A. pullulans을 이용한 pullulan생산의 PH영향의 모델링 및 최적화

이중헌, 신성의, 권규혁, 김선일, 차월석

조선대학교 화학공학과

The modeling and optimization of pH effect on the pullulan production using A. pullulans

Jung-heon Lee, Sung-Eui Shin, Kyu-hyuk Kwon, Sun-il Kim, Wol-suk Cha

Department of Chemical Engineering, Chosun University, Kwangju, KOREA

The effect of pH on the cell growth and pullulan production has been studied. The morphology of A. pullulanse was changed with the change of fermentation pH and the production of pullulan was also changed. From the experiment, the optimal pH for cell growth and pullulan production has been studied. The optimal pH for the cell growth was 6.9 and that for the pullulan production was 3.9. The optimal pH profile was calculated with Pontryagins minimum principle.

Introduction

Pullulan is one of the polysaccharide composed of □-1,6-linked glucose and used for the edible film and other biomaterials. Pullulan is synthesized by A. pullulans under cell growth conditions. Pullulan has been used as raw materials for food, medical, printing, coating, and packaging film due to the excellent properties and its stability. The usage of pullulan will also be furthur expanded.

The effect of cell culture condition on the production of pullulan has been studied widely in respect to pH, DO, temperature, nitrogen source, carbon to nitrogen source ratio. Lee et al. studied the effect of initial pH on the production of pullulan. The optimum initial pH was found to maximize the pullulan production. Since cells produces acid by products during fermentation, the pH of fermentor decreased continuously. Kim et al. studied the effect of pH on the production by controlling the pH at a constant value.

The production of secondary metabolites such as polysaccharide, amino acids, and proteins is different from cell mass production. The optimal condition for product formation is usually different from that of cell growth. Therefore, it is necessary to control the environmental condition optimal for cell growth and product formation. Since the optimal pH for cell growth is different from that of product formation, the systematic approach is necessary to compute optimal control profils and to maximize the pullulan production with A. pullulanas.

In this research, the mathematical model will be developed by reflecting the pH variation and used for the calculation of optimal pH profiles.

Model Development

From the experimental results, the effect of pH on cell growth and pullulan formation was studied. The glucose effect was also studied as the effect of nutrient concentration. The mathematical models with three variables such as cell mass, glucose, and pullulan, were developed by considering the pH and glucose effects.

[eqn: {dX over dt}{}=□X~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)]              [eqn: {dS over dt}{}={-}{{□X}over{Y_X/S}}{-}{{□X}over{Y_P/S}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)]                [eqn: {dP over dt}{}=□X{}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(3)]               where X is the cell concentration, S is the substrate concentration, P is the pullulan concentration, and V is the fermentor volume. The specific growth, and product formation rates, □and □ are functions of substrate and pH. YX/S and YP/S are cell mass and pullulan yields from glucose, respectively.

The YX/S and YP/S were observed to be 0.41 and 0.57, respectively. The effect of pH on the cell growth and pullulan formation was observed from the experimental data. With the various pH, the cell mass profile and the pullulan profile were shown in Figure 1(a,b). Since the optimal pH for cell growth was different from that of pullulan formation, the pullulan production was changed with the different pH. The cell mass was highest at pH 7 and the pullulan formation was highest at pH 4. The specific growth rate with the different pH was calculated and shown in Figure 2. The specific growth rate was expressed as a polynomial function of pH and the correlation was expressed as following equation.

[eqn: □{}=(0.1142-0.066×PH+0.01797×PH{}^2{}-{}0.001315×PH{}^3{})({S}over{0.2+S} )~~~~~~~~(4)]     The specific production rate was calculated from Figure 1 and was also expressed as a polynomial function of pH(Figure 2).

[eqn: □{}=(-0.2634+0.2179×PH+0.04304×PH{}^2{}+{}0.002593×PH{}^3{})( {S}over{0.2+S})~~~~~(5)]

Since the optimal pH for cell mass is different from that of pullulan formation, it is necessary to calculate optimal pH profiles for the maximal production of pullulan. The optimization algorithm was proposed to calculate optimal pH profiles.

Application of Minimum Principles

Minimum principle was proposed to calculate optimal pH profiles. From the state equation, the Hamiltonian was calculated as following equation.

[eqn: H{}={}□_1{}{dot X}+□_2{dotS}+□_3{dotP}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(6)]

The adjoint variables were calculated from the partial derivation of Hamiltonian with respect to state variables and represented by the following equations. The final conditions of adjoint variable were calculated with transversality conditions.

[eqn: -{dot□_1}={∂H OVER ∂X}={□_1}□+{□_2}LEFT( -{□ over Y_{X/S}}-{□ over Y_{P/X}} RIGHT)+{□_3}□ `````````~~~~~~~{□_1}(t_{f}{})=0~~~~~(7)]

[eqn: -{dot□_2}={∂H OVER ∂S}={□_1}□'X+{□_2} LEFT ( -{□' over Y_{X/S}}-{□' over Y_{P/X}} RIGHT )X+{□_3}□'X {}`````{} }{□_2}(t_{f}{})=0~~~~~(8)]

[eqn: -{dot□_2}={∂H OVER ∂P}=0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{□_3}(t_{f}{})=-1~~~(9)]

where  denotes the derivation respect to substrate concentration. The optimal pH profiles were calculated to satisfy the partial derivation of Hamiltonian with respect to pH made 0.

[eqn: {∂H} over {∂[PH]}=0={□_1}{{∂□} over {∂[PH]}}-{□_2} LEFT [ {1 over Y_{X/S}}{{∂□} over {∂[PH]}}+{1 over Y_{P/S}}{{∂□} over {∂[PH]}} RIGHT ]+{□_3}{∂□} over {∂[PH]}~~~~~~(10)]

The pH profiles was calculated with gradient iteration algorithm

Results

The optimal pH control profiles were calculated with the different final time. As the increase of final time, the performance increased to a maximum value. When the initial glucose concentration was 50 g/l, the maximum pullulan concentration achieved was 15.3 g/l which is higher than constant pH control (14.8 g/l). The optimal pH started at 6.9 optimal for cell growth and ended at 4.9 optimal for pullulan production.

References

1. J.H. Lee, I.Y. Lee, M.K. Kim, and Y.H. Park, Optimal pH control of batch processes for production of curdlan by Agrobacterium species, Journal of Industrial Microbiology & Biotechnology , 23, 143-148, 1999.

2. Kun Na, Ki-Young Lee, and Don-Hee Park, Effects of pH and Nitrogen Sources on the Pullulan Production by A. pullulans, Korean J. Biotechnol. Bioeng., 11: 497-503, 1996.

3. JH Kim, JY Hui, ML Kim, JH Lee, and SK Kim, Effect of pH on the Pullulan Production with A. pullulans, 2000 Kor. Biotechnology Symposium, P224:287-290, 2000.  .

4. K Ono, N Yasuda, and S. Ueda, Effect of pH on Pullulan Elaboration by A. pullulans S-1, Agric. Biol. Chem. 41:2113-2118, 1977.