Cell cycle synchronization of Cupriavidus necator by continuous phasing measured via flow cytometry

The continuous phasing technique was successfully used to obtain a high degree of cell cycle synchrony in cultures of the model organism Ralstonia eutropha JMP 134 (today reclassified into Cupriavidus necator). The responses of the organism were evaluated with flow cytometric determinations of DNA contents and cell size (by fluorescence and forward scatter measurements, respectively, after staining with the DNA-binding dye 4',6-diamidino-2'-phenylindole, DAPI), and cell concentration, after staining with the nucleic acid binding dye LDS-751. The strain was cultivated on a mineral medium with pyruvic acid sodium salt as the limiting carbon and energy source. Famine conditions, and thus cell dormancy, were achieved in every cycle. The best synchronization, according to the determination of DNA contents, was induced with phasing cycle durations of at least 4 h. The method allows the induction of synchrony for an indefinite period if the medium is exchanged rapidly and precisely. The results show that the time required for a complete cell cycle of Cupriavidus necator JMP 134 is independent of the chosen phasing cycle duration, provided that each process cycle lasts at least 3 h which is much longer than the time needed for a single DNA replication cycle. With shorter cycling periods DNA-synthesis is carried out in an uncoupled manner and only weak cell cycle synchrony can be attained. The results also show that DNA-synthesis can only be undertaken by cells when they have exceeded a critical size.     

Dynamic aspects of radiorespirometry during the cell cycle of Candida utilis: Some observations in phased culture under carbon-, nitrogen-, and phosphorus-limited growth

Many changes that occur in a cell during the cell cycle can be demonstrated in synchronous cultures and can reveal dimensions of cell metabolism not attainable by the study of balanced growth of asynchronous populations in batch cultures or the steady state in chemostat cultures. The release of ¹⁴CO₂ from specifically labeled glucose by phased (continuously synchronized) cultures follows a characteristic pattern (profile) that depends upon the stage in the cell cycle and the period of labeling used. Successive profiles throughout a cycle showed differences that were altered under different nutrient-limiting growth conditions. Profiles obtained with glucose-1-¹⁴C, glucose-2-¹⁴C, glucose-3,4-¹⁴C, and glucose-6-¹⁴C and phased cells of Candida utilis under N-, P-, and C-limited growth demonstrated the variable character of the metabolic activity that occurred in the cells while contour changes within the profiles across the cycle indicated possible correlations with activities of the hexose monophosphate, Embden-Meyerhof-Parnas, and tricarboxylic acid cycle pathways during the cell cycle. The basis of these changes and their use as elementary parameters for study of problems of physiological changes in vivo are considered.     

Patterns of DNA Synthesis and Cell Division in Marine Dinoflagellates1

Changes in mean cell size, DNA and cell density were monitored at 6-h intervals for 72 h in populations of six species (eight clones) of marine dinoflagellates to determine the temporal relationships between the cell cycle events of DNA replication and cytokinesis. Batch cultures were maintained at 15 or 20°C on a 12-h light: 12-h dark photoperiod. Cell densities and size frequency distributions were determined conductimetrically and the amount of DNA within populations was measured fluorometrically. A variety of intra- and interspecific relationships were observed, ranging from parallel phasing of cell cycle processes to variations which involved the temporal uncoupling of DNA synthesis from the phased pattern of cell division which is characteristic of dinoflagellate cell cycles. Daily growth rates of individual populations varied from 0.05 (Gymnodinium nelsoni) to 2.08 (Amphidinium carteri) cell divisions day^-1 and DNA doubling rates ranged from 0 to 1.14 day^-1. Mean doubling rates for DNA were usually 30–40% lower than those for cells. The degree of difference in these rates and the amount of variability evident in cell cycle sequences may be major factors in determining the rate and extent of development of dinoflagellate populations in nature.     

Variations in the Adenylate Energy Charge During Phased Growth (Cell Cycle) of Candida utilis Under Energy Excess and Energy-Limiting Growth Conditions

The variations in the levels of adenine nucleotides during the phased growth (cell cycle) of the yeast Candida utilis growing under nitrogen, sulfate, or iron limitation with glycerol as carbon source have been determined. Synchronous cultures were obtained by the continuous phasing technique, and the results were compared with those of chemostat cultures growing at similar growth rates and under the same types of nutrient limitation. Whereas the chemostat experiments indicated only the average energy status of cultures growing at random, results from phased cultures showed that the adenylate energy charge, defined as (ATP + (1/2)ADP)/(ATP + ADP + AMP) (where ATP, ADP, and AMP signify adenosine 5'-triphosphate, -diphosphate, and -monophosphate, respectively), varied during the phased growth of the yeast. These variations were related to the stage of development of the cells and to the type of nutrient limitation. In every case the energy charge dropped to a low value during the first half of the phasing cycle (cell cycle). Whereas the energy charge was maintained at relatively high levels (ranging from 0.78 to 0.94), for sulfate- or nitrogen-limited cultures, it was very low when iron was the growth-limiting nutrient (0.44 to 0.78). In spite of the low energy charge, the yeast continued to grow under iron limitation. The main component of the adenylate pool of the iron-limited culture was ADP and not ATP as observed with other types of nutrient limitation. It is concluded that under iron limitation the growth of the organism is limited by energy and that under energy-limited growth the energy charge of a growing organism is maintained at low levels. The reason for maintaining a low energy charge in an energy-limited culture is discussed.     

A framework for whole-cell mathematical modeling

The default framework for modeling biochemical processes is that of a constant-volume reactor operating under steady-state conditions. This is satisfactory for many applications, but not for modeling growth and division of cells. In this study, a whole-cell modeling framework is developed that assumes expanding volumes and a cell-division cycle. A spherical newborn cell is designed to grow in volume during the growth phase of the cycle. After 80% of the cycle period, the cell begins to divide by constricting about its equator, ultimately affording two spherical cells with total volume equal to twice that of the original. The cell is partitioned into two regions or volumes, namely the cytoplasm (Vcyt) and membrane (Vmem), with molecular components present in each. Both volumes change during the cell cycle; Vcyt changes in response to osmotic pressure changes as nutrients enter the cell from the environment, while Vmem changes in response to this osmotic pressure effect such that membrane thickness remains invariant. The two volumes change at different rates; in most cases, this imposes periodic or oscillatory behavior on all components within the cell. Since the framework itself rather than a particular set of reactions and components is responsible for this behavior, it should be possible to model various biochemical processes within it, affording stable periodic solutions without requiring that the biochemical process itself generates oscillations as an inherent feature. Given that these processes naturally occur in growing and dividing cells, it is reasonable to conclude that the dynamics of component concentrations will be more realistic than when modeled within constant-volume and/or steady-state frameworks. This approach is illustrated using a symbolic whole cell model.     

Morphologically-structured models of growing budding yeast populations

It has been well recognized that many key aspects of cell cycle regulation are encoded into the size distributions of growing budding yeast populations due to the tight coupling between cell growth and cell division present in this organism. Several attempts have been made to model the cell size distribution of growing yeast populations in order to obtain insight on the underlying control mechanisms, but most were based on the age structure of asymmetrically dividing populations. Here we propose a new framework that couples a morphologically-structured representation of the population with population balance theory to formulate a dynamic model for the size distribution of growing yeast populations. An advantage of the presented framework is that it allows derivation of simpler models that are directly identifiable from experiments. We show how such models can be derived from the general framework and demonstrate their utility in analyzing yeast population data. Finally, by employing a recently proposed numerical scheme, we proceed to integrate numerically the full distributed model to provide predictions of dynamics of the cell size structure of growing yeast populations.     

Flow cytometry and cell cycle kinetics in continuous and fed-batch fermentations of budding yeast.

Cell size distributions, obtained either as protein distribution by flow cytometry or as cell volume distribution by a Coulter counter, give relevant information about the growth conditions of populations of budding yeast Saccharomyces cerevisiae. We have previously found a good correlation between these distributions and the growth rate in continuous cultures (Ranzi et al., Biotechnol. Bioeng. 1986, 28, 185-190). We now present determinations of the protein distributions and cell volume distributions during different fed-batch fermentations performed with a simple on/off controller. Since during the fed-batch fermentation a true steady state is not obtained, the distributions continuously change with time, but nevertheless we observed a good correlation between the average of both distributions and the actual growth rate. The behavior of the cell size distributions can be interpreted on the basis of a two-threshold cell cycle model in which both the critical protein content at budding (Ps) and the critical protein content for cell division (Pm) are differently modulated by the growth rate. Additional findings will be presented showing that this model can be used to successfully explain the insurgence and the maintenance of oscillatory states in continuous cultures.     

A SIMPLE COMPUTER SIMULATION MODEL FOR GROWING CELL POPULATIONS: ANALYSIS OF SYNCHRONIZED HELA CELL CULTURES

A simple simulation model is presented for growing cell populations. It consists of various ‘classes’of cells (usually thirty) with different cell cycle durations. The cells of each class are distributed in ‘compartments’(thirty to fifty) with different ages. A ‘typical cell’of each compartment is chosen at random and its behaviour weighed according to the number of cells of the compartment. When the parameters for cycle phase durations (G₂, S, G₁ and M) obtained from Quastler-Sherman curves on HeLa cell cultures are fed into the model and the initial distribution of cells is randomized according to the law of exponential growth, the model behaves as an exponentially growing culture with near stable values for the percentage of cells in the various phases of the cell cycle. The level of noise due to random sampling is not objectionable. The behaviour of the model is compared to that of HeLa cultures synchronized by two successive treatments with 2 mM thymidine. While a complete block of S gives very inadequate results, a slowing down of this phase to 25 or 30% of its original speed is enough to simulate all the modifications produced by the thymidine treatment on the cultures. It is not necessary to postulate any other effect. These biological conclusions are reached in spite of the simplicity of the system. The behaviour of the model stresses the fact that for simulating the actual behaviour of cell populations, some parameters of the cell cycle have to be known with considerable accuracy, others are less critical. The model is compared with other mathematical models of cell populations recently proposed and ways to improve it are discussed.     

First generation synchrony of isolated Hyphomicrobium swarmer populations

A method is described for obtaining synchronously growing swarmer cell populations of Hyphomicrobium sp. strain B-522. This was accomplished by isolating young swarmers from random cultures by centrifugation and filtration. Cell multiplication occurred during 38% of the growth cycle in populations synchronized in this manner. Observations were made of the changes in cellular morphology which occurred during the growth cycle. Of the 14.25 h required for the doubling in cell numbers, an average of 5 h passed before the swarmer cells began to develop their hyphae. This time varied over a range of 10 h. The time interval between the beginning of hyphal development and the beginning of bud formation was 3.5 to 4.5 h. The maturation of the first buds and their separation from the mother cells were completed in 5.5 h. The duration of these steps is compared to those measured previously in agar slide cultures.     

Variance within homogeneous phytoplankton populations, I: Theoretical framework for interpreting histograms

A framework is presented for interpreting frequency distributions of volume or fluorescence as measured by a flow cytometer on homogeneous phytoplankton populations. The framework, based on both laboratory experience and theoretical concepts, is illustrated with the use of a simulation model. Asynchronous, synchronous, and phased populations were simulated, with constant and variable growth patterns over the cell cycle. Though simulations produced a wide variety of histogram shapes, including multimodal distributions, the primary difference between asynchronous and synchronous/phased distributions lies in their temporal variation. Histograms that are constant in time indicate asynchronous populations; when populations are not asynchronous, their histogram shapes vary with a periodicity on the same time scale as the cell cycle. A probability density function for the case of asynchronous populations with a constant growth rate is derived. When fitted to simulated histograms this two-parameter density function yields estimates of the two parameters: mean and variance of cell volume (or mass) at age 0.     

INFLUENCE OF ENVIRONMENTAL FACTORS AND POPULATION COMPOSITION ON THE TIMING OF CELL DIVISION IN THALASSIOSIRA FLUVIATILIS (BACILLARIOPHYCEAE) GROWN ON LIGHT/DARK CYCLES1

Cell division patterns in Thalassiosira fluviatilis grown in a cyclostat were analyzed as a function of temperature, photoperiod, nutrient limitation and average cell size of the population. Typical cell division patterns in populations doubling more than once per day had multiple peaks in division rate each day, with the lowest rates always being greater than zero. Division bursts occurred in both light and dark periods with relative intensities depending on growth conditions. Multiple peaks in division rate were also found, when population growth rates were reduced to less than one doubling per day by lowering temperature, nutrients, or photoperiod and the degree of division phasing was not enhanced. Temperature and nutrient limitation shifted the timing of the major division burst relative to the light/dark cycle. Average cell volume of the inoculum was found to be a significant determinant of the average population growth rate and the timing and magnitude of the peaks in division rate. The results are interpreted in the context of a cell cycle model in which generation times are “quantized” into values separated by a constant time interval.     

Freeze preservation of synchrony in cultures of enterobacteriaceae synchronized by continuous phasing in phosphate-limited media

In order to achieve synchronization of cell division by continuous phasing, the growth of enteric bacteria has been limited by inorganic phosphate. After a short starvation, the culture was automatically diluted twofold so that the limiting nutrient allowed for one doubling exactly. An automatic device was designed to carry out repeated cycles of growth, starvation and dilution with adjustable periodicity. After 12-24 automatic cycles, which were usually achieved largely overnight, synchronous cell divisions could be observed for several generations in nonlimiting culture conditions. When portions of the phased culture were frozen and kept at low temperature for periods up to several months, these freeze-preserved populations exhibited a synchronous growth upon thawing and cultivation. This technique has thus the potential of providing synchronized cultures of a variety of bacterial strains at the desired time.     

Cell cycle,cell size and mitochondrial activity of hybridoma cells during batch cultivation

Cell cycle, cell size and rhodamine 123 fluorescence in cell populations of two batch cultures were analysed and quantified with a fluorescence-activated cell sorter (FACS). Two cultures derived from either exponential or stationary phase innocula were investigated in order to demonstrate the dependency of the subsequent cell growth on innoculum condition. The results demonstrated that the level of activity of cells in the innoculum culture could have a significant effect on cellular activity during the initial phase of the inoculated culture, as it advances through its growth cycle. Positive correlation was found between the cell size and mitochondrial activity (as measured by rhodamine 123 uptake) with S and G₂ fractions as the cell progressed through the cell cycle. The enumeration of the fractions of cell cycle phases has helped in prediction of the changes in cell numbers following perturbation of the culture condition.     

Continuous phased culture--a technique for growing, analyzing, and using microbial cells

Continuous phased growth produces a culture in which most of the cells in the population are in the same stage of their development. The cell, thereby amplified by the size of the synchronous population, may be examined in the phased culture at any desired growth rate. Changes taking place in the cell after the cell cycle, i.e., post-cycle changes, may be examined by a modification of the procedure. Further systematic applications of the method permit a rational approach to problems of cell growth and metabolism. The phasing technique recognizes the cells as the fundamental unit for experimental investigation, and offers a great potential in the analysis of the cell throughout its cycle, a relatively unexploited field in cell physiology and fermentation. Experiments with yeasts and bacteria illustrate some of the applications and progress made so far.     

Cell population dynamics during the differentiative phase of tissue development

The dynamics of a cell population whose numbers are growing exponentially have been described well by a mathematical model based on the theory of age-dependent branching processes. Such a model, however, does not cover the period following exponential growth when cell differentiation curtails population size. This paper offers an extension to the branching process model to remedy this deficiency. The extended model is ideal for describing embryonic growth; its use is illustrated with data from embryonic retina. The model offers a better computational framework for the interpretation of a variety of data (growth curves of cell numbers, DNA histograms, thymidine labelling indices, FLM curves, BUdR-labelled mitoses curves) because age-distributions can be calculated at any stage of development, not just during exponential growth. Proportions of cells in the various phases of the cell cycle can be computed as growth slows. Such calculations show the gradual transition from a population dominated by cells which are young with respect to cell cycle age to one dominated by those which are old, and the effects such biases have on the proportions of cells in each phase.     

Morphological and functional differentiation in epithelial cultures obtained from human skin explants

The present study was undertaken to characterize primary epithelial cultures obtained from human skin explants as experimental systems for studies of the differentiation process. When human skin explants were incubated at 34-35 degrees C, fibroblastic growth was strongly inhibited, whereas the epithelial growth proceeded unchanged. The lateral growth of the epithelial cells could be divided into two phases - a migratory and a proliferative one. Only cultures incubated at 35 degrees C or below completed the morphological differentiation process before sloughing, whereas no qualitative difference in protein synthesis was observed between cultures incubated at temperatures from 33-37 degrees C. Cultured epidermal cells were labelled with 3H-thymidine and analysed by flow cytometry and cell sorting. Cells sorted from the S- and G2-phase populations were further analysed by autoradiography and a considerable heterogeneity as to the nuclear labelling was disclosed. A large fraction of S-phase cells were found to be totally unlabelled. The grain count distributions revealed similar cell cycle subpopulations as have been shown to occur in vivo. The relationship of these subpopulations to the differentiation process is discussed.     

Balance of cell proliferation and death among dynamic populations: a mathematical model

Developmental changes in cell numbers represent the dynamic balance between cell proliferation and death. One obstacle to assessing this balance is an inability to quantify the total amount of cell death, i.e., with a positive indicator such as terminal dUTP nick end labeling (TUNEL) or caspase activity. A novel mathematical model is described wherein data on daily cell growth (the change in cell number) and cell cycle kinetics can be used to determine the total amount of cell death. Two sets of data from previously published studies were tested in this model; primary cultured cortical neurons and B104 neuroblastoma cells. These two preparations have contrasting features: neuronal cultures are heterogeneous and have relatively few cells that are actively cycling (i.e., the growth fraction for these cells is low), whereas B104 cells are relatively homogeneous cultures in which the growth fraction is high. In primary cortical cultures, there was a balance in cell production and death. Treatment with a potent anti-mitogen, ethanol (400 mg/dl), affected this balance principally by reducing cell production, although the rate of cell death was also increased. In untreated B104 cells, there was eight-fold more cell production than cell death. Growth factors such as platelet-derived growth factor BB doubled cell production. Ethanol reduced cell production by >60%, and it eliminated growth factor-mediated cell production. All of these changes occurred in the absence of an effect on the amount of cell death. Thus, the model is ideal for predicting the effects of an epigenetic factor (e.g., a growth factor, toxin, or pharmacological agent) on cell development and can be useful in determining the consequences of a genetic manipulation as well.     

A simple model for cell volume and developmental compartments in nutrient limited cyclostat cultures of algae

Daily light-dark cycles can entrain cell growth and division cycles in populations of algae growing in nutrient limited continuous cultures, or cyclostats. In this study a simple model for the flux of cells between discrete developmental stages is formulated for periodic cyclostat cultures of algae. Cell growth, in terms of volume, was set as being constant within a given developmental compartment, but variable between compartments. Growth within a given compartment or transition between compartments was restricted to specific intervals of the subjective day. The model was calibrated to phosphate limited cyclostat growth of Euglena gracilis, with the intervals for transition between compartments fixed at the times relative to the subjective dawn corresponding to critical transition points in the phased cell cycle of this organism. The model output for mean population volume per cell agreed well with experimental data. Although greatly simplified, the periodic behavior of the model volume frequency distributions for the discrete compartments provide reasonable approximation of experimentally determined distributions.     

Growth of cell populations with arbitrarily distributed cycle durations. II. extended model for correlated cycle durations of mother and daughter cells

A model is proposed that describes the growth of cell populations, in which the cycle durations of mother and daughter and of sister cells can be correlated. The model accounts for arbitrary frequency distributions of cycle durations and for arbitrary correlations. Depending on the mother-daughter correlations, the frequency distribution of cycle durations either remains the same or changes from one cell generation to the next one. Both phenomena are described in the literature for different cell populations. Sister-sister correlations are shown to influence only numerical values in the model but not the model's structure. Model calculations with different types of correlations are compared with growth data on the ciliate Tetrahymena geleii.