Fast and reliable calibration of solid substrate fermentation kinetic models using advanced non-linear programming techniques
Juan J. Arrieta
Financial support: Projects FONDECYT 1030325 and 7040084.
Keywords: dynamic models, Gibberella fujikuroi, Gibberellic acid, nonlinear models, parameter estimation, secondary metabolites, solid substrate cultivation.
Calibration 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 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 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.