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.     

Cell growth and division in Escherichia coli: a common genetic control involved in cell division and minicell formation

Escherichia coli Div 124(ts) is a conditional-lethal cell division mutant formed from a cross between a mutant that produces polar anucleated minicells and a temperature-sensitive cell division mutant affected in a stage of cross-wall synthesis. Under permissive growth temperature (30 C), Div 124(ts) grows and produces normal progeny cells and anucleated minicells from its polar ends. When transferred to nonpermissive growth temperature (42 C), growth and macromolecular synthesis continue, but cell division and minicell formation are inhibited. Growth at 42 C results in formation of filamentous cells showing some constrictions along the length of the filaments. Return of the filaments from 42 to 30 C results in cell division and minicell formation in association with the constrictions and other areas along the length of the filaments. This gives rise to a "necklace-type" array of cells and minicells. Recovery of cell division is observed after a lag and is followed by a burst in cell division and finally by a return to the normal growth characteristic of 30 C cultures. Recovery of cell division takes place in the presence of chloramphenicol or nalidixic acid when these are added at the time of shift from 42 to 30 C, and indicates that a division potential for filament fragmentation is accumulated while the cells are at 42 C. This division potential is used for the production of both minicells and cells of normal length. The conditional-lethal temperature sensitive mutation controls a step(s) in cross-wall synthesis common to cell division and minicell formation.     

Manipulation of leaf shape by modulation of cell division

The role of cell division as a causal element in plant morphogenesis is debatable, with accumulating evidence supporting the action of cell division-independent mechanisms. To directly test the morphogenic function of cell division, we have utilised a microinduction technique to locally and transiently manipulate the expression in transgenic plants of two genes encoding putative effectors of the cell cycle, a tobacco A-type cyclin and a yeast cdc25. The results show that local expression of these genes leads to modulation of cell division patterns. Moreover, whereas altered cell division in the apical meristem had no influence on organogenesis, local induction of cell proliferation on the flanks of young leaf primordia led to a dramatic change in lamina development and, thus, leaf shape. These data indicate that the role of cell division in plant morphogenesis is context dependent and identify cell division in the leaf primordium as a potential target for factors regulating leaf shape.     

Cell elongation and division probability during the Escherichia coli growth cycle.

A new method is presented for determining the growth rate and the probability of cell division (separation) during the cell cycle, using size distributions of cell populations grown under steady-state conditions. The method utilizes the cell life-length distribution, i.e., the probability that a cell will have any specific size during its life history. This method was used to analyze cell length distributions of six cultures of Escherichia coli, for which doubling times varied from 19 to 125 min. The results for each culture are in good agreement with a single model of growth and division kinetics: exponential elongation of cells during growth phase of the cycle, and normal distributions of length at birth and at division. The average value of the coefficient of variation was 13.5% for all strains and growth rates. These results, based upon 5,955 observations, support and extend earlier proposals that growth and division patterns of E. coli are similar at all growth rates and, in addition, identify the general growth pattern of these cells to be exponential.     

Extracellular control of cell size

Both cell growth (cell mass increase) and progression through the cell division cycle are required for sustained cell proliferation. Proliferating cells in culture tend to double in mass before each division, but it is not known how growth and division rates are co-ordinated to ensure that cell size is maintained. The prevailing view is that coordination is achieved because cell growth is rate-limiting for cell-cycle progression. Here, we challenge this view. We have investigated the relationship between cell growth and cell-cycle progression in purified rat Schwann cells, using two extracellular signal proteins that are known to influence these cells. We find that glial growth factor (GGF) can stimulate cell-cycle progression without promoting cell growth. We have used this restricted action of GGF to show that, for cultured Schwann cells, cell growth rate alone does not determine the rate of cell-cycle progression and that cell size at division is variable and depends on the concentrations of extracellular signal proteins that stimulate cell-cycle progression, cell growth, or both.     

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.     

The initiation of B cell clonal expansion occurs independently of pre-B cell receptor formation.

Current models of B cell development posit that clonal expansion occurs as a direct result of Ig H chain expression. To test this hypothesis, we isolated a population of early B cells in which H chain recombination is initiated and assessed V(H)DJ(H) rearrangements in both cycling and noncycling cells. We found that actively dividing cells within this population are enriched for H chain rearrangements that are productive when compared with their counterparts in G(0)/G(1), apparently supporting a role for H chain expression in initiating early B cell division; entrance into the cell cycle was accompanied by V(H) gene-dependent H chain selection. However, we also identified a phenotypically identical population of actively cycling early B cells in the absence of H chain expression in recombination activating gene knockout mice. In addition, actively cycling early B cells could be detected in pre-B cell receptor (pBCR)-negative lambda5 knockout mice, but we found no evidence for V(H)-dependent H chain selection in this population. Given these results, we suggest that the initiation of clonal expansion, at this early stage in B cell development, occurs independently of H chain expression. Although the cycling cell pool is enriched for pBCR-positive cells in mice expressing surrogate L chain, pBCR formation is not required for the initiation of cell division.     

The biological essence of resting cells in cell populations

Turnover of cell macromolecules and the diversity of turnover rates in cycling and resting cells is proposed as the underlying fundamental basis for a set of biological phenomena that involve growth, aging, and resistance of normal and tumor cell populations to damage by alkylating agents.It is postulated that in cycling cells the degradation rates are minimal or approaching zero, while in resting cells they are reaching the maximal possible values which are inherent characteristic features of each biological species. The biological advantage of the resting state lies in the ability of these cells to turn to maximal rates of degradation of cell macromolecules. During this process the level of accumulated cellular misinformation infthe form of altered misfunctioning macromolecules is substantially reduced and the cell becomes partially or completely rejuvenated. All cell populations are thought to contain a pool of rejuvenating resting cells, which have a certain probability of reverting to the cycling state.     

Role of DNA synthesis in secretion of immunoglobulin from murine B cells stimulated by T cell derived lymphokines

We have investigated whether cell division is required for induction of Ig secretion from three types of B cells, which represent distinct activation states: normal splenic B cells, anti-Ig-treated B cells, and a monoclonal murine B cell tumor, BCL1. Polyclonal Ig secretion was stimulated in vitro by LPS or by lymphokines produced by EL-4 cells (EL-4 SN), which includes B cell growth factor II (BCGF II). LPS and EL-4 SN were mitogenic for all three cell populations and stimulated substantial IgM secretion from both B cells and anti-Ig blasts. Aphidicolin, a reversible inhibitor of DNA synthesis, abolished IgM secretion from B cells and anti-Ig blasts induced by either mitogen, indicating that Ig-secreting cells in these cultures are part of a cycling population. BCL1 tumor cells respond to BCGF II (but not to interleukin 2 or B cell stimulatory factor 1) with IgM secretion and cell division, allowing a direct assessment of the influence of BCGF II-stimulated cell division on secretion of IgM. Secretion by these cells during the first 24 hr of culture was not substantially affected by aphidicolin, but secretion at 48 or 72 hr was markedly inhibited. Culture of BCL1 cells for 48 hr with aphidicolin alone had no effect on cell viability or on subsequent responsiveness if the drug was removed, eliminating non-specific toxicity as an explanation of the drug's effect. Addition of aphidicolin during the last 24 hr of culture to either normal B cells or BCL1 cells was much less effective at inhibiting IgM secretion. These results indicate that the cells that secrete IgM in response to BCGF II also synthesize DNA when exposed to this factor. Thus, induction of high-rate Ig secretion from murine B cells by some stimuli, including BCGF II, may require at least one round of cell division.     

Punctuated cell cycling in the regeneration blastema of urodele amphibians

Abstract. We previously assumed that all cells in the regeneration blastema are randomly distributed throughout the cell cycle and actively cycling towards the next mitotic division. We now show that data from continuous labeling (³H-thymidine) experiments do not support this view and favor instead the hypothesis that the blastema cell cycle is punctuated in the g₁ phase wherein cells can enter what we term a transiently quiescent (TQ) position. We call this hypothesis the punctuated cycling (PC) hypothesis. We further propose that the relative sizes of the quiescent and actively cycling populations explain (1) variations in rates of regeneration in different sizes of urodele amphibians, (2) the rate and success of regeneration in different species, and (3) how various controlling factors, such as injury, nerves, growth factors, wound epidermis, and hormones, influence the initiation and progression of the regeneration process. This PC hypothesis is important for interpreting previous pulse labeling data, is consistent with recently obtained continuous labeling data, and is experimentally testable.     

Cell proliferation and cell differentiation in tissue cultures of adult muco-cilliary epithelia.

Explants and monolayers from a variety of muco-ciliary epithelia were cultivated in vitro and the kinetics of their proliferation and differentiation described. New epithelial lining and epithelial-like monolayer sheets of cells formed in which the migration cells were all originally undifferentiated cycling stem cells. The divided and differentiated in ML growth into cell types characteristic of the tissue source: however, the control mechanisms which regulate cell division and cell differentiation in the tissues were lost outside the tissue framework. Cell division and cyto-differentiation in ML growths both in ciliated and in mucus-producing cells, were not always mutually exclusive.     

Multi-type branching models to describe cell differentiation programs

Cell proliferation and differentiation is described by a multi-type branching process, a probability model that defines the inheritance of cell type. Cell type is defined by (i) a repression index related to the time required for S-phase entry and (ii) phenotype as determined by cell markers and division history. The inheritance of cell type is expressed as the expected number and type of progeny cells produced by a mother cell given her type. Expressions for the expected number and type of cells produced by a multi-cellular (bulk culture) system are derived from the general model by making the simplifying assumption that cell generation times are independent. The multi-type Smith-Martin model (MSM) makes the further assumption that cell generation times are lag-exponentially distributed with phenotype transitions occurring just before entry into S-phase. The inheritance-modified MSM (IMSM) model includes the influence of generation time memory so that mother and daughter generation times are correlated. The expansion of human cord blood CD34⁺ cells by haematopoietic growth factors was division tracked in bulk culture using carboxyfluorescein diacetate, succinimidyl ester (CFDA-SE). The MSM model was fitted to division tracking data to indentify cell cycle length, and the rates of CD34 antigen down-regulation and apoptosis. The IMSM model was estimated for mouse granulocyte-macrophage progenitors using live cell imaging data. Multi-type branching models describe cell differentiation dynamics at both single- and multi-cell scales, providing a new paradigm for systematic analysis of stem and progenitor cell development.     

The effect of oxidizing agents on cell division and shape

Certain oxidizing agents such as vitaminK(VK) and lipid peroxides were found to suppress an increase in cytoplasmic Ca2+ concentration by growth factors, and inhibit on cell proliferation. These oxidizing agents induced a marked change in cell shape. In a detailed analysis of each phase in the cell cycle, the inhibition of an increase in cytoplasmic Ca2+ and cell division occurred only when the agents were added at G0/G1 phase. The addition to S or M phase cells did not influence in cytoplasmic Ca2+ and cell division. These experimental results suggest that these oxidizing agents may inhibit the transfer of stimulation signals from growth factors by acting on cell membrane sites and suppress subsequent DNA replication and mitotic division.     

Control models of cell cycle transit, exit, and arrest

Several distinct cycles mediate the events which occur between one cell division and the next. In micro-organisms there are generally two cycles. One governs biomass growth, the other DNA synthesis and cell division. In higher eukaryotes there can be as many as four distinct cycles, with growth, DNA synthesis, cell division, and nuclear division each possessing its own functional sequence of events. These cycles are controlled and coordinated by several different regulatory mechanisms. Restriction points are specific steps in the cycle whose completion is governed by external regulatory agents. One set of restriction points requires nutrients and growth hormones for step completion. Another set serves as receptors for differentiating factors which cause cycle arrest and initiate cellular differentiation. There is currently a debate as to whether restriction point inhibition involves permanent arrest or temporary arrest with a stochastic arrested-state residence time controlled by a transition probability mechanism. Tissue sizing is a process of negative feedback inhibition mediated by intercellular communication via cell surface contact and the extracellular matrix. Sizers commonly operate throughout broad portions of the cycle and appear to cause a slowing of cycle transit velocity rather than arrest. Sizers are probably the major regulatory mechanism for cell growth under conditions of nutrient and growth factor excess. They also generate compensatory proliferation following wounding or cell death. A growing body of evidence suggests that both the transit velocity, with which cells move through their several cycles, and the coordination of the cycles are controlled by intracellular regulatory mechanisms which behave as biological oscillators. These oscillators trigger complex sequences of events such as DNA synthesis and cell division.     

Sensitivity of cell division and cell elongation to low water potentials in soybean hypocotyls

Summary The response of cell division and cell elongation to low cell water potentials was studied in etiolated, intact soybean hypocotyls desiccated either by withholding water from seedlings or by subjecting hypocotyls to pressure. Measurements of hypocotyl water potential and osmotic potential indicated that desiccation by withholding water resulted in osmotic adjustment of the hypocotyls so that turgor remained almost constant. The adjustment appeared to involve transport of solutes from the cotyledons to the hypocotyl and permitted growth of the seedlings at water potentials which would have been strongly inhibitory had adjustment not occurred. Growth was ultimately inhibited in hypocotyls due to inhibition of cell division and cell elongation to a similar degree. The inhibition of cell elongation appeared to result from a change in the minimum turgor necessary for growth. On the other hand, when intact hypocotyls were exposed to pressure for 3 h, osmotic adjustment did not occur, turgor decreased, and the sensitivity of growth to low cell water potentials increased, presumably due to inhibition of cell elongation. Thus, although cell division was sensitive to low cell water potentials in soybean hypocotyls, cell elongation had either the same sensitivity or was more sensitive, depending on whether the tissue adjusted osmotically. Osmotic adjustment of hypocotyls may represent a mechanism for preserving growth in seedlings germinating in desiccated soil.Supported by a grant from the Illinois Agricultural Experiment Station, University of Illinois and grant 1-T1-GM-1380 from the United States Public Health Service.     

XIAO is involved in the control of organ size by contributing to the regulation of signaling and homeostasis of brassinosteroids and cell cycling in rice

Organ size is determined by cell number and size, and involves two fundamental processes: cell proliferation and cell expansion. Although several plant hormones are known to play critical roles in shaping organ size by regulating the cell cycle, it is not known whether brassinosteroids (BRs) are also involved in regulating cell division. Here we identified a rice T-DNA insertion mutant for organ size, referred to as xiao, that displays dwarfism and erect leaves, typical BR-related phenotypes, together with reduced seed setting. XIAO is predicted to encode an LRR kinase. The small stature of the xiao mutant resulted from reduced organ sizes due to decreased cell numbers resulting from reduced cell division rate, as supported by the observed co-expression of XIAO with a number of genes involved in cell cycling. The xiao mutant displayed a tissue-specific enhanced BR response and greatly reduced BR contents at the whole-plant level. These results indicated that XIAO is a regulator of BR signaling and cell division. Thus, XIAO may provide a possible connection between BRs and cell-cycle regulation in controlling organ growth.     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

A plant cell division algorithm based on cell biomechanics and ellipse-fitting

Background and Aims

The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models developed to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or is updated intermittently on a separate time scale to the mechanics. This study presents a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. Actual growth of the cell wall is simulated simultaneously with the mechanics.

Methods

The cell is considered as a closed, thin-walled structure, maintained in tension by turgor pressure. The cell walls are represented as linear elastic elements that obey Hooke''s law. Cell expansion is induced by turgor pressure acting on the yielding cell-wall material. A system of differential equations for the positions and velocities of the cell vertices as well as for the actual growth of the cell wall is established. Readiness to divide is determined based on cell size. An ellipse-fitting algorithm is used to determine the position and orientation of the dividing wall. The cell vertices, walls and cell connectivity are then updated and cell expansion resumes. Comparisons are made with experimental data from the literature.

Key Results

The generic plant cell division algorithm has been implemented successfully. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. Development of the algorithm highlighted the importance of ellipse-fitting to produce randomness (biological variability) even in symmetrically dividing cells. Unlike previous models, a differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with the position and velocity of the vertices.

Conclusions

The algorithm presented can produce different tissues varying in topological and geometrical properties. This flexibility to produce different tissue types gives the model great potential for use in investigations of plant cell division and growth in silico.