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Connecting Function and Topology (of small biological circuits)

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).

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Connecting Function and Topology (of small biological circuits)

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  1. 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

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

  3. Function follows form! Form follows function!

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

  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. … … … … 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

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

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

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

  14. 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

  15. 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

  16. Coarse-graining the biological network

  17. 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

  18. ? Distribution of Q values

  19. Functional modules Bistability Sharp boundaries Bistability

  20. Modules for 3-node networks

  21. 108 possible combinations

  22. 44 combinations form the skeletons for all robust networks (Q>0.1) Q=0.58 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

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

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

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

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

  28. 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

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

  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)

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