A novel approach for estimating growth phases and parameters of bacterial population in batch culture

Abstract

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 and 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 and 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 and the declining phase. Total DNA content was measured by flow cytometry and 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.

Accurate assessment of antibiotic susceptibility and screening resistant strains of a bacterial population by linear gradient plate

“…The CKC method was proposed to describe dynamic changes in bacterial populations exposed to linear concentration increases of a drug. The CKC from BC 99 to BC 1 can be used to calculate the BC 50 and other parameters [17,34,35]. The differential analysis method is based on turbidity to exclude the interference of resting cells in the bacterial population.…”

Discussion on research methods of bacterial resistant mutation mechanisms under selective culture—uncertainty analysis of data from the Luria-Delbrück fluctuation experiment

“…The strain was sampled at one-hour intervals during the first 12 h, and at two-hour intervals thereafter. At least three samples were taken per time point, and the CV (coefficient of variation) was found to be less than 5% [35]. The kinetics curve of batch culture approximates closely to the Boltzmann-Sigmoid curve (R 2 =0.98).…”

“…Though Luria and Delbrück, and Newcombe, noted that colonies from initially resistant cells differ in size and transparency from those appearing at later culture times, neither team offered an explanation of these differences [2,3]. In our previous studies of the relationship between antibacterial drugs and the occurrence and propagation of bacterial resistant mutants, we observed that resistant colonies varied in size and that small colonies invariably appeared at later culture stages [34][35][36][37][38][39][40][41][42][43]. Assuming that one bacterial cell multiplies into 1×10 7 cells after 23-24 divisions at 37°C, a single mutation should occur within 812 h, which can become a visible colony within the next 812 h [25,26].…”

“…Microbiology and molecular biology studies reveal that, apart from severely lethal effects such as high temperature and extraordinary physical damage, flora death induced by selective damage is a dynamic process, determined by the combined action of selective factor dose and treatment time. Under selective damage, the differences in hereditary and physiological characteristics between resistant and sensitive cells are too complex to be generalized as "all or nothing" [34][35][36][37][38][39][40]. From research on the interactions between bacteria and phages/drugs, it is known that the probability of bacteria being attacked by phages (or drugs) depends on phage density (or drug concentration) and action time.…”

“…Combining related progress [23][24][25][26][27][28][29][30][31][32][33] in microbiology and molecular biology in recent years and the studies conducted in our laboratory [34][35][36][37][38][39][40][41][42][43], this paper first analyzes microbi-ological evidences for the Luria-Delbrück hypothesis, and discusses limitations and errors in applying the hypothesis to observed data and statistical analysis. It proceeds with a statistical re-analysis of the Luria-Delbrück data, from which new inferences are made.…”