Parametric analysis of volume distributions of Schizosaccharomyces pombe and other cells

Time-lapse photomicrographic data have been obtained on mating strains of the yeast Schizosaccharomyces pombe to evaluate the effect of the variability of the patterns of cell cycle behavior on population structure. These have been used to design a computer model which accepts volume distribution data from exponential cultures of a cell and yields estimates of the mean and standard deviation of daughter cell volume and telophase cell volume, as well as a stop-grow point, and the degree of cell volume doubling. Given a cell population's volume distribution and a volume distribution from a subpopulation, the program will estimate the mean age and display how the age is distributed in the subpopulation. Several cell types have been examined.     

<Emphasis Type="Italic">Chlamydomonas reinhardtii:</Emphasis> duration of its cell cycle and phases at growth rates affected by light intensity

In the cultures of the alga Chlamydomonas reinhardtii, division rhythms of any length from 12 to 75 h were found at a range of different growth rates that were set by the intensity of light as the sole source of energy. The responses to light intensity differed in terms of altered duration of the phase from the beginning of the cell cycle to the commitment to divide, and of the phase after commitment to cell division. The duration of the pre-commitment phase was determined by the time required to attain critical cell size and sufficient energy reserves (starch), and thus was inversely proportional to growth rate. If growth was stopped by interposing a period of darkness, the pre-commitment phase was prolonged corresponding to the duration of the dark interval. The duration of the post-commitment phase, during which the processes leading to cell division occurred, was constant and independent of growth rate (light intensity) in the cells of the same division number, or prolonged with increasing division number. It appeared that different regulatory mechanisms operated through these two phases, both of which were inconsistent with gating of cell division at any constant time interval. No evidence was found to support any hypothetical timer, suggested to be triggered at the time of daughter cell release.     

Using single cell cultivation system for on-chip monitoring of the interdivision timer in <Emphasis Type="Italic">Chlamydomonas reinhardtii</Emphasis> cell cycle

Regulation of cell cycle progression in changing environments is vital for cell survival and maintenance, and different regulation mechanisms based on cell size and cell cycle time have been proposed. To determine the mechanism of cell cycle regulation in the unicellular green algae Chlamydomonas reinhardtii, we developed an on-chip single-cell cultivation system that allows for the strict control of the extracellular environment. We divided the Chlamydomonas cell cycle into interdivision and division phases on the basis of changes in cell size and found that, regardless of the amount of photosynthetically active radiation (PAR) and the extent of illumination, the length of the interdivision phase was inversely proportional to the rate of increase of cell volume. Their product remains constant indicating the existence of an 'interdivision timer'. The length of the division phase, in contrast, remained nearly constant. Cells cultivated under light-dark-light conditions did not divide unless they had grown to twice their initial volume during the first light period. This indicates the existence of a 'commitment sizer'. The ratio of the cell volume at the beginning of the division phase to the initial cell volume determined the number of daughter cells, indicating the existence of a 'mitotic sizer'.     

Cell Growth and Division: I. A Mathematical Model with Applications to Cell Volume Distributions in Mammalian Suspension Cultures

A mathematical model is formulated for the development of a population of cells in which the individual members may grow and divide or die. A given cell is characterized by its age and volume, and these parameters are assumed to determine the rate of volume growth and the probability per unit time of division or death. The initial value problem is formulated, and it is shown that if cell growth rate is proportional to cell volume, then the volume distribution will not converge to a time-invariant shape without an added dispersive mechanism. Mathematical simplications which are possible for the special case of populations in the exponential phase or in the steady state are considered in some detail. Experimental volume distributions of mammalian cells in exponentially growing suspension cultures are analyzed, and growth rates and division probabilities are deduced. It is concluded that the cell volume growth rate is approximately proportional to cell volume and that the division probability increases with volume above a critical threshold. The effects on volume distribution of division into daughter cells of unequal volumes are examined in computer models.     

Control of cell size at division in fission yeast by a growth-modulated size control over nuclear division

In the fission yeast Schizosaccharomyces pombe, nutritional reduction of growth rate by supplying poor nitrogen, carbon or phosphate sources causes a decrease in cell size. The effect on cell division following three different nutritional shifts-up has been investigated. In all cases, about 20% of the cells divide at the original cell length, and then cell division stops for a period. Cell division then resumes at the new faster rate, cell length at division being characteristic of the new medium. Further investigation reveals that the first effect of the shift is to inhibit nuclear division rapidly and completely. These results are strongly suggestive of the operation of a cell size requirement for entry into nuclear division. The cell size necessary for nuclear division is set, or modulated, by the prevailing growth conditions. This model is confirmed by a nutritional shift-down, where nuclear division and cell division are stimulated after the shift. Cell length at division falls rapidly until the new shorter length is attained, when a new steady state is assumed at a slower growth rate. The control system is compared with that in bacteria, and its implications for various models proposed for the control of timing of mitosis are discussed.     

Sloppy size control of the cell division cycle

In an asynchronous, exponentially proliferating cell culture there is a great deal of variability among individual cells in size at birth, size at division and generation time (= age at division). To account for this variability we assume that individual cells grow according to some given growth law and that, after reaching a minimum size, they divide with a certain probability (per unit time) which increases with increasing cell size. This model is called sloppy size control because cell division is assumed to be a random process with size-dependent probability. We derive general equations for the distribution of cell size at division, the distribution of generation time, and the correlations between generation times of closely related cells. Our theoretical results are compared in detail with experimental results (obtained by Miyata and coworkers) for cell division in fission yeast, Schizosaccharomyces pombe. The agreement between theory and experiment is superior to that found for any other simple models of the coordination of cell growth and division.     

The initiation of cell wall synthesis in parasynchronous cultures of Schizosaccharomyces pombe

Summary Schizosaccharomyces pombe has been grown in parasynchronous culture to study the synthesis of cell wall material. After a lag period of 2.5h following inoculation the cells began to grow, as measured by optical density, dry weight and cell size. The cell number remained constant until 4.5h after inoculation when approximately 70% of the population divided synchronously. Immunofluorescence studies of the growing cells have shown that new wall material is inserted at the cell apices from 2.5 h after inoculation; this result is supported by radio-isotope labelling data which indicated that synthesis of new cell wall material also commenced 2.5 h after inoculation. The incorporation experiments also demonstrated an interruption in cell wall synthesis during the cell separation stage. The composition of the cell wall material varied during the growth cycle, with maximum nitrogen levels at inoculation and following cell division. No serological differences could be detected in the cell walls during the growth cycle.     

Buoyant density constancy of Schizosaccharomyces pombe cells.

Buoyant densities of cells from exponentially growing cultures of the fission yeast Schizosaccharomyces pombe 972h- with division rates from 0.14 to 0.5 per h were determined by equilibrium centrifugation in Percoll gradients. Buoyant densities were independent of growth rate, with an average value (+/- standard error) of 1.0945 (+/- 0.00037) g/ml. When cells from these cultures were separated by size, mean cell volumes were independent of buoyant density, indicating that buoyant densities also were independent of cell age during the division cycle. These results support the suggestion that most or all kinds of cells that divide by equatorial fission may have similar, evolutionarily conserved mechanisms for regulation of buoyant density.     

Control by cytokinins of the cellular behavior in the plate meristem of zucchini cotyledons

The temporal and spatial effects of exogenous cytokinins on both cell expansion and division activity in the plate meristem of cultured zucchini cotyledons were studied. N ⁶-benzylaminopurine (1–100 μM) and N-(2-chloro-4pyridyl)-N′-phenylurea (4PU-30) (0.1–100 μM) greatly stimulated the cell growth and division. They provoked multiple cell cycles, formation of larger clusters of daughter cells and an increase of the final number of cells. Both cytokinins led to earlier achievement of final cotyledon size and shortened the cell doubling time. By contrast to the purine cytokinin, phenylurea cytokinin 4PU-30 enlarged the cotyledon predominantly in length. Zeatin and kinetin were less effective, particularly in stimulating cell expansion. In low concentrations, all cytokinins were more effective in stimulating division activity rather than expansion. The cells in the cotyledon margins displayed a higher division activity, especially when treated with exogenous cytokinins. The final cotyledon and cluster areas were not of the strict proportional dependence upon the number of their cells. These results provide a novel example where stimulated cell division fails to evoke a respective increase in the final organ size.     

Fractal modeling of pulmonary blood flow heterogeneity

The heterogeneity of pulmonary blood flow is not adequately described by gravitational forces alone. We investigated the flow distributions predicted by two fractally branching vascular models to determine how well such networks could explain the observed heterogeneity. The distribution of flow was modeled with a dichotomously branching tree in which the fraction of blood flow from the parent to the daughter branches was gamma and 1-gamma repeatedly at each generation. In one model gamma was held constant throughout the network, and in the other model gamma varied about a mean of 0.5 with a standard deviation of sigma. Both gamma and sigma were optimized in each model for the best fit to pulmonary blood flow data from experimental animals. The predicted relative dispersion of flow from the two model fractal networks produced an excellent fit to the observed data. These fractally branching models relate structure and function of the pulmonary vascular tree and provide a mechanism to describe the spatially correlated distribution of flow and the gravity-independent heterogeneity of blood flow.     

Influence of environmental stress on distributions of times to first division in Escherichia coli populations, as determined by digital-image analysis of individual cells

The distributions of times to first cell division were determined for populations of Escherichia coli stationary-phase cells inoculated onto agar media. This was accomplished by using automated analysis of digital images of individual cells growing on agar and calculation of the "box area ratio." Using approximately 300 cells per experiment, the mean time to first division and standard deviation for cells grown in liquid medium at 37 degrees C and inoculated on agar and incubated at 20 degrees C were determined as 3.0 h and 0.7 h, respectively. Distributions were observed to tail toward the higher values, but no definitive model distribution was identified. Both preinoculation stress by heating cultures at 50 degrees C and postinoculation stress by growth in the presence of higher concentrations of NaCl increased mean times to first division. Both stresses also resulted in an increase in the spread of the distributions that was proportional to the mean division time, the coefficient of variation being constant at approximately 0.2 in all cases. The "relative division time," which is the time to first division for individual cells expressed in terms of the cell size doubling time, was used as measure of the "work to be done" to prepare for cell division. Relative division times were greater for heat-stressed cells than for those growing under osmotic stress.     

MreB is important for cell shape but not for chromosome segregation of the filamentous cyanobacterium Anabaena sp. PCC 7120

MreB is a bacterial actin that plays important roles in determination of cell shape and chromosome partitioning in Escherichia coli and Caulobacter crescentus. In this study, the mreB from the filamentous cyanobacterium Anabaena sp. PCC 7120 was inactivated. Although the mreB null mutant showed a drastic change in cell shape, its growth rate, cell division and the filament length were unaltered. Thus, MreB in Anabaena maintains cell shape but is not required for chromosome partitioning. The wild type and the mutant had eight and 10 copies of chromosomes per cell respectively. We demonstrated that DNA content in two daughter cells after cell division in both strains was not always identical. The ratios of DNA content in two daughter cells had a Gaussian distribution with a standard deviation much larger than a value expected if the DNA content in two daughter cells were identical, suggesting that chromosome partitioning is a random process. The multiple copies of chromosomes in cyanobacteria are likely required for chromosome random partitioning in cell division.     

Utilization of amino acids by Chromatium sp. strain D

Summary The duration of various morphologically distinct phases in the division cycle of the marine heterotroph Cryptothecodinium cohnii was measured in cultures initiated with synchronously excysted swarmer cells. Parent cysts were selectively isolated on plastic surfaces and progeny of a narrow age distribution harvested in a specifically conditioned medium. The swarmer phase, an interval of predivisional encystment, daughter cell formation and excystment were 5.0, 3.0 and 2.0 h respectively. Two major kinds of cytokinesis (production of 2 and 4 daughter cells) were observed resulting in a mean daughter cell number of 2.7 under these conditions. Other growth parameters for this dinoflagellate are described.     

Mutants altered in the control co-ordinating cell division with cell growth in the fission yeast Schizosaccharomyces pombe

Summary The control co-ordinating cell division with cell growth has been investigated in the fission yeast Schizosaccharomyces pombe. Twenty-five mutants altered in this control have been isolated which have the same growth rate as wild type but divide at a smaller cell size. The mutants define two genes wee 1 and wee 2, both of which are involved in a control initiating mitosis when the cell attains a critical size.     

Increase in cell mass during the division cycle of Escherichia coli B/rA.

Increase in the mean cell mass of undivided cells was determined during the division cycle of Escherichia coli B/rA. Cell buoyant densities during the division cycle were determined after cells from an exponentially growing culture were separated by size. The buoyant densities of these cells were essentially independent of cell age, with a mean value of 1.094 g ml-1. Mean cell volume and buoyant density were also determined during synchronous growth in two different media, which provided doubling times of 40 and 25 min. Cell volume and mass increased linearly at both growth rates, as buoyant density did not vary significantly. The results are consistent with only one of the three major models of cell growth, linear growth, which specifies that the rate of increase in cell mass is constant throughout the division cycle.     

Inflating bacterial cells by increased protein synthesis

Understanding how the homeostasis of cellular size and composition is accomplished by different organisms is an outstanding challenge in biology. For exponentially growing Escherichia coli cells, it is long known that the size of cells exhibits a strong positive relation with their growth rates in different nutrient conditions. Here, we characterized cell sizes in a set of orthogonal growth limitations. We report that cell size and mass exhibit positive or negative dependences with growth rate depending on the growth limitation applied. In particular, synthesizing large amounts of “useless” proteins led to an inversion of the canonical, positive relation, with slow growing cells enlarged 7‐ to 8‐fold compared to cells growing at similar rates under nutrient limitation. Strikingly, this increase in cell size was accompanied by a 3‐ to 4‐fold increase in cellular DNA content at slow growth, reaching up to an amount equivalent to ~8 chromosomes per cell. Despite drastic changes in cell mass and macromolecular composition, cellular dry mass density remained constant. Our findings reveal an important role of protein synthesis in cell division control.     

Cell cycle dynamics inferred from the static properties of cells in balanced growth

The duration of a morphological phase of the cell cycle is reflected in the steady state distribution of the sizes of cells in that phase. Relationships presented here provide a method for estimating the timing and variability of any cell cycle phase. It is shown that the mean size of cells initiating and finishing any phase can be estimated from (1) the frequency of cells exhibiting the distinguishing morphological or autoradiographic features of the phase; (2) the mean size of cells in the phase; and (3) their coefficient of variation. The calculations are based on a submodel of the Koch-Schaechter Growth Controlled Model which assumes that (i) the distribution of division sizes is Gaussian; (ii) there is no correlation in division sizes between successive generations; and (iii) every cell division gives rise to two daughter cells of equal size. The calculations should be useful for a wider range of models, however, because the extrapolation factors are not sensitive to the chosen model. Criteria are proposed to allow the user to check the method's applicability for any experimental case. The method also provides a more efficient test of the dependence of growth on cell size than does the Collins-Richmond method. This is because the method uses the mean and coefficient of variation of the size of the total population, in conjunction with those of the cells in a final phase of the cell cycle, to test potential growth laws. For Escherichia coli populations studied by electron microscopy, an exponential growth model provided much better agreement than did a linear growth model. The computer simulations were used to generate rules for three types of cell phases: those that end at cell division, those that start at cell division, and those totally contained within a single cell cycle. For the last type, additional criteria are proposed to establish if the phase is well enough contained for the formulae and graphs to be used. The most useful rule emerging from these computer studies is that the fraction of the cell cycle time occupied by a phase is the product of the frequency of the phase and the ratio of the mean size of cells in that phase to the mean size of all cells in the population. A further advantage of the techniques presented here is that they use the 'extant' distributions that were actually measured, and not hypothesized distributions nor the special distributions needed for Collins-Richmond method that can only be calculated from the observed distributions of dividing or newborn cells on the basis of an assumed growth law.     

The coordination of cell growth and division — intentional or Incidental?

During balanced growth of cells in culture all extensive properties of the culture — e.g. cell number, total mass, total DNA content — increase exponentially at the same specific growth rate. Therefore, in some average sense, each component of a cell must double between birth and division. For DNA there exists an elaborate mechanism to ensure precise replication of the genetic material and accurate partitioning of identical copies of the genome to the two daughter cells. Do cells possess another mechanism that intentionally relates the timing of cell division to overall increase in cell size, or is the coordination of growth and division an incidental consequence of size-independent rules for progress through the cell cycle?.     

Continuous cultivation of fission yeast: Analysis of single-cell protein synthesis kinetics

A fundamental problem in microbial reactor analysis is identification of the relationship between environment and individual cell metabolic activity. Population balance equations provide a link between experimental measurements of composition frequency functions in microbial populations on the one hand and macromolecular synthesis kinetics and cell division control parameters for single cells on the other. Flow microfluorometry measurements of frequency functions for single-cell protein content in Schizosaccharomyces pombe in balanced exponential growth have been analyzed by two different methods. One approach utilizes the integrated form of the population balance equation known as the Collins-Richmond equation, and the other method involves optimization of parameters in assumed kinetic and cell division functional forms in order to best fit measured frequency functions with corresponding model solutions. Both data interpretation techniques indicate that rates of protein synthesis increase most in small protein content cells as the population specific growth rate increases, leading to parabolic single-cell protein synthesis kinetics at large specific growth rates. Utilization of frequency function data for an asynchronous population is shown in this case to be a far more sensitive method for determination of single-cell kinetics than is monitoring the metabolic dynamics of a single cell or, equivalently, synchronous culture analyses.