Development of Predictive Growth Model of Vibrio parahaemolyticus Using Mathematical Quantitative Model

Predictive growth model of Vibrio parahaemolyticus in modified surimi-based imitation crab broth was investigated. Growth curves of V. parahaemolyticus were obtained by measuring cell concentration in culture broth under different conditions ($Initial\;cell\;level,\;1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}\;colony\;forming\;unit\;(CFU)/mL$; temperature, 15, 25 37, and $40^{\circ}C$; pH 6, 7, and 8) and applying them to Gompertz model. Microbial growth indicators, maximum specific growth rate (k), lag time (LT), and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of V. parahaemolyticus increased with increasing temperature, reaching maximum rate at $37^{\circ}C$. LT and GT were also the shortest at $37^{\circ}C$. pH and initial cell number did not influence k, LT, and GT values significantly (p>0.05). Polynomial model, $k=a{\cdot}\exp(-0.5{\cdot}((T-T_{max}/b)^{2}+((pH-pH_{max)/c^{2}))$, and square root model, ${\sqrt{k}\;0.06(T-9.55)[1-\exp(0.07(T-49.98))]$, were developed to express combination effects of temperature and pH under each initial cell number using Gauss-Newton Algorism of Sigma plot 7.0 (SPSS Inc.). Relative coefficients between experimental k and k Predicted by polynomial model were 0.966, 0.979, and 0.965, respectively, at initial cell numbers of $1{\times}10^{2},\;1{\times}10^{3},\;and\;1{\times}10^{4}CFU/mL$, while that between experimental k and k Predicted by square root model was 0.977. Results revealed growth of V. parahaemolyticus was mainly affected by temperature, and square root model showing effect of temperature was more credible than polynomial model for prediction of V. parahaemolyticus growth.

수학적 정량평가모델을 이용한 Vibrio parahaemolyticus의 성장 예측모델의 개발

수산식품에서 문제가 되는 식중독 균인 V. parahaemolyticus를 대상으로 온도, pH 및 초기균수에 따른 균의 성장 실험 결과를 데이터베이스화하여 이를 바탕으로 균의 성장을 정량적으로 평가할 수 있는 수학적 모델을 개발하였다. $1.0{\times}10^{2},\;1.0{\times}10^{3},\;1.0{\times}10^{4}\;CFU/mL$의 각 초기균수 조건에서 실험치와 예측치의 상관계수는 각각 0.966, 0.979, 0.965으로 나타났다. 또한, 초기균수를 고려하지 않은 모델식은 상관계수가 0.966으로 다음과 같이 나타났다. Polynomial model: $$k=1.10{\cdot}\exp(-0.5(((T-34.14)/9.09)^{2}+((pH-6.59)/4.68)^{2}))$$ 균의 증식 지표치인 최대증식속도상수 k는 온도에 지배적인 영향을 받았으며, pH 및 초기균수에 따른 유의적인 차이는 없었으므로 (P>0.05), k와 온도와의 관계식인 square root model로 나타내었다. Square root model: $${\sqrt{k}\;0.06(T-9.55)[1-\exp(0.07(T-49.98))]$$ V. parahaemolyticus의 경우, square root model에 의한 실험치와 예측치의 상관계수는 0.977로 polynomial model보다 높은 적용성을 나타내었다.