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

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. 2

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

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

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. 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. Aim: To apply this fan-out concept to gene circuits. To provide an operational method for measuring it. Aim: To apply this fan-out concept to gene circuits. To provide an operational method for measuring it. 6

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

Module Interface Process without a Downstream Module X 8

X 9

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. (Del Vecchio, Ninfa, and Sontag. MSB 2008) Retroactivity 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. (Del Vecchio, Ninfa, and Sontag. MSB 2008) Retroactivity X Dynamics of slows down. (Del Vecchio, Ninfa, and Sontag. MSB 2008) Dynamics of slows down. (Del Vecchio, Ninfa, and Sontag. MSB 2008) 11

Module Interface Process with a Downstream Module X 12

Module Interface Process with a Downstream Module X 13

Module Interface Process with a Downstream Module X 14

Module Interface Process with Wiring X 15

Module Interface Process with a Downstream Module X 16

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

Cut-off Frequency  Slower response  lower cut-off frequency. 18 Signal Gain: tt

Gene-Circuit Fan-out 19 Cut-off Frequency  c for Desired Operating Frequency Range Desired Maximum Operating Frequency

Gene-Circuit Fan-out 20 Operatin Frequency Range Cut-off Frequency  c for Desired Operating Frequency Range

Gene-Circuit Fan-out 21 Cut-off Frequency  c for Desired Operating Frequency Range

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

Gene-Circuit Fan-out 23

Gene Circuit Fan-out (F  ) 24  Two experiments are required: 1.Without any promoter  RC estimated. 2.With P t promoters  R(C+P t C 1 ) estimated.  Number of P t is pre-determined by the origin of replication.

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

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

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

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

Gene Circuit Fan-out in More General Interfaces (III)  Oligomer TFs regulating multiple operators. 29 X O1O1 O2O2

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. 30 X Z  For each output X Z

X Ø PbPb How to increase fan-out 31 1.Negative feedback. 2.Increase degradation rate constant. 3.Make an output gene highly expressed. X X G1 G2G3Gn

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

When an output signal drives multiple inputs, 33  Longer correlation in time. ( Kim and Sauro arXiv: v1 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)

When an output signal drives multiple inputs, 34  Longer correlation in time. ( Kim and Sauro arXiv: v1 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)

Retroactivity (stochastic vs. deterministic) Free TF concentration [k d ] = nM

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) NSF Theoretical Biology University of Washington Hong Qian 37

Thank you! 38