Analog VLSI Neural Circuits CS599 – computational architectures in biological vision.
Connecting Function and Topology (of small biological circuits)
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Transcript of Connecting Function and Topology (of small biological circuits)
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Connecting Function and Topology(of small biological circuits)
International Workshop and Conference on Network Science, Queens, NY, May 22, 2007
Chao Tang
University of California, San Francisco
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Collaborators
Prof. Qi OuyangProf. Luhua Lai (CTB, PKU)
Wenzhe Ma (Center for Theoretical BiologyPeking UniversityUCSF)
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Form follows function!
Function follows form!
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“Function Follows Form” -- 29,100 hits
“Form Follows Function” -- 363,000 hits
(As of 5/19/2007)
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Form follows function
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Function follows form
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Function and form in biology
Molecular
MicroscopicMacroscopic
Organismic
? ? ? ?
PatterningSignal transductionHomeostasisAdaptationCell polarizationCell division… …
BistabilityOscillation
[A]
t
A A
t
[A]
A
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Gene cascade of segmentation
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What kinds of networks can perform this function?
Why did nature pick the one in fly?
How would i design it?
Need at least two components
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Enumerate all 2-node networks
E
W
E
W
4x2=8 edges
3 possibilities per edge
38=6561 networks
A
B
A
B
A
B
… … … …
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Model of regulation
B
kAAV
dtdB
nn
n
A B
)(1 BkA
AdtdB
nn
n
,VBB Define then
n,k
k
n/4k
A
nn
n
kAA
A
nn
n
kAA
1A B
)),,((1 BnkAHdtdB
iiii
B
A1
A2B
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An example
A
B
A
B
A
B
)(1
)(1
32
2
1
1
Bk+A
Ak+A
kdtdB
Ak+B
kdtdA
nnout
nout
nn
n
B
nn
n
A
Q=fraction of parameter space that can perform the function
… …
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Distribution of Q values
What are these 45 networks?
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Skeletons and families
EssentialNeutralBadVery bad
Three and half topological features:Positive loop on EPositive loop on WMutual intercellular activation of E and WMutual repression if extracellular loop
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Topology follows function
…… E W E W EW
E
W
A
nn
n
kAA
A
A
kAAV
dtdA
nn
n
E
W
…… E W E W EW WE
WE
WE
W WW
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Coarse-graining the biological network
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3-node networks
E
S
W
E
S
W
3x6=18 edges318=387,420,489 networks
Only two extracellular signaling315=14,348,907
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Distribution of Q values
?
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Bistability
Bistability
Sharp boundaries
Functional modules
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Modules for 3-node networks
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108 possible combinations
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44 combinations form the skeletons for all robust networks (Q>0.1)
Q=0.63Q=0.59 Q=0.58
Q=0.50
Q=0.48Q=0.34
Q=0.66Q=0.66 Q=0.63
Q=0.26Q=0.29
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Family size versus Q value
Skeletons with larger Q have larger family size
EssentialNeutralBadVery bad
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Q values of the modules
E E
W W
W E W E
E module
W module
B module
Q = QE×QW×QB ?
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Two candidates for bionetwork
Derek Lessing and Roel Nusse, (1998) Development 125, 1469-1476Marita Buescher, et al. (2004) Current Biology, 14, 1694-1702Hsiu-Hsiang Lee and Manfred Frasch, Development 127, 5497-5508 (2000)
?
?
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ptc mutant
E WW E
wild type
E WW EW W WEW
patched mutant
continuous Hh signaling
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zw3(shaggy) mutant
E WW E
wild type
continuous Wingless signaling
E WW EWE
zw3 mutant
E E E
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Mutant tests for the two candidates
Wild type E WW E
patched mutant E WW EW W WEW
zw3 mutant, or ectopic expression of Wg E WW EWEE E E
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Why fly picked this one?
The best without any direct auto positive loop
Q=0.61 Q=0.36
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Summary• Robust functionality drastically limits network topology.
• Modular structure originates from subfunctions
• Modularity provides combinatorial variability
– Evolvability and pleiotropy
• The one selected by nature may be optimized under biological constraints
– Hh and Wg signaling are utilized in other functions
• More complex functions from simpler modules
– Examples in transcription control and protein domains
– Hierarchical build up of modules
• Simplicity of biological systems
Molecular Systems Biology 2, 70 (2007)