A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a "standard component" modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with "standard components" can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

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

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.

From START to FINISH: computational analysis of cell cycle control in budding yeast.

In the cell division cycle of budding yeast, START refers to a set of tightly linked events that prepare a cell for budding and DNA replication, and FINISH denotes the interrelated events by which the cell exits from mitosis and divides into mother and daughter cells. On the basis of recent progress made by molecular biologists in characterizing the genes and proteins that control START and FINISH, we crafted a new mathematical model of cell cycle progression in yeast. Our model exploits a natural separation of time scales in the cell cycle control network to construct a system of differential-algebraic equations for protein synthesis and degradation, post-translational modifications, and rapid formation and dissociation of multimeric complexes. The model provides a unified account of the observed phenotypes of 257 mutant yeast strains (98% of the 263 strains in the data set used to constrain the model). We then use the model to predict the phenotypes of 30 novel combinations of mutant alleles. Our comprehensive model of the molecular events controlling cell cycle progression in budding yeast has both explanatory and predictive power. Future experimental tests of the model's predictions will be useful to refine the underlying molecular mechanism, to constrain the adjustable parameters of the model, and to provide new insights into how the cell division cycle is regulated in budding yeast.

Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model.

BACKGROUND: Parameter estimation from experimental data is critical for mathematical modeling of protein regulatory networks. For realistic networks with dozens of species and reactions, parameter estimation is an especially challenging task. In this study, we present an approach for parameter estimation that is effective in fitting a model of the budding yeast cell cycle (comprising 26 nonlinear ordinary differential equations containing 126 rate constants) to the experimentally observed phenotypes (viable or inviable) of 119 genetic strains carrying mutations of cell cycle genes. RESULTS: Starting from an initial guess of the parameter values, which correctly captures the phenotypes of only 72 genetic strains, our parameter estimation algorithm quickly improves the success rate of the model to 105-111 of the 119 strains. This success rate is comparable to the best values achieved by a skilled modeler manually choosing parameters over many weeks. The algorithm combines two search and optimization strategies. First, we use Latin hypercube sampling to explore a region surrounding the initial guess. From these samples, we choose ∼20 different sets of parameter values that correctly capture wild type viability. These sets form the starting generation of differential evolution that selects new parameter values that perform better in terms of their success rate in capturing phenotypes. In addition to producing highly successful combinations of parameter values, we analyze the results to determine the parameters that are most critical for matching experimental outcomes and the most competitive strains whose correct outcome with a given parameter vector forces numerous other strains to have incorrect outcomes. These "most critical parameters" and "most competitive strains" provide biological insights into the model. Conversely, the "least critical parameters" and "least competitive strains" suggest ways to reduce the computational complexity of the optimization. CONCLUSIONS: Our approach proves to be a useful tool to help systems biologists fit complex dynamical models to large experimental datasets. In the process of fitting the model to the data, the tool identifies suggestive correlations among aspects of the model and the data.

Top-down network analysis to drive bottom-up modeling of physiological processes.

Top-down analyses in systems biology can automatically find correlations among genes and proteins in large-scale datasets. However, it is often difficult to design experiments from these results. In contrast, bottom-up approaches painstakingly craft detailed models that can be simulated computationally to suggest wet lab experiments. However, developing the models is a manual process that can take many years. These approaches have largely been developed independently. We present LINKER, an efficient and automated data-driven method that can analyze molecular interactomes to propose extensions to models that can be simulated. LINKER combines teleporting random walks and k-shortest path computations to discover connections from a source protein to a set of proteins collectively involved in a particular cellular process. We evaluate the efficacy of LINKER by applying it to a well-known dynamic model of the cell division cycle in Saccharomyces cerevisiae. Compared to other state-of-the-art methods, subnetworks computed by LINKER are heavily enriched in Gene Ontology (GO) terms relevant to the cell cycle. Finally, we highlight how networks computed by LINKER elucidate the role of a protein kinase (Cdc5) in the mitotic exit network of a dynamic model of the cell cycle.

Oscillatory dynamics of cell cycle proteins in single yeast cells analyzed by imaging cytometry.

Progression through the cell division cycle is orchestrated by a complex network of interacting genes and proteins. Some of these proteins are known to fluctuate periodically during the cell cycle, but a systematic study of the fluctuations of a broad sample of cell-cycle proteins has not been made until now. Using time-lapse fluorescence microscopy, we profiled 16 strains of budding yeast, each containing GFP fused to a single gene involved in cell cycle regulation. The dynamics of protein abundance and localization were characterized by extracting the amplitude, period, and other indicators from a series of images. Oscillations of protein abundance could clearly be identified for Cdc15, Clb2, Cln1, Cln2, Mcm1, Net1, Sic1, and Whi5. The period of oscillation of the fluorescently tagged proteins is generally in good agreement with the inter-bud time. The very strong oscillations of Net1 and Mcm1 expression are remarkable since little is known about the temporal expression of these genes. By collecting data from large samples of single cells, we quantified some aspects of cell-to-cell variability due presumably to intrinsic and extrinsic noise affecting the cell cycle.

Stochastic exit from mitosis in budding yeast: model predictions and experimental observations.

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.

Global challenges as inspiration: a classroom strategy to foster social responsibility.

Social responsibility is at the heart of the Engineer's Creed embodied in the pledge that we will dedicate [our] professional knowledge and skill to the advancement and betterment of human welfare... [placing] public welfare above all other considerations. However, half century after the original creed was written, we find ourselves in a world with great technological advances and great global-scale technologically-enabled peril. These issues can be naturally integrated into the engineering curriculum in a way that enhances the development of the technological skill set. We have found that these global challenges create a natural opportunity to foster social responsibility within the engineering students whom we educate. In freshman through senior-level materials engineering courses, we used five guiding principles to shape several different classroom activities and assignments. Upon testing an initial cohort of 28 students had classroom experiences based on these five principles, we saw a shift in attitude: before the experience, 18% of the cohort viewed engineers as playing an active role in solving global problems; after the experiences, 79% recognized the engineer's role in solving global-scale problems. In this paper, we present how global issues can be used to stimulate thinking for socially-responsible engineering solutions. We set forth five guiding principles that can foster the mindset for socially responsible actions along with examples of how these principles translate into classroom activities.

Analysis of a generic model of eukaryotic cell-cycle regulation.

We propose a protein interaction network for the regulation of DNA synthesis and mitosis that emphasizes the universality of the regulatory system among eukaryotic cells. The idiosyncrasies of cell cycle regulation in particular organisms can be attributed, we claim, to specific settings of rate constants in the dynamic network of chemical reactions. The values of these rate constants are determined ultimately by the genetic makeup of an organism. To support these claims, we convert the reaction mechanism into a set of governing kinetic equations and provide parameter values (specific to budding yeast, fission yeast, frog eggs, and mammalian cells) that account for many curious features of cell cycle regulation in these organisms. Using one-parameter bifurcation diagrams, we show how overall cell growth drives progression through the cell cycle, how cell-size homeostasis can be achieved by two different strategies, and how mutations remodel bifurcation diagrams and create unusual cell-division phenotypes. The relation between gene dosage and phenotype can be summarized compactly in two-parameter bifurcation diagrams. Our approach provides a theoretical framework in which to understand both the universality and particularity of cell cycle regulation, and to construct, in modular fashion, increasingly complex models of the networks controlling cell growth and division.

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.

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.

Cycling without the cyclosome: modeling a yeast strain lacking the APC.

The construction of viable Saccharomyces cerevisiae strains that lack the anaphase promoting complex (APC) was recently reported. The normally lethal deletions of APC genes were suppressed by the double deletion of the PDS1 and CLB5 genes in conjunction with the insertion of multiple copies of the SIC1 gene controlled by its endogenous promoter. It was proposed that cyclic expression and degradation of Sic1 results in oscillations of Clb/CDK activity necessary for the cell cycle. We have used an updated version of a mathematical model of the yeast cell cycle to model strains that lack the APC. With a few modifications, the model accurately simulates the viability of Apc- strains, as well as the phenotypes of 27 other previously characterized strains. We discuss a few minor inconsistencies between the model and experiment, and how these may inform future revisions to the model.

Modeling regulatory networks at Virginia Tech.

The life of a cell is governed by the physicochemical properties of a complex network of interacting macromolecules (primarily genes and proteins). Hence, a full scientific understanding of and rational engineering approach to cell physiology require accurate mathematical models of the spatial and temporal dynamics of these macromolecular assemblies, especially the networks involved in integrating signals and regulating cellular responses. The Virginia Tech Consortium is involved in three specific goals of DARPA's computational biology program (Bio-COMP): to create effective software tools for modeling gene-protein-metabolite networks, to employ these tools in creating a new generation of realistic models, and to test and refine these models by well-conceived experimental studies. The special emphasis of this group is to understand the mechanisms of cell cycle control in eukaryotes (yeast cells and frog eggs). The software tools developed at Virginia Tech are designed to meet general requirements of modeling regulatory networks and are collected in a problem-solving environment called JigCell.

Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.

The physiological responses of cells to external and internal stimuli are governed by genes and proteins interacting in complex networks whose dynamical properties are impossible to understand by intuitive reasoning alone. Recent advances by theoretical biologists have demonstrated that molecular regulatory networks can be accurately modeled in mathematical terms. These models shed light on the design principles of biological control systems and make predictions that have been verified experimentally.