Integrative analysis of cell cycle control in budding yeast

Mathematical Model Explaining the Role of CDC6 in the Diauxic Growth of CDK1 Activity during the M-Phase of the Cell Cycle

In this paper we propose a role for the CDC 6 protein in the entry of cells into mitosis. This has not been considered in the literature so far. Recent experiments suggest that CDC 6 , upon entry into mitosis, inhibits the appearance of active CDK 1 and cyclin B complexes. This paper proposes a mathematical model which incorporates the dynamics of kinase CDK 1 , its regulatory protein cyclin B, the regulatory phosphatase CDC 25 and the inhibitor CDC 6 known to be involved in the regulation of active CDK 1 and cyclin B complexes. The experimental data lead us to formulate a new hypothesis that CDC 6 slows down the activation of inactive complexes of CDK 1 and cyclin B upon mitotic entry. Our mathematical model, based on mass action kinetics, provides a possible explanation for the experimental data. We claim that the dynamics of active complexes CDK 1 and cyclin B have a similar nature to diauxic dynamics introduced by Monod in 1949. In mathematical terms we state it as the existence of more than one inflection point of the curve defining the dynamics of the complexes.

Advanced Modeling of Cellular Proliferation: Toward a Multi-scale Framework Coupling Cell Cycle to Metabolism by Integrating Logical and Constraint-Based Models

Biological functions require a coherent cross talk among multiple layers of regulation within the cell. Computational efforts that aim to understand how these layers are integrated across spatial, temporal, and functional scales represent a challenge in Systems Biology. We have developed a computational, multi-scale framework that couples cell cycle and metabolism networks in the budding yeast cell. Here we describe the methodology at the basis of this framework, which integrates on off-the-shelf logical (Boolean) models of a minimal yeast cell cycle with a constraint-based model of metabolism (i.e., the Yeast 7 metabolic network reconstruction). Models are implemented in Python code using the BooleanNet and COBRApy packages, respectively, and are connected through the Boolean logic. The methodology allows for incorporation of interaction data, and validation through -omics data. Furthermore, evolutionary strategies may be incorporated to explore regulatory structures underlying coherent cross talks among regulatory layers.

PyBioNetFit and the Biological Property Specification Language

In systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

A stochastic model of size control in the budding yeast cell cycle

BACKGROUND

Cell size is a key characteristic that significantly affects many aspects of cellular physiology. There are specific control mechanisms during cell cycle that maintain the cell size within a range from generation to generation. Such control mechanisms introduce substantial variabilities to important properties of the cell cycle such as growth and division. To quantitatively study the effect of such variability in progression through cell cycle, detailed stochastic models are required.

RESULTS

In this paper, a new hybrid stochastic model is proposed to study the effect of molecular noise and size control mechanism on the variabilities in cell cycle of the budding yeast Saccharomyces cerevisiae. The proposed model provides an accurate, yet computationally efficient approach for simulation of an intricate system by integrating the deterministic and stochastic simulation schemes. The developed hybrid stochastic model can successfully capture several key features of the cell cycle observed in experimental data. In particular, the proposed model: 1) confirms that the majority of noise in size control stems from low copy numbers of transcripts in the G1 phase, 2) identifies the size and time regulation modules in the size control mechanism, and 3) conforms with phenotypes of early G1 mutants in exquisite detail.

CONCLUSIONS

Hybrid stochastic modeling approach can be used to provide quantitative descriptions for stochastic properties of the cell cycle within a computationally efficient framework.

Reverse engineering genetic networks using nonlinear saturation kinetics

A gene regulatory network (GRN) represents a set of genes along with their regulatory interactions. Cellular behavior is driven by genetic level interactions. Dynamics of such systems show nonlinear saturation kinetics which can be best modeled by Michaelis-Menten (MM) and Hill equations. Although MM equation is being widely used for modeling biochemical processes, it has been applied rarely for reverse engineering GRNs. In this paper, we develop a complete framework for a novel model for GRN inference using MM kinetics. A set of coupled equations is first proposed for modeling GRNs. In the coupled model, Michaelis-Menten constant associated with regulation by a gene is made invariant irrespective of the gene being regulated. The parameter estimation of the proposed model is carried out using an evolutionary optimization method, namely, trigonometric differential evolution (TDE). Subsequently, the model is further improved and the regulations of different genes by a given gene are made distinct by allowing varying values of Michaelis-Menten constants for each regulation. Apart from making the model more relevant biologically, the improvement results in a decoupled GRN model with fast estimation of model parameters. Further, to enhance exploitation of the search, we propose a local search algorithm based on hill climbing heuristics. A novel mutation operation is also proposed to avoid population stagnation and premature convergence. Real life benchmark data sets generated in vivo are used for validating the proposed model. Further, we also analyze realistic in silico datasets generated using GeneNetweaver. The comparison of the performance of proposed model with other existing methods shows the potential of the proposed model.

Dissecting the mechanisms of cell division

Cell division is a highly regulated and carefully orchestrated process. Understanding the mechanisms that promote proper cell division is an important step toward unraveling important questions in cell biology and human health. Early studies seeking to dissect the mechanisms of cell division used classical genetics approaches to identify genes involved in mitosis and deployed biochemical approaches to isolate and identify proteins critical for cell division. These studies underscored that post-translational modifications and cyclin-kinase complexes play roles at the heart of the cell division program. Modern approaches for examining the mechanisms of cell division, including the use of high-throughput methods to study the effects of RNAi, cDNA, and chemical libraries, have evolved to encompass a larger biological and chemical space. Here, we outline some of the classical studies that established a foundation for the field and provide an overview of recent approaches that have advanced the study of cell division.

Cell size and morphological properties of yeast Saccharomyces cerevisiae in relation to growth temperature

Cell volume is an important parameter for modelling cellular processes. Temperature-induced variability of cellular size, volume, intracellular granularity, a fraction of budding cells of yeast Saccharomyces cerevisiae CEN.PK 113-7D (in anaerobic glucose unlimited batch cultures) were measured by flow cytometry and matched with the performance of the biomass growth (maximal specific growth rate (μmax), specific rate of glucose consumption, the rate of maintenance, biomass yield on glucose). The critical diameter of single cells was 7.94 μm and it is invariant at growth temperatures above 18.5°C. Below 18.5°C, it exponentially increases up to 10.2 μm. The size of the bud linearly depends on μmax, and it is between 50% at 5°C and 90% at 31°C of the averaged single cell. The intracellular granularity (side scatter channel (SSC)-index) negatively depends on μmax. There are two temperature regions (5-31°C vs. 33-40°C) where the relationship between SSC-index and various cellular parameters differ significantly. In supraoptimal temperature range (33-40°C), cells are less granulated perhaps due to a higher rate of the maintenance. There is temperature dependent passage through the checkpoints in the cell cycle which influences the μmax. The results point to the existence of two different morphological states of yeasts in these different temperature regions.

Efficiently Encoding Complex Biochemical Models with the Multistate Model Builder (MSMB)

Biologists seek to create increasingly complex molecular regulatory network models. Writing such a model is a creative effort that requires flexible analysis tools and better modeling languages than offered by many of today's biochemical model editors. Our Multistate Model Builder (MSMB) supports multistate models created using different modeling styles that suit the modeler rather than the software. MSMB defines a simple but powerful syntax to describe multistate species. Our syntax reduces the number of reactions needed to encode the model, thereby reducing the cognitive load involved with model creation. MSMB gives extensive feedback during all stages of model creation. Users can activate error notifications, and use these notifications as a guide toward a consistent, syntactically correct model. Any consistent model can be exported to SBML or COPASI formats. We show the effectiveness of MSMB's multistate syntax through realistic models of cell cycle regulation and mRNA transcription. MSMB is an open-source project implemented in Java and it uses the COPASI API. Complete information and the installation package can be found at http://copasi.org/Projects/ .

A transcriptome-wide analysis deciphers distinct roles of G1 cyclins in temporal organization of the yeast cell cycle

Oscillating gene expression is crucial for correct timing and progression through cell cycle. In Saccharomyces cerevisiae, G1 cyclins Cln1-3 are essential drivers of the cell cycle and have an important role for temporal fine-tuning. We measured time-resolved transcriptome-wide gene expression for wild type and cyclin single and double knockouts over cell cycle with and without osmotic stress. Clustering of expression profiles, peak time detection of oscillating genes, integration with transcription factor network dynamics, and assignment to cell cycle phases allowed us to quantify the effect of genetic or stress perturbations on the duration of cell cycle phases. Cln1 and Cln2 showed functional differences, especially affecting later phases. Deletion of Cln3 led to a delay of START followed by normal progression through later phases. Our data and network analysis suggest mutual effects of cyclins with the transcriptional regulators SBF and MBF.

The cell-cycle transcriptional network generates and transmits a pulse of transcription once each cell cycle

Multiple studies have suggested the critical roles of cyclin-dependent kinases (CDKs) as well as a transcription factor (TF) network in generating the robust cell-cycle transcriptional program. However, the precise mechanisms by which these components function together in the gene regulatory network remain unclear. Here we show that the TF network can generate and transmit a "pulse" of transcription independently of CDK oscillations. The premature firing of the transcriptional pulse is prevented by early G1 inhibitors, including transcriptional corepressors and the E3 ubiquitin ligase complex APCCdh1. We demonstrate that G1 cyclin-CDKs facilitate the activation and accumulation of TF proteins in S/G2/M phases through inhibiting G1 transcriptional corepressors (Whi5 and Stb1) and APCCdh1, thereby promoting the initiation and propagation of the pulse by the TF network. These findings suggest a unique oscillatory mechanism in which global phase-specific transcription emerges from a pulse-generating network that fires once-and-only-once at the start of the cycle.

Control of Eukaryotic DNA Replication Initiation-Mechanisms to Ensure Smooth Transitions

DNA replication differs from most other processes in biology in that any error will irreversibly change the nature of the cellular progeny. DNA replication initiation, therefore, is exquisitely controlled. Deregulation of this control can result in over-replication characterized by repeated initiation events at the same replication origin. Over-replication induces DNA damage and causes genomic instability. The principal mechanism counteracting over-replication in eukaryotes is a division of replication initiation into two steps—licensing and firing—which are temporally separated and occur at distinct cell cycle phases. Here, we review this temporal replication control with a specific focus on mechanisms ensuring the faultless transition between licensing and firing phases.

Flavin-based metabolic cycles are integral features of growth and division in single yeast cells

The yeast metabolic cycle (YMC) is a fascinating example of biological organization, in which cells constrain the function of specific genetic, protein and metabolic networks to precise temporal windows as they grow and divide. However, understanding the intracellular origins of the YMC remains a challenging goal, as measuring the oxygen oscillations traditionally associated with it requires the use of synchronized cultures growing in nutrient-limited chemostat environments. To address these limitations, we used custom-built microfluidic devices and time-lapse fluorescence microscopy to search for metabolic cycling in the form of endogenous flavin fluorescence in unsynchronized single yeast cells. We uncovered robust and pervasive metabolic cycles that were synchronized with the cell division cycle (CDC) and oscillated across four different nutrient conditions. We then studied the response of these metabolic cycles to chemical and genetic perturbations, showing that their phase synchronization with the CDC can be altered through treatment with rapamycin, and that metabolic cycles continue even in respiratory deficient strains. These results provide a foundation for future studies of the physiological importance of metabolic cycles in processes such as CDC control, metabolic regulation and cell aging.

Modeling the dynamic behavior of biochemical regulatory networks

Strategies for modeling the complex dynamical behavior of gene/protein regulatory networks have evolved over the last 50 years as both the knowledge of these molecular control systems and the power of computing resources have increased. Here, we review a number of common modeling approaches, including Boolean (logical) models, systems of piecewise-linear or fully non-linear ordinary differential equations, and stochastic models (including hybrid deterministic/stochastic approaches). We discuss the pro's and con's of each approach, to help novice modelers choose a modeling strategy suitable to their problem, based on the type and bounty of available experimental information. We illustrate different modeling strategies in terms of some abstract network motifs, and in the specific context of cell cycle regulation.

Mathematical modeling identifies Lck as a potential mediator for PD-1 induced inhibition of early TCR signaling

Programmed cell death-1 (PD-1) is an inhibitory immune checkpoint receptor that negatively regulates the functioning of T cell. Although the direct targets of PD-1 were not identified, its inhibitory action on the TCR signaling pathway was known much earlier. Recent experiments suggest that the PD-1 inhibits the TCR and CD28 signaling pathways at a very early stage ─ at the level of phosphorylation of the cytoplasmic domain of TCR and CD28 receptors. Here, we develop a mathematical model to investigate the influence of inhibitory effect of PD-1 on the activation of early TCR and CD28 signaling molecules. Proposed model recaptures several quantitative experimental observations of PD-1 mediated inhibition. Model simulations show that PD-1 imposes a net inhibitory effect on the Lck kinase. Further, the inhibitory effect of PD-1 on the activation of TCR signaling molecules such as Zap70 and SLP76 is significantly enhanced by the PD-1 mediated inhibition of Lck. These results suggest a critical role for Lck as a mediator for PD-1 induced inhibition of TCR signaling network. Multi parametric sensitivity analysis explores the effect of parameter uncertainty on model simulations.

Revisiting a skeleton model for the mammalian cell cycle: From bistability to Cdk oscillations and cellular heterogeneity

A network of cyclin-dependent kinases (Cdks) regulated by multiple negative and positive feedback loops controls progression in the mammalian cell cycle. We previously proposed a detailed computational model for this network, which consists of four coupled Cdk modules. Both this detailed model and a reduced, skeleton version show that the Cdk network is capable of temporal self-organization in the form of sustained Cdk oscillations, which correspond to the orderly progression along the different cell cycle phases G1, S (DNA replication), G2 and M (mitosis). We use the skeleton model to revisit the role of positive feedback (PF) loops on the dynamics of the mammalian cell cycle by showing that the multiplicity of PF loops extends the range of bistability in the isolated Cdk modules controlling the G1/S and G2/M transitions. Resorting to stochastic simulations we show that, through their effect on the range of bistability, multiple PF loops enhance the robustness of Cdk oscillations with respect to molecular noise. The model predicts that a rise in the total level of Cdk1 also enlarges the domain of bistability in the isolated Cdk modules as well as the range of oscillations in the full Cdk network. Surprisingly, stochastic simulations indicate that Cdk1 overexpression reduces the robustness of Cdk oscillations towards molecular noise; this result is due to the increased distance between the two branches of the bistable switch at higher levels of Cdk1. At intermediate levels of growth factor stochastic simulations show that cells may randomly switch between cell cycle arrest and cell proliferation, as a consequence of fluctuations. In the presence of Cdk1 overexpression, these transitions occur even at low levels of growth factor. Extending stochastic simulations from single cells to cell populations suggests that stochastic switches between cell cycle arrest and proliferation may provide a source of heterogeneity in a cell population, as observed in cancer cells characterized by Cdk1 overexpression.

Using both qualitative and quantitative data in parameter identification for systems biology models

In systems biology, qualitative data are often generated, but rarely used to parameterize models. We demonstrate an approach in which qualitative and quantitative data can be combined for parameter identification. In this approach, qualitative data are converted into inequality constraints imposed on the outputs of the model. These inequalities are used along with quantitative data points to construct a single scalar objective function that accounts for both datasets. To illustrate the approach, we estimate parameters for a simple model describing Raf activation. We then apply the technique to a more elaborate model characterizing cell cycle regulation in yeast. We incorporate both quantitative time courses (561 data points) and qualitative phenotypes of 119 mutant yeast strains (1647 inequalities) to perform automated identification of 153 model parameters. We quantify parameter uncertainty using a profile likelihood approach. Our results indicate the value of combining qualitative and quantitative data to parameterize systems biology models.

Much of the data generated in biology is qualitative, but exploiting such data to inform models of biological systems remains a challenge. Here, the authors demonstrate an approach that allows use of both quantitative and qualitative data for parameterising dynamical models.

Accuracy Analysis of Hybrid Stochastic Simulation Algorithm on Linear Chain Reaction Systems

Noise in cellular systems is often modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), but the low efficiency of the SSA limits its application to large biochemical networks. To improve the efficiency of stochastic simulations, Haseltine and Rawlings (HR) proposed a hybrid algorithm, which combines ordinary differential equations for traditional deterministic models and the SSA for stochastic models. In this paper, accuracy of the HR hybrid method is studied based on a linear chain reaction system. Mathematical analysis and numerical results both show that the HR hybrid method is accurate if either the quantity of reactant molecules in fast reactions is above a certain threshold, or the reaction rates of fast reactions are much larger than those of slow reactions. This analysis also shows that the HR hybrid method approximates the chemical master equation well for a much greater region in system parameter space than the slow-scale SSA and the stochastic quasi-steady-state assumption methods.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

DSGRN: Examining the Dynamics of Families of Logical Models

We present a computational tool DSGRN for exploring the dynamics of a network by computing summaries of the dynamics of switching models compatible with the network across all parameters. The network can arise directly from a biological problem, or indirectly as the interaction graph of a Boolean model. This tool computes a finite decomposition of parameter space such that for each region, the state transition graph that describes the coarse dynamical behavior of a network is the same. Each of these parameter regions corresponds to a different logical description of the network dynamics. The comparison of dynamics across parameters with experimental data allows the rejection of parameter regimes or entire networks as viable models for representing the underlying regulatory mechanisms. This in turn allows a search through the space of perturbations of a given network for networks that robustly fit the data. These are the first steps toward discovering a network that optimally matches the observed dynamics by searching through the space of networks.

Modeling-Based Investigation of the Effect of Noise in Cellular Systems

Noise is pervasive in cellular biology and inevitably affects the dynamics of cellular processes. Biological systems have developed regulatory mechanisms to ensure robustness with respect to noise or to take advantage of stochasticity. We review here, through a couple of selected examples, some insights on possible robustness factors and constructive roles of noise provided by computational modeling. In particular, we focus on (1) factors that likely contribute to the robustness of oscillatory processes such as the circadian clocks and the cell cycle, (2) how reliable coding/decoding of calcium-mediated signaling could be achieved in presence of noise and, in some cases, enhanced through stochastic resonance, and (3) how embryonic cell differentiation processes can exploit stochasticity to create heterogeneity in a population of identical cells.

Semi-supervised network inference using simulated gene expression dynamics

Motivation

Inferring the structure of gene regulatory networks from high-throughput datasets remains an important and unsolved problem. Current methods are hampered by problems such as noise, low sample size, and incomplete characterizations of regulatory dynamics, leading to networks with missing and anomalous links. Integration of prior network information (e.g. from pathway databases) has the potential to improve reconstructions.

Results

We developed a semi-supervised network reconstruction algorithm that enables the synthesis of information from partially known networks with time course gene expression data. We adapted partial least square-variable importance in projection (VIP) for time course data and used reference networks to simulate expression data from which null distributions of VIP scores are generated and used to estimate edge probabilities for input expression data. By using simulated dynamics to generate reference distributions, this approach incorporates previously known regulatory relationships and links the network to the dynamics to form a semi-supervised approach that discovers novel and anomalous connections. We applied this approach to data from a sleep deprivation study with KEGG pathways treated as prior networks, as well as to synthetic data from several DREAM challenges, and find that it is able to recover many of the true edges and identify errors in these networks, suggesting its ability to derive posterior networks that accurately reflect gene expression dynamics.

Availability and implementation

R code is available at https://github.com/pn51/postPLSR.

Contact

rbraun@northwestern.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Bayesian data integration for quantifying the contribution of diverse measurements to parameter estimates

Motivation

Computational models in biology are frequently underdetermined, due to limits in our capacity to measure biological systems. In particular, mechanistic models often contain parameters whose values are not constrained by a single type of measurement. It may be possible to achieve better model determination by combining the information contained in different types of measurements. Bayesian statistics provides a convenient framework for this, allowing a quantification of the reduction in uncertainty with each additional measurement type. We wished to explore whether such integration is feasible and whether it can allow computational models to be more accurately determined.

Results

We created an ordinary differential equation model of cell cycle regulation in budding yeast and integrated data from 13 different studies covering different experimental techniques. We found that for some parameters, a single type of measurement, relative time course mRNA expression, is sufficient to constrain them. Other parameters, however, were only constrained when two types of measurements were combined, namely relative time course and absolute transcript concentration. Comparing the estimates to measurements from three additional, independent studies, we found that the degradation and transcription rates indeed matched the model predictions in order of magnitude. The predicted translation rate was incorrect however, thus revealing a deficiency in the model. Since this parameter was not constrained by any of the measurement types separately, it was only possible to falsify the model when integrating multiple types of measurements. In conclusion, this study shows that integrating multiple measurement types can allow models to be more accurately determined.

Availability and implementation

The models and files required for running the inference are included in the Supplementary information.

Contact

l.wessels@nki.nl.

Supplementary information

Supplementary data are available at Bioinformatics online.

An integrated microfluidic device for the sorting of yeast cells using image processing

The process of detection and separation of yeast cells based on their morphological characteristics is critical to the understanding of cell division cycles, which is of vital importance to the understanding of some diseases such as cancer. The traditional process of manual detection is usually tedious and inconsistent. This paper presents a microfluidic device integrated with microvalves for fluid control for the sorting of yeast cells using image processing algorithms and confirmation based on their fluorescent tag. The proposed device is completely automated, low cost and easy to implement in an academic research setting. Design details of the integrated microfluidic system are highlighted in this paper, along with experimental validation. Real time cell sorting was demonstrated with a cell detection rate of 12 cells per minute.

Exploring the Underlying Mechanisms of the Xenopus laevis Embryonic Cell Cycle

The cell cycle is an indispensable process in proliferation and development. Despite significant efforts, global quantification and physical understanding are still challenging. In this study, we explored the mechanisms of the Xenopus laevis embryonic cell cycle by quantifying the underlying landscape and flux. We uncovered the Mexican hat landscape of the Xenopus laevis embryonic cell cycle with several local basins and barriers on the oscillation path. The local basins characterize the different phases of the Xenopus laevis embryonic cell cycle, and the local barriers represent the checkpoints. The checkpoint mechanism of the cell cycle is revealed by the landscape basins and barriers. While landscape shape determines the stabilities of the states on the oscillation path, the curl flux force determines the stability of the cell cycle flow. Replication is fundamental for biology of living cells. We quantify the input energy (through the entropy production) as the thermodynamic requirement for initiation and sustainability of single cell life (cell cycle). Furthermore, we also quantify curl flux originated from the input energy as the dynamical requirement for the emergence of a new stable phase (cell cycle). This can provide a new quantitative insight for the origin of single cell life. In fact, the curl flux originated from the energy input or nutrition supply determines the speed and guarantees the progression of the cell cycle. The speed of the cell cycle is a hallmark of cancer. We characterized the quality of the cell cycle by the coherence time and found it is supported by the flux and energy cost. We are also able to quantify the degree of time irreversibility by the cross correlation function forward and backward in time from the stochastic traces in the simulation or experiments, providing a way for the quantification of the time irreversibility and the flux. Through global sensitivity analysis upon landscape and flux, we can identify the key elements for controlling the cell cycle speed. This can help to design an effective strategy for drug discovery against cancer.

Computational modelling of meiotic entry and commitment

In response to developmental and environmental conditions, cells exit the mitotic cell cycle and enter the meiosis program to generate haploid gametes from diploid germ cells. Once cells decide to enter the meiosis program they become irreversibly committed to the completion of meiosis irrespective of the presence of cue signals. How meiotic entry and commitment occur due to the dynamics of the regulatory network is not well understood. Therefore, we constructed a mathematical model of the regulatory network that controls the transition from mitosis to meiosis in Schizosaccharomyces pombe. Upon nitrogen starvation, yeast cells exit mitosis and undergo conjugation and meiotic entry. The model includes the regulation of Mei2, an RNA binding protein required for conjugation and meiotic entry, by multiple feedback loops involving Pat1, a kinase that keeps cells in mitosis, and Ste11, a transcription activator required for the sexual differentiation. The model accounts for various experimental observations and demonstrates that the activation of Mei2 is bistable, which ensures the irreversible commitment to meiosis. Further, we show by integrating the meiosis-specific regulation with a cell cycle model, the dynamics of cell cycle exit, G1 arrest and entry into meiosis under nitrogen starvation.

A toolbox for discrete modelling of cell signalling dynamics

We present a library of network motifs for the development of complex and realistic biological network models using the BioModelAnalyzer, and demonstrate their wider value by using them to construct a model of the cell cycle.

From word models to executable models of signaling networks using automated assembly

Word models (natural language descriptions of molecular mechanisms) are a common currency in spoken and written communication in biomedicine but are of limited use in predicting the behavior of complex biological networks. We present an approach to building computational models directly from natural language using automated assembly. Molecular mechanisms described in simple English are read by natural language processing algorithms, converted into an intermediate representation, and assembled into executable or network models. We have implemented this approach in the Integrated Network and Dynamical Reasoning Assembler (INDRA), which draws on existing natural language processing systems as well as pathway information in Pathway Commons and other online resources. We demonstrate the use of INDRA and natural language to model three biological processes of increasing scope: (i) p53 dynamics in response to DNA damage, (ii) adaptive drug resistance in BRAF‐V600E‐mutant melanomas, and (iii) the RAS signaling pathway. The use of natural language makes the task of developing a model more efficient and it increases model transparency, thereby promoting collaboration with the broader biology community.

Cell cycle time series gene expression data encoded as cyclic attractors in Hopfield systems

Modern time series gene expression and other omics data sets have enabled unprecedented resolution of the dynamics of cellular processes such as cell cycle and response to pharmaceutical compounds. In anticipation of the proliferation of time series data sets in the near future, we use the Hopfield model, a recurrent neural network based on spin glasses, to model the dynamics of cell cycle in HeLa (human cervical cancer) and S. cerevisiae cells. We study some of the rich dynamical properties of these cyclic Hopfield systems, including the ability of populations of simulated cells to recreate experimental expression data and the effects of noise on the dynamics. Next, we use a genetic algorithm to identify sets of genes which, when selectively inhibited by local external fields representing gene silencing compounds such as kinase inhibitors, disrupt the encoded cell cycle. We find, for example, that inhibiting the set of four kinases AURKB, NEK1, TTK, and WEE1 causes simulated HeLa cells to accumulate in the M phase. Finally, we suggest possible improvements and extensions to our model.

Cell cycle—the process in which a parent cell replicates its DNA and divides into two daughter cells—is an upregulated process in many forms of cancer. Identifying gene inhibition targets to regulate cell cycle is important to the development of effective therapies. Although modern high throughput techniques offer unprecedented resolution of the molecular details of biological processes like cell cycle, analyzing the vast quantities of the resulting experimental data and extracting actionable information remains a formidable task. Here, we create a dynamical model of the process of cell cycle using the Hopfield model (a type of recurrent neural network) and gene expression data from human cervical cancer cells and yeast cells. We find that the model recreates the oscillations observed in experimental data. Tuning the level of noise (representing the inherent randomness in gene expression and regulation) to the “edge of chaos” is crucial for the proper behavior of the system. We then use this model to identify potential gene targets for disrupting the process of cell cycle. This method could be applied to other time series data sets and used to predict the effects of untested targeted perturbations.

Reconciling conflicting models for global control of cell-cycle transcription

Models for the control of global cell-cycle transcription have advanced from a CDK-APC/C oscillator, a transcription factor (TF) network, to coupled CDK-APC/C and TF networks. Nonetheless, current models were challenged by a recent study that concluded that the cell-cycle transcriptional program is primarily controlled by a CDK-APC/C oscillator in budding yeast. Here we report an analysis of the transcriptome dynamics in cyclin mutant cells that were not queried in the previous study. We find that B-cyclin oscillation is not essential for control of phase-specific transcription. Using a mathematical model, we demonstrate that the function of network TFs can be retained in the face of significant reductions in transcript levels. Finally, we show that cells arrested at mitotic exit with non-oscillating levels of B-cyclins continue to cycle transcriptionally. Taken together, these findings support a critical role of a TF network and a requirement for CDK activities that need not be periodic.

Systems Level Modeling of the Cell Cycle Using Budding Yeast

Proteins involved in the regulation of the cell cycle are highly conserved across all eukaryotes, and so a relatively simple eukaryote such as yeast can provide insight into a variety of cell cycle perturbations including those that occur in human cancer. To date, the budding yeast Saccharomyces cerevisiae has provided the largest amount of experimental and modeling data on the progression of the cell cycle, making it a logical choice for in-depth studies of this process. Moreover, the advent of methods for collection of high-throughput genome, transcriptome, and proteome data has provided a means to collect and precisely quantify simultaneous cell cycle gene transcript and protein levels, permitting modeling of the cell cycle on the systems level. With the appropriate mathematical framework and sufficient and accurate data on cell cycle components, it should be possible to create a model of the cell cycle that not only effectively describes its operation, but can also predict responses to perturbations such as variation in protein levels and responses to external stimuli including targeted inhibition by drugs. In this review, we summarize existing data on the yeast cell cycle, proteomics technologies for quantifying cell cycle proteins, and the mathematical frameworks that can integrate this data into representative and effective models. Systems level modeling of the cell cycle will require the integration of high-quality data with the appropriate mathematical framework, which can currently be attained through the combination of dynamic modeling based on proteomics data and using yeast as a model organism.

Dissipative structures and biological rhythms

Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca⁺⁺ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.

Quantitative Systems Biology to decipher design principles of a dynamic cell cycle network: the "Maximum Allowable mammalian Trade-Off-Weight" (MAmTOW)

Network complexity is required to lend cellular processes flexibility to respond timely to a variety of dynamic signals, while simultaneously warranting robustness to protect cellular integrity against perturbations. The cell cycle serves as a paradigm for such processes; it maintains its frequency and temporal structure (although these may differ among cell types) under the former, but accelerates under the latter. Cell cycle molecules act together in time and in different cellular compartments to execute cell type-specific programs. Strikingly, the timing at which molecular switches occur is controlled by abundance and stoichiometry of multiple proteins within complexes. However, traditional methods that investigate one effector at a time are insufficient to understand how modulation of protein complex dynamics at cell cycle transitions shapes responsiveness, yet preserving robustness. To overcome this shortcoming, we propose a multidisciplinary approach to gain a systems-level understanding of quantitative cell cycle dynamics in mammalian cells from a new perspective. By suggesting advanced experimental technologies and dedicated modeling approaches, we present innovative strategies (i) to measure absolute protein concentration in vivo, and (ii) to determine how protein dosage, e.g., altered protein abundance, and spatial (de)regulation may affect timing and robustness of phase transitions. We describe a method that we name “Maximum Allowable mammalian Trade–Off–Weight” (MAmTOW), which may be realized to determine the upper limit of gene copy numbers in mammalian cells. These aspects, not covered by current systems biology approaches, are essential requirements to generate precise computational models and identify (sub)network-centered nodes underlying a plethora of pathological conditions.

An engineering design approach to systems biology

Measuring and modeling the integrated behavior of biomolecular-cellular networks is central to systems biology. Over several decades, systems biology has been shaped by quantitative biologists, physicists, mathematicians, and engineers in different ways. However, the basic and applied versions of systems biology are not typically distinguished, which blurs the separate aspirations of the field and its potential for real-world impact. Here, we articulate an engineering approach to systems biology, which applies educational philosophy, engineering design, and predictive models to solve contemporary problems in an age of biomedical Big Data. A concerted effort to train systems bioengineers will provide a versatile workforce capable of tackling the diverse challenges faced by the biotechnological and pharmaceutical sectors in a modern, information-dense economy.

Predicting network modules of cell cycle regulators using relative protein abundance statistics

BACKGROUND

Parameter estimation in systems biology is typically done by enforcing experimental observations through an objective function as the parameter space of a model is explored by numerical simulations. Past studies have shown that one usually finds a set of "feasible" parameter vectors that fit the available experimental data equally well, and that these alternative vectors can make different predictions under novel experimental conditions. In this study, we characterize the feasible region of a complex model of the budding yeast cell cycle under a large set of discrete experimental constraints in order to test whether the statistical features of relative protein abundance predictions are influenced by the topology of the cell cycle regulatory network.

RESULTS

Using differential evolution, we generate an ensemble of feasible parameter vectors that reproduce the phenotypes (viable or inviable) of wild-type yeast cells and 110 mutant strains. We use this ensemble to predict the phenotypes of 129 mutant strains for which experimental data is not available. We identify 86 novel mutants that are predicted to be viable and then rank the cell cycle proteins in terms of their contributions to cumulative variability of relative protein abundance predictions. Proteins involved in "regulation of cell size" and "regulation of G1/S transition" contribute most to predictive variability, whereas proteins involved in "positive regulation of transcription involved in exit from mitosis," "mitotic spindle assembly checkpoint" and "negative regulation of cyclin-dependent protein kinase by cyclin degradation" contribute the least. These results suggest that the statistics of these predictions may be generating patterns specific to individual network modules (START, S/G2/M, and EXIT). To test this hypothesis, we develop random forest models for predicting the network modules of cell cycle regulators using relative abundance statistics as model inputs. Predictive performance is assessed by the areas under receiver operating characteristics curves (AUC). Our models generate an AUC range of 0.83-0.87 as opposed to randomized models with AUC values around 0.50.

CONCLUSIONS

By using differential evolution and random forest modeling, we show that the model prediction statistics generate distinct network module-specific patterns within the cell cycle network.

Prospects and problems for standardizing model validation in systems biology

There are currently no widely shared criteria by which to assess the validity of computational models in systems biology. Here we discuss the feasibility and desirability of implementing validation standards for modeling. Having such a standard would facilitate journal review, interdisciplinary collaboration, model exchange, and be especially relevant for applications close to medical practice. However, even though the production of predictively valid models is considered a central goal, in practice modeling in systems biology employs a variety of model structures and model-building practices. These serve a variety of purposes, many of which are heuristic and do not seem to require strict validation criteria and may even be restricted by them. Moreover, given the current situation in systems biology, implementing a validation standard would face serious technical obstacles mostly due to the quality of available empirical data. We advocate a cautious approach to standardization. However even though rigorous standardization seems premature at this point, raising the issue helps us develop better insights into the practices of systems biology and the technical problems modelers face validating models. Further it allows us to identify certain technical validation issues which hold regardless of modeling context and purpose. Informal guidelines could in fact play a role in the field by helping modelers handle these.

First-passage time approach to controlling noise in the timing of intracellular events

In the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events despite such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Analytical calculations are performed for the first-passage time distribution in stochastic models of gene expression. Derivation of these formulas motivates an interesting question: Is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean? Counterintuitively, results show that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative, or any combination of them) will always amplify noise in event timing. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage [Formula: see text] Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable [Formula: see text] protein up to a threshold, and precision in timing is achieved via feedforward rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.

Molecular Network Dynamics of Cell Cycle Control: Periodicity of Start and Finish

The cell division cycle is controlled by a complex regulatory network which ensures that the phases of the cell cycle are executed in the right order. This regulatory network receives signals from the environment, monitors the state of the DNA, and decides timings of cell cycle events. The underlying transcriptional and post-translational regulatory interactions lead to complex dynamical responses, such as the oscillations in the levels of cell cycle proteins driven by intertwined biochemical reactions. A cell moves between different phases of its cycle similar to a dynamical system switching between its steady states. The complex molecular network driving these phases has been investigated in previous computational systems biology studies. Here, we review the critical physiological and molecular transitions that occur in the cell cycle and discuss the role of mathematical modeling in elucidating these transitions and understand cell cycle synchronization.

Advances and challenges in logical modeling of cell cycle regulation: perspective for multi-scale, integrative yeast cell models

The eukaryotic cell cycle is robustly designed, with interacting molecules organized within a definite topology that ensures temporal precision of its phase transitions. Its underlying dynamics are regulated by molecular switches, for which remarkable insights have been provided by genetic and molecular biology efforts. In a number of cases, this information has been made predictive, through computational models. These models have allowed for the identification of novel molecular mechanisms, later validated experimentally. Logical modeling represents one of the youngest approaches to address cell cycle regulation. We summarize the advances that this type of modeling has achieved to reproduce and predict cell cycle dynamics. Furthermore, we present the challenge that this type of modeling is now ready to tackle: its integration with intracellular networks, and its formalisms, to understand crosstalks underlying systems level properties, ultimate aim of multi-scale models. Specifically, we discuss and illustrate how such an integration may be realized, by integrating a minimal logical model of the cell cycle with a metabolic network.

To senesce or not to senesce: how primary human fibroblasts decide their cell fate after DNA damage

Excessive DNA damage can induce an irreversible cell cycle arrest, called senescence, which is generally perceived as an important tumour-suppressor mechanism. However, it is unclear how cells decide whether to senesce or not after DNA damage. By combining experimental data with a parameterized mathematical model we elucidate this cell fate decision at the G1-S transition. Our model provides a quantitative and conceptually new understanding of how human fibroblasts decide whether DNA damage is beyond repair and senesce. Model and data imply that the G1-S transition is regulated by a bistable hysteresis switch with respect to Cdk2 activity, which in turn is controlled by the Cdk2/p21 ratio rather than cyclin abundance. We experimentally confirm the resulting predictions that to induce senescence i) in healthy cells both high initial and elevated background DNA damage are necessary and sufficient, and ii) in already damaged cells much lower additional DNA damage is sufficient. Our study provides a mechanistic explanation of a) how noise in protein abundances allows cells to overcome the G1-S arrest even with substantial DNA damage, potentially leading to neoplasia, and b) how accumulating DNA damage with age increasingly sensitizes cells for senescence.

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.

The interplay between chromosome stability and cell cycle control explored through gene-gene interaction and computational simulation

Chromosome stability models are usually qualitative models derived from molecular-genetic mechanisms for DNA repair, DNA synthesis, and cell division. While qualitative models are informative, they are also challenging to reformulate as precise quantitative models. In this report we explore how (A) laboratory experiments, (B) quantitative simulation, and (C) seriation algorithms can inform models of chromosome stability. Laboratory experiments were used to identify 19 genes that when over-expressed cause chromosome instability in the yeast Saccharomyces cerevisiae To better understand the molecular mechanisms by which these genes act, we explored their genetic interactions with 18 deletion mutations known to cause chromosome instability. Quantitative simulations based on a mathematical model of the cell cycle were used to predict the consequences of several genetic interactions. These simulations lead us to suspect that the chromosome instability genes cause cell-cycle perturbations. Cell-cycle involvement was confirmed using a seriation algorithm, which was used to analyze the genetic interaction matrix to reveal an underlying cyclical pattern. The seriation algorithm searched over 10(14) possible arrangements of rows and columns to find one optimal arrangement, which correctly reflects events during cell cycle phases. To conclude, we illustrate how the molecular mechanisms behind these cell cycle events are consistent with established molecular interaction maps.

The CDK-APC/C Oscillator Predominantly Entrains Periodic Cell-Cycle Transcription

Throughout cell-cycle progression, the expression of multiple transcripts oscillate, and whether these are under the centralized control of the CDK-APC/C proteins or can be driven by a de-centralized transcription factor (TF) cascade is a fundamental question for understanding cell-cycle regulation. In budding yeast, we find that the transcription of nearly all genes, as assessed by RNA-seq or fluorescence microscopy in single cells, is dictated by CDK-APC/C. Three exceptional genes are transcribed in a pulsatile pattern in a variety of CDK-APC/C arrests. Pursuing one of these transcripts, the SIC1 inhibitor of B-type cyclins, we use a combination of mathematical modeling and experimentation to provide evidence that, counter-intuitively, Sic1 provides a failsafe mechanism promoting nuclear division when levels of mitotic cyclins are low.

Selection on Network Dynamics Drives Differential Rates of Protein Domain Evolution

The long-held principle that functionally important proteins evolve slowly has recently been challenged by studies in mice and yeast showing that the severity of a protein knockout only weakly predicts that protein's rate of evolution. However, the relevance of these studies to evolutionary changes within proteins is unknown, because amino acid substitutions, unlike knockouts, often only slightly perturb protein activity. To quantify the phenotypic effect of small biochemical perturbations, we developed an approach to use computational systems biology models to measure the influence of individual reaction rate constants on network dynamics. We show that this dynamical influence is predictive of protein domain evolutionary rate within networks in vertebrates and yeast, even after controlling for expression level and breadth, network topology, and knockout effect. Thus, our results not only demonstrate the importance of protein domain function in determining evolutionary rate, but also the power of systems biology modeling to uncover unanticipated evolutionary forces.

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.

Coherent organization in gene regulation: a study on six networks

Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. Here we analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation in three organisms or cell types each, and show that they follow a version of Hebb's rule which we have termed coherence. More precisely, we find that simultaneously expressed genes with a common target are less likely to act antagonistically at the attractors of the regulatory dynamics. We then investigate the dependence of coherence on structural parameters, such as the mean number of inputs per node and the activatory/repressory interaction ratio, as well as on dynamically determined quantities, such as the basin size and the number of expressed genes.

The MYpop toolbox: Putting yeast stress responses in cellular context on single cell and population scales

Systems biology holds the promise to integrate multiple sources of information in order to build ever more complete models of cellular function. To do this, the field must overcome two significant challenges. First, the current strategy to model average cells must be replaced with population based models accounting for cell-to-cell variability. Second, models must be integrated with each other and with basic cellular function. This requires a core model of cellular physiology as well as a multiscale simulation platform to support large-scale simulation of culture or tissues from single cells. Here, we present such a simulation platform with a core model of yeast physiology as scaffold to integrate and simulate SBML models. The software automates this integration helping users simulate their model of choice in context of the cell division cycle. We benchmark model merging, simulation and analysis by integrating a minimal model of osmotic stress into the core model and analyzing it. We characterize the effect of single cell differences on the dynamics of osmoadaptation, estimating when normal cell growth is resumed and obtaining an explanation for experimentally observed glycerol dynamics based on population dynamics. Hence, the platform can be used to reconcile single cell and population level data.

Model-Based Analysis of Cell Cycle Responses to Dynamically Changing Environments

Cell cycle progression is carefully coordinated with a cell's intra- and extracellular environment. While some pathways have been identified that communicate information from the environment to the cell cycle, a systematic understanding of how this information is dynamically processed is lacking. We address this by performing dynamic sensitivity analysis of three mathematical models of the cell cycle in Saccharomyces cerevisiae. We demonstrate that these models make broadly consistent qualitative predictions about cell cycle progression under dynamically changing conditions. For example, it is shown that the models predict anticorrelated changes in cell size and cell cycle duration under different environments independently of the growth rate. This prediction is validated by comparison to available literature data. Other consistent patterns emerge, such as widespread nonmonotonic changes in cell size down generations in response to parameter changes. We extend our analysis by investigating glucose signalling to the cell cycle, showing that known regulation of Cln3 translation and Cln1,2 transcription by glucose is sufficient to explain the experimentally observed changes in cell cycle dynamics at different glucose concentrations. Together, these results provide a framework for understanding the complex responses the cell cycle is capable of producing in response to dynamic environments.