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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
Manchester Interdisciplinary Biocentre (MIB)
The University of Manchester
Yue et al., Molecular BioSystems, 2, 2006
stiff nonlinear ODE model
Hoffmann et al., Science, 298, 2002
Nelson et al., Sicence, 306, 2004
Sen and Baltimore,Cell, 46, 1986
stampedand limit-cycle oscillations
Limit cycle oscillations:
additive, uncorrelated and normally distributed with zero mean and constant variance.
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).
reduce the searching space for parameter estimation
Max D. Morris, Technometrics, 33, 1991
k28, k29, k36, k38
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, IkBaSensitive parameters of NF-kB model
(b) Jin, Yue et al., ACC2007
(a) Hoffmann et al., Science (2002)
The fitting result of NF-kBn in the IkBa-NF-kB model
maximise the identification information while minimizing the number of experiments
What to design?
Basic measure of optimality:
Fisher Information Matrix
lower bound for the variance of unbiased identifiable parameters
95% confidence intervals when :-
IKK=0.01μM (r) modified E-optimal design
IKK=0.06μM (b) E-optimal 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)
Contribution of measurement states
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 ”