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Optimization of polyhydroxyalkanoates bioproduction, based on a cybernetic mathematical model

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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.

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Abbreviations

α1 :

Specific enzyme 1 synthesis rate (1/h)

\(\alpha_{1}^{*}\) :

Specific enzyme 1 constitutive synthesis rate (1/h)

α2 :

Specific enzyme 2 synthesis rate (1/h)

\(\alpha_{2}^{*}\) :

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)

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)

\({\text{k}}_{{\text{L}}}{{\text{a}}}\) :

Oxygen mass transfer coefficient (1/h)

KP :

Inhibition constant 1 of product formation by the content of intracellular polymer

K0 :

Lag phase constant 1 for the beginning of the residual biomass formation phase

K1 :

Lag phase constant 2 for the beginning of the residual biomass formation phase (h)

K1C :

Limitation constant of active biomass formation rate by carbon (g/L)

\({\text{K}}_{{1{\text{C}}}}^{{\text{E}}}\) :

Limitation constant of specific enzyme 1 synthesis rate by carbon (g/L)

K1Ci :

Inhibition constant of active biomass formation rate by carbon (g/L)

K13 :

Limitation constant of active biomass formation rate by nitrogen (g/L)

\({\text{K}}_{13}^{{\text{E}}}\) :

Limitation constant of specific enzyme 1 synthesis rate by nitrogen (g/L)

K14 :

Limitation constant of active biomass formation rate by oxygen (mg/L)

\({\text{K}}_{14}^{{\text{E}}}\) :

Limitation constant of specific enzyme 1 synthesis rate by oxygen (mg/L)

K2C :

Limitation constant of PHB product formation rate by carbon (g/L)

\({\text{K}}_{{2{\text{C}}}}^{{\text{E}}}\) :

Limitation constant of specific enzyme 2 synthesis rate by carbon (g/L)

K2Ci :

Inhibition constant of PHB product formation rate by carbon (g/L)

K24 :

Limitation constant of PHB product formation rate by oxygen (mg/L)

\({\text{K}}_{24}^{{\text{E}}}\) :

Limitation constant of specific enzyme 2 synthesis rate by oxygen (mg/L)

K24i :

Inhibition constant of PHB product formation rate by oxygen (mg/L)

K25i :

Inhibition constant of PHB product formation rate by propionic acid (g/L)

K34 :

Limitation constant of PHV product formation rate by oxygen (mg/L)

K34i :

Inhibition constant of PHV product formation rate by oxygen (mg/L)

K35 :

Limitation constant of PHV product formation rate by propionic acid (g/L)

K35i :

Inhibition constant of PHV product formation rate by propionic acid (g/L)

mS1 :

Glucose consumption coefficient due to maintenance (1/h)

mS2 :

Fructose consumption coefficient due to maintenance (1/h)

mS3 :

Nitrogen consumption coefficient due to maintenance (1/h)

mS4 :

Oxygen consumption coefficient due to maintenance (1/h)

mS5 :

Propionic acid consumption coefficient due to maintenance (1/h)

n24 :

Constant of PHB production inhibition by oxygen

n34 :

Constant of PHV production inhibition by oxygen

nP :

Constant of inhibition of products formation by the content of intracellular polymer

n25i :

Inhibition constant of PHB product formation rate by propionic acid

P1 :

PHB polymer (g/L)

P2 :

PHV polymer (g/L)

S1 :

Glucose concentration in the reactor (g/L)

S2 :

Fructose concentration in the reactor (g/L)

S3 :

Nitrogen concentration in the reactor (g/L)

S4 :

Dissolved oxygen concentration (mg/L)

\({\text{S}}_{4}^{*}\) :

Concentration of dissolved oxygen at 100% saturation (mg/L)

S5 :

Propionic acid concentration in the reactor (g/L)

S1e :

S1 feed concentration (g/L)

S2e :

S2 feed concentration (g/L)

S3e :

S3 feed concentration (g/L)

S5e :

S5 feed concentration (g/L)

\({\text{u}}_{1}^{*}\) :

Maximum value of the cybernetic variable that controls E1 synthesis

V:

Volume (L)

X:

Total biomass (g/L)

Xr :

Active biomass (g/L)

YP1S1 :

Glucose to PHB yield (g/g)

YP1S2 :

Fructose to PHB yield (g/g)

YP1S4 :

Oxygen to PHB yield (g/mg)

YP1S5 :

Propionic acid to PHB yield (g/g)

YP2S1 :

Glucose to PHV yield (g/g)

YP2S2 :

Fructose to PHV yield (g/g)

YP2S4 :

Oxygen to PHV yield (g/mg)

YP2S5 :

Propionic acid to PHV yield (g/g)

YXrS1 :

Glucose to active biomass yield (g/g)

YXrS2 :

Fructose to active biomass yield (g/g)

YXrS3 :

Nitrogen to active biomass yield (g/g)

YXrS4 :

Oxygen to active biomass yield (g/mg)

YXrS5 :

Propionic acid to active biomass yield (g/g)

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Acknowledgments

Rosane A. M. Piccoli thanks the State of São Paulo Research Foundation for the doctoral scholarship.

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Authors and Affiliations

  1. IPT-Instituto de Pesquisas Tecnológicas do Estado de SP, BIONANO-Núcleo de Bionanomanufatura, LBI-Laboratório de Biotecnologia Industrial, C.P. 0141, CEP 01064-970, São Paulo, SP, Brasil

    Rosane Moniz Piccoli, Valter Oliveira & Natália Bonifácio Marteleto

  2. USP-Universidade de São Paulo, Escola Politécnica, Departamento de Engenharia Mecânica, CEP 05508-030, São Paulo, SP, Brasil

    Luís Henrique Camargo Quiroz & Agenor de Toledo Fleury

  3. USP-Programa de Pós-Graduação Interunidades em Biotecnologia, CEP 05508-900, São Paulo, SP, Brasil

    Natália Bonifácio Marteleto

  4. Laboratório Nacional de Biorrenováveis (LNBR), Centro Nacional de Pesquisa Em Energia E Materiais (CNPEM), CEP 13083-970, Campinas, SP, Brasil

    Antonio Bonomi

Authors
  1. Rosane Moniz Piccoli
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  2. Luís Henrique Camargo Quiroz
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  3. Agenor de Toledo Fleury
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  4. Valter Oliveira
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  5. Natália Bonifácio Marteleto
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  6. Antonio Bonomi
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Correspondence to Rosane Moniz Piccoli.

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Piccoli, R.M., Quiroz, L.H.C., de Toledo Fleury, A. et al. Optimization of polyhydroxyalkanoates bioproduction, based on a cybernetic mathematical model. Braz. J. Chem. Eng. 37, 643–652 (2020). https://doi.org/10.1007/s43153-020-00047-5

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