构建限制性培养条件下细菌群体生长模型的探讨

A New Method for Estimating Growth Behavior of Bacterial Population under Restrictive Culture Conditions

依据E.coli菌株在摇瓶和发酵罐培养条件下菌群增长过程光密度值的变化,在改进了数据平滑和微分求导方法的基础上,以瞬时速率和瞬时增量为目标函数表征菌群增长的动力学过程.瞬时速率表现为指数衰减模式,而瞬时增量的过程曲线因接种量而异,由它们所表征的生长动力学过程都不存在延迟期和稳定期.动力学曲线的形状由接种物中含有的处于分裂状态的细胞数所决定,它是菌群内源性的增长能力(来自细胞分裂的连续发生)和由增长引发的外源性阻抑力(营养物质的减少和代谢产物的增加)相互作用的结果.由瞬时速率和瞬时增量还可推导出菌群增长的倍增时间及体积生产效率等参量.研究结果可为解决logistic方程和Monod方程在拟合菌群增长过程曲线时遇到的不确定性等难题提供有效的数学分析方法.

According to the changes in optical density （A600） of E. coli population in shake flask-culture and ferment culture and by using an improved data-smoothing method and then differential derivation, the two kinetic parameters, instantaneous rate （Vinst） and instantaneous increment （Vinc）, as response variable were estimated and could be used to accurately characterize the kinetics of bacterial population growth. The leinst showed exponential decay pattern, while the kinetic pattern of Vinc varied and depended on the inoculum＇s size. In either case for Vinst or for Vinc, the kinetic curves appear neither delay period nor stable period. In fact, the pattern of kinetic growth curve were determined by the number of cells under division status, which was the result of the interaction between endogenous growth ability （which is from the continuous cell-cyclic division） and exogenous growth inhibitory force （caused by the decreased nutrients and increased metabolites）. In addition, based on the dividing pattern of bacterial cell, another response variable, doubling time （Q）, was also used to express the endogenous kinetic behavior. And then a bioengineering parameter, volumetric productivity, can be calculated according to the instantaneous increment （Vinc）. This research can provide an effective mathematical analysis to resolve the problems of uncertainty in using logistic and Monod equation to fit the growth curve of E. coll.