Systems biology: Modeling large biological networks

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Systems biology Modeling large biological
networks

Richard Notebaart
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Systems theory
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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 to large systems
- Integrative bioinformatics - (Network)
modeling
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Reconstruction of networks from omics for
systems analysis

• Gene expression networks based on micro-array
  data and clustering of genes with similar
  expression values over different conditions (i.e.
  correlations).
• Protein-protein interaction networks based on
  yeast-two-hybrid approaches.
• Metabolic networks network of interacting
  metabolites through biochemical reactions.

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How to reconstruct metabolic networks?

• Genome annotation allows for reconstruction
• If an annotated gene codes for an enzyme it can
  (in most cases) be associated to a reaction

Genome-scale network
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Reconstructed genome-scale networks
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Data visualization via Gene-Protein-Reaction
relations (formalized knowledge)
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From network to model
The Modeling Ideal - A complete kinetic
description

• FluxRxn1 f(pH, temp, concentration,
  regulators,)
• Can model fluxes and concentrations over time
• 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
For genome-scale networks there is no detailed
kinetic description -gt too many reactions
involved!
B
A
C

• Theory
• Complete knowledge
• Solution is a single point

• Genome-scale
• Incomplete knowledge
• Solution is a space

Flux B
Flux B
Flux A
Flux A
Flux C
Flux C
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Genome-scale modeling

• How to model genome-scale networks?
• We need
• A metabolic reaction network
• Exchange reactions link between environment and
  reaction network (systems boundary)
• Constraints that limit network function
• Mass balancing (conservation) of metabolites in
  the systems
• Exchange fluxes with environment
• Goal prediction of growth and reaction fluxes

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From network to constraint-based model
Mass balancing

• 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

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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

Flux balance on component Xi
V2
V1
Xi
V1 V2 V3 ? V1 - V2 - V3 0
V3

• Normally, ngtm so the system is underdetermined
• No unique solution!

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What is underdetermined?

• Determined System (2 equations, 2 unknowns)
• XY2
• 2X-Y1
• Solution X1, Y1
• Underdetermined System (1 equation, 2 unknowns)
  
  XY2
• Unbounded!
• In metabolism ? more fluxes (unknowns) than
  metabolites (equations)

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Impose constraints
B
A
C
Exchange reactions allow nutrients to be taken up
from the environment with a certain maximum flux
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Interpretation of solution space
B
A
C
Solution space, Convex cone, Flux cone
C
One allowable functional state (flux
distribution) of network given constraints
B
A
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Flux balance analysis (FBA)
C
Constraints set bounds on solution space, but
where in this space does the real solution lie?
B
A
FBA optimize for that flux distribution that
maximizes an objective function (e.g. biomass
flux) subject to S.v0 and ajvjßj Thus, it
is assumed that organisms are evolved for maximal
growth -gt efficiency!
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Prediction of microbial evolution by flux balance
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 for v2, 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 fully C 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 silico flux correlations
Emmerling M. et al. J Bacteriol. 2002 Segre D.
et al. PNAS, 2002
Notebaart RA. et al. (2008), PLoS Comput Biol
In silico and measured flux correlations are in
agreement
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Flux coupling for data analysis

• Does flux coupling relate to transcriptional
  co-regulation of genes?

Intra-operonic
Inter-operonic
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 of genes?

TF similarity number of shared TFs / total
involved TFs
Notebaart RA. et al. (2008), PLoS Comput Biol
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Flux coupling for data analysis
odd ratio (OR) how much more likely is an event
X relative to event Y
Flux coupled genes in the E. coli metabolism are
more likely lost or gained together over evolution
Pal C. and Papp B. et al. (2005), Nature Genetics
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Summary / conclusions

• Systems biology studying living
  cells/tissues/etc by exploring their components
  and their interactions
• Even without detailed knowledge of kinetics,
  genome-scale modeling is still possible
• Genome-scale modeling has shown to be relevant in
  studying evolution and to interpret omics data
• Major challenge is to integrate knowledge of
  kinetics and genome-scale networks