An Intro To Systems Biology: Design Principles of Biological Circuits

1. An Intro To Systems Biology: Design Principles of Biological Circuits Uri Alon Presented by: Sharon Harel

2. Agenda • Introduction • Auto-regulation • Feed-forward loop

3. Life of a cell • Cells live in complex environments and can sense many different signals: • Physical parameters • Biological signaling molecules • Nutrients or harmful chemicals • Internal state of the cell • Cell response is producing appropriate proteins that act on the internal or external environment

4. Transcription factors • Cells use transcription factors to represent environmental states. • Designed to switch rapidly between active & inactive. • Regulate the rate of transcription of genes: • Change the probability per unit time that RNAp binds to the promoter and creates an mRNA molecule. • Can be activators or repressors.

5. Transcription network • Transcription factors are encoded by genes, which are regulated by transcription factors, which are regulated by transcription factors … • Transcription networks describe all the regulatory transcription interactions in a cell

6. Nodes: genes • Directed edges: transcriptional regulation • Sign on edged: activation or repression • Network input: environmental signals

7. Input function - activator • Input function – strength of the effect of a t.f on the transcription rate of target gene. • Hill function: • Logical function:

8. Input function - repressor • Hill function: • Logical function:

9. Multi dimensional input functions • All activators present: • At least one activator present: • Non Boolean:

10. Dynamics and response time • Single edge in a network: • Production of Y is balanced by protein degradation and dilution: • Change in concentration of Y: • Steady state:

12. Detecting network motifs • Looking for meaningful network patterns with statistical significance. • Network Motif – Patterns that occur in the real network significantly more often than in randomized network. • Idea: these patterns have been preserved over evolutionary timescale against mutations that randomly change edges.

13. Erdos-Renyi random networks • Same number of nodes and edges. • Directed edges assigned at random. • N nodes  N2 possible edges. • Probability edge position is occupied:

14. Autoregulation

15. Autoregulation – A network motif • Autoregulation – regulation of a gene by its own product. • Graph: a self edge. • Example E.coli graph has 40 self edges, 34 of them are repressors (negative autoregulation). • Is that significant?

16. Autoregulation – the statistics • What is the probability of having k self edges in an ER network? • One self edge: Pself=1/N • k self edges:

17. Statistics – cont. • In our E. coli network: N=424, E=519 • Difference in STD units:

18. Why negative autoregulation? • Dynamics of X: • At early times: • Steady state:

19. Negative Autoregulation • Response time: • Evolutionary selection on β and K

20. Negative auto vs. simple • Mathematically controlled comparison • Best of both worlds: rapid production and desired steady state

21. Robustness to production fluctuations • Production rate β fluctuates over time. • Twin cells differ in production rate of all proteins in O(1) up to O(10). • Repression threshold K is more fixed. • Simple regulation is affected strongly by β: • Negative autoregulation is not:

22. Feed-forward loop

23. Sub graphs in ER networks • Probability edge position is occupied: P=E/N2 • Occurrences of sub graph G(n,g) in an ER network: • Mean connectivity: λ=E/N

24. X Y X Y Z Z Three-node patterns • There are 13 possible sub-graphs with 3 nodes Feed forward loop Feedback loop

25. Feed-Forward is a network motif • The feed-forward loop (FFL) is a strong motif. • The only motif of the 13 possible 3-node patterns

26. Feed-forward types

27. C1-FFL with AND logic

28. C1-FFL equations • For transcription factor Y: • For gene Z:

29. C1-FFL as a delay element • Consider the response to 2 steps of signal Sx : • ON step – Sx is absent and then appears. • OFF step – Sx is present and then disappears. • Assumption: SY is always present.

30. Delay following ON step ON step Production of Y* accumulation of Y* Y* threshold Production of Z

31. C1-FFL + AND graphs

32. C1-FFL + OR logic - Example • Sign-sensitive delay in the OFF step: X* can activate gene Z by itself, but both X* and Y* have to fall below their KZ levels for the activation to stop. • Allows maintaining expression even if signal momentarily lost.

33. I1-FFL • Two parallel but opposing paths: the direct path activates Z and the other represses Z. • Z shows high expression when X* is bound and low expression when Y* is bound. • Use: pulse generator & fast response time.

34. I1-FFL equations • Accumulation of Y: • For gene Z: X*, Y*<KYZ Z production at βz Y* accumulates until Y*=KYZ

35. I1-FFL equations – cont. Z production at β’z Y* represses Z

36. I1-FFL graphs

37. I1-FFL response time • Half of steady state is reached during the fast stage: • F – repression coefficient. The larger the coefficient (the stronger the repression) the shorter the response time.

38. I1-FFL - example • Galactose system in E. coli • Low expression of Gal genes when Glu present. • When both are absent Gal genes have low but significant expression (“getting ready”). • When Gal appears – full expression of Gal genes

39. Other FFL types • The other 6 types of FFL are rare in transcription networks. • Some of the lack responsiveness to one of the signals. • Example: I4-FFL

40. I4-FFL vs. I1-FFL

41. Questions?