Fan-out in Gene Regulatory Networks

1. Fan-out in Gene Regulatory Networks Kyung Hyuk Kim Senior Fellow Department of Bioengineering University of Washington, Seattle 2nd International Workshop on Bio-design Automation (June 15, 2010)

2. Outline • Introduce the concept of fan-out • Measure of modularity • Relationship to retroactivity • Provide a method for estimating the fan-out and retroactivity from gene expression noise.

3. Motivation When a functioning gene circuit drives downstream circuit components, how many of them can be connected without affecting the functioning circuit? Tunable synthetic gene oscillator by Jeff Hasty’s group. (Stricker, et al. Nature 2008)

4. Motivation Module 1 (Oscillator) Module 2 Question: What is the maximum number of the downstream circuits that can be driven without any change in the period or amplitude?

5. DC Fan-out (for Static Responses) Fan-out: Maximum number of inputs that an output of a logic gate (TTL) can drive. The more inputs driven, the larger current needs to be delivered from the output to maintain correct logic voltages. When the current from the output reaches a limit, Max number of the inputs = DC Fan-out  10 for typical TTL.

6. DC Fan-out (for Static Responses) Fan-out: Maximum number of inputs that an output of a logic gate (TTL) can drive. The more inputs driven, the larger current needs to be delivered from the output to maintain correct logic voltages. When the current from the output reaches a limit, Max number of the inputs = DC Fan-out  10 for typical TTL. Aim: To apply this fan-out concept to gene circuits. To provide an operational method for measuring it.

7. Module Interface (Example) Module Interface Module 1 Module 2

8. Module Interface Process without a Downstream Module X

9. Module Interface Process without a Downstream Module X

10. Module Interface Process with a Downstream Module Assumption: Fast binding-unbinding  Quasi-equilibrium. Degradation of bound TFs is much slower than that of fee TFs. X (Del Vecchio, Ninfa, and Sontag. MSB 2008) Retroactivity

11. Module Interface Process with a Downstream Module Assumption: Fast binding-unbinding  Quasi-equilibrium. Degradation of bound TFs is much slower than that of fee TFs. X (Del Vecchio, Ninfa, and Sontag. MSB 2008) Dynamics of slows down. (Del Vecchio, Ninfa, and Sontag. MSB 2008) Retroactivity

12. Module Interface Process with a Downstream Module X

13. Module Interface Process with a Downstream Module X

14. Module Interface Process with a Downstream Module X

15. Module Interface Process with Wiring X

16. Module Interface Process with a Downstream Module X

17. Dynamic Responses for Different Number of Downstream Modules no downstream promoter. one promoter. two (identical) promoters. PT promoters.

18. Cut-off Frequency Slower response  lower cut-off frequency. t t • Signal Gain:

19. Gene-Circuit Fan-out Desired Operating Frequency Range Desired Maximum Operating Frequency Cut-off Frequency cfor

20. Gene-Circuit Fan-out Operatin Frequency Range Desired Operating Frequency Range Cut-off Frequency cfor

21. Gene-Circuit Fan-out Desired Operating Frequency Range Cut-off Frequency cfor

22. Gene-Circuit Fan-out Desired Operating Frequency Range Cut-off Frequency (c)

23. Gene-Circuit Fan-out

24. Gene Circuit Fan-out (F) • Two experiments are required: • Without any promoter  RC estimated. • With Pt promoters  R(C+PtC1) estimated.  Number of Pt is pre-determined by the origin of replication. 24

25. Gene Circuit Fan-out in More General Interfaces (I) Oligomer transcription factors Feedback – f(X) Directed degradation by proteases – g(X) Ø X X Pb

26. Gene Circuit Fan-out in More General Interfaces (I) Oligomer transcription factors Feedback – f(X) Directed degradation by proteases – g(X) X

27. Gene Circuit Fan-outin More General Interfaces (I) The fan-out is given as the same function The operational method for measuring the fan-out is the same as before.

28. Gene Circuit Fan-out in More General Interfaces (II) Two kinds of promoter plasmids with different origins of replication and different promoter affinities. X Ori2 Ori1

29. Gene Circuit Fan-out in More General Interfaces (III) Oligomer TFs regulating multiple operators. O1 O2 X

30. Gene Circuit Fan-out in More General Interfaces (IV) Each different TF binds to its specific operator without affecting the binding affinity of the other. X Z • For each output X Z

31. How to increase fan-out X • Negative feedback. • Increase degradation rate constant. • Make an output gene highly expressed. Ø X G2 G3 Gn G1 Pb

32. How can we measure RCtot? By using gene expression noise!  Autocorrelation of gene expression noise.

33. When an output signal drives multiple inputs, • Longer correlation in time.( Kim and Sauro arXiv:0910.5522v1 2009, Del Vecchio et al. CDC 2009) • Autocorrelation quantifies the correlation in time.(Weinberger, Dar, and Simpson. Nature Genetics 2008,Rosenfeld, Young, Alon, Swain, Elowitz. Science 2005)

34. When an output signal drives multiple inputs, • Longer correlation in time.( Kim and Sauro arXiv:0910.5522v1 2009, Del Vecchio et al. CDC 2009) • Autocorrelation quantifies the correlation in time.(Weinberger, Dar, and Simpson. Nature Genetics 2008,Rosenfeld, Young, Alon, Swain, Elowitz. Science 2005)

35. Conclusion Introduced the concept and quantitative measure of fan-out for genetic circuits. Proposed an efficient method to estimate the fan-out experimentally. In the process of estimating the fan-out, retroactivity can be also estimated. The mechanisms for enhancing the fan-out are proposed.

36. Acknowledgement Herbert Sauro (PI) Hong Qian NSF Theoretical Biology University of Washington

37. Thank you!