Experimental investigations of multiple steady states in aerobic continuous cultivations of Saccharomyces cerevisiae

The steady-state behavior of a glucose-limited, aerobic, continuous cultivation of Saccharomyces cerevisiae CEN.PK113-7D was investigated around the critical dilution rate. Oxido-reductive steady states were obtained at dilution rates up to 0.09 h(-1) lower than the critical dilution rate by operating the bioreactor as a productostat, where the dilution rate was controlled on the basis of an ethanol measurement. Thus, the experimental investigations revealed that multiple steady states exist in a region of dilution rates below the critical dilution rate. The existence of multiple steady states was attributed to two distinct physiological effects occurring when growth changed from oxidative to oxido-reductive: (i) a decrease in the efficiency of ATP production and utilization (at ethanol concentrations below 3 g/L) and (ii) repression of the oxidative metabolism (at higher ethanol concentrations). The first effect was best observed at low ethanol concentrations, where multiple steady states were observed even when no repression of the oxidative metabolism was evident, i.e., the oxidative capacity was constant. However, at higher ethanol concentrations repression of the oxidative metabolism was observed (the oxidative capacity decreased), and this resulted in a broader range of dilution rates where multiple steady states could be found.     

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.     

Chemostat cultures of yeasts, continuous culture fundamentals and simple unstructured mathematical models.

Fundamental aspects of chemostat cultures are reviewed. Using yeast cultures as examples, it is shown that steady states in chemostats may be predicted quantitatively by combining the correct number of unstructured kinetic models with expressions for existing stoichiometric constraints. The necessary number of such kinetic models corresponds to the number of limiting substrates and increases with the number of different metabolic pathways available to the strain. This is demonstrated by an experimental comparison of yeast growth limited by glucose alone for which metabolism is oxidative, and growth doubly limited by both glucose and oxygen, which occurs according to an oxido-reductive metabolism. The steady state data for such experiments can in principle be predicted based on a minimal amount of information by a simple stoichiometric model. It represents the overall stoichiometry of growth by a superposition of a fully oxidative and a fully reductive growth reaction and uses the concept of "aerobicity" to characterize the relative importance of the two reactions.     

Optimising enzyme production by bakers yeast in continuous culture: physiological knowledge useful for process design and control

Saccharomyces cerevisiae was grown in aerobic continuous culture on a defined minimal medium, with glucose (40 g.l⁻¹) as the growth-limiting carbon source, to acquire knowledge useful in process design and for model-based control. Steady-state concentrations of biomass, glucose, ethanol and activities of model products alcohol dehydrogenase, hexokinase, malate dehydrogenase, glucose-6-phosphate dehydrogenase and iso-citrate dehydrogenase were determined at dilution rates (D) between 0.06 h⁻¹ and 0.323 h⁻¹ (close to μ_max). Enzyme activities showed productivity trends related to the transition from oxidative to oxido-reductive growth. Conclusions are drawn from the data with regard to designing a new process for production of intracellular enzymes. Issues of process stability as well as productivity are discussed.     

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Effects of a hexokinase II deletion on the dynamics of glycolysis in continuous cultures of Saccharomyces cerevisiae

In glucose-limited aerobic chemostat cultures of a wild-type Saccharomyces cerevisiae and a derived hxk2 null strain, metabolic fluxes were identical. However, the concentrations of intracellular metabolites, especially fructose 1,6-bisphosphate, and hexose-phosphorylating activities differed. Interestingly, the hxk2 null strain showed a higher maximal growth rate and higher Crabtree threshold dilution rate, revealing a higher oxidative capacity for this strain. After a pulse of glucose, aerobic glucose-limited cultures of wild-type S. cerevisiae displayed an overshoot in the intracellular concentrations of glucose 6-phosphate, fructose 6-phosphate, and fructose 1,6-bisphosphate before a new steady state was established, in contrast to the hxk2 null strain which reached a new steady state without overshoot of these metabolites. At low dilution rates the overshoot of intracellular metabolites in the wild-type strain coincided with the immediate production of ethanol after the glucose pulse. In contrast, in the hxk2 null strain the production of ethanol started gradually. However, in spite of the initial differences in ethanol production and dynamic behaviour of the intracellular metabolites, the steady-state fluxes after transition from glucose limitation to glucose excess were not significantly different in the wild-type strain and the hxk2 null strain at any dilution rate.     

The effect of vitamins and amino acids on glucose uptake in aerobic chemostat cultures of three Saccharomyces cerevisiae strains

In the respiro-fermentative region of aerobic chemostat cultures at steady state, Saccharomyces cerevisiae CBS 8066 produced high concentrations of ethanol with concomitant low levels of residual glucose which followed Monod kinetics. By contrast, very high residual glucose concentrations were observed in cultures of S. cerevisiae strains ATCC 4126 and NRRL Y132 at dilution rates above 60% of the washout dilution rate, resulting in much lower ethanol concentrations, even though clearly glucose-limited at lower dilution rates in the respiratory region. The addition of a vitamin mixture resulted in decreased residual glucose concentrations in respiro-fermentative cultures of all three strains, but the effect was much more pronounced with strains ATCC 4126 and NRRL Y132. Meso-inositol was mainly responsible for this effect, although with strain ATCC 4126 other vitamins as well as an amino acid mixture were also required to minimise the steady-state residual glucose levels. The residual glucose concentration in continuous culture was, therefore, greatly dependent on the growth factor requirements of the particular yeast strain, which apparently increased on increasing the dilution rate into the respiro-fermentative region. The strain differences with respect to growth factor requirements at high dilution rates, which were not evident at low dilution rates, had a profound effect on the kinetics of glucose assimilation in aerobic chemostat culture.     

Gene Regulation in Continuous Cultures: A Unified Theory for Bacteria and Yeasts

During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially (diauxie) or simultaneously. The ubiquity of these growth patterns suggests that they may be driven by a universal mechanism common to all microbial species. Recently, we showed that a minimal model accounting only for enzyme induction and dilution, the two processes that occur in all microbes, explains the phenotypes observed in batch cultures of various wild-type and mutant/recombinant cells (Narang and Pilyugin in J. Theor. Biol. 244:326–348, 2007). Here, we examine the extension of the minimal model to continuous cultures. We show that: (1) Several enzymatic trends, attributed entirely to cross-regulatory mechanisms, such as catabolite repression and inducer exclusion, can be quantitatively explained by enzyme dilution. (2) The bifurcation diagram of the minimal model for continuous cultures, which classifies the substrate consumption pattern at any given dilution rate and feed concentrations, provides a precise explanation for the empirically observed correlations between the growth patterns in batch and continuous cultures. (3) Numerical simulations of the model are in excellent agreement with the data. The model captures the variation of the steady state substrate concentrations, cell densities, and enzyme levels during the single- and mixed-substrate growth of bacteria and yeasts at various dilution rates and feed concentrations. This variation is well approximated by simple analytical expressions that furnish deep physical insights. (4) Since the minimal model describes the behavior of the cells in the absence of cross-regulatory mechanisms, it provides a rigorous framework for quantifying the effect of these mechanisms. We illustrate this by analyzing several data sets from the literature.     

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.     

Cultivation of Saccharomyces cerevisiae in continuous culture

Summary Growth of Saccharomyces cerevisiae was investigated under aerobic conditions in a glucose limited chemostat. The steady state concentrations of cells, glucose and ethanol were measured in dependence of the dilution rate. The growth rate showed a biphasic dependence from the glucose concentration. A shift from respiratory to fermentative metabolism (Crabtree-effect) altering heavily the cell yield and the ethanol yield took place in the range of dilution rates between 0.3 h^-1 and 0.5 h^-1. Therefore the classical theory of continuous cultures is not applicable on aerobic growth of Saccharomyces cerevisiae under glucose limitation without introducing further premises. On the other hand the steady state cell concentration as a function of the dilution rate fits well the theoretically calculated curves, if cells are cultivated under conditions where only fermentation or respiration is possible.     

Oscillatory behavior of Saccharomyces cerevisiae in continuous culture: I. Effects of pH and nitrogen levels

The appearance of sustained oscillations in bioreactor variables (biomass and nutrient concentrations) in continuous cultures of Saccharomyces cerevisiae indicates the complex nature of microbial systems, the inadequacy of current growth kinetic models, and the difficulties which may arise in bioprocess control and optimization. In this study we investigate continuous bioreactor behavior over a range of operating conditions (dilution rate, feed glucose concentration, feed ammonium concentration, dissolved oxygen, and pH) to determine the process requirements which lead to oscillatory behavior. We present new results which indicate that high feed ammonium concentrations may eliminate oscillations and that under oscillatory conditions ammonium levels are generally low and oscillatory as well. The effects of pH are complex and oscillations were only observed at pH values 5.5 and 6.5; no oscillations were observed at a pH of 4.5. Under our nominal operating conditions (feed glucose concentration 10 g/L, dilution rate 0.145 h(-1), feed ammonium concentration 0.0303M, dissolved oxygen level 50%, pH 5.5, and T = 30 degrees C) we found two possible final bioreactor states depending on the transient used to reach the nominal operating conditions. One of the states was oscillatory and characteristic of oxidative metabolism and the other was nonoscillatory and fermentative.     

Molar growth yields of Zymomonas mobilis on glucose after the transition from anaerobic to aerobic continuous growth

An increase in the molar growth yield (Y_X/S = 14.3–20.3 g/mol) on glucose (25 mM) was achieved after the transition of Zymomonas mobilis ATCC 29191 from anaerobic to aerobic steady state growth at dilution rates of D = 0.31–0.40 1/h and under oxygen-unlimited conditions. The transfer of anaerobically or aerobically grown steady state cells into a fresh medium resulted in the higher values of Y_X/S. A positive correlation was established between biomass and acetaldehyde yield within the range of 5–9 mM acetaldehyde in the medium. An inhibitory effect of the exogenously added acetaldehyde (K_i = 16.7 ± 2.8 mM) on the ATPase activity was observed in vitro, using cell-free extracts of anaerobically grown Z. mobilis. The results obtained provide evidence that the increased values of biomass yield could be explained by the redirection of ATP usage during aerobic growth of Z. mobilis.     

Enzymic analysis of the crabtree effect in glucose-limited chemostat cultures of Saccharomyces cerevisiae

The physiology of Saccharomyces cerevisiae CBS 8066 was studied in glucose-limited chemostat cultures. Below a dilution rate of 0.30 h-1 glucose was completely respired, and biomass and CO2 were the only products formed. Above this dilution rate acetate and pyruvate appeared in the culture fluid, accompanied by disproportional increases in the rates of oxygen consumption and carbon dioxide production. This enhanced respiratory activity was accompanied by a drop in cell yield from 0.50 to 0.47 g (dry weight) g of glucose-1. At a dilution rate of 0.38 h-1 the culture reached its maximal oxidation capacity of 12 mmol of O2 g (dry weight)-1 h-1. A further increase in the dilution rate resulted in aerobic alcoholic fermentation in addition to respiration, accompanied by an additional decrease in cell yield from 0.47 to 0.16 g (dry weight) g of glucose-1. Since the high respiratory activity of the yeast at intermediary dilution rates would allow for full respiratory metabolism of glucose up to dilution rates close to mumax, we conclude that the occurrence of alcoholic fermentation is not primarily due to a limited respiratory capacity. Rather, organic acids produced by the organism may have an uncoupling effect on its respiration. As a result the respiratory activity is enhanced and reaches its maximum at a dilution rate of 0.38 h-1. An attempt was made to interpret the dilution rate-dependent formation of ethanol and acetate in glucose-limited chemostat cultures of S. cerevisiae CBS 8066 as an effect of overflow metabolism at the pyruvate level. Therefore, the activities of pyruvate decarboxylase, NAD+- and NADP+-dependent acetaldehyde dehydrogenases, acetyl coenzyme A (acetyl-CoA) synthetase, and alcohol dehydrogenase were determined in extracts of cells grown at various dilution rates. From the enzyme profiles, substrate affinities, and calculated intracellular pyruvate concentrations, the following conclusions were drawn with respect to product formation of cells growing under glucose limitation. (i) Pyruvate decarboxylase, the key enzyme of alcoholic fermentation, probably already is operative under conditions in which alcoholic fermentation is absent. The acetaldehyde produced by the enzyme is then oxidized via acetaldehyde dehydrogenases and acetyl-CoA synthetase. The acetyl-CoA thus formed is further oxidized in the mitochondria. (ii) Acetate formation results from insufficient activity of acetyl-CoA synthetase, required for the complete oxidation of acetate. Ethanol formation results from insufficient activity of acetaldehyde dehydrogenases.(ABSTRACT TRUNCATED AT 400 WORDS)     

Enzymic analysis of the crabtree effect in glucose-limited chemostat cultures of Saccharomyces cerevisiae.

The physiology of Saccharomyces cerevisiae CBS 8066 was studied in glucose-limited chemostat cultures. Below a dilution rate of 0.30 h-1 glucose was completely respired, and biomass and CO2 were the only products formed. Above this dilution rate acetate and pyruvate appeared in the culture fluid, accompanied by disproportional increases in the rates of oxygen consumption and carbon dioxide production. This enhanced respiratory activity was accompanied by a drop in cell yield from 0.50 to 0.47 g (dry weight) g of glucose-1. At a dilution rate of 0.38 h-1 the culture reached its maximal oxidation capacity of 12 mmol of O2 g (dry weight)-1 h-1. A further increase in the dilution rate resulted in aerobic alcoholic fermentation in addition to respiration, accompanied by an additional decrease in cell yield from 0.47 to 0.16 g (dry weight) g of glucose-1. Since the high respiratory activity of the yeast at intermediary dilution rates would allow for full respiratory metabolism of glucose up to dilution rates close to mumax, we conclude that the occurrence of alcoholic fermentation is not primarily due to a limited respiratory capacity. Rather, organic acids produced by the organism may have an uncoupling effect on its respiration. As a result the respiratory activity is enhanced and reaches its maximum at a dilution rate of 0.38 h-1. An attempt was made to interpret the dilution rate-dependent formation of ethanol and acetate in glucose-limited chemostat cultures of S. cerevisiae CBS 8066 as an effect of overflow metabolism at the pyruvate level. Therefore, the activities of pyruvate decarboxylase, NAD+- and NADP+-dependent acetaldehyde dehydrogenases, acetyl coenzyme A (acetyl-CoA) synthetase, and alcohol dehydrogenase were determined in extracts of cells grown at various dilution rates. From the enzyme profiles, substrate affinities, and calculated intracellular pyruvate concentrations, the following conclusions were drawn with respect to product formation of cells growing under glucose limitation. (i) Pyruvate decarboxylase, the key enzyme of alcoholic fermentation, probably already is operative under conditions in which alcoholic fermentation is absent. The acetaldehyde produced by the enzyme is then oxidized via acetaldehyde dehydrogenases and acetyl-CoA synthetase. The acetyl-CoA thus formed is further oxidized in the mitochondria. (ii) Acetate formation results from insufficient activity of acetyl-CoA synthetase, required for the complete oxidation of acetate. Ethanol formation results from insufficient activity of acetaldehyde dehydrogenases.(ABSTRACT TRUNCATED AT 400 WORDS)     

Demonstration of the Crabtree effect in Phaffia rhodozyma during continuous and fed-batch cultivation

By monitoring cell yield and fermentation products during fed-batch and continuous growth, Pfaffia rhodozyma was shown to exhibit the Crabtree effect. In fed-batch culture at feed concentrations of 27 and 55 g glucose/l there was good agreement between the observed biomass formation and that predicted by a mass balance model. At 125 g glucose/l in the feed, biomass formation was less than predicted and fermentation products such as ethanol and acetic acid accumulated in the culture medium. In continuous culture with a feed concentration of 10 g glucose/l, the Crabtree effect became apparent at a dilution rate of 0.1 h -1 . Aerobic fermentation did not occur provided the sugar substrate was maintained at a concentration of less than 0.5 g/l. Although the cell yield coefficient was reduced from 0.5 g/g to 0.16 g/g during aerobic fermentation, the carotenoid content of the cells was unaffected.     

The biooxidation of methanol,ethanol and isopropanol by a defined co-culture at elevated temperatures

The introduction of more imaginative enrichment and isolation procedures has permitted the isolation of pure cultures of thermotolerant methylotrophic bacteria, a group that was previously unknown. One potential application for such bacteria is in the aerobic biotreatment of petrochemical industry wastewaters at elevated temperatures. Here, the growth and biooxidation characteristics of one such bacterium, Bacillus sp. NCIB 12522, in co-culture with a Gram-negative thermophilic non-methylotrophic solvent utilizing bacterium, NA 17, on a mixture of methanol, ethanol and isopropanol, under both steady and transient state continuous flow culture conditions are reported. The results indicate that at dilution rates <0.2 h^–1 effective biooxidation can be achieved at temperatures between 50° and 57 °C. As a result of step increases in bioreactor feed concentrations, the fraction of the methylotroph present in the co-culture changed according to whether the methanol or the ethanol concentrations were increased, but when isopropanol was increased, no change in the methylotroph fraction occurred between the initial and final steady states.     

Oscillatory behaviour control in a continuous culture under double-substrate limitation

The paper discusses the possibility of using a mixture of two growth limiting substrates to induce or eliminate self-sustained oscillations in a continuous culture process. The proportion of both substrates in the mixture is treated as a new control variable. The presented approach is based on the assumption that the oscillatory behaviour occurs for selected substrates in some range of dilution rates. Because a double-substrate limitation may occur, the analysis is performed for two fundamental substrate utilization patterns: simultaneous consumption and diauxic growth. By using model simulations and bifurcation analysis, we show that an appropriate proportion of two substrates in the mixture allows for the control of the oscillatory behaviour.     

The relationship between transport kinetics and glucose uptake by Saccharomyces cerevisiae in aerobic chemostat cultures

The steady-state residual glucose concentrations in aerobic chemostat cultures of Saccharomyces cerevisiae ATCC 4126, grown in a complex medium, increased sharply in the respiro-fermentative region, suggesting a large increase in the apparent k_s value. By contrast, strain CBS 8066 exhibited much lower steady-state residual glucose concentrations in this region. Glucose transport assays were conducted with these strains to determine the relationship between transport kinetics and sugar assimilation. With strain CBS 8066, a high-affinity glucose uptake system was evident up to a dilution rate of 0.41 h^–1, with a low-affinity uptake system and high residual glucose levels only evident at the higher dilution rates. With strain ATCC 4126, the high-affinity uptake system was present up to a dilution rate of about 0.38 h^–1, but a low-affinity uptake system was discerned already from a dilution rate of 0.27 h^–1, which coincided with the sharp increase in the residual glucose concentration. Neither of the above yeast strains had an absolute vitamin requirement for aerobic growth. Nevertheless, in the same medium supplemented with vitamins, no low-affinity uptake system was evident in cells of strain ATCC 4126 even at high dilution rates and the steady-state residual glucose concentration was much lower. The shift in the relative proportions of the high and low-affinity uptake systems of strain ATCC 4126, which might have been mediated by an inositol deficiency through its effect on the cell membrane, may offer an explanation for the unusually high steady-state residual glucose concentrations observed at dilution rates above 52% of the wash-out dilution rate.     

Formation of fermentation products and extracellular protease during anaerobic growth of Bacillus licheniformis in chemostat and batch-culture

For a relaxed (rel-), protease producing (A-type) and a stringent (rel+), not-protease producing (B-type) variant of Bacillus licheniformis we determined fermentation patterns and products, growth parameters and alkaline protease-production (if any) in anaerobic, glucose-grown chemostats and batch-cultures. Glucose is dissimilated via glycolysis and oxidative pentose phosphate pathway simultaneously; the relative share of these two routes depends on growth phase (in batch) and specific growth rate (in chemostat). Predominant products are lactate, glycerol and acetaldehyde for A-type batches and acetaldehyde, ethanol, acetate and lactate for B-type batches. Both types show a considerable acetaldehyde production. In chemostat cultures, the fermentation products resemble those in batch-culture. From the anaerobic batches and chemostats, we conclude that the A-type (with low ATP-yield) will have a YATPmax of probably 12.9 g/mol and the B-type (with high ATP-yield) a YATPmax of about 10.1 g/mol. For batch-cultures, both types have about the same, high Yglucose (12 g/mol). So, the slow-growing A-type has a relatively high efficiency of anaerobic growth (i.e. an efficient use of ATP) and the fast-growing B-type a relatively low efficiency of anaerobic growth. In aerobic batch-cultures, we found 48, respectively 41% glucose-carbon conversion into mainly glycerol and pyruvate, respectively acetate as overflow metabolites in the A- and B-type. In both aerobic and anaerobic batch-cultures of the A-type, protease is produced predominantly in the logarithmic and early stationary phase, while a low but steady production is maintained in the stationary phase. Protease production occurs via de novo synthesis; up to 10% of the total protease in a culture is present in a cell-associated form. Although anaerobic protease production (expressed as protease per amount of biomass) is much higher than for aerobic conditions, specific rates of production are in the same range as for aerobic conditions while, most important, the substrate costs of anaerobic production are very much higher than for aerobic conditions.     

Chemostat-cultivated Escherichia coli at high dilution rate: multiple steady states and drift

The representation of metabolic network reaction kinetics in a scaled, polynomial form can allow for the prediction of multiple steady states. The polynomial formalism is used to study chemostat-cultured Escherichia coli which has been observed to exhibit two multiple steady states under ammonium ion-limited growth conditions: a high cell density-low ammonium ion concentration steady state and a low cell density-high ammonium ion concentration steady state. Additionally, the low-cell-density steady state has been observed to drift to the high-cell-density steady state. Inspection of the steady-state rate expressions for the ammonium ion transport/assimilation network (in polynomial form) suggests that at low ammonium ion concentrations, two steady states are possible. One corresponds to heavy use of the glutamine synthetase-glutamate synthase (GLNS-GS) branch and the second to heavy use of the glutamate dehydrogenase (GDH) branch. Realization of the predicted intracellular steady states is also found to be dependent on the parameters of the transport process. Moreover, the two steady states differ in where their energy intensity lies. To explain the drift, GLNS, which is inducible under low ammonium ion concentrations, is suggested to be a "memory element." A chemostat-based model is developed to illustrate that perturbations in dilution rate can lead to drift between the two steady states provided that the disturbance in dilution rate is sufficiently large and/or long in duration.