Fundação para a Ciência e a Tecnologia (FCT

Costa, Rafael S.

Ferreira, E. C.

Rocha, I.

Ferreira, Eugénio C.

Universidade do Minho: RepositoriUM

Model Reduction based on dynamic sensitivity analysis: A systems biology case of studyINTRODUCTIONThe complexity of dynamic mathematical models due to large number ofparameters is a major obstacle for their effective use in optimization andcontrol processes. Furthermore, the experimental estimation of a greatnumber of parameters is often an unfeasible task [1]. Therefore, modelreduction represents a key step to eliminate unimportant parameters andto uncover the most important control pathways of the models. Severaltechniques for parameter model reduction exist, including methodsbased on sensitivity analysis [2].AIMHere, the complex E. coli dynamic model describing the carbon centralmetabolism [3] which has 25 species participating in 30 reactions andwith 116 parameters was used to:• Identify key parameters that have more impacts on the globalsystems.• Study a model reduction strategy based on univariate analysis ofthe Euclidean-norm to consider the effect to all metabolites.9 Dynamic sensitivity analysis was successful used for the complex model structurereduction9 Kinetic model parameters can be rejected from the rate expressions with verylimited effect on the system behaviour9 Up to 41 of 116 parameters are rejected without significant changes in the mainspecies and fluxes9 Different global sensitivity methods will be performed to compare with the localsensitivityAcknowledgements References [1] F.R.Sidoli, A.Mantalaris, and S.P.Asprey, Industrial & Engineering Chemistry Research 44 (2005) 868-878.[2] T.Turanyi, Journal of Mathematical Chemistry 5 (1990) 203-248.[3] Chassagnole, C., et al. Biotechnology and Bioengineering 79 (2002) 53-73.DYNAMIC MODEL OF CENTRAL CARBON METABOLISMR. S. Costa,  I. Rocha and E. C. FerreiraIBB-Institute for Biotechnology and Bioengineering, Centre of Biological Engineering, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal(Email: {rafacosta, irocha, ecferreira}@deb.uminho.pt)OVERVIEWMETHODOLOGYCONCLUSIONS AND FUTURE WORKRESULTSFigure 1. Metabolic network from the central carbon metabolism of E. coli (adapted from [3]).Complex Mechanistic Model:- 25 Species- 30 Enzyme Kinetics- 116 ParametersSENSITIVITY ANALYSISjiijjjjijjiji pptXpXppppXppXtSln),(ln)(2)()()(, ∂∂≈×ΔΔ−−Δ+=- Computing sensitivity analysis in Matlab- Dynamic sensitivity analysis based on Euclidean-norm),,()( 0XptftX ji =- Nonlinear ODE model∑ −=jijiji XrvdtdX μ∑ ∑= == nk pi jij tSnOS 1 1 2, )(1Figure 2. Comparison between experimental (symbols) and simulated data (gray solid line:reduced model based on local sensitivity and black dashed line: original model) of the mainspecies: GLCEX (extracellular glucose), G6P (glucose-6-phospate), F6P (fructose-6-phospate),FDP (fructose-1,6-bisphosphate), GAP (glyceradehyde-3-phosphate) and PYR (pyruvate)variation with time in E. coli, after a glucose pulse (10 s). For GLCEX the lines are overlapped.Of all the 116 parameters from the complex model analyzed, 41 (35.3%)parameters were rejected without significant changes on the model prediction.Further 24 (20.7%) parameters were found to have significant influence on thesystems, although their overall sensitivity (OSj) was low, and as such werealso not considered in the model reduction. Although the metabolicallystructured model was affected by the model reduction, the dynamics of thenetwork are generally well represented. By comparing the simulation results ofthe original and the reduced model, it can be showed that species trajectoriesdid not change considerably with time (Figure 2) and also for the fluxestrajectories (Figure 3).COMPARISON ORIGINAL  AND REDUCED MODELFigure 3. Time courses of PTS (phosphotransferase system), PFK (phoshofruuctokinase), PDH(pyruvate dehydrogenase) and PGDH (6-phophogluconate dehydrogenase) fluxes during steady-state conditions and after a glucose pulse (10 s). Comparison between simulated data, gray solidline: reduced model and black dashed line: original modelThe authors thank Dr. Chassagnole, who provided the experimental data set.

Model reduction based on dynamic sensitivity analysis: a systems biology case of study

http://repositorium.sdum.uminho.pt/bitstream/1822/8421/3/Poster_Costa%5b1%5d.pdf

Model reduction based on dynamic sensitivity analysis : a systems biology case of study

Abstract

Similar works

Full text

Available Versions

Universidade do Minho: RepositoriUM