On microbial states of growth†

It is crucial to the reproducibility of results and their proper interpretation that the conditions under which experiments are carried out be defined with rigour and consistency, in this review we attempt to clarify the differences and interrelationships among steady, balanced and exponential states of culture growth. Basic thermodynamic concepts are used to introduce the idea of steady-state growth in open, biological systems. The classical, sometimes conflicting, definitions of steady-state and balanced growth are presented, and a consistent terminology is proposed. The conditions under which a culture in balanced growth is also in exponential growth and in steady-state growth are indicated. It is pointed out that steady-state growth always implies both balanced and exponential growth, and examples in which the converse does not hold are described. More complex situations are then characterized and the terminology extended accordingly. This leads to the notion of normal growth and growth that can be synchronous or otherwise unbalanced but still reproducible, and to the condition of approximate steady state manifested by growth in batch culture and by asymmetrically dividing cells, which is analysed in some detail.     

Effect of pulse frequency on the osteogenic differentiation of mesenchymal stem cells in a pulsatile perfusion bioreactor

Perfusion bioreactors are a promising in vitro strategy to engineer bone tissue because they supply needed oxygen and nutrients and apply an osteoinductive mechanical stimulus to osteoblasts within large porous three-dimensional scaffolds. Model two-dimensional studies have shown that dynamic flow conditions (e.g., pulsatile oscillatory waveforms) elicit an enhanced mechanotransductive response and elevated expression of osteoblastic proteins relative to steady flow. However, dynamic perfusion of three-dimensional scaffolds has been primarily examined in short term cultures to probe for early markers of mechanotransduction. Therefore, the objective of this study was to investigate the effect of extended dynamic perfusion culture on osteoblastic differentiation of primary mesenchymal stem cells (MSCs). To accomplish this, rat bone marrow-derived MSCs were seeded into porous foam scaffolds and cultured for 15 days in osteogenic medium under pulsatile regimens of 0.083, 0.050, and 0.017 Hz. Concurrently, MSCs seeded in scaffolds were also maintained under static conditions or cultured under steady perfusion. Analysis of the cells after 15 days of culture indicated that alkaline phosphatase (ALP) activity, mRNA expression of osteopontin (OPN), and accumulation of OPN and prostaglandin E(2) were enhanced for all four perfusion conditions relative to static culture. ALP activity, OPN and OC mRNA, and OPN protein accumulation were slightly higher for the intermediate frequency (0.05 Hz) as compared with the other flow conditions, but the differences were not statistically significant. Nevertheless, these results demonstrate that dynamic perfusion of MSCs may be a useful strategy for stimulating osteoblastic differentiation in vitro.     

Multiplicity and stability analysis of microorganisms in continuous culture: effects of metabolic overflow and growth inhibition

Metabolic overflow (enhanced uptake of substrate and secretion of intermediates) is a phenomenon often observed for cells grown under substrate excess. Growth inhibition by substrate and/or product is also normally found for this kind of culture. An effort is made in this work to analyze the dynamic behavior of a continuous culture subject to metabolic overflow and growth inhibition by substrate and/or product. Analysis of a model system shows that in a certain range of operating conditions three nonwashout steady state solutions are possible. Local stability analysis indicates that only two of them are stable thus leading to multiplicity and hysteresis. Further analysis of the intrinsic effects of different terms describing the metabolic overflow and growth inhibitions reveals that for the model system and the parameters considered, the combined effects of product inhibition and an enhanced formation rate of product under substrate excess cause the multiplicity and hysteresis. Growth inhibition by substrate and/or an enhanced substrate uptake appear not to be necessary conditions. The combined effects of enhanced product formation and product inhibition can also lead to unusual dynamic behavior such as a prolonged time period to reach a steady state, oscillatory transition from one steady state to another, and sustained oscillations. Using the occurrence of multiplicity and oscillation as criteria, the operating regime of a continuous culture can be divided into four domains: one with multiplicity and oscillation, one with unique steady state but possible oscillatory behavior, the other two with unique and stable steady state. The model predictions are in accordance with recent experimental results. The results presented in this work may be used as guidelines for choosing proper operating conditions of similar culture systems to avoid undesired instability and multiplicity. Copyright 1998 John Wiley & Sons, Inc.     

Effects of synergistic signaling by phytochrome A and cryptochrome1 on circadian clock-regulated catalase expression.

Persistent oscillation in constant conditions is a defining characteristic of circadian rhythms. However, in plants transferred into extended dark conditions, circadian rhythms in mRNA abundance commonly damp in amplitude over two or three cycles to a steady state level of relatively constant, low mRNA abundance. In Arabidopsis, catalase CAT3 mRNA oscillations damp rapidly in extended dark conditions, but unlike catalase CAT2 and the chlorophyll a/b binding protein gene CAB, in which the circadian oscillations damp to low steady state mRNA abundance, CAT3 mRNA oscillations damp to high steady state levels of mRNA abundance. Mutational disruption of either phytochrome- or cryptochrome-mediated light perception prevents damping of the oscillations in CAT3 mRNA abundance and reveals strong circadian oscillations that persist for multiple cycles in extended dark conditions. Damping of CAT3 mRNA oscillations specifically requires phytochrome A but not phytochrome B and also requires the cryptochrome1 blue light receptor. Therefore, we conclude that synergistic signaling mediated through both phytochrome A and cryptochrome1 is required for damping of circadian CAT3 mRNA oscillations in extended dark conditions.     

Coexistence of S. cerevisiae and E. coli in chemostat under substrate competition and product inhibition

A mixed culture of Saccharomyces cerevisiae and Escherichia coli was established in a stable coexistence steady state in a chemostat under constant operating conditions. The species competed for glucose, the growth-limiting resource, and produced acetate and ethanol. The acetic acid was shown to be very inhibitory to E. coli in pure culture at pH 5 while ethanol inhibition was only marginal. No significant inhibition of S. cerevisiae growth was observed by either acetate or ethanol. Pure culture parameters were measured and used in the analysis. Linearized stability analysis for the case when both organisms produce the inhibitor showed that a transition through three stable outcomes was possible as the feed concentration is lowered. Experimental studies verified these predictions, and successive transitions from a yeast growth steady state, to a coexistence steady state, and to an E. coli growth steady state were obtained by lowering the glucose concentration in the feed from 10 to 5 to 2.5 g/L, respectively. This dynamic behavior is distinct from the outcomes of other competition-inhibition combinations and experimentally demonstrates for the first time that coexistence is possible due to substrate competition and product inhibition.     

Transport of glucose intoSaccharomyces cerevisiae RXII

Evidence is submitted that glucose is found in a chemically unaltered form in cells ofSaccharomyces cerevisiae RXII incubated with glucose, if the culture is grown under aerobic conditions at 30°C and is in the logarithmic phase of growth at the moment of harvesting. Under these conditions, the course of formation of a glucose steady state can be studied under aerobic and anaerobic incubation conditions. The steady state glucose concentration in the cells is the linear function of the glucose concentration in the medium.     

Continuous culture growth of photoautotrophic cell suspensions from Chenopodium rubrum

The construction and operation of a continuous culture system for the propagation of cell suspensions from Chenopodium rubrum under photoautotrophic conditions has been described. A dilution rate of 0.16/day gave an equilibrium culture density of 1,100,000 cells/ml and a mean doubling time of 150 hours. During continuous culture steady state conditions with respect to nutrient uptake, cell protein and chlorophyll content, starch accumulation, in vitro activities of enzymes related to different metabolic pathways could be established. Photosynthetic CO₂ assimilation of steady state cells was about 100 mol CO₂/mg chlorophyll x hour. Dark CO₂ fixation was 3% of the light values.     

A comparison of tomato (Lycopersicon esculentum) lectin with its deglycosylated derivative

A regime is proposed for the design of coupled enzyme assays in which auxiliary enzymes are added at concentrations proportional to their Km values. Under these conditions it is possible to calculate the complete time course of the assay including the time required for the system to approach its steady state. The consequence of increasing the number of coupling enzymes is shown to be a considerable decrease in time required to reach the steady state provided that the overall transient time remains the same. The method is extended to the general consideration of pathways and shows that pathways of the same length exhibit identical temporal responses provided that the units of concentration and time used are based on the steady-state concentration of intermediates and the transient time respectively. An unexpected finding is that increasing the number of intermediates in a pathway can decrease the time required to enter a steady state.     

The dynamics of continuous microbial culture described by cell age distribution and concentration of one substrate

A mathematical model has been considered in which the known equation of McKendrick and Von Foerster for cell age distribution is combined with that for substrate concentration. The dependence of cell division rate on cell age has been taken as a step function. The interrelation between culture parameters describing the substrate consumption and cell division has been found. The shape of cell age distribution as well as the values of substrate and cell concentrations in steady and transient states have been investigated. Stationary regimes at the initial culture state synchronized by ages have been found to be established as damped oscillations and age waves. Under definite conditions the transition from one steady growth regime to another includes sharp single-time age synchronization of the culture.     

Kinetic analysis of L-lysine production by a fluoropyruvate sensitive mutant of B.lactofermentum

The kinetics of L-lysine production by a fluoropyruvate sensitive (FP^s) mutant of B.lactofermentum have been analysed in batch and continuous culture. Under optimal conditions (viz. T = 30° C, pH = 7.0, DO = 10 % air saturation) it was established that the initial phosphate level could be used to extend the batch culture to give an L-lysine.HCl concentration of 68.0 g/l and a yield of 0.43 g/g. In continuous culture the yield increased at low dilution rates under conditions similar to those for extended batch culture.     

Cybernetic modeling and regulation of metabolic pathways in multiple steady states of hybridoma cells

Hybridoma cells utilize a pair of complementary and partially substitutable substrates, glucose and glutamine, for growth. It has been shown that cellular metabolism shifts under different culture conditions. When those cultures at different metabolic states are switched to a continuous mode, they reach different steady states under the same operating conditions. A cybernetic model was constructed to describe the complementary and partial substitutable nature of substrate utilization. The model successfully predicted the metabolic shift and multiple steady-state behavior. The results are consistent with the experimental observation that the history of the culture affects the resulting steady state.     

Inhibition kinetics of phenol degradation from unstable steady-state data

Multiplicity of steady states of a continuous culture with an inhibitory substrate was used to estimate kinetic parameters under steady-state conditions. A continuous culture of Pseudomonas cepacia G4, using phenol as the sole source of carbon and energy, was overloaded by increasing the dilution rate above the critical dilution rate. The culture was then stabilized in the inhibitory branch by a proportional controller using the carbon dioxide concentration in the reactor exhaust gas as the controlled variable and the dilution rate as the manipulated variable. By variation of the set point, several unstable steady states in the inhibitory branch were investigated and the specific phenol conversion rates calculated. In addition, phenol degradation was investigated under substrate limitation (chemostat operation).The results show that the phenol degradation by P. cepacia can be described by the same set of inhibition parameters under substrate limitation and under high substrate concentrations in the inhibitory branch. Biomass yield and maintenance coefficients were identical. Fitting of the data to various inhibition models resulted in the best fit for the Yano and Koga equation. The well-known Haldane model, which is most often used to describe substrate inhibition by phenol, gave the poorest fit. The described method allows a precise data estimation under steady-state conditions from the maximum of the biological reaction rate up to high substrate concentrations in the inhibitory branch. Inhibition parameter estimation by controlling unstable steady states may thus be useful in avoiding discrepancies between data generated by batch runs and their application to continuous cultures which have been often described in the literature. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 567-576, 1997.     

Nonlinear dynamics of eucaryotic pyruvate dehydrogenase multienzyme complex: decarboxylation rate,oscillations, and multiplicity

Pyruvate conversion to acetyl-CoA by the pyruvate dehydrogenase (PDH) multienzyme complex is known as a key node in affecting the metabolic fluxes of animal cell culture. However, its possible role in causing possible nonlinear dynamic behavior such as oscillations and multiplicity of animal cells has received little attention. In this work, the kinetic and dynamic behavior of PDH of eucaryotic cells has been analyzed by using both in vitro and simplified in vivo models. With the in vitro model the overall reaction rate (nu(1)) of PDH is shown to be a nonlinear function of pyruvate concentration, leading to oscillations under certain conditions. All enzyme components affect nu(1) and the nonlinearity of PDH significantly, the protein X and the core enzyme dihydrolipoamide acyltransferase (E2) being mostly predominant. By considering the synthesis rates of pyruvate and PDH components the in vitro model is expanded to emulate in vivo conditions. Analysis using the in vivo model reveals another interesting kinetic feature of the PDH system, namely, multiple steady states. Depending on the pyruvate and enzyme levels or the operation mode, either a steady state with high pyruvate decarboxylation rate or a steady state with significantly lower decarboxylation rate can be achieved under otherwise identical conditions. In general, the more efficient steady state is associated with a lower pyruvate concentration. A possible time delay in the substrate supply and enzyme synthesis can also affect the steady state to be achieved and leads to oscillations under certain conditions. Overall, the predictions of multiplicity for the PDH system agree qualitatively well with recent experimental observations in animal cell cultures. The model analysis gives some hints for improving pyruvate metabolism in animal cell culture.     

Cyclic stretch downregulates arterial vascular connexin43 protein expression: an ex vivo study

Vascular cells may communicate through gap junctions that are formed by connexin (Cx) proteins. We investigated differential regulation of arterial gap junctions by steady and cyclic stretch and the underlying mechanotransduction pathways. Ex vivo culture of rabbit thoracic aortas was used to investigate regulation of Cx43 by cyclic stretch. After culturing for 6 or 24 h, Cx43 protein levels were quantified using Western blot. Cultures under a pulsatile pressure (mean 80 mmHg, pulse 30 mmHg) decreased Cx43 protein at both 6 and 24 h as compared with cultures under a steady pressure (80 mmHg). The regulation of Cx43 protein was mediated by pulsatile pressure-induced cyclic stretch, not by cyclic stress. Protein levels of active and total Src were also decreased by cyclic stretch at 24 h. The Src- specific inhibitor PP1 in steady culture only or in both steady and pulsatile culture conditions eliminated the difference in Cx43 protein levels between the two culture conditions. Addition of reactive oxygen species inhibitor apocynin to the pulsatile culture abolished the differences in Src and Cx43 protein levels between the two cultures. Thus, Src and reactive oxygen species appear to play a role in cyclic stretch-mediated regulation of Cx43 protein. These results are likely to have important implications in cardiovascular physiology and pathophysiology under conditions wherein significant alterations in the level of cyclic stretch are present.     

Unsteady-state operation of continuous fermentor for enhancement of cell mass production

The transient behavior of continuous fermentation is studied concentrating on the time scale intrinsic to the system. The time scale is the time required for the fermentorto reach a stable steady state after the disturbance of cell mass is introduced. When the cell concentration is disturbed from the steady-state value, in particular, at the dilution rate near washout, the transient period becomes extended significantly, and the steady state is resumed sluggishly. This sluggish transient behavior could be turned to an advantage for enhancing the cell mass output rate. The proposed transient operation is a continuous fermentation whereby a positive disturbance in the cell mass is introduced, so that the cell concentration is higher than the steady-state value for an extended transient period. It is shown that a significantly higher cell mass production than that from the steady-state continuous fermentation can be achieved. Simple experiments were performed to demonstrate the improvement of cell (Candida utilis) productivity.     

Mixed culture biooxidation of phenol. III. Existence of multiple steady states in continuous culture with wall growth

It is shown that two steady states exist in certain regions of operation of a 2-liter continuous stirred tank biological reactor. Transition was made from one steady state to another by applying shock loads of either phenol substrate which is inhibitory to the culture at high concentrations or by adding large additional amounts of concentrated organisms. The existence of the multiple steady states is ascribed to the existence of wall growth, and their position is determined by the amount of wall growth. Transient behavior of the system did not follow the predictions of the simple wall growth model but the culture appeared to undergo a lag period immediately after applying the shock load to the system. It is concluded that the stability of a continuous culture utilizing an inhibitory substrate is improved by increasing the degree of wall growth and decreasing the substrate feed concentration. It is also concluded that small scale experiments can usually not be interpreted correctly unless the effect of wall growth is taken into account.     

Multiplying steady-state culture in multi-reactor system

Cultivation of microorganisms in batch experiments is fast and economical but the conditions therein change constantly, rendering quantitative data interpretation difficult. By using chemostat with controlled environmental conditions the physiological state of microorganisms is fixed; however, the unavoidable stabilization phase makes continuous methods resource consuming. Material can be spared by using micro scale devices, which however have limited analysis and process control capabilities. Described herein are a method and a system combining the high throughput of batch with the controlled environment of continuous cultivations. Microorganisms were prepared in one bioreactor followed by culture distribution into a network of bioreactors and continuation of independent steady state experiments therein. Accelerostat cultivation with statistical analysis of growth parameters demonstrated non-compromised physiological state following distribution, thus the method effectively multiplied steady state culture of microorganisms. The theoretical efficiency of the system was evaluated in inhibitory compound analysis using repeated chemostat to chemostat transfers.     

Analysis of continuous cultures of recombinant methylotrophs

Static and dynamic characteristics of continuous cultures of recombinant methylotrophs, which are designed to improve the selectivity of plasmid-bearing cells and the plasmid stability, are investigated in detail. Operational regions in which coexistence (survival of plasmid-bearing and plasmid-free cells) operation is feasible have been identified in the entire space of kinetic parameters and operating variables. The stability characteristics of each steady state are examined. The existence of oscillatory states around the coexistence steady state is investigated using the dynamic (Hopf) bifurcation analysis. For proper startup of the continuous culture operation, it is critical to identify the sets of initial conditions, if any, which lead to transients that ultimately result in washout of plasmid-bearing cells and avoid such conditions. For the numerical illustrations presented, the coexistence steady state happens to be locally stable over much of its region of existence, particular for the operating conditions corresponding to maximum productivity.     

Approximation of continuous growth of Cephalotaxus harringtonia plant cell cultures using fed-batch operation

In Cephalotaxus harringtonia plant cell cultures, periods of batch growth that are limited by hexose uptake are too short to make an accurate estimate of the Monod saturation constant. Continuous cultures are infeasible on a laboratory scale, and semicontinuous cultures require too frequent sampling. Fed-batch operation, consisting of intermittent removal from a culture that is fed continuously, was investigated as a possible solution to these problems. For a constant feed rate, computer simulations showed that a steady state can be achieved which is useful for studying growth at different specific growth rates. In terms of the dilution rate it was confirmed that the operation is essentially equivalent to continuous culture when the samples represent a small fraction of the total culture volume. Experiments with glucose or fructose as the carbon source were carried out in shake flasks fed by a multichannel syringe pump. Results indicate that Monod kinetics based on medium glucose levels cannot adequately describe growth under these conditions. Monod's expression for specific growth rate using internal glucose concentration gives an improved correlation.     

Adaptation to Cadmium by Klebsiella aerogenes Growing in Continuous Culture Proceeds Mainly via Formation of Cadmium Sulfide

The adaptation of Klebsiella aerogenes to high levels of cadmium was studied in continuous culture under conditions of glucose limitation. When up to 6 × 10⁻⁴ M cadmium was added to a culture in steady state, growth ceased instantaneously but resumed within 5 h (dilution rate, 0.1 h⁻¹). When again in steady state, these adapted cells exhibited a far greater tolerance to cadmium than did unadapted cells (not previously exposed to cadmium) when tested on solid media containing different concentrations of cadmium. This relative insensitivity of adapted cells to cadmium was subsequently lost in continuous culture within 5 days after omitting cadmium from the influent medium. Thus, the phenomenon was an inducible physiological process. Adapted cells contained substantial amounts of cadmium (up to 2.4% of the bacterial dry weight). The cadmium content of the cells was dependent on growth conditions and was found to be proportional to the inorganic sulfide content of the cells in all cases. This suggested that formation of CdS is probably the most important mechanism of detoxification in this organism. The presence of large numbers of electron-dense granules on the cell surface (absent in cultures without added cadmium) provided additional support for this conclusion.