The kinetic significance of cell size : II. Size distributions of resting and proliferating cells during interphase

This second part in a two part report describes the kinetic, cell size and nuclear size characteristics of S phase cells and cells with greatly protracted generation times (‘resting’ cells) in a cell line of human lymphoid cells. The median cell and nuclear sizes of S phase cells were greater than the corresponding median sizes observed in the whole population. Resting cells (operationally defined as unlabelled cells after 5 days of continuous labelling with [³H]TdR) have cell and nuclear size distributions overlapping with the cell and nuclear size distributions of the whole population. These resting cells are kinetically characterized by means of the observed labelling index vs time data during continuous labelling. The implication of these results are discussed.     

Geometrical constraints in the scaling relationships between genome size, cell size and cell cycle length in herbaceous plants

Plant nuclear genome size (GS) varies over three orders of magnitude and is correlated with cell size and growth rate. We explore whether these relationships can be owing to geometrical scaling constraints. These would produce an isometric GS-cell volume relationship, with the GS-cell diameter relationship with the exponent of 1/3. In the GS-cell division relationship, duration of processes limited by membrane transport would scale at the 1/3 exponent, whereas those limited by metabolism would show no relationship. We tested these predictions by estimating scaling exponents from 11 published datasets on differentiated and meristematic cells in diploid herbaceous plants. We found scaling of GS-cell size to almost perfectly match the prediction. The scaling exponent of the relationship between GS and cell cycle duration did not match the prediction. However, this relationship consists of two components: (i) S phase duration, which depends on GS, and has the predicted 1/3 exponent, and (ii) a GS-independent threshold reflecting the duration of the G1 and G2 phases. The matches we found for the relationships between GS and both cell size and S phase duration are signatures of geometrical scaling. We propose that a similar approach can be used to examine GS effects at tissue and whole plant levels.     

The probability of G1 cells to enter into S increases with their size while S length decreases with cell enlargement in Allium cepa

The distribution of cell surface area projection (cell size) has been measured at birth and at initiation of DNA synthesis in steady-state populations of Allium cepa root meristems. The conditional probability, P(I/G1), that initiation occurs given that the event of being in G1 also occurs has been estimated from these data. P(I/G1) was found to increase when cells became larger. The distribution of G1 duration has been constructed from indicated cell size distributions. The absolute frequencies of G1 times showed a maximum in the zone of cells with short G1 periods; about 14% of cells appear to enter into S with G1 congruent to 1 h. These results suggest that the increase of P(I/G1) was due to cell enlargement and not to cell aging. By comparing the cell size distribution at initiation of S and at the end of this period, a drastic reduction of cell size variability during DNA replication was observed and both curves were seen as rather similar in shape although they obviously had different modal points. These observations support that there is a negative correlation between the initiation size and the duration of genome duplication, and that cells which initiate DNA synthesis with the same size have a similar replication time. From this hypothesis, a plot of S duration versus cell size at initiation of this period was constructed by comparing the distributions of cell size at start and end of replication; this plot was also consistent with the existence of a negative correlation between cell initiation size and S length.     

Loss of growth homeostasis by genetic decoupling of cell division from biomass growth: implication for size control mechanisms

Growing cells adjust their division time with biomass accumulation to maintain growth homeostasis. Size control mechanisms, such as the size checkpoint, provide an inherent coupling of growth and division by gating certain cell cycle transitions based on cell size. We describe genetic manipulations that decouple cell division from cell size, leading to the loss of growth homeostasis, with cells becoming progressively smaller or progressively larger until arresting. This was achieved by modulating glucose influx independently of external glucose. Division rate followed glucose influx, while volume growth was largely defined by external glucose. Therefore, the coordination of size and division observed in wild‐type cells reflects tuning of two parallel processes, which is only refined by an inherent feedback‐dependent coupling. We present a class of size control models explaining the observed breakdowns of growth homeostasis.     

Mathematical model of a cell size checkpoint

How cells regulate their size from one generation to the next has remained an enigma for decades. Recently, a molecular mechanism that links cell size and cell cycle was proposed in fission yeast. This mechanism involves changes in the spatial cellular distribution of two proteins, Pom1 and Cdr2, as the cell grows. Pom1 inhibits Cdr2 while Cdr2 promotes the G2 → M transition. Cdr2 is localized in the middle cell region (midcell) whereas the concentration of Pom1 is highest at the cell tips and declines towards the midcell. In short cells, Pom1 efficiently inhibits Cdr2. However, as cells grow, the Pom1 concentration at midcell decreases such that Cdr2 becomes activated at some critical size. In this study, the chemistry of Pom1 and Cdr2 was modeled using a deterministic reaction-diffusion-convection system interacting with a deterministic model describing microtubule dynamics. Simulations mimicked experimental data from wild-type (WT) fission yeast growing at normal and reduced rates; they also mimicked the behavior of a Pom1 overexpression mutant and WT yeast exposed to a microtubule depolymerizing drug. A mechanism linking cell size and cell cycle, involving the downstream action of Cdr2 on Wee1 phosphorylation, is proposed.     

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.     

Heterotrimeric G proteins and regulation of size asymmetry during cell division

The generation of daughter cells of different fate and size depends on the orientation, positioning and morphology of the mitotic spindle. In both C. elegans and Drosophila, heterotrimeric G proteins have emerged as central and conserved regulators of this process. Although the same molecular players are involved in worms and flies, there are clear differences in the mechanisms used. Interestingly, recent work in mammalian cells suggests that heterotrimeric G proteins may control spindle positioning in higher organisms during symmetric and asymmetric cell divisions.     

Environmental and genetic variations of wing size,cell size and cell division rate,inDrosophila melanogaster

Variations in the wing size ofDrosophila melanogaster are induced by controlled internal (sex, degree of inbreeding) and external (temperature, egg-density) conditions. Moreover, uncontrolled individual variations of the wing size, within each of the experimental groups, are considered. A new mounting technique of the wings, for the purpose of wing length and cell density measurements, is reported.From the inter-and the intra-group analyses, the following relationships were found: 1. Wing size variations are positively correlated with both cell size and total cell number. 2. Variation of the duration of development is positively correlated with the duration of the cellular generation time. Some contradictions in the existing literature on this subject are discussed.Centre National de Radiobiologie et de Génétique     

Cell size, cell cycle and transition probability in mouse fibroblasts

This paper describes the relationship between cell size and cell division in two situations. In the first, quiescent cells were sorted on the basis of cell size using a fluorescence-activated cell sorter and returned to culture. The results of this type of experiment are compatible with the idea that once cells have completed a size-dependent lag, the rate of entry of cells into S phase is controlled by a rate-limiting random event (or transition).The second kind of experiment follows the kinetics of complete cell cycles in rapidly proliferating cells whose mothers had been sorted on the basis of cell size. The cells born of small mother cells have longer cycle times than cells derived from large mothers. The difference in the cycle time of these two classes was due to differences in the B phase of the cell cycle [containing S, G2, M and part of G1 (G1B)], transition probability being the same in both size classes. Our results show that S, G2 and M are unaffected by size, thus confining the effect of size to G1B. It seems probable that the variability of B phase in cloned cell populations is partly due to variations of cell size at division, and correlations between the cycle times of sister cells result because sibling cells are more similar in size than unrelated cells. The major factor controlling cell division in mouse fibroblasts is shown, however, to be the transition probability; size has a more minor role.     

Kinetic analysis of cell size and DNA content distributions during tumor cell proliferation: Ehrlich ascites tumor study.

In order to study the growth dynamics of proliferating and non-proliferating cells utilizing discrete-time state equations, the cell cycle was divided into a finite number of age compartments. In analysing tumor growth, the kinetic parameters associated with a retardation in the growth rate of tumors were characterized by computer simulation in which the simulated results of the growth curve, the growth fraction, and the mean generation time were adjusted to fit the experimental data. The cell age distibution during the period of growth was obtained and by a linear transformation of the state transition matrices, was employed to specify the cell size and DNA content distributions. In an application of the model, the time-course behavior of cell cycle parameters of Ehrlich ascites tumor is illustrated, and the parameters important for the transition of cells in the proliferating compartment to the non-proliferating compartment are discussed, particularly in relation to the G1-G0 and G2-G0 transitions of non-cycling cells as revealed by the variation of cell size distribution.     

DAF1, a mutant gene affecting size control, pheromone arrest, and cell cycle kinetics of Saccharomyces cerevisiae.

The mating pheromone alpha-factor arrests Saccharomyces cerevisiae MATa cells in the G1 phase of the cell cycle. Size control is also exerted in G1, since cells do not exit G1 until they have attained a critical size. A dominant mutation (DAF1-1) which causes both alpha-factor resistance and small cell size (volume about 0.6-fold that of the wild type) has been isolated and characterized genetically and by molecular cloning. Several alpha-factor-induced mRNAs were induced equivalently in daf1+ and DAF1-1 cells. The DAF1-1 mutation consisted of a termination codon two-thirds of the way through the daf1+ coding sequence. A chromosomal deletion of DAF1 produced by gene transplacement increased cell volume about 1.5-fold; thus, DAF1-1 may be a hyperactive or deregulated allele of a nonessential gene involved in G1 size control. Multiple copies of DAF1-1 also greatly reduced the duration of the G1 phase of the cell cycle.     

Regulation of cell size in the yeast Saccharomyces cerevisiae.

For cells of the yeast Saccharomyces cerevisiae, the size at initiation of budding is proportional to growth rate for rates from 0.33 to 0.23 h-1. At growth rates lower than 0.23 h-1, cells displayed a minimum cell size at bud initiation independent of growth rate. Regardless of growth rate, cells displayed an increase in volume each time budding was initiated. When abnormally small cells, produced by starvation for nitrogen, were placed in fresh medium containing nitrogen but with different carbon sources, they did not initiate budding until they had grown to the critical size characteristic of that medium. Moreover, when cells were shifted from a medium supporting a low growth rate and small size at bud initiation to a medium supporting a higher growth rate and larger size at bud initiation, there was a transient accumulation of cells within G1. These results suggest that yeast cells are able to initiate cell division at different cell sizes and that regulation of cell size occurs within G1.     

Systematic identification of cell size regulators in budding yeast

Cell size is determined by a complex interplay between growth and division, involving multiple cellular pathways. To identify systematically processes affecting size control in G1 in budding yeast, we imaged and analyzed the cell cycle of millions of individual cells representing 591 mutants implicated in size control. Quantitative metric distinguished mutants affecting the mechanism of size control from the majority of mutants that have a perturbed size due to indirect effects modulating cell growth. Overall, we identified 17 negative and dozens positive size control regulators, with the negative regulators forming a small network centered on elements of mitotic exit network. Some elements of the translation machinery affected size control with a notable distinction between the deletions of parts of small and large ribosomal subunit: parts of small ribosomal subunit tended to regulate size control, while parts of the large subunit affected cell growth. Analysis of small cells revealed additional size control mechanism that functions in G2/M, complementing the primary size control in G1. Our study provides new insights about size control mechanisms in budding yeast.     

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

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

Potential for control of signaling pathways via cell size and shape

BACKGROUND: In order for signals generated at the plasma membrane to reach intracellular targets, activated messengers, such as G proteins and phosphoproteins, must diffuse through the cytoplasm. If the deactivators of these messengers, GTPase activating proteins (GAPs) and phosphatases, respectively, are sufficiently active in the cytoplasm, then the signal could in principle decay before reaching the target and a stable spatial gradient in phosphostate would be generated. Recent experiments document the existence of such gradients in living cells and suggest a role for them in mitotic spindle morphogenesis and cell migration. However, how such systems behave theoretically when embedded in a cell of varying size or shape has not been considered. RESULTS: Here we use a simple mathematical model to explore the theoretical consequences of a plasma membrane bound activator (i.e., guanine nucleotide exchange factor, GEF, or kinase) and a cytoplasmic deactivator (i.e., GAP or phosphatase), and we find that as a model cell grows, the substrate becomes progressively dephosphorylated as a result of decreased proximity to the activator. Conversely, as a cell spreads and flattens, the substrate becomes globally phosphorylated because of increased proximity of the substrate to the activator. Similarly, in the leading edge of polarized cells and in protrusions such as lamellipodia or filopodia, the substrate is highly phosphorylated. As a specific test of the model, we found that the experimentally observed preferential activation of the G protein Cdc42 in the periphery of fibroblasts that was recently reported is consistent with model predictions. CONCLUSIONS: We conclude that cell-signaling pathways can theoretically be turned on and off, both locally and globally, in response to alterations in cell size and shape.     

Minimal requirements for robust cell size control in eukaryotic cells

Most cell types living in a stable environment tend to keep a constant characteristic size over successive generations. Size homeostasis requires that cells exert a tight control over the size at which they divide. Cell size control is not only robust against various noises, but also highly flexible since cell sizes can vary tremendously, notably as a function of nutrient levels. We formulated a minimal mathematical model of the eukaryotic cell cycle in which the cell size control operates through a cell growth-dependent bifurcation in the cell cycle dynamics. Such a bifurcation mechanism can readily explain the occurrence of a minimum critical size at division under limiting growth conditions. However, it also predicts that cells should become progressively larger and larger under prolific growth conditions. We argue that the cell size control can be reinforced at fast growth rates by adding a new cell cycle inhibitory activity whose strength would increase with the cell growth rate. We further show that various sources of noise may also generate a large variability in cell size at division and interdivision time that exhibit characteristic exponential tail distributions, without compromising the robustness of the cell size control.     

Nucleolar size and the activity of rRNA transport in the course of morphogenetic reduction of cell dimensions

In antheridial filaments of Chara vulgaris during the first period of spermatogenesis which consists of 6 synchronous cell division cycles there occurs a gradual decrease in sizes of cells entering successive mitoses. Present studies indicate that this process is correlated with a considerable reduction of total nucleolar volume in late G2 phase which, in turn, brings about decrease in sizes of nucleoli reappearing in telophase of the subsequent cell cycle. A consequence of the above phenomenon evidenced using 3H uridine autoradiography is a gradual increase--from one generation to the next--in an amount of rRNA transported into cytoplasm due to an increase in number of small nucleoli which were found to be more active in transport than larger nucleoli. This process leads to a lowering of an increase in nucleolar volumes during consecutive interphase periods owing to a progressively limited accumulation of rRNA for the sake of daughter cells, i.e. to a spontaneously magnifying reduction of nucleolar sizes in the forthcoming cell generations. Thus, diminution of nucleoli observed during the development of antheridial filaments seems to be due to a chain-series of processes connected with mechanisms which possibly regulate rRNA transport and accompany morphogenetic events.     

Involvement of Rho-type GTPase in control of cell size in Saccharomyces cerevisiae

Maintaining specific cell size, which is important for many organisms, is achieved by coordinating cell growth and cell division. In the budding yeast Saccharomyces cerevisiae, the existence of two cell-size checkpoints is proposed: at the first checkpoint, cell size is monitored before budding at the G1/S transition, and at the second checkpoint, actin depolymerization occurring in the small bud is monitored before the G2/M transition. Morphological analyses have revealed that the small GTPase Rho1p participates in cell-size control at both the G1/S and the G2/M boundaries. One group of rho1 mutants (rho1A) underwent premature entry into mitosis, leading to the birth of abnormally small cells. In another group of rho1 mutants (rho1B), the mother cells failed to reach an appropriate size before budding, and expression of the G1 cyclin Cln2p began at an earlier phase of the cell cycle. Analyses of mutants defective in Rho1p effector proteins indicate that Skn7p, Fks1p and Mpk1p are involved in cell-size control. Thus, Rho1p and its downstream regulatory pathways are involved in controlling cell size in S. cerevisiae.     

The puc1 cyclin regulates the G1 phase of the fission yeast cell cycle in response to cell size

Eukaryotic cells coordinate cell size with cell division by regulating the length of the G1 and G2 phases of the cell cycle. In fission yeast, the length of the G1 phase depends on a precise balance between levels of positive (cig1, cig2, puc1, and cdc13 cyclins) and negative (rum1 and ste9-APC) regulators of cdc2. Early in G1, cyclin proteolysis and rum1 inhibition keep the cdc2/cyclin complexes inactive. At the end of G1, the balance is reversed and cdc2/cyclin activity down-regulates both rum1 and the cyclin-degrading activity of the APC. Here we present data showing that the puc1 cyclin, a close relative of the Cln cyclins in budding yeast, plays an important role in regulating the length of G1. Fission yeast cells lacking cig1 and cig2 have a cell cycle distribution similar to that of wild-type cells, with a short G1 and a long G2. However, when the puc1(+) gene is deleted in this genetic background, the length of G1 is extended and these cells undergo S phase with a greater cell size than wild-type cells. This G1 delay is completely abolished in cells lacking rum1. Cdc2/puc1 function may be important to down-regulate the rum1 Cdk inhibitor at the end of G1.     

Checking cell size in yeast

To remain viable, cells have to coordinate cell growth with cell division. In yeast, this occurs at two control points: the boundaries between G1 and S phases, also known as Start, and between G2 and M phases. Theoretically, coordination can be achieved by independent regulation of growth and division, or by participation of surveillance mechanisms in which cell size feeds back into cell-cycle control. This article discusses recent advances in the identification of sizing mechanisms in budding and in fission yeast, and how these mechanisms integrate with environmental stimuli. A comparison of the G1-S and G2-M size-control modules in the two species reveals a degree of conservation higher than previously thought. This reinforces the notion that internal sizing could be a conserved feature of cell-cycle control throughout eukaryotes.