Transcript Stochastic Control Analysis and Module Interface Condition

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)
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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.
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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)
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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?
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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.
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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.
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Module Interface
(Example)
Module Interface
Module 1
Module 2
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Module Interface Process
without a Downstream Module
X
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Module Interface Process
without a Downstream Module
X
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Module Interface Process with a
Downstream Module
X
(Del Vecchio, Ninfa, and Sontag. MSB 2008)
Assumption:
 Fast binding-unbinding
 Quasi-equilibrium.
 Degradation of bound TFs is
much slower than that of fee
TFs.
Retroactivity
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Module Interface Process with a
Downstream Module
X
(Del Vecchio, Ninfa, and Sontag. MSB 2008)
Assumption:
 Fast binding-unbinding
 Quasi-equilibrium.
Dynamics of
slows down.
 Degradation of bound TFs is
much
slower
than
that
of feeMSB 2008)
(Del
Vecchio,
Ninfa,
and
Sontag.
TFs.
Retroactivity
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Module Interface Process with a
Downstream Module
X
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Module Interface Process with a
Downstream Module
X
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Module Interface Process with a
Downstream Module
X
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Module Interface Process with Wiring
X
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Module Interface Process with a
Downstream Module
X
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Dynamic Responses for Different
Number of Downstream Modules
no downstream promoter.
one promoter.
two (identical) promoters.
PT promoters.
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Cut-off Frequency
 Slower response  lower cut-off frequency.
t
t
• Signal Gain:
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Gene-Circuit Fan-out
Desired Operating Frequency Range
Cut-off Frequency
c for
Desired Maximum
Operating Frequency
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Gene-Circuit Fan-out
Desired
Operatin
Operating
Frequency
Frequency
RangeRange
Cut-off Frequency
c for
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Gene-Circuit Fan-out
Desired Operating Frequency Range
Cut-off Frequency
c for
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Gene-Circuit Fan-out
Desired Operating Frequency Range
Cut-off Frequency (c)
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Gene-Circuit Fan-out
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Gene Circuit Fan-out (F)
 Two experiments are required:
1.
Without any promoter  RC estimated.
2.
With Pt promoters  R(C+PtC1) estimated.
 Number of Pt is pre-determined by the origin of replication.
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Gene Circuit Fan-out
in More General Interfaces (I)
 Oligomer transcription factors
 Feedback – f(X)
 Directed degradation by proteases – g(X)
X
X
Ø
Pb
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Gene Circuit Fan-out
in More General Interfaces (I)
 Oligomer transcription factors
 Feedback – f(X)
 Directed degradation by proteases – g(X)
X
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Gene Circuit Fan-out
in More General Interfaces (I)
 The fan-out is given as the same function
 The operational method for measuring the fanout is the same as before.
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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
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Gene Circuit Fan-out
in More General Interfaces (III)
 Oligomer TFs regulating multiple operators.
X
O1
O2
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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
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How to increase fan-out
1. Negative feedback.
X
G1
G2
G3
2. Increase degradation rate
constant.
Gn
3. Make an output gene highly
expressed.
X
Ø
Pb
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How can we measure RCtot?
By using gene expression noise!
 Autocorrelation of gene expression noise.
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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)
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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)
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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.
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Acknowledgement
Herbert Sauro (PI)
Hong Qian
NSF
Theoretical Biology
University of Washington
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Thank you!
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