Download Genetic Toggle Switch without Cooperative Binding

Stochastic Simulations of Genetic
Regulatory Networks:
The Genetic Toggle Switch
Adiel Loinger
Ofer Biham
Nathalie Q. Balaban
Azi Lipshtat
Yishai Shimoni
Baruch Barzel
Guy Hetzroni
Dan Mendels
Introduction
E. coli transcriptional
regulation network
Data taken from
RegulonDB
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Introduction
Transcriptional Repression:
promoter
gene
When the promoter is vacant
the gene is expressed
(mRNAs and proteins are
being synthesized)
promoter
gene
When the promoter is occupied
by a repressor, transcription is
suppressed (mRNAs and
proteins are not synthesized)
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Introduction
Some important parameters:
• The Hill-coefficient h represents the number of repressors
required to bind simultaneously in order to perform the regulation
h=2
A
A
h=1
A
• The repression strength is represented by a parameter k (the
ratio between binding and unbinding rates).
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Introduction
Deterministic and Stochastic Analysis
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The Genetic Switch
• A mutual repression circuit.
• Two proteins A and B negatively regulate each other’s
synthesis
• This architecture is also called the general switch
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The Genetic Switch
• Exists in the lambda phage
• Also synthetically constructed on plasmids in E. coli by
Gardner, Cantor and Collins [Nature 403,339 (2000)]
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The Genetic Switch
• Previous studies using deterministic rate equations
concluded that for Hill-coefficient h=1 there is a
single steady state solution and no bistability.
• Conclusion - cooperative binding (Hill-coefficient
h>1) is required for a switch
Gardiner, Cantor and Collins, Nature, 403, 339 (2000)
Cherry and Adler, J. Theor. Biol. 203, 117 (2000)
Warren and ten Wolde, Phys. Rev. Lett. 92, 128101 (2004)
Walczak et al., Biophys. J. 88, 828 (2005)
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The Switch
• Stochastic analysis using master
equation and Monte Carlo
simulations reveals the reason:
• For weak repression we get
coexistence of A and B proteins
• For strong repression we get three
possible states:
 A domination
 B domination
 Simultaneous repression (deadlock)
• None of these state is really stable
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The Switch
• In order that the system will
become a switch, the dead-lock
situation (= the peak near the
origin) must be eliminated.
• Cooperative binding does this –
The minority protein type has
hard time to recruit two proteins
• But there exist other options…
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The Exclusive Switch
An overlap exists
between the promoters
of A and B and they
cannot be occupied
simultaneously
The rate equations still have a
single steady state solution
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The Exclusive Switch
• However, stochastic analysis
reveals that the system is
truly a switch
• The probability distribution is
composed of two peaks
• The separation between
these peaks determines the
quality of the switch
k=1
k=50
Lipshtat, Loinger, Balaban and Biham, Phys. Rev. Lett. 96, 188101 (2006)
Lipshtat, Loinger, Balaban and Biham, Phys. Rev. E 75, 021904 (2007)
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The Exclusive Switch
• Spontaneous transitions
occur between the two
states of the switch
• The stability of the
switch is characterized
by the mean time
between transitions
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Plasmids
• The synthetic toggle switch was encoded on
plasmids in E. coli.
• Plasmids are circular self replicating DNA molecules
which include only few genes.
• The number of plasmids in a cell can be controlled.
How does the number of plasmids affect the
switching time?
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The effect of plasmids copy number
• Warren and ten Wolde
[PRL 92, 128101 (2004)]
showed that for a single
plasmid with h = 2, the
exclusive switch is more
stable than the general
switch.
This does not hold for
a high plasmid copy
number
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The effect of plasmids copy number
Loinger and Biham, preprint
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Summary
• Stochastic analysis is required for studying
genetic circuits with feedback
• Subtle features may play a major role
• Additional research topics include:
 Other types of modules (Repressilator, Mixed
feedback loop, etc)
 Other levels of regulation (Post-Transcriptional,
Protein-Protein Interactions)
 Analysis of complex networks
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