Sensitivity analysis and experimental design case study of an nf k b signal pathway
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Fifth International Conference on Sensitivity Analysis of Model Output, June 18-22, 2007, Budapest, Hungary. Sensitivity Analysis and Experimental Design - case study of an NF- k B signal pathway. H ong Yue Manchester Interdisciplinary Biocentre (MIB) The University of Manchester

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Sensitivity analysis and experimental design case study of an nf k b signal pathway l.jpg

Fifth International Conference on Sensitivity Analysis of Model Output, June 18-22, 2007, Budapest, Hungary

Sensitivity Analysis and Experimental Design- case study of an NF-kB signal pathway

Hong Yue

Manchester Interdisciplinary Biocentre (MIB)

The University of Manchester

[email protected]


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Motivation Model Output, June 18-22, 2007, Budapest, Hungary

Sensitivity analysis

Correlation

analysis

Identifiability

analysis

Robust/uncertainty

analysis

Model

reduction

Parameter

estimation

Experimental

design

Yue et al., Molecular BioSystems, 2, 2006


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Outline Model Output, June 18-22, 2007, Budapest, Hungary

  • Complexity ofNF-kB signal pathway

  • Local and global sensitivity analysis

  • Optimal/robust experimental design

  • Conclusionsand future work


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NF- Model Output, June 18-22, 2007, Budapest, HungarykB signal pathway

stiff nonlinear ODE model

Hoffmann et al., Science, 298, 2002

Nelson et al., Sicence, 306, 2004

Sen and Baltimore,Cell, 46, 1986


Complexity of nf k b signal pathway l.jpg
Complexity of NF- Model Output, June 18-22, 2007, Budapest, HungarykB signal pathway

  • Nonlinearity: linear, bilinear, constant terms

  • Large number of parameters and variables, stiff ODEs

  • Different oscillation patterns

    stampedand limit-cycle oscillations

  • Stochastic issues, cross-talks, etc.


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Time-dependent sensitivities (local) Model Output, June 18-22, 2007, Budapest, Hungary

  • Sensitivity coefficients

  • Direct difference method (DDM)

  • Scaled (relative) sensitivity coefficients

  • Sensitivity index


Local sensitivity rankings l.jpg
Local sensitivity rankings Model Output, June 18-22, 2007, Budapest, Hungary


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Sensitivities with oscillatory output Model Output, June 18-22, 2007, Budapest, Hungary

Limit cycle oscillations:

Non-convergent sensitivities

Damped oscillations:

convergent sensitivities


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Sensitivities and LS estimation Model Output, June 18-22, 2007, Budapest, Hungary

  • Assumption on measurement noise:

additive, uncorrelated and normally distributed with zero mean and constant variance.

  • Least squares criterion for parameter estimation

  • Gradient

  • Hessian matrix


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Sensitivities and LS estimation Model Output, June 18-22, 2007, Budapest, Hungary

  • Correlation matrix

  • Fisher information matrix


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Understanding correlations from SA Model Output, June 18-22, 2007, Budapest, Hungary

Similarity in the shape of sensitivity coefficients:

K28 and k36 are correlated

Sensitivity coefficients for NF-kBn.

cost functions w.r.t. (k28, k36) and (k9, k28).


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Univariate uncertainty range for oscillations Model Output, June 18-22, 2007, Budapest, Hungary

[0.1,12] k36

[0.1,1000] k36

Benefit:

reduce the searching space for parameter estimation


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Global sensitivity analysis: Morris method Model Output, June 18-22, 2007, Budapest, Hungary

  • Log-uniformly distributed parameters

  • Random orientation matrix in Morris Method

Max D. Morris, Technometrics, 33, 1991


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sensitivity ranking Model Output, June 18-22, 2007, Budapest, Hungary

μ-σ plane

GSA

LSA


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Local sensitive Model Output, June 18-22, 2007, Budapest, Hungary

Global sensitive

k28, k29, k36, k38

k52, k61

k9, k62

k19, k42

k9: IKKIkBa-NF-kB catalytic

k62: IKKIkBa catalyst

k19: NF-kB nuclear import

k42: constitutive IkBb translation

k29: IkBa mRNA degradation

k36: constituitiveIkBa translation

k28: IkBa inducible mRNA synthesis

k38: IkBan nuclear import

k52: IKKIkBa-NF-kB association

k61: IKK signal onset slow adaptation

IKK, NF-kB, IkBa

Sensitive parameters of NF-kB model


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Improved data fitting via estimation of sensitive parameters Model Output, June 18-22, 2007, Budapest, Hungary

(b) Jin, Yue et al., ACC2007

(a) Hoffmann et al., Science (2002)

The fitting result of NF-kBn in the IkBa-NF-kB model


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Optimal experimental design Model Output, June 18-22, 2007, Budapest, Hungary

Aim:

maximise the identification information while minimizing the number of experiments

What to design?

  • Initial state values: x0

  • Which states to observe: C

  • Input/excitation signal: u(k)

  • Sampling time/rate

Basic measure of optimality:

Fisher Information Matrix

Cramer-Rao theory

lower bound for the variance of unbiased identifiable parameters


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q Model Output, June 18-22, 2007, Budapest, Hungary2

q1

Optimal experimental design

Commonly used design principles:

  • A-optimal

  • D-optimal

  • E-optimal

  • Modified E-optimal design

95% confidence interval

The smaller the joint confidence intervals are, the more information is contained in the measurements


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Design of IKK activation: intensity Model Output, June 18-22, 2007, Budapest, Hungary

95% confidence intervals when :-

IKK=0.01μM (r) modified E-optimal design

IKK=0.06μM (b) E-optimal design


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Robust experimental design Model Output, June 18-22, 2007, Budapest, Hungary

Aim:

designthe experiment which should valid for a range of parameter values

Measurement set selection

This gives a (convex) semi-definite programming problem for which there are many standard solvers(Flaherty, Jordan, Arkin, 2006)


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Robust experimental design Model Output, June 18-22, 2007, Budapest, Hungary

Contribution of measurement states

Uncertainty degree


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Conclusions Model Output, June 18-22, 2007, Budapest, Hungary

  • Different insights from local and global SA

  • Importance of SA in systems biology

  • Benefits of optimal/robust experimental design

Future works

  • SA of limit cycle oscillatory systems

  • Global sensitivity analysis and robust design


Acknowledgement l.jpg
Acknowledgement Model Output, June 18-22, 2007, Budapest, Hungary

Prof. Douglas B. Kell: principal investigator (Manchester Interdisciplinary Biocentre, MIB)

Dr. Martin Brown, Mr. Fei He, Prof. Hong Wang (Control Systems Centre)

Dr. Niklas Ludtke (MIB)

Prof. David S. Broomhead (School of Mathematics)

Ms. Yisu Jin (Central South University, China)

BBSRC project “Constrained optimization of metabolic and signalling pathway models: towards an understanding of the language of cells ”


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