Mathematical modeling for mixed culture growth of two bacterial populations with opposite substrate preferences

An unstructured mathematical model is proposed for mixed culture growth of two different bacterial species that exhibit "opposite" substrate preferences in response to the "same" environmental conditions. The model incorporates enzymatic control mechanisms such as induction, repression, and inhibition in the microorganisms as manifested in their preferential utilization of substrates and microbial interactions such as amensalism and competition. The model predicts cell mass, substrate concentrations, dissolved oxygen tension, as well as key enzyme levels. The predictions of the model are compared with experimental data for pure culture growth and for mixed culture growth on two substrates, glucose and citrate, in a batch reactor.     

Modelling of microbial growth for sequential utilization in a multisubstrate environment

Microbial growth in multisubstrate environments is posed as a problem of multivariable constraint optimization. The optimization aims at maximizing the instantaneous growth rate of cells. The model developed for microbial growth using this hypothesis involves simple representation of complex cell structure as an optimization function which regulates the interplay of cellular machinery. The model parameters are estimated using single substrate growth data. Model simulation fits very well with earlier published experimental data of bacterial growth of Klensiella oxytoca on a variety of sugar mixtures involving glucose, fructose, lactose, and xylose. Moreover, the model is also able to predict the diauxic growth of Saccharomyces cerevisiae on glucose and galactose. One of the interesting outcomes of the above representation is the ability to prove analytically that the growth on the mixture of two sugars will be diauxic if one of the substrates has a very low K_s value and a high μ_m value.     

Control of mixed-substrate utilization in continuous cultures of Escherichia coli

The chemostat culture technique was used to study the control mechanisms which operate during utilization of mixtures of glucose and lactose and glucose and l-aspartic acid by populations of Escherichia coli B6. Constitutive mutants were rapidly selected during continuous culture on a mixture of glucose and lactose, and the beta-galactosidase level of the culture increased greatly. After mutant selection, the specific beta-galactosidase level of the culture was a decreasing function of growth rate. In cultures of both the inducible wild type and the constitutive mutant, glucose and lactose were simultaneously utilized at moderate growth rates, whereas only glucose was used in the inducible cultures at high growth rates. Catabolite repression was shown to be the primary mechanism of control of beta-galactosidase level and lactose utilization in continuous culture on mixed substrates. In batch culture, as in the chemostat, catabolite repression acting by itself on the lac enzymes was insufficient to prevent lactose utilization or cause diauxie. Interference with induction of the lac operon, as well as catabolite repression, was necessary to produce diauxic growth. Continuous cultures fed mixtures of glucose and l-aspartic acid utilized both substrates at moderate growth rates, even though the catabolic enzyme aspartase was linearly repressed with increasing growth rate. Although the repression of aspartase paralleled the catabolite repression of beta-galactosidase, l-aspartic acid could be utilized even at very low levels of the catabolic enzyme because of direct anabolic incorporation into protein.     

Regulation of the utilization of glucose and aromatic substrates in four strains of Pseudomonas putida

During the oxidation of various mixtures of glucose and aromatic substrates by four strains of Pseudomonas putida, diauxic growth was not observed. Strain A3.12 grew faster on benzoate than on glucose, whereas three other strains showed faster growth on glucose than on the aromatic test substrates. Growth rates on mixtures of glucose and aromatics were intermediate between those on the single substrates.The presence of glucose in media containing aromatic substrates accelerated in the bacteria the appearance of the ability to oxidize aromatic substrates. During growth of the organisms on binary mixtures of aromatics, simultaneous utilization of these compounds occurred, the utilization ratio depending on the quality of the compounds as carbon and energy sources. Addition of glucose to dual aromatic substrate media greatly increased the utilization ratio in favour of the better aromatic substrate.With decreasing concentration of glucose in relation to that of aromatic substrates, the rate of carbon assimilation from glucose increased. Enzymological and radiochemical studies demonstrated that even in the presence of an excess of aromatic substrates, glucose was exclusively catabolized via the 2-keto-3-deoxy-6-phosphogluconate pathway. In contrast, the rate of carbon assimilation from ¹⁴C-ring-labelled benzoate and anisate was unaffected by the presence of an excess of glucose.Abbreviations KDPG 2-keto-3-deoxy-6-phosphogluconate - PP pentose-phosphate - OD optical density     

Kinetic models for the growth of Escherichia coli with mixtures of sugars under carbon-limited conditions

In natural environments, heterotrophic microorganisms encounter complex mixtures of carbon sources, each of which is present only at very low concentrations. Under such conditions no significant growth could be expected if cells utilized only one of the available carbon compounds as suggested by the principle of diauxic growth. Indeed, there is much evidence that microbial cells utilize many carbon sources simultaneously. In order to predict bacterial growth under such conditions we developed a model describing the specific growth rate as a function of the individual concentrations of several simultaneously utilized carbon substrates. Together with multisubstrate models previously published, this model was evaluated for its ability to describe growth of Escherichia coli during the simultaneous utilization of mixtures of sugars in carbon-limited continuous culture. Using the micromax and Ks constants determined for single substrate growth with six different sugars, the model was able for most experiments to adequately describe the specific growth rate of the culture, i.e., the experimentally set dilution rate, from the measured concentrations of the individual sugars. The model provides an explanation why bacteria can still grow relatively fast under environmental conditions where the concentrations of carbon substrates are usually extremely low.     

Regulation of beta-1, 4-Glucosidase Expression by Candida wickerhamii

Candida wickerhamii NRRL Y-2563 expressed beta-glucosidase activity (3 to 8 U/ml) constitutively when grown aerobically in complex medium containing either glycerol, succinate, xylose, galactose, or cellobiose as the carbon source. The addition of a high concentration of glucose (>75 g/liter) repressed beta-glucosidase expression (<0.3 U/ml); however, this yeast did produce beta-glucosidase when the initial glucose concentration was 相似文献   

Regulation of growth of Acinetobacter calcoaceticus NCIB8250 on L-mandelate in batch culture.

Batch culture of Acinetobacter calcoaceticus in L-mandelate- or phenylglyoxylate-salts medium showed an unusual non-exponential pattern unless the inoculum had been grown on benzyl alcohol. There were transient accumulations of benzaldehyde and benzyl alcohol caused by the limitation of L-mandelate oxidation by low activities of benzaldehyde dehydrogenase and the diversion of reducing power to the formation of benzyl alcohol. In vivo enzymic activities were estimated from patterns of substrate utilization in batch cultures containing pairs of substrates. When bacteria previously grown in L-mandelate-salts medium were inoculated into media containing L-mandelate and a second carbon source, metabolism of L-mandelate was arithmetical in the presence of benzoate, catechol or succinate, but accelerated on exhaustion of the second substrate. This indicated repression of the enzymes involved in L-mandelate oxidation. Inoculation of bacteria grown in benzoate-salts medium into medium containing L-mandelate and benzoate gave diauxie with initial utilization of benzoate. Similar experiments showed that benzoate oxidation was not repressed by catechol and only partially repressed by succinate. Measurement of L-mandelate dehydrogenase, phenylglyoxylate carboxy-lyase and benzaldehyde dehydrogenase I in bacterial extracts showed no evidence for feedback inhibition by intermediates of the pathway. The rates of L-mandelate and benzoate utilization by bacterial suspensions were inhibited by succinate and catechol but not by other intermediates of the pathway.     

Cybernetic modeling of microbial growth on multiple substrates

The internal regulatory processes, which underlie a variety of behavior in microbial growth on multiple substrates, are viewed as a manifestation of an invariant strategy to optimize some goal of the cells. A goal-seeking or cybernetic model is proposed here, with the optimization obased on a short-term perspective of response to the environment. The model parameters are determined from the growth data on single substrates. The model predicts the entire range of microbial growth behavior on multiple substrates from simultaneous utilization of all sugars to sequential utilization with pronounced diauxic lags. It is shown to predict the many variations of the diauxic phenomenon in different growth conditions. The transients in continuous culture growth on mixed substrates caused by varying the feed strategies are easily simulated by this model. The framework of this model can be applied to batch or continuous culture growth of many bacteria on different combinations of substrates.     

Sequential utilization of substrates by Pseudomonas putida CSV86: signatures of intermediate metabolites and online measurements

Pseudomonas putida CSV86 preferentially utilizes aromatics over glucose and co-metabolizes them with organic acids. On aromatics plus glucose, CSV86 utilized aromatics first with concomitant appearance of transient metabolites such as salicylate, benzaldehyde and benzoate. Citrate was the main extracellular metabolite observed during glucose uptake. The strain showed simultaneous utilization of organic acids and aromatic compounds. Based on the metabolite analysis and growth profiles, we hypothesize that the repression of glucose utilization could be due to organic acid intermediates generated from aromatic compound metabolism. The online measurements indicate the instantaneous metabolic state of the culture. For example, the CO₂ evolution and agitation speed show peak values during the two growth phases in the diauxic growth while dissolved oxygen values show decrease at the corresponding durations. These measurements correlated well with the offline measurements but provided a better time resolution of the process.     

Sequential Substrate Removal in a Dilute System by Heterogeneous Microbial Populations

The sequential metabolism of substrates by heterogeneous bacterial populations has been previously reported from this laboratory in studies with high substrate concentrations. This phenomenon has now been shown to occur at very dilute substrate concentrations, i.e., 5 mg/liter of glucose plus 5 mg/liter of sorbitol, in studies conducted under the conditions of the standard biochemical oxygen demand (BOD) test. Sequential metabolism of these substrates resulted in a diphasic curve of accumulated oxygen uptake wherein the two phases were separated by a discernible plateau. These findings illustrate one possible explanation for the generation of discontinuity in the kinetic course of carbonaceous BOD exertion.     

Physiology of Geobacter metallireducens under excess and limitation of electron donors. Part I. Batch cultivation with excess of carbon sources

For microorganisms that play an important role in bioremediation, the adaptation to swift changes in the availability of various substrates is a key for survival. The iron-reducing bacterium Geobacter metallireducens was hypothesized to repress utilization of less preferred substrates in the presence of high concentrations of easily degradable compounds. In our experiments, acetate and ethanol were preferred over benzoate, but benzoate was co-consumed with toluene and butyrate. To reveal overall physiological changes caused by different single substrates and a mixture of acetate plus benzoate, a nano-liquid chromatography–tandem mass spectrometry-based proteomic approach (nano-LC–MS/MS) was performed using label-free quantification. Significant differential expression during growth on different substrates was observed for 155 out of 1477 proteins. The benzoyl-CoA pathway was found to be subjected to incomplete repression during exponential growth on acetate in the presence of benzoate and on butyrate as a single substrate. Peripheral pathways of toluene, ethanol, and butyrate degradation were highly expressed only during growth on the corresponding substrates. However, low expression of these pathways was detected in all other tested conditions. Therefore, G. metallireducens seems to lack strong carbon catabolite repression under high substrate concentrations, which might be advantageous for survival in habitats rich in fatty acids and aromatic hydrocarbons.     

Regulation of β-1, 4-Glucosidase Expression by Candida wickerhamii

Candida wickerhamii NRRL Y-2563 expressed β-glucosidase activity (3 to 8 U/ml) constitutively when grown aerobically in complex medium containing either glycerol, succinate, xylose, galactose, or cellobiose as the carbon source. The addition of a high concentration of glucose (>75 g/liter) repressed β-glucosidase expression (<0.3 U/ml); however, this yeast did produce β-glucosidase when the initial glucose concentration was ≤50 g/liter. When grown aerobically in medium containing glucose plus the above-listed carbon sources, diauxic utilization of the carbon source was observed and the expression of β-glucosidase was glucose repressed. Surprisingly, glucose repression did not occur when the cells were grown anaerobically. When grown anaerobically in medium containing 100 g of glucose per liter, C. wickerhamii produced 6 to 9 U of enzyme per ml and did not demonstrate diauxic utilization of glucose-cellobiose mixtures. To our knowledge, this is the first report of apparent derepression of a glucose-repressed enzyme by anaerobiosis.     

Catabolic enzyme levels in bacteria grown on binary and ternary substrate mixtures in continuous culture

Bacteria grow on multicomponent substrates in most natural and engineered environments. To advance our ability to model bacterial growth on such substrates, axenic cultures were grown in chemostats at a low specific growth rate and a constant total energy flux on binary and ternary substrate mixtures and were assayed for key catabolic enzymes for each substrate. The substrates were benzoate, salicylate, and glucose, and the enzymes were catechol 1,2-dioxygenase, gentisate 1,2-dioxygenase, and glucose-6-phosphate dehydrogenase, respectively. The binary mixtures were salicylate with benzoate and salicylate with glucose. Measurements were also made of oxygen uptake rate by whole cells in response to each substrate. The effects of the substrate mixture on the oxygen uptake rate paralleled the effects on the measured enzymes. Catechol 1,2-dioxygenase exhibited a threshold response before synthesis occurred. Below the threshold flux of benzoate through the chemostat, either basal enzyme levels or nonspecific enzymes kept reactor concentrations too low for enzyme synthesis. Above the threshold, enzyme levels were linearly related to the fraction of the total energy flux through the chemostat due to benzoate. Gentisate 1,2-dioxygenase exhibited a linear response to the salicylate flux when mixed with benzoate, but a threshold response when mixed with glucose. Glucose-6-phosphate dehydrogenase activity increased in direct proportion to the glucose flux through the chemostat over the entire range studied. The results from two ternary mixtures were consistent with those from the binary mixtures.     

Sequential bioavailability of sedimentary organic matter to heterotrophic bacteria

Aquatic sediments harbour diverse microbial communities that mediate organic matter degradation and influence biogeochemical cycles. The pool of bioavailable carbon continuously changes as a result of abiotic processes and microbial activity. It remains unclear how microbial communities respond to heterogeneous organic matrices and how this ultimately affects heterotrophic respiration. To explore the relationships between the degradation of mixed carbon substrates and microbial activity, we incubated batches of organic‐rich sediments in a novel bioreactor (IsoCaRB) that permitted continuous observations of CO₂ production rates, as well as sequential sampling of isotopic signatures (δ¹³C, Δ¹⁴C), microbial community structure and diversity, and extracellular enzyme activity. Our results indicated that lower molecular weight (MW), labile, phytoplankton‐derived compounds were degraded first, followed by petroleum‐derived exogenous pollutants, and finally by higher MW polymeric plant material. This shift in utilization coincided with a community succession and increased extracellular enzyme activities. Thus, sequential utilization of different carbon pools induced changes at both the community and cellular level, shifting community composition, enzyme activity, respiration rates, and residual organic matter reactivity. Our results provide novel insight into the accessibility of sedimentary organic matter and demonstrate how bioavailability of natural organic substrates may affect the function and composition of heterotrophic bacterial populations.     

Studies on Induction and Repression in Activated Sludge Systems

Both repression and induction of substrate utilization have been the subject of many basic research investigations employing pure cultures. In this investigation these effects were studied using heterogeneous microbial populations prevalent in such biological treatment processes as activated sludge systems.Diauxic substrate removal by activated sludge was observed in a multicomponent medium consisting of glucose and sorbitol. The sludge was acclimated solely to sorbitol; however, the presence of glucose blocked sorbitol removal until glucose was completely utilized. Both diphasic and triphasic oxygen utilization was shown for activated sludges metabolizing multicomponent synthetic wastes consisting of glucose, melibiose, and lactose. It appears from these studies that melibiose utilization was suppressed by the presence of glucose and, although melibiose induced acclimation to lactose, the presence of melibose suppressed lactose utilization. Studies were also conducted using glycogen and starch systems in which it was found that acclimation to either compound conferred immediate acclimation to the other. It was also found that loss of acclimation to lactose was a passive phenomenon and its kinetics could be predicted on the basis of simple diluting out of the enzyme(s) responsible for such acclimation.     

New patterns of mixed-substrate utilization during batch growth of Escherichia coli K12

Microbial growth on mixtures of substrates is of considerable engineering and biological interest. Most of the work until now has dealt with microbial growth on binary mixtures of sugars or polyols. In these cases, it is often found that no matter how the inoculum is precultured, only one of the two substrates is consumed in the first growth phase, leading to the diauxic growth pattern. The goal of the experiments reported here is to investigate growth on mixtures containing at least one organic acid. These experiments show that the substrate utilization patterns in such mixtures are qualitatively different from the diauxic growth pattern. For instance, during growth of Escherichia coli K12 on certain binary mixtures of organic acids, the two substrates are utilized simultaneously, and the mixed-substrate maximum specific growth rate exceeds the single-substrate maximum specific growth rate on either one of the two constituent substrates. Furthermore, the very same mixed-substrate maximum specific growth and substrate uptake rates are observed no matter how the inoculum is precultured. On the other hand, in a mixture of glucose and pyruvate, the maximum specific growth rate seems to depend on the preculturing conditions, thus suggesting the existence of multiple physiological quasi-steady states. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 747-757, 1997.     

Cybernetic modeling of the cephalosporin C fermentation process by Cephalosporium acremonium

A cybernetic mathematical model has been developed to describe the production of cephalosporin C. In developing the model, diauxic behavior of substrate consumption, morphological differentiation of cells, and catabolite repression of cephalosporin C production by the preferred substrate, glucose, were considered. The proposed model was tested on the experimental data from the literature and could adequately describe the morphological differentiation of cells, the sequential utilization of carbon sources and the production of cephalosporin C. It could be a useful tool to optimize the production of cephalosporin C by Cephalosporium acremonium in batch, fed-batch or continuous operations.     

Two distinct pathways for anaerobic degradation of aromatic compounds in the denitrifying bacterium Thauera aromatica strain AR-1

Denitrifying bacteria degrade many different aromatic compounds anaerobically via the well-described benzoyl-CoA pathway. We have shown recently that the denitrifiers Azoarcus anaerobius and Thauera aromatica strain AR-1 use a different pathway for anaerobic degradation of resorcinol (1,3-dihydroxybenzene) and 3,5-dihydroxybenzoate, respectively. Both substrates are converted to hydroxyhydroquinone (1,2,4-trihydroxybenzene). In the membrane fraction of T. aromatica strain AR-1 cells grown with 3,5-dihydroxybenzoate, a hydroxyhydroquinone-dehydrogenating activity of 74 nmol min(-1)(mg protein)-1 was found. This activity was significantly lower in benzoate-grown cells. Benzoate-grown cells were not induced for degradation of 3,5-dihydroxybenzoate, and cells grown with 3,5-dihydroxybenzoate degraded benzoate only at a very low rate. With a substrate mixture of benzoate plus 3,5-dihydroxybenzoate, the cells showed diauxic growth. Benzoate was degraded first, while complete degradation of 3,5-dihydroxybenzoate occurred only after a long lag phase. The 3,5-dihydroxybenzoate-oxidizing and the hydroxyhydroquinone-dehydrogenating activities were fully induced only during 3,5-dihydroxybenzoate degradation. Synthesis of benzoyl-CoA reductase appeared to be significantly lower in 3,5-dihydroxybenzoate-grown cells as shown by immunoblotting. These results confirm that T. aromatica strain AR-1 harbors, in addition to the benzoyl-CoA pathway, a second, mechanistically distinct pathway for anaerobic degradation of aromatic compounds. This pathway is inducible and subject to catabolite repression by benzoate.     

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.     

Comparative analysis of some models of gene regulation in mixed-substrate microbial growth

Mixed-substrate microbial growth is of fundamental interest in microbiology and bioengineering. Several mathematical models have been developed to account for the genetic regulation of such systems, especially those resulting in diauxic growth. In this work, we compare the dynamics of three such models (Narang, 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121; Thattai and Shraiman, 2003. Metabolic switching in the sugar phosphotransferase system of Escherichia coli. Biophys. J. 85(2), 744-754; Brandt et al., 2004. Modelling microbial adaptation to changing availability of substrates. Water Res. 38, 1004-1013). We show that these models are dynamically similar--the initial motion of the inducible enzymes in all the models is described by the Lotka-Volterra equations for competing species. In particular, the prediction of diauxic growth corresponds to "extinction" of one of the enzymes during the first few hours of growth. The dynamic similarity occurs because in all the models, the inducible enzymes possess properties characteristic of competing species: they are required for their own synthesis, and they inhibit each other. Despite this dynamic similarity, the models vary with respect to the range of dynamics captured. The Brandt et al. model always predicts the diauxic growth pattern, whereas the remaining two models exhibit both diauxic and non-diauxic growth patterns. The models also differ with respect to the mechanisms that generate the mutual inhibition between the enzymes. In the Narang model, mutual inhibition occurs because the enzymes for each substrate enhance the dilution of the enzymes for the other substrate. The Brandt et al. model superimposes upon this dilution effect an additional mechanism of mutual inhibition. In the Thattai and Shraiman model, the mutual inhibition is entirely due to competition for the phosphoryl groups. For quantitative agreement with the data, all models must be modified to account for specific mechanisms of mutual inhibition, such as inducer exclusion.