Batch- and Continuous-Culture Transients for Two Substrate Systems

Batch growth of Escherichia coli in the presence of equal initial concentrations of glucose and a secondary substrate (xylose) is characterized by sequential utilization of the substrates, whereas continuous-culture systems with equal concentrations of the two substrates in the feed are characterized by complete utilization of both substrates at both high and low dilution rates. Such systems at steady state at a low dilution rate, when suddenly shifted to a higher dilution rate, experience a transient drop in population density accompanied by accumulation of the secondary substrate but virtually no accumulation of glucose. Systems at steady state with 200 mg of glucose per liter were found to undergo a transient population decrease and eventual recovery when switched to feed containing 200 mg of a secondary substrate per liter.     

Transport-limited growth in the chemostat and its competitive inhibition; A theoretical treatment

Summary An equation expressing the specific growth rate of heterotrophic cell populations in terms of yield factor and transport rate is proposed. From this equation expressions are derived for the specific growth rate when the transport of the energy source is growth0limiting. These expressions are applied to cell population growth in the chemostat limited by the transport of the energy source or of other substrates and simple mathematical tools are provided for obtaining estimates of the transport parameters. An equation is derived which predicts that at constant dilution rate in the chemostat the concentration of any substrate (whether or not the source of energy) the transport of which is growth limiting, is a linear function of the concentration of a competitive inhibitor of its transport. With this equation estimates of the Michaelis constants of competitive transport inhibitors can be obtained. The growth rate equation of Monod (1942) is discussed.     

Continuous cultures limited by a gaseous substrate: Development of a simple, unstructured mathematical model and experimental verification with Methanobacterium thermoautotrophicum

This article presents a simple, unstructured mathematical model describing microbial growth in continuous culture limited by a gaseous substrate. The model predicts constant gas conversion rates and a decreasing biomass concentration with increasing dilution rate. It has been found that the parameters influencing growth are primarily the gas transfer rate and the dilution rate. Furthermore, it is shown that, for correct simulation of growth, the influence of gaseous substrate consumption on the effective gas flow through the system has to be taken into account.Continuous cultures of Methanobacterium thermoautotrophicum were performed at three different gassing rates. In addition to the measurement of the rates of biomass production, product formation, and substrate consumption, microbial heat dissipation was assessed using a reaction calorimeter. For the on-line measurement of the concentration of the growth-limiting substrate, H(2), a specially developed probe has been used. Experimental data from continuous cultures were in good agreement with the model simulations. An increase in gassing rate enhanced gaseous substrate consumption and methane production rates. However, the biomass yield as well as the specific conversion rates remained constant, irrespective of the gassing rate. It was found that growth performance in continuous culture limited by a gaseous substrate is substantially different from "classic" continuous culture in which the limiting substrate is provided by the liquid feed. In this report, the differences between both continuous culture systems are discussed.     

Protozoan feeding and bacterial wall growth.

Monod's model is often assumed to describe the kinetics of feeding of a protozoan population on a bacterial population in a chemostat. An earlier study (J. L. Jost et al., J. Bacteriol., 113, 84 (1973)) of the feeding of Tetrahymena pyriformis on either Escherichia coli or Azotobacter vinelandii found that this model correctly predicted the occurrence of sustained oscillations of population densities but made predictions of minimum bacterial population densities that were much smaller than those observed. The earlier study removed the discrepancy between the model and data by replacing Monod's model with a different model. It is shown in the present study that the discrepancy can be explained equally as well if Monod's model for the feed relation is retained and if, in addition, growth of bacteria on the chemostat walls is allowed for in the model equations.     

Microbial Ecophysiology of Whey Biomethanation: Comparison of Carbon Transformation Parameters, Species Composition, and Starter Culture Performance in Continuous Culture

Changes in lactose concentration and feed rate altered bacterial growth and population levels in a whey-processing chemostat. The bacterial population and methane production levels increased in relation to increased lactose concentrations comparable to those in raw whey (6%) and converted over 96% of the substrate to methane, carbon dioxide, and cells. Sequential increases in the chemostat dilution rate demonstrated excellent biomethanation performance at retention times as low as 25 h. Retention times shorter than 25 h caused prevalent bacterial populations and methane production to decrease, and intermediary carbon metabolites accumulated in the following order: acetate, butyrate, propionate, lactate, ethanol, and lactose. Bacterial species dominated in the chemostat as a function of their enhanced substrate uptake and growth kinetic properties. The substrate uptake kinetic properties displayed by the mixed chemostat population were equivalent to those of individual species measured in pure culture, whereas the growth kinetic properties of species in mixed culture were better than those measured in pure culture. A designed starter culture consisting of Leuconostoc mesenteroides, Desulfovibrio vulgaris, Methanosarcina barkeri, and Methanobacterium formicicum displayed biomethanation performance, which was similar to that of a diverse adapted mixed-culture inoculum, in a continuous contact digestor system to which 10 g of dry whey per liter was added. Preserved starter cultures were developed and used as inocula for the start-up of a continuous anaerobic digestion process that was effective for biomethanation of raw whey at a retention time of 100 h.     

The Population Biology of Bacterial Plasmids: A PRIORI Conditions for the Existence of Conjugationally Transmitted Factors

A mathematical model for the population dynamics of conjugationally transmitted plasmids in bacterial populations is presented and its properties analyzed. Consideration is given to nonbacteriocinogenic factors that are incapable of incorporation into the chromosome of their host cells, and to bacterial populations maintained in either continuous (chemostat) or discrete (serial transfer) culture. The conditions for the establishment and maintenance of these infectious extrachromosomal elements and equilibrium frequencies of cells carrying them are presented for different values of the biological parameters: population growth functions, conjugational transfer and segregation rate constants. With these parameters in a biologically realistic range, the theory predicts a broad set of physical conditions, resource concentrations and dilution rates, where conjugationally transmitted plasmids can become established and where cells carrying them will maintain high frequencies in bacterial populations. This can occur even when plasmid-bearing cells are much less fit (i.e., have substantially lower growth rates) than cells free of these factors. The implications of these results and the reality and limitations of the model are discussed and the values of its parameters in natural populations speculated upon.     

Kinetics of substrate utilization in adenine-limited chemostat cultures of Bacillus subtilis KYA741.

The specific rates of limiting substrate utilization were investigated in adenine- or glucose-limited chemostat cultures of Bacillus subtilis KYA741, an adenine-requiring strain, at 37 degrees C. With the glucose-limited cultures, the specific rate of glucose consumption versus dilution rate gave a linear relationship from which the true growth yield and maintenance coefficient were determined to be 0.09 mg of bacteria per mg of glucose and 0.2 mg of glucose per mg of bacteria per h, respectively. With the adenine-limited cultures, adenine as the limiting substrate was not completely consumed at lower dilution rates (e.g., D less than 0.1), unlike in the glucose-limited cultures. When a linear relationship of specific rate of adenine consumption versus dilution rate was extrapolated to zero dilution rate, a negative value for the specific rate of adenine consumption, -0.01 mg of adenine per mg of bacteria per h, was obtained, giving a true growth yield for adenine of 5.2 mg of bacteria per mg of adenine. On the other hand, the maintenance coefficient of oxygen uptake gave a positive value of 8.1 x 10(-3) mmol/mg of bacteria per h. Based on previous results showing that adenine is resupplied by lysing cells, we developed kinetic models of adenine utilization and cell growth that gave a good estimation of the peculiar behavior of cell growth and adenine utilization in adenine-limited chemostat cultures.     

Metabolic regulation in bacterial continuous cultures: II

The transient behavior of a continuous culture of Klebsiella pneumoniae with mixed feed of glucose and xylose arising from step-up and step-down in dilution rates and from a feed-switching experiment is presented. he organism gradually switches from simultaneous utilization of the substrates at low growth rates to preferred utilization of the faster substrate (i.e, supporting a higher growth rate) at high dilution rates. The metabolic lags following a step increase in dilution rate and a significant accumulation of the slower substrate during the transient period result from the effects of metabolic regulation. The cybernetic modeling approach that successfully described the foregoing situations with single-substrate feeds is employed to describe mixed substrate behavior. The parameters in the mixed-substrate (glucose and xylose) model are the same as those in the single-substrate models with the singular exception of the rate constant for the xylose growth enzyme synthesis. The reason for this discrepancy is discussed in detail. It appears that the constitutive rate of enzyme synthesis for growth on a given substrate may be related to the past history of the organism in regard to whether or not the organism has been exposed to the particular substrate. Thus, the results further demonstrate the ability of the framework to effectively describe metabolic regulation in batch, fedbatch, and continuous microbial cultures.     

A stoichiometric organic matter decomposition model in a chemostat culture

Biodegradation, the disintegration of organic matter by microorganism, is essential for the cycling of environmental organic matter. Understanding and predicting the dynamics of this biodegradation have increasingly gained attention from the industries and government regulators. Since changes in environmental organic matter are strenuous to measure, mathematical models are essential in understanding and predicting the dynamics of organic matters. Empirical evidence suggests that grazers’ preying activity on microorganism helps to facilitate biodegradation. In this paper, we formulate and investigate a stoichiometry-based organic matter decomposition model in a chemostat culture that incorporates the dynamics of grazers. We determine the criteria for the uniform persistence and extinction of the species and chemicals. Our results show that (1) if at the unique internal steady state, the per capita growth rate of bacteria is greater than the sum of the bacteria’s death and dilution rates, then the bacteria will persist uniformly; (2) if in addition to this, (a) the grazers’ per capita growth rate is greater than the sum of the dilution rate and grazers’ death rate, and (b) the death rate of bacteria is less than some threshold, then the grazers will persist uniformly. These conditions can be achieved simultaneously if there are sufficient resources in the feed bottle. As opposed to the microcosm decomposition models’ results, in a chemostat culture, chemicals always persist. Besides the transcritical bifurcation observed in microcosm models, our chemostat model exhibits Hopf bifurcation and Rosenzweig’s paradox of enrichment phenomenon. Our sensitivity analysis suggests that the most effective way to facilitate degradation is to decrease the dilution rate.

     

Protein degradation in anaerobic digestion: influence of volatile fatty acids and carbohydrates on hydrolysis and acidogenic fermentation of gelatin

Summary The hydrolysis and fermentation of gelatin in the presence of a carbohydrate by gelatin-adapted mixed anaerobic bacterial populations in putatively carbon-limited chemostat cultures is investigated. It was shown that the degradation of the protein is progressively retarded with increasing dilution rates, as well as with increased concentrations of carbohydrates present in the feed as a second substrate. That this is not due to high concentrations of fermentation products in the reactor was established. Moreover, the carbohydrate is totally fermented at all dilution rates. It is concluded that for optimal performance of an anaerobic digestion system purifying waste waters containing carbohydrate/protein mixtures, fermentation of carbohydrates should be spatially separated from hydrolysis and fermentation of the protein.     

Cultivation of Escherichia coli with mixtures of 3-phenylpropionic acid and glucose: steady-state growth kinetics.

The fate of pollutants in the environment is affected by the presence of easily degradable carbon sources. As a step towards understanding these complex interactions, a model system was explored: the degradation of mixtures of glucose (i.e., an easily degradable substrate) and 3-phenylpropionic acid (3ppa) (a model pollutant) by Escherichia coli ML 30 was studied systematically in carbon-limited continuous culture. The two substrates were always consumed simultaneously regardless of the dilution rate applied. Even at dilution rates higher than the maximum specific growth rate for 3ppa (0.35 +/- 0.05 h-1), the two carbon substrates were utilized together. When cells were grown at a constant dilution rate with different mixtures of 3ppa and glucose, in which 3ppa contributed between 5 and 90% of carbon substrate in the feed medium, the steady-state concentrations of 3ppa and glucose were approximately proportional to the ratio of the two substrates in the feed medium. When cells were cultivated at different dilution rates with a 1:1 mixture (based on carbon) of glucose and 3ppa, an overall maximum specific growth rate of 0.90 +/- 0.05 h-1 and a Monod substrate saturation constant for 3ppa (Ks) of 600 to 700 micrograms liter-1, similar to that measured during growth with 3ppa alone, fitted the experimentally determined steady-state 3ppa concentrations. However, due to the highly differing substrate affinity constants for 3ppa and glucose (Ks approximately 30 to 70 micrograms liter-1), the total steady-state carbon concentration in the culture at a constant dilution rate was determined mainly by the steady-state 3ppa carbon concentration, and it increased with increasing proportions of 3ppa in the feed medium.     

Growth models of the continuous bacterial leaching of iron pyrite by Thiobacillus ferrooxidans

The leaching of iron pyrite by Thiobacillus ferrooxidans was studied in a continuous stirred tank reactor at a variety of dilution rates (0.012-0.22 h(-1)), pyrite surface areas (18-194 m(2)/L), and inlet soluble substrate (Fe(2+)) concentrations (0-3000 ppm). The bacterial leaching rate was found to increase with increasing pyrite surface area, dilution rate, and inlet Fe(2+) concentration. The concentration of bacteria in solution was related to the concentration of bacteria attached to the pyrite surface by a Langmuir-type adsorption-desorption relation. Fitting the experimental data to this relation yielded a value for the area occupied per bacterium of 86 mum(2). This result is consistent with the concept of preferential bacterial attachment of certain sites on the solid. A bacterial growth model was developed that included both bacterial growth in solution and growth of bacteria attached to the pyrite surface. The specific growth rate of the attached bacteria was calculated from this model and was found to increase with increasing solid dilution rate and to decrease with increasing pyrite surface area and soluble substance concentration. An explanation of these results based on an active-inactive site mechanisms was also developed.     

Stoichiometry of carbohydrate fermentation and microbial growth efficiency in a continous culture of mixed rumen bacteria

Summary A population of mixed rumen bacteria was maintained in a chemostat at four different dilution rates, with glocose as the growth limiting carbon and energy substrate. Increasing the dilution rate shifted the proportions of end products: methane decreased and propionate increased. Fermentation and hydrogen balances were calculated from the fermentation end products. Values were similar to earlier ones from batch incubations of rumen contents. This suggests that theoretical overall reaction schemes for carbohydrate fermentation in the rumen, proposed earlier, are also valid in continuous culture.A positive correlation between dilution rate and microbial growth efficiency (gN_inc./kg OM_f was observed, confirming earlier work.Apparently conflicting results of chemostat work and recent in vivo experiments are discussed.     

Effect of variable nutrient supply rates on the RNA level of a heterotrophic bacterial strain

The heterotrophic bacterial strain HIS 53 was grown in a continuous culture under chemostat conditions and at sinusoidal or stepwise variations of the dilution rate; aspartate, ammonium, and phosphate were the growth-limiting nutrients. Within a specific nutrient limitation the growth yield was constant and independent of the applied environmental conditions. Compared with the reference chemostat culture, sinusoidal variations of the dilution rate increased the cellular RNA level by 19%–53% dependent on the growth limitation; stepwise variations caused an increase of the RNA level by 28%–41%. It was hypothesized that under the variable environmental conditions in the natural habitat the physiological potential of the organism is enhanced by some such increase of the cellular RNA level. As a consequence these increased RNA levels influence the competition between heterotrophic bacteria and, as a result, also the composition of the population of heterotrophic bacteria.     

Validity of the tritiated thymidine method for estimating bacterial growth rates: measurement of isotope dilution during DNA synthesis.

The rate of tritiated thymidine incorporation into DNA was used to estimate bacterial growth rates in aquatic environments. To be accurate, the calculation of growth rates has to include a factor for the dilution of isotope before incorporation. The validity of an isotope dilution analysis to determine this factor was verified in experiments reported here with cultures of a marine bacterium growing in a chemostat. Growth rates calculated from data on chemostat dilution rates and cell density agreed well with rates calculated by tritiated thymidine incorporation into DNA and isotope dilution analysis. With sufficiently high concentrations of exogenous thymidine, de novo synthesis of deoxythymidine monophosphate was inhibited, thereby preventing the endogenous dilution of isotope. The thymidine technique was also shown to be useful for measuring growth rates of mixed suspensions of bacteria growing anaerobically. Thymidine was incorporated into the DNA of a range of marine pseudomonads that were investigated. Three species did not take up thymidine. The common marine cyanobacterium Synechococcus species did not incorporate thymidine into DNA.     

Simultaneous utilization of methanol-glucose mixtures by Hansenula polymorpha in chemostat: Influence of dilution rate and mixture composition on utilization pattern

The utilization of mixtures of methanol (C(1)) and glucose (C(6)) of different composition by the methylotrophic yeast Hansenula polymorpha was studied in carbon-limited chemostat culture. For all mixtures tested a similar utilization pattern was observed: At low dilution rates both carbon sources were utilized simultaneously, but at high dilution rates the cells used glucose only and the unutilized methanol accumulated in the culture medium. When grown with C(1) only, the cells exhibited a critical dilution rate D(c)(C(1)) of 0.19 h(-1), but when C(1)-C(6) mixtures were used as the carbon and energy substrate, the yeast was able to completely utilize C(1) at dilution rates considerably higher than D(c)(C(1)). The dilution rate at which the transition from C(1)-C(6) growth to C(6) growth occurred (D(t)) was strictly dependent on the composition of the C(1)-C(6) mixture in the feed, and D(t) increased with decreasing proportions of C(1) in the mixture. During mixed substrate growth the formation of biomass from the two substrates was additive. The results reported indicate that the utilization of C(1)-C(6) mixtures and hence D(t) in H. polymorpha are subject to two different regulatory regimes. When the cells were growing with C(1)-C(6) mixtures containing more than 60% C(1), the transition form C(1)-C(6) to C(6) growth was most probably influenced by the maximum C(1) oxidizing capacity of the cells, whereas for growth with mixtures containing less than 40% C(1), a growth rate of 0.28-0.30 h(-1) seemed to be the limiting barrier for the simultaneous utilization of the components of the binary carbon and energy substrate mixture.     

Yield and maintenance relations of yeast growth in the chemostat at superoptimal temperatures

A model is proposed that accounts for the decreases in yield which occur in chemostat cultures of mesophilic yeasts at superoptimal growth temperatures. Two yield depressing effects were identified, one due to increased maintenance requirements by the viable fraction of the population, the other due to energy substrate dissipation by the nonviable fraction. The two effects are functions of the dilution rate, as is the fraction of nonviable cells. Experimental results were obtained on the yield, maintenance, and dissipation of energy substrate in a glucose-limited chemostat culture of a respiration-deficient mutant of Saccharomyces cerevisiae at 39°C. The rates of glucose utilization for maintenance and for dissipation constituted, respectively, 33–28% and 15–9% of the total glucose utilization rate over the range of dilution rates tested (0.038–0.064 hr^?1), while the yield varied over this range from 0.066–0.085 g of biomass (dry wt) per gram of glucose.     

The dynamics of single-substrate continuous cultures: the role of transport enzymes

A chemostat limited by a single growth-limiting substrate displays a rich spectrum of dynamics. Depending on the flow rate and feed concentration, the chemostat settles into a steady state or executes sustained oscillations. The transients in response to abrupt increases in the flow rate or the feed concentration are also quite complex. For example, if the increase in the flow rate is small, there is no perceptible change in the substrate concentration. If the increase in the flow rate is large, there is a large increase in the substrate concentration lasting several hours or days before the culture adjusts to a new steady state. In the latter case, the substrate concentration and cell density frequently undergo damped oscillations during their approach to the steady state. In this work, we formulate a simple structured model containing the inducible transport enzyme as the key intracellular variable. The model displays the foregoing dynamics under conditions similar to those employed in the experiments. The model suggests that long recovery times (on the order of several hours to several days) can occur because the initial transport enzyme level is too small to cope with the increased substrate supply. The substrate concentration, therefore, increases until the enzyme level is built up to a sufficiently high level by the slow process of enzyme induction. Damped and sustained oscillations can occur because transport enzyme synthesis is autocatalytic, and hence, destabilizing. At low dilution rates, the response of stabilizing processes, such as enzyme dilution and substrate consumption, becomes very slow, leading to damped and sustained oscillations.     

Steady state and transient growth of autotrophic nitrifying bacteria

Growth of the autotrophic nitrifying bacteria Nitrosomonas europaea and Nitrobacter sp. was studied in continuous culture. Steady state growth kinetics of both organisms conformed with that predicted by chemostat theory, modified to account for maintenance energy requirement. Steady state data were used to calculate the maximum specific growth rate, the saturation constant for growth, the true growth yield and the maintenance coefficient. Transient growth was studied by imposing step changes in dilution rate. Step increases resulted in overshoots and oscillations in substrate concentration before establishment of a new steady state while step decreases in dilution rate were followed by monotonic changes in substrate concentration. The size of overshoots in substrate concentration following step increases in dilution rate was dependent on both the magnitude of the increase and of the dilution rate prior to the change.