A semicontinuous culture model that links cell growth to extracellular nutrient concentration

During semicontinuous culture, a sample of fixed volume is removed at regular time intervals to make measurements and/or harvest culture components, and an equal volume of fresh medium is immediately added to the culture, thereby instantaneously enhancing nutrient concentrations and diluting cell concentration. The resulting cell concentration versus time curve (i.e., the actual cell growth curve) has a saw-toothed appearance because of the periodic dilution of cell concentration. The observed cell concentrations correspond to the peaks of the saw-toothed curve. Cell growth rates are estimated from the locus of observed cell concentrations (i.e., from the apparent growth curve obtained by connecting the peaks of the saw-toothed curve). The sole preexisting model (Fencl's mode) for estimating cell growth rate is valid only when the cells are growing exponentially at a constant rate between samplings. This model has limited validity: despite the periodic enhancement of nutrient concentration, cell growth between samplings eventually causes nutrient depletion, and the cells cease to grow exponentially. Failure to recognize the limits of validity for Fencl' model has resulted in many erroneous applications of the model and, consequently, many incorrect estimates of cell growth rates. To provide a means for correctly estimating cell growth rates, Fencl's exponential model was extended, and a new model that describes the effects of nutrient depletion on cell growth in semi-continuous culture was obtained. The new model shows that exhaustion of a single growth-limiting nutrient in semicontinuous culture causes the locus of cell concentrations observed at time intervals of Deltat to follow a logistic growth curve. The actual cell growth rate was shown to equal the apparent logistic growth rate plus the effective dilution rate -Deltat(-1) In (1 - f), where f is the ratio of sample volume to total culture volume. Moreover, the model predicts that both the apparent logistic growth rate and the apparent steady-state cell concentration should rise linearly with the concentration of growth-limiting nutrient in the input medium, but fall linearly with increases in the effective dilution rate. The new logistic model for nutrient-limited cell growth in semicontinuous culture was successfully tested using published data for Asterionella formosa, Cyclotella meneghiniana, Daucus carota, and strain L mouse cells.     

High viable cell concentration fed-batch cultures of hybridoma cells through on-line nutrient feeding

A hybridoma cell line was cultivated in fed-batch cultures using a low-protein, serum-free medium. On-line oxygen uptake rate (OUR) measurement was used to adjust the nutrient feeding rate based on glucose consumption, which was estimated on-line using the stoichiometric relations between glucose and oxygen consumption. Through on-line control of the nutrient feeding rate, not only sufficients were supplied for cell growth and antibody production, but also the concentrations of glucose and other important nutrients such as amino acids were maintained at low levels during the cell growth phase. During the cultivation, cell metabolism changed from high lactate production and low oxygen consumption to low lactate production and high oxygen consumption. As a result the accumulation of lactate was reduced and the growth phase was extended. In comparison with the batch cultures, in which cells reached a concentration of approximately 2 x 10(6) cells/mL, a very high concentration of 1.36 x 10(7) cells/mL with a high cell viability (>90%) was achieved in the fed-batch culture. By considering the consumption of glucose and amino acids, as well as the production of cell mass, metabolites, and antibodies, a well-closed material balance was established. Our results demonstrate the value of coupling on-line OUR measurement and the stoichiometric realations for dynamic nutrient feeding in high cell concentration fed batch cultures. (c) 1995 John Wiley & Sons, Inc.     

Effect of biomass concentration on the specific solvent productivity ofClostridium acetobutylicum in chemostat culture

Summary Using a defined medium in chemostat culture, an inverse relationship between the biomass concentration and the specific butanol productivity has been observed. It is suggested that this is due to the cell population not being homogeneous, and that a change in the nutrient balance leads to a cha in the relative proportions of acidogenic, solventogenic and inert cells (spores).     

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells is, however, a wide-open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.     

A fluorescence-based assay for measuring the viable cell concentration of mixed microbial communities in soil

Microbial cell concentration is a particularly important bioindicator of soil health and a yardstick for determining biological quotients which are likely to gain in ecological significance if they are calculated in relation to the viable, rather than total, microbial density. A dual-staining technique with fluorescent dyes was used for the spectrofluorimetric quantitative determination of the concentration of viable microbial cells present in three different soil types. This is a novel and substantially modified application of the dual-staining procedure implemented in the LIVE/DEAD BacLight viability kit which has never been successfully applied to the quantification of naturally occurring soil microbial communities. Indigenous microbial cell concentrations were quantified using an internal standard, i.e. spiking environmental samples with suspensions containing different concentrations of live E. coli cells, and external calibration, by comparing fluorescence emission by indigenous bacteria and known concentrations of E. coli in nutrient saline. Two types of environmental samples were tested: bacterial preparations obtained by density gradient centrifugation and soil suspensions. In both cases, prior dilution of the sample was necessary to minimise fluorescence quenching by soil particulate matter. Spectrofluorimetric measurements of indigenous cell concentration in bacterial preparations were in close agreement with those found using epifluorescence microscopy. Limits of detection of 5x10(6) for the soil bacterial preparations and 8x10(7) for the soil suspensions were estimated. Deviations observed when soil suspensions are dealt with are likely due to the selection of a unique bacterial strain for standardisation and calibration. Thorough testing of a variety of reference bacteria and fungi is suggested to determine a more accurate average fluorescence enhancement per microbial cell or mass unit.     

Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH.

Tumors and multicellular tumor spheroids can develop gradients in oxygen concentration, glucose concentration, and extracellular pH as they grow. In order to calculate these gradients and assess their impact on tumor growth, it is necessary to quantify the effect of these variables on tumor cell metabolism and growth. In this work, the oxygen consumption rates, glucose consumption rates, and growth rates of EMT6/Ro mouse mammary tumor cells were measured at a variety of oxygen concentrations, glucose concentrations, and extracellular pH levels. At an extracellular pH of 7.25, the oxygen consumption rate of EMT6/Ro cells increased by nearly a factor of 2 as the glucose concentration was decreased from 5.5 mM to 0.4 mM. This effect of glucose concentration on oxygen consumption rate, however, was slight at an extracellular pH of 6.95 and disappeared completely at an extracellular pH of 6.60. The glucose consumption rate of EMT6/Ro cells increased by roughly 40% when the oxygen concentration was reduced from 0.21 mM to 0.023 mM and decreased by roughly 60% when the extracellular pH was decreased from 7.25 to 6.95. The growth rate of EMT6/Ro cells decreased with decreasing oxygen concentration and extracellular pH; however, severe conditions were required to stop cell growth (0.0082 mM oxygen and an extracellular pH of 6.60). Empirical correlations were developed from these data to express EMT6/Ro cell growth rates, oxygen consumption rates, and glucose consumption rates, as functions of oxygen concentration, glucose concentration, and extracellular pH. These empirical correlations make it possible to mathematically model the gradients in oxygen concentration, glucose concentration, and extracellular pH in EMT6/Ro multicellular spheroids by solution of the diffusion/reaction equations. Computations such as these, along with oxygen and pH microelectrode measurements in EMT6/Ro multicellular spheroids, indicated that nutrient concentration and pH levels in the inner regions of spheroids were low enough to cause significant changes in nutrient consumption rates and cell growth rates. However, pH and oxygen concentrations measured or calculated in EMT6/Ro spheroids where quiescent cells have been observed were not low enough to cause the cessation of cell growth, indicating that the observed quiescence must have been due to factors other than acidic pH, oxygen depletion, or glucose depletion.     

Effect of high substrate concentration and cell feedback on kinetic behavior of heterogeneous populations in completely mixed systems

Growth kinetics of heterogeneous populations of sewage origin were studied in completely mixed reactors of the once-through type at a high concentration of incoming substrate, 3000 mg/l glucose, and in systems employing cell feedback or sludge recycle at an incoming substrate concentration of 1000 mg/1 glucose. The recycle flow rate employed was 25% of the incoming feed flow, and the concentration of cells in the recycle was maintained as closely as possible at 150% of the cell concentration in the reactor. Studies were made at various dilution rates. Throughout these studies, batch experiments using cells grown at the various dilution rates were made to determine k_s and μ_m values. As in previous studios using heterogeneous populations, the relationship between specific growth rates μ and substrate concentration S was represented better by the Monod equation than by any other which was tested. The growth “constants” μ_m, k_s, and Y were found to fall in the same general range as those determined in previous studies in once-through systems operated at 1000 mg/l glucose. It was observed that cell recycle, even at the relatively low concentration factor employed in these studies, greatly enhanced the flocculating and settling characteristics of the cells.     

Protein and lipid concentration in the haemolymph of Danais chrysippus. Linn

Proteins and lipids in the haemolymph in both the sexes of the Danais chrysippus has been observed during the first gonotropic cycle. The concentration fluctuations in these haemolymph metabolites are correlated with the physiological state of the insect. The total protein and lipid concentration in the haemolymph of unmated females have been found to be low than the concentration found for the normal females although it followed the same type of oscillations in the concentration as have been observed for normal females.     

4-hydroxy-2,3 trans-nonenal nuclear concentration inversely correlates with the growth rate of T leukemia cells

4-hydroxy-2,3 trans-nonenal is the major diffusible product generated by linoleic and arachidonic acids peroxidation. Its endogenous content is inversely related to the rate of cell proliferation and directly related to the level of cell differentiation. As previously reported, the nuclear localization of the aldehyde has been observed by means of a fluorescent antibody and confocal microscopy, and its concentration measured by electrospray/mass spectrometry, a sensitive and selective method for 4-hydroxy-2,3 trans-nonenal determination, on nuclear extracts of leukemic cells. With the aim to establish a possible correlation between the peroxidation product nuclear concentration and cell growth rate, Jurkat 6 leukemic cells have been used and the aldehyde measured by electrospray/mass spectrometry. The cells arrested in G1 show a content of 4-hydroxy-2,3 trans-nonenal significantly increased with respect to control ones.     

Variations in the total sterols, free sterols and sterol esters concentration during embryogenesis in Dysdercus similis (Freeman)

In the present study fluctuations in the total sterols, free sterols and sterols esters concentration has been recorded day to day during embryogenesis. Oscillations in the total sterol correlated with the biosynthesis and/or utilization of cholesterol occur in the eggs while free sterols are used in the maintenance of cell membranes. The role of sterol ester is not known but their increase may be correlated with the accretion of oleic and linoleic fatty acids.     

Green and senescent leaf phenolics showed spatial autocorrelation in a Quercus robur population in northwestern Spain

Intraspecific variation in polyphenols may be important both for the resistance of plants to herbivory and for nutrient cycling in terrestrial ecosystems. The spatial pattern and scale of polyphenol concentration in natural populations are practically unknown, despite multiple evidence that resources influencing leaf phenolics (such as light or nutrient availability) show spatial dependence at the scale of meters to tens of meters. By using geostatistical methods, we evaluated the spatial variability in polyphenol concentration in green and senescent leaves in a pedunculate oak (Quercus robur L.) population of 125 individuals. The spatial pattern of light and nutrient availability for plants was also evaluated. Leaf polyphenols were more variable than other leaf properties, and green polyphenols were significantly correlated with radiation, leaf mass per unit area and leaf N concentration. Both green and senescent leaf polyphenol concentration showed spatial dependence at distances below 6 to 10 m, with structural (spatial) variance explaining between 50 and 80% of the total variance. The variance not explained by space was assumed to be due to individual genotypic variability. Stochastic maps of leaf phenolics in the area showed that the probability of finding high phenolics level was not random. These findings may be important to understand the spatial heterogeneity of plant-herbivore interactions, leaf litter decomposition and mineralization rate.     

Alteration of mammalian cell metabolism by dynamic nutrient feeding

The metabolism of hybridoma cells was controlled to reduce metabolic formation in fed-batch cultures by dynamically feeding a salt-free nutrient concentrate. For this purpose, on-line oxygen uptake rate (OUR) measurement was used to estimate the metabolic demand of hybridoma cells and to determine the feeding rate of a concentrated solution of salt-free DMEM/F12 medium supplemented with other medium components. The ratios among glucose, glutamine and other medium components in the feeding nutrient concentrate were adjusted stoichiometrically to provide balanced nutrient conditions for cell growth. Through on-line control of the feeding rate of the nutrient concentrate, both glucose and glutamine concentrations were maintained at low levels of 0.5 and 0.2 mM respectively during the growth stage. The concentrations of the other essential amino acids were also maintained without large fluctuations. The cell metabolism was altered from that observed in batch cultures resulting in a significant reduction of lactate, ammonia and alanine production. Compared to a previously reported fed-batch culture in which only glucose was maintained at a low level and only a reduced lactate production was observed, this culture has also reduced the production of other metabolites, such as ammonium and alanine. As a result, a high viable cell concentration of more than 1.0 × 10⁷ cells/mL was achieved and sustained over an extended period. The results demonstrate an efficient nutrient feeding strategy for controlling cell metabolism to achieve and sustain a high viable cell concentration in fed-batch mammalian cell cultures in order to enhance the productivity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Precision of sensing cell length via concentration gradients

Unicellular organisms are typically found to have a characteristic cell size. To achieve a homeostatic distribution of cell sizes over many generations requires that cell length is actively sensed and regulated. However, the mechanisms by which cell size is controlled remain poorly understood. Recent experiments in fission yeast have shown that cell length is controlled in part by polar gradients of the protein Pom1 together with localized measurement of concentration at midcell. Dilution as the cell grows leads to a reduction in the midcell protein concentration, which lifts a block on mitosis. Here we analyze the precision of this mechanism for length sensing in the presence of inevitable intrinsic noise in the processes leading to formation and measurement of this gradient. We find that the use of concentration gradients allows for more robust length sensing than a comparable spatially uniform system, and allows for reliable length determination even if the average protein concentration throughout the cell remains constant as the cell grows. Optimal values for the gradient decay length and receptor dissociation constant emerge from maximizing sensitivity while minimizing the impact of density fluctuations.     

Influence of external concentration fluctuations on leukocyte chemotactic orientation

The quantitative dependence of leukocyte chemotactic orientation on imprecision in the measurement of chemoattractant concentrations from thermal fluctuations is analyzed. First, a mathematical model relating orientation to differences in receptor occupancy across cell dimensions is developed. This is then coupled with an extension of Berg and Purcell's analysis (1) of the precision of attractant concentration measurements by means of receptor occupancy. Our results show that thermal fluctuations in external concentrations can limit the accuracy of orientation, unless the measurement noise is reduced by averaging the measurements over a period of time. Comparison of our model predictions to experimental orientation data suggests that leukocytes do overcome this limitation, and allows estimation of the time-averaging period necessary to do so. For the orientation observed in a visual bridge assay by Zigmond (2) using the attractant peptide FNLLP, we estimate that receptor occupancy measurements for spatial comparison across cell dimensions must be averaged for a few minutes. Otherwise, the fluctuations in the attractant concentration near the cell will be too great to allow the observed degree of orientation. Our analysis also suggests that the ratio of signal-to-signal noise does not adequately characterize orientation accuracy. Accurate orientation can, in some situations, occur when this ratio is substantially less than unity; in other situations, a ratio much greater than unity is required for accurate orientation.     

Increasing intraspecific diversity increases predictability in population survival in the face of perturbations

It has been proposed that biodiversity can be important for ecosystem functioning and act as an insurance against perturbations and environmental fluctuations. To date, theoretical work supports this idea but direct experimental evidence is still to some extent ambiguous and debated. The main reason for this debate – and the lack of strong empirical support – is due to unavoidable experimentally and statistically inherent variance reduction effects. Here we present the results of an experimental study that circumvents earlier hidden treatments. By random draw without replacement, we collected 180 full-sibling batches of an amphipod from a large pool of possible parents. Assembled amphipod populations with diversity levels ranging from one to ten were exposed to either a single perturbation (nutrient enrichment) or two combined perturbations (nutrient enrichment and desiccation). The results show that the variance in the number of surviving individuals decreased with increasing diversity in the combined perturbations treatment. Predictability in population survival thus seemed to be higher in more diverse assemblages. Our results, together with a simple model suggest that variance-decreasing effects can be due to actual real world statistical sampling effects of increasing diversity.     

Response kinetics of tethered bacteria to stepwise changes in nutrient concentration

We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial response and the adaptation to the sustained concentration of the chemical. This was carried out by tethering motile cells by their flagella to glass slides and following the rotational behaviour of their cell bodies in response to the nutrient change. Computerised motion analysis was used to analyse the behaviour. Distributions of run and stop times were obtained from rotation data for tethered cells. Exponential and Weibull fits for these distributions, and variability in individual responses are discussed. In terms of parameters derived from the run and stop time distributions, we compare the responses to stepwise changes in the nutrient concentration and the long-term behaviour of 84 cells under 12 propionate concentration levels from 1 nM to 25 mM. We discuss traditional assumptions for the random walk approximation to bacterial swimming and compare them with the observed R. sphaeroides motile behaviour.     

Relative addition rate and external concentration; Driving variables used in plant nutrition research

Abstract An increasing literature accounting for various types of experiments indicates that far lower external nutrient concentrations are required by plants than is usually thought to be the case. It is concluded that the ion uptake capacity of the roots, as described by the carrier concept, is high compared to that required for maintenance of the internal concentration. Serious errors in experimental conclusions are associated with insufficient and constant nutrient addition rates. The main errors are caused by non-steady states of the plants both with regard to the internal nutrient concentrations and the relative growth rate. A dynamic concept has been proposed for direct use as the treatment variable within the range of sub-optimum nutrition. The nutritional factor is expressed as a flow, the relative nutrient addition rate in laboratory studies and the nutrient flux density in the field. The experimental use of the relative addition rate has led to steady-state nutrient status and relative growth rate and the interpretation of plant responses which differ fundamentally from accepted views. Thus, for instance, deficiency symptoms disappear, as in natural conditions, when the internal nitrogen concentration is stable, independent of level. The nutrition/growth relationships are very different from those observed when external concentration is varied. The regression line of relative growth rate on relative addition rate passes near to the origin at an angle close to 45 to the axes, which implies that the obtained relative growth rate approximates closely the treatment variable. A striking example of observed differences is the positive effect on nitrogen fixation exerted by high relative nitrogen addition rates compared to the well-known negative effect of increasing external nitrogen concentration. The application of fertilizer on the basis of the nutrient flux density concept provides the possibility of supplying fertilizers corresponding to the consumption potential of the vegetation and to the natural flux density resulting from mineralization in the soil. Nitrogen utilization is high under such conditions and the resulting feedback of nutrition on the mineralization rate suggests that there will be a long-term increase in fertility.     

Enhanced production of podophyllotoxin by Podophyllum hexandrum using in situ cell retention bioreactor

The rhizomes of the rare plant Podophyllum hexandrum contain podophyllotoxin, which is a precursor of the anticancer drugs etoposide and teniposide. Batch cultivation of Podophyllum hexandrum was conducted using optimized medium in a 3 L bioreactor, which resulted in biomass and podophyllotoxin concentrations of 21.4 g/L and 13.8 mg/L in 24 and 26 days, respectively. The batch kinetics was used to identify the mathematical model. The model was extrapolated to identify the nutrient feeding rate (150 mL/d) and substrate concentration (105 g/L) in the incoming feed for nonlimiting and noninhibitory glucose concentration in the cell retention bioreactor. An improvement in cell growth to 53 g/L and intracellular podophyllotoxin accumulation of 48.8 mg/L was achieved in 60 days, when the bioreactor was operated in continuous cell retention cultivation mode.     

The design and development of a biosensor to measure the concentration of meconium in amniotic fluid

Meconium aspiration syndrome occurs in 0.2% to 1% of all deliveries and has a mortality rate as high as 18%. The disease is responsible for 2% of all perinatal deaths. Meconium may be classified as being thick or thin, but this assessment is normally performed visually by clinicians. A "meconiumcrit" analysis has been developed to objectively define the concentration of meconium. However, this analysis does not provide real-time continuous readings. This study focused on the design and development of a sensor to provide an objective, continuous, real-time assessment of meconium thickness. Meconium has an absorption spectrum centered at 410 nm and observes Beer's law. Blue light centered at 430 nm was delivered through meconium solutions, and a photodiode translated the strength of the incoming light into a voltage. This voltage was analyzed by a microcontroller to determine the concentration of meconium.