Dynamics of a continuous culture with catalysis of the growth-limiting substrate by an enzyme of the cells

In the present paper we discuss the behaviour of solutions of a dynamical system describing the growth of cells in a well-mixed continuous culture where the supply of the growth-limiting nutrient depends on the activity of an enzyme outside the cell membrane. It turns out that for positive dilution rates there exists an exponentially attractive two-dimensional simplex. Furthermore, the reversed system restricted to this simplex is quasimonotone. In every case all trajectories tend to an equilibrium state.     

The basis of synchronization by repetitive dilution of a growing culture

Cultures of Escherichia coli have been synchronized by periodic dilution with fresh growth medium in the laboratory of Francois Kepes. When diluted by a large factor into complete test medium, the treated cultures undergo up to 12 synchronous divisions. This long term synchrony must result from an adjustment process during the periodic dilution procedure so that all cells have nearly identical biochemical properties. Robert Pritchard (University of Leicester, personal communication) suggested that this phasing would happen if the uptake of a critical nutrient was limited by the surface area of the cell during a portion of the dilution cycle. If his suggestion is valid, a general method for synchronization of almost any organism that grows exponentially and divides by binary fission into equal sized daughters should be achievable. A computer program was devised to simulate the growth of an initially asynchronous culture under periodic dilution with medium containing a single limiting nutrient. Various models of cell shape and growth were tested along with various models for the growth-limiting substrate uptake.     

Bacterial competition in serial transfer culture

A mathematical model of bacterial competition for a single growth-limiting substrate in serial transfer culture is formulated. Each bacterial strain is characterized by a growth response function, e.g. Monod function determined by a maximum growth rate and half-saturation nutrient concentration, and the length of its lag phase following the dilution event. The goal of our study is to understand what factors determine an organisms fitness or competitive ability in serial transfer culture. A motivating question is: how many strains can coexist in serial transfer culture? Unlike competition in the chemostat, coexistence of two strains can occur in serial transfer culture. Numerical simulations suggest that more than two may coexist.     

Application of fed-batch culture to citric acid production by Aspergillus niger: The effects of dilution rate and dissolved oxygen tension

Studies in conventional batch culture confirmed that the maximum citric acid production rate occurred prior to exhaustion of the growth-limiting nutrient, i.e., when the growth rate was nonzero. The effects of dilution rate and the culture dissolved oxygen tension (DOT) were studied in chemostat culture. Maximum citric acid yield and production rate were observed at low dilution rate (0.017 h(-1)) and high DOT value (90% of saturation). These findings were applied to a nitrogen-limited fed batch culture, and allowed a productivity increase of 100% when compared with conventional batch culture.     

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.     

A new principle of continuous flow cell cultivation

Summary A completely liquid-filled culture chamber with gas exchange across a synthetic membrane (Larsen andNilsson 1985) was incorporated into an automatic continuous flow system. The absence of an airliquid interface in the system permits removal of cell samples, and addition of fresh medium, under strictly sterile conditions. In this system,Tetrahymena pyriformis can be kept under optimal growth conditions in a rich nutrient medium and any defined cell density may be maintained for extended periods of time by varying the dilution rate of the culture. Furthermore, it has been possible to demonstrate, in the slope of the growth curve, even small changes which are difficult to detect in batch cultures since the duration of these changes is short. In the continuous flow system, the relative cell volume distribution and the food vacuole forming capacity of the cells were unaltered; however, all cells contained small refractive granules. The system permits the culture volume to be varied, but a standard volume of 20 ml was maintained in most experiments. Since the culture volume is small, the system requires less than one liter of fresh medium per week to maintain the cells in the exponentially multiplying growth phase.     

Competition between an Escherichia coli tyrosine auxotroph and a prototrophic revertant in glucose- and tyrosine-limited chemostats

A tyrosine-requiring strain of Escherichia coli was grown in tyrosine-limited chemostats at a range of dilution rates between 0.08 h^-1 and 0.42 h^-1, conditions which always resulted in the selection of a prototrophic revertant population able to synthesise tyrosine. Analysis of the two-membered mixed cultures which arose showed that the prototrophic population outgrew the auxotroph since its growth rate was not restricted by the growth-limiting concentrations of exogenous tyrosine. During the take-over of the culture, the prototroph population grew exponentially but the specific growth rate increased with decreasing dilution rate of the competition experiments. In glucose-limited chemostats (in the presence of non-growth-limiting concentrations of tyrosine) of the tyrosine-requiring strain, prototrophs were never detected. Constructed two-membered mixed cultures with both populations competing for limiting amounts of glucose, showed that the prototroph was less competitive than the auxotroph.This work was supported by a grant from the Science Research Council.     

Regulation of autotrophic and heterotrophic metabolism in Pseudomonas oxalaticus OX1: Growth on mixtures of oxalate and formate in continuous culture

Pseudomonas oxalaticus was grown in carbon- and energy-limited continuous cultures either with oxalte or formate or with mixtures of these substrates. During growth on the mixtures, simultaneous utilization of the two substrates occurred at all dilution rates tested. Under these conditions oxalate repressed the synthesis of ribulosebisphosphate carboxylase. The degree of this repression was dependent on the dilution rate and the ratio of oxalate and formate in the medium reservoir. At a fixed oxalate/formate ratio repression was greatest at intermediate dilution rates, whereas derepression occurred at both low and high dilution rates. Progressive depression of ribulosebisphosphate carboxylase synthesis and of autotrophic CO₂ fixation at low dilution rates was attributed to the decreasing concentration of intracellular repressor molecule(s), parallel to the decreasing concentration of the growth-limiting substrates in the culture. To account for the derepression at higher dilution rates, it is proposed that the rate of oxalyl-CoA production from oxalate limits the supply of metabolic intermediates and that additional energy and reducing power generated from formate drains the pools of metabolic intermediates sufficiently to lower the intracellular concentration of the repressor(s). During growth of Pseudomonas oxalaticus on the heterotrophic substrate oxalate alone, at dilution rates below 10% of the maximum specific growth rate, derepression of ribulosebisphosphate carboxylase synthesis and of autotrophic CO₂ fixation was observed to a level which was 50% of that observed during growth on formate alone at the same dilution rate. It is concluded that in Pseudomonas oxalaticus the synthesis of enzymes involved in autotrophic CO₂ fixation via the Calvin cycle is regulated by a repression/derepression mechanism and that the contribution of autotrophic CO₂ fixation to the biosynthesis of cell material in this organism is mainly controlled via the synthesis of these enzymes.Abbreviations RuBPCase ribulosebisphosphate carboxylase - PMS phenazine methosulphate - DCPIP 2,6-dichlorophenolindophenol - FDH formate dehydrogenase - S_R concentration of growth-limiting substrate in reservoir     

Discrepancies between cell volume and organic content in semi-continuous cultures of a marine microalga

J. FÁBREGAS, A. CID, E. MORALES, B. CORDERO AND A. OTERO. 1996. Changes in average cell volume, measured by flow cytometry, and cell organic content were studied in light/dark synchronized semi-continuous cultures of the marine microalga Phaeodactylum tricornutum . Cell volume and organic content both increased with nutrient concentration at all the renewal rates tested. Cell volume against renewal rate, at each nutrient concentration, followed a U-shaped curve with smallest cells at intermediate renewal rates. In contrast, cell organic content decreased continuously with increasing renewal rate. The variation in cell volume and organic content, related to culture conditions, should be taken into account if biochemical composition and productivity of microalgal cultures are assessed on the basis of cell counts.     

Dynamics and control of continuous microbial propagators to subject substrate inhibition

Inhibitory substrate levels are common in industrial fermentations and in biological waste-water treatment of many industrial wastes. Continuous microbial cultures are unstable to certain disturbances, such as shock loading by inhibitory substrates. Two feedback proportional control strategies are analyzed and compared for a simple model culture assumed represent able by the culture concentrations of biomass and a single rate-limiting and growth-limiting nutrient (substrate). One control strategy, the well known turbidostat, consists of adjusting culture holding time (e.g., by flow rate adjustment) in response to deviations in turbidity or some other measure of culture biomass concentration. The other control strategy is to adjust holding time in response to deviations in limiting nutrient concentrations in the culture. This second control strategy, termed the nutristat, can be superior to the turbidostat in many applications. The sign and magnitude of the dimensionless group {(X /YD )[dμ/dS]s }, is shown to be an important determinant, in the behavior of the open loop and the two closed loop processes. This characteristic group is positive when the specific growth rate is increased by increases in the nutrient concentration, zero when the growth rate is unaffected by the nutrient concentration, and negative in the presence of nutrient or substrate inhibition. The effects of process modifications and of modeling assumptions on the control of the process are discussed and more sophisticated control schemes are also proposed.     

Effect of growth conditions on the rate of loss of the plasmid pAT153 from continuous cultures of Escherichia coli HB101

Abstract The plasmid pAT153 was lost less rapidly from carbon, nitrogen, phosphorous or sulphur-limited continuous cultures of Escherichia coli HB101 as the dilution rate increased. At a fixed dilution rate of 0.3 h⁻¹, the plasmid was maintained longer as the growth-limiting nutrient was changed from glucose to casamino acids (nitrogen-limited), phosphate or sulphate. These differences in the stability of maintenance were not due to parallel changes in the plasmid copy number. We propose that the rate of loss of pAT153 from E. coli HB101 is determined primarily by the ratio of growth rates of plasmid-containing bacteria and plasmid-free bacteria. This ratio increases with increasing growth rate and depends markedly on the growth-limiting nutrient, sulphate-limited growth being particularly suitable for the maintenance of this host-plasmid combination.     

Amino acid limited growth of starter cultures in milk

The specific growth rates of several Streptococcus cremoris strains were 10–40% lower in milk than in other growth in media. The growth rates in milk increased when an amino acid mixture or casein was added, whereas, when milk was diluted, the specific growth rate of the streptococci decreased. This decrease could be overcome by bringing the casein concentration in the diluted milk back to the normal value (3%). This indicates that casein-hydrolysis proceeded at a rate too low for the streptococci to reach their potential maximum specific growth rates in milk so that growth in milk is essentially amino acid-limited. This was subsequently demonstrated for S. cremoris by continuous cultivation in media with low casein concentrations. At a low dilution rate casein hydrolysis was fast enough to supply the cells with enough amino acids and lactose was growth-limiting, whereas at higher dilution rates amino acids became growth-limiting. In cultures exponentially growing in milk the concentration of free amino acids was measured to determine which amino acid(s) was(were) absent and could possibly limit growth. A number of essential amino acids (leucine, methionine, glutamate and in some cases phenylalanine) were not detected and addition of these, together, stimulated the growth of S. cremoris in milk. The amino acids leucine and phenylalanine appeared to play a particularly important role in this stimulation. These two are, supposedly, the first amino acids that become limiting during growth in milk. The effect of competition for casein and amino acids by different organisms was studied in continuous cultures. At different dilution rates different strains became dominant in these mixed cultures, suggesting that differences in apparent affinity constants (K_S) for casein, leucine and glutamate existed between the strains.     

Growth rate and control of development of the photosynthetic apparatus in Chloroflexus aurantiacus

Chloroflexus aurantiacus was grown photoheterotrophically in a chemostat in order to study the influence of growth rate on the formation of bacteriochlorophyll a (Bchl a) which represents the membrane-bound photosynthetic pigment complexes, and of Bchl c which represents the light harvesting pigment-proteins of the chlorosome. Steady state cell protein levels as well as specific Bchl a contents increased linearly and specific Bchl c contents exponentially when the dilution rate, representing growth rate, was decreased. In spite of differences in the light intensities, continuous cultures growing at comparable growth rates and densities exhibited comparable specific contents of both Bchls and largely identical molar ratios of Bchl c/Bchl a. The growth rate of constantly illuminated batch cultures was varied by changing the concentration of growth-limiting nutrients. Cultures growing at higher growth rates showed higher cell densities but lower specific Bchl levels as well as lower molar ratios of Bchl c/Bchl a than cultures growing at low growth rate. Determination of the light energy flux required for half-maximal saturation of photosynthetic activity (light dependent proton extrusion) by chemostat cultures showed a dependency of that activity by the content of cellular Bchl c. In summary, the results suggest that, growth rate or a factor regulating growth rate, rather than light affected specific Bchl levels and because of the increasing molar ratio of Bchl c to Bchl a, the light harvesting capacity and photosynthetic efficiency of the photosynthetic apparatus.     

Kinetic study of hybridoma cell growth in continuous culture: II. Behavior of producers and comparison to nonproducers

A hybridoma cell line, AFP-27-P, was cultivated in continuous culture under glucose-limited conditions. The viable cell concentration, dead-cell concentration, and cell volume all varied with the dilution rate. A model previously developed for a nonproducing clone of the same cell line, AFP-27-NP, was extended to describe the behavior of the cells. The relationship between the specific growth rate and glucose concentration is described by a function similar to the Monod model. A threshold glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. The relationship between the death rate and the glucose concentration is described by an inverted Monod-type function. Furthermore, the yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper range of specific growth rates. No maintenance term for glucose consumption is used; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepts the specific growth rate at a value close to the minimum growth rate. The productivity of antibody as a function of the specific growth rate is described by a mixed type model with a noon-growth-associated term and a negative-growth-associated term. The values for the model parameters were determined from regression analysis of the steady state data.     

Growth kinetics of Escherichia coli with galactose and several other sugars in carbon-limited chemostat culture

Kinetic models for microbial growth describe the specific growth rate (mu) as a function of the concentration of the growth-limiting nutrient (s) and a set of parameters. A typical example is the model proposed by Monod, where mu is related to s using substrate affinity (Ks) and the maximum specific growth rate (mu max). The preferred method to determine such parameters is to grow microorganisms in continuous culture and to measure the concentration of the growth-limiting substrate as a function of the dilution rate. However, owing to the lack of analytical methods to quantify sugars in the microgram per litre range, it has not been possible to investigate the growth kinetics of Escherichia coli in chemostat culture. Using an HPLC method able to determine steady-state concentrations of reducing sugars, we previously have shown that the Monod model adequately describes glucose-limited growth of E. coli ML30. This has not been confirmed for any other sugar. Therefore, we carried out a similar study with galactose and found steady-state concentrations between 18 and 840 micrograms.L-1 for dilution rates between 0.2 and 0.8.h-1, respectively. With these data the parameters of several models giving the specific growth rate as a function of the substrate concentration were estimated by nonlinear parameter estimation, and subsequently, the models were evaluated statistically. From all equations tested, the Monod model described the data best. The parameters for galactose utilisation were mu max = 0.75.h-1 and Ks = 67 micrograms.L-1. The results indicated that accurate Ks values can be estimated from a limited set of steady-state data when employing mu max measured during balanced growth in batch culture. This simplified procedure was applied for maltose, ribose, and fructose. For growth of E. coli with these sugars, mu max and Ks were for maltose 0.87.h-1, 100 micrograms.L-1; for ribose 0.57.h-1, 132 micrograms.L-1, and for fructose 0.70.h-1, 125 micrograms.L-1.     

Kinetic Analyses of Desulfurization of Dibenzothiophene by Rhodococcus erythropolis in Continuous Cultures

Rhodococcus erythropolis N1-36, a desulfurization strain, was grown in continuous culture at 10 different dilution rates with 50 (mu)M dibenzothiophene sulfone (DBTO(inf2)) as the growth-limiting nutrient. The steady-state biomass, concentrations of substrate (DBTO(inf2)) and product (monohydroxybiphenyl), saturation constant (0.39 (mu)M DBTO(inf2)), and cell yield coefficient (9 mg of biomass(middot)(mu)M(sup-1) DBTO(inf2)) were measured. Continuous cultures at five temperatures allowed calculation of activation energy (0.84 kcal(middot)mol(sup-1) [ca. 3.5 kJ(middot)mol(sup-1)]) near the optimal temperature (30(deg)C) for growth. A washout technique was used to calculate the maximum specific growth rate (0.235 h(sup-1)), a value equivalent to a minimum generation time of 2.95 h.     

Siderophores Produced by Nitrogen-Fixing Azotobacter vinelandii OP in Iron-Limited Continuous Culture

Azotobacter vinelandii requires a high complement of iron and an efficient iron acquisition system to support nitrogen fixation. To circumvent problems inherent in batch culture trace metal studies, continuous cultures were used to measure the response of A. vinelandii to iron stress. Iron was found to be growth limiting for nitrogen-fixing A. vinelandii at a concentration as high as 12.5 muM; iron was growth sufficient at 25 muM. Iron-stressed A. vinelandii in continuous culture formed 2,3-hydroxybenzoic acid (DHB), 2-N,6-N-di-(2,3-dihydroxybenzoyl)-l-lysine (DHBL), and a chromophoric yellow-green fluorescent peptide (YGFP). At a fixed dilution rate of 0.1 h, steady-state growth occurred at growth-limiting iron concentrations. DHB and DHBL were quantitatively measured during iron-limited steady states and iron-sufficient states by Arnow colorimetric assays. YGFP was determined by absorbance measurements taken at 380 nm, and the concentration was calculated from the reported specific absorption coefficient. Biomass increased and DHBL, DHB, and YGFP concentrations decreased as the concentration of growth-limiting iron was increased in the culture vessel and medium reservoirs. DHBL was the major siderophore and YGFP was the minor siderophore species produced during iron-limited equilibrium growth. A low level of DHB and YGFP, but no DHBL, was formed under iron-sufficient conditions. These results provide further physiological evidence that DHB, YGFP, and especially DHBL may function as siderophores in nitrogen-fixing A. vinelandii.     

Effect of Nutrient Concentration on the Growth of Escherichia coli

The relationship between specific growth rate of Escherichia coli and the concentration of limiting nutrient (glucose or phosphate or tryptophan) has been determined for populations in a steady state. At high concentrations the specific growth rate is independent of the concentration of nutrient, but at low concentrations the specific growth rate is a strong function of the nutrient concentration. Such a relationship was predicted by Monod; however, Monod's equation does not predict the relationship over the entire range of nutrient concentration. If parameters of the equation are estimated from the results obtained at low concentrations, then at high concentrations of nutrient, the specific growth rate is significantly higher than that predicted by Monod's equation. These results were interpreted on the basis that the rate of growth is controlled by at least two parallel reactions and that the affinities of the enzymes catalyzing these reactions are different. The relationship between specific growth rate and mean cell volume was also measured, and the results indicate that mean cell volume depends not only on the specific growth rate but also on the nature of the limiting nutrient. There are different mean cell volumes at the same specific growth rate established by different limiting nutrients. Therefore, the mean cell volume is not uniquely determined by the specific growth rate.     

A Simple and Inexpensive Design of Chemostat Enabling Steady-state Growth of Acer pseudoplatanus L. Cells under Phosphate-limiting Conditions

Operational and constructional details are given of a relativelysimple and inexpensive chemostat designed for the continuousculture of plant cells in suspension. This apparatus permitscontrol of the growth rate of sycamore, Acer pseudoplatanusL. cells in steady-state conditions. By alteration of the rateof input of medium different steady-state growth rates wereobtained over a wide range (mean doubling times from 182 h to36 h). In order to establish a growth-limiting nutrient thetime course of nutrient uptake in batch culture was measured.In batch culture the maximum growth obtained was proportionalto the initial concentration of phosphate when this was belowa concentration of 17 µg P per ml (as phosphate). It isalso shown in chemostat culture that the steady-state cell densityis proportional to the phosphate concentration in the mediumwhen this is below 17 µg P per ml (as phosphate). Phosphatewas therefore established to be the growth rate-limiting nutrientin chemostat culture at a concentration of 8•5 µgP per ml (as phosphate).     

Predicting Production in Light-Limited Continuous Cultures of Algae

Equations relating productivity, growth rate, cell concentration, and light absorption lead to the prediction that, when incident light is below saturating intensity, maximal productivity will occur at half the maximal growth rate. The freshwater alga Chlorella pyrenoidosa TX71105 and the marine alga Dunaliella tertiolecta were grown in a small continuous culture apparatus with turbidostatic control. With both cultures, the cell concentration showed a linear decrease with dilution rate. Productivity was maximal at about one-half the maximal dilution rate. Average mass per cell increased near the maximal dilution rate, causing some asymmetry in the productivity versus dilution rate curve. The chlorophyll content per unit mass decreased in this region, but the chlorophyll content per cell remained constant. Best production rate in a light-limited algal culture was obtained when the growth rate at very low cell concentration was determined in the apparatus and the dilution rate was set at one-half that value.