The control of mitosis in Physarum polycephalum. The effect of lowering the DNA: mass ratio by UV irradiation

Time-keeping and decision-making in the cell cycle

Cell growth, DNA replication, mitosis and division are the fundamental processes by which life is passed on from one generation of eukaryotic cells to the next. The eukaryotic cell cycle is intrinsically a periodic process but not so much a ‘clock’ as a ‘copy machine’, making new daughter cells as warranted. Cells growing under ideal conditions divide with clock-like regularity; however, if they are challenged with DNA-damaging agents or mitotic spindle disrupters, they will not progress to the next stage of the cycle until the damage is repaired. These ‘decisions’ (to exit and re-enter the cell cycle) are essential to maintain the integrity of the genome from generation to generation. A crucial challenge for molecular cell biologists in the 1990s was to unravel the genetic and biochemical mechanisms of cell cycle control in eukaryotes. Central to this effort were biochemical studies of the clock-like regulation of ‘mitosis promoting factor’ during synchronous mitotic cycles of fertilized frog eggs and genetic studies of the switch-like regulation of ‘cyclin-dependent kinases' in yeast cells. In this review, we uncover some secrets of cell cycle regulation by mathematical modelling of increasingly more complex molecular regulatory networks of cell cycle ‘clocks’ and ‘switches’.

Dilution and titration of cell-cycle regulators may control cell size in budding yeast

The size of a cell sets the scale for all biochemical processes within it, thereby affecting cellular fitness and survival. Hence, cell size needs to be kept within certain limits and relatively constant over multiple generations. However, how cells measure their size and use this information to regulate growth and division remains controversial. Here, we present two mechanistic mathematical models of the budding yeast (S. cerevisiae) cell cycle to investigate competing hypotheses on size control: inhibitor dilution and titration of nuclear sites. Our results suggest that an inhibitor-dilution mechanism, in which cell growth dilutes the transcriptional inhibitor Whi5 against the constant activator Cln3, can facilitate size homeostasis. This is achieved by utilising a positive feedback loop to establish a fixed size threshold for the Start transition, which efficiently couples cell growth to cell cycle progression. Yet, we show that inhibitor dilution cannot reproduce the size of mutants that alter the cell’s overall ploidy and WHI5 gene copy number. By contrast, size control through titration of Cln3 against a constant number of genomic binding sites for the transcription factor SBF recapitulates both size homeostasis and the size of these mutant strains. Moreover, this model produces an imperfect ‘sizer’ behaviour in G1 and a ‘timer’ in S/G2/M, which combine to yield an ‘adder’ over the whole cell cycle; an observation recently made in experiments. Hence, our model connects these phenomenological data with the molecular details of the cell cycle, providing a systems-level perspective of budding yeast size control.

Proliferating cells need to coordinate the initiation of genome replication and cell division with cell growth. In particular, the average time between two division events must precisely allow for a doubling in cell volume. Any systematic deviation from this balance would lead to progressive changes in cell size over consecutive generations and to a breakdown of biochemical processes. Here, we study two molecular mechanisms by which budding yeast cells might achieve this coordination. Through mathematical modelling, we show that the dilution of an inhibitor of cell cycle progression by cell growth can facilitate size homeostasis. But this mechanism fails to reproduce the size of mutant cells in which parts of the control machinery have been altered. By contrast, the titration of an activator against a constant number of genomic sites recapitulates these data and achieves size homeostasis. Since the control network of cell cycle progression in budding yeast is structurally similar to mammalian cells, our model could indicate a common mechanism for size control.

Enrichment and screening of heat-sensitive mutants of Physarum polycephalum

A new method for the isolation of temperature-sensitive mutants of Physarum polycephalum is described. It involves enrichment and prescreening of mutagenized amoebae followed by screening at both the plasmodial and amoebal stage. A total of 74 temperature-sensitive strains were recovered of which 26 were temperature-sensitive only as plasmodia, 35 only as amoebae and 13 in both stages. After a shift to the nonpermissive temperature, DNA and protein synthesis were followed in temperature-sensitive plasmodia to discover if the lesion affected functions of the nuclear cycle.

Growth during the cell cycle

During the cell cycle, major bulk parameters such as volume, dry mass, total protein, and total RNA double and such growth is a fundamental property of the cell cycle. The patterns of growth in volume and total protein or RNA provide an "envelope" that contains and may restrict the gear wheels. The main parameters of cell cycle growth were established in the earlier work when people moved from this field to the reductionist approaches of molecular biology, but very little is known on the patterns of metabolism. Most of the bulk properties of cells show a continuous increase during the cell cycle, although the exact pattern of this increase may vary. Since the earliest days, there have been two popular models, based on an exponential increase and linear increase. In the first, there is no sharp change in the rate of increase through the cycle but a smooth increase by a factor of two. In the second, the rate of increase stays constant through much of the cycle but it doubles sharply at a rate change point (RCP). It is thought that the exponential increase is caused by the steady growth of ribosome numbers and the linear pattern is caused by a doubling of the structural genes during the S period giving an RCP--a "gene dosage" effect. In budding yeast, there are experiments fitting both models but on balance slightly favoring "gene dosage." In fission yeast, there is no good evidence of exponential increase. All the bulk properties, except O2 consumption, appear to follow linear patterns with an RCP during the short S period. In addition, there is in wild-type cells a minor RCP in G2 where the rate increases by 70%. In mammalian cells, there is good but not extensive evidence of exponential increase. In Escherichia coli, exponential increase appears to be the pattern. There are two important points: First, some proteins do not show peaks of periodic synthesis. If they show patterns of exponential increase both they and the total protein pattern will not be cell cycle regulated. However, if the total protein pattern is not exponential, then a majority of the individual proteins will be so regulated. If this majority pattern is linear, then it can be detected from rate measurements on total protein. However, it would be much harder at the level of individual proteins where the methods are at present not sensitive enough to detect a rate change by a factor of two. At a simple level, it is only the exponential increase that is not cell cycle regulated in a synchronous culture. The existence of a "size control" is well known and the control has been studied for a long time, but it has been remarkably resistant to molecular analysis. The attainment of a critical size triggers the periodic events of the cycle such as the S period and mitosis. This control acts as a homeostatic effector that maintains a constant "average" cell size at division through successive cycles in a growing culture. It is a vital link coordinating cell growth with periodic events of the cycle. A size control is present in all the systems and appears to operate near the start of S or of mitosis when the cell has reached a critical size, but the molecular mechanism by which size is measured remains both obscure and a challenge. A simple version might be for the cell to detect a critical concentration of a gene product.

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.

The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions

A deterministic/probabilistic model of the cell division cycle is analysed mathematically and compared to experimental data and to other models of the cell cycle. The model posits a random-exiting phase of the cell cycle and a minimum-size requirement for entry into the random-exiting phase. By design, the model predicts exponential "beta-curves", which are characteristic of sister cell generation times. We show that the model predicts "alpha-curves" with exponential tails and hyperbolic-sine-like shoulders, and that these curves fit observed generation-time data excellently. We also calculate correlation coefficients for sister cells and for mother-daughter pairs. These correlation coefficients are more negative than is generally observed, which is characteristic of all size-control models and is generally attributed to some unknown positive correlation in growth rates of related cells. Next we compare theoretical size distributions with observed distributions, and we calculate the dependence of average cell mass on specific growth rate and show that this dependence agrees with a well-known relation in bacteria. In the discussion we argue that unequal division is probably not the source of stochastic fluctuations in deterministic size-control models, transition-probability models with no feedback from cell size cannot account for the rapidity with which the new, stable size distribution is established after perturbation, and Kubitschek's rate-normal model is not consistent with exponential beta-curves.

Control of cell-cycle timing in early embryos of Caenorhabditis elegans

A technique has been developed for extruding either substantial amounts of cytoplasm without nuclei or individual nuclei with small amounts of cytoplasm from early embryos of C. elegans after perforating the eggshell with a laser microbeam. This technique, in conjunction with laser-induced cell fusion, has allowed the altering of nuclear/cytoplasmic ratios and the exposing of the nucleus of one cell to cytoplasm from another. Using these approaches the roles of nuclei and cytoplasm in determining the different cell-cycle periods of the several blastomere lineages in early embryos have been examined. It was found that nuclei in a common cytoplasm divide synchronously; enucleated blastomeres retain a cycling period characteristic of their lineage; cycling period is not substantially affected by changes in the ratio of nuclear to cytoplasmic volumes or the DNA content per cell; the period of a cell from one lineage can be substantially altered by introduction of cytoplasm from a cell of another lineage with a different period; and short-term effects of foreign cytoplasm on the timing of the subsequent mitosis differ depending on position of the donor cell in the cell cycle. These results are discussed in connection with models for the action of cytoplasmic factors in controlling cell-cycle timing.

Mitotic delays and macromolecular synthesis in G2 phase-irradiated plasmodia of Physarum polycephalum

Mitotically synchronous surface plasmodia of Physarum polycephalum were irradiated at different times of G2 phase with doses of UV ranging from 350 to 2800 Jm-2. The UV sensitivity, measured in terms of delay in progression towards mitosis, gradually declined through G2 phase to almost zero in early prophase, when irradiated with 350 Jm-2 of UV. However, with higher doses, 700 and 1400 Jm-2, late G2 was found to be even more susceptible than early G2. The delay in these cases rises for the last 0.1 part of the cycle up to a UV-transition point in early prophase. Thus, processes which were not sensitive to a lower dose of UV are affected by higher doses. Above 700 Jm-2, delay was not directly proportional to dose. With doses above 1400 Jm-2, the delays obtained were more variable, although some tendency for an increased delay is observed in plasmodia irradiated in late G2 when compared with those irradiated in middle G2. The least UV-sensitive phase is between -0.2 and -0.4 part of the cycle in relation to mitosis (0 point). Both RNA synthesis and protein synthesis are inhibited in plasmodia irradiated at any time during G2 phase with 1400 Jm-2 of UV. However, on an average, irradiation in late G2 caused the most inhibitions.

Unstable activator models for size control of the cell cycle

The unstable activator model of Wheals & Silverman (1982) is extended to account for the delay of nuclear division in the acellular slime mold, Physarum polycephalum, that is caused by pulse treatments with inhibitors of protein synthesis. The model is solved exactly to predict the delay as a function of the half-life of the activator. The Wheals-Silverman model is found to give results comparable, but not superior, to other unstable activator models of the cell cycle.

Isolation of cell size mutants of a fission yeast by a new selective method: characterization of mutants and implications for division control mechanisms

Previously known cell size (wee) mutations of fission yeast suppress the mitotic block caused by a defective cdc25 allele. Some 700 revertants of cdc25-22 were obtained after ultraviolet mutagenesis and selection at the restrictive temperature. Most revertants carried the original cdc25 lesion plus a mutation in or very close to the wee1 gene. Two partial wee1 mutations of a new type were found among the revertants. Two new wee mutations mapping at the cdc2 gene (cdc2-w mutants) were also obtained. The various mutations were examined for their effects on cell division size, their efficiency as cdc25 suppressors, and their dominance relations. Full wee1 mutations were found to suppress cdc25 lesions very efficiently, whereas partial wee1 mutations were poor suppressors. The cdc25 suppression ability of cdc2-w mutations was allele specific for cdc2, suggesting bifunctionality of the gene product. The wee1 mutations were recessive for cdc25 suppression; cdc2-w mutations were dominant. A model is proposed for the genetic control of mitotic timing and cell division size, in which the cdc2+ product is needed and is rate limiting for mitosis. The cdc2+ activity is inhibited by the wee1+ product, whereas the cdc25+ product relieves this inhibition.

Cycloheximide-induced mitotic delay in Physarum polycephalum

Cycloheximide pulses applied to Physarum polycephalum surface plasmodia delay mitosis. Pulses applied in G2 cause a delay of mitosis which is linearly dependent on the phase in the cell cycle at which the pulse is applied. A 30 min pulse of 10 micrograms/ml cycloheximide starting in G2 at time t after mitosis induces an excess delay (delay in excess of pulse duration) of the next mitosis of (0.55) t-1.3 h. The excess delays induced by 7 h pulses during G2 are at most 1 h larger. Pulses applied less than 30 min before mitosis induce only small delays.