Analysis of bioreactor experimental data by the application of metabolic pathway stoichiometry to polyhydroxyalkanoate production by Alcaligenes Eutrophus

Analysis of bioreactor experimental data by the application of metabolic pathway stoichiometry to polyhydroxyalkanoate production by

Alcaligenes Eutrophus

R.AM. PICCOLI, J.G.C. GOMEZ, A. BONOMI, L. FERRAZ, F.M. KAPRITCHKOFF, 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, P. P. O. Box 0141, 01064-970, São Paulo - SP, Brazil, Phone: [phone], Fax: [phone], E-mail: [e-mail]

(Received: January 19, 1999; Accepted: April 27, 1999)

Abstract - In biochemical processes, the stoichiometry can be the result of macroscopic balances (where the microorganism is specified by the elementary composition and only the chemical reactions of the conversion process are considered) or the balances of the metabolic pathway, where biochemical knowledge available for metabolic reactions, in addition to the chemical characteristics of the system, are considered. It is possible to identify several linear relationships among the conversion rates in these processes. While several rates are measured, others can be calculated. If a calculated conversion rate is also measured, measurement errors or errors of the described model can be detected or even diagnosed by comparing these values, and accurate estimates can be obtained by combining them.

Keywords: Polyhydroxyalkanoate production, metabolic modeling, measurement errors.

INTRODUCTION

Polyhydroxyalkanoates are a class of biodegradable polymers that has been widely studied during the last ten years. The poly-3-hydroxybutyrate-co-3-hydroxyvalerate copolymer (P3HB-co-P3HV) has received particular attention as a possible substitute for the conventional plastics produced from petroleum due to its desirable properties. The Alcaligenes eutrophus bacterium was selected for the production of these polymers as it is capable of accumulating a large amount of polymer (70 - 80%) with a high molecular weight and no synthesis of any byproducts.

The synthesis of the copolymer (3PHB-co-3PHV) can be outlined by a set of biochemical equations, as follows:

(1) Entner-Doudoroff pathway for the carbohydrate oxidation:

GLU + FRU + ADP + Pi + 3NAD⁺ + NADP⁺ + 2CoASH ® 2AcCoA + 3NADH + 2CO₂ +ATP + NADPH

(2) a-oxidation of the propionic acid not utilized by the PHV synthesis:

PAc + 3NAD⁺ + CoASH + ATP ® AcCoA + 3NADH +CO₂ +AMP +PPi

(3) 3HB-CoA synthesis:

2AcCoA + NADPH ® 3HB-CoA + NADP⁺ +CoASH

(4) 3HV-CoA synthesis:

AcCoA + PAc + ATP + NADPH ® 3HV-CoA + NADP⁺ +AMP + PPi

(5) 3HB-CoA or 3HV-CoA polymerization:

3HB-CoA or 3HV-CoA + P(3HB-co-3HV)n ® CoASH + P(3HB-co-3HV)n+1

(6) Oxidation of the acetil-coA not utilized during the P3HB-co-P3HV synthesis:

AcCoA + 3NAD⁺ + NADP⁺ + ADP + Pi ® 2CO2 + 3NADH + NADPH + ATP

(7) Reoxidation of coenzymes by oxygen:

2NADH + O₂® 2NAD+ +2H₂O

(8) NADPH reduction by the action of the transhydrogenase enzyme:

NADH + NADP⁺ + ATP ® NAD⁺ +NADPH + ADP +Pi

The development of the metabolic model is quite useful to validate the metabolic networks and consequently the flux distribution analysis, where key branch points can be identified and maximum theoretical yields can be determined.

MATERIALS AND METHODS

Microrganism

The bacteria Alcaligenes eutrophus DSM545, acquired from the DSM Collection (Deutsche Sammlung vor Mikrorganismen und Zellkulturen) and preserved in liquid nitrogen, was used in the experiments performed.

Culture Medium

Mineral medium for growth:

KH₂PO₄ – 1.29 g/L;

(NH₄)₂SO₄ – 1.83 g/L;

Ammonium Ferric Citrate – 0.06 g/L;

CaCl₂.2H₂O – 0.01 g/L;

MgSO₄.7H₂O – 0.55 g/L;

Glucose – 15.0 g/L;

Fructose – 15.0 g/L;

Trace elements solution – 2.0 ml/L.

Mineral medium for biopolymer accumulation: different concentrations of glucose, fructose and propionic acid were added to the system in a fed-batch operation.

Analytical Methods*

Cell Mass Concentration:

Dry Weight Method

Intracellular 3HB and 3HV Units: Gas Chromatography

Sugars Concentration: High Performance Liquid Chromatography

Nitrogen Concentration: Kjeldahl Method

Acids Concentration: Gas Chromatography * (Bonomi et al.,1996)

Experimental Conditions

Inoculum Production: Two 15h runs in a rotary shaker (New Brunswick G-25), 30°C, 200rpm

Bioreactor: 14L Braun Biostat ED

Working Volume @ 7L

Temperature = 32°C

pH = 7.0 (controlled)

Agitation Speed: 300 – 1200 rpm

Aeration Flow Rate: 4.0 L/min.

Mathematical Resolution Method

Once the metabolic reactions are known, they can be expressed as a linear combination of all the reactions in the metabolic pathway. If there are J linearly independent reactions for I chemical species, the reactions can be mathematically expressed by

where a_ji is the stoichiometric coefficient of the ith chemical species in the jth metabolic reaction. The species considered in the metabolic pathway include intermediate components not accumulating in the pathway, as well as reagents and products of the overall reaction (Tsai & Lee, 1988). Thus, equation (1) can be written in matrix form:

A. r = 0 (2)

where A is the stoichiometric matrix and r is the vector of the conversion rates.

From the vectors of the measured rates (r_m) and the unmeasured rates (possibly calculated) (r_c), the matrix can be divided as follows:

A_c. r_c + A_m. r_m = 0 (3)

The vector of the unmeasured rates can be expressed in terms of the measured rates as follows:

r_c = - pinv (A_c).A_m.r_m (4)

where pinv (A_c) is the pseudo-inverse matrix A_c.

Substituting equation (4) into (3):

(A_m –A_c. pinv(A_c). A_m). r_m = 0 (5)

where the term (A_m –A_c.pinv(A_c).A_m) is denominated redundancy matrix R (Van der Heijden et al., 1994). The rank (R) should be larger than zero to facilitate he balance of the conversion rates. This matrix indicates the possibility of calculating unmeasured rates of r_c.

Thus, the expression R.r_m is replaced by an expression that contains only the balanced measured rates (r_m) and the redundancy matrix whose lines and columns related to the unbalanced rates were removed.

R'.r_m = e (6)

The residual e from the presence of measurement errors used to calculate the statistical test h with a Chi-square distribution is

h=e^T.P_e-1.e (7)

where P_e-1 is the covariance matrix of the e elements. Values of h provide the required confidence level (proof of the occurrence of measurement errors), with degrees of freedom which are equal to the rank of matrix R'.

RESULTS

Production of the intracellular P3HB-co-P3HV copolymer is performed in two different phases. The first phase is characterized by the growth of the microrganism, which results in high active biomass concentrations (Xr), and a second phase results in the accumulation of the intracellular copolymer fraction, favored by the unbalancing of the medium that halts cell multiplication. Glucose and fructose are the carbon sources in both phases, and propionic acid is the carbon source added in the second phase as a precursor of the 3HV units of the copolymer.

To evaluate the fitting of this metabolic model to experimental data, four experiments were analyzed (Figure 1). All these experiments were programmed to obtain 12 g/L of active biomass (Xr) in the first phase (batch mode with 7 liters of medium). The second phase (conducted in fed-batch mode with a constant feed rate of 120 ml/h) had different concentrations of carbon sources, as shown below:

Experiment 1 - 50.0g/L of glucose, 50.0g/L of fructose, 45.0g/L of propionic acid;

Experiment 2 - 50.0g/L of glucose, 50.0g/L of fructose, 67.5g/L of propionic acid;

Experiment 3 - 85.0g/L of glucose, 85.0 g/L of fructose, 76.5g/L of propionic acid;

Experiment 4 - 100.0g/L of glucose, 100.0g/L of fructose, 45.0g/L of propionic acid;

Figure 1: Experimental data on active biomass concentration (A), amount of PHB (B) and PHV (C) produced, amount of glucose and fructose (D) , Oxygen (E) and propionic acid (F) consumed, obtained from Experiment 1 ( n ), Experiment 2 ( ¨ ), Experiment 3 ( l ) and Experiment 4 ( ¡ ).

From the experimental results obtained in the copolymer accumulation phase, the specific rates of substrate consumption and production of PHB and PHV units (measured in mmol/gh) were calculated (Tables ¹ to ⁴). A variation coefficient (standard deviation/measured rate) equal to 12% was associated with the vector of the measured rates.

Table 2: Experiment 2 (h = 0.82) – Confidence level equal to 33.6% (2 degrees of freedom)

Table 3: Experiment 3 (h = 0.21) – Confidence level equal to 9.9% (2 degrees of freedom)

The MACROBAL 2.02 software (Hellinga, 1997) was employed to give the estimated rates based on the proposed model, as well as the new standard deviation associated with these estimates and the statistical parameter h.

CONCLUSION

By observing Tables ¹ to ⁴, it is possible to conclude that the proposed metabolic model fits well with the experimental data for the different situations analyzed at a maximum confidence level of 34%. Another conclusion derived from the results is that large errors in the different measurements do not exist. Furthermore, the formation of byproducts can be discarded, since the metabolic model used, which fits well with the experimental data, does not anticipate this formation.

In the situation analyzed, an increase in the accuracy of some measures (last column of Tables ¹ to ⁴) was insured as only five measured rates were necessary for system balancing and six rates were measured.

This approach should still be of great value in the analysis of the P3HB-co-P3HV synthesis, since the model adjusts well to laboratory experiments. Therefore, it will be possible to correlate variations in the behavior of the bacteria as a consequence of factors that cannot be detected by analytical methods (for instance, deficit or excess of energy or reducing power) but that can be estimated based on the proposed model.

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 thank CNPQ and FAPESP for their support.

NOMENCLATURE

AcCoA Acetyl coenzyme A

ATP Adenosine triphosphate

CoASH Free coenzyme A

CO2 Carbon dioxide

FRU Fructose

GLC Glucose

NADH Nicotinamide adenine dinucleotide, reduced

NADPH Nicotinamide adenine dinucleotide phosphate, reduced

O2 Oxygen

PAc Propionic acid

Pi Inorganic phosphate

REFERENCES

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. Annals of the V SHEB, Maringá, PR, december (1996).

Hellinga, C., Macrobal 2.02, Delft University of Technology, The Netherlands (1997).

Van Der Heijden, R.T.J.M., Heijnen, J.J., Hellinga, C., Romein, B. and Luyben, K.Ch.M., Linear Constraint Relations in Biochemical Reaction System: I. Classification of the Calculability and the Balanceability of Conversion Rates. Biotechnol. Bioeng. 43, pp. 3-10 (1994).

Tsai, S.P. and Lee, Y.H., Application of Metabolic Pathway Stoichiometry to Statistical Analysis of Bioreactor Measurement Data, Biotechnol. Bioeng. 32, pp.713-715 (1988).

• 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 produçăo de plástico biodegradável por via fermentativa - Estudos preliminares visando a modelagem matemática. Annals of the V SHEB, Maringá, PR, december (1996).
• Hellinga, C., Macrobal 2.02, Delft University of Technology, The Netherlands (1997).
• Van Der Heijden, R.T.J.M., Heijnen, J.J., Hellinga, C., Romein, B. and Luyben, K.Ch.M., Linear Constraint Relations in Biochemical Reaction System: I. Classification of the Calculability and the Balanceability of Conversion Rates. Biotechnol. Bioeng 43, pp. 3-10 (1994).

Table 1: Experiment 1 (h = 0.13) – Confidence level equal to 6% (2 degrees of freedom)

Table 4: Experiment 4 (h = 0.77) – Confidence level equal to 32% (2 degrees of freedom)

Publication Dates

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

History

• Accepted
  27 Apr 1999
• Received
  19 Jan 1999