1. 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

2. Collaborators Prof. Qi Ouyang Prof. Luhua Lai (CTB, PKU) Wenzhe Ma (Center for Theoretical Biology Peking University UCSF)

3. Form follows function! Function follows form!

4.  “Function Follows Form” -- 29,100 hits  “Form Follows Function” -- 363,000 hits (As of 5/19/2007)

5. Form follows function

6. Function follows form

7. Function and form in biology Molecular Microscopic Macroscopic Organismic ? ? Patterning Signal transduction Homeostasis Adaptation Cell polarization Cell division … Bistability Oscillation [A] t A A t A

8. Gene cascade of segmentation

9. 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

10. Enumerate all 2-node networks E W E W 4x2=8 edges 3 possibilities per edge 3 8 =6561 networks A B A B A B …

11. Model of regulation A B Define then  n,k k n/4k A A A B A1A1 A2A2 B

12. An example A B A B A B Q=fraction of parameter space that can perform the function … …

13. Distribution of Q values What are these 45 networks?

14. Skeletons and families Essential Neutral Bad Very bad Three and half topological features: Positive loop on E Positive loop on W Mutual intercellular activation of E and W Mutual repression if extracellular loop

15. Topology follows function …… EWEWEW E W A A E W …… EWEWEW WEWE WEWE WEWE WWW

16. Coarse-graining the biological network

17. 3-node networks E S W E S W 3x6=18 edges 3 18 =387,420,489 networks Only two extracellular signaling 3 15 =14,348,907

18. Distribution of Q values ?

19. Bistability Sharp boundaries Functional modules

20. Modules for 3-node networks

21. 108 possible combinations

22. 44 combinations form the skeletons for all robust networks (Q>0.1) Q=0.63 Q=0.59 Q=0.58 Q=0.50 Q=0.48 Q=0.34 Q=0.66 Q=0.63 Q=0.26 Q=0.29

23. Family size versus Q value Skeletons with larger Q have larger family size Essential Neutral Bad Very bad

24. Q values of the modules EEWWWEWE E module W module B module Q = Q E ×Q W ×Q B ?

25. Two candidates for bionetwork Derek Lessing and Roel Nusse, (1998) Development 125, 1469-1476 Marita Buescher, et al. (2004) Current Biology, 14, 1694-1702 Hsiu-Hsiang Lee and Manfred Frasch, Development 127, 5497-5508 (2000) ? ?

26. ptc mutant EWWE wild type EWWEWWWEW patched mutant continuous Hh signaling 

27. zw3(shaggy) mutant EWWE wild type continuous Wingless signaling EWWEWE zw3 mutant EEE  

28. Mutant tests for the two candidates Wild type EWWE patched mutant EWWEWWWEW zw3 mutant, or ectopic expression of Wg EWWEWEEEE     

29. Why fly picked this one? The best without any direct auto positive loop Q=0.61 Q=0.36

30. 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)