A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria

When the growth of bacteria in a chemostat is controlled by limiting the supply of a single essential nutrient, the growth rate is affected both by the concentration of this nutrient in the culture medium and by the amount of time that it takes for the chemical and physiological processes that result in the production of new biomass. Thus, although the uptake of nutrient by cells is an essentially instantaneous process, the addition of new biomass is delayed by the amount of time that it takes to metabolize the nutrient. Mathematical models that incorporate this "delayed growth response" (DGR) phenomenon have been developed and analysed. However, because they are formulated in terms of parameters that are difficult to measure directly, these models are of limited value to experimentalists. In this paper, we introduce a DGR model that is formulated in terms of measurable parameters. In addition, we provide for this model a complete set of criteria for determining persistence versus extinction of the bacterial culture in the chemostat. Specifically, we show that DGR plays a role in determining persistence versus extinction only under certain ranges of chemostat operating parameters. It is also shown, however, that DGR plays a role in determining the steady-state nutrient and bacteria concentrations in all instances of persistence. The steady state and transient behavior of solutions of our model is found to be in agreement with data that we obtained in growing Escherichia coli 23716 in a chemostat with glucose as a limiting nutrient. One of the theoretical predictions of our model that does not occur in other DGR models is that under certain conditions a large delay in growth response might actually have a positive effect on the bacteria's ability to persist.     

Limit cycles in a chemostat model for a single species with age structure

We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location in parameter space of the Hopf bifurcations for special cases of our model. The onset of cycling is largely independent of both the form of the resource uptake function and the shape of the maternity function.     

Nonlinear control for algae growth models in the chemostat

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells’ growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.     

Ammonium-limited growth and uptake by Oscillatoria agardhii in chemostat cultures

Growth of Oscillatoria agardhil was studied in ammonium-limited chemostat cultures, at various dilution rates (=growth rates, μ). The uptake kinetics for ammonium of nitrogen (ammonium or nitrate)-limited chemostat cultures also was investigated. The kinetics of ammonium-limited growth could be adequately described by both the Monod and Droop equations, and were closely similar to the nitrate-limited growth kinetics of this species. The uptake kinetics for ammonium showed similarities as well as differences with the uptake kinetics for nitrate. The similarities were apparent in the uptake capacity values for ammonium and nitrate , which were identical, high and independent of μ. The differences were to be found in the half-saturation constants for ammonium uptake and nitrate uptake , the former being hardly influenced by μ. A consitutive, high affinity, system is likely to operate in the uptake and assimilation of ammonium by nitrogen-limited O. agardhii. The use of ammonium uptake parameters in studies of growth-limiting factors in nature can provide information as to whether a nitrogen-limitation prevails in natural habitats of this species.     

Allee dynamics generated by protection mutualisms can drive oscillations in trophic cascades

Understanding the relative effect of top predators and primary producers on intermediate trophic levels is a key question in ecology. Most previous work, however, has not considered either realistic nonlinearities in feedback between trophic levels or the effect of mutualists on trophic cascades. Here, we develop a realistic model for a protection mutualism that explicitly includes interactions between a protected herbivore and both its food plant and generalist predators. In the absence of protection, herbivores and plant resources approach a stable equilibrium, provided that predation is not so high as to cause herbivore extinction. In contrast, adding protection by mutualists increases the range of dynamical outcomes to include unstable equilibria, stable and unstable limit cycles, and heteroclinic orbits. By reducing the impact of predators, protection by mutualists can allow herbivores to exert strong negative effects on their host plants, which in turn can lead to repeated cycles of overexploitation and recovery. Our results indicate that it may be essential to consider protection mutualisms to understand the dynamics of trophic cascades. Conversely, it may be essential to explicitly include dynamical feedback between plants and herbivores to fully understand the population and community dynamical consequences of protection mutualism.     

An analysis of the growth of Gluconobacter oxydans in chemostat cultures

Gluconobacter oxydans was grown successively in glucose and nitrogen-limited chemostat cultures. Construction of mass balances of organisms growing at increasing dilution rates in glucose-limited cultures, at pH 5.5, revealed a major shift from extensive glucose metabolism via the pentose phosphate pathway to the direct pathway of glucose oxidation yielding gluconic acid. Thus, whereas carbon dioxide production from glucose accounted for 49.4% of the carbon input at a dilution rate (D)=0.05 h^-1, it accounted for only 1.3% at D=0.26 h^-1. This decline in pentose phosphate pathway activity resulted in decreasing molar growth yields on glucose. At dilution rates of 0.05 h^-1 and 0.26 h^-1 molar growth yields of 19.5 g/mol and 3.2 g/mol, respectively, were obtained. Increase of the steady state glucose concentration in nitrogen-limited chemostat cultures maintained at a constant dilution rate also resulted in a decreased flow of carbon through the pentose phosphate pathway. Above a threshold value of 15–20 mM glucose in the culture, pentose phosphate pathway activity almost completely inhibited. In G. oxydans the coupling between energy generation and growth was very inefficient; yield values obtained at various dilution rates varied between 0.8–3.4 g/cells synthesized per 0.5 mol of oxygen consumed.     

Energy conservation by pyrroloquinoline quinol-linked xylose oxidation in Pseudomonas putida NCTC 10936 during carbon-limited growth in chemostat culture

Abstract When grown in carbon source-limited chemostat cultures with lactate or glucose as the carbon and energy source and xylose as an additional source of reducing equivalents, Pseudomonas putida NCTC 10936 oxidized xylose to xylonolactone and xylonate. No other products were formed from this pentose, nor was it incorporated into biomass. The presence of xylose in these cultures resulted in higher Y_glucose and Y_lactate values as compared to cultures without xylose indicating that biologically useful energy was conserved during the periplasmic oxidation of xylose. As the Y₀ values for growth on glucose or on lactate alone were equal to the Y₀ values with xylose as co-substrate, it is concluded that for flucose- or lactate-limited growth energy conservation by PQQH₂ oxidation is as efficient as by NADH₂ oxidation.     

Metabolic fluxes during the growth of thermotolerant methylotrophic Bacillus strains in methanol-sufficient chemostat cultures

Growth of the thermotolerant methylotrophic Bacillus strain TS1 in methanol-limited chemostat culture showed that the substrate was oxidized solely to biomass and CO₂. When a pulse of methanol was added to the growth vessel anabolism could be shown to be dissociated from catabolism for a transient period of time. Present data shows that when the organism was grown with a limitation other than carbon, some of the substrate was channelled into metabolite over-production. When the organism was grown under N-limitation 2-oxoglutarate accumulated in the culture medium in small amounts whilst acetate accumulated under all carbon excess conditions. Although the average carbon recovery was 92%, analysis of the culture filtrates for other metabolites failed to show significant amounts of any individual product above those detected in carbon-limited growth comditions. The results are discussed in relation to published data.     

Long-term oscillations in grassland productivity induced by drought

Disturbances such as drought have immediate impacts on ecosystem functioning, but little is known about long-term dynamic consequences of disturbance. Here, we show that a major drought perturbed prairie grassland from nearly constant average annual production, and induced 9 years of oscillations with a 2-year period. This pattern occurred in unmanipulated plots in many widely separated fields that were part of two different long-term studies. Using direct and indirect tests, we could reject the hypothesis that the oscillations were externally imposed by climate or herbivores. Weak evidence supported the hypothesis that oscillations were internally generated, caused by a litter and nitrogen dependent feedback on productivity. This hypothesis was supported by the results of two other long-term studies, in which burning and, separately, nitrogen addition eliminated the 2-year oscillations in plant production. However, more direct evidence failed to support the litter hypothesis. A final, but untested hypothesis was suggested by the observation that production tended to be synchronized amongst dominant plants. Drought may have synchronized production dynamics amongst plants with biennially greater allocation to above-ground growth. Regardless of the specific mechanism, our results show that a single disturbance may have long-lasting effects on the dynamics of plant production.     

Sustained and transient oscillations and chaos induced by delayed antiviral immune response in an immunosuppressive infection model

Sustained and transient oscillations are frequently observed in clinical data for immune responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. To account for these oscillations, we incorporate the time lag needed for the expansion of immune cells into an immunosuppressive infection model. It is shown that the delayed antiviral immune response can induce sustained periodic oscillations, transient oscillations and even sustained aperiodic oscillations (chaos). Both local and global Hopf bifurcation theorems are applied to show the existence of periodic solutions, which are illustrated by bifurcation diagrams and numerical simulations. Two types of bistability are shown to be possible: (i) a stable equilibrium can coexist with another stable equilibrium, and (ii) a stable equilibrium can coexist with a stable periodic solution.     

Resonant properties in the paddlefish electrosensory system caused by delayed feedback

Introduction The paddlefish electrosensory system consists of receptor cells in the skin that sense minute electric fields from their prey, small water fleas. The receptors thereby measure the difference of the voltage at the skin surface against the voltage inside the animal. Due to a high skin impedance, this internal voltage is considered to be relatively fixed. Results We found, however, that this internal voltage can fluctuate. It shows damped oscillations to a single short electric field pulse and changes, with some time delay, according to the previous history of stimulation, and shows resonance at a certain frequency. Conclusions Computer simulations show that these phenomena can be explained by the presence of delayed feedback where the internal voltage is part of the feedback loop.     

Alginate molecular mass produced by <Emphasis Type="Italic">Azotobacter vinelandii</Emphasis> in response to changes of the O<Subscript>2</Subscript> transfer rate in chemostat cultures

Alginate production by Azotobacter vinelandii growing in chemostat cultures was evaluated under different O₂ transfer rates (OTR). As a result of modifying the culture’s agitation rate from 300 to 500 rpm, the OTR increased from 9 to 15.1 mmol l⁻¹ h⁻¹ and a slight variation in the alginate production (1.7–2.2 g l⁻¹) was observed. At a constant growth rate (0.1 h⁻¹), the mean molecular mass of the alginate was strongly influenced by changes in the OTR, varying from 860 to 1,690 kDa. These results support a possible relationship between alginate polymerization-depolymerization process and the O₂ uptake rate.     

Anomalies in the growth kinetics of Saccharomyces cerevisiae strains in aerobic chemostat cultures

Aerobic glucose-limited chemostat cultivations were conducted with Saccharomyces cerevisiae strains NRRL Y132, ATCC 4126 and CBS 8066, using a complex medium. At low dilution rates all three strains utilised glucose oxidatively with high biomass yield coefficients, no ethanol production and very low steady-state residual glucose concentrations in the culture. Above a threshold dilution rate, respiro-fermentative (oxido-reductive) metabolism commenced, with simultaneous respiration and fermentation occurring, which is typical of Crabtree-positive yeasts. However, at high dilution rates the three strains responded differently. At high dilution rates S. cerevisiae CBS 8066 produced 7–8 g ethanol L⁻¹ from 20 g glucose L⁻¹ with concomitant low levels of residual glucose, which increased markedly only close to the wash-out dilution rate. By contrast, in the respiro-fermentative region both S. cerevisiae ATCC 4126 and NRRL Y132 produced much lower levels of ethanol (3–4 g L⁻¹) than S. cerevisiae CBS 8066, concomitant with very high residual sugar concentrations, which was a significant deviation from Monod kinetics and appeared to be associated either with high growth rates or with a fermentative (or respiro-fermentative) metabolism. Supplementation of the cultures with inorganic or organic nutrients failed to improve ethanol production or glucose assimilation. Journal of Industrial Microbiology & Biotechnology (2000) 24, 231–236. Received 09 August 1999/ Accepted in revised form 18 December 1999     

Metabolic and energetic aspects of the growth of Bacillus stearothermophilus in glucose-limited and glucose-sufficient chemostat culture

With a glucose-limited chemostat culture of Bacillus stearothermophilus, increasing the incubation temperature progressively from 45°C to 63°C led to a progressive marked increase in the maintenance rates of glucose and oxygen consumption. Hence, at a fixed low dilution rate the yield values with respect to glucose and oxygen decreased substantially with increased temperature. However, the apparent Y _glucose ^max and values did not decrease but actually increased with temperature, being highest at 63°C (i.e., close to the maximum growth temperature). With glucose-sufficient cultures growing at a fixed low dilution rate (0.2 h^–1) and at their optimum temperature (55°C), glucose and oxygen consumption rates invariably were higher than that of a corresponding glucose-limited culture. Cation (K⁺ or Mg²⁺)-limited cultures expressed the highest metabolic rates and with the K⁺ limited culture this rate was found to be very markedly temperature dependent. As the temperature was increased from 45°C to 63°C the rate of glucose consumption increased 1.8-fold, and that of oxygen consumption by 3.7-fold. The culture pH value also exerted a noticeable effect on the metabolic rate of a glucose-limited culture, particularly at the extremes of pH tolerance (5.5 and 8.5, respectively). A K⁺-limited culture was less affected with respect to metabolic rate by the culture pH value though the steady state bacterial concentration, and thus the cellular K⁺ content, changed substantially. These results are discussed in relation to previous findings of the behaviour of this organism in batch culture, and to the behaviour of other thermophilic Bacillus species in chemostat culture.     

Transient peaks in the delayed luminescence from Scenedesmus obtusiusculus induced by phosphorus starvation and carbon dioxide deficiency

Cells of the unicellular green alga Scenedesmus obtusiusculus (Chod.) were starved of phosphorus for 24, 48, 72 and 96 h, and the decay kinetics of the delayed luminescence from the differently starved cells was monitored for several minutes. Cells starved for 24 h showed similar delayed luminescence decay kinetics and accumulated output of photons as control cells after excitation with white light. Two transient peaks (with several components) in the decay kinetics of delayed luminescence were observed after 48 h of phosphorus starvation but not after 72 or 96 h. The amplitude of the transient peaks varied depending on the length of the excitation period with white light and on the length of the dark period preceding light excitation. High CO₂ availability induced no transient peak, whereas low CO₂ availability induced a high transient peak. Transient peaks could not be induced by excitation with light of 660 or 680 nm and only a single transient peak developed using 700 nm light. The kinetics of the delayed luminescence was changed, and the accumulated output of photons was decreased when the pH of the medium was changed from 7.2 to 9.5, both in cells starved for phosphorus for 96 h and in controls. The data indicate that a complicated metabolic pattern is involved in the mechanisms giving rise to the observed transient peaks in the delayed luminescence. The main factors may be a reduction in the translocation of trioses from chloroplasts, a concomitant reduction in Calvin cycle activities and changes in the amount of ATP and reducing agents available.     

Cadmium produces a delayed mitogenic response and modulates the EGF response in quiescent NRK cells

Recent studies have shown that cadmium, at subtoxic levels, may induce a response characteristic of that elicited by a type of growth factor that supports the anchorage independent growth of cells that are not fully transformed. That is, Cd⁺⁺ was found to replace transforming growth factor beta in supporting soft agar growth of NRK-49F cells. To tes the extent to which Cd⁺⁺ further mimics transforming growth factor beta in its effects and to establish response patterns that suggest possible molecular mechnisms of action, we have determined the effects of Cd⁺⁺ and/or epidermal growth factor (EGF) on DNA synthesis in quiescent NRK-49F cells. We found that subtoxic doses of Cd⁺⁺ modulate EGF-induced DNA synthesis in a dose-dependent fashion. Although Cd⁺⁺ effects on early (16–24 hr) EGF-induced DNA synthesis are primarily inhibitory, later effects involve stimulation as well. Subtoxic doses of Cd⁺⁺ did not stimulate DNA synthesis in quiescent cells within 24 hr of addition. At later times (40 or 64 hr), however, an increase in DNA synthesis of up to threefold was induced by 0.25 M Cd⁺⁺. This pattern of mitogenic response, involving inhibition of early growth-factor induced DNA synthesis and stimulation of late DNA synthesis, is consistent with that reported to be effected in some instances by transforming growth factor beta. Because a defined pattern of gene expression also is associated with the mitogenic responses to transforming growth factor beta, future studies at the molecular level can definitively test the degree to which Cd⁺⁺ and transforming growth factor beta effects are common.Abbreviations CFE colony forming efficiency - EGF epidermal growth factor - MT metallothionein - PGDF paltelet derived growth factor - TGF transforming growth factor     

Transient permeability induced by alkyl derivatives of amphotericin B in lipid membranes

Individual ionic channels were shown to be formed in the brain cholesterol containing phospholipid membranes by two-sided addition of the amphotericin B alkyl derivatives. At concentrations between 10⁻⁸ and 10⁻⁷ M, the resulting conductance appeared to be transient. Existence of different antibiotic assemblies was justified by the kinetic analysis of the membrane conductance decline following the antibiotic washing out. In order to account for the transient characteristics of the induced conductance, it was proposed that the antibiotic oligomers incorporate into the membrane from the aqueous phase, form channels aggregating with cholesterol, and then dissociate in the bilayer into non-active degraded oligomeric or monomeric forms.     

Contribution to the study of periodic chronic myelogenous leukemia

The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.