Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.

Morphological parameters of the cell division cycle have been examined in Escherichia coli B/r A and K. Whereas the shape factor (length of newborn cell/width) of the two strains was the same at rapid growth (doubling time, tau, less than 60 min), with decreasing growth rate the dimensions of the two strains did change so that B/r A cells became more rounded and B/r K cells became more elongated. The process of visible cell constriction (T period) lasted longer in B/r A than in B/r K during slow growth, reaching at tau = 200 min values of 40 and 17 min, respectively. The time between termination of chromosome replication and cell division (D period) was found to be longer in B/r A than in B/r K. As a result, in either strain completion of chromosome replication seemed always to occur before initiation of cell constriction. Nucleoplasmic separation did not coincide with termination as during rapid growth but occurred in both strains within the T period, about 10 min before cell division.     

Timing the start of division in E. coli: a single-cell study

We monitor the shape dynamics of individual E. coli cells using time-lapse microscopy together with accurate image analysis. This allows measuring the dynamics of single-cell parameters throughout the cell cycle. In previous work, we have used this approach to characterize the main features of single-cell morphogenesis between successive divisions. Here, we focus on the behavior of the parameters that are related to cell division and study their variation over a population of 30 cells. In particular, we show that the single-cell data for the constriction width dynamics collapse onto a unique curve following appropriate rescaling of the corresponding variables. This suggests the presence of an underlying time scale that determines the rate at which the cell cycle advances in each individual cell. For the case of cell length dynamics a similar rescaling of variables emphasizes the presence of a breakpoint in the growth rate at the time when division starts, tau(c). We also find that the tau(c) of individual cells is correlated with their generation time, tau(g), and inversely correlated with the corresponding length at birth, L(0). Moreover, the extent of the T-period, tau(g) - tau(c), is apparently independent of tau(g). The relations between tau(c), tau(g) and L(0) indicate possible compensation mechanisms that maintain cell length variability at about 10%. Similar behavior was observed for both fast-growing cells in a rich medium (LB) and for slower growth in a minimal medium (M9-glucose). To reveal the molecular mechanisms that lead to the observed organization of the cell cycle, we should further extend our approach to monitor the formation of the divisome.     

The cell cycle in Escherichia coli B/r

Cell division and DNA synthesis were measured in synchronous cultures of E. coll B/r growing in glucose minimal medium at 37 °. The kinetic curves were analysed in order to find the variability of replication initiation, termination, and cell division events during the cell cycle. It is inferred that under the conditions used, cells begin to divide 17 min (D₀ = minimum D-period) after each termination of chromosome replication with a constant probability per unit of time (half-life = 4·5–6 min). This randomness produces an asymmetric frequency distribution of D-periods, similar but mirror-symmetric frequency distributions of initiation and termination periods, a symmetric, non-Gaussian distribution of interdivision intervals, and complex kinetic changes in the rate of DNA synthesis as a function of cell age. The results suggest that replication and division are precisely controlled with respect to mass accumulation, and the apparent variability of cell cycle events would only result from the use of the time of cell separation as a reference point for the definition of cell age rather than initiation or termination of replication.     

Escherichia coli DNA distributions measured by flow cytometry and compared with theoretical computer simulations.

A computer simulation routine has been made to calculate the DNA distributions of exponentially growing cultures of Escherichia coli. Calculations were based on a previously published model (S. Cooper and C.E. Helmstetter, J. Mol. Biol. 31:519-540, 1968). Simulated distributions were compared with experimental DNA distributions (histograms) recorded by flow cytometry. Cell cycle parameters were determined by varying the parameters to find the best fit of theoretical to experimental histograms. A culture of E. coli B/r A with a doubling time of 27 min was found to have a DNA replication period (C) of 43 min and an average postreplication period (D) of 22 to 23 min. Similar cell cycle parameters were found for a 60-min B/r A culture. Initiations of DNA replication at multiple origins in one and the same cell were shown to be essentially synchronous. A slowly growing B/r A culture (doubling time, 5.5 h) had an average prereplication period (B) of 2.3 h; C = 2.4 h and D = 0.8 h. It was concluded the the C period has a constant duration of 43 min (at 37 degrees C) at fast growth rates (doubling times, less than 1 h) but increases at slow growth rates. Thus, our results obtained with unperturbed exponential cultures in steady state support the model of Cooper and Helmstetter which was based on data obtained with synchronized cells.     

Bromodeoxyuridine labeling and flow cytometric identification of replicating Saccharomyces cerevisiae cells: lengths of cell cycle phases and population variability at specific cell cycle positions.

An immunofluorescent staining procedure has been developed to identify, with flow cytometry, replicating cells of Saccharomyces cerevisiae after incorporation of bromodeoxyuridine (BrdUrd) into the DNA. Incorporation of BrdUrd is made possible by using yeast strains with a cloned thymidine kinase gene from the herpes simplex virus. An exposure time of 4 min to BrdUrd results in detectable labeling of the DNA. The BrdUrd/DNA double staining procedure has been optimized and the flow cytometry measurements yield histograms comparable to data typically obtained for mammalian cells. On the basis of the accurate assessment of cell fractions in individual cell cycle phases of the asynchronously growing cell population, the average duration of the cell cycle phases has been evaluated. For a population doubling time of 100 min it was found that cells spend in average 41 min in the replicating phase and 24 min in the G2+M cell cycle period. Assuming that mother cells immediately reenter the S phase after cell division, daughter cells spend 65 min in the G1 cell cycle phase. Together with the single cell fluorescence parameters, the forward-angle light scattering intensity (FALS) has been determined as an indicator of cell size. Comparing different temporal positions within the cell cycle, the determined FALS distributions show the lowest variability at the beginning of the S phase. The developed procedure in combination with multiparameter flow cytometry should be useful for studying the kinetics and regulation of the budding yeast cell cycle.     

Effects of stochastic channel gating and distribution on the cardiac action potential

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000 ms) was essentially caused by stochastic channel gating of I_Ks, persistent I_Na and I_Ca,L. In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.     

Effects of asymmetric division on a stochastic model of the cell division cycle

The stochastic model of cell division formulated by Alt and Tyson is generalized to the case of imprecise binary fission. Closed-form expressions are derived for the generation-time distribution, the birth-size and division-size distributions, the beta curve, and the correlation coefficient of generation times of sister cells. The theoretical results are compared to observations of cell division statistics in a culture of fission yeast.     

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.     

Morphological analysis of nuclear separation and cell division during the life cycle of Escherichia coli.

Quantitative electron microscope observations were performed on Escherichia coli B/r after balanced growth with doubling times (tau) of 32 and 60 min. The experimental approach allowed the timing of morphological events during the cell cycle by classifying serially sectioned cells according to length. Visible separation of the nucleoplasm was found to coincide with the time of termination of chromosome replication as predicted by the Cooper-Helmstetter model. The duration of the process of constrictive cell division (10 min) appeared to be independent of the growth rate for tau equals 60 min or less but to increase with increase doubling time in more slowly growing cells. Physiological division, i.e., compartmentalization prior to physical separation of the cells, was only observed to occur in the last minute of the cell cycle. The morphological results indicate that cell elongation continues during the division process in cells with tau equals 32 min, but fails to continue in cells with tau equals 60 min.     

Interpreting CFSE Obtained Division Histories of B Cells in Vitro with Smith–Martin and Cyton Type Models

The fluorescent dye carboxyfluorescin diacetate succinimidyl ester (CFSE) classifies proliferating cell populations into groups according to the number of divisions each cell has undergone (i.e., its division class). The pulse labeling of cells with radioactive thymidine provides a means to determine the distribution of times of entry into the first cell division. We derive in analytic form the number of cells in each division class as a function of time using the cyton approach that utilizes independent stochastic distributions for the time to divide and the time to die. We confirm that our analytic form for the number of cells in each division class is consistent with the numerical solution of a set of delay differential equations representing the generalized Smith–Martin model with cell death rates depending on the division class. Choosing the distribution of time to the first division to fit thymidine labeling data for B cells stimulated in vitro with lipopolysaccharide (LPS) and either with or without interleukin-4 (IL-4), we fit CFSE data to determine the dependence of B cell kinetic parameters on the presence of IL-4. We find when IL-4 is present, a greater proportion of cells are recruited into division with a longer average time to first division. The most profound effect of the presence of IL-4 was decreased death rates for smaller division classes, which supports a role of IL-4 in the protection of B cells from apoptosis.     

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.     

Division behavior and shape changes in isogenic ftsZ, ftsQ, ftsA, pbpB, and ftsE cell division mutants of Escherichia coli during temperature shift experiments.

Isogenic ftsZ, ftsQ, ftsA, pbpB, and ftsE cell division mutants of Escherichia coli were compared with their parent strain in temperature shift experiments. To improve detection of phenotypic differences in division behavior and cell shape, the strains were grown in glucose-minimal medium with a decreased osmolality (about 100 mosM). Already at the premissive temperature, all mutants, particularly the pbpB and ftsQ mutants, showed an increased average cell length and cell mass. The pbpB and ftsQ mutants also exhibited a prolonged duration of the constriction period. All strains, except ftsZ, continued to initiate new constrictions at 42 degrees C, suggesting the involvement of FtsZ in an early step of the constriction process. The new constrictions were blunt in ftsQ and more pronounced in ftsA and pbpB filaments, which also had elongated median constrictions. Whereas the latter strains showed a slow recovery of cell division after a shift back to the permissive temperature, ftsZ and ftsQ filaments recovered quickly. Recovery of filaments occurred in all strains by the separation of newborn cells with an average length of two times LO, the length of newborn cells at the permissive temperature. The increased size of the newborn cells could indicate that the cell division machinery recovers too slowly to create normal-sized cells. Our results indicate a phenotypic resemblance between ftsA and pbpB mutants and suggest that the cell division gene products function in the order FtsZ-FtsQ-FtsA, PBP3. The ftsE mutant continued to constrict and divide at 42 degrees C, forming short filaments, which recovered quickly after a shift back to the permissive temperature. After prolonged growth at 42 degree C, chains of cells, which eventually swelled up, were formed. Although the ftsE mutant produced filaments in broth medium at the restrictive temperature, it cannot be considered a cell division mutant under the presently applied conditions.     

Generality of the growth kinetics of the average individual cell in different bacterial populations.

The kinetics of growth of all the cells in a population is reflected in the shape of the size distribution of the population. To ascertain whether the kinetics of growth of the average individual cell is similar for different strains or growth conditions, we compared the shape of normalized size distributions obtained from steady-state populations. Significant differences in the size distributions were found, but these could be ascribed either to the precision achieved at division or to a constriction period which is long relative to the total cell cycle time. The remaining difference is quite small. Thus, without establishing the pattern itself, it is concluded that the basic course of growth is very similar for the various Escherichia coli strains examined and probably also for other rod-shaped bacteria. The effects of differences in culture technique (batch or chemostat culture), growth rate, and differences among strains were not found to influence the shape of the size distributions and hence the growth kinetics in a direct manner; small differences were found, but only when the precision at division or the fraction of constricted cells (long constriction period) were different as well.     

ANALYSIS OF THE VARIABILITY IN CLEAVAGE TIMES AND DEMONSTRATION OF A MITOTIC GRADIENT DURING THE CLEAVAGE STAGES OF NOTHOBRANCHIUS GUENTHERI

Living embryos of the annual cyprinodont fish Nothobranchius guentheri were observed under the microscope. Detailed records were made of the time of cell division, disappearance of the nucleus and of the position of each cell within the blastoderm up to and including the sixth cleavage. Combination of these data revealed the presence of a mitotic gradient, a cell division gradient and a gradient of cell cycle duration in the 8-cell, 16-cell and 32-cell stage. Comparison of the variabilities in the duration of the interphase and mitosis reveals that differences between sister cell intercleavage times in the 8-, 16- and 32-cell stage are, for the most part, due to the variability in the duration of the mitotic process. It is concluded that the DNA-division cycle is composed of at least two parallel series of events. We found the random transition model of cell cycle control, originally based on the analysis of intermitotic times of mammalian cells in tissue culture, helpful also in analysing intercleavage time variability in embryonic cells.     

A stochastic model of cell replicative senescence based on telomere shortening, oxidative stress, and somatic mutations in nuclear and mitochondrial DNA.

Human diploid fibroblast cells can divide for only a limited number of times in vitro, a phenomenon known as replicative senescence or the Hayflick limit. Variability in doubling potential is observed within a clone of cells, and between two sister cells arising from a single mitotic division. This strongly suggests that the process by which cells become senescent is intrinsically stochastic. Among the various biochemical mechanisms that have been proposed to explain replicative senescence, particular interest has been focussed on the role of telomere reduction. In the absence of telomerase--an enzyme switched off in normal diploid fibro-blasts-cells lose telomeric DNA at each cell division. According to the telomere hypothesis of cell senescence, cells eventually reach a critically short telomere length and cell cycle arrest follows. In support of this concept, forced expression of telomerase in normal fibroblasts appears to prevent cell senescence. Nevertheless, the telomere hypothesis in its basic form has some difficulty in explaining the marked stochastic variations seen in the replicative lifespans of individual cells within a culture, and there is strong empirical and theoretical support for the concept that other kinds of damage may contribute to cellular ageing. We describe a stochastic network model of cell senescence in which a primary role is played by telomere reduction but in which other mechanisms (oxidative stress linked particularly to mitochondrial damage, and nuclear somatic mutations) also contribute. The model gives simulation results that are in good agreement with published data on intra-clonal variability in cell doubling potential and permits an analysis of how the various elements of the stochastic network interact. Such integrative models may aid in developing new experimental approaches aimed at unravelling the intrinsic complexity of the mechanisms contributing to human cell ageing.     

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.     

Timing of FtsZ Assembly in Escherichia coli

The timing of the appearance of the FtsZ ring at the future site of division in Escherichia coli was determined by in situ immunofluorescence microscopy for two strains grown under steady-state conditions. The strains, B/rA and K-12 MC4100, differ largely in the duration of the D period, the time between termination of DNA replication and cell division. In both strains and under various growth conditions, the assembly of the FtsZ ring was initiated approximately simultaneously with the start of the D period. This is well before nucleoid separation or initiation of constriction as determined by fluorescence and phase-contrast microscopy. The durations of the Z-ring period, the D period, and the period with a visible constriction seem to be correlated under all investigated growth conditions in these strains. These results suggest that (near) termination of DNA replication could provide a signal that initiates the process of cell division.     

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.