Cybernetic structured modeling of the production of polyhydroxyalkanoates by Alcaligenes Eutrophus

Cybernetic structured modeling of the production of polyhydroxyalkanoates by Alcaligenes Eutrophus

L. FERRAZ, A. BONOMI, R. A. M. PICCOLI, F. M. KAPRITCHKOFF, W. SCHMIDELL, R. C. P. ALLI, C. Y. TAKANO, M. N. MATTOS, V. OLIVEIRA and V. FONTOLAN

Agrupamento de Biotecnologia, Divisão de Química, Instituto de Pesquisas Tecnológicas do Estado de São Paulo S/A, C. P. Box 0141, 01064-970, São Paulo - SP, Brazil,

Phone: [phone], Fax: [phone]

E-mail: [e-mail]

(Received: January 19; 1999; Accepted: April 28, 1999)

Abstract - This paper presents a cybernetic structured mathematical model developed for the fermentation step of the process of production of the copolymer of polyhydroxyalkanoates by the bacteria Alcaligenes eutrophus. This process is performed in two different fermentation stages. The first emphasizes the growth of the microorganism in a batch operation without substrates limitations, while in the second, the focus is on copolymer production by a fed-batch operation in the absence of the nitrogen source. This paper presents the results of the treatment of experimental data and of preliminary parameter estimation. The fitting of the proposed model to the experimental data of a standard experiment showed a good agreement.

Keywords: Production of polyhydroxyalkanoates, mathematical modeling, cybernetic model.

INTRODUCTION

Environmental conservation is currently an aspect of great importance for large sectors of human society and for the international scientific community. Among the numerous environmental problems faced by urban centers, it is possible to point to the large amount of plastic waste, originally produced by the petrochemical industries, which is accumulating at waste disposal sites due to degradation difficulties. Therefore, it is necessary to develop alternative plastic materials, due to the high cost of selective garbage collection and plastic recycling.

The polyhydroxyalkanoates (PHAs) are polymers that are accumulated by several bacterial species, cultivated in a special unbalanced medium as intracellular granules functioning as energy and carbon storage. They are a viable alternative for the production, on an industrial scale, of biodegradable plastics from renewable raw materials. Linear co-polyesters of b-hydroxybutyric (HB) and b-hydroxyvaleric (HV) acids have been produced and commercialized by the English ICI since 1988. Presently the American Monsanto holds the legal rights for this patent.

To improve the commercial viability of copolymer production P(HB-co-HV), it is necessary to study the optimization of this process. The first step of this optimization is the formulation of a mathematical model that represents the microbial cultivation of the proposed system, covering a large spectrum of values for the state and operating variables.

Cybernetic modeling, one of the categories of the so-called structured models (those that consider intracellular components in their formulation), is based on the hypothesis that, although the detailed model of the regulating processes occurring inside the microbial cell is extremely complex, these processes can be interpreted as a reflection of optimum usage strategies for commonly limited storage materials (Kompala et al., 1984).

The option to use a cybernetic model to represent the phenomenology of this process was based on the notorious heterogeneity of the cellular material present in the bacteria as a result of different enzymatic induction and repression strategies, as well as the activation and inhibition of these enzymes. In the mathematical model, the total cellular mass corresponds to the polymer and the active biomass, while the active biomass represents all the intracellular material except the polymeric fraction produced.

MATERIALS AND METHODS

Microorganism

All the experiments were performed utilizing a strain of the bacteria Alcaligenes eutrophus, DSM 545, maintained in liquid nitrogen or lyophilized at the IPT's Culture Collection. The microbial strain was maintained by replications of the master strain in tubes with nutrient agar preserved in the refrigerator.

Culture Media

Inoculum preparation was performed in two stages. The first stage, to reactivate the microorganism, used nutrient medium with 5.0 g.l^-1 of peptone and 3.0 g.l^-1 of meat extract. The second stage, to adapt the microorganism to growth conditions, used mineral medium with 3.5 g.l^-1 of Na₂HPO₄, 1.5 g.l^-1 of KH₂PO₄, 3.0 g.l^-1 of (NH₄)₂SO₄, 0.06 g.l^-1 of ammonium ferric citrate, 0.01 g.l^-1 of CaCl₂.2H₂O, 0.20 g.l^-1 of MgSO₄.7H₂O, 10.0 g.l^-1 of glucose and 1.0 ml.l^-1 of a trace element solution. The composition of the mineral medium, for growth in the bioreactor, was 1.29 g.l^-1 of KH₂PO₄, 1.83 g.l^-1 of (NH₄)₂SO₄, 0.05 g.l^-1 of ammonium ferric citrate, 0.02 g.l^-1 of CaCl₂.2H₂O, 0.55 g.l^-1 of MgSO₄.7H₂O, 15.0 g.l^-1 of glucose, 15.0 g.l^-1 of fructose and 2.0 ml.l^-1 of a trace element solution. The mineral medium added during the fed-batch operation, for polymer accumulation, was composed of 51.3 g.l^-1 of glucose, 51.3 g.l^-1 of fructose and 45.6 g.l^-1 of propionic acid. For the mineral medium, in both phases of the process in the bioreactor, component concentrations were variable and the values previously reported refer to the standard experiments.

Analytical Methods

In the samples periodically removed from the bioreactor, the following analyses were performed: cell mass concentration (dry-weight method), intracellular polymer content in HB and HV units (gas chromatography), sugar concentration (liquid chromatography – HPLC), nitrogen concentration (Kjeldahl method) and acids (occasionally present) concentration (gas chromatography) (Bonomi et al., 1996).

Experimental Conditions

The inoculum was prepared in two stages in a rotary shaker (New Brunswick G-25) at 30°C and 200 rpm, each stage lasting 15 hours. All the experiments in the bioreactor were performed at a temperature of 32°C and with the pH controlled at 7.0, in a 14 L Braun Biostat ED, with the dissolved oxygen controlled and all the operating variables monitored on line.

RESULTS AND DISCUSSION

The strategy followed to formulate the mathematical model for this fermentation process was based on the performance of three types of experiments: experiments to model the growth, experiments to model the accumulation and standard experiments. The growth modeling experiments aimed at studying the first phase of the process (batch) under different conditions of growth medium availability, generating different forms of microbial growth. The accumulation modeling experiments aimed at studying the second phase of the process (fed-batch) under different conditions of substrate availability to the cultivation medium, bringing about different accumulation profiles. The standard experiments were performed to test the reproducibility of the prepared inoculum and of the fermentation process itself, with the purpose of determining the pure experimental error of the process state variables. All the experiments performed are described in detail in Ferraz (1998). Figure ¹ presents the experimental values of total biomass, sugars and PHB concentrations obtained in a standard experiment.

Figure 1: Standard Experiment. (< ) experimental values; (---) preliminary fitting; (^___) final fitting. X_t ... total biomass concentration; P₁ ... PHB concentration; S_c ... sugar concentration.

Mathematical Model Formulation

All the experimental data were treated on a mass basis, in order to consider the perturbations caused by feedings, sample withdrawals and evaporation (Takano et al., 1997).

A cybernetic model to represent the process was proposed, taking into account the phenomena related to the kinetics of active biomass growth and P(HB-co-HV) production, observed while conducting the programmed experiments. The proposed cybernetic modeling for the synthesis of PHB has already been presented in technical literature in a simpler process than the one considered in this paper (Yoo and Kim, 1994; Bonomi et al., 1996). Equations 1 to 25 below represent the complete cybernetic model proposed.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

This proposed cybernetic model contains 53 parameters – 14 fixed ones (n₂₄, n₃₄, Y_P1S!, K_mS1, Y_P1S2, K_mS2, K_mS3, Y_P1S4, Y_P2S4, K_mS4, S₄*, Y_P1S5, Y_P2S5 and K_mS5) and 39 adjustable ones.

Preliminary Parameter Estimation

A preliminary estimation of the set of adjustable model parameters was achieved based on model linearizations and simplifications and using the treated experimental data. This methodology is presented in detail for the modeling of the fermentation step of the vitamin C production process in Bonomi et al. (1993). The resulting set of parameters can be found in Ferraz (1998). Figure 1 illustrates the results of the model simulation with the preliminarily adjusted parameters for one of the standard experiments.

Final Parameter Estimation

The model parameters were estimated by applying the flexible geometric simplex method proposed by Nelder and Mead and known as the flexible polyhedron search (Himmelblau, 1972). For a more effective application of this technique, the results of the preliminary search were used as the initial guess. Figure 1 illustrates the model simulation results with the final adjusted parameters for one of the standard experiments.

CONCLUSIONS

The results obtained with the model simulation for the condition of a standard experiment make it possible to conclude that the proposed model adequately represents the characteristic phenomenology of the two-phase process. Nevertheless, it is still not possible to assume that this model fits all the experimentally tested conditions well. For this purpose, i.e., to guarantee model validity, it will be necessary to do an overall fit of the model parameters to the entire set of experiments performed, followed by a statistical analysis of the model simulations, comparing the results with the estimated pure experimental error.

ACKNOWLEDGMENTS

The results reported in this paper are part of the project "Development of Advanced Technology for the Automation and Control of the Polyhydroxyalkanoates Copolymer Production by Fermentation", sponsored by CNPq under PADCT Program Agreement 62.0199/94.6. The authors are grateful for CNPq support. One of the authors (AB), who has been granted a research fellowship, is also grateful for the support of CNPq.

NOMENCLATURE

E₁ specific level of the "key" enzyme for growth (g.g^-1)

E₂ specific level of the "key" enzyme for biopolymer accumulation (g.g^-1)

F total volumetric feed rate (l.h^-1)

F₁ volumetric substrates feed rate (l.h^-1)

F₂ volumetric feed rate for pH control with NH₄OH (l.h^-1)

K₁₃ saturation parameter for growth rate by nitrogen concentration (g.l^-1)

K₁₃^E saturation parameter for enzyme E₁ production rate by nitrogen concentration (g.l^-1)

K₁₄ saturation parameter for growth rate by oxygen concentration (mg.l^-1)

K₁₄^E saturation parameter for enzyme E₁ production rate by oxygen concentration (mg.l^-1)

K_1C saturation parameter for growth rate by carbon sources concentration (g.l^-1)

K_1C^E saturation parameter for enzyme E₁ production rate by carbon sources concentration (g.l^-1)

K_1Ci inhibition parameter for growth rate by carbon sources concentration (g.l^-1)

K₂₄ saturation parameter for PHB production rate by oxygen concentration (mg.l^-1)

K₂₄^E saturation parameter for enzyme E₂ production rate by oxygen concentration (mg.l^-1)

K_24i inhibition parameter for PHB production rate by oxygen concentration (mg.l^-1)

K_2C saturation parameter for PHB production rate by carbon sources concentration (g.l^-1)

K_2C^E saturation parameter for enzyme E₂ production rate by carbon sources concentration (g.l^-1)

K_2Ci inhibition parameter for PHB production rate by carbon sources concentration (g.l^-1)

K₃₄ saturation parameter for PHV production rate by oxygen concentration (mg.l^-1)

K_34i inhibition parameter for PHV production rate by oxygen concentration (mg.l^-1)

K₃₅ saturation parameter for PHV production rate by propionic acid concentration (g.l^-1)

K_35i inhibition parameter for PHV production rate by propionic acid concentration (g.l^-1)

K_La oxygen volumetric transfer coefficient (h^-1)

K_mS1 saturation parameter for glucose maintenance consumption rate by glucose concentration (g.l^-1)

K_mS2 saturation parameter for fructose maintenance consumption rate by fructose concentration (g.l^-1)

K_mS3 saturation parameter for nitrogen maintenance consumption rate by nitrogen concentration (g.l^-1)

K_mS4 saturation parameter for oxygen maintenance consumption rate by oxygen concentration (mg.l^-1)

K_mS5 saturation parameter for propionic acid maintenance consumption rate by propionic acid concentration (g.l^-1)

K_P inhibition parameter for PHB and PHV production rate by polymer content of microbial cells (g.g^-1)

m_S1 glucose maintenance consumption rate (g.g^-1.h^-1)

m_S2 fructose maintenance consumption rate (g.g^-1.h^-1)

m_S3 nitrogen maintenance consumption rate (g.g^-1.h^-1)

m_S4 oxygen maintenance consumption rate (mg.g^-1.h^-1)

m_S5 propionic acid maintenance consumption rate (g.g^-1.h^-1)

n₂₄ inhibition parameter for PHB production rate by oxygen concentration (mg.l^-1)

n₃₄ inhibition parameter for PHV production rate by oxygen concentration (mg.l-1)

n_P inhibition parameter for PHB and PHV production rate by polymer content of microbial cells

P₁ PHB concentration (g.l^-1)

P₂ PHV concentration (g.l^-1)

R₁ growth rate (g.l^-1.h^-1)

R₂ PHB production rate (g.l^-1.h^-1)

R₃ PHV production rate (g.l^-1.h^-1)

r_E1 specific rate of enzyme E₁ production (g.g^-1.h^-1)

r_E2 specific rate of enzyme E₂ production (g.g^-1.h^-1)

S₁ glucose concentration (g.l^-1)

S₂ fructose concentration (g.l^-1)

S₃ ammonium ion concentration (g.l^-1)

S₄ dissolved oxygen concentration (mg.l^-1)

S₄* equilibrium concentration of dissolved oxygen (mg.l^-1)

S₅ propionic acid concentration (g.l^-1)

S_C total concentration of carbon sources (g.l^-1)

u₁ cybernetic variable for control of the synthesis mechanism of enzyme E₁

u₁* maximum value of the cybernetic variable for control of the synthesis mechanism of enzyme E₁

u₂ cybernetic variable for control of the synthesis mechanism of enzyme E₂

V reactor volume (l)

v₁ cybernetic variable for control of the activity of enzyme E₁

v₂ cybernetic variable for control of the activity of enzyme E₂

X total biomass concentration (g.l^-1)

X_r active biomass concentration (g.l^-1)

Y_P1S! stoichiometric factor for glucose to PHB conversion (g.g^-1)

Y_P1S2 stoichiometric factor for fructose to PHB conversion (g.g^-1)

Y_P1S4 stoichiometric factor for oxygen to PHB conversion (g.mg^-1)

Y_P1S5 stoichiometric factor for propionic acid to PHB conversion (g.g^-1)

Y_P2S4 stoichiometric factor for oxygen to PHV conversion (g.mg^-1)

Y_P2S5 stoichiometric factor for propionic acid to PHV conversion (g.g^-1)

Y_XrS1 yield factor for glucose to active biomass conversion (g.g^-1)

Y_XrS2 yield factor for fructose to active biomass conversion (g.g^-1)

Y_XrS3 yield factor for nitrogen to active biomass conversion (g.g^-1)

Y_XrS4 yield factor for oxygen to active biomass conversion (g.mg^-1)

Y_XrS5 yield factor for propionic acid to active biomass conversion (g.g^-1)

a₁ maximum specific production rate of enzyme E₁ (g.g^-1.h^-1)

a₁* basal specific production rate of enzyme E₁ (g.g^-1.h^-1)

a₂ maximum specific production rate of enzyme E₂ (g.g^-1.h^-1)

a₂* basal specific production rate of enzyme E₂ (g.g^-1.h^-1)

b₁ denaturation rate of enzyme E₁ (h^-1)

b₂ denaturation rate of enzyme E₂ (h^-1)

m specific total biomass production rate (h^-1)

m₁ specific growth rate parameter (g.g^-1.h^-1)

m_1,max maximum specific growth rate (h^-1)

m₂ parameter of specific rate of PHB production (g.g^-1.h^-1)

m2_,max maximum specific PHB production rate (h^-1)

m3 parameter of specific rate of PHV production (g.g^-1.h^-1)

m_3,max maximum specific PHV production rate (h^-1).

REFERENCES

Bonomi, A., Augusto, E.F.P., Barbosa, N.S., Magossi, L.R. and Santos, A.L., Unstructured Model Proposal for the Microbial Oxidation of D-Sorbitol to L-Sorbose. Journal of Biotechnology, vol. 31, pp.39-59, 1993.

Bonomi, A., Piccoli, R.A.M., Ferraz, L., Kapritchkoff, F.M., Alli, R.C.P., Mattos, M.N., Oliveira, V., Takano, C.Y. and Fontolan, V., Processo de Produção de Plástico Biodegradável Por Via Fermentativa - Estudos Preliminares Visando a Modelagem Matemática. Paper to be published in the Annals of the V SHEB, Maringá, PR, December 1996.

Ferraz, L., Document for the Qualifying Exam, MSc Program in Chemical Engineering, Escola Politécnica, Universidade de São Paulo, 1998.

Himmelblau, D.M., Applied Nonlinear Programming. McGraw-Hill, New York, 1972.

Kompala, D.S., Ramkrishna, D., Tsao, G.T., Cybernetic Modeling of Microbial Growth on Multiple Substrates. Biotechnology and Bioengineering, vol. 26, pp.1272-1281, 1984.

Takano, C.Y., Ferraz, L., Piccoli, R.A.M., Kapritchkoff, F.M. and Bonomi, A., Correção de Dados Experimentais para Cálculo de Velocidades Específicas e Coeficientes de Rendimento em Processos Fermentativos. In: II COBEQ-IC, Uberlândia, MG. Annals, pp. 28-31, 1997.

Yoo, S. and Kim, W., Cybernetic Model for Synthesis of Poly-b-hydroxybutyric Acid in Alcaligenes eutrophus. Biotechnology and Bioengineering, vol. 43, pp.1043-1051, 1994.

Publication Dates

• Publication in this collection
  15 Sept 1999
• Date of issue
  June 1999

History

• Accepted
  28 Apr 1999
• Received
  19 Jan 1999