A mathematical model for cell size control in fission yeast

Experimental investigations of cell size control in fission yeast Schizosaccharomyces pombe have illustrated that the cell cycle features ‘sizer’ and ‘timer’ phases which are distinguished by a growth rate changing point. Based on current biological knowledge of fission yeast size control, we propose here a model of ordinary differential equations (ODEs) for a possible explanation of the facts and control mechanism which is coupled with the cell cycle. Simulation results of the ODE model are demonstrated to agree with experimental data for the wild type and the cdc2-33 mutant. We show that the coupling of cell growth to cell division by translational control may account for observed properties of size control in fission yeast. As the translational control in the expression of cycle proteins Cdc13 and Cdc25 constructs positive feedback loops, the dynamical activities of the key components undergoes a rapid rising after a preliminary stage of slow increase. The coupling of this dynamical behavior to the elongation of the cell naturally gives rise to a rate change point and to ‘sizer’ and ‘timer’ phases, which characterize the cell cycle of fission yeast.     

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.     

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.     

Mathematical modeling of fission yeast Schizosaccharomyces pombe cell cycle: exploring the role of multiple phosphatases

Cell cycle is the central process that regulates growth and division in all eukaryotes. Based on the environmental condition sensed, the cell lies in a resting phase G0 or proceeds through the cyclic cell division process (G1??S??G2??M). These series of events and phase transitions are governed mainly by the highly conserved Cyclin dependent kinases (Cdks) and its positive and negative regulators. The cell cycle regulation of fission yeast Schizosaccharomyces pombe is modeled in this study. The study exploits a detailed molecular interaction map compiled based on the published model and experimental data. There are accumulating evidences about the prominent regulatory role of specific phosphatases in cell cycle regulations. The current study emphasizes the possible role of multiple phosphatases that governs the cell cycle regulation in fission yeast S. pombe. The ability of the model to reproduce the reported regulatory profile for the wild-type and various mutants was verified though simulations.     

Fission yeast cells undergo nuclear division in the absence of spindle microtubules

Mitosis in eukaryotic cells employs spindle microtubules to drive accurate chromosome segregation at cell division. Cells lacking spindle microtubules arrest in mitosis due to a spindle checkpoint that delays mitotic progression until all chromosomes have achieved stable bipolar attachment to spindle microtubules. In fission yeast, mitosis occurs within an intact nuclear membrane with the mitotic spindle elongating between the spindle pole bodies. We show here that in fission yeast interference with mitotic spindle formation delays mitosis only briefly and cells proceed to an unusual nuclear division process we term nuclear fission, during which cells perform some chromosome segregation and efficiently enter S-phase of the next cell cycle. Nuclear fission is blocked if spindle pole body maturation or sister chromatid separation cannot take place or if actin polymerization is inhibited. We suggest that this process exhibits vestiges of a primitive nuclear division process independent of spindle microtubules, possibly reflecting an evolutionary intermediate state between bacterial and Archeal chromosome segregation where the nucleoid divides without a spindle and a microtubule spindle-based eukaryotic mitosis.     

Functional characterization of a B-type cell cycle switch 52 in rice (OsCCS52B)

Plant growth and development depend on a precise coordination between cell division and cell expansion. In this study, a rice cell cycle switch 52 B (OsCCS52B) was functionally characterized using two approaches: overexpression of the gene product in fission yeast and characterization of an insertion mutant line 1B-10423. In wild-type plants, OsCCS52B is highly expressed in generative organs such as flowers and kernels. Overexpression of OsCCS52B induces cell elongation and slower cell proliferation in fission yeast. Characterization of the mutant line 1B-10423 revealed that the mutant exhibits semi-dwarf and smaller kernel phenotypes. In addition, microscopic analysis of mutant kernels showed that the reduced kernel size was due to a reduced cell size. However, the nuclear size and ploidy level were unaffected. These results suggest that OsCCS52B may be involved in cell expansion regulation in rice endosperm.     

Controls over the timing of DNA replication during the cell cycle of fission yeast

The controls acting over the timing of DNA replication (S) during the cell cycle have been investigated in the fission yeast Schizosaccharomyces pombe. The cell size at which DNA replication takes place has been determined in a number of experimental situations such as growth of nitrogen-starved cells, spore germination and synchronous culture of wee mutant and wild-type strains. It is shown that in wee mutant strains and in wild type grown under conditions in which the cells are small, DNA replication takes place in cells of the same size. This suggests that there is a minimum cell size beneath which the cell cannot initiate DNA replication and it is this control which determines the timing of S during the cell cycle of the wee mutant. Fast growing wild-type cells are too large for this size control to be expressed. In these cells the timing of S may be controlled by the completion of the previous nuclear division coupled with a requirement for a minimum period in G1. Thus in S. pombe there are two different controls over the timing of S, either of which can be operative depending upon the size of the cell at cell division. It is suggested that these two controls may form a useful conceptual framework for considering the timing control over S in mammalian cells.     

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.     

A genome–wide screen to identify genes controlling the rate of entry into mitosis in fission yeast

We have carried out a haploinsufficiency (HI) screen in fission yeast using heterozygous deletion diploid mutants of a genome-wide set of cell cycle genes to identify genes encoding products whose level determines the rate of progression through the cell cycle. Cell size at division was used as a measure of advancement or delay of the G2-M transition of rod-shaped fission yeast cells. We found that 13 mutants were significantly longer or shorter (greater than 10%) than control cells at cell division. These included mutants of the cdc2, cdc25, wee1 and pom1 genes, which have previously been shown to play a role in the timing of entry into mitosis, and which validate this approach. Seven of these genes are involved in regulation of the G2-M transition, 5 for nuclear transport and one for nucleotide metabolism. In addition we identified 4 more genes that were 8–10% longer or shorter than the control that also had roles in regulation of the G2-M transition or in nuclear transport. The genes identified here are all conserved in human cells, suggesting that this dataset will be useful as a basis for further studies to identify rate-limiting steps for progression through the cell cycle in other eukaryotes.     

Effects of asymmetric division on a stochastic model of the cell division cycle

The stochastic model of cell division formulated by Alt and Tyson is generalized to the case of imprecise binary fission. Closed-form expressions are derived for the generation-time distribution, the birth-size and division-size distributions, the beta curve, and the correlation coefficient of generation times of sister cells. The theoretical results are compared to observations of cell division statistics in a culture of fission yeast.     

Colcemid-resistant mutants of fission yeast have an altered cell cycle

Cell-cycle progression is altered in some colcemid-resistant mutants of fission yeast. The duration of particular stages of the cell cycle is different but total doubling time is unchanged from that of wild type. Cell-plate formation is prolonged relative to wild type but concomitant DNA synthesis is not affected. Separation of daughter cells is inhibited in some strains, giving rise to unusual cell morphologies. Control of cell division is altered in two ways: Critical size for division is increased. The probability of division a function of size is decreased.     

The protein kinase kin1 is required for cellular symmetry in fission yeast

The fission yeast Schizosaccharomyces pombe is a highly polarized unicellular eukaryote with two opposite growing poles in which F-actin cytoskeleton is focused. The KIN1/PAR-1/MARK protein family is composed of conserved eukaryotic serine/threonine kinases which are involved in cell polarity, microtubule stability or cell cycle regulation. Here, we investigate the function of the fission yeast KIN1/PAR-1/MARK member, kin1p. Using a deletion allele (kin1Delta), we show that kin1 mutation promotes a delay in septation. Kin1p regulates the structure of the new cell end after cytokinesis by modulating cell wall remodeling. Abnormal shaped interphase kin1Delta cells misplace F-actin patches and the premitotic nucleus. Thus, mitotic kin1Delta cells misposition the F-actin ring assembly site that is dependent on the position of the interphase nucleus. The resulting asymmetric cell division produces daughter cells with distinct shapes. Overexpressed kin1p accumulates asymmetrically at the cell cortex and affects cell shape, F-actin organization and microtubules. Our results suggest that correct dosage of kin1p at the cortex is required for spatial organization of the fission yeast cell.     

Nuclear and division-plane positioning revealed by optical micromanipulation

The position of the division plane affects cell shape and size, as well as tissue organization. Cells of the fission yeast Schizosaccharomyces pombe have a centrally placed nucleus and divide by fission at the cell center. Microtubules (MTs) are required for the central position of the nucleus. Genetic studies lead to the hypothesis that the position of the nucleus may determine the position of the division plane. Alternatively, the division plane may be positioned by the spindle or by morphogen gradients or reaction diffusion mechanisms. Here, we investigate the role of MTs in nuclear positioning and the role of the nucleus in division-plane positioning by displacing the nucleus with optical tweezers. A displaced nucleus returned to the cell center by MT pushing against the cell tips. Nuclear displacement during interphase or early prophase resulted in asymmetric cell division, whereas displacement during prometaphase resulted in symmetric division as in unmanipulated cells. These results suggest that the division plane is specified by the predividing nucleus. Because the yeast nucleus is centered by MTs during interphase but not in mitosis, we hypothesize that the establishment of the division plane at the beginning of mitosis is an optimal mechanism for accurate symmetric division in these cells.     

Genetic analysis of cell morphogenesis in fission yeast--a role for casein kinase II in the establishment of polarized growth.

We have initiated a study to identify genes regulating cell morphogenesis in the fission yeast Schizosaccharomyces pombe. Five genes have been identified, orb1-orb5, whose mutation gives rise to spherical cells, indicative of an inability to polarize growth. Two further genes have been identified, tea1 and ban1, whose mutant alleles have disturbed patterns of tip growth, leading to T-shaped and curved cells. In fission yeast, sites of cell wall deposition are defined by actin localization, with actin distributions and therefore growth patterns undergoing cell cycle stage-specific reorganization. Studies of double mutants constructed between orb5-19 and various cdc mutants blocked before and after cell division show that orb5 is required for the re-establishment of polar growth following cytokinesis. This indicates that the mutant allele orb5-19 is defective in the reinitiation of polarized growth, even though actin reorganization to the cell tips occurs normally. orb5 encodes a fission yeast homologue of casein kinase II alpha. We propose that this kinase plays a role in the translation of cell polarity into polarized growth, but not in the establishment of polarity itself.     

Cell Cycle Control by a Minimal Cdk Network

In present-day eukaryotes, the cell division cycle is controlled by a complex network of interacting proteins, including members of the cyclin and cyclin-dependent protein kinase (Cdk) families, and the Anaphase Promoting Complex (APC). Successful progression through the cell cycle depends on precise, temporally ordered regulation of the functions of these proteins. In light of this complexity, it is surprising that in fission yeast, a minimal Cdk network consisting of a single cyclin-Cdk fusion protein can control DNA synthesis and mitosis in a manner that is indistinguishable from wild type. To improve our understanding of the cell cycle regulatory network, we built and analysed a mathematical model of the molecular interactions controlling the G1/S and G2/M transitions in these minimal cells. The model accounts for all observed properties of yeast strains operating with the fusion protein. Importantly, coupling the model’s predictions with experimental analysis of alternative minimal cells, we uncover an explanation for the unexpected fact that elimination of inhibitory phosphorylation of Cdk is benign in these strains while it strongly affects normal cells. Furthermore, in the strain without inhibitory phosphorylation of the fusion protein, the distribution of cell size at division is unusually broad, an observation that is accounted for by stochastic simulations of the model. Our approach provides novel insights into the organization and quantitative regulation of wild type cell cycle progression. In particular, it leads us to propose a new mechanistic model for the phenomenon of mitotic catastrophe, relying on a combination of unregulated, multi-cyclin-dependent Cdk activities.     

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.     

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.     

A protein kinase specifically associated with proliferative forms of Trypanosoma brucei is functionally related to a yeast kinase involved in the co-ordination of cell shape and division

The life cycle of African trypanosomes is characterized by the alternation of proliferative and quiescent stages but the molecular details of this process remain unknown. Here, we describe a new cytoplasmic protein kinase from Trypanosoma brucei, termed TBPK50, that belongs to a family of protein kinases involved in the regulation of the cell cycle, cell shape and proliferation. TBPK50 is expressed only in proliferative forms but is totally absent in quiescent cells despite the fact that the gene is constitutively transcribed at the same level throughout the life cycle. It is probable that TBPK50 has very specific substrate requirements as it was unable to transphosphorylate a range of classical phosphoacceptor substrates in vitro, although an autophosphorylation activity was readily detectable in the same assays. Complementation studies using a fission yeast mutant demonstrated that TBPK50 is a functional homologue of Orb6, a protein kinase involved in the regulation of cellular morphology and cell cycle progression in yeast. These results link the expression of TBPK50 and the growth status of trypanosomes and support the view that this protein kinase is likely to be involved in the control of life cycle progression and cell division of these parasites.