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A numerical procedure for model identifiability analysis applied to enzyme kinetics

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Abstract
The proper calibration of models describing enzyme kinetics can be quite challenging. In the literature, different procedures are available to calibrate these enzymatic models in an efficient way. However, in most cases the model structure is already decided on prior to the actual calibration exercise, thereby bypassing the challenging task of model structure determination and identification. Parameter identification problems can thus lead to ill-calibrated models with low predictive power and large model uncertainty. Every calibration exercise should therefore be preceded by a proper model structure evaluation by assessing the local identifiability characteristics of the parameters. Moreover, such a procedure should be generic to make sure it can be applied independent from the structure of the model. We hereby apply a numerical identifiability approach which is based on the work of Walter and Pronzato (1997) and which can be easily set up for any type of model. In this paper the proposed approach is applied to the forward reaction rate of the enzyme kinetics proposed by Shin and Kim (1998). Structural identifiability analysis showed that no local structural model problems were occurring. In contrast, the practical identifiability analysis revealed that high values of the forward rate parameter V-f led to identifiability problems. These problems were even more pronounced at higher substrate concentrations, which illustrates the importance of a proper experimental design to avoid (practical) identifiability problems. By using the presented approach it is possible to detect potential identifiability problems and avoid pointless calibration (and experimental!) effort.
Keywords
structural identifiability, model analysis, practical identifiability, enzyme kinetics

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Chicago
Van Daele, Timothy, Stijn Van Hoey, Krist V Gernaey, Ulrich Krühne, and Ingmar Nopens. 2015. “A Numerical Procedure for Model Identifiability Analysis Applied to Enzyme Kinetics.” In Computer Aided Chemical Engineering, ed. Krist V Gernaey, Jakob K Huusom, and Rafiqul Gani, 37:575–580. Amsterdam, The Netherlands: Elsevier.
APA
Van Daele, T., Van Hoey, S., Gernaey, K. V., Krühne, U., & Nopens, I. (2015). A numerical procedure for model identifiability analysis applied to enzyme kinetics. In K. V. Gernaey, J. K. Huusom, & R. Gani (Eds.), Computer Aided Chemical Engineering (Vol. 37, pp. 575–580). Presented at the 12th International symposium on Process Systems Engineering (PSE) ; 25th European symposium on Computer Aided Process Engineering (ESCAPE), Amsterdam, The Netherlands: Elsevier.
Vancouver
1.
Van Daele T, Van Hoey S, Gernaey KV, Krühne U, Nopens I. A numerical procedure for model identifiability analysis applied to enzyme kinetics. In: Gernaey KV, Huusom JK, Gani R, editors. Computer Aided Chemical Engineering. Amsterdam, The Netherlands: Elsevier; 2015. p. 575–80.
MLA
Van Daele, Timothy, Stijn Van Hoey, Krist V Gernaey, et al. “A Numerical Procedure for Model Identifiability Analysis Applied to Enzyme Kinetics.” Computer Aided Chemical Engineering. Ed. Krist V Gernaey, Jakob K Huusom, & Rafiqul Gani. Vol. 37. Amsterdam, The Netherlands: Elsevier, 2015. 575–580. Print.
@inproceedings{6830166,
  abstract     = {The proper calibration of models describing enzyme kinetics can be quite challenging. In the literature, different procedures are available to calibrate these enzymatic models in an efficient way. However, in most cases the model structure is already decided on prior to the actual calibration exercise, thereby bypassing the challenging task of model structure determination and identification. Parameter identification problems can thus lead to ill-calibrated models with low predictive power and large model uncertainty. Every calibration exercise should therefore be preceded by a proper model structure evaluation by assessing the local identifiability characteristics of the parameters. Moreover, such a procedure should be generic to make sure it can be applied independent from the structure of the model. 
We hereby apply a numerical identifiability approach which is based on the work of Walter and Pronzato (1997) and which can be easily set up for any type of model. In this paper the proposed approach is applied to the forward reaction rate of the enzyme kinetics proposed by Shin and Kim (1998). Structural identifiability analysis showed that no local structural model problems were occurring. In contrast, the practical identifiability analysis revealed that high values of the forward rate parameter V-f led to identifiability problems. These problems were even more pronounced at higher substrate concentrations, which illustrates the importance of a proper experimental design to avoid (practical) identifiability problems. By using the presented approach it is possible to detect potential identifiability problems and avoid pointless calibration (and experimental!) effort.},
  author       = {Van Daele, Timothy and Van Hoey, Stijn and Gernaey, Krist V and Kr{\"u}hne, Ulrich and Nopens, Ingmar},
  booktitle    = {Computer Aided Chemical Engineering},
  editor       = {Gernaey, Krist V and Huusom, Jakob K and Gani, Rafiqul},
  isbn         = {9780444635785},
  issn         = {1570-7946},
  language     = {eng},
  location     = {Cophenhagen, Denmark},
  pages        = {575--580},
  publisher    = {Elsevier},
  title        = {A numerical procedure for model identifiability analysis applied to enzyme kinetics},
  volume       = {37},
  year         = {2015},
}

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