The Structure, Function, and Evolution of Biological Systems

1. The Structure, Function, and Evolution of Biological Systems Instructor: Van Savage Spring 2010 Quarter 4/15/2010

2. Alon Book

3. 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)

4. Draw network for these regulations 2 • Arrows denote direction of regulation and give two types of edges or links for each possible gene pair • Edges are not color coded in this work, although they could be to denote activation or repression. More on that later. • Gene regulation and epistatic networks could be combined but has not been done. Regulation may be a type of epistasis. • New type of self link. Not possible for epistasis. How common are these? 1 3 5 4 6

5. E coli network has been measured 2 • N=424 genes, E=519 total edges, and 40 of those are self edges • Is this a lot or a little? What do we compare with? 1 3 5 4 6 Ep=E/N is expected number of self edges For network below N=6 and E=8 edges, so Ep=4/3 Variance is approximately E/N (Poisson), so standard deviation is 2/Sqrt(3), so for our example The one self edge is expected by random chance For E Coli Ep=1.2+/-1.1, so many more self edges that expected

6. Why are there so many self edges? 2 Selection for self edges Frozen accident Without faithful regulation for certain genes there can be major problems, and genes are most faithful to themselves 4. Some dynamical advantage 1 3 5 4 6

7. Compare with unregulated unregulated Xst=β/α and T1/2=Xst/2β regulated Hill function Can now adjust speed, β, without affecting asymptote/steady state, which is fixed physiologically. Allows faster response times.

8. What about activation instead of repression? Hill function Slows down response time and allows for a type of memory

9. What other types of “motifs” might be possible to look for? Consider all possible network with 3 nodes. Only 13 possibilities. How do we look to see if a give motif is overrepresented in the data?

10. All 3-node subgraphs

11. 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

12. 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.

13. FFLs in E Coli

14. Possible types of FFLs

15. Types of FFLs in Yeast and E Coli

16. What are function of FFLs? Now, can add detail of whether arrows are activating or repressing One is coherent and one is incoherent Coherent allows us to integrate two signals with and AND or an OR gate. AND creates delays in response to make sure signal is really there OR creates delays in fall to make sure signal is really gone Incoherent allows integration of two contradictory signals Other types cause interference or cross signals

17. Problems with this approach All subgraphs are taken out of context. Is that reasonable or appropriate? How useful is it?

18. Next class we will move onto papers using networks motifs for gene regulation First Homework set is due in two weeks (April 20, 2010).