A mutation in the ATP2 gene abrogates the age asymmetry between mother and daughter cells of the yeast Saccharomyces cerevisiae

The yeast Saccharomyces cerevisiae reproduces by asymmetric cell division, or budding. In each cell division, the daughter cell is usually smaller and younger than the mother cell, as defined by the number of divisions it can potentially complete before it dies. Although individual yeast cells have a limited life span, this age asymmetry between mother and daughter ensures that the yeast strain remains immortal. To understand the mechanisms underlying age asymmetry, we have isolated temperature-sensitive mutants that have limited growth capacity. One of these clonal-senescence mutants was in ATP2, the gene encoding the beta-subunit of mitochondrial F(1), F(0)-ATPase. A point mutation in this gene caused a valine-to-isoleucine substitution at the ninetieth amino acid of the mature polypeptide. This mutation did not affect the growth rate on a nonfermentable carbon source. Life-span determinations following temperature shift-down showed that the clonal-senescence phenotype results from a loss of age asymmetry at 36 degrees, such that daughters are born old. It was characterized by a loss of mitochondrial membrane potential followed by the lack of proper segregation of active mitochondria to daughter cells. This was associated with a change in mitochondrial morphology and distribution in the mother cell and ultimately resulted in the generation of cells totally lacking mitochondria. The results indicate that segregation of active mitochondria to daughter cells is important for maintenance of age asymmetry and raise the possibility that mitochondrial dysfunction may be a normal cause of aging. The finding that dysfunctional mitochondria accumulated in yeasts as they aged and the propensity for old mother cells to produce daughters depleted of active mitochondria lend support to this notion. We propose, more generally, that age asymmetry depends on partition of active and undamaged cellular components to the progeny and that this "filter" breaks down with age.     

A bimolecular mechanism for the cell size control of the cell cycle

A molecular model for the control of cell size has been developed. It is based on two molecules, one (I) acts as an inhibitor of the entrance into S phase, and it is synthetised just after cell separation in a fixed amount per nucleus. The other (A) is an activator of the S phase, and it is synthetised at a ratio proportional to the overall protein accumulation. The activator reacts stoichiometrically with (I), and after all the (I) molecules have been titrated, (A) begins to accumulate. When it reaches a threshold value, it triggers the onset of DNA replication. This model was tested by simulation and when applied to the case of unequal division explains a number of features of an exponentially growing yeast cell population: (a) the lengths of TP (cycle time of parent cells) and TD (cycle time of daughter cells) verify the condition exp(- KTP ) + exp(- KTD ) = 1; (b) the changes of the average cell size of populations at different growth rates; (c) the frequency of parents and daughters at various growth rates; (d) the increase of cell size at bud initiation for cells of increasing genealogical age; (e) the existence of a TP - TB period (difference between the cycle time of parents and the length of budded phase) that depends linearly upon the doubling time of the population.     

Morphologically-structured models of growing budding yeast populations

It has been well recognized that many key aspects of cell cycle regulation are encoded into the size distributions of growing budding yeast populations due to the tight coupling between cell growth and cell division present in this organism. Several attempts have been made to model the cell size distribution of growing yeast populations in order to obtain insight on the underlying control mechanisms, but most were based on the age structure of asymmetrically dividing populations. Here we propose a new framework that couples a morphologically-structured representation of the population with population balance theory to formulate a dynamic model for the size distribution of growing yeast populations. An advantage of the presented framework is that it allows derivation of simpler models that are directly identifiable from experiments. We show how such models can be derived from the general framework and demonstrate their utility in analyzing yeast population data. Finally, by employing a recently proposed numerical scheme, we proceed to integrate numerically the full distributed model to provide predictions of dynamics of the cell size structure of growing yeast populations.     

Asymmetrical division of Saccharomyces cerevisiae.

The unequal division model proposed for budding yeast (L. H. Hartwell and M. W. Unger, J. Cell Biol. 75:422-435, 1977) was tested by bud scar analyses of steady-state exponential batch cultures of Saccharomyces cerevisiae growing at 30 degrees C at 19 different rates, which were obtained by altering the carbon source. The analyses involved counting the number of bud scars, determining the presence or absence of buds on at least 1,000 cells, and independently measuring the doubling times (gamma) by cell number increase. A number of assumptions in the model were tested and found to be in good agreement with the model. Maximum likelihood estimates of daughter cycle time (D), parent cycle time (P), and the budded phase (B) were obtained, and we concluded that asymmetrical division occurred at all growth rates tested (gamma, 75 to 250 min). D, P, and B are all linearly related to gamma, and D, P, and gamma converge to equality (symmetrical division) at gamma = 65 min. Expressions for the genealogical age distribution for asymmetrically dividing yeast cells were derived. The fraction of daughter cells in steady-state populations is e-alpha P, and the fraction of parent cells of age n (where n is the number of buds that a cell has produced) is (e-alpha P)n-1(1-e-alpha P)2, where alpha = IN2/gamma; thus, the distribution changes with growth rate. The frequency of cells with different numbers of bud scars (i.e., different genealogical ages) was determined for all growth rates, and the observed distribution changed with the growth rate in the manner predicted. In this haploid strain new buds formed adjacent to the previous buds in a regular pattern, but at slower growth rates the pattern was more irregular. The median volume of the cells and the volume at start in the cell cycle both increased at faster growth rates. The implications of these findings for the control of the cell cycle are discussed.     

Random transitions,size control,and inheritance in cell population dynamics

A general model of cell population dynamics is derived and analyzed. The model uses the continuous structure variables age and size, and thus distinguishes individual cells with respect to such properties as cycle length and division size. The model allows the occurrence of random transitions as cells progress through the cell cycle, the control of cell size upon cell cycle events, and the inheritance of properties from mother to daughter cells. The concepts of asynchronous exponential growth, α-curves, β-curves, mother-daughter transit time correlations, and sister-sister transit time correlations are formalized. The existence and uniqueness of solutions to the model is proved.     

Analysis of protein distribution in budding yeast

Flow cytometry is a fast and sensitive method that allows monitoring of different cellular parameters on large samples of a population. Protein distributons give relevant information on growth dynamics, since they are related to the age distribution and depend on the law of growth of the population and the law of protein accumulation during the cell cycle. We analyzed protein distributions to evaluate alternative growth models for the budding yeast Saccharomyces cerevisiae and to monitor the changes in population dynamics that result from environmental modifications; such an analysis could potentially give parameters useful in the control of biotechnological processes. Theoretical protein distributions (taking into account the unequal division of yeast cells and the exponential law of protein accumulation during a cell cycle) quantitatively fit experimental distributions, once appropriate variability sources are introduced. Best fits are obtained when the protein threshold required for bud emergence increases at each new generation of parent cells.     

A stochastic, molecular model of the fission yeast cell cycle: role of the nucleocytoplasmic ratio in cycle time regulation

We propose a stochastic version of a recently published, deterministic model of the molecular mechanism regulating the mitotic cell cycle of fission yeast, Schizosaccharomyces pombe. Stochasticity is introduced in two ways: (i) by considering the known asymmetry of cell division, which produces daughter cells of slightly different sizes; and (ii) by assuming that the nuclear volumes of the two newborn cells may also differ. In this model, the accumulation of cyclins in the nucleus is proportional to the ratio of cytoplasmic to nuclear volumes. We have simulated the cell-cycle statistics of populations of wild-type cells and of wee1(-) mutant cells. Our results are consistent with well known experimental observations.     

The centrosome and asymmetric cell division

Asymmetric stem cell division is a mechanism widely employed by the cell to maintain tissue homeostasis, resulting in the production of one stem cell and one differentiating cell. However, asymmetric cell division is not limited to stem cells and is widely observed even in unicellular organisms as well as in cells that make up highly complex tissues. In asymmetric cell division, cells must organize their intracellular components along the axis of asymmetry(sometimes in the context of extracellular architecture). Recent studies have described cell asymmetry in many cell types, and in many cases such asymmetry involves the centrosome (or spindle pole body in yeast) as the center of cytoskeleton organization. In this review, I summarize recent discoveries in cellular polarity that lead to an asymmetric outcome, with a focus on centrosome function.     

Steady-State growth of budding yeast populations in well-mixed continous-flow microbial reactors

A population-balance mathematical model of microbial growth in a flow reactor is formulated which incorporates an asymmetric-division, budding-cycle model of coordinated cell and nuclear division cycles for the budding yeast Saccharomyces cerevisiae. Analytical solutions are obtained for limiting nutrient and cell-number concentrations in the reactor as functions of basic cell cycle parameters. Frequency functions for cell mass and DNA content in the resident yeast population are also derived under different assumptions concerning cell mass and DNA synthesis and bud scar accumulation. These results, which correspond to experimentally observable medium and population variables, provide new bases for evaluating budding-yeast-cell cycle models and for deducing kinetics of mass and DNA synthesis in single cells growing in steady-state, asynchronous populations.     

A model for restriction point control of the mammalian cell cycle

Inhibition of protein synthesis by cycloheximide blocks subsequent division of a mammalian cell, but only if the cell is exposed to the drug before the "restriction point" (i.e. within the first several hours after birth). If exposed to cycloheximide after the restriction point, a cell proceeds with DNA synthesis, mitosis and cell division and halts in the next cell cycle. If cycloheximide is later removed from the culture medium, treated cells will return to the division cycle, showing a complex pattern of division times post-treatment, as first measured by Zetterberg and colleagues. We simulate these physiological responses of mammalian cells to transient inhibition of growth, using a set of nonlinear differential equations based on a realistic model of the molecular events underlying progression through the cell cycle. The model relies on our earlier work on the regulation of cyclin-dependent protein kinases during the cell division cycle of yeast. The yeast model is supplemented with equations describing the effects of retinoblastoma protein on cell growth and the synthesis of cyclins A and E, and with a primitive representation of the signaling pathway that controls synthesis of cyclin D.     

Buoyant density constancy of Schizosaccharomyces pombe cells.

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

Age structure of methanol-assimilating Candida boidinii cells

A population of Candida boidinii was grown under the chemostat conditions at a dilution rate of 0.14-0.20 h-1 in a mineral medium with methanol as a sole source of carbon and energy. Its age structure was analysed taking account of the reproductive age (the number of cycles) and the cyclic age of the cells (the phase of a cell cycle). Four morphological phases of the cycle, namely, one phase of preparation for budding and three successive budding phases, were compared with the phases G1, S, G2 and M. In terms of their reproductive age, the cells can be arranged as follows: (1) cells that formed no buds at all, 43 +/- 5%; (2) cells after one cycle of budding, 28 +/- 4%; (3) cells from which two and more daughter cells have separated, 29 +/- 4%. The age structure of an yeast population must be analysed when it is necessary to estimate its physiological heterogeneity or to elaborate the cultivation of microorganisms involving the control over the age structure of the population.     

Phenotypic plasticity and effects of selection on cell division symmetry in Escherichia coli

Aging has been demonstrated in unicellular organisms and is presumably due to asymmetric distribution of damaged proteins and other components during cell division. Whether the asymmetry-induced aging is inevitable or an adaptive and adaptable response is debated. Although asymmetric division leads to aging and death of some cells, it increases the effective growth rate of the population as shown by theoretical and empirical studies. Mathematical models predict on the other hand, that if the cells divide symmetrically, cellular aging may be delayed or absent, growth rate will be reduced but growth yield will increase at optimum repair rates. Therefore in nutritionally dilute (oligotrophic) environments, where growth yield may be more critical for survival, symmetric division may get selected. These predictions have not been empirically tested so far. We report here that Escherichia coli grown in oligotrophic environments had greater morphological and functional symmetry in cell division. Both phenotypic plasticity and genetic selection appeared to shape cell division time asymmetry but plasticity was lost on prolonged selection. Lineages selected on high nutrient concentration showed greater frequency of presumably old or dead cells. Further, there was a negative correlation between cell division time asymmetry and growth yield but there was no significant correlation between asymmetry and growth rate. The results suggest that cellular aging driven by asymmetric division may not be hardwired but shows substantial plasticity as well as evolvability in response to the nutritional environment.     

The centrosome and asymmetric cell division

Asymmetric stem cell division is a mechanism widely employed by the cell to maintain tissue homeostasis, resulting in the production of one stem cell and one differentiating cell. However, asymmetric cell division is not limited to stem cells and is widely observed even in unicellular organisms as well as in cells that make up highly complex tissues. In asymmetric cell division, cells must organize their intracellular components along the axis of asymmetry (sometimes in the context of extracellular architecture). Recent studies have described cell asymmetry in many cell types and in many cases such asymmetry involves the centrosome (or spindle pole body in yeast) as the center of cytoskeleton organization. In this review, I summarize recent discoveries in cellular polarity that lead to an asymmetric outcome, with a focus on centrosome function.Key words: stem cell, asymmetric division, niche, centrosome, spindle orientation     

Slit scanning of Saccharomyces cerevisiae cells: quantification of asymmetric cell division and cell cycle progression in asynchronous culture.

Slit scanning flow cytometry has been applied to the analysis of the cell cycle and cell-cycle-dependent events in Saccharomyces cerevisiae, yielding information on the low-resolution spatial distribution of cellular components in single cells of unperturbed cell populations. Because this process is rapid, large numbers of cells can be analyzed to give distributions of parameters in a given population. To study asymmetric cell division and cell cycle progression, forward-angle light scattering (FALS) signals together with fluorescence signals from acriflavine-stained nuclei have been measured in cells from exponentially growing yeast populations. An algorithm has been developed that assigns the position of the bud neck in the FALS signals so that both FALS and DNA signals can be analyzed in terms of the contributions from the mother cell and the cell bud. The data indicate that mother cell FALS, on average, remains constant while FALS due to the cell bud increases as a cell progresses through the cell cycle. By identifying mitotic cells and measuring their properties, we have found that the coefficient of variation for the distribution of FALS is smallest within the dividing cell population and largest within the newborn cell population, in accordance with the critical size control mechanism of yeast cell growth. The use of this experimental approach to provide data for statistical population models is discussed.     

Changes in the volutin levels in yeast cells during cell cycle

Dimeric distribution of the cell number of Saccharomyces cerevisiae is analysed according to the volume and content of volutin in them. Dynamics of the age composition of the population in time when changing the medium limiting growth for the balanced one is considered. The data obtained indicate that volutin may serve as a regulator when the yeast cells pass the starting point in the division cycle, however, this event has no contrary effect on volutin accumulation.     

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

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

Modelling the fission yeast cell cycle.

The molecular networks regulating basic physiological processes in a cell can be converted into mathematical equations (eg differential equations) and solved by a computer. The division cycle of eukaryotic cells is an important example of such a control system, and fission yeast is an excellent test organism for the computational modelling approach. The mathematical model is tested by simulating wild-type cells and many known cell cycle mutants. This paper describes an example where this approach is useful in understanding multiple rounds of DNA synthesis (endoreplication) in fission yeast cells that lack the main (B-type) mitotic cyclin, Cdc13. It is proposed that the key physiological variable driving progression through the cell cycle during balanced growth and division is the mass/DNA ratio, rather than the mass/nucleus ratio.     

Combining Magnetic Sorting of Mother Cells and Fluctuation Tests to Analyze Genome Instability During Mitotic Cell Aging in Saccharomyces cerevisiae

Saccharomyces cerevisiae has been an excellent model system for examining mechanisms and consequences of genome instability. Information gained from this yeast model is relevant to many organisms, including humans, since DNA repair and DNA damage response factors are well conserved across diverse species. However, S. cerevisiae has not yet been used to fully address whether the rate of accumulating mutations changes with increasing replicative (mitotic) age due to technical constraints. For instance, measurements of yeast replicative lifespan through micromanipulation involve very small populations of cells, which prohibit detection of rare mutations. Genetic methods to enrich for mother cells in populations by inducing death of daughter cells have been developed, but population sizes are still limited by the frequency with which random mutations that compromise the selection systems occur. The current protocol takes advantage of magnetic sorting of surface-labeled yeast mother cells to obtain large enough populations of aging mother cells to quantify rare mutations through phenotypic selections. Mutation rates, measured through fluctuation tests, and mutation frequencies are first established for young cells and used to predict the frequency of mutations in mother cells of various replicative ages. Mutation frequencies are then determined for sorted mother cells, and the age of the mother cells is determined using flow cytometry by staining with a fluorescent reagent that detects bud scars formed on their cell surfaces during cell division. Comparison of predicted mutation frequencies based on the number of cell divisions to the frequencies experimentally observed for mother cells of a given replicative age can then identify whether there are age-related changes in the rate of accumulating mutations. Variations of this basic protocol provide the means to investigate the influence of alterations in specific gene functions or specific environmental conditions on mutation accumulation to address mechanisms underlying genome instability during replicative aging.     

Analysis of a model of cell cycle in eukaryotes

A dynamic model of the cell cycle for eukaryotic cells, which takes into account the rates of ribosome and protein synthesis and the discontinuous events of DNA replication and cell division, is analyzed. It is shown that, by changing the values of the parameters, three different cell cycle regimens are possible, which are similar to cell cycle patterns experimentally observed and which show the action of different control mechanisms. The model allows the determination of the macromolecular levels as a function of the cycle time. Taking into consideration the age distribution function of the cells in an ideal exponentially growing population, mathematical relations are calculated that link the levels of macromolecular components (protein, ribosomes and DNA) to the temporal parameters of the cell cycle, such as the relative duration of the S phase. It is also shown that the relative length of all cell cycle phases may be determined if the labelling index and the relative DNA content of the cell population are known. All these relations suggest new and convenient procedures to determine cell cycle parameters.