Papers by Carlos Enrique Labastida Martínez
IFAC-PapersOnLine, 2020
Fast growing E. coli cells in glucose-aerobic conditions excrete fermentation byproducts such as ... more Fast growing E. coli cells in glucose-aerobic conditions excrete fermentation byproducts such as acetate. This phenomenon is known as overflow metabolism and can pose a major problem in industrial bio-processes. In this paper, we study optimal control strategies for feeding a fed-batch reactor subject to overflow metabolism. We consider that acetate has an inhibitor effect on the glucose uptake, and we also consider the cost associated to process duration. In our approach, using the Pontryagin Maximum Principle and numerical solutions we describe the optimal feeding policy that maximizes biomass productivity and minimizes the cost duration of the process. We show that a singular regime is possible, in which cells grow at a slow rate to prevent acetate formation. If the cost associated to the process is too high, only bang-bang solutions are allowed.
Journal of Mathematical Biology, 2021
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Journal of Differential Equations, 2020
The periodically forced light-limited Droop model represents microalgae growth under co-limitatio... more The periodically forced light-limited Droop model represents microalgae growth under co-limitation by light and a single substrate, accounting for periodic fluctuations of factors such as light and temperature. In this paper, we describe the global dynamics of this model, considering general monotone growth and uptake rate functions. Our main result gives necessary and sufficient conditions for the existence of a positive periodic solution (i.e. a periodic solution characterized by the presence of microalgae) which is globally attractive. In our approach, we reduce the model to a cooperative planar periodic system. Using results on periodic Kolmogorov equations and on monotone sub-homogeneous dynamical systems, we describe the global dynamics of the reduced system. Then, using the theory of asymptotically periodic semiflows, we extend the results on the reduced system to the original model. To illustrate the applicability of the main result, we include an example considering a standard microalgae population model.
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Papers by Carlos Enrique Labastida Martínez