Cell volume distributions reveal cell growth rates and division times

A population of cells in culture displays a range of phenotypic responses even when those cells are derived from a single cell and are exposed to a homogeneous environment. Phenotypic variability can have a number of sources including the variable rates at which individual cells within the population grow and divide. We have examined how such variations contribute to population responses by measuring cell volumes within genetically identical populations of cells where individual members of the population are continuously growing and dividing, and we have derived a function describing the stationary distribution of cell volumes that arises from these dynamics. The model includes stochastic parameters for the variability in cell cycle times and growth rates for individual cells in a proliferating cell line. We used the model to analyze the volume distributions obtained for two different cell lines and one cell line in the absence and presence of aphidicolin, a DNA polymerase inhibitor. The derivation and application of the model allows one to relate the stationary population distribution of cell volumes to extrinsic biological noise present in growing and dividing cell cultures.     

Application of biocathode in microbial fuel cells: cell performance and microbial community

Instead of the utilization of artificial redox mediators or other catalysts, a biocathode has been applied in a two-chamber microbial fuel cell in this study, and the cell performance and microbial community were analyzed. After a 2-month startup, the microorganisms of each compartment in microbial fuel cell were well developed, and the output of microbial fuel cell increased and became stable gradually, in terms of electricity generation. At 20 ml/min flow rate of the cathodic influent, the maximum power density reached 19.53 W/m3, while the corresponding current and cell voltage were 15.36 mA and 223 mV at an external resistor of 14.9 Omega, respectively. With the development of microorganisms in both compartments, the internal resistance decreased from initial 40.2 to 14.0 Omega, too. Microbial community analysis demonstrated that five major groups of the clones were categorized among those 26 clone types derived from the cathode microorganisms. Betaproteobacteria was the most abundant division with 50.0% (37 of 74) of the sequenced clones in the cathode compartment, followed by 21.6% (16 of 74) Bacteroidetes, 9.5% (7 of 74) Alphaproteobacteria, 8.1% (6 of 74) Chlorobi, 4.1% (3 of 74) Deltaproteobacteria, 4.1% (3 of 74) Actinobacteria, and 2.6% (2 of 74) Gammaproteobacteria.     

Hydrolysates from Atlantic cod (Gadus morhua L.) viscera as components of microbial growth media

Three hydrolysates made from cod viscera by different enzymatic hydrolysis procedures were tested as a combined source for nitrogen, amino acids and vitamins in microbial growth media. Using a panel of five different microbes: Escherichia coli, Bacillus subtilis, Lactobacillus sakei, Saccharomyces cerevisiae and Aspergillus niger, the performance of these viscera hydrolysates was compared to the performance of common commercial peptones in an automated growth analyzer (Bioscreen C). The results show that the fish hydrolysates in general are promising alternatives to currently available commercial nitrogen sources of other origins. In the case of the food-grade and nutritionally fastidious L. sakei, two of the fish hydrolysates were clearly superior to all tested commercial peptones. For several microbes, the choice of the proteolytic enzymes used to produce the fish hydrolysate had considerable impact on performance of the resulting hydrolysate, both in terms of maximum growth rate and biomass production. In terms of hydrolysate performance, the generally best enzyme for production of a fish peptone from cod viscera was found to be Alcalase.     

Stimulation of quiescent cells by individual polypeptide growth factors is limited to one cell cycle

Since little is known about the function of polypeptide growth factors as regulators of multiple cell cycles, we compared the ability of FGF1, PDGF-AB and serum to induce a second round of DNA synthesis in Swiss 3T3 cells previously exposed to either FGF1, PDGF-AB or serum during the first cell cycle using [14C]- and [3H]thymidine in a double labeling system to distinguish between the first and second cell cycles. Surprisingly, we observed that cells exposed to either FGF1 or PDGF-AB in the first cell cycle were unable to synthesize DNA in response to FGF1 or PDGF-AB in the second cell cycle; yet these cells responded well to serum as a second cycle mitogen. Interestingly, while cells exposed to either FGF1 or PDGF-AB in the second cycle displayed normal receptor-mediated signaling and expressed cyclin D and E, they, like senescent fibroblasts and endothelial cells, failed to express cyclin A, and the continuous exposure of cells to either FGF1 or PDGF-AB resulted in a decrease in the kinase activity of the cyclin E/cdk2 complex. In addition, an increased association of this complex was observed with p21 CIP in an FGF1-dependent manner as well as with p27 KIP in a PDGF-AB-dependent manner. Lastly, the downregulation of p21 expression using an antisense strategy was able to partially rescue the replicative response of Swiss 3T3 cells to FGF1 in the second cycle. These data suggest that (i) FGF1 and PDGF-AB may limit their mitogenic effect to a single cell cycle, (ii) entry into the second round of replication is serum dependent and (iii) the self-limiting nature of FGF1 and PDGF-AB correlates with the accumulation of the cdk inhibitors, p21 and p27, respectively.     

Steady size distributions for cells in one-dimensional plant tissues

We consider a population of cells growing and dividing steadily without mortality, so that the total cell population is increasing, but the proportion of cells in any size class remains constant. The cell division process is non-deterministic in the sense that both the size at which a cell divides, and the proportions into which it divides, are described by probability density functions. We derive expressions for the steady size/birth-size distribution (and the corresponding size/age distribution) in terms of the cell birth-size distribution, in the particular case of one-dimensional growth in plant organs, where the relative growth rate is the same for all cells but may vary with time. This birth-size distribution is shown to be the principal eigenfunction of a Fredholm integral operator. Some special cases of the cell birth-size distribution are then solved using analytical techniques, and in more realistic examples, the eigen-function is found using a simple, generally applicable numerical iteration.     

The influence of cell volume changes on tumour cell proliferation

Ion channels and cell volume control participate in a wide variety of cellular functions, including cell proliferation. According to the pump-leak model or the double Donnan system, the cell volume is constant in physiological medium so long as the cell metabolism and the Na-K pump are not inhibited and the passive Na⁺ permeability is not dramatically increased. At short term, this model has been supported by a large number of experiments made on different cell types. However, at long term, it may be insufficient to describe the volume control because it does not take into account the fact that cells possess a large number of membrane transporters and interconnected volume regulatory mechanisms. In this review, we present recent results indicating that, in physiological conditions, ion channels may have important roles in cell volume control. Furthermore, we emphasize that cell proliferation and volume are phenomenologically correlated. On the basis of the macromolecular crowding theory, the possibility that the cell osmolyte and water content mediates this correlation is discussed.Abbreviations 4-AP 4-aminopyridine - NPPB 5-nitro-2-(3-phenylpropylamino)benzoic acid - TEA tetraethylammonium - TOR target of rapamycin Presented at the Biophysical Society Meeting on Ion channels—from structure to desease held in May 2003, Rennes, France     

Analytical solution for the extremums of cell water volume and cell volume using a two-parameter model

Based on a two-parameter model [Cryobiology 37 (1998) 271-289], the analytical solution for the extremums of cell water volume and cell volume for a two-solute system are obtained. Compared with the numerical solution, the analytical solution offers an accurate but simple choice. The approximate solution [Cryobiology 40 (2000) 64-83] for the extremum of cell water volume is also discussed, the reason for the deviation is presented.     

On the lag phase and initial decline of microbial growth curves

The lag phase is generally thought to be a period during which the cells adjust to a new environment before the onset of exponential growth. Characterizing the lag phase in microbial growth curves has importance in food sciences, environmental sciences, bioremediation and in understanding basic cellular processes. The goal of this work is to extend the analysis of cell growth curves and to better estimate the duration of the lag phase. A non-autonomous model is presented that includes actively duplicating cells and two subclasses of non-duplicating cells. The growth curves depend on the growth and death rate of these three subpopulations and on the initial proportion of each. A deterministic and a stochastic model are both developed and give the same results. A notable feature of the model is the decline of cells during the early stage of the growth curve, and the range of parameters when this decline occurs is identified. A limited growth model is also presented that accounts for the lag, exponential growth and stationary phase of microbial growth curves.     

Estimating non-isothermal bacterial growth in foods from isothermal experimental data

AIM: To develop a mathematical method to estimate non-isothermal microbial growth curves in foods from experiments performed under isothermal conditions and demonstrate the method's applicability with published growth data. METHODS AND RESULTS: Published isothermal growth curves of Pseudomonas spp. in refrigerated fish at 0-8 degrees C and Escherichia coli 1952 in a nutritional broth at 27.6-36 degrees C were fitted with two different three-parameter 'primary models' and the temperature dependence of their parameters was fitted by ad hoc empirical 'secondary models'. These were used to generate non-isothermal growth curves by solving, numerically, a differential equation derived on the premise that the momentary non-isothermal growth rate is the isothermal rate at the momentary temperature, at a time that corresponds to the momentary growth level of the population. The predicted non-isothermal growth curves were in agreement with the reported experimental ones and, as expected, the quality of the predictions did not depend on the 'primary model' chosen for the calculation. CONCLUSIONS: A common type of sigmoid growth curve can be adequately described by three-parameter 'primary models'. At least in the two systems examined, these could be used to predict growth patterns under a variety of continuous and discontinuous non-isothermal temperature profiles. SIGNIFICANCE AND IMPACT OF THE STUDY: The described mathematical method whenever validated experimentally will enable the simulation of the microbial quality of stored and transported foods under a large variety of existing or contemplated commercial temperature histories.     

Integrated hydrogen production process from cellulose by combining dark fermentation, microbial fuel cells, and a microbial electrolysis cell

Hydrogen gas production from cellulose was investigated using an integrated hydrogen production process consisting of a dark fermentation reactor and microbial fuel cells (MFCs) as power sources for a microbial electrolysis cell (MEC). Two MFCs (each 25 mL) connected in series to an MEC (72 mL) produced a maximum of 0.43 V using fermentation effluent as a feed, achieving a hydrogen production rate from the MEC of 0.48 m³ H₂/m³/d (based on the MEC volume), and a yield of 33.2 mmol H₂/g COD removed in the MEC. The overall hydrogen production for the integrated system (fermentation, MFC and MEC) was increased by 41% compared with fermentation alone to 14.3 mmol H₂/g cellulose, with a total hydrogen production rate of 0.24 m³ H₂/m³/d and an overall energy recovery efficiency of 23% (based on cellulose removed) without the need for any external electrical energy input.     

A method to distinguish microbial acclimation from reduced growth rates in perturbed ecosystems

Abstract Predicting variations in microbial growth rates (μ) in Nature requires a method that will detect departures from optimal μ, determine the time scale at sub-optimal μ, and measure the restoration or reversibility toward optimal μ. Isotopic flux measurements are equivocal because of uncertainties in their relationship to μ, particularly in non-steady state condictions. After perturbing a natural microbial community and a clone of the phytoplankter Selenastrum capricornutum with two different toxicants, we examined the kinetics of the adenylate energy charge, and followed changes in biomass over time with the total adenylate and chlorophyll a concentrations. We determined that exposure to cadmium resulted in a reduction in μ; reversible within a short time, whereas exposure to the industrial effluent caused an exponential loss of adenylates and complete inhibition of growth. Upon perturbing a microbiol community, the study of adenylate energy charge kinetics detects departures from optimal μ, measures their duration and reversibility.     

Stress relaxation of cell walls and the yield threshold for growth

Theory predicts that, for growing plant cells isolated from a supply of water, stress relaxation of the cell wall should decrease cell turgor pressure (P) until the yield threshold for cell expansion is reached. This prediction was tested by direct P measurements of pea (Pisum sativum L.) stem cortical cells before and after excision of the growing region and isolation of the growing tissue from an external water supply. Cell P was measured with the micro-pressure probe under conditions which eliminated transpiration. Psychrometric measurements of water potential confirmed the pressureprobe measurements. Following excision, P of the growing cells decreased in 1 h by an average of 1.8 bar to a mean plateau value of 2.8 bar, and remained constant thereafter. Treatment with 10^-5 M indole-3-acetic acid or 10^-5 M fusicoccin (known growth stimulants) accelerated the rate of P relaxation, whereas various treatments which inhibit growth slowed down or completely stopped P relaxation in apical segments. In contrast, P of basal (nongrowing) segments gradually increased because of absorption of solutes from the cell-wall free space of the tissue. Such solute absorption also occurred in apical segments, but wall relaxation held P at the yield threshold in those segments which were isolated from an external water supply. These results provide a new and rapid method for measuring the yield threshold and they show that P in intact growing pea stems exceeds the yield threshold by about 2 bar. Wall relaxation is shown here to affect the water potential and turgor pressure of excised growing segments. In addition, solute release and absorption upon excision may influence the water potential and turgor pressure of nongrowing excised plant tissues.Abbreviations and symbols IAA indole-3-acetic acid - P turgor pressure - SE standard error of the mean - water potential     

Effect of temperature on the growth of individual cucumber fruits

In order to study the effect of temperature on the growth of individual fruits in cucumber (cucumis sativus L. cv. Corona), fruits were grown at 17. 5. 20,25 and 30°C continuously or the fruit temperature was changed from 17. 5 to 27.5°C or vice versa. Fruit development appeared to be closely related to the temperature sum. When the growth of a fruit was not constrained by assimilate supply, a decrease in growing period with increasing temperature was more than compensated for by a strong increase in growth rate, resulting in an increase in final fruit weight. However, when the growth of a fruit was constrained by assimilate supply, the increase in growth rate with increasing temperature was small and did not compensate for the decrease in growing period, resulting in a decrease in final fruit weight. Determinations of cell number and size showed that the effect of temperature on fruit growth was due to effects on cell expansion rather than on cell division. When growth was not constrained by assimilate supply. However, when assimilate supply did constrain fruit growth the number of cells per fruit decreased with increasing temperature, while the effect on cell size was negligible. In all stages of fruit development, the growth rate of a cucumber fruit responded within one day to a change in temperature. It was not irreversibly impaired by a low temperature (17. 5°C) during the early development of a fruit. A high temperature treatment (27. 5°C), however, had a great effect on the growth rate of a fruit after the temperature treatment had terminated. At all stages of fruit development (even before anthesis) a period of four days at 27. 5°C resulted in a pronounced stimulation of the growth rate afterwards at 17. 5°C.     

Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture

This paper presents a new method to analyze clonal data on oligodendrocyte development in cell culture. The process of oligodendrocyte generation from precursor cells is modelled as a multi-type Bellman-Harris branching process as suggested in an earlier paper [K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Proschel, M. Noble, An alternative stochastic model of generation of oligodendrocytes in cell culture, J. Math. Biol. 43 (2001) 22]. This model has been extended to allow for death of oligodendrocytes as well as a dissimilar distribution of the first mitotic cycle duration as compared to the subsequent cycles of precursor cells, which lengths are assumed to be independent and identically distributed random variables. Since the time-span of oligodendrocytes is not directly observable in clonal data, plausible parametric assumptions are invoked to make estimation problems tractable. In particular, the time to cell death follows a two-parameter gamma distribution, while the lapse of time between the event of cell death and the event of cell disintegration is assumed to be exponentially distributed. A simulated pseudo maximum likelihood method for estimation of model parameters has been developed using simulation-based approximations of the expected numbers and variance-covariance matrices for different types of cells. Finite sample properties of the estimation procedure are studied by computer simulations. The proposed method is illustrated with an analysis of the clonal development of O-2A progenitor cells isolated from the rat optic nerve and the corpus callosum.     

Asynchrony in the growth and motility responses to environmental changes by individual bacterial cells

Knowing how individual cells respond to environmental changes helps one understand phenotypic diversity in a bacterial cell population, so we simultaneously monitored the growth and motility of isolated motile Escherichia coli cells over several generations by using a method called on-chip single-cell cultivation. Starved cells quickly stopped growing but remained motile for several hours before gradually becoming immotile. When nutrients were restored the cells soon resumed their growth and proliferation but remained immotile for up to six generations. A flagella visualization assay suggested that deflagellation underlies the observed loss of motility. This set of results demonstrates that single-cell transgenerational study under well-characterized environmental conditions can provide information that will help us understand distinct functions within individual cells.     

Modeling of typical microbial cell growth in batch culture

A mathematical model was developed, based on the time dependent changes of the specific growth rate, for prediction of the typical microbial cell growth in batch cultures. This model could predict both the lag growth phase and the stationary growth phase of batch cultures, and it was tested with the batch growth ofTrichoderma reesei andLactobacillus delbrucckii.     

Stability of the steady-state size distribution in a model of cell growth and division

The approach to steady-state size distribution is studied for a growing population of cells. The model incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase.This work was supported by the National Science Foundation under Grant No. MCS 8300559This work was supported by the National Science Foundation under Grant No. MCS 8301104     

A quantitative cytochemical study of the growth of individual mast cells

Summary For individual mast cells, relationships between their dry mass and their content of heparin and 5-hydroxytryptamine (5-HT) were studied. This was achieved by measuring these parameters successively on identical cells, by means of quantitative cytochemical techniques. The peritoneal mast cells have a very long life span and a slow turnover of granule components. Increase of the dry weight of the cells may therefore be taken as an expression of cellular growth. Mast cell populations from younger and older animals were analysed in an attempt to evaluate the influence of cell-aging and animal-aging on the growth of the mast cells. The analysis was based on allometric (log-log) plots and linear regressions. Within the cell populations there were strong mutual correlations between the cell parameters studied, without any obvious deviations from linearity. However, the slopes of the allometric lines indicated a somewhat different mode of growth for mast cells from younger and older animals. The capacity of the mast cells to accumulate 5-HT after a single injection of its precursor, 5-hydroxytryptophan, was used as a functional test. In relation to the cell weight, the induced increase of 5-HT was greater for lighter than for heavier mast cells. This difference between light and heavy mast cells was greater for cells from younger than from older animals. These differences in growth and functional properties between mast cells from younger and older animals were interpreted as an effect of aging of the animals rather than of aging of the cells.Supported by grants from the Swedish Medical Research Council, Project no 2235I wish to express my sincere thanks to Professor Lennart Enerbäck for valuable and constructive criticism of this paper. I also wish to thank Lecturer Erik Leander for valuable statistical advice