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Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides

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Abstract

Starting from a relatively detailed model of a bioprocess producing fructo-oligosaccharides, a set of experimental data collected in batch and fed-batch experiments is exploited to estimate the unknown model parameters. The original model includes the growth of the fungus Aureobasidium pullulans which produces the enzymes responsible for the hydrolysis and transfructosylation reactions, and as such contains 25 kinetic parameters and 16 pseudo-stoichiometric coefficients, which are not uniquely identifiable with the data at hand. The aim of this study is, therefore, to show how sensitivity analysis and quantitative indicators based on the Fisher information matrix can be used to reduce the detailed model to a practically identifiable model. Parametric sensitivity analysis can indeed be used to progressively simplify the model to a representation involving 15 kinetic parameters and 8 pseudo-stoichiometric coefficients. The reduced model provides satisfactory prediction and can be convincingly cross validated.

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Abbreviations

GF:

Sucrose concentration (\({\text{g}\, {\rm L}^{-1}}\))

\({\text{GF}}_2\) :

1-Kestose concentration (\({\text{g}\,{\rm L}^{-1}}\))

\({{\text{GF}}_3}\) :

Nystose concentration (\({\text{g}\, {\rm L}^{-1}}\))

GF\(_4\) :

Fructofuranosylnystose concentration (\({\text{g} \,{\rm L}^{-1}}\))

F:

Fructose concentration (\({\text{g}\, {\rm L}^{-1}}\))

G:

Glucose concentration (\({\text{g} \,{\rm L}^{-1}}\))

X :

Biomass concentration (\({\text{g} \,{\rm L}^{-1}}\))

\(r_i, i=1,\ldots ,4\) :

Hydrolysis reaction rates (\({\text{g} \,{\rm L}^{-1} \,{\rm h}^{-1}}\))

\(r_i, i=5,6,7\) :

Transfructosylation reaction rates (\({\text{g} \,{\rm L}^{-1}\, {\rm h}^{-1}}\))

\(r_i, i=8,9\) :

Biomass production reaction rates (\({\text{g} \,{\rm L}^{-1} \,{\rm h}^{-1}}\))

\(k_i, i=1,\ldots ,14\) :

Pseudo-stoichiometric coefficients

\(Y_\text{F}\) :

Biomass yield coefficient from fructose

\(Y_\text{G}\) :

Biomass yield coefficient from glucose

\({\text{Vmh}_\text{GF}}\) :

Maximum hydrolysis rate for sucrose (\({\text{g}\,{\rm L}^{-1}\,{\rm h}^{-1}}\))

\({\text{Kmh}_\text{GF}}\) :

Michaelis–Menten constant for sucrose (\({\text{g} \,{\rm L}^{-1}}\))

\(\text{Vmh}_{{\rm GF}_i}\) :

Maximum hydrolysis rate for \({\rm GF}_i\) (\({\text{g}\, {\rm L}^{-1}\,{\rm h}^{-1}}\))

\(\text{Kmh}_{{\rm GF}_i}\) :

Michaelis–Menten constant for \(\text{GF}_i\) (\({\text{g} \,{\rm L}^{-1}}\))

\(\text{Kih}_{{\rm GF}_i}\) :

Substrate inhibition constant for \(\text{GF}_i\) (\({\text{g} \,{\rm L}^{-1}}\))

\(\text{VmT}_{{\rm GF}}\) :

Maximum transfructosylation rate for sucrose (\({\text{g}\,{\rm L}^{-1}\,{\rm h}^{-1}}\))

Kmst:

Michaelis–Menten constant for sucrose (\({\text{g} \,{\rm L}^{-1}}\))

Ksts:

Substrate inhibition constant for sucrose (\({\text{g} \,{\rm L}^{-1}}\))

Kgst:

Competitive inhibition constant for glucose

\({{\rm VmT}_{{\rm GF}_i}}\) :

Maximum transfructosylation rate for \(\text{GF}_i\) (\({\text{g}\,{\rm L}^{-1}{\rm h}^{-1}}\))

\(\text{Kmt}_{\text{GF}_i}\) :

Michaelis–Menten constant for \(\text{GF}_i\) (\({\text{g} \,{\rm L}^{-1}}\))

\(\text{Kit}_{{\rm GF}_i}\) :

Competitive inhibition constant for \(\text{GF}_i\)

\(\mu _{\rm mF}\) :

Maximum specific growth rate for fructose (\(\text{h}^{-1}\))

\(K_\text{F}\) :

Monod constant of fructose (\({\text{g}\,{\rm L}^{-1}}\))

\(\mu _\text{mG}\) :

Maximum specific growth rate for glucose (\({{\rm h}^{-1}}\))

\(K_\text{G}\) :

Monod constant of glucose (\({\text{g}\,{\rm L}^{-1}}\))

V :

Culture volume (L)

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Acknowledgements

The authors thank the financial support from the F.R.S.-FNRS, the Belgium National Fund for the Scientific Research (Research Project 24643.08). C. Nobre thanks the Fundação para a Ciência e Tecnologia for the strategic funding of UID/BIO/04469 /2013 unit.

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Authors and Affiliations

  1. LAMSIN (LR-99-ES20), National Engineering School of Tunis, University of Tunis El Manar, 1002, Tunis, Tunisia

    R. Fekih-Salem

  2. Automatic Control Laboratory, Faculty of Engineering, University of Mons, 7000, Mons, Belgium

    L. Dewasme & A. Vande Wouwer

  3. Department of Chemical and Biochemical Engineering, Faculty of Engineering, University of Mons, 7000, Mons, Belgium

    Cristiana Cordeiro Castro & A.-L. Hantson

  4. Centre of Biological Engineering, University of Minho, 4710-057, Braga, Portugal

    C. Nobre

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  1. R. Fekih-Salem
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Correspondence to L. Dewasme.

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Fekih-Salem, R., Dewasme, L., Castro, C.C. et al. Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides. Bioprocess Biosyst Eng 42, 1793–1808 (2019). https://doi.org/10.1007/s00449-019-02176-9

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