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Robustness, clustering &
evolutionary conservation
Robustness, clustering &
evolutionary conservation
Stefan WuchtyStefan WuchtyCenter of Network ResearchCenter of Network Research
Department of PhysicsDepartment of PhysicsUniversity of Notre DameUniversity of Notre Dame
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Complex systems
Made of many non-identical elements connected by diverse interactions.
NETWORK
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protein-gene
interactions
protein-protein
interactions
PROTEOME
GENOME
Citrate Cycle
METABOLISM
Bio-chemical reactions
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protein-protein
interactions
PROTEOME
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Yeast protein networkNodes: proteins
Links: physical interactions (binding)
P. Uetz, et al. Nature, 2000; Ito et al., PNAS, 2001; …
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Topology of the protein network
)exp()(~)( 00
k
kkkkkP
H. Jeong, S.P. Mason, A.-L. Barabasi & Z.N. Oltvai, Nature, 2001
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RobustnessComplex systems maintain their basic functions even under errors and failures
(cell mutations; Internet router breakdowns)
node failure
fc
0 1Fraction of removed nodes, f
1
S
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Robustness of scale-free networks
1
S
0 1ffc
Attacks
3 : fc=1
(R. Cohen et. al., PRL, 2000)
Failures
Topological error tolerance
R. Albert et.al. Nature, 2000
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Yeast protein network- lethality and topological position -
Highly connected proteins are more essential (lethal)...
H. Jeong et al., Nature, 2001
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Modules in biological systems
Metabolic networks Protein networks
E. Ravasz et al., Science, 2002
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Can we identify the modules?
),min(
),(),(
jiT kk
jiJjiO J(i,j): # of nodes both i and j link to; +1 if there is a direct (i,j) link
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Metabolism: E. Ravasz et al., Science, 2002Protein interactions: Rives and Galitski, PNAS, 2003 Spirin and Mirny, PNAS, 2003
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Open questionsDoes the application of standart clusteringalgorithms reflect real modules well?
Since e.g. one protein can be part of more than one protein complex overlapping clustering algorithms should give better results.
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Motifs Small subnetworks that appear in real world networks
significantly more often than in random graphs.
(Milo et al., Science, 2002; Conant and Wagner, Nature Gen., 2003, Shen-Orr et al., Nature Gen., 2002, Milo et al, Science, 2004)
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From the particular to the universal
A.-L- Barabasi & Z. Oltvai, Science, 2002
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Topology and Evolution
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Topology and Evolution
S. Wuchty, Z. Oltvai & A.-L. Barabasi, Nature Genetics, 2003
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S. Wuchty, Genome Res., 2004
Topology and evolution
- General distribution of orthologs:E = N(o)/N(p)
- degree-dependent distribution of orthologsek = Nk(o)/Nk
Orthologous Excess Retention:ERk = ek/E
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Clustering in protein interaction networks
Goldberg and Roth, PNAS, 2003
high clustering = high quality of interaction
|))(||,)(min(|
|)()(| |)(||)(|
|)(||)(|log
wNvN
wNvNi
vwwN
N
iwN
vNN
i
vNC
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Does that also hold for evolutionary conservation?
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Protein-protein interaction data are highly flawed:
90% false positives, 50% false negatives
Von Mering et al., Nature, 2002
How stable are these results?
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Something else?
Eisen et al., PNAS, 1998
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Open question
?
Wuchty et al., submitted, 2004
?
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Plasmodium falciparum• Eukaryotic organism• Malaria parasite• Genome size 23 MB, 14 chromosomes• 5300 genes (estimated, Hall et al., Nature 2002,
Gardner et al., Nature, 2002) • No protein interaction data available• Co-expression data available (Bozdech et al.,
PloS, 2003, LeRoch et al., Science, 2003)• 868 orthologs with Yeast (InParanoid, Remm et
al. J. Mol. Biol., 2001)
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Plasmodium falciparum
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Plasmodium falciparum
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Inferred protein interaction network
in P. falciparum• 667 nodes, 3,564 weighted interactions
• Clustering
i
iii aeQ )( 2 i
iii aeQ )( 2
- Iteratively pruning edges starting with the least weighted link- Quality of clusters is assessed by their modularity
i
iii aeQ )( 2
until a maximum is reached.
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All edges shown with Cvw > 1.Colorcode red: Cvw > 4, yellow: Cvw > 3, green: Cvw > 2, blue: Cvw > 1
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What does that mean?
Validation of results?
Co-expression patternsBozdech et al. PLoS, 2003
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replication
exo/protesome
DN
A processing
translation
RN
A processing
ribososome
Wuchty, Barabasi, Ferdig and Adams, in preperation
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What‘s next?
• Uncovering evolutionary cores of interactions in other organisms.
• Application of a Maximum Set Cover Algorithm to predict protein interactions (Huang, Kaanan, Wuchty, Izaguirre and Cheng, submitted) to unfold the interactome using the evolutionary cores and experimentally derived interactions.