에탄올 생산 균주 Saccharomyces cerevisiae ATCC 248858의 비성장속도에 관한 수학적 모형연구

Investigated of Mathematical Model for the Specific Growth Rate of Ethanol Producing Microorganism, Saccharomyces cerevisiae ATCC 24858

An이ew식과 Aiba삭을 조합하여 에탄올 생산단주인 Saccharomyces cerevisiae ATCC 24858의 비성장속도를 당농도와 에탄올 농도의 함수로 표현하였다. 기침의 저해영향을 받지 않는 최대 당농도 $S_m$은 150 g/L이며 기질의 저해영향은 기질농도 S와 $S-S_{max}$항의 함수로 표현되었다. 최대 비성장 속도 ${\mu}max 는 0.49 hr^{-1}, Monod상수 K_s$는 19 g/L, Andrew식의 기질저해상수 $K_1$는 139 g/L이였다. 또한 비성장속도에 영향을 마치지 앓는 최대알콜농도 Pm이 존재하였으며 그 값은 2 g/L 이였다. 따라서 Aiba식에서 비성장속도에 영향을 미치는 에탄올 농도항은 P-Pm으보 표현되었다. 본 연구의 알코올생산균주에 대한 비성장속도의 완성된 수식은 디음과 같으며 이 수식에 위한 계산값은 평균오차 6% 내외의 범위에서 실험값과 일치하였다.

The mathematical model of specific growth rate of Saccharomyces cerevisiae ATCC 24858 is proposed as a function of sugar and ethanol concentrations by the combination of Andrew's equation and Aiba's equation. The maximum concentration of sugar Sm, which was the highest concentration of sugar not having any effect on the growth inhibition, was 150 g/L and the substrate inhibition was expressed as a function of (S-Sm). The maximum specific growth inhibition, was 150 g/L and the substrate inhibition was expressed as a function of (S-Sm). The maximum specific growth rate ${\mu}m$, Monod's constant Ks, and Andrew's inhibition constant KI were 0.49 hr-1, 19 g/L, and 139 g/L, respectively. The maximum ethanol concentration, Pm, which did not show any inhibition effect on the specific growth rate was found to be 2 g/L. Therefore, the ethanol inhibition was represented as a function of (P-Pm). The final mathematical model for the specific growth rate of the microorganism in this work is proposed as the following. And the average percent of errors between the calculated specific growth rate and the experimental values was 5.96%.