Logistic方程在微生物分批培养动力学中的应用

The Application of Logistic Equation in Kinetics of Microbial Batch Culture

将生态学领域中的Logistic方程引入微生物动力学的研究中,建立了3个分别基于Monod方程、Herbert方程和Logistic方程的关于培养基中的微生物浓度(x)和底物浓度(s)的模型以形成对照.同时建立了基于Logistic方程的关于微生物浓度(x)和时间(t)的模型.这些均采用实验数据拟合以证明其精确性.该工作有助于研究微生物生长特性,同时有助于进一步地研究可生化降解的有机物在水体的微生物作用下的氧化分解过程,建立新的河流、湖泊、水库等生物学水质模型.本研究中采用的数值方法是非线性最小二乘法、Interior reflectiveNewton算法.在Lorynebacteriumglutamicum分批培养和Pseudomonassp.分批培养中,基于Logistic方程的x s模型拟合的相关系数分别是0.9940和0.9867.在Pseudomonassp.分批培养中,x t模型拟合的相关系数是0.9972.

This paper introduced Logistic equation in the field of ecology to the study of the kinetics of microbial batch culture. Three models of biomass concentration (x) in the culture medium as functions of substrate concentration(s)based respectively on Monod equation, Herbert equation and Logistic equation were established for comparison. A model of biomass concentration(x)as function of time(t)based on Logistic equation was also established. And these models were simulated according to experimental data to testify their validity. This work is helpful to the study of microbial growth, and to the study of the oxidative decomposition process of degradable organic substances decomposed by microorganism in water environment. This will lead to new biological water quality models in rivers, lakes, reservoirs, etc. The numerical methods used in this study were nonlinear least-square method and interior-reflective Newton methods. The simulation coefficients in the models of x-s based on Logistic equation were 0.994 0 and 0.986 7 respectively according to Lorynebacterium glutamicum batch culture and Pseudomonas sp. batch culture. The simulation coefficient in the model of x-t was 0.997 2 according to Pseudomonas sp. batch culture.