Overview of current research (Declan Bates)

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

http://www.le.ac.uk/

http://www.le.ac.uk/

http://www.le.ac.uk/engineering/dgb3

http://www.le.ac.uk/bl/phh4/

http://www.le.ac.uk/engineering/staff/Postlethwaite

http://www.le.ac.uk/engineering/jrk7

http://www.epsrc.ac.uk/

http://www.bbsrc.ac.uk/Welcome.html


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


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


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


Dictyostelium discoideum

From http://www.ruf.rice.edu/~evolve


Dictyostelium discoideum

extra-cellular

intracellularMaeda, et al, Science, Vol. 304 (875), May 2004


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


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


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


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


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


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



• Linear periodically time-varying

• Discretise




10-6 10-4 10-2 100 1020

100

200

300

400

500

600

700

800

900

[rad/sec]

bo

und

Upper BoundLower Bound


The system is guaranteed to be stable inside of the following range:



• Nonlinear Optimisation Problem

Does the time response with produce a limit cycle?

Yes : Increase No :

Decrease


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


• Nonlinear Optimisation Problem

[Internal cAMP] Oscillation


Robustness Analysis: stochastic model

• Stochastic model


• 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.


Propensity function

……..


10-3

10-2

10-1

100

0

10

20

30

40

50

60

Frequency [rad/min]

Internal cAMP Power Spectrum


• 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


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



• 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



• Synchronisation through external cAMP



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]



• Synchronisation with more cells: Chemical Langevin Equation

• Formulate the increment with matching the mean and the variance up to the first-order of


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


• 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


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


• Power Spectrum


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

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Overview of current research (Declan Bates)

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