connecting function and topology (of small biological circuits)
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Connecting Function and Topology (of small biological circuits). Chao Tang University of California, San Francisco. International Workshop and Conference on Network Science, Queens, NY, May 22, 2007. Collaborators. Wenzhe Ma (Center for Theoretical Biology Peking University UCSF). - PowerPoint PPT PresentationTRANSCRIPT
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
Collaborators
Prof. Qi OuyangProf. Luhua Lai (CTB, PKU)
Wenzhe Ma (Center for Theoretical BiologyPeking UniversityUCSF)
Form follows function!
Function follows form!
“Function Follows Form” -- 29,100 hits
“Form Follows Function” -- 363,000 hits
(As of 5/19/2007)
Form follows function
Function follows form
Function and form in biology
Molecular
MicroscopicMacroscopic
Organismic
? ? ? ?
PatterningSignal transductionHomeostasisAdaptationCell polarizationCell division… …
BistabilityOscillation
[A]
t
A A
t
[A]
A
Gene cascade of segmentation
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
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
… … … …
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
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
… …
Distribution of Q values
What are these 45 networks?
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
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
Coarse-graining the biological network
3-node networks
E
S
W
E
S
W
3x6=18 edges318=387,420,489 networks
Only two extracellular signaling315=14,348,907
Distribution of Q values
?
Bistability
Bistability
Sharp boundaries
Functional modules
Modules for 3-node networks
108 possible combinations
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
Family size versus Q value
Skeletons with larger Q have larger family size
EssentialNeutralBadVery bad
Q values of the modules
E E
W W
W E W E
E module
W module
B module
Q = QE×QW×QB ?
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)
?
?
ptc mutant
E WW E
wild type
E WW EW W WEW
patched mutant
continuous Hh signaling
zw3(shaggy) mutant
E WW E
wild type
continuous Wingless signaling
E WW EWE
zw3 mutant
E E E
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
Why fly picked this one?
The best without any direct auto positive loop
Q=0.61 Q=0.36
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)