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Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Overview of current research (Declan Bates)Robustness of deterministic & stochastic models of D. discoideum cAMP oscillations (Jongrae Kim)
Research supported by:
Systems Biology Lab
www.sblab.org
Declan Bates Pat Heslop-Harrison Ian Postlethwaite Jongrae Kim Najl Valeyev Prathyush Menon
IEEE Colloquium on Control in Systems Biology, University of Sheffield, 26th March 2007
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Overview of current research• Combined in silico and in vitro robustness analysis of biochemical networks:
– cAMP oscillations in fields of chemotactic Dictyostelium cells– Regulation of gene expression in the tryptophan operon of E.coli
• Multisite protein-ligand interactions:– Modelling mechanisms underlying multifunctional target regulation by multisite proteins– Selective and differential activation of Ca2+-CaM targets
• Reverse engineering biomolecular networks: – Methods for inferring network architectures – Dealing with noise in time-series data
• Projects with external collaborators:– Modelling and analysis of mechanisms underlying inflammation
(with Dr. Michael Seed, William Harvey Research Institute)– Pathophysiological modelling of hypoxaemia
(with Dr. Jonathan Hardman, University of Nottingham)
J. Kim, D.G. Bates, I. Postlethwaite, L. Ma and P. Iglesias, "Robustness Analysis of Biochemical Network Models", IET Systems Biology, 2006
N.V. Valeyev, P. Heslop-Harrison, I. Postlethwaite, N. Kotov, and D.G. Bates, ``Multiple binding sites make proteins multifunctional'', FEBS-SysBio2007, Gosau, Austria, 2007.
J. Kim, D.G. Bates, P. Heslop-Harrison, I. Postlethwaite and K.-H. Cho, "Least-Squares Methods for Identifying Biochemical Regulatory Networks from Noisy Measurements", BMC Bioinformatics, 2007
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
IEEE UK&RI Control Systems Chapter, Colloquium on Control in Systems Biology
University of Sheffield, Sheffield, UK, 26th March 2006
Robustness of Deterministic & Stochastic Models of D. discoideum cAMP Oscillations
Jongrae Kim*,‡,Ian Postlethwaite*,‡, Pat Heslop-Harrison†,‡, Declan G. Bates*,‡
*Control & Instrumentation Research Group, Dept. of Engineering, University of Leicester, Leicester, UK†Department of Biology, University of Leicester, Leicester, UK
‡Systems Biology Lab., University of Leicester, Leicester, UK, www.sblab.org
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Outline
• Introduction– Dictyostelium discoideum– basic molecular biology– Laub-Loomis model
• Robustness Analysis– the deterministic model
Worst-case parameter combination– the stochastic model
converting from a deterministic to a stochastic model synchronisation of cAMP oscillations
• Conclusions
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Dictyostelium discoideum
From http://www.ruf.rice.edu/~evolve
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Dictyostelium discoideum
extra-cellular
intracellularMaeda, et al, Science, Vol. 304 (875), May 2004
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Basic Molecular Biology
• Basic Elements
C
O
C
C C
C
1´
2´3´
4´
5´
C
C N
NC CH
N
HC
NH
NH2
P
O
O-
OO
Sugar Base : Adenine
Phosphate: Triphosphate
P
O
O-
OOP
O
O-
O-O
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Basic Molecular Biology• ATP (Adenosine TriPhosphate)
C
C N
NC CH
N
HC
NH
NH2
C
O
C
C C
C
1´
2´3´
4´
5´P
O
O-
OOP
O
O-
OOP
O
O-
OO
OH OH
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Basic Molecular Biology• Cyclic 3´, 5´- AMP (Cyclic Adenosine MonoPhosphate)
C
C N
NC CH
N
HC
NH
NH2
C
O
C
C C
C
1´
2´3´
4´
5´
P
O
O
O
O
O OH
adenylate cyclase (ACA)
ACA
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Basic Molecular Biology• 5´ AMP
cAMP phosphodiesterase
C
C N
NC CH
N
HC
NH
NH2
C
O
C
C C
C
1´
2´3´
4´
5´P
O
O-
OO
OH OH
cAMP
ACA
CAR1
ERK2
REG A
PKA
phosphodiesterase
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Laub-Loomis Model
• Laub-Loomis cAMP Oscillation model“the model is robust in that 25-fold changes in the kinetic constants linking the activities have only minor effects on the predicted frequency”
“two-fold changes make little difference in either the frequency or amplitude of the oscillations in enzymatic activities”
Laub & Loomis, Molecular Biology of the Cell, 1998
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: deterministic model
• Linear analysis Kim, J., Bates, D. G., Postlethwaite, I., Ma L. and Iglesias P.A., "Robustness Analysis of Biochemical Network Models", Vol 153, No. 3, IET Systems Biology, May 2006, pp. 96-104
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: deterministic model
• Linear periodically time-varying
• Discretise
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: deterministic model
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
10-6 10-4 10-2 100 1020
100
200
300
400
500
600
700
800
900
[rad/sec]
bo
und
Upper BoundLower Bound
Robustness Analysis: deterministic model
The system is guaranteed to be stable inside of the following range:
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: deterministic model
• Nonlinear Optimisation Problem
Does the time response with produce a limit cycle?
Yes : Increase No :
Decrease
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
0 1 2 3 4 5 60.5
1
1.5
0 1 2 3 4 5 60.5
1
1.5
0 1 2 3 4 5 60.5
1
1.5
Robustness Analysis: deterministic model
• Nonlinear Optimisation Problem
[Internal cAMP] Oscillation
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: stochastic model
• Stochastic model
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
• Stochastic simulation: Gillespie’s-direct method– S1. When does the next reaction occur?
(Probability that each reaction occurs during )
(Probability that no reaction occurs from to )
– S2. Which reaction happens from to ?
– S3. Set the current time and go to the step S1.
Robustness Analysis: stochastic model
Propensity function
……..
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
10-3
10-2
10-1
100
0
10
20
30
40
50
60
Frequency [rad/min]
Internal cAMP Power Spectrum
Robustness Analysis: stochastic model
• Result: Oscillations re-emerge for the worst parameter combination!
Maeda, et al, Science, Vol. 304 (875), May 2004
0 500 1000 1500 2000
100
200
300
400
500
600
time [min]
[Inte
rnal
cA
MP
# o
f mol
ecul
es]
0 10 20 30200
250
300
350
400
time [min]
[# o
f mol
ecul
es]
cAMPERK2
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
10-2
10-1
100
10-2
100
102
104
frequency [rad/min]
Pow
er S
pect
rum
Robustness Analysis: stochastic model• Is the stochastic model robust to variations in the parameters and
initial conditions?
10-2
10-1
100
10-2
100
102
104
frequency [rad/min]
Pow
er S
pect
rum
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: stochastic model
• cAMP oscillations of multiple cells:
0 50 100 150 2000
100
200
300
400
500
600
700
time [min]
[# o
f int
erna
l cA
MP
mol
ecul
es]
10 Cells
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: stochastic model
• Synchronisation through external cAMP
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: stochastic model
0 20 40 60 80 1000
200
400
600
800
1000
time [min]
[# o
f int
erna
l cA
MP
mol
ecul
es]
10 Cells
0 20 40 60 80 1000
100
200
300
400
500
600
700
time [min]
[# o
f int
erna
l cA
MP
mol
ecul
es]
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Robustness Analysis: stochastic model
• Synchronisation with more cells: Chemical Langevin Equation
• Formulate the increment with matching the mean and the variance up to the first-order of
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
1950 1960 1970 1980 1990 20000
100
200
300
400
500
600
700
time [min]
[# o
f int
erna
l cA
MP
mol
ecul
es]
Synchronised cells
Robustness Analysis: stochastic model
• 100-cells
150 160 170 180 190 2000
100
200
300
400
500
600
700
time [min]
[# o
f int
erna
l cA
MP
mol
ecul
es]
Separated cells
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
10-2
10-1
100
10
20
30
40
50
60
70Synchronised cells
frequency [rad/min]
Pow
er S
pect
rum
10-2
10-1
100
10
20
30
40
50
60
70Separated cells
frequency [rad/min]
Pow
er S
pect
rum
3-cells10-cells100-cells
3-cells10-cells100-cells
Robustness Analysis: stochastic model
• Power Spectrum
Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org
Conclusions
• Robustness analysis of oscillations in biological systems:
– Deterministic and stochastic models may exhibit radically different levels of robustness
– Deterministic and stochastic models not equivalent even for high molecular concentrations
• Analysis provides an explanation for the robustness of D. discoideum cAMP oscillations:
– Individual cells: Stochastic fluctuation– Culture cells: Synchronisation between cells
• Qualitative changes of D. discoideum cells to a slug initiated by the internal cAMP concentration change