robustness and modularity in metabolic networksalexander/bled11.pdf · 2011-04-13 · •...
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Robustness and Modularity
in Metabolic Networks
Alexander Ullrich
BioinformaticsUniversity of Leipzig
Bled, February 17
Metabolic Networks
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Metabolic Networks
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Robustness
• Ability to function despite changes
• Genetic Changes: Mutations,...
• Epigenetic Changes: Fluctuations in Molecule concetrations
• Complex Systems are highly robust
• Scale-free Networks are particularly robust
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Modularity
• Module: (structural) subsystem with distinct function
• Key organizing principle of biological networks
• High Clustering Coefficient suggests Modularity
• However, Origin and Preservation of Modularity notunderstood
• Changing Goals or Environments
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Motivation
• Biological systems develop desired properties• Robustness, Flexibility, Modularity, Evolvability, ...• Properties are connected
• Well studied, but their emergence is less well understood• Investigate the evolution of metabolic networks• Analyse network structure and metabolic functions
• Answers beyond analyzing real-world data
→ a multi-scale computational model of early metabolism→ appropriate measures for network properties
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Simulation
• Protocellular entity
• Bag of ribozymes
• Algebraic chemistry model
• Exchange of molecules with the environment
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Simulation - Overview
O O
flux v
B
flux v
C
flux vA
A
C
B
D
E
U U
UA
G
C G
CG
CC
GG
A
GG
UCC
UA
G
AA
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Simulation - Growth
O
O
O
O44.3
O
O
O
O
O
44.3
O
O
O
O
O
66.4
O
O
O
O
O
O66.4
N
N N
O
O
384.
O
O
O
O
O
O
O
70.0
O
O
O
O
O
O
O
O
70.0
N
N
N
N
O
O
25.4
N
N
O
O
O141. N
N
O
O
O
O
141.
O
O
O
O
O
O
66.4
O
O
O
O
O
O
O
66.4
O
O
O
O
O
O
O
66.4
O
O
O
O
O
O
O
O
66.4
N
N N
N
N
O
O
34.4
N
N N
O
O
O
329.
N
N N
O
O
O
O
329.
N
N
N
N
O
O
N
21.0
N
N
N
O
O
O
50.4
N
N
N
O
O
O
O
50.4
N
100
18.6
27.0
6.80
N
C−
−106
−92.
−185
O
46.3
O
O70.0
4.12O
O
−8.4
153.
70.0
70.0384.
52.8
N
N
O
O
O
4.12
O
O
O
O4.12
N
N N
41.7
N N
N
N
N
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
N
N N N
N
N
N N
N
N
N
N
N
N N
O
O
N
N
N
O
O
N
N
N
66.4
66.4
4.12
66.4
66.4
4.12
−2.4−2.4
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O O
O
O
O
O
O
O
O
cyanide, formaldehyde glycol; aldolcondensation, tautomerization
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Simulation - Stochastic Network Generator
Faulon, J-L, (2001) J Chem Inf Comput Sci 41:894-908
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General network analysis
• Connectivity Distribution• small vs big• early vs evolved
• Clustering Coefficient, Centrality, Entropy, ...• simulated vs real world
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after 10 Generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 50 Generations
0.0001
0.001
0.01
0.1
1
freq
uenc
y
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after 100 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 250 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 500 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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Changing Environment - after 100 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 250 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 500 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 750 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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after 1000 generations
1 10 100connectivity
0.0001
0.001
0.01
0.1
1fr
eque
ncy
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Metabolic network analysis
We have sets of edges forming meaningful complex entities↓
pathways
• number of pathways → flexibilty
• change in case of single/multiple knockouts → robustness
• number of acceptable knockouts → robustness
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Metabolic Pathway Analysis
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
R9
→
A
B
C
D
E
F
R1 R2 R3 R4 R5 R6 R7 R8 R90
B
B
B
B
B
@
1 −1 0 0 −1 0 −1 0 00 1 −1 0 0 0 0 0 00 1 0 1 −1 0 0 0 00 0 0 0 0 1 −1 0 00 0 0 0 0 0 1 −1 00 0 0 0 1 0 0 1 −1
1
C
C
C
C
C
A
←R1R2R3R4R5R6R7R8R9
↓
S ∗ vi = 0v1 v2 . . . vn−1 vn
0
B
B
B
B
B
B
B
B
B
B
B
@
2 −1 . . . 0 01 −1 . . . −1 −11 −1 . . . −1 −10 1 . . . 1 01 0 . . . 0 −10 0 . . . 1 20 0 . . . 1 20 0 . . . 1 21 0 . . . 1 1
1
C
C
C
C
C
C
C
C
C
C
C
A
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Metabolic Pathway Analysis
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
R9
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
R9A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
R9
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
R9A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
R9
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Knockout effects
single R1 =
∑r
i=1 z i
r ∗ zdepletion R2 =
∑n
i=1 R i1
n
multiple R3(k) =
∑s(k)i=1 z i
s(k) ∗ zoverall R3(≤ K ) =
K∑
k=1
R3(k)pk
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Minimal Knockout sets
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
Target
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
Target A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
Target A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
Target
{R1} {R5, R6} {R3, R4, R8}
NO knockout sets
A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
Target A
D
B C
F
E
R1
R6
R2
R7
R3 R4
R5
R8
Target
{R2, R3, R4, R5} {R6, R7, R8}
Knockout set size distribution → Robustness (bigger is better)
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after 10 generations
0 5 10 15 20 25 30knockout set size
0
0.05
0.1
0.15
0.2
0.25
freq
uenc
y
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after 20 generations
0 5 10 15 20 25 30knockout set size
0
0.05
0.1
0.15
0.2
0.25
freq
uenc
y
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after 50 generations
0 5 10 15 20 25 30knockout set size
0
0.05
0.1
0.15
0.2
0.25
freq
uenc
y
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after 100 generations
0 5 10 15 20 25 30knockout set size
0
0.05
0.1
0.15
0.2
0.25
freq
uenc
y
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after 250 generations
0 5 10 15 20 25 30knockout set size
0
0.05
0.1
0.15
0.2
0.25
freq
uenc
y
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after 500 generations
0 5 10 15 20 25 30knockout set size
0
0.05
0.1
0.15
0.2
0.25
freq
uenc
y
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Changing Environment - after 10 generations
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
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after 50 generations
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
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after 250 generations
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
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after 500 generations
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
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after 1000 generations
0 5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
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Chemical Organizations
Self-maintaining and closed sets of molecules and reactions↓
chemical organizations
• Hierarchies of organizations
• Shape of Hierarchies → robustness
• Size distribution of organizations → robustness, modularity
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Chemical Organizations
0
1 2 4
3 6 7 5
8 9 10
11
0
1 2 4
3 5 6 11
7 13 8 10
9 12
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Level Size Distribution - after 500 generations
0 2 4 6 80
0.2
0.4
0.6
0.8
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Chemical Organizations
0
1 2 3 19
4 5 18 6 17 16
7 14 15 12 13
9 11 10
8
0
1 2 19
4 18 17 16 12
15 13 9 14 10 7
11 8 6 5
3
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Changing Environment - after 500 generations
0 1 2 3 4 5 6 7organizations per level
0
0.1
0.2
0.3
0.4fr
eque
ncy
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Organization Size Distribution - after 500 generations
0 2 4 6 80
0.2
0.4
0.6
0.8
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Changing Environment - after 1000 generations
0 1 2 3 4 5 6 7level
0
0.1
0.2
0.3
0.4re
lativ
e or
gani
zatio
n si
ze
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Work in Progress
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FBA
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Flux barrier analysis
• linear optimization: EMs modeled as system of linearequations
• constraints: limits on reactions, exclusion of combinations ofEMs
• barrier tree
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Reaction barrier analysis
• linear optimization: stoichiometrix matrix
• constraints: limits on reactions, exclusion of combinations ofreactions
• barrier tree
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Flux similarity
• Compute pairwise similarity of elementary modes
• similarity between metabolites (in+out / all) throughtopological indices
• similarity between enzymes/reactions by comparing transitionstate structure
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Conclusion
• Summary• Structural and Functional measures for Robustness and
Modularity• Follow the Law (Connectivity Distribution)• Size Matters (Knockout set Size)• Shape too (Chemical organization Hierarchy)
• Outlook• Investigate single networks (flux barriers, flux similarity)• Different scenarios (Horizontal Gene Transfer)• Structural modularity (Clustering Coefficient)
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Acknowledgements
Christoph Flamm
Peter Stadler
Konstantin Klemm
Martin Mann
Markus Rohrschneider
Peter Dittrich
Dennis Goerlich
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