Hierarchy and Feedback in the Evolution of Transcription Networks

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Hierarchy and Feedback in the Evolution of
Transcription Networks

• Marco Cosentino Lagomarsino
• (Univ. of Milano, INFN, and Institut Curie, Paris
  )

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OUTLINE

• Introduction. Topology of Transcription Networks.
  
• Feedback and Hierarchy on Model and Empirical
  Networks.
• Evolution. A Comparative View.

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• Transcription Netwoks
• and Their Topology

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Central Dogma of Molecular Biology
DNA -gt RNA -gt Protein Function
REGULATION Information Flow
Network Approach
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Transcription Network
Approach 1) global 2) simple
E.coli network
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Transcription Network
Directed graph / Factor graph. Two kinds of nodes
Regulatory (TFs) Targets, or structural genes
(TGs)
Degree sequences
0 1 0 0 ...
A

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Current approaches small networks
(lt 50 genes, e.g. Lambda phage)
Statics Shea-Ackers model (1985).
Thermodynamics of RNAP binding (compute
attachment probability with partition
function) Dynamics Simulations (ODEs,
Gillespie Algorithm).
Combinatorial logic (Buchler et al PNAS
02) (Bintu et. al. Curr Opin Genet Dev 05)
Analysis of stochastic paths in lambda phage
infection (McAdams and Arkin Genetics 98)
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Current approaches large networks
(gt 500 genes, e.g. E.coli, S.cerevisiae)
Structural analysis Example network motifs
subgraphs that are more recurrent than in
random networks
Randomizations Ensemble of random
graphs with the same degree sequences as E.
coli, but shuffled links
Can be done with Montecarlo Importance
Sampling (Fusco et al, Bioinformatics, to appear)
Network motifs in E. coli (Shen-orr et al Nat
Genet 02)
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Feedback vs Hierarchy
Feedback Multistability, periodicity, (Thomas,
Kauffman, Savageau) Example Phage ??(Arkin et
al Genetics 98) Hierarchy Organization of
the transcription program Example SIM motif
(Shen-Orr et al Nat Genet 02)
Switch involves mutual Negative feedback
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2. Feedback and Hierarchy in Model and
Empirical TNs
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Quantitative evaluation of feedback.leaf
removal algorithms
Leaf node with no output Root node with no
input Cannot be involved in feedback Idea.
Remove iteratively tree-like regions of the graph
starting from leaves or roots. Possible
Outcomes -Remove the whole graph (hierarchical
tree) -Stop at a core of variables
(feedback) Iterations hierarchical layers
(Mezard et al. J. Stat Phys 02)
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Quantitative evaluation of feedbackleaf
removal algorithms
Three Variants a) Remove from input or from
output b) Remove from both directions c)
Remove transcription gates (hyperlinks). (Can
break simple loops connected to roots)
Core
Examples
cycles tree
cycles
complex cycles
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Simplest model random graphs
Fixed in-degree p N nodes M regulated nodes
p
Include Input-Output structure
RELEVANT PARAMETER ?? M/N

Example Leaf removal variant (a) (10000 graphs,
N1000)
Phase Transition Typical behavior
(nodes in core)?
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Exchangeable model networks
(F.Bassetti et al, PRE 2007)
Example. Null Ensemble for transcription networks
Throw out-links with a coin with bias
??distributed as
FLEXIBLE FOR ANALYTICAL INVESTIGATIONS
Degree distribution
Network Motifs
Boolean Optimization
(Mandrà et al, in preparation)
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Model random graphs phase diagram
??core fraction of leaves in the core
Example LRa (analytical)
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Connection of Leaf Removal with matrix algebra

• Leaf removal attempts a simple triangulation of
  the adjacency matrix A (set of leaves block of
  I).
• It is connected with the solution of the linear
  system Ax b in the Galois field of Boolean
  variables
• Correspondence between graph and algebraic
  structures (e.g. hypercycle, h hA 0)
• This is a Boolean optimization problem of the
  Satisfiability kind (Cosentino Lagomarsino et al
  q-bio 2006)

I
A
I
0

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Connection with Boolean Networks, random (Xor)SAT

• This SAT-like problem that can be used to count
  the fixed points of the associated Random Boolean
  (or Kauffman) Networks (Cosentino Lagomarsino et
  al, Phys Rev Lett 2005)
• The clustering of the solutions can also be
  controlled.
• The phase, or regime of feedback, is related also
  to the dynamic behavior of the associated
  Kauffman Network.
• (Cosentino Lagomarsino et al, in preparation)

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E. coli networkHierarchy with mostly
self-feedback
(Shen-Orr data set, RegulonDB 5.5)
YES!
NO!
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Comparing Topologies
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Observations
Two Bacteria

• Many ARs (50)
• Preferentially Feedforward Structure
• Few Computational Layers

vs One Yeast

• Fewer ARs (10)
• More Feedback than Bacteria, but less than
  randomized
• More Computational Layers

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WHY ?
Functional Constraints in Bacteria

• Low production time
• Autoregulators can already perform complex
  functions
• Feedback can be implemented beyond transcription
  (faster)

And Yeast?
HP Higher complexity less constraints
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3. Evolution and selective pressure

• Main Drives
• DNA Duplication
• Horizontal Gene Transfer
• Link shuffling by binding site mutations

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Model inheritance of interactions
Duplication Mutation of binding sites leads
to link deletions (with some probability). Selecti
ve pressure
Simple quantitative (null) model. Link
duplication preserves hierarchy.
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Model inheritance of autoregulations
Duplication initially brings feedback Mutat
ion of binding sites can preserve links (with
some probability)
AR duplication can redefine hierarchy and
propagate feedback.
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Simple considerations
Probabilities of link conservation
Probabilities of node conservation
Example conservation of one copy, evolution of
AR fraction
Selective pressures
- For a nonzero fixed point in the fraction of
ARs one needs - To erase crosstalk
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Evolutionary analysis
Comparison of homology classes with network
interactions
Method SUPERFAMILY domain architectures (Babu
et.al. Nat Genet 04)
A
B
C

Protein Domain Architecture
(Structural Definition)
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Evolutionary analysis
Comparison of homology classes with network
interactions
Network interactions
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Results for E.coli
Duplication and autoregulations
Duplication and layers
Horizontal Transfer
(Cosentino Lagomarsino et al. PNAS 2007,
Sellerio et al, in preparation)
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One example (regulonDB)
Sequence level problem of specificity of
duplicate autoregulators
overlap
Clustering of binding sites with score based on
Logos
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Comparative Analysis
Duplication and Degree Distributions
(Sellerio et al, in preparation)
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Comparative Analysis
Duplication and Autoregulations
Found in all three cases. Elimination of
crosstalk specific of E.coli
Hierarchy
Conserved in all three cases. In yeast, most
feedback is confined within homology classes
(Sellerio et al, in preparation)
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Comparative Analysis
Homodimer and Heterodimer TFs
E.coli Most TFs are homodimers NO heterodimers
formed by duplication
Yeast Most TFs form heterodimers They come from
duplication of homodimers
(Sellerio et al, in preparation)
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Conclusions Outlook

• Feedback and hierarchy are important topological
  features in transcription networks
• Connection with constraint satisfaction problems
• Evolution can be formulated as a concrete problem
• Qualitative Difference Between Yeast and Bacteria

• Current work
• Development of evolutionary models for large
  scale genetic networks
• Functional models for expression, dynamics ...
• Nucleoid shaping proteins

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Univ. Milano Bruno Bassetti Patrizia Jona Diana
Fusco Alessandro Sellerio Carlo Maffi Salvatore
Mandrà
Inst. Curie Paris Hervé Isambert Kirill
Evlampiev Univ. Pavia Federico Bassetti

• Thank You!

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Functional Redundancy in E. coli
Neural Network approach to functional annotations

• 1 activation
• 1 repression
• Random thresholds ?

Example flagella network
Redundancy Gap
(with G. Franzese, Univ. Barcelona)