Author(s):
Ataíde, Filipe André Prata 
Date: 2007
Persistent ID: http://hdl.handle.net/10362/1065
Origin: Repositório Institucional da UNL
Subject(s): Algoritmos genéticos; Bioquímica; Cinética enzimática; Design experimental; Engenharia química; Optimização
Description
The main objective of this work was to investigate the application of experimental
design techniques for the identification of Michaelis-Menten kinetic parameters. More
specifically, this study attempts to elucidate the relative advantages/disadvantages of employing complex experimental design techniques in relation to equidistant sampling when applied to different reactor operation modes. All studies were supported by simulation data of a generic enzymatic process that obeys to the Michaelis-Menten kinetic equation.
Different aspects were investigated, such as the influence of the reactor operation mode
(batch, fed-batch with pulse wise feeding and fed-batch with continuous feeding) and
the experimental design optimality criteria on the effectiveness of kinetic parameters
identification. The following experimental design optimality criteria were investigated:
1) minimization of the sum of the diagonal of the Fisher information matrix (FIM)
inverse (A-criterion), 2) maximization of the determinant of the FIM (D-criterion), 3)
maximization of the smallest eigenvalue of the FIM (E-criterion) and 4) minimization
of the quotient between the largest and the smallest eigenvalue (modified E-criterion).
The comparison and assessment of the different methodologies was made on the basis
of the Cramér-Rao lower bounds (CRLB) error in respect to the parameters vmax and Km
of the Michaelis-Menten kinetic equation.
In what concerns the reactor operation mode, it was concluded that fed-batch (pulses) is
better than batch operation for parameter identification. When the former operation
mode is adopted, the vmax CRLB error is lowered by 18.6 % while the Km CRLB error is
lowered by 26.4 % when compared to the batch operation mode. Regarding the optimality criteria, the best method was the A-criterion, with an average vmax CRLB of
6.34 % and 5.27 %, for batch and fed-batch (pulses), respectively, while presenting a
Km’s CRLB of 25.1 % and 18.1 %, for batch and fed-batch (pulses), respectively. As a
general conclusion of the present study, it can be stated that experimental design is
justified if the starting parameters CRLB errors are inferior to 19.5 % (vmax) and 45%
(Km), for batch processes, and inferior to 42 % and to 50% for fed-batch (pulses)
process. Otherwise equidistant sampling is a more rational decision. This conclusion
clearly supports that, for fed-batch operation, the use of experimental design is likely to largely improve the identification of Michaelis-Menten kinetic parameters.
