Chao Tang UCSF and PKU

1. Analyzing the function-topology relationship in the drosophila segment polarity network-- Why fly picked this network Chao Tang UCSF and PKU

2. Wenzhe Ma, Luhua Lai, Qi OuyangCenter for Theoretical Biology, Peking University Collaborators:

3. Cell-cell signaling in pattern formation

4. Gene cascade of segmentation

5. Segmentation polarity network From von Dassow, et al., J Exp Zool. 2002 Oct 15;294(3):179-215.

6. Function of the SP network Setting up sharp and stable boundaries between parasegments (“top view”)

7. A robust network George von Dassow, Eli Meir, Edwin M. Munro & Garrett M. Odell, NATURE406, 188 (2000) Nicholas T. Ingolia, PLOS Biology2, 805 (2004) • Randomly sample the parameter space • Hit rate (Q) = fraction of parameter space that can perform the biological function • Hit rate: 0.5% ~ 90%48 • A robust functional module! 25%=50%2

8. What kinds of networks can perform this function?Why did nature pick this network?How would i design it? Need at least two components

9. … … … … A B A B A B Enumerate all 2-node networks 4x2=8 edges 3 possibilities per edge 38=6561 networks E E W W

10. n/4k B A A1 B A A k A2 Model of regulation n,k A B t then Define

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

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

13. Essential Neutral Bad Very bad Skeletons and families 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

14. A E E W W A … … W E W E W E … … W E W E W E W E W W E W W E W Topology follows function

15. Coarse-graining the biological network

16. 3-node networks 3x6=18 edges 318=387,420,489 networks E E Only two extracellular signaling 315=14,348,907 S S W W

17. ? Distribution of Q values

18. Functional modules Bistability Sharp boundaries Bistability

19. Modules for 3-node networks

20. 108 possible combinations

21. 44 combinations form the skeletons for all robust networks (Q>0.1) Q=0.58 Q=0.66 Q=0.63 Q=0.59 Q=0.50 Q=0.66 Q=0.63 Q=0.29 Q=0.34 Q=0.26 Q=0.48

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

23. E E W W W E W E Q values of the modules Q = QE×QW×QB ? E module W module B module

24. 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) ?

25. patched mutant W W E E W W W W E ptc mutant wild type  W E W E continuous Hh signaling

26.   zw3 mutant W E E E E W W E E zw3(shaggy) mutant wild type W E W E continuous Wingless signaling

27. W E W E       W W E E W W W W E zw3 mutant, or ectopic expression of Wg W E E E E W W E E Wild type patched mutant Mutant tests for the two candidates

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

29. a = 1.37 Small Q but many Large Q but a few 4-node nets a = 1.3 P(Q) ~ 1/Qa What is nature’s first pick?  Q×P(Q) ~ 1/Qa-1

30. Space of networks Q>0.001 Q>0.01

31. 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