Use of stochastic models to assess the effect of environmental factors on microbial growth

We present a novel application of a stochastic ecological model to the study and analysis of microbial growth dynamics as influenced by environmental conditions in an extensive experimental data set. The model proved to be useful in bridging the gap between theoretical ideas in ecology and an applied problem in microbiology. The data consisted of recorded growth curves of Escherichia coli grown in triplicate in a base medium with all 32 possible combinations of five supplements: glucose, NH(4)Cl, HCl, EDTA, and NaCl. The potential complexity of 2(5) experimental treatments and their effects was reduced to 2(2) as just the metal chelator EDTA, the presumed osmotic pressure imposed by NaCl, and the interaction between these two factors were enough to explain the variability seen in the data. The statistical analysis showed that the positive and negative effects of the five chemical supplements and their combinations were directly translated into an increase or decrease in time required to attain stationary phase and the population size at which the stationary phase started. The stochastic ecological model proved to be useful, as it effectively explained and summarized the uncertainty seen in the recorded growth curves. Our findings have broad implications for both basic and applied research and illustrate how stochastic mathematical modeling coupled with rigorous statistical methods can be of great assistance in understanding basic processes in microbial ecology.     

Ecology theory disentangles microbial dichotomies

Microbes are often discussed in terms of dichotomies such as copiotrophic/oligotrophic and fast/slow-growing microbes, defined using the characterisation of microbial growth in isolated cultures. The dichotomies are usually qualitative and/or study-specific, sometimes precluding clear-cut results interpretation. We can unravel microbial dichotomies as life history strategies by combining ecology theory with Monod curves, a laboratory mathematical tool of bacterial physiology that relates the specific growth rate of a microbe with the concentration of a limiting nutrient. Fitting of Monod curves provides quantities that directly correspond to key parameters in ecological theories addressing species coexistence and diversity, such as r/K selection theory, resource competition and community structure theory and the CSR triangle of life strategies. The resulting model allows us to reconcile the copiotrophic/oligotrophic and fast/slow-growing dichotomies as different subsamples of a life history strategy triangle that also includes r/K strategists. We also used the number of known carbon sources together with community structure theory to partially explain the diversity of heterotrophic microbes observed in metagenomics experiments. In sum, we propose a theoretical framework for the study of natural microbial communities that unifies several existing proposals. Its application would require the integration of metagenomics, metametabolomics, Monod curves and carbon source data.     

On the lag phase and initial decline of microbial growth curves

The lag phase is generally thought to be a period during which the cells adjust to a new environment before the onset of exponential growth. Characterizing the lag phase in microbial growth curves has importance in food sciences, environmental sciences, bioremediation and in understanding basic cellular processes. The goal of this work is to extend the analysis of cell growth curves and to better estimate the duration of the lag phase. A non-autonomous model is presented that includes actively duplicating cells and two subclasses of non-duplicating cells. The growth curves depend on the growth and death rate of these three subpopulations and on the initial proportion of each. A deterministic and a stochastic model are both developed and give the same results. A notable feature of the model is the decline of cells during the early stage of the growth curve, and the range of parameters when this decline occurs is identified. A limited growth model is also presented that accounts for the lag, exponential growth and stationary phase of microbial growth curves.     

Temporal scaling of bacterial taxa is influenced by both stochastic and deterministic ecological factors

Microorganisms operate at a range of spatial and temporal scales acting as key drivers of ecosystem properties. Therefore, many key questions in microbial ecology require the consideration of both spatial and temporal scales. Spatial scaling, in particular the species-area relationship (SAR), has a long history in ecology and has recently been addressed in microbial ecology. However, the temporal analogue of the SAR, the species-time relationship, has received far less attention even in the science of general ecology. Here we focus upon the role of temporal scaling in microbial ecological patterns by coupling molecular characterization of bacterial communities in discrete island (bioreactor) systems with a macroecological approach. Our findings showed that the temporal scaling exponent (slope), and therefore taxa turnover of the bacterial taxa-time relationship decreased as selective pressure (industrial wastewater concentration) increased. Also, as the concentration of industrial wastewater increased across the bioreactors, we observed a gradual switch from stochastic community assembly to more deterministic (niche)-based considerations. The identification of broad-scale statistical patterns is particularly relevant to microbial ecology, as it is frequently difficult to identify individual species or their functions. In this study, we identify wide-reaching statistical patterns of diversity and show that they are shaped by the prevalent underlying ecological factors.     

Extractable Microbial DNA Pool and Microbial Activity in Paleosols of Southern Urals

An evaluation of microbial DNA pools was performed using direct quantitative isolation of DNA from contemporary soils of Southern Urals and paleosols sealed under burial mounds early in the Bronze Age more than 5000 years B.P. Significant regression dependence was found between the biomass and DNA contents in these soils (R ²= 0.97). Activity and dominant ecological strategies of microbial communities of paleosols and contemporary southern black soil were compared from growth parameters obtained by analysis of respiratory curves. The ratio of maximum specific growth rates of soil microorganisms on glucose and on yeast extract was shown to provide an auxotrophy index for soil microbial communities.     

Scaling up: how do exogenous fluctuations in individual-based resource competition models re-emerge in aggregated stochastic population models?

In applied population dynamics the choice of stochastic per capita growth function has implications for population viability analyses, management recommendations, and pest control. This model choice is often based on statistical criteria, mathematical tractability or personal preferences, and general ecological guidelines are either too vague or entirely missing. To identify such guidelines, it is important to understand how exogenous and endogenous factors interact at the individual level and re-emerge at the aggregated population level. We therefore study different types of resource competition (contest vs. scramble competition) and different types of exogenous fluctuations (food and weather fluctuations) at the individual level in a simple individual-based simulation model. We statistically fit the resulting time series to find out (1) which functional form of the growth function (‘hyperbolic’ or ‘exponential’) better describes contest and scramble competition and (2) whether the pattern of population fluctuations resulting from the simulations can be assigned to vertical, lateral or nonlinear perturbations in the stochastic growth function (a classification scheme suggested by Royama 1992, Analytical Population Dynamics, Chapman and Hall, London). We found that the same type of competition can result in ‘hyperbolic’ or ‘exponential’ functional forms, depending on the type of exogenous fluctuations. So it is the interplay between exogenous variability and endogenous resource competition that affects model performance. In contrast to the widespread assumption of vertical (additive) perturbations, our findings highlight the importance of (non-additive) lateral and nonlinear perturbations and their combinations with vertical perturbations. The choice of the stochastic growth function should therefore consider not only statistical criteria but also ecological guidelines. We derive such ecological guidelines from our analysis.     

Quantitative patterns of development of community of <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis> dissociants

The stationary phase of batch culture of Pseudomonas aeruginosa dissociants has been described by a variational model of consumption and growth. The generalized entropy functional was used as the objective function. The model parameters include the requirements of the dissociants for the main nutrients: carbon, nitrogen, and phosphorus. The variational model was used to calculate the limiting regions and microbial community composition during stationary growth for different initial combinations of the resources as a function of the limiting resources. A correspondence between the experimental data and model calculations has been demonstrated. A possibility to control the community structure is discussed.     

Sequence-dependent model of genes with dual σ factor preference

Escherichia coli uses σ factors to quickly control large gene cohorts during stress conditions. While most of its genes respond to a single σ factor, approximately 5% of them have dual σ factor preference. The most common are those responsive to both σ⁷⁰, which controls housekeeping genes, and σ³⁸, which activates genes during stationary growth and stresses. Using RNA-seq and flow-cytometry measurements, we show that ‘σ⁷⁰⁺³⁸ genes’ are nearly as upregulated in stationary growth as ‘σ³⁸ genes’. Moreover, we find a clear quantitative relationship between their promoter sequence and their response strength to changes in σ³⁸ levels. We then propose and validate a sequence dependent model of σ⁷⁰⁺³⁸ genes, with dual sensitivity to σ³⁸ and σ⁷⁰, that is applicable in the exponential and stationary growth phases, as well in the transient period in between. We further propose a general model, applicable to other stresses and σ factor combinations. Given this, promoters controlling σ⁷⁰⁺³⁸ genes (and variants) could become important building blocks of synthetic circuits with predictable, sequence-dependent sensitivity to transitions between the exponential and stationary growth phases.     

Ecological Application of Antibiotics as Respiratory Inhibitors of Bacterial Populations

Two terregenous and four marine bacterial isolates were treated with six antibiotics and antibiotic combinations. Comparisons made between responses of cells in early and late logarithmic and stationary growth phases indicated variable sensitivity to the agents. Bacteria in stationary and late log-phase cultures exhibited the greatest resistance, whereas the early log-phase cells exhibited greatest antibiotic susceptibility. We conclude that the tested antibiotics cannot be used for ecological purposes to delineate bacterial respiration in mixed microbial communities.     

Bacterial Degradation of EDTA

Degradation of EDTA (ethylenediaminetetraacetic acid) or metal–EDTA complexes by cell suspensions of the bacterial strain DSM 9103 was studied. The activity of EDTA degradation was the highest in the phase of active cell growth and decreased considerably in the stationary phase, after substrate depletion in the medium. Exponential-phase cells were incubated in HEPES buffer (pH 7.0) with 1 mM of uncomplexed EDTA or EDTA complexes with Mg²⁺, Ca²⁺, Mn²⁺, Pb²⁺, Co²⁺, Cd²⁺, Zn²⁺, Cu²⁺, or Fe³⁺. The metal–EDTA complexes (Me–EDTA) studied could be divided into three groups according to their degradability. EDTA complexes with stability constants K below 10¹⁶ (log K < 16), such as Mg–EDTA, Ca–EDTA, and Mn–EDTA, as well as uncomplexed EDTA, were degraded by the cell suspensions at a constant rate to completion within 5–10 h of incubation. Me–EDTA complexes with log K above 16 (Zn–EDTA, Co–EDTA, Pb–EDTA, and Cu–EDTA) were not completely degraded during a 24-h incubation, which was possibly due to the toxic effect of the metal ions released. No degradation of Cd–EDTA or Fe(III)–EDTA by cell suspensions of strain DSM 9103 was observed under the conditions studied.     

Understanding evolutionary and ecological dynamics using a continuum limit

Continuum limits in the form of stochastic differential equations are typically used in theoretical population genetics to account for genetic drift or more generally, inherent randomness of the model. In evolutionary game theory and theoretical ecology, however, this method is used less frequently to study demographic stochasticity. Here, we review the use of continuum limits in ecology and evolution. Starting with an individual‐based model, we derive a large population size limit, a (stochastic) differential equation which is called continuum limit. By example of the Wright–Fisher diffusion, we outline how to compute the stationary distribution, the fixation probability of a certain type, and the mean extinction time using the continuum limit. In the context of the logistic growth equation, we approximate the quasi‐stationary distribution in a finite population.     

Properties of a lipase produced by Beauveria bassiana: purification and biochemical studies

Lipases are some of the crucial enzymes during the fungal penetrating process of the insect integument. Due to the importance and lack of information on the microbial lipases of Beauveria bassiana, investigations were carried out to purify and biochemically characterize these enzymes. The results obtained on growth medium demonstrated the highest activity of lipase 6 days after inoculation while the pH of the medium was 7.1. After three purification steps, the purified enzyme was 9.91-fold with specific activity of 20816 U/mg protein, recovery of 25% and molecular weight of 25 kDa. The purified lipase had the optimal pH and temperature at 7 and 35°C and was stable for 36–72 h under those conditions. Ca^{2 +} significantly increased the enzyme activity and NaCl decreased it at all the tested concentrations. In addition, Mn^{2 +} had no effect on enzyme activity but Mg^{2 +} and Zn^{2 +} increased it only at the highest concentration used. Three out of the four inhibitors used, significantly decreased the purified lipase activity so that most inhibition and changes in the enzyme kinetic parameters were obtained by using different concentrations of EDTA. Knowledge of enzymology provides important information for the development of fungi as microbial pest control agents opening new avenues for study of the role of enzymes in virulence.     

Counting Viruses and Bacteria in Photosynthetic Microbial Mats

Viral abundances in benthic environments are the highest found in aquatic systems. Photosynthetic microbial mats represent benthic environments with high microbial activity and possibly high viral densities, yet viral abundances have not been examined in such systems. Existing extraction procedures typically used in benthic viral ecology were applied to the complex matrix of microbial mats but were found to inefficiently extract viruses. Here, we present a method for extraction and quantification of viruses from photosynthetic microbial mats using epifluorescence microscopy (EFM) and flow cytometry (FCM). A combination of EDTA addition, probe sonication, and enzyme treatment applied to a glutaraldehyde-fixed sample resulted in a substantially higher viral (5- to 33-fold) extraction efficiency and reduced background noise compared to previously published methods. Using this method, it was found that in general, intertidal photosynthetic microbial mats harbor very high viral abundances (2.8 × 10¹⁰ ± 0.3 × 10¹⁰ g⁻¹) compared with benthic habitats (10⁷ to 10⁹ g⁻¹). This procedure also showed 4.5- and 4-fold-increased efficacies of extraction of viruses and bacteria, respectively, from intertidal sediments, allowing a single method to be used for the microbial mat and underlying sediment.     

Kinetics and Modeling of Lactic Acid Production by Lactobacillus plantarum

An unstructured model was developed to describe bacterial growth, substrate utilization, and lactic acid production by Lactobacillus plantarum in cucumber juice. Significant lactic acid production occurred during growth, as well as stationary phases. The percentage of acid produced after growth ceased was a function of the medium composition. Up to 51% of the lactic acid was produced after growth ceased when NaCl was not present in the medium, whereas not more than 18% of the total lactic acid was produced after the growth ceased in presence of NaCl, probably because of an increase in the cell death rate. An equation relating the specific death rate and NaCl concentration was developed. With the kinetic model proposed by R. Luedeking and E. L. Piret (J. Biochem. Microbiol. Technol. Eng. 1:393-412, 1958) for lactic acid production rate, the growth-associated and non-growth-associated coefficients were determined as 51.9 (±4.2) mmol/g of cells and 7.2 (±0.9) mmol/g of cells h^-1 respectively. The model was demonstrated for batch growth of L. plantarum in cucumber juice. Mathematical simulations were used to predict the influence of variations in death rate, proton concentration when growth ceased, and buffer capacity of the juice on the overall fermentation process.     

Effect of carbon:nitrogen ratio on kinetics of phenol biodegradation byAcinetobacter johnsonii in saturated sand

In polluted soil or ground water, inorganic nutrients such as nitrogen may be limiting, so that Monod kinetics for carbon limitation may not describe microbial growth and contaminant biodegradation rates. To test this hypothesis we measured¹⁴CO₂ evolved by a pure culture ofAcinetobacter johnsonii degrading 120 µg¹⁴C-phenol per ml in saturated sand with molar carbon:nitrogen (CN) ratios ranging from 1.5 to 560. We fit kinetics models to the data using non-linear least squares regression. Phenol disappearance and population growth were also measured at CN1.5 and CN560.After a 5- to 10-hour lag period, most of the¹⁴CO₂ evolution curves at all CN ratios displayed a sigmoidal shape, suggesting that the microbial populations grew. As CN ratio increased, the initial rate of¹⁴CO₂ evolution decreased. Cell growth and phenol consumption occurred at both CN1.5 and CN560, and showed the same trends as the¹⁴CO₂ data. A kinetics model assuming population growth limited by a single substrate best fit the¹⁴CO₂ evolution data for CN1.5. At intermediate to high CN ratios, the data were best fit by a model originally formulated to describe no-growth metabolism of one substrate coupled with microbial growth on a second substrate. We suggest that this dual-substrate model describes linear growth on phenol while nitrogen is available and first-order metabolism of phenol without growth after nitrogen is depleted.     

Effects of iron and chelation on Lake Kinneret bacteria

The response of natural populations of bacteria (prepared by passing Lake Kinneret water through 1 m filters) to additions of Fe²⁺ and/or the chelator ethylenediaminetetraacetic acid (EDTA) was followed by measuring the incorporation of ³H-thymidine into >0.2 m particulates, and also by determining the increments in cell numbers after 24 h. In most cases, a stimulation of ³H-thymidine incorporation was observed in supplemented samples relative to untreated controls after 3 and 24 h incubation. The increase in bacterial numbers was also enhanced by these supplements. Generally, EDTA alone evoked a greater stimulation than Fe²⁺; combined supplements gave no further increase. This response pattern appeared consistently throughout the year in samples taken from near-surface lake waters. These results suggest that the availability of iron or chelators may play an important role in regulating bacterial metabolism and growth even in aquatic ecosystems like Lake Kinneret where ambient concentrations of total Fe are relatively high. Offprint request to: T. Berman.     

Enhanced Phytoremediation of Cadmium-Contaminated Soil by Parthenium hysterophorus Plant: Effect of Gibberellic Acid (GA3) and Synthetic Chelator,Alone and in Combinations

The roles of gibberellic acid (GA₃) and ethylenediaminetetraacetic acid (EDTA) in phytoremediation of cadmium (Cd)-contaminated soil by Parthenium hysterophorus plant was investigated. GA₃ (10^?9, 10^?7, and 10^?5M) was applied as a foliar spray. EDTA was added to soil in a single dose (160 mg/kg soil) and split doses (40 mg/kg soil, four split doses). GA₃ and EDTA were used separately and in various combinations. P. hysterophorus was selected due to its fast growth and unpalatable nature to herbivores to reduce the entrance of metal into the food chain. The Cd phytoextraction potential of the P. hysterophorus plant was evaluated for the first time. Cd significantly reduced plant growth and dry biomass (DBM). GA₃ alone increased the plant growth and biomass in Cd-contaminated soil, whereas EDTA reduced it. GA₃ in combination with EDTA significantly increased the growth and biomass. The highest significant DBM was found in treatment T3 (10^?5M GA₃). All treatments of GA₃ or EDTA significantly enhanced the plant Cd uptake and accumulation compared with control (C1). The highest significant root and stem Cd concentrations were found in the combination treatment T11 (GA₃ 10^?5M + EDTA split doses), whereas in leaves it was found in the EDTA treatments. Cd concentration in plant parts increased in the order of stem < leaves < roots. The combination treatment T9 (GA₃ 10^?7M + EDTA split doses) showed the significantly highest total Cd accumulation (8 times greater than control C1, i.e., only Cd used). The GA₃ treatments accumulated more than 50% of the total Cd in the roots, whereas the EDTA treatments showed more than 50% in the leaves. Root dry biomass showed a positive and significant correlation with Cd accumulation. GA₃ is environment friendly as compared with EDTA. Therefore, further investigation of GA₃ is recommended for phytoremediation research for the remediation of metal-contaminated soil.     

The use of automated tubidimetric data for the construction of kinetic models

Summary An automated tubidimetric instrument (Bioscreen) was used to observe the growth response ofListeria monocytogenes to combinations of temperature (15–30°C), hydrogen-ion (0.1–21.9 m) (equivalent pH 4.66–7.0) and NaCl concentration (0.5–9.5% w/v). Compared to traditional plate count techniques, the technique allowed many more data points to be captured and replicates to be used, with less expenditure of effort. Optical density curves were filtered (smoothed) to minimize the effect of signal noise and the mean signal from uninoculated wells was subtracted to minimize the effect of signal draft. A novel procedure for fitting growth curves to optical density data has been developed. The procedure involves the use of the logistic function and a calibration equation for fitting, in a single step, in the dimension of optical density. This approach allowed the four parameters of the logistic equation to be derived at each set of experimental conditions. A quadratic response surface was then fitted to the curve parameters using temperature, NaCl and hydrogen-ion concentration as three independent variables. Predicted time to 1000-fold increase in cell numbers compared well to predictions from predictive microbial growth equations generated in other laboratories using traditional plate counting. We propose that this technique should be further evaluated as a method for generating data for modeling the kinetics of microbial growth.Mention of brand or firm names does not constitute an endorsement by the US Department of Agriculture over others of a similar nature not mentioned.     

Aspects of Salt Tolerance in a NaCl-Selected Stable Cell Line of Citrus sinensis

A NaCl-tolerant cell line which was selected from ovular callus of `Shamouti' orange (Citrus sinensis L. Osbeck) proved to be a true cell line variant. This conclusion is based on the following observations. (a) Cells which have been removed from the selection pressure for at least four passages retain the same NaCl tolerance as do cells which are kept constantly on 0.2 molar NaCl. (b) Na⁺ and Cl⁻ uptake are considerably lower in salt-tolerant cells (R-10) than in salt-sensitive cells (L-5) at a given external NaCl concentration. (c) Growth of salt-tolerant cells is markedly suppressed upon replacement of NaCl by KCl, whereas the growth of salt-sensitive cells is only slightly affected. Accumulation of K⁺ and Cl⁻ accompanies the inhibition of growth. Experiments carried out with sodium and potassium sulfate suggest that the toxic effect is due to the accumulated Cl⁻. (d) Removal of Ca²⁺ from the growth medium severely inhibits the growth of salt-tolerant cells in the presence of NaCl, while it has a minor effect on growth of salt-sensitive cells in the presence of NaCl. (e) Electron micrographs show that the salt-tolerant cells have very big vacuoles when exposed to salt, while the size of the vacuoles of the salt-sensitive cells does not change.