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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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


Sensitivity analysis













Yue et al., Molecular BioSystems, 2, 2006


  • Complexity ofNF-kB signal pathway

  • Local and global sensitivity analysis

  • Optimal/robust experimental design

  • Conclusionsand future work

NF-kB 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-kB 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.

Time-dependent sensitivities (local)

  • Sensitivity coefficients

  • Direct difference method (DDM)

  • Scaled (relative) sensitivity coefficients

  • Sensitivity index

Local sensitivity rankings

Sensitivities with oscillatory output

Limit cycle oscillations:

Non-convergent sensitivities

Damped oscillations:

convergent sensitivities

Sensitivities and LS estimation

  • Assumption on measurement noise:

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

  • Least squares criterion for parameter estimation

  • Gradient

  • Hessian matrix

Sensitivities and LS estimation

  • Correlation matrix

  • Fisher information matrix

Understanding correlations from SA

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).

Univariate uncertainty range for oscillations

[0.1,12] k36

[0.1,1000] k36


reduce the searching space for parameter estimation

Global sensitivity analysis: Morris method

  • Log-uniformly distributed parameters

  • Random orientation matrix in Morris Method

Max D. Morris, Technometrics, 33, 1991

sensitivity ranking

μ-σ plane



Local sensitive

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

Improved data fitting via estimation of sensitive parameters

(b) Jin, Yue et al., ACC2007

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

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

Optimal experimental design


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



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

Design of IKK activation: intensity

95% confidence intervals when :-

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

IKK=0.06μM (b) E-optimal design

Robust experimental design


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)

Robust experimental design

Contribution of measurement states

Uncertainty degree


  • 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


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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