Fast and reliable calibration of solid substrate fermentation kinetic models using advanced non-linear programming techniques

Abstract

Financial support: Projects FONDECYT 1030325 and 7040084.Keywords: dynamic models, Gibberella fujikuroi, Gibberellic acid, nonlinear models, parameter estimation, secondary metabolites, solid substrate cultivation. Abbreviations: NLP: non-linear programSeqSO: sequential solution/optimization SimSO: simultaneous solution/optimization SSF: Solid substrate fermentationCalibration of mechanistic kinetic models describing microorganism growth and secondary metabolite production on solid substrates is difficult due to model complexity given the sheer number of parameters needing to be estimated and violation of standard conditions of numerical regularity. We show how *Corresponding author advanced non-linear programming techniques can be applied to achieve fast and reliable calibration of a complex kinetic model describing growth of Gibberella fujikuroi and production of gibberellic acid on an inert solid support in glass columns. Experimental culture data was obtained under different temperature and Araya, M.M. et al.2 water activity conditions. Model differential equations were discretized using orthogonal collocations on finite elements while model calibration was formulated as a simultaneous solution/optimization problem. A special purpose optimization code (IPOPT) was used to solve the resulting large-scale non-linear program. Convergence proved much faster and a better fitting model was achieved in comparison with the standard sequential solution/optimization approach. Furthermore, statistical analysis showed that most parameter estimates were reliable and accurate.Solid substrate fermentation (SSF) can be defined as the cultivation of microorganisms on solid substrates devoid of or deficient in free water (Pandey, 2003). SSF has several advantages (Hölker and Lenz, 2005) over more conventional submerged fermentation, and many promising lab-scale SSF processes are periodically reported in the literature (John et al. 2006; Krasniewski et al. 2006;Lechner and Papinutti, 2006;Sabu et al. 2006). Unfortunately, very few of these processes enter commercial production (Hölker and Lenz, 2005) due to the magnitude of the technical difficulties in operating and optimizing large scale SSF bioreactors. Since modern process control and optimization engineering techniques are model based, mathematical modelling should significantly improve the chances of successfully transforming an SSF process from laboratory to commercial production.Nevertheless, a number of factors make modelling SSF processes particularly trying: the absence of reliable on-line measurements of relevant cultivation variables (like biomass and nutrient concentration) and the system's inherent complexity, considering that microorganism interaction with the environment and its growth and production kinetics are still not well understood on a micro scale (Mitchell et al. 2004). In addition, the more useful mechanistic dynamic models proposed are highly complex and have many parameters that need to be estimated from extensive good quality experimental data. Acq...

Improved calibration of a solid substrate fermentation model

“…Later, we will show how the fitted parameters compare with those reported by Araya et al (2007) using Orthogonal Collocation on Finite Elements (OCFE). Finally, we contrast the performance of the global optimization technique used here, with standard techniques used in previous publications.…”

“…In the case of the full set of 14 parameters, we calculated all 14 standard deviations leading to an (14 x 14)-FIM matrix, whereas only the statistical information of the 9 relevant parameters is compared. In the case of the 14 parameters found by Araya et al (2007) the same 5 parameters were held fixed leading to a (9 x 9)-FIM matrix for the remaining nine in order to make their estimates comparable to ours.…”

“…Under all culture conditions, good parameter fits were produced. In Table 6 the objective function values were compared to the ones found in Araya et al (2007) and Gelmi et al (2002).…”

“…In this section we present the t-values and confidence intervals for the estimated set of 14 and 9 parameters, while also comparing our t-values to those reported by Araya et al (2007).…”

“…As a consequence of the post-regression analysis, a modified model with a reduced parameter set was postulated and fitted to the experimental data using SSm. The fitted parameters were further compared to the ones presented in Araya et al (2007), using an alternative orthogonal collocation on finite element (OCFE) optimization method.…”