Using mathematical analysis, a new method has been developed for studying the growth kinetics of bacterial populations in batch culture. First, sampling data were smoothed with the spline interpolation method. Second, the instantaneous rates were derived by numerical differential techniques; finally, the derived data were fitted with the Gaussian function to obtain growth parameters. We named this the Spline-Numerical-Gaussian or SNG method. This method yielded more accurate estimates of the growth rates of bacterial populations; new parameters. It was possible to divide the growth curve into four different but continuous phases based on changes in the instantaneous rates. The four phases are the accelerating growth phase, the constant growth phase, the decelerating growth phase; the declining phase. Total DNA content was measured by flow cytometry; varied depending on the growth phase. The SNG system provides a very powerful tool for describing the kinetics of bacterial population growth. The SNG method avoids the unrealistic assumptions generally used in the traditional growth equations.
Different types of the Logistic model are constructed based on a simple assumption that the microbial populations are all composed of homogeneous members and consequently, the condition of design for the initial value of these models has to be rather limited in the case of N(t_0)=N_0. Therefore, these models cannot distinguish the dynamic behavior of the populations possessing the same N0 from heteroge-neous phases. In fact, only a certain ratio of the cells in a population is dividing at any moment during growth progress, termed as θ, and thus, ddNt not only depends on N, but also on θ. So θ is a necessary element for the condition design of the initial value. Unfortunately, this idea has long been neglected in widely used growth models. However, combining together the two factors (N0 and θ ) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using instantaneous rates (Vinst) to express growth progress. Previous studies in our laboratory sug-gested that the Vinst curve of the bacterial populations all showed a Guassian function shape and thus, the different growth phases can be reasonably distinguished. In the present study, the Gaussian dis-tribution function was transformed approximately into an analytical form (0.5x ibxYi αe=20) that can be conveniently used to evaluate the growth parameters and in this way the intrinsic growth behavior of a bacterial species growing in heterogeneous phases can be estimated. In addition, a new method has been proposed, in this case, the lag period and the double time for a bacterial population can also be reasonably evaluated. This approach proposed could thus be expected to reveal important insight of bacterial population growth. Some aspects in modeling population growth are also discussed.
ZHANG HuaiQiang, LU LiLi, YAN XueLan & GAO PeiJi State Key Laboratory of Microbial Technology, Shandong University, Jinan 250100, China
