The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions

A deterministic/probabilistic model of the cell division cycle is analysed mathematically and compared to experimental data and to other models of the cell cycle. The model posits a random-exiting phase of the cell cycle and a minimum-size requirement for entry into the random-exiting phase. By design, the model predicts exponential "beta-curves", which are characteristic of sister cell generation times. We show that the model predicts "alpha-curves" with exponential tails and hyperbolic-sine-like shoulders, and that these curves fit observed generation-time data excellently. We also calculate correlation coefficients for sister cells and for mother-daughter pairs. These correlation coefficients are more negative than is generally observed, which is characteristic of all size-control models and is generally attributed to some unknown positive correlation in growth rates of related cells. Next we compare theoretical size distributions with observed distributions, and we calculate the dependence of average cell mass on specific growth rate and show that this dependence agrees with a well-known relation in bacteria. In the discussion we argue that unequal division is probably not the source of stochastic fluctuations in deterministic size-control models, transition-probability models with no feedback from cell size cannot account for the rapidity with which the new, stable size distribution is established after perturbation, and Kubitschek's rate-normal model is not consistent with exponential beta-curves.     

Random epigenetic modulation of CHO cells by repeated knockdown of DNA methyltransferases increases population diversity and enables sorting of cells with higher production capacities

Chinese hamster ovary (CHO) cells produce a large share of today's biopharmaceuticals. Still, the generation of satisfactory producer cell lines is a tedious undertaking. Recently, it was found that CHO cells, when exposed to new environmental conditions, modify their epigenome, suggesting that cells adapt their gene expression pattern to handle new challenges. The major aim of the present study was to employ artificially induced, random changes in the DNA-methylation pattern of CHO cells to diversify cell populations and consequently increase the finding of cell lines with improved cellular characteristics. To achieve this, DNA methyltransferases and/or the ten-eleven translocation enzymes were downregulated by RNA interference over a time span of ∼16 days. Methylation analysis of the resulting cell pools revealed that the knockdown of DNA methyltransferases was highly effective in randomly demethylating the genome. The same approach, when applied to stable CHO producer cells resulted in (a) an increased productivity diversity in the cell population, and (b) a higher number of outliers within the population, which resulted in higher specific productivity and titer in the sorted cells. These findings suggest that epigenetics play a previously underestimated, but actually important role in defining the overall cellular behavior of production clones.     

Measurements and models of synchronous growth of fission yeast induced by temperature oscillations

Pulsing of temperature in a fermentor at intervals coincident with cell generation time was used to induce synchrony in a population of the fission yeast Schizosaccharomyces pombe. Measurements of culture protein, RNA, and DNA during synchronous growth confirm continuous synthesis of protein and RNA and discontinuos synthesis of DNA as previously reported. Flow microfluorometry of populations at different times during the synchrony cycle was used to monitor the changes in single-cell protein. RNA, and DNA frequency functions. These measurements illustrate very clearly the degree of synchrony and patterns of macromolecular synthesis and also confirm previous estimates of the cellular protein contents characteristic of dividing cells. Additional insights into single-cell kinetics and division controls are provided by two-parameter flow microfluorometry measurements and by mathematical modeling of population dynamics. Such data are necessary foundations for robust population balance models of microbial processes.     

Correlation between cell size and position within the division cycle in suspension cultures of Chang liver cells

Chang liver cells from exponentially growing suspension cultures have been separated by sedimentation at unit gravity. Determinations of the protein content per cell showed that the fractionation procedure resulted in good separation of cells of different size. On the other hand, the DNA content of individual cells from the fractions, as determined cytofluorimetrically, indicated considerable heterogeneity in the size of cells from the same stage of the division cycle. On the basis of earlier results on intermitotic growth and the variation in the length of the cell cycle in homogeneous cell populations, a mathematical model has been constructed and tested using a computer program. The present results on the size distribution of cells from the different stages of the mitotic cycle are consistent with a regeneration of size heterogeneity in each cell generation, as a result of the dispersion of intermitotic times. The variation in cell cycle times may be related to a probabilistic event in the G1 period. In the mathematical model it was necessary to include a mechanism by which the regeneration of abnormally large cells is prevented. The experimental data are compatible with a gradually increasing inhibition of growth in cells larger than a certain size (circa 400 pg protein per cell).     

Microdissection Studies on the Polarity of Unequal Division in Grasshopper Neuroblasts: II. Cell Division in Binucleate Neuroblasts

The grasshopper neuroblast divides unequally to produce two types of cells: a large daughter neuroblast that contains a doughnut-shaped nucleus and repeats unequal division with definite polarity, and a small daughter ganglion cell that has a spherical nucleus with low mitotic activity. Binucleate neuroblasts were induced by preventing cytokinesis in the course of microdissection experiments, and subsequent divisions were traced to analyze the factors that determine the polarity of unequal division.
In binucleate neuroblasts, both daughter chromosome groups developed into neuroblast-type nuclei. Mitosis of the two nuclei proceeded synchronously. Although the axes of the two mitotic apparatuses formed at late prophase were random in direction, they became parallel with the original division axis at metaphase. The two mitotic apparatuses shifted simultaneously toward the ganglion cell side during anaphase, just as in normal neuroblasts, and the binucleate cell divided unequally. These findings showed that the poearity of unequal division is strictly maintained in grasshpper neuroblasts, even when they contain two nuclei.     

Cytokinesis in eukaryotes.

Cytokinesis is the final event of the cell division cycle, and its completion results in irreversible partition of a mother cell into two daughter cells. Cytokinesis was one of the first cell cycle events observed by simple cell biological techniques; however, molecular characterization of cytokinesis has been slowed by its particular resistance to in vitro biochemical approaches. In recent years, the use of genetic model organisms has greatly advanced our molecular understanding of cytokinesis. While the outcome of cytokinesis is conserved in all dividing organisms, the mechanism of division varies across the major eukaryotic kingdoms. Yeasts and animals, for instance, use a contractile ring that ingresses to the cell middle in order to divide, while plant cells build new cell wall outward to the cortex. As would be expected, there is considerable conservation of molecules involved in cytokinesis between yeast and animal cells, while at first glance, plant cells seem quite different. However, in recent years, it has become clear that some aspects of division are conserved between plant, yeast, and animal cells. In this review we discuss the major recent advances in defining cytokinesis, focusing on deciding where to divide, building the division apparatus, and dividing. In addition, we discuss the complex problem of coordinating the division cycle with the nuclear cycle, which has recently become an area of intense research. In conclusion, we discuss how certain cells have utilized cytokinesis to direct development.     

CORRELATION BETWEEN CELL SIZE AND POSITION WITHIN THE DIVISION CYCLE IN SUSPENSION CULTURES OF CHANG LIVER CELLS

Chang liver cells from exponentially growing suspension cultures have been separated by sedimentation at unit gravity. Determinations of the protein content per cell showed that the fractionation procedure resulted in good separation of cells of different size. On the other hand, the DNA content of individual cells from the fractions, as determined cytofluorimetrically, indicated considerable heterogeneity in the size of cells from the same stage of the division cycle. On the basis of earlier results on intermitotic growth and the variation in the length of the cell cycle in homogeneous cell populations, a mathematical model has been constructed and tested using a computer program. The present results on the size distribution of cells from the different stages of the mitotic cycle are consistent with a regeneration of size heterogeneity in each cell generation, as a result of the dispersion of intermitotic times. The variation in cell cycle times may be related to a probabilistic event in the G₁ period. In the mathematical model it was necessary to include a mechanism by which the regeneration of abnormally large cells is prevented. The experimental data are compatible with a gradually increasing inhibition of growth in cells larger than a certain size (circa 400 pg protein per cell).     

Cytokinesis in Eukaryotes

Cytokinesis is the final event of the cell division cycle, and its completion results in irreversible partition of a mother cell into two daughter cells. Cytokinesis was one of the first cell cycle events observed by simple cell biological techniques; however, molecular characterization of cytokinesis has been slowed by its particular resistance to in vitro biochemical approaches. In recent years, the use of genetic model organisms has greatly advanced our molecular understanding of cytokinesis. While the outcome of cytokinesis is conserved in all dividing organisms, the mechanism of division varies across the major eukaryotic kingdoms. Yeasts and animals, for instance, use a contractile ring that ingresses to the cell middle in order to divide, while plant cells build new cell wall outward to the cortex. As would be expected, there is considerable conservation of molecules involved in cytokinesis between yeast and animal cells, while at first glance, plant cells seem quite different. However, in recent years, it has become clear that some aspects of division are conserved between plant, yeast, and animal cells. In this review we discuss the major recent advances in defining cytokinesis, focusing on deciding where to divide, building the division apparatus, and dividing. In addition, we discuss the complex problem of coordinating the division cycle with the nuclear cycle, which has recently become an area of intense research. In conclusion, we discuss how certain cells have utilized cytokinesis to direct development.     

The involvement of two cdc2-related kinases (CRKs) in Trypanosoma brucei cell cycle regulation and the distinctive stage-specific phenotypes caused by CRK3 depletion

Cyclin-dependent protein kinases are among the key regulators of eukaryotic cell cycle progression. Potential functions of the five cdc2-related kinases (CRK) in Trypanosoma brucei were analyzed using the RNA interference (RNA(i)) technique. In both the procyclic and bloodstream forms of T. brucei, CRK1 is apparently involved in controlling the G(1)/S transition, whereas CRK3 plays an important role in catalyzing cells across the G(2)/M junction. A knockdown of CRK1 caused accumulation of cells in the G(1) phase without apparent phenotypic change, whereas depletion of CRK3 enriched cells of both forms in the G(2)/M phase. However, two distinctive phenotypes were observed between the CRK3-deficient procyclic and bloodstream forms. The procyclic form has a majority of the cells containing a single enlarged nucleus plus one kinetoplast. There is also an enhanced population of anucleated cells, each containing a single kinetoplast known as the zoids (0N1K). The CRK3-depleted bloodstream form has an increased number of one nucleus-two kinetoplast cells (1N2K) and a small population containing aggregated multiple nuclei and multiple kinetoplasts. Apparently, these two forms have different mechanisms in cell cycle regulation. Although the procyclic form can be driven into cytokinesis and cell division by kinetoplast segregation without a completed mitosis, the bloodstream form cannot enter cytokinesis under the same condition. Instead, it keeps going through another G(1) phase and enters a new S phase resulting in an aggregate of multiple nuclei and multiple kinetoplasts in an undivided cell. The different leakiness in cell cycle regulation between two stage-specific forms of an organism provides an interesting and useful model for further understanding the evolution of cell cycle control among the eukaryotes.     

Phased cell division in a natural population of Dinophysis sacculus and the in situ measurement of potential growth rate

A method for the in situ estimation of the potential growthrate of the dinoflagellate Dinophysis sacculus based on thepattern of cell division and the duration of the cell cyclephases according to the model of McDuff and Chisholm (Limnol.Oceanogr., 27, 783–788, 1982) is proposed. In order toobserve the cell cycle and measure the in situ growth rate ofD.sacculus, water samples were taken from Alfacs Bay in theEbro River Delta, Spain, in May and June 1994, and kept in thelaboratory under a light-dark cycle similar to that in the field.The pattern of cell division in the D.sacculus population wasestablished by intensive sampling over 24 h periods. The maximumfrequency of cells undergoing cytokinesis was observed at dawnand that of recently divided cells 2 h later. Based on the patternof cell division and the duration of the various cell cyclephases, a generation time between 2 and 5 days was estimated.Subsequently, in situ estimates of the growth rate for D.sacculuswere carried out in St Carles de la Ràpita harbour duringOctober 1995. A mean generation time of 7 days was estimated.     

Brief cytochalasin-induced disruption of microfilaments during a critical interval in 1-cell C. elegans embryos alters the partitioning of developmental instructions to the 2-cell embryo

We are investigating the involvement of the microfilament cytoskeleton in the development of early Caenorhabditis elegans embryos. We previously reported that several cytoplasmic movements in the zygote require that the microfilament cytoskeleton remain intact during a narrow time interval approximately three-quarters of the way through the first cell cycle. In this study, we analyze the developmental consequences of brief, cytochalasin D-induced microfilament disruption during the 1-cell stage. Our results indicate that during the first cell cycle microfilaments are important only during the critical time interval for the 2-cell embryo to undergo the correct pattern of subsequent divisions and to initiate the differentiation of at least 4 tissue types. Disruption of microfilaments during the critical interval results in aberrant division and P-granule segregation patterns, generating some embryos that we classify as 'reverse polarity', 'anterior duplication', and 'posterior duplication' embryos. These altered patterns suggest that microfilament disruption during the critical interval leads to the incorrect distribution of developmental instructions responsible for early pattern formation. The strict correlation between unequal division, unequal germ-granule partitioning, and the generation of daughter cells with different cell cycle periods observed in these embryos suggests that the three processes are coupled. We hypothesize that (1) an 'asymmetry determinant', normally located at the posterior end of the zygote, governs asymmetric cell division, germ-granule segregation, and the segregation of cell cycle timing elements during the first cell cycle, and (2) the integrity or placement of this asymmetry determinant is sensitive to microfilament disruption during the critical time interval.     

Flow cytometry to sort mammalian cells in cytokinesis.

BACKGROUND: Cell division or cytokinesis, which results from a series of events starting in metaphase, is the mechanism by which the mother cell cytoplasm is divided between the two daughter cells. Hence it is the final step of the cell division cycle. The aim of the present study was to demonstrate that mammalian cells undergoing cytokinesis can be sorted selectively by flow cytometry. MATERIALS AND METHODS: Cultures of HeLa cells were arrested in prometaphase by nocodazole, collected by mitotic shake-off and released for 90 min into fresh medium to enrich for cells undergoing cytokinesis. After ethanol fixation and DNA staining, cells were sorted based on DNA content and DNA fluorescence signal height. RESULTS: We define a cell population that transiently accumulates when synchronized cells exit mitosis before their entry into G1. We show that this population is highly enriched in cells undergoing cytokinesis. In addition, this population of cells can be sorted and analyzed by immunofluorescence and western blotting. CONCLUSIONS: This method of cell synchronization and sorting provides a simple means to isolate and biochemically analyze cells in cytokinesis, a period of the cell cycle that has been difficult to study by cell fractionation.     

On the distribution of cell cycle generation times

The problem of whether the cell cycle is a deterministic or probabilistic process is widely discussed in the current literature (P. Nurse, Nature, 286, pp. 9–10, 1980). In this report the question of fluctuations of cell cycle period is treated in the limits of the membrane model of cell division regulation. The parametric analysis of the equations set both for normal and tumour cells is carried out. We describe the bifurcation parameters in the neighbourhood of which the system can amplify the small fluctuations. The presence of white noise in parameters describing the lipids and antioxidants influxes into membrane is examined by methods of Marcovian processes and also by direct stochastic computer simulation. The equation for the distribution function of generation times is obtained and the increase of dispersion and mean cycle time during the changes of those parameters which would be connected with cell culture density is calculated.The influence of parameter fluctuations upon the cycle period for both normal and tumour cells is compared in the framework of model assumptions. The ratio of dispersion of generation time distribution to mean period value for an ensemble of tumour cells is shown to be several times greater than that for normal ones.In the discussion the problem of the presence of a premitotical (G₀₂) resting state and of the possibility of its experimental detection is considered.     

Analysis of protein distribution in budding yeast

Flow cytometry is a fast and sensitive method that allows monitoring of different cellular parameters on large samples of a population. Protein distributons give relevant information on growth dynamics, since they are related to the age distribution and depend on the law of growth of the population and the law of protein accumulation during the cell cycle. We analyzed protein distributions to evaluate alternative growth models for the budding yeast Saccharomyces cerevisiae and to monitor the changes in population dynamics that result from environmental modifications; such an analysis could potentially give parameters useful in the control of biotechnological processes. Theoretical protein distributions (taking into account the unequal division of yeast cells and the exponential law of protein accumulation during a cell cycle) quantitatively fit experimental distributions, once appropriate variability sources are introduced. Best fits are obtained when the protein threshold required for bud emergence increases at each new generation of parent cells.     

The effects of 5α-dihydrotestosterone on the kinetics of cell proliferation in rat prostate

The regenerating rat prostate was used as an experimental model to determine the effects of 5alpha-dihydrotestosterone on certain parameters of cell proliferation, including the duration of the phases of the cell cycle and the size of the cellular growth fraction. Rats castrated 7 days previously were treated with daily subcutaneous injections of 5alpha-dihydrotestosterone for 14 days; 48h after the beginning of therapy, cells in the process of DNA synthesis were labelled with a single injection of radioactive thymidine and the progress of these cells through the division cycle was observed. Cell-cycle analysis was performed by fractionating prostatic nuclei according to their position in the cell cycle by using the technique of velocity sedimentation under unit gravity. The results indicate that during regeneration the cell population undergoes 1.8 doublings with a doubling time of 40h, and that the process involves almost four rounds of cell division with a cell-generation time of 20h. The growth fraction at any time is about 0.5, and about half the daughter cells produced do not re-enter the proliferative cycle. All cells present at the start of regeneration eventually undergo at least one division during the course of regeneration, although any given cell can divide from one to four times.