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

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

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  1. 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 h.yue@manchester.ac.uk

  2. Motivation Sensitivity analysis Correlation analysis Identifiability analysis Robust/uncertainty analysis Model reduction Parameter estimation Experimental design Yue et al., Molecular BioSystems, 2, 2006

  3. Outline • Complexity ofNF-kB signal pathway • Local and global sensitivity analysis • Optimal/robust experimental design • Conclusionsand future work

  4. 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

  5. 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.

  6. Time-dependent sensitivities (local) • Sensitivity coefficients • Direct difference method (DDM) • Scaled (relative) sensitivity coefficients • Sensitivity index

  7. Local sensitivity rankings

  8. Sensitivities with oscillatory output Limit cycle oscillations: Non-convergent sensitivities Damped oscillations: convergent sensitivities

  9. 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

  10. Sensitivities and LS estimation • Correlation matrix • Fisher information matrix

  11. 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).

  12. Univariate uncertainty range for oscillations [0.1,12] k36 [0.1,1000] k36 Benefit: reduce the searching space for parameter estimation

  13. Global sensitivity analysis: Morris method • Log-uniformly distributed parameters • Random orientation matrix in Morris Method Max D. Morris, Technometrics, 33, 1991

  14. sensitivity ranking μ-σ plane GSA LSA

  15. 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

  16. 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

  17. Optimal experimental design 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

  18. q2 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

  19. Design of IKK activation: intensity 95% confidence intervals when :- IKK=0.01μM (r) modified E-optimal design IKK=0.06μM (b) E-optimal design

  20. Robust experimental design 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)

  21. Robust experimental design Contribution of measurement states Uncertainty degree

  22. Conclusions • 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

  23. Acknowledgement 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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