Comparison Of Growth Kinetics And Physiological Characteristics Of E.coli CVCC249 Under Both Batch And Continuous Culture

Under batch culture conditions, a bacterial population may be heterogeneous in many important characteristics, such as age-specific reproduction and death rates, cell shape and size and biochemical activities; therefore, the growth of bacterial population presents a nonlinear process with very complicated dynamics. Thus, due to such complexity, the construction of the growth model has to be based on some plausible or implicit assumptions, such as introducing the "β" factor into the Malthus equation (dN/dt=rN ) asin Logistic equation (dN/dt=rN -βN²), parameter "s" as in Gompertz equation(dN/dt=μ₀Ne^-st) and parameter "m" (shape factor) as in Richards equation(Vt = A(1- Be^-kt)^1/(1-m)). Generally, these models are constructed based on some simplisedassumptions that may not reflect the well known properties of a biological system and cannot be adapted for all circumstances.There is a tendency in mathematics to rush into the analysis of a growth model without truly understanding the underlying biology. For example, the term CnNⁱ (i≥3) hasbeen introduced to the polynomial growth equation(dN/dt=F(N)=C₀+C₁N+C₂N²+…+C_nNⁱ),however, the biological significance of theparameters in the model is unclear. Similarly, non-linearity equations with multi-parameters were proposed in biological studies, but did not serve the purposes. It was difficult or impossible to find a sufficient scheme to establish an adequate definition of biological parameters. An exponential polygonal model for population growth has been recently proposed, but it does not provide a sufficient basis for distinction of the growth curve. Microbiologically, it is usually assumed that bacteria divide by a process referred to as binary fission in which one cell divides to produce two cells and a bacterial population is homogeneous. Naturally, there is no complete homogeneous system for a bacterial population and it is only a hypothesized state.Experimental design and investigation of this thesis focuses on the above mentioned problems. Using the instantaneous growth rate as an index, we analyzed the kinetics characteriactic of a bacterial population at different conditions, discussed the formation mechanism of the population kinetics, and elucidated the relationship between the population heterogeneity and the instantanneous growth rate. Based on the analysis of growth kinetics, a new method was developed to study the growth kinetics of bacterial populations and to distinguish the growth phases in batch culture. We extensively discussed many difficulties confronted by Logistic growth model when describing microbial growth. Five new discoveries were established during my Ph.D. studies, as follows:1. A novel approach was developed for estimating growth phases and parameters of bacterial population in batch cultureUsing mathematical analysis, a new method has been developed to study the growth kinetics of bacterial populations in batch culture. First, sample 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. They are the accelerating growth phase, the constant growth phase, the decelerating growth phase and the declining phase (Fig.1.). Total DNA content was measured by flow cytometry and it varied with 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 traditional growth equations. During past 50 years, 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(t₀)=N₀. Therefore, these models cannot reflect the different dynamic behavior of the populations possessing the same No from heterogeneous phases. In fact, only a certain ratio of the cells in a population is dividing at any time duringgrowth progress, termed asθ, and thus,dN/dt not only depends on N, but also onθ. SoN(t₀)=N₀ 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 andθ) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using instantaneous rates (V_inst) to express growth progress. Previous studies in our laboratory suggested that the V_inst, 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 distribution function was transformed approximately into an analytical form(Y_i=αe^{[-0.5((x_i-x₀)/b)2]})that can be conveniently used to evaluate the growth parameters and inthis 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 doubling time for a bacterial population can also be reasonably evaluated. This approach proposed could thus be expected to reveal insight of bacterial population growth. Some aspects in modeling population growth are also discussed.2. A new method was proposed for estimating the effect of physiological heterogeneity of E.coli population on antibiotic susceptivity testAccording to the instantaneous growth rate (dN/dt) of E.coli CVCC249 growing in batch culture, the entire growth curve was distinguished into four phases: accelerating growth phase, constant growth phase, decelerating growth phase and declining phase.Each of four phases have obvious variation in physiological and biochemical properties, including total DNA content, total protein content and MTT-dehydrogenase activity, etc. that leaded to the difference in their antibiotic susceptivity. Antibiotic susceptivity of a population sampled from each phase was tested respectively by Concentration-killing Curve (CKC) approachfollowing the formula N =N₀/1+e⁽ r(x-BC₅₀)), showing as normal distribution at individual cell levelfor an internal population, in which the median bactericidal concentration BC₅₀ representedthe mean level of susceptivity, while the bactericidal span BC_1-99=2/r lnN₀ indicated thevariation degree of the antibiotic susceptivity. Furthermore, tested by CKC approach, the antibiotic susceptivity of E.coli CVCC249 population in each physiological phase to gentamicin or enoxacin varied: susceptivity of population in constant growth phase and declining phase all increased, compared with that in accelerating growth phase, for gentamicin but declined for enoxacin. This primary investigation revealed that physiological phase should be taken account of in the context of both antibiotic susceptivity test and research into antimicrobial mechanism and bacterial resistance (Fig.2.). However there are few reports regarding this aspect, therefore, further research using different kinds of antibiotics with synchronized continuous culture of different bacterial strains is necessary(Fig.3.). 3. A new model was proposed for expressing the reproduction of a heterogeneous bacterial populationAccording to the Fibonacci sequence analysis, three parameters, the recurrent coefficient, the incremental recurrent coefficient, and the net increment (%), were used to analyze the growth and reproduction behaviour of E.coli under batch and continuous culture. The analysis result suggested that under continuous culture, E. coli CVCC 249 divided as in regular model of 1_-M (mother)→1_-M(mother ) + 1_-D (daughter)→…termed as 1→1 + 1'…model. Under batch culture, the net increment of the population growth continuously decrease and finally a zero rate will be reached due to nutrition exhaust and the production increase as inhibitor that can lead to the prolonged generation time. All curves including the instantaneous rate, DNA and protein biosynthesis, and MTT activity appear to fit in the normal distribution. Under same batch culture, the net increment (%) will decrease with the increase in the inoculum size, but the highter biomass will be obtained at larger inoculum size. As steady state cultures were used as the inoculum, the growth dynamic behaviour was similar to that lower inoculum size. Under continuous culture, individual at low growth rate wash out with the increase in the dilution rate and the population growth curve present a normal distribution which is similar to that cell size distribution. The research results showed that the incremental recurrent coefficient for sequence is 1.0 (Fig.4.), which suggests that the bacteria reproduce in regular model of 1→1 + 1'…This new model will provide a good indication for accurately determining the mutation rate and the degree susceptivity of bacteria to antibiotic et al. 4. The instantaneous reaction rate was used to express the catalytic efficiency ofβ-galactosidaseTo overcome the difficulties in determining the initial rate (V₀) of enzyme-catalyzed reactions based on the classic Michaelis-Menten kinetic assumption and to avoid the uncertainty of calculating the catalytic rate constant (k_cat) by extrapolation of V_maxand k_m data, the instantaneous reaction rate was used to estimate the k_cat ofβ-galactosidase. This was based on analysis of the changes in relationship between input data [the value of added O-nitrophenylβ-D-galactoside (ONPG)] and output data [the instantaneous rate of O-nitrophenol (ONP) formation] for entire process of the enzyme-catalyzed reaction. The amount of ONP was determined based on the online UV-visible dynamic spectrum during the entire course of the reaction and its instantaneous change rate (v_inst) was directly derived from the dynamic spectrum curve. v_inst was used as an objective function to determine the optimum assay conditions forβ-galactosidase activity with variables such as temperature, time, pH, and the ratio of [E] to [S]. Under these optimal assay conditions, the maximum value of v_inst (v_inst-max) and the corresponding concentration of enzyme ([E] inst-max) could be accurately determined. Then the k_cat of p-galactosidase was calculated with the formula: k_cat = v_inst-max/[E]_inst-max .The amount ofβ-galactosidase in a sample could also be easily determined by this approach without a pre-purification step. The general effectiveness of this new approach and the problems of applying the Michaelis-Menten approximation, particularly for estimating the initial velocity, are also discussed in detail.The disappearance of ONPG and the appearance of ONP were synchronously measured during the hydrolysis of ONPG byβ-galactosidase using UV-visible spectrum in situ on-line. The conversion process of ONPG to ONP was calculated using d[ONPG]/dt - d[ONP]/dt (Fig.5.). The combined effects of temperature and time on v_inst and v_inc were expressed as relative variability and visualized by the isograms method - contour plots. With this approach, new insights into the irreversible-continuous conversion of ONPG to ONP during hydrolysis can be clearly observed. That is, the intermediate was a moving-mass flow in three-dimensional space from substrate converting to product during hydrolysis and the temperature-time compensating effects. The dynamic behavior of the intermediate was effectively visualized in a two-dimensional plot (Fig.6.). The results of the present study provide evidence to support the isograms method as a useful tool in understanding the reaction mechanisms of enzyme catalysis. 5. A new model for enzyme-catalyzed reaction was proposed based on a case study on the hydrolysis of ONPG byβ-galactosidaseBased on the synchronously measuring the disappearance of ONPG and the appearance of ONP during hydrolysis of ONPG byβ-galactosidase, the existence of ES-complex as an intermediate can be estimated by the differences between d[ONPG]/dt and d[ONP]/dt. The new de Donder equation (v_f/v_r=exp (A_i/RT)) was used to calculate the changes in Gibbs free energy (dG_i=-RT·ln(d[ONPG]/dt)/(d[ONP]/dt)) (Fig.7.). The results suggested that the interaction of substrate with enzyme in binding process is controlled by the active sites on the surface of enzyme and the conversion of substrate to product is an irreversible reaction. Combining current experimental findings with the previous studies, a new model termed as an irreversible-catalysis model was proposed for glycosidase-catalyzed reaction, written as (?),in which the regenerated enzyme from the dissociation ofES-complex will re-bind with substrate and then the catalysis is going again. The product formed plays key roles as a completive inhibitor for catalysis process.