Integrative analysis of cell cycle control in budding yeast

The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of >100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wild-type and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.     

Logical analysis of the budding yeast cell cycle

The budding yeast Saccharomyces cerevisiae is a model organism that is commonly used to investigate control of the eukaryotic cell cycle. Moreover, because of the extensive experimental data on wild type and mutant phenotypes, it is also particularly suitable for mathematical modelling and analysis. Here, I present a new Boolean model of the budding yeast cell cycle. This model is consistent with a wide range of wild type and mutant phenotypes and shows remarkable robustness against perturbations, both to reaction times and the states of component genes/proteins. Because of its simple logical nature, the model is suitable for sub-network analysis, which can be used to identify a four node core regulatory circuit underlying cell cycle regulation. Sub-network analysis can also be used to identify key sub-dynamics that are essential for viable cell cycle control, as well as identifying the sub-dynamics that are most variable between different mutants.     

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.     

Kinetic analysis of a molecular model of the budding yeast cell cycle

The molecular machinery of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than for any other eukaryotic organism. In recent years, many elegant experiments on budding yeast have dissected the roles of cyclin molecules (Cln1-3 and Clb1-6) in coordinating the events of DNA synthesis, bud emergence, spindle formation, nuclear division, and cell separation. These experimental clues suggest a mechanism for the principal molecular interactions controlling cyclin synthesis and degradation. Using standard techniques of biochemical kinetics, we convert the mechanism into a set of differential equations, which describe the time courses of three major classes of cyclin-dependent kinase activities. Model in hand, we examine the molecular events controlling "Start" (the commitment step to a new round of chromosome replication, bud formation, and mitosis) and "Finish" (the transition from metaphase to anaphase, when sister chromatids are pulled apart and the bud separates from the mother cell) in wild-type cells and 50 mutants. The model accounts for many details of the physiology, biochemistry, and genetics of cell cycle control in budding yeast.     

Mathematical model of the morphogenesis checkpoint in budding yeast

The morphogenesis checkpoint in budding yeast delays progression through the cell cycle in response to stimuli that prevent bud formation. Central to the checkpoint mechanism is Swe1 kinase: normally inactive, its activation halts cell cycle progression in G2. We propose a molecular network for Swe1 control, based on published observations of budding yeast and analogous control signals in fission yeast. The proposed Swe1 network is merged with a model of cyclin-dependent kinase regulation, converted into a set of differential equations and studied by numerical simulation. The simulations accurately reproduce the phenotypes of a dozen checkpoint mutants. Among other predictions, the model attributes a new role to Hsl1, a kinase known to play a role in Swe1 degradation: Hsl1 must also be indirectly responsible for potent inhibition of Swe1 activity. The model supports the idea that the morphogenesis checkpoint, like other checkpoints, raises the cell size threshold for progression from one phase of the cell cycle to the next.     

A mathematical model of mitotic exit in budding yeast: the role of Polo kinase

Cell cycle progression in eukaryotes is regulated by periodic activation and inactivation of a family of cyclin-dependent kinases (Cdk's). Entry into mitosis requires phosphorylation of many proteins targeted by mitotic Cdk, and exit from mitosis requires proteolysis of mitotic cyclins and dephosphorylation of their targeted proteins. Mitotic exit in budding yeast is known to involve the interplay of mitotic kinases (Cdk and Polo kinases) and phosphatases (Cdc55/PP2A and Cdc14), as well as the action of the anaphase promoting complex (APC) in degrading specific proteins in anaphase and telophase. To understand the intricacies of this mechanism, we propose a mathematical model for the molecular events during mitotic exit in budding yeast. The model captures the dynamics of this network in wild-type yeast cells and 110 mutant strains. The model clarifies the roles of Polo-like kinase (Cdc5) in the Cdc14 early anaphase release pathway and in the G-protein regulated mitotic exit network.     

Towards understanding of the complex structure of growing yeast populations

In a growing Saccharomyces cerevisiae population, cell size is finely modulated according to both the chronological and genealogical ages. This generates the complex heterogeneous structure typical of budding yeast populations. In recent years, there has been a growing interest in developing mathematical models capable of faithfully describing population dynamics at the single cell level. A multistaged morphologically structured model has been lately proposed based on the population balance theory. The model was able to describe the dynamics of the generation of a heterogeneous growing yeast population starting from a sub-population of daughter unbudded cells. In this work, which aims at validating the model, the simulated experiment was performed by following the release of a homogeneous population of daughter unbudded cells. A biparametric flow cytometric approach allowed us to analyse the time course joint distribution of DNA and protein contents at the single cell level; this gave insights into the coupling between growth and cell cycle progression that generated the final population structure. The comparison between experimental and simulated size distributions revealed a strong agreement for some unexpected features as well. Therefore, the model can be considered as validated and extendable to more complex situations.     

Swm1/Apc13 is an evolutionarily conserved subunit of the anaphase-promoting complex stabilizing the association of Cdc16 and Cdc27

The anaphase-promoting complex (APC/C) is a large ubiquitin-protein ligase which controls progression through anaphase by triggering the degradation of cell cycle regulators such as securin and B-type cyclins. The APC/C is an unusually complex ligase containing at least 10 different, evolutionarily conserved components. In contrast to APC/C's role in cell cycle regulation little is known about the functions of individual subunits and how they might interact with each other. Here, we have analyzed Swm1/Apc13, a small subunit recently identified in the budding yeast complex. Database searches revealed proteins related to Swm1/Apc13 in various organisms including humans. Both the human and the fission yeast homologues are associated with APC/C subunits, and they complement the phenotype of an SWM1 deletion mutant of budding yeast. Swm1/Apc13 promotes the stable association with the APC/C of the essential subunits Cdc16 and Cdc27. Accordingly, Swm1/Apc13 is required for ubiquitin ligase activity in vitro and for the timely execution of APC/C-dependent cell cycle events in vivo.     

Quantitative characterization of a mitotic cyclin threshold regulating exit from mitosis

Regulation of cyclin abundance is central to eukaryotic cell cycle control. Strong overexpression of mitotic cyclins is known to lock the system in mitosis, but the quantitative behavior of the control system as this threshold is approached has only been characterized in the in vitro Xenopus extract system. Here, we quantitate the threshold for mitotic block in budding yeast caused by constitutive overexpression of the mitotic cyclin Clb2. Near this threshold, the system displays marked loss of robustness, in that loss or even heterozygosity for some regulators becomes deleterious or lethal, even though complete loss of these regulators is tolerated at normal cyclin expression levels. Recently, we presented a quantitative kinetic model of the budding yeast cell cycle. Here, we use this model to generate biochemical predictions for Clb2 levels, asynchronous as well as through the cell cycle, as the Clb2 overexpression threshold is approached. The model predictions compare well with biochemical data, even though no data of this type were available during model generation. The loss of robustness of the Clb2 overexpressing system is also predicted by the model. These results provide strong confirmation of the model's predictive ability.     

Regularities and irregularities in the cell cycle of the fission yeast,Schizosaccharomyces pombe (a review)

In an exponentially growing wild-type fission yeast culture a size control mechanism ensures that mitosis is executed only if the cells have reached a critical size. However, there is some scattering both in cell length at birth (BL) and in cycle time (CT). By computational simulations we show here that this scattering cannot be explained solely by asymmetric cell division, therefore we assume that nuclear division is a stochastic, asymmetric process as well. We introduce an appropriate stochastic variable into a mathematical model and prove that this assumption is suitable to describe the CT vs. BL graph in a wild-type fission yeast population. In a double mutant of fission yeast (namely wee1-50 cdc25 delta) this CT vs. BL plot is even more curious: cycle time splits into three different values resulting in three clusters in this coordinate system. We show here that it is possible to describe these quantized cycles by choosing the appropriate values of the key parameters of mitotic entry and exit and even more the clustered behavior may be simulated by applying a further stochastic parameter.     

Stochastic exit from mitosis in budding yeast

Unlike many mutants that are completely viable or inviable, the CLB2-dbΔ clb5Δ mutant of Saccharomyces cerevisiae is inviable in glucose but partially viable on slower growth media such as raffinose. On raffinose, the mutant cells can bud and divide but in each cycle there is a chance that a cell will fail to divide (telophase arrest), causing it to exit the cell cycle. This effect gives rise to a stochastic phenotype that cannot be explained by a deterministic model. We measure the inter-bud times of wild type and mutant cells growing on raffinose and compute statistics and distributions to characterize the mutant’s behavior. We convert a detailed deterministic model of the budding yeast cell cycle to a stochastic model and determine the extent to which it captures the stochastic phenotype of the mutant strain. Predictions of the mathematical model are in reasonable agreement with our experimental data and suggest directions for improving the model. Ultimately, the ability to accurately model stochastic phenotypes may prove critical to understanding disease and therapeutic interventions in higher eukaryotes.     

Inactivation of the cyclin-dependent kinase Cdc28 abrogates cell cycle arrest induced by DNA damage and disassembly of mitotic spindles in Saccharomyces cerevisiae.

Eukaryotic cells may halt cell cycle progression following exposure to certain exogenous agents that damage cellular structures such as DNA or microtubules. This phenomenon has been attributed to functions of cellular control mechanisms termed checkpoints. Studies with the fission yeast Schizosaccharomyces pombe and mammalian cells have led to the conclusion that cell cycle arrest in response to inhibition of DNA replication or DNA damage is a result of down-regulation of the cyclin-dependent kinases (CDKs). Based on these studies, it has been proposed that inhibition of the CDK activity may constitute a general mechanism for checkpoint controls. Observations made with the budding yeast Saccharomyces cerevisiae, however, appear to disagree with this model. It has been shown that high levels of mitotic CDK activity are present in the budding yeast cells arrested in G2/mitosis as the result of DNA damage or replication inhibition. In this report, we show that a novel mutant allele of the CDC28 gene, encoding the budding yeast CDK, allowed cell cycle passage through mitosis and nuclear division in the presence of DNA damage and the microtubule toxin nocodazole at a restrictive temperature. Unlike the checkpoint-defective mutations in CDKs of fission yeast and mammalian cells, the cdc28 mutation that we identified was recessive and resulted in a loss of the CDK activity, including the Clb2-, Clb5-, and Clb6-associated, but not the Clb3-associated, CDK activities. Examination of several known alleles of cdc28 revealed that they were also, albeit partially, defective in cell cycle arrest in response to UV-generated DNA damage. These findings suggest that Cdc28 kinase in budding yeast may be required for cell cycle arrest resulting from DNA damage and disassembly of mitotic spindles.     

Mitochondrial manoeuvres: latest insights and hypotheses on mitochondrial partitioning during mitosis in Saccharomyces cerevisiae

Movement and positional control of mitochondria and other organelles are coordinated with cell cycle progression in the budding yeast, Saccharomyces cerevisiae. Recent studies have revealed a checkpoint that inhibits cytokinesis when there are severe defects in mitochondrial inheritance. An established checkpoint signaling pathway, the mitotic exit network (MEN), participates in this process. Here, we describe mitochondrial motility during inheritance in budding yeast, emerging evidence for mitochondrial quality control during inheritance, and organelle inheritance checkpoints for mitochondria and other organelles.     

Cell size at S phase initiation: an emergent property of the G1/S network

The eukaryotic cell cycle is the repeated sequence of events that enable the division of a cell into two daughter cells. It is divided into four phases: G₁, S, G₂, and M. Passage through the cell cycle is strictly regulated by a molecular interaction network, which involves the periodic synthesis and destruction of cyclins that bind and activate cyclin-dependent kinases that are present in nonlimiting amounts. Cyclin-dependent kinase inhibitors contribute to cell cycle control. Budding yeast is an established model organism for cell cycle studies, and several mathematical models have been proposed for its cell cycle. An area of major relevance in cell cycle control is the G₁ to S transition. In any given growth condition, it is characterized by the requirement of a specific, critical cell size, P_S, to enter S phase. The molecular basis of this control is still under discussion. The authors report a mathematical model of the G₁ to S network that newly takes into account nucleo/cytoplasmic localization, the role of the cyclin-dependent kinase Sic1 in facilitating nuclear import of its cognate Cdk1-Clb5, Whi5 control, and carbon source regulation of Sic1 and Sic1-containing complexes. The model was implemented by a set of ordinary differential equations that describe the temporal change of the concentration of the involved proteins and protein complexes. The model was tested by simulation in several genetic and nutritional setups and was found to be neatly consistent with experimental data. To estimate P_S, the authors developed a hybrid model including a probabilistic component for firing of DNA replication origins. Sensitivity analysis of P_S provides a novel relevant conclusion: P_S is an emergent property of the G₁ to S network that strongly depends on growth rate.     

Timing Robustness in the Budding and Fission Yeast Cell Cycles

Robustness of biological models has emerged as an important principle in systems biology. Many past analyses of Boolean models update all pending changes in signals simultaneously (i.e., synchronously), making it impossible to consider robustness to variations in timing that result from noise and different environmental conditions. We checked previously published mathematical models of the cell cycles of budding and fission yeast for robustness to timing variations by constructing Boolean models and analyzing them using model-checking software for the property of speed independence. Surprisingly, the models are nearly, but not totally, speed-independent. In some cases, examination of timing problems discovered in the analysis exposes apparent inaccuracies in the model. Biologically justified revisions to the model eliminate the timing problems. Furthermore, in silico random mutations in the regulatory interactions of a speed-independent Boolean model are shown to be unlikely to preserve speed independence, even in models that are otherwise functional, providing evidence for selection pressure to maintain timing robustness. Multiple cell cycle models exhibit strong robustness to timing variation, apparently due to evolutionary pressure. Thus, timing robustness can be a basis for generating testable hypotheses and can focus attention on aspects of a model that may need refinement.     

Identifying responsive modules by mathematical programming: an application to budding yeast cell cycle

High-throughput biological data offer an unprecedented opportunity to fully characterize biological processes. However, how to extract meaningful biological information from these datasets is a significant challenge. Recently, pathway-based analysis has gained much progress in identifying biomarkers for some phenotypes. Nevertheless, these so-called pathway-based methods are mainly individual-gene-based or molecule-complex-based analyses. In this paper, we developed a novel module-based method to reveal causal or dependent relations between network modules and biological phenotypes by integrating both gene expression data and protein-protein interaction network. Specifically, we first formulated the identification problem of the responsive modules underlying biological phenotypes as a mathematical programming model by exploiting phenotype difference, which can also be viewed as a multi-classification problem. Then, we applied it to study cell-cycle process of budding yeast from microarray data based on our biological experiments, and identified important phenotype- and transition-based responsive modules for different stages of cell-cycle process. The resulting responsive modules provide new insight into the regulation mechanisms of cell-cycle process from a network viewpoint. Moreover, the identification of transition modules provides a new way to study dynamical processes at a functional module level. In particular, we found that the dysfunction of a well-known module and two new modules may directly result in cell cycle arresting at S phase. In addition to our biological experiments, the identified responsive modules were also validated by two independent datasets on budding yeast cell cycle.     

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.