Self‐organized partitioning of dynamically localized proteins in bacterial cell division

How cells manage to get equal distribution of their structures and molecules at cell division is a crucial issue in biology. In principle, a feedback mechanism could always ensure equality by measuring and correcting the distribution in the progeny. However, an elegant alternative could be a mechanism relying on self‐organization, with the interplay between system properties and cell geometry leading to the emergence of equal partitioning. The problem is exemplified by the bacterial Min system that defines the division site by oscillating from pole to pole. Unequal partitioning of Min proteins at division could negatively impact system performance and cell growth because of loss of Min oscillations and imprecise mid‐cell determination. In this study, we combine live cell and computational analyses to show that known properties of the Min system together with the gradual reduction of protein exchange through the constricting septum are sufficient to explain the observed highly precise spontaneous protein partitioning. Our findings reveal a novel and effective mechanism of protein partitioning in dividing cells and emphasize the importance of self‐organization in basic cellular processes.     

A new mathematical approach predicts individual cell growth behavior using bacterial population information

A theoretical methodology has been developed for studying the growth kinetics of bacterial cells. It utilizes the steady-state cell length distribution in a bacterial population to predict the dependency of growth and division rates on cell length and age. The mathematical model has been applied to the analysis of two bacterial populations, a wild-type strain of Bacillus subtilis, and a minicell-producing strain that carries the divIVB1 mutation. The results show that our model describes the wild-type population very well and that the assumptions typically used in traditional methods are unrealistic. In the case of the minicell-producing mutant we find evidence that the rate of cell division must be a function not only of cell size but also of cell age.     

Age Distribution of Human Diploid Fibroblasts: A Stochastic Model for In Vitro Aging

Variation in the lifespan of mass cultures and clones of human diploid fibroblasts can be explained on the basis of variation in the length of the mitotic cycle. This variation is of biological significance; the intrinsic standard deviation of culture lifespan is equal to about 10% of the mean. We constructed a two-parameter stochastic model based on the following assumptions: the time between successive divisions of a given cell is of random duration; cells divide or lose the ability to divide independently of one another; the probability that a cell can undergo further division is constant up to some maximum number of divisions and zero thereafter. We determined numerically the proportion of nondividing cells and the distribution of cell generations. Samples taken by Monte Carlo means from a hypothetical in vitro population were compared with clonal survival data obtained experimentally. The fit between experimental and theoretical findings was within the range of sampling variation. If we accept our model as being applicable to human diploid cell culture, we can draw the following conclusions: the proportion of dividing cells is an inadequate index of a population's age; even in populations in which almost all cells are still capable of division, a majority of the cells have less than eight generations remaining to them. At each subcultivation the ultimate fate of a culture is determined by the disposition of a relatively small number of “young” cells.     

Probabilistic RNA partitioning generates transient increases in the normalized variance of RNA numbers in synchronized populations of Escherichia coli

We explore the effects of probabilistic RNA partitioning during cell division on the normalized variance of RNA numbers across generations of bacterial populations. We first characterize these effects in model cell populations, where gene expression is modeled as a delayed stochastic process, as a function of the synchrony in cell division, the rate of division, and the RNA degradation rate. We further explore the additional variance that arises if the partitioning is biased. Next, in Escherichia coli cells expressing RNA tagged with MS2d-GFP, we measured the normalized variance of RNA numbers across several generations, with cell divisions synchronized by heat shock. We show that synchronized cell populations exhibit transient increases in normalized variance following cell divisions, as predicted by the model, which are not observed in unsynchronized populations. We conclude that errors in partitioning of RNA molecules generate diversity between the offspring of individual bacteria and thus constitute a form of reproductive bet-hedging.     

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.     

Oriented cell divisions asymmetrically segregate aPKC and generate cell fate diversity in the early Xenopus embryo

A key feature of early vertebrate development is the formation of superficial, epithelial cells that overlie non-epithelial deep cells. In Xenopus, deep and superficial cells show a range of differences, including a different competence for primary neurogenesis. We show that the two cell populations are generated during the blastula stages by perpendicularly oriented divisions. These take place during several cell divisions, in a variable pattern, but at a percentage that varies little between embryos and from one division to the next. The orientation of division correlates with cell shape suggesting that simple geometric rules may control the orientation of division in this system. We show that dividing cells are molecularly polarised such that aPKC is localised to the external, apical, membrane. Membrane localised aPKC can be seen as early as the one-cell stage and during the blastula divisions, it is preferentially inherited by superficial cells. Finally, we show that when 64-cell stage isolated blastomeres divide perpendicularly and the daughters are cultured separately, only the progeny of the cells that inherit the apical membrane turn on the bHLH gene, ESR6e. We conclude that oriented cell divisions generate the superficial and deep cells and establish cell fate diversity between them.     

Localization of Actin mRNA during the Establishment of Cell Polarity and Early Cell Divisions in Fucus Embryos

Localization of mRNA is a well-described mechanism to account for the asymmetric distribution of proteins in polarized somatic cells and embryos of animals. In zygotes of the brown alga Fucus, F-actin is localized at the site of polar growth and accumulates at the cell plates of the first two divisions of the embryo. We used a nonradioactive, whole-mount in situ hybridization protocol to show the pattern of actin mRNA localization. Until the first cell division, the pattern of actin mRNA localization is identical to that of total poly(A)+ RNA, that is, a symmetrical distribution in the zygote followed by an actin-dependent accumulation at the thallus pole at the time of polar axis fixation. At the end of the first division, actin mRNA specifically is redistributed from the thallus pole to the cell plates of the first two divisions in the rhizoid. This specific pattern of localization in the zygote and embryo involves the redistribution of previously synthesized actin mRNA. The initial asymmetry of actin mRNA at the thallus pole of the zygote requires polar axis fixation and microfilaments but not microtubules, cell division, or polar growth. However, redistribution of actin mRNA from the thallus pole to the first cell plate is insensitive to cytoskeletal inhibitors but is dependent on cell plate formation. The F-actin that accumulates at the rhizoid tip is not accompanied by the localization of actin mRNA. However, maintenance of an accumulation of actin protein at the cell plates of the rhizoid could be explained, at least partially, by a mechanism involving localization of actin mRNA at these sites. The pattern and requirements for actin mRNA localization in the Fucus embryo may be relevant to polarization of the embryo and asymmetric cell divisions in higher plants as well as in other tip-growing plant cells.     

Dlg,Scrib and Lgl regulate neuroblast cell size and mitotic spindle asymmetry

Asymmetric cell division is important in generating cell diversity from bacteria to mammals. Drosophila melanogaster neuroblasts are a useful model system for investigating asymmetric cell division because they establish distinct apical-basal cortical domains, have an asymmetric mitotic spindle aligned along the apical-basal axis, and divide unequally to produce a large apical neuroblast and a small basal daughter cell (GMC). Here we show that Discs large (Dlg), Scribble (Scrib) and Lethal giant larvae (Lgl) tumour suppressor proteins regulate multiple aspects of neuroblast asymmetric cell division. Dlg/Scrib/Lgl proteins show apical cortical enrichment at prophase/metaphase, and then have a uniform cortical distribution. Mutants have defects in basal protein targeting, a reduced apical cortical domain and reduced apical spindle size. Defects in apical cell and spindle pole size result in symmetric or inverted neuroblast cell divisions. Inverted divisions correlate with the appearance of abnormally small neuroblasts and large GMCs, showing that neuroblast/GMC identity is more tightly linked to cortical determinants than cell size. We conclude that Dlg/Scrib/Lgl are important in regulating cortical polarity, cell size asymmetry and mitotic spindle asymmetry in Drosophila neuroblasts.     

Automatic generation of lymphocyte heterogeneity: Division-dependent changes in the expression of CD27, CCR7 and CD45 by activated human naive CD4+ T cells are independently regulated

Lymphocyte differentiation is a complex process regulated by the integration of signals received through a variety of cell surface receptors that results in populations of differentiated cells that have acquired novel characteristics and effector functions. Differentiation of T and B lymphocytes into effector cells, such as cytokine-secreting CD4+ T cells, cytotoxic CD8+ T cells and Ig-secreting B cells, as well as alterations in cell surface phenotype, have been reported to be associated with cell division. Nevertheless, the genesis of heterogeneity in effector cell type is unknown. A strictly deterministic view holds that heterogeneity arises from distinct signalling histories for each functionally or phenotypically different cell type. In contrast, a probabilistic interpretation proposes that internal stochastic regulation of gene expression gives rise to lymphocytes of mixed phenotypes. To help distinguish between these explanations, we examined the expression of CD27, CCR7, CD45RA and CD45RO by human naive CD4+ T cells in the context of the division history of the lymphocyte. Our results show that each marker independently changes with progressive divisions, strongly supporting the proposal that phenotypic heterogeneity in lymphocytes can arise as the result of independent stochastic processes controlling the expression of individual molecules.     

CELL DEVELOPMENT DURING EARLY EMBRYOGENESIS IN CAPSELLA AND GOSSYPIUM

The early stages of embryo development in Gossypium hirsutum (cotton) and Capsella bursapastoris were examined with regard to patterns of cell development, embryo and cell size, and distribution of cell divisions. A striking reduction in the total size of the cotton embryo was observed following the first division of the embryo. This decrease in total embryo size continued for several more divisions, and it was not until the embryo contained approximately 75 cells that its total size was larger than the zygote. Distinctive patterns of cell divisions were found in both embryos and indicate that changes in groups of cells undergoing mitosis are of fundamental importance in understanding the development of form in the embryo. A greater degree of variation in development of cell lineages than is generally reported was observed in both embryos.     

Characterization and efficacy of PKH26 as a probe to study the replication history of the human hematopoietic KG1a progenitor cell line

The PKH26 dye can, in principle, be used for the study of asymmetric cell divisions (ASDs). A requirement for the identification of ASDs based on fluorescence intensity is that the PKH26 dye is distributed equally between daughter cells at each division, but this has not been demonstrated at a single-cell level. The efficacy of PKH26 as a probe for the study of ASDs was examined using the human hematopoietic KG1a cell. An automated time-lapse fluorescent microscope system was used to determine changes in cell size and fluorescence intensity during culture, and track cell divisions. The images of daughter cells were analyzed using the Isee software to determine the distribution of PKH26 dye between daughter cells. Ratios of cell size, mean fluorescence intensity, and total fluorescence intensity were calculated by dividing the values for one daughter cell by the value of the other daughter cell. The ratios for cell size, mean intensity, and total intensity were 1.13 +/- 0.12, 1.08 +/- 0.07, and 1.15 +/- 0.14 (mean +/- SD), respectively. Thus, PKH26 is not distributed equally to both daughter cells upon cell division. However, the replication history of individual KG1a cells can be reliably deduced for up to three divisions based solely on the mean and total fluorescence intensity of the PKH26 dye, using PKH26 concentrations below the chemical and phototoxic limits (2 microM).     

Predicted steady-state cell size distributions for various growth models

The question of how an individual bacterial cell grows during its life cycle remains controversial. In 1962 Collins and Richmond derived a very general expression relating the size distributions of newborn, dividing and extant cells in steady-state growth and their growth rate; it represents the most powerful framework currently available for the analysis of bacterial growth kinetics. The Collins-Richmond equation is in effect a statement of the conservation of cell numbers for populations in steady-state exponential growth. It has usually been used to calculate the growth rate from a measured cell size distribution under various assumptions regarding the dividing and newborn cell distributions, but can also be applied in reverse--to compute the theoretical cell size distribution from a specified growth law. This has the advantage that it is not limited to models in which growth rate is a deterministic function of cell size, such as in simple exponential or linear growth, but permits evaluation of far more sophisticated hypotheses. Here we employed this reverse approach to obtain theoretical cell size distributions for two exponential and six linear growth models. The former differ as to whether there exists in each cell a minimal size that does not contribute to growth, the latter as to when the presumptive doubling of the growth rate takes place: in the linear age models, it is taken to occur at a particular cell age, at a fixed time prior to division, or at division itself; in the linear size models, the growth rate is considered to double with a constant probability from cell birth, with a constant probability but only after the cell has reached a minimal size, or after the minimal size has been attained but with a probability that increases linearly with cell size. Each model contains a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. In the present article, the various growth laws are described and rigorous mathematical expressions developed to predict the size distribution of extant cells in steady-state exponential growth; in the following paper, these predictions are tested against high-quality experimental data.     

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.     

Myogenic stem cell commitment probability remains constant as a function of organismal and mitotic age

Chicken myogenic stem cells can undergo symmetric and asymmetric cell divisions. Symmetric divisions produce two stem cells or two cells committed to terminal muscle differentiation. Asymmetric divisions produce one stem cell and one committed cell. Committed cells undergo four divisions, and their progeny differentiate into postmitotic, biochemically distinct muscle cells, which can be identified immunocytochemically. The control of stem cell commitment was investigated in vitro by means of cell cloning and subcloning experiments, and computer modeling. We found that stem cell commitment is a process which can be modeled as a stochastic event, with a central tendency or probability of 0.2 +/- 0.1. This value is independent of organismal or mitotic age of the stem cells, cell density, or growth in a mitogen-poor environment. Myogenic stem cells stop dividing after approximately 30 divisions in vitro. Since the probability of commitment to terminal differentiation remains below 0.5, clonal senescence and terminal differentiation are separate processes in this system.     

A molecular beacon defines bacterial cell asymmetry

Many cells divide asymmetrically by generating two different cell ends or poles prior to cell division, but the mechanisms by which cells distinguish one pole from the other is poorly understood. In this issue of Cell, Huitema et al. (2006) and Lam et al. (2006) describe a protein that defines one specific pole of a bacterial cell by localizing to the site of cell division to be inherited by both progeny at the resulting new poles.     

Genetic Manipulation of Glycogen Allocation Affects Replicative Lifespan in E. coli

In bacteria, replicative aging manifests as a difference in growth or survival between the two cells emerging from division. One cell can be regarded as an aging mother with a decreased potential for future survival and division, the other as a rejuvenated daughter. Here, we aimed at investigating some of the processes involved in aging in the bacterium Escherichia coli, where the two types of cells can be distinguished by the age of their cell poles. We found that certain changes in the regulation of the carbohydrate metabolism can affect aging. A mutation in the carbon storage regulator gene, csrA, leads to a dramatically shorter replicative lifespan; csrA mutants stop dividing once their pole exceeds an age of about five divisions. These old-pole cells accumulate glycogen at their old cell poles; after their last division, they do not contain a chromosome, presumably because of spatial exclusion by the glycogen aggregates. The new-pole daughters produced by these aging mothers are born young; they only express the deleterious phenotype once their pole is old. These results demonstrate how manipulations of nutrient allocation can lead to the exclusion of the chromosome and limit replicative lifespan in E. coli, and illustrate how mutations can have phenotypic effects that are specific for cells with old poles. This raises the question how bacteria can avoid the accumulation of such mutations in their genomes over evolutionary times, and how they can achieve the long replicative lifespans that have recently been reported.     

How does a bacterium grow during its cell cycle?

Rod-shaped bacteria such as Escherichia coli and Bacillus subtilis appear to extend continuously in length between divisions. However, the kinetics of growth of the individual cell in the steady state is still unknown. A brief, critical account of the main approaches used to determine the pattern of surface extension is given. In general, these approaches are of three types. Firstly, attempts have been made to relate average cell size to growth rate of the culture and to determine possible stages in the cell cycle at which the rate of length extension might change. Secondly, comparisons have been made between the measured length distribution of cells and theoretical distributions, based on three primary hypotheses (linear, bilinear and exponential growth). Thirdly, the principle of Collins and Richmond, involving the calculation of growth rate from the length distributions of extant, separating and new-born cells, is described. It is emphasized that there is a strong element of variation in size at different stages of the cell cycle. This variation imposes severe limitations on models which utilize only average cellular dimensions. We conclude that the Collins-Richmond principle affords the most powerful approach to the analysis of bacterial growth kinetics. However, we propose that the method be modified to permit calculation of separate rates of growth of cells between discernible events in the cell cycle, as well as simply between birth and division.     

Asymmetric Numb distribution is critical for asymmetric cell division of mouse cerebral cortical stem cells and neuroblasts

Stem cells and neuroblasts derived from mouse embryos undergo repeated asymmetric cell divisions, generating neural lineage trees similar to those of invertebrates. In Drosophila, unequal distribution of Numb protein during mitosis produces asymmetric cell divisions and consequently diverse neural cell fates. We investigated whether a mouse homologue m-numb had a similar role during mouse cortical development. Progenitor cells isolated from the embryonic mouse cortex were followed as they underwent their next cell division in vitro. Numb distribution was predominantly asymmetric during asymmetric cell divisions yielding a beta-tubulin III(-) progenitor and a beta-tubulin III(+) neuronal cell (P/N divisions) and predominantly symmetric during divisions producing two neurons (N/N divisions). Cells from the numb knockout mouse underwent significantly fewer asymmetric P/N divisions compared to wild type, indicating a causal role for Numb. When progenitor cells derived from early (E10) cortex undergo P/N divisions, both daughters express the progenitor marker Nestin, indicating their immature state, and Numb segregates into the P or N daughter with similar frequency. In contrast, when progenitor cells derived from later E13 cortex (during active neurogenesis in vivo) undergo P/N divisions they produce a Nestin(+) progenitor and a Nestin(-) neuronal daughter, and Numb segregates preferentially into the neuronal daughter. Thus during mouse cortical neurogenesis, as in Drosophila neurogenesis, asymmetric segregation of Numb could inhibit Notch activity in one daughter to induce neuronal differentiation. At terminal divisions generating two neurons, Numb was symmetrically distributed in approximately 80% of pairs and asymmetrically in 20%. We found a significant association between Numb distribution and morphology: most sisters of neuron pairs with symmetric Numb were similar and most with asymmetric Numb were different. Developing cortical neurons with Numb had longer processes than those without. Numb is expressed by neuroblasts and stem cells and can be asymmetrically segregated by both. These data indicate Numb has an important role in generating asymmetric cell divisions and diverse cell fates during mouse cortical development.     

Reoccurring neural stem cell divisions in the adult zebrafish telencephalon are sufficient for the emergence of aggregated spatiotemporal patterns

Regulation of quiescence and cell cycle entry is pivotal for the maintenance of stem cell populations. Regulatory mechanisms, however, are poorly understood. In particular, it is unclear how the activity of single stem cells is coordinated within the population or if cells divide in a purely random fashion. We addressed this issue by analyzing division events in an adult neural stem cell (NSC) population of the zebrafish telencephalon. Spatial statistics and mathematical modeling of over 80,000 NSCs in 36 brain hemispheres revealed weakly aggregated, nonrandom division patterns in space and time. Analyzing divisions at 2 time points allowed us to infer cell cycle and S-phase lengths computationally. Interestingly, we observed rapid cell cycle reentries in roughly 15% of newly born NSCs. In agent-based simulations of NSC populations, this redividing activity sufficed to induce aggregated spatiotemporal division patterns that matched the ones observed experimentally. In contrast, omitting redivisions leads to a random spatiotemporal distribution of dividing cells. Spatiotemporal aggregation of dividing stem cells can thus emerge solely from the cells’ history.

An interdisciplinary study of the rules governing cell divisions in a population of neural stem cells in the zebrafish brain reveals the existence of aggregated spatio-temporal division patterns of rapid cell cycles in stem cells, and shows that these patterns can be explained by a simple agent-based model relying solely on the cells‘ division history.     

Formation of the embryonic-abembryonic axis of the mouse blastocyst: relationships between orientation of early cleavage divisions and pattern of symmetric/asymmetric divisions

Setting aside pluripotent cells that give rise to the future body is a central cell fate decision in mammalian development. It requires that some blastomeres divide asymmetrically to direct cells to the inside of the embryo. Despite its importance, it is unknown whether the decision to divide symmetrically versus asymmetrically shows any spatial or temporal pattern, whether it is lineage-dependent or occurs at random, or whether it influences the orientation of the embryonic-abembryonic axis. To address these questions, we developed time-lapse microscopy to enable a complete 3D analysis of the origins, fates and divisions of all cells from the 2- to 32-cell blastocyst stage. This showed how in the majority of embryos, individual blastomeres give rise to distinct blastocyst regions. Tracking the division orientation of all cells revealed a spatial and temporal relationship between symmetric and asymmetric divisions and how this contributes to the generation of inside and outside cells and thus embryo patterning. We found that the blastocyst cavity, defining the abembryonic pole, forms where symmetric divisions predominate. Tracking cell ancestry indicated that the pattern of symmetric/asymmetric divisions of a blastomere can be influenced by its origin in relation to the animal-vegetal axis of the zygote. Thus, it appears that the orientation of the embryonic-abembryonic axis is anticipated by earlier cell division patterns. Together, our results suggest that two steps influence the allocation of cells to the blastocyst. The first step, involving orientation of 2- to 4-cell divisions along the animal-vegetal axis, can affect the second step, the establishment of inside and outside cell populations by asymmetric 8- to 32-cell divisions.