Finite-time parametric identification for the model representing the metabolic and genetic regulatory effects of sequential aerobic respiration and anaerobic fermentation processes in Escherichia coli.

Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a large number of parameters involved and that it is difficult to obtain them experimentally. This study presents an algorithm to obtain a finite-time parameter characterization of the model used to describe changes in the metabolic behaviour of Escherichia coli associated with environmental changes. In this scheme, super-twisting algorithm was proposed to recover the derivative of all the proteins and mRNA of E. coli associated to changes in the concentration of oxygen available in the growth media. The 75 identified parameters in this study maintain the biological coherence of the system and they were estimated with no more than 20% error with respect to the real ones included in the proposed model.