The ideal free distribution and bacterial growth on two substrates

A population dynamical model describing growth of bacteria on two substrates is analyzed. The model assumes that bacteria choose substrates in order to maximize their per capita population growth rate. For batch bacterial growth, the model predicts that as the concentration of the preferred substrate decreases there will be a time at which both substrates provide bacteria with the same fitness and both substrates will be used simultaneously thereafter. Preferences for either substrate are computed as a function of substrate concentrations. The predicted time of switching is calculated for some experimental data given in the literature and it is shown that the fit between predicted and observed values is good. For bacterial growth in the chemostat, the model predicts that at low dilution rates bacteria should feed on both substrates while at higher dilution rates bacteria should feed on the preferred substrate only. Adaptive use of substrates permits bacteria to survive in the chemostat at higher dilution rates when compared with non-adaptive bacteria.     

Effect of growth conditions on heat resistance of Arizona bacteria grown in a chemostat.

The effects of various growth conditions on the heat resistance of Arizona bacteria grown in a continuous-culture device (chemostat) were studied. Using either glucose, NH4Cl, NaH2PO4, or MgCl2 as the rate-limiting nutrient, it was found that the heat resistance, in all cases depended on the dilution rate and, hence, growth rate of the culture. Cells grown at high dilution rates were less heat resistant than those grown at low dilution rates. If, however, the dilution rate was maintained at a constant rate, the higher the growth temperature, the more heat resistant were the cells. Also at any given dilution rate, the cells were most heat resistant when grown at a near neutral pH. Most survival curves were biphasic in shape, indicating the presence in the population of two fractions of cells, one fraction being more resistant than the other. The size of the more heat-resistant fraction varied from almost 100% in very slow-growing cultures to practically 0% in cultures grown at a dilution rate of 0.67 h-1.     

Dynamics of chemostat in which one microbial population grows on multiple complementary nutrients

The equations of a chemostat in which one microbial population grows on multiple rate-limiting nutrients are formulated. The dynamics of a chemostat involving growth on complementary nutrients is studied through stability analysis of the system of equations. Some conditions are derived that relate the dynamic behavior of the chemostat to its operating conditions and can be applied to any model for the specific growth rate of the population. It is shown that, if maintenance of the population is neglected, the system exhibits no sustained or damped oscillations. If maintenance of the population is considered, damped oscillations are observed for some operating conditions.     

Dynamic effects related to steady-state multiplicity in continuous Saccharomyces cerevisiae cultivations

The behavioral differences between chemostat and productostat cultivation of aerobic glucose-limited Saccharomyces cerevisiae were investigated. Three types of experiments were conducted: a chemostat, where the dilution rate was shifted up or down in stepwise manner; and a productostat, with either stepwise changed or a rampwise increased ethanol setpoint, i.e., an accelero-productostat. The transient responses from chemostat and productostat experiments were interpreted using a simple metabolic flux model. In a productostat it was possible to obtain oxido-reductive steady states at dilution rates far below Dcrit due to a strong repression of the respiratory system. However, these steady states could not be obtained in a chemostat, since a dilution rate shift-down from an oxido-reductive steady state led to a derepression of the respiratory system. It can therefore be concluded that the range of dilution rates where steady-state multiplicity can be obtained differs depending on the operation mode and that this dilution rate multiplicity range may appear larger in a productostat than in a chemostat. A more narrow multiplicity range, however, was obtained when the productostat was operated as an accelero-productostat.     

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.     

Growth characteristics and expression of iron-regulated outer-membrane proteins of chemostat-grown biofilm cells of Pseudomonas aeruginosa.

An in vitro chemostat system was used to study the growth and the expression of iron-regulated outer-membrane proteins (IROMPs) by biofilm cells of Pseudomonas aeruginosa cultivated under conditions of iron limitation. The population of the planktonic cells decreased when the dilution rate was increased. At a dilution rate of 0.05 h-1, the populations of planktonic cells of both mucoid and nonmucoid P. aeruginosa were 3 x 10(9) cells/mL. This value dropped to 5 x 10(6) cells/mL when the dilution rate was increased to 1.0 h-1. The reverse was observed for the biofilm cells. The number of biofilm cells colonising the silicone tubing increased when the dilution rate was increased. The number of biofilm cells of the mucoid strain at steady state was 2 x 10(8) cells/cm (length) when the dilution rate was fixed at 0.05 h-1. The figure increased to 8 x 10(9) cells/cm when the dilution rate was increased to 1.0 h-1. The population of biofilm cells of the nonmucoid strain was 9 x 10(7) cells/cm (length) when the dilution rate was 0.05 h-1. It increased to 2 x 10(9) cells/cm when the dilution rate was set at 1.0 h-1. The expression of IROMPs was induced in the biofilm cells of both mucoid and nonmucoid strains when the dilution rates were 0.05 and 0.2 h-1. IROMPs were reduced but still detectable at the dilution rate of 0.5 h-1. However, the expression of IROMPs was repressed when the dilution rate was increased to 1.0 h-1. The data suggest that the biofilm cells of P. aeruginosa switch on the expression of IROMPs to assist iron acquisition when the dilution rate used for the chemostat run is below 0.5 h-1. The high affinity iron uptake system is not required by the biofilm cells when the dilution rate is increased because the trace amount of iron present in the chemostat is sufficient for the growth of adherent biofilm cells.     

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.     

A mathematical model of the nutrient dynamics of phytoplankton in a nitrate-limited environment

Insofar as saturation kinetics are applicable to the growth of phytoplankton in laboratory experiments and to growth in nature, the computer modeling of intracellular nutrient partitioning in populations of cells can lead to better understanding of the dynamics of natural populations. A three-compartment mathematical model was developed to represent a phytoplankton population having the capability to store nitrogen in a nitrate-limited environment. Parameters were estimated by fitting the model to data from two chemostat experiments reported by Caperon (1968). The model was used to simulate growth dynamics observed in chemostat and batch experiments. The model demonstrated the changes which may occur in the nitrogenous constituents of a phytoplankton population with time and environmental conditions. The model also demonstrates three phenomena which have been observed in field and laboratory experiments but which are not represented by the customary Monod model: (1) uptake rates may significantly exceed not growth rates, (2) high growth rates may be encountered at very low environmental nitrate concentrations, and (3) the ratio of internal nitrogen to population size may change significantly during a study period. It is suggested that the amount of nitorgen in storage may be used as an indicator of the physiological state of a monospecific population. Parameters for the one-compartment Monod model were estimated by customary methods form data generated by the three-compartment model. It was shown that difficulties encountered in estimating the yield coefficient and the decay coefficient may be attributed to the intracellular storage phenomenon. It was also demonstrated that the one-compartment Monod model was inadequate to accurately represent population growth in chemostat experiments when intracellular storage is a significant factor.     

Kinetics of biphasic growth of yeast in continuous and fed-batch cultures

The influence of dilution rate on the production of biomass, ethanol, and invertase in an aerobic culture of Saccharomyces carlsbergensis was studied in a glucose-limited chemostat culture. A kinetic model was developed to analyze the biphasic growth of yeast on both the glucose remaining and the ethanol produced in the culture. The model assumes a double effect where glucose regulates the flux of glucose catabolism (respiration and aerobic fermentation) and the ethanol utilization in yeast cells. The model could successfully demonstrate the experimental results of a chemostat culture featuring the monotonic decrease of biomass concentration with an increase of dilution rate higher than 0.2 hr^?1 as well as the maximum ethanol concentration at a particular dilution rate around 0.5 hr^?1. Some supplementary data were collected from an ethanol-limited aerobic chemostat culture and a glucose-limited anaerobic chemostat culture to use in the model calculation. Some parametric constants of cell growth, ethanol production, and invertase formation were determined in batch cultures under aerobic and anaerobic states as summarized in a table in comparison with the chemostat data. Using the constants, a prediction of the optimal control of a glucose fed-batch yeast culture was conducted in connection with an experiment for harvesting a high yield of yeast cells with high invertase activity.     

An examination of the thresholds of enrichment: a resource-based growth model

A model of single-species growth in the chemostat on two non-reproducing, growth-limiting, noninhibitory, perfectly substitutable resources is considered. The medium in the growth vessel is enriched by increasing the input concentration of one of the resources. Analytical methods are used to determine the effects of enrichment on the asymptotic behaviour of the model for different dilution rates. It is shown that there exists a threshold value for the dilution rate which depends on the maximal growth rate of the species on each of the resources. Provided the dilution rate is below the threshold, enrichment is beneficial in the sense that the carrying capacity of the environment is increased, regardless of which resource is used to enrich the environment. When the dilution rate is increased beyond the threshold, it becomes important to consider which resource is used for enrichment. For one of the resources it is shown that, while moderate enrichment can be beneficial, sufficient enrichment leads to the extinction of the microbial population. For the other resource, enrichment leads from washout or initial condition dependent outcomes to survival, and is thus beneficial. There are important implications of these results to the management of natural aquatic ecosystems. For example, while enrichment may be beneficial to the microbial species during the summer months, it can lead to their decimation during spring run-off, when the natural dilution rate is higher.Research partially supported by an Ontario Graduate Scholarship. This author's contribution was motivated by results in her Ph.D. thesis at McMaster UniversityResearch supported by the National Sciences and Engineering Research Council of Canada.     

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.     

Bacterial Growth on Surfaces: Automated Image Analysis for Quantification of Growth Rate-Related Parameters

A fast routine method for estimating bacterial cell growth rates by using the metachromatic dye acridine orange is described. The method allows simultaneous estimates of cellular RNA and DNA contents of single cells. Acridine orange staining can be used as a nonspecific supplement to quantitative species-specific hybridizations with fluorescence-labelled ribosomal probes to estimate the single-cell concentration of RNA. By automated analysis of digitized images of stained cells, we determined four independent growth rate-related parameters: cellular RNA and DNA contents, cell volume, and the frequency of dividing cells in a cell population. These parameters were used to compare physiological states of liquid-suspended and surface-growing Pseudomonas putida KT2442 in chemostat cultures. The major finding is that the correlation between substrate availability and cellular growth rate found for the free-living cells was not observed for the surface-bound cells; in contrast, the data indicate an almost constant growth rate for attached cells which was independent of the dilution rate in the chemostat.     

Adaptive steady-state optimization of biomass productivity in continuous fermentors

An adaptive steady-state optimization algorithm is presented and applied to the problem of optimizing the production of biomass in continuous fermentation processes. The algorithm requires no modeling information but is based on an on-line identified linear model, locates the optimum dilution rate, and maintains the chemostat at its optimum operating condition at all times. The behavior of the algorithm is tested against a dynamic model of a chemostat that incorporates metabolic time delay, and it is shown that large disturbances in the subtrate feed concentration and the specific growth rate, causing a shift in the optimum, are handled well. The developed algorithm is also used to drive a methylotroph single-cell production process to its optimum.     

Mixed Continuous Cultures of Polyvinyl Alcohol-Utilizing Symbionts Pseudomonas putida VM15A and Pseudomonas sp. Strain VM15C

Stable mixed continuous cultures of Pseudomonas sp. strain VM15C and Pseudomonas putida VM15A, the former of which produced a polyvinyl alcohol (PVA)-degrading enzyme and the latter of which produced an essential growth factor for PVA utilization by strain VM15C, were established with PVA as the sole source of carbon and energy with chemostat cultivation. A high extent of PVA degradation was achieved at dilution rates of less than 0.030/h. The predominant strain in the cultures was the primary metabolizer of PVA, strain VM15C. The growth supporter, strain VM15A, existed as a minor population, although its population was maintained at an almost constant level throughout a dilution region in which the VM15C population decreased markedly as the dilution rate was raised. A crude growth factor which was prepared from a culture supernatant of strain VM15A and increased the specific growth rate of strain VM15C with PVA in an axenic batch culture was also effective for enhancing the VM15C population and PVA degradation in the mixed continuous culture at a high dilution rate (0.064/h). This indicated that the growth-limiting substrate for strain VM15C in the mixed continuous culture is the growth factor produced by strain VM15A.     

Study of the dynamic behavior of the chemostat system

This paper deals with a theoretical study on the dynamic, character of the chemostat system. It. is primarily based on the Monod model for growth limitation, although certain more complex models are considered. Since the Monod model is described in terms of two variables, an analysis by use of a phase plane plot will show the various possible types of behavior theoretically expected for transient conditions of the system. In this paper it will be shown that the chemostat system might show an overshoot (or an underswing) with respect to changes in cell and substrate concentrations, depending on the extent to which the system might be disturbed from steady-slate conditions. Other types of transient behavior ran also be expected when one of the system parameters such as dilution rate or input substrate concentration is disturbed in a stepwise manner. The simple Monod chemostat model was found never to oscillate in either a damped or a sustained manner as has been experimentally reported. Discussion is included about the transient behavior of other chemostat models such as that involving a variable yield coefficient, i.e., including the effect of cell maintenance requirements.     

LIGHT/DARK-PHASED CELL DIVISION IN EUGLENA GRACILIS (Z) (EUGLENOPHYCEAE) IN PO4-LIMITED CONTINUOUS CULTURE1

Eugene gracilis Klebs (Z) was grown in a cyclostat (continuous culture on a light/dark cycle) at growth limiting levels of phosphate. Cell division was restricted to the dark period regardless of the proportion of the cells dividing during each 24 h period. Growth rate, as reflected by the amplitude of the cell density oscillation, was correlated with dilution rate. The width of the division gate was analyzed using a phasing index and found to be narrowest at dilution rates where the mean generation time of the cell population was an even multiple of 24 h. The effect was attributed to enhanced phasing of the cell division process by the biological clock of Euglena. Residual phosphate levels in the cyclostat were less than 0.3 μM PO₄ at all submaximal growth rates. Cellular phosphorus concentration increased with dilution rate as described by a hyperbola saturating at D_max= 0.74 day⁻¹ with 8 × 10⁻⁸μM P/cell as the minimum intracellular phosphorus concentration for growth. The results are discussed, in terms of the inherent similarities and differences between a cyclostat and a steady state chemostat, and the advantages of the cyclostat for studies in phytoplankton ecology.     

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.     

Modeling lipid accumulation in oleaginous fungi in chemostat cultures: I. Development and validation of a chemostat model for Umbelopsis isabellina

Lipid-accumulating fungi may be able to produce biodiesel precursors from agricultural wastes. As a first step in understanding and evaluating their potential, a mathematical model was developed to describe growth, lipid accumulation and substrate consumption of the oleaginous fungus Umbelopsis isabellina (also known as Mortierella isabellina) in submerged chemostat cultures. Key points of the model are: (1) if the C-source supply rate is limited, maintenance has a higher priority than growth, which has a higher priority than lipid production; (2) the maximum specific lipid production rate of the fungus is independent of the actual specific growth rate. Model parameters were obtained from chemostat cultures of U. isabellina grown on mineral media with glucose and NH₄ ⁺. The model describes the results of chemostat cultures well for D > 0.04 h⁻¹, but it has not been validated for lower dilution rates because of practical problems with the filamentous fungus. Further validation using literature data for oleaginous yeasts is described in part II of this paper. Our model shows that not only the C/N-ratio of the feed, but also the dilution rate highly influences the lipid yield in chemostat cultures.     

Algal defenses,population stability,and the risk of herbivore extinctions: a chemostat model and experiment

The effects of inducible defenses and constitutive defenses on population dynamics were investigated in a freshwater plankton system with rotifers as predators and different algal strains as prey. We made predictions for these systems using a chemostat predator–prey model and focused on population stability and predator persistence as a function of flow-through rate. The model exhibits three major types of behavior at a high nutrient concentration: (1) at high dilution rates, only algae exist; (2) at intermediate dilution rates, algae and rotifers show stable coexistence; (3) at low dilution rates, large population fluctuations occur, with low minimum densities entailing a risk of stochastic rotifer extinctions. The size and location of the corresponding areas in parameter space critically depend on the type of algal defense strategy. In an 83-day high-nutrient chemostat experiment we changed the dilution rate every 3 weeks, from 0.7 to 0.5 to 0.3 to 0.1 per day. Within this range of dilution rates, rotifers and algae coexisted, and population fluctuations of algae clearly increased as dilution rates decreased. The CV of herbivore densities was highest at the end of the experiment, when the dilution rate was low. On day 80, herbivorous rotifers had become undetectable in all three chemostats with permanently defended algae (where rotifer densities had already been low) and in two out of three chemostats where rotifers had been feeding on algae with inducible defenses (that represented more edible food). We interpret our results in relation to the paradox of enrichment.