space,
but where in this space does the real
solution lie?
FBA: optimize for that flux distribution thatmaximizes an objective function (e.g. biomass
flux) subject to S.v=0 and jvjj
Thus, it is assumed that organisms are evolved
for maximal growth -> efficiency!
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Prediction of microbial evolution by fluxbalance analysis (in E. coli)
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Flux coupling / correlations
Genome-scale analysis to determine whether two fluxes (v1 and
v2) are:
Fully coupled: a non-zero flux of v1 implies a non-zero fixed flux for
v2 (and vice versa)
Directionally coupled: a non-zero flux v1 implies a non-zero flux forv2, but not necessarily the reverse
Uncoupled: a non-zero flux v1 does not imply a non-zero flux for v2
(and vice versa)
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Flux coupling / correlations
A and B: directionally
B and C: fullyC and D: uncoupled
Flux coupling: maximize and minimize the flux through one
reaction and constrain the other by a finite value (e.g. 1)
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Measured Vs. In silicoflux correlations
Emmerling M. et al. J Bacteriol. 2002Segre D. et al.PNAS, 2002
In silicoand measured flux correlations are in agreement
Notebaart RA. et al. (2008), PLoS Comput Biol
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Flux coupling for data analysis
Does flux coupling relate to transcriptional co-regulation ofgenes?
Notebaart RA. et al. (2008), PLoS Comput Biol
Intra-operonic
Inter-operonic
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Flux coupling for data analysis
Does flux coupling relate to transcriptional co-regulation ofgenes?
Notebaart RA. et al. (2008), PLoS Comput Biol
TF similarity = number of shared TFs / total involved TFs
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Flux coupling for data analysis
Flux coupled genes in the E. coli metabolism are more likely lost or
gained together over evolution
Coupling type Event #Events OR*(95% c.i.)
Fully coupled Transfer 5964.6 (24.2
168.8)
Fully coupled Loss 1,624 50.0 (41.859.6)
Directionally
coupled Transfer 78
60.3 (24.3
147.2)
Directionally
coupledLoss 2,833 9.6 (8.311.1)
*odd ratio (OR): how much more likely is an event X relative to event Y
Pal C. and Papp B. et al. (2005), Nature Genetics
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Summary / conclusions
Systems biology: studying living cells/tissues/etc byexploring their components and their interactions
Even without detailed knowledge of kinetics, genome-scalemodeling is still possible
Genome-scale modeling has shown to be relevant in studyingevolution and to interpret ~omics data
Major challenge is to integrate knowledge of kinetics andgenome-scale networks