Optimization of polyhydroxyalkanoates bioproduction, based on a cybernetic mathematical model
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ORIGINAL PAPER
Optimization of polyhydroxyalkanoates bioproduction, based on a cybernetic mathematical model Rosane Moniz Piccoli1 · Luís Henrique Camargo Quiroz2 · Agenor de Toledo Fleury2 · Valter Oliveira1 · Natália Bonifácio Marteleto1,3 · Antonio Bonomi4 Received: 10 October 2019 / Revised: 4 June 2020 / Accepted: 9 July 2020 © Associação Brasileira de Engenharia Química 2020
Abstract This work discusses the optimization of the biopolymer PHAs production by Ralstonia eutropha, in a bioreactor carried out under fed-batch mode. Although the optimization of fed-batch fermentations involves the manipulation of the substrate feed rate, which generates a singular optimal control problem, the optimal trajectory can be also set by adjusting small segments by non-linear programming. The cybernetic structured mathematical model used here in is described by a system of 12 differential equations; the strategy involves the maximization/minimization of an Objective Function considering the model as a set of implicit constraints and the discretization of the manipulated variables (substrate feed rates). The sequential quadratic program method is used to solve the optimization problem. PHAs productivity is taken as the objective function and its results are compared to those documented in the literature. Keyword Optimization of bioprocesses · Polyhydroxyalkanoates · Biodegradable plastic List of symbols α1 Specific enzyme 1 synthesis rate (1/h) 𝛼1∗ Specific enzyme 1 constitutive synthesis rate (1/h) α2 Specific enzyme 2 synthesis rate (1/h) 𝛼2∗ Specific enzyme 2 constitutive synthesis rate (1/h) β1 Specific decay rate of enzyme 1 (1/h) β2 Specific decay rate of enzyme 2 (1/h) μ1,max Maximum specific rate of active biomass formation (1/h) μ2,max Maximum specific rate of PHB product formation (1/h)
* Rosane Moniz Piccoli [email protected] 1
IPT-Instituto de Pesquisas Tecnológicas do Estado de SP, BIONANO-Núcleo de Bionanomanufatura, LBILaboratório de Biotecnologia Industrial, C.P. 0141, CEP 01064‑970 São Paulo, SP, Brasil
2
USP-Universidade de São Paulo, Escola Politécnica, Departamento de Engenharia Mecânica, CEP 05508‑030 São Paulo, SP, Brasil
3
USP-Programa de Pós-Graduação Interunidades em Biotecnologia, CEP 05508‑900 São Paulo, SP, Brasil
4
Laboratório Nacional de Biorrenováveis (LNBR), Centro Nacional de Pesquisa Em Energia E Materiais (CNPEM), CEP 13083‑970 Campinas, SP, Brasil
μ3,max Maximum specific rate of PHV product formation (1/h) E1 Enzyme 1 concentration (g/L) E2 Enzyme 2 concentration (g/L) F Global flow rate (g/h) (*) F1 Feed flow rate (g/h) F2 PH control flow rate (g/h) (**) KmS1 Limitation constant of glucose in cellular maintenance (g/L) KmS2 Limitation constant of fructose in cellular maintenance (g/L) KmS3 Limitation constant of nitrogen in cellular maintenance (g/L) KmS4 Limitation constant of oxygen in cellular maintenance (mg/L) KmS5 Limitation constant of propionic acid in cellular maintenance (g/L) kL a Oxygen mass transfer coefficient (1/h) KP Inhibitio
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