Checkpoints in the cell cycle from a modeler's perspective

A Stochastic Model of the Yeast Cell Cycle Reveals Roles for Feedback Regulation in Limiting Cellular Variability

The cell division cycle of eukaryotes is governed by a complex network of cyclin-dependent protein kinases (CDKs) and auxiliary proteins that govern CDK activities. The control system must function reliably in the context of molecular noise that is inevitable in tiny yeast cells, because mistakes in sequencing cell cycle events are detrimental or fatal to the cell or its progeny. To assess the effects of noise on cell cycle progression requires not only extensive, quantitative, experimental measurements of cellular heterogeneity but also comprehensive, accurate, mathematical models of stochastic fluctuations in the CDK control system. In this paper we provide a stochastic model of the budding yeast cell cycle that accurately accounts for the variable phenotypes of wild-type cells and more than 20 mutant yeast strains simulated in different growth conditions. We specifically tested the role of feedback regulations mediated by G1- and SG2M-phase cyclins to minimize the noise in cell cycle progression. Details of the model are informed and tested by quantitative measurements (by fluorescence in situ hybridization) of the joint distributions of mRNA populations in yeast cells. We use the model to predict the phenotypes of ~30 mutant yeast strains that have not yet been characterized experimentally.

The cell division cycle—the process by which a living cell makes a new replica of itself—is fundamental to all aspects of biological growth, development and reproduction. If cells make mistakes in cell cycle progression, they may die or give birth to aberrant progeny. Such mistakes are the root cause of serious human diseases such as cancer. Hence, we would like to understand how cells control cell cycle events and correct mistakes before they do serious damage. Yeast cells are especially suited to studying cell cycle progression because so much is known about the underlying molecular control system, and because yeast cells—being so small—are especially vulnerable to random fluctuations in molecular regulators of the cell cycle. Experimental studies have identified feedback signals in the regulatory network that appear to keep these fluctuations within manageable limits. To place these proposals in a rigorous theoretical framework, we present a stochastic model of the major feedback controls in the yeast cell cycle. Our model accounts accurately for a range of observations about cell cycle variability in wild-type and mutant cells, and makes a host of verifiable predictions about mutant strains that are seriously compromised in cell cycle progression.

Experimental testing of a new integrated model of the budding yeast Start transition

Mathematical modeling of the cell cycle has unveiled recurrent features and emergent behaviors of cellular networks. Constructing new mutants and performing experimental tests during development of a new model of the budding yeast cell cycle yields a more efficient modeling process and results in several testable hypotheses.

The cell cycle is composed of bistable molecular switches that govern the transitions between gap phases (G1 and G2) and the phases in which DNA is replicated (S) and partitioned between daughter cells (M). Many molecular details of the budding yeast G1–S transition (Start) have been elucidated in recent years, especially with regard to its switch-like behavior due to positive feedback mechanisms. These results led us to reevaluate and expand a previous mathematical model of the yeast cell cycle. The new model incorporates Whi3 inhibition of Cln3 activity, Whi5 inhibition of SBF and MBF transcription factors, and feedback inhibition of Whi5 by G1–S cyclins. We tested the accuracy of the model by simulating various mutants not described in the literature. We then constructed these novel mutant strains and compared their observed phenotypes to the model’s simulations. The experimental results reported here led to further changes of the model, which will be fully described in a later article. Our study demonstrates the advantages of combining model design, simulation, and testing in a coordinated effort to better understand a complex biological network.

The ethanol extract isolated from Weiqi Decoction induces G₂/M arrest and apoptosis in AGS cells

OBJECTIVE

To evaluate the effects of the ethanol extract isolated from Weiqi Decoction (WQD-EE) on AGS cell proliferation and apoptosis.

METHODS

By using high-performance liquid chromatography with ultraviolet detectors (HPLC-UV) assay and MTT method, the main compounds in WQD-EE and cell viability were detected. And cell cycle distributions were determined by flow cytometry with propidium iodine (PI) staining while apoptosis was detected by flow cytometry with annexin V/PI double staining. Finally, caspase-3 activities were measured by colorimetric method and protein expression was determined by Western blotting.

RESULTS

HPLC analysis showed that naringin (35.92 μg/mg), nobiletin (21.98 μg/mg), neohesperidin (17.98 μg/mg) and tangeretin (0.756 μg/mg) may be the main compounds in WQD-EE. WQD-EE not only inhibited AGS and MCF 7 cell proliferation in a dose-dependent manner, but also blocked cell cycle progression at G2/M stage as well as inducing cell apoptosis at concentrations triggering significant inhibition of proliferation and cell cycle arrest in AGS cells. While at 0.5 mg/mL, WQD-EE significantly increased caspase-3 activity by 2.75 and 7.47 times at 24 h and 48 h, respectively. Moreover, WQD-EE in one hand reduced protein expressions of p53 and cyclin B1, and in other hand enhanced protein expressions of cytochrome c and Bax. Protein levels of Bcl-2, Fas L and Fas were not significantly affected by WQD-EE.

CONCLUSIONS

WQD-EE inhibits AGS cell proliferation through G2/M arrest due to down-regulation of cyclin B1 protein expression, and promotes apoptosis by caspase-3 and mitochondria-dependent pathways, but not by p53-dependent pathway.

Molecular mechanisms creating bistable switches at cell cycle transitions

Progression through the eukaryotic cell cycle is characterized by specific transitions, where cells move irreversibly from stage i−1 of the cycle into stage i. These irreversible cell cycle transitions are regulated by underlying bistable switches, which share some common features. An inhibitory protein stalls progression, and an activatory protein promotes progression. The inhibitor and activator are locked in a double-negative feedback loop, creating a one-way toggle switch that guarantees an irreversible commitment to move forward through the cell cycle, and it opposes regression from stage i to stage i−1. In many cases, the activator is an enzyme that modifies the inhibitor in multiple steps, whereas the hypo-modified inhibitor binds strongly to the activator and resists its enzymatic activity. These interactions are the basis of a reaction motif that provides a simple and generic account of many characteristic properties of cell cycle transitions. To demonstrate this assertion, we apply the motif in detail to the G1/S transition in budding yeast and to the mitotic checkpoint in mammalian cells. Variations of the motif might support irreversible cellular decision-making in other contexts.

System-level feedbacks control cell cycle progression

Repetitive cell cycles, which are essential to the perpetuation of life, are orchestrated by an underlying biochemical reaction network centered around cyclin-dependent protein kinases (Cdks) and their regulatory subunits (cyclins). Oscillations of Cdk1/CycB activity between low and high levels during the cycle trigger DNA replication and mitosis in the correct order. Based on computational modeling, we proposed that the low and the high kinase activity states are alternative stable steady states of a bistable Cdk-control system. Bistability is a consequence of system-level feedback (positive and double-negative feedback signals) in the underlying control system. We have also argued that bistability underlies irreversible transitions between low and high Cdk activity states and thereby ensures directionality of cell cycle progression.

A quantitative study of the division cycle of Caulobacter crescentus stalked cells

Progression of a cell through the division cycle is tightly controlled at different steps to ensure the integrity of genome replication and partitioning to daughter cells. From published experimental evidence, we propose a molecular mechanism for control of the cell division cycle in Caulobacter crescentus. The mechanism, which is based on the synthesis and degradation of three “master regulator” proteins (CtrA, GcrA, and DnaA), is converted into a quantitative model, in order to study the temporal dynamics of these and other cell cycle proteins. The model accounts for important details of the physiology, biochemistry, and genetics of cell cycle control in stalked C. crescentus cell. It reproduces protein time courses in wild-type cells, mimics correctly the phenotypes of many mutant strains, and predicts the phenotypes of currently uncharacterized mutants. Since many of the proteins involved in regulating the cell cycle of C. crescentus are conserved among many genera of α-proteobacteria, the proposed mechanism may be applicable to other species of importance in agriculture and medicine.

The cell cycle is the sequence of events by which a growing cell replicates all its components and divides them more or less evenly between two daughter cells. The timing and spatial organization of these events are controlled by gene–protein interaction networks of great complexity. A challenge for computational biology is to build realistic, accurate, predictive mathematical models of these control systems in a variety of organisms, both eukaryotes and prokaryotes. To this end, we present a model of a portion of the molecular network controlling DNA synthesis, cell cycle–related gene expression, DNA methylation, and cell division in stalked cells of the α-proteobacterium Caulobacter crescentus. The model is formulated in terms of nonlinear ordinary differential equations for the major cell cycle regulatory proteins in Caulobacter: CtrA, GcrA, DnaA, CcrM, and DivK. Kinetic rate constants are estimated, and the model is tested against available experimental observations on wild-type and mutant cells. The model is viewed as a starting point for more comprehensive models of the future that will account, in addition, for the spatial asymmetry of Caulobacter reproduction (swarmer cells as well as stalked cells), the correlation of cell growth and division, and cell cycle checkpoints.

Quantitative modeling in cell biology: what is it good for?

Recently, there has been a surge in the number of pioneering studies combining experiments with quantitative modeling to explain both relatively simple modules of molecular machinery of the cell and to achieve system-level understanding of cellular networks. Here we discuss the utility and methods of modeling and review several current models of cell signaling, cytoskeletal self-organization, nuclear transport, and the cell cycle. We discuss successes of and barriers to modeling in cell biology and its future directions, and we argue, using the field of bacterial chemotaxis as an example, that the closer the complete systematic understanding of cell behavior is, the more important modeling becomes and the more experiment and theory merge.

Parameter estimation for a mathematical model of the cell cycle in frog eggs

Parameter values for a kinetic model of the nuclear replication-division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthogonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the "guesstimates" of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable.

The Silicon Cell initiative: working towards a detailed kinetic description at the cellular level

The Silicon Cell initiative aims to understand cellular systems on the basis of the characteristics of their components. As a tool to achieve this, detailed kinetic models at the network reaction level are being constructed. Such detailed kinetic models are extremely useful for medical and biotechnological applications and form strong tools for fundamental studies. Several recently constructed detailed kinetic models on metabolism (glycolysis), signal transduction (EGF receptor), and the eukaryotic cell cycle (Saccharomyces cerevisiae) have been used to exemplify the Silicon Cell project. These models are stored and made accessible via the JWS Online Cellular Systems Modeling project, a web-based repository of kinetic models. Using a web-browser the models can be interrogated via a user-friendly graphical interface. The goal of the two projects is to combine models on parts of cellular systems and ultimately to construct detailed kinetic models at the cellular level.

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.

Coupling the cell cycle to cell growth

In order to multiply, both prokaryotic and eukaryotic cells go through a series of events that are collectively called the cell cycle. However, DNA replication, mitosis and cell division may also be viewed as having their own, in principle independent, cycles, which are tied together by mechanisms extrinsic to the cell cycle--the checkpoints--that maintain the order of events. We propose that our understanding of cell-cycle regulation is enhanced by viewing each event individually, as an independently regulated process. The nature of the parameters that regulate cell-cycle events is discussed and, in particular, we argue that cell mass is not such a parameter.

Network dynamics and cell physiology

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, movement and information processing. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks. To understand this dance, a new breed of theoretical molecular biologists reproduces these networks in computers and in the mathematical language of dynamical systems.

Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions

In recent years, molecular biologists have uncovered a wealth of information about the proteins controlling cell growth and division in eukaryotes. The regulatory system is so complex that it defies understanding by verbal arguments alone. Quantitative tools are necessary to probe reliably into the details of cell cycle control. To this end, we convert hypothetical molecular mechanisms into sets of nonlinear ordinary differential equations and use standard analytical and numerical methods to study their solutions. First, we present a simple model of the antagonistic interactions between cyclin-dependent kinases and the anaphase promoting complex, which shows how progress through the cell cycle can be thought of as irreversible transitions (Start and Finish) between two stable states (G1 and S-G2-M) of the regulatory system. Then we add new pieces to the "puzzle" until we obtain reasonable models of the control systems in yeast cells, frog eggs, and cultured mammalian cells.

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.

Instabilities in phosphorylation-dephosphorylation cascades and cell cycle checkpoints

The G2-M checkpoint in the cell cycle is identified with a set of phosphorylation-dephosphorylation (PD) cycles involving Cdc25 and the maturation-promoting factor (MPF); these PD cycles are coupled in a way that generates an instability. This instability arises out of a transcritical bifurcation which could be exploited by the G2 DNA damage checkpoint pathway in order to arrest or delay entry into mitosis. The coupling between PD cycles involving Wee1 and MPF does not lead to an instability and therefore Wee1 may not be a crucial target of the checkpoint pathway. A set of PD cycles exhibiting transcritical bifurcation also possesses the integrative ability of a checkpoint for 'checking' that prerequisites are satisfied prior to the next cell cycle event. Such a set of coupled PD cycles is suggested to be a core mechanism of cell cycle checkpoints.