Multi-stability of synthetic genetic networks
with repressive cell-to-cell communication
StoMP 2009
"Noisy Bugs: modelling and microbiology"
16/07/09
Ekkehard Ullner
Institute for Complex Systems and Mathematical Biology, University of Aberdeen
e.ullner@abdn.ac.uk
Sunday, 12 July 2009
How do varieties arise?
T. Shin et al., Nature 415, p. 859, 2002.
Sunday, 12 July 2009
The control of the protein production
The protein structure is encoded in the genes.
The process occurs in two steps:
•
•
Transcription: DNA ! RNA
Translation: RNA ! protein
The central dogma of biology: DNA ! RNA ! protein
Problem: natural genetic networks are too complicated
for time resolved modelling
Sunday, 12 July 2009
Difficulties for the modelling
•
•
•
natural genetic networks are huge
structure not complete resolved
interaction dynamics often unknown
R. Dobrin et al.,
BMC!Bioinformatics 5, p. 10, 2004.
! reduce complexity
! synthetic genetic networks
Sunday, 12 July 2009
Synthetic genetic networks
•
•
•
artificial genetic modules
consist of a limited number of genes
designed to operate isolated from the rest of the
cellular machinery
•
test system for special functions of natural gene
networks
•
greatly reduced complexity of natural networks
Sunday, 12 July 2009
The repressilator
• a network of three transcriptional repressors that inhibit
one another in a cyclic way
• synthetic genetic clock
M. Elowitz et al., Nature 403, p. 335, 2000.
Sunday, 12 July 2009
The modified repressilator
with quorum sensing
CI
cI
t
Te
R
La
c
I
lacI
tetR
AI
M.B. Elowitz and S Leibner, Nature 405, p. 335, 2000.
J. García-Ojalvo, M.B. Elowitz and S.H. Strogatz, PNAS 101, p. 10955, 2004.
E. Ullner, A. Zaikin, E. I. Volkov, and J. García-Ojalvo, Phys. Rev. Lett. 99, 148103, 2007.
Sunday, 12 July 2009
The modified repressilator
with quorum sensing
CI
cI
lacI
lacI
tR
La
cI
Te
cI
La
LuxR
tetR
Lac
I
luxI
AI
AI
M.B. Elowitz and S Leibner, Nature 405, p. 335, 2000.
J. García-Ojalvo, M.B. Elowitz and S.H. Strogatz, PNAS 101, p. 10955, 2004.
E. Ullner, A. Zaikin, E. I. Volkov, and J. García-Ojalvo, Phys. Rev. Lett. 99, 148103, 2007.
Sunday, 12 July 2009
The modified repressilator
with quorum sensing
CI
cI
lacI
lacI
LuxR
tR
La
cI
Te
tetR
Lac
TetR
I
luxI
AI
AI
M.B. Elowitz and S Leibner, Nature 405, p. 335, 2000.
J. García-Ojalvo, M.B. Elowitz and S.H. Strogatz, PNAS 101, p. 10955, 2004.
E. Ullner, A. Zaikin, E. I. Volkov, and J. García-Ojalvo, Phys. Rev. Lett. 99, 148103, 2007.
Sunday, 12 July 2009
Reinforcing repressive
coupling
tR
tR
Te
cI
lacI
LuxR
cI
La
Te
La
lacI
LuxR
I
Lac
tetR
CI
cI
lacI
cI
lacI
La
CI
cI
luxI
AI
tetR
I
Lac
TetR
AI
luxI
AI
AI
reinforcing: phase attractive
repressive: phase advanced
150
100
protein CI (Bi)
protein CI (Bi)
60
50
0
0
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40
20
50
100
time
150
200
0
600
800
1000
time
1200
14
The modified repressilator model
ȧ i
=
− ai +
ḃ i
=
− bi +
ċ i
=
− ci +
Ȧ i
Ḃ i
Ċ i
Ṡ i
=
a (a i
=
=
=
1+
C in
1+
A in
1+
B in
tetR
cI
+
Si
1 + Si
− Ai)
b (b i − B i )
c (c i − C i )
− k s 0 S i + k s 1 B i − ( S i − Q S̄ )
lacI
TetR
CI
LacI
auto inducer
related with cell density
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The stable dynamic regimes
oscillatory
Bi(CI)
80
200
40
150
150
0
19800 20000
19600
time
100
50
00
200
400 600
time
800
protein Bi (CI)
protein Bi (CI)
0
1700
100
1800 1900
time
200 300
time
400
2000
500
200
150
150
100
100
50
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10
single fixed point
d)
200
00
50
00
1000
clustering
c)
100
20
Bi (CI)
200
protein Bi (CI)
b)
protein Bi (CI)
a)
inhomogen limit cycle
200
400 600
time
800
1000
50
00
100
200 300
time
400
500
Multi-stability
by varying cell density Q
1000
400
200
single fixed point
clustering
inhomogeneous limit cycle
600
oscillatory
# of regimes
800
0
0
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0.1
0.2
0.3
Q
0.4
0.5
0.6
0.7
The bifurcation analysis
TR2
LP5
10
TR1
HB2
a1
HB1
BP2
LP2
HB3 HB4
LP4
LP5
1
BP1
LP1
LP5
HB1
HB2
clustering
inhomogen limit cycle
oscillatory
single fixed point
LP2
0.1
0
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0.2
0.4
0.6
Q
0.8
1
1.2
The system size effect
N=18
1000
800
800
200
600
single fixed point
400
IHLC
400
single fixed point
oscillatory
600
# of regimes
1000
oscillatory
# of regimes
N=5
200
IHLC
0
0
0.1
0.2
IHSS
IHSS
0.3
0
Q
0.4
0.5
0.6
0.7
0
0.1
0.2
0.3
Q
0.4
0.5
0.6
0.7
The artificial differentiation (IHLC, IHSS) becomes more
likely in large ensembles
The system size influences the position of IHLC and IHSS
Sunday, 12 July 2009
Chaos: a source of uncertainty
strong chaos - short-time cluster
b)
c)
d)
50
50
40
40
40
40
30
20
10
30
20
10
0
5000
5100
time
5200
0
5300
protein Bi (CI)
50
protein Bi (CI)
50
protein Bi (CI)
protein Bi (CI)
a)
30
20
10
19300
time
19400
19500
0
30100
30
20
10
30200
time
30300
30400
0
35000
18
16
oscillator
14
12
10
8
6
4
2
0
0
1
2
time
3
4
4
x 10
cluster formation in the presence of chaos
from time to time a reorganisation takes place
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35100
time
35200
35300
Noise in genetic networks
•
•
•
Chemical reactions are probabilistic
•
The deterministic system gives the dynamical skeleton for the
Low copy numbers of genes, RNAs and proteins evoke fluctuations
Fluctuations in other cellular components lead to extrinsic noise
noisy system
•
•
Can genetic noise evoke jumps between the multi-stable states?
For simplicity: we assume Gaussian white and independent noise
effects the transcription
Sunday, 12 July 2009
Noise-induced switches between
the multi-stable states
oscillatory ! ihlc
single fixed point
" ihlc " oscillatory
oscillatory " ihlc "
single fixed point
Sunday, 12 July 2009
Conclusion
• Synthetic genetic networks are perfect test systems
• The repressive cell-to-cell communication enables very rich
dynamics including multi-stability, clustering and chaos
• The oscillation death could be a mechanism of artificial cell
differentiation
• The deterministic system determines the skeleton for the
noisy one
• Genetic noise can evoke sudden jumps between the coexisting
dynamical regimes
• Design of artificial genetic chips with desired functions
Sunday, 12 July 2009
Acknowledgements
Prof. Jordi García-Ojalvo
Universitat Politécnica de Catalunya, Terrassa, Spain
Prof. Evgenii Volkov
Dep. Theoretical Physics, Lebedev Physical Inst., Moscow, Russia
Dr. Aneta Koseska
Institute of Physics, University of Potsdam, Germany
Prof. Alexey Zaikin
Departments of Mathematics and Institute of Women Health, University
College London, U.K.
financial support by
Sunday, 12 July 2009
.
Acknowledgements
Prof. Jordi García-Ojalvo
Prof. Evgenii Volkov
Dr. Aneta Koseska
Prof. Alexey Zaikin
Thank you for your
attention and interest!
Sunday, 12 July 2009