The Structure, Function, and Evolution of Biological Systems

1. The Structure, Function, and Evolution of Biological Systems Instructor: Van Savage Spring 2010 Quarter 4/22/2010

2. Other important ways to construct gene networks: Gene regulation and motifs • Organism must be able to respond to environment and gene expression is one way to do this • One gene can create a protein that either activates or represses another gene X Y activation X Y repression X Y X* promoter region (easily evolvable)

3. Overrepresentation There are N2 possible edges between N genes, so chance of picking specific edge is 1/N2. If there are E edges in network, you have E chances to pick it, so p~E/N2 chance of picking edge. For a given subgraph, Nnchance of picking the n correct nodes and pg chance of picking correct g edges in subgraph. Expected number of subgraphs with n nodes and g edges is where a is symmetry number and λ=E/N is mean connectivity

4. Keep connectivity fixed while increasing network size For n=3 subgraphs Two edge patterns become more common Three edge patterns stay constant proportion Four and higher edge patterns become vanishingly small Only one n=3 subgraph is overrepresented: Feed Forward Loop FBL FFL 42 FFLs exist. We would expect on the order of λ3~1.7+/-1.1 0 FBLs exist. May even be selected against.

5. Mileyko et al.

6. Positive feedback equations with implicit dependence on copy number x are monomers (unactivated), y are dimers (activated) d0 are occupied states and d1 are unoccupied m is mRNA, σ is transcription, γpis degradation k± is binding/unbinding, κ± is coupling/uncoupling for dimers N=d/C is copy number

7. Bistable Feedback

8. Toggle Switch

9. Repressilator

10. Positive feedback equations with implicit dependence on copy number

11. Quasi steady state approximation (QSSA) Not really used. They just look at equilibrium and steady states without worrying about relative time scales.

12. Positive feedback solutions using quasi steady state approximation (QSSA)

13. Equilibrium concentration with copy number Transition in copy number occurs at Vary numbers of whole motifs, not of nodes within motif

14. Condition for transition

15. Plot of transition with copy number

16. Plot of transition with copy number

17. Multiple stable states ratios

18. Transition in oscillations as well

19. Physical values of parameters

20. Stouffer and Bascompte

21. Equations for motifs and food webs mortality to predation Growth rate maintenance consumption Density dependence Type 2 functional response

22. Scaling of terms with mass Choose time scale of 1 Mass-specific metabolic rate Consumption rate relative to metabolic rate Very particular choice of parameter values. Out to 4 decimal. Likely means there results are extremely sensitive and not robust. Connectance is low and size is medium.

23. Persistence of motifs more frequent less frequent Different Results than given in Milo. Omnovory is FFL. Persistence is measured as fraction of species That persist after a specified number of time steps.

24. Contribution of motifs to whole web persistence

25. Contribution of motifs to whole web persistence

26. Conclusions and questions Motif persistence is not tied to web persistence Most common motifs are tied to web persistence Are there larger motifs where persistence in isolation and persistence of whole web do match? If so, those motifs might be the real building blocks. Do webs with different patterns of motifs that imply less persistence have greater short term robustness? How do prey selection and dynamics of motifs and motif representation change in time? What does this mean for our results?

27. Second Homework set is due in two weeks (May 4, 2010).