Integrative analysis of cell cycle control in budding yeast

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

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

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9090-7) contains supplementary material, which is available to authorized users.

From quiescence to proliferation: Cdk oscillations drive the mammalian cell cycle

We recently proposed a detailed model describing the dynamics of the network of cyclin-dependent kinases (Cdks) driving the mammalian cell cycle (Gérard and Goldbeter, 2009). The model contains four modules, each centered around one cyclin/Cdk complex. Cyclin D/Cdk4–6 and cyclin E/Cdk2 promote progression in G1 and elicit the G1/S transition, respectively; cyclin A/Cdk2 ensures progression in S and the transition S/G2, while the activity of cyclin B/Cdk1 brings about the G2/M transition. This model shows that in the presence of sufficient amounts of growth factor the Cdk network is capable of temporal self-organization in the form of sustained oscillations, which correspond to the ordered, sequential activation of the various cyclin/Cdk complexes that control the successive phases of the cell cycle. The results suggest that the switch from cellular quiescence to cell proliferation corresponds to the transition from a stable steady state to sustained oscillations in the Cdk network. The transition depends on a finely tuned balance between factors that promote or hinder progression in the cell cycle. We show that the transition from quiescence to proliferation can occur in multiple ways that alter this balance. By resorting to bifurcation diagrams, we analyze the mechanism of oscillations in the Cdk network. Finally, we show that the complexity of the detailed model can be greatly reduced, without losing its key dynamical properties, by considering a skeleton model for the Cdk network. Using such a skeleton model for the mammalian cell cycle we show that positive feedback (PF) loops enhance the amplitude and the robustness of Cdk oscillations with respect to molecular noise. We compare the relative merits of the detailed and skeleton versions of the model for the Cdk network driving the mammalian cell cycle.

Size homeostasis can be intrinsic to growing cell populations and explained without size sensing or signalling

The cell division cycle orchestrates cellular growth and division. The machinery underpinning the cell division cycle is well characterized, but the actual cue(s) driving the cell division cycle remains unknown. In rapidly growing and dividing yeast cells, this cue has been proposed to be cell size. Presumably, a mechanism communicating cell size acts as gatekeeper for the cell division cycle via the G(1) network, which triggers G(1) exit only when a critical size has been reached. Here, we evaluate this hypothesis with a minimal core model linking metabolism, growth and the cell division cycle. Using this model, we (a) present support for coordinated regulation of G(1)/S and G(2)/M transition in Saccharomyces cerevisiae in response to altered growth conditions, (b) illustrate the intrinsic antagonism between G(1) progression and cell size and (c) provide evidence that the coupling of growth and division is sufficient to allow for size homeostasis without directly communicating or measuring cell size. We show that even with a rudimentary version of the G(1) network consisting of a single unregulated cyclin, size homeostasis is maintained in populations during autocatalytic growth when the geometric constraint on nutrient supply is considered. Taken together, our results support the notion that cell size is a consequence rather than a regulator of growth and division.

A boolean model of the cardiac gene regulatory network determining first and second heart field identity

Two types of distinct cardiac progenitor cell populations can be identified during early heart development: the first heart field (FHF) and second heart field (SHF) lineage that later form the mature heart. They can be characterized by differential expression of transcription and signaling factors. These regulatory factors influence each other forming a gene regulatory network. Here, we present a core gene regulatory network for early cardiac development based on published temporal and spatial expression data of genes and their interactions. This gene regulatory network was implemented in a Boolean computational model. Simulations reveal stable states within the network model, which correspond to the regulatory states of the FHF and the SHF lineages. Furthermore, we are able to reproduce the expected temporal expression patterns of early cardiac factors mimicking developmental progression. Additionally, simulations of knock-down experiments within our model resemble published phenotypes of mutant mice. Consequently, this gene regulatory network retraces the early steps and requirements of cardiogenic mesoderm determination in a way appropriate to enhance the understanding of heart development.

Ergodic sets as cell phenotype of budding yeast cell cycle

It has been suggested that irreducible sets of states in Probabilistic Boolean Networks correspond to cellular phenotype. In this study, we identify such sets of states for each phase of the budding yeast cell cycle. We find that these “ergodic sets” underly the cyclin activity levels during each phase of the cell cycle. Our results compare to the observations made in several laboratory experiments as well as the results of differential equation models. Dynamical studies of this model: (i) indicate that under stochastic external signals the continuous oscillating waves of cyclin activity and the opposing waves of CKIs emerge from the logic of a Boolean-based regulatory network without the need for specific biochemical/kinetic parameters; (ii) suggest that the yeast cell cycle network is robust to the varying behavior of cell size (e.g., cell division under nitrogen deprived conditions); (iii) suggest the irreversibility of the Start signal is a function of logic of the G1 regulon, and changing the structure of the regulatory network can render start reversible.

A checkpoints capturing timing-robust Boolean model of the budding yeast cell cycle regulatory network

Background

Cell cycle process of budding yeast (Saccharomyces cerevisiae) consists of four phases: G1, S, G2 and M. Initiated by stimulation of the G1 phase, cell cycle returns to the G1 stationary phase through a sequence of the S, G2 and M phases. During the cell cycle, a cell verifies whether necessary conditions are satisfied at the end of each phase (i.e., checkpoint) since damages of any phase can cause severe cell cycle defect. The cell cycle can proceed to the next phase properly only if checkpoint conditions are met. Over the last decade, there have been several studies to construct Boolean models that capture checkpoint conditions. However, they mostly focused on robustness to network perturbations, and the timing robustness has not been much addressed. Only recently, some studies suggested extension of such models towards timing-robust models, but they have not considered checkpoint conditions.

Results

To construct a timing-robust Boolean model that preserves checkpoint conditions of the budding yeast cell cycle, we used a model verification technique, ‘model checking’. By utilizing automatic and exhaustive verification of model checking, we found that previous models cannot properly capture essential checkpoint conditions in the presence of timing variations. In particular, such models violate the M phase checkpoint condition so that it allows a division of a budding yeast cell into two before the completion of its full DNA replication and synthesis. In this paper, we present a timing-robust model that preserves all the essential checkpoint conditions properly against timing variations. Our simulation results show that the proposed timing-robust model is more robust even against network perturbations and can better represent the nature of cell cycle than previous models.

Conclusions

To our knowledge this is the first work that rigorously examined the timing robustness of the cell cycle process of budding yeast with respect to checkpoint conditions using Boolean models. The proposed timing-robust model is the complete state-of-the-art model that guarantees no violation in terms of checkpoints known to date.

Enabling dynamic network analysis through visualization in TVNViewer

Background

Many biological processes are context-dependent or temporally specific. As a result, relationships between molecular constituents evolve across time and environments. While cutting-edge machine learning techniques can recover these networks, exploring and interpreting the rewiring behavior is challenging. Information visualization shines in this type of exploratory analysis, motivating the development ofTVNViewer (http://sailing.cs.cmu.edu/tvnviewer), a visualization tool for dynamic network analysis.

Results

In this paper, we demonstrate visualization techniques for dynamic network analysis by using TVNViewer to analyze yeast cell cycle and breast cancer progression datasets.

Conclusions

TVNViewer is a powerful new visualization tool for the analysis of biological networks that change across time or space.

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.

An overview of existing modeling tools making use of model checking in the analysis of biochemical networks

Model checking is a well-established technique for automatically verifying complex systems. Recently, model checkers have appeared in computer tools for the analysis of biochemical (and gene regulatory) networks. We survey several such tools to assess the potential of model checking in computational biology. Next, our overview focuses on direct applications of existing model checkers, as well as on algorithms for biochemical network analysis influenced by model checking, such as those using binary decision diagrams (BDDs) or Boolean-satisfiability solvers. We conclude with advantages and drawbacks of model checking for the analysis of biochemical networks.

A journey from reductionist to systemic cell biology aboard the schooner Tara

In this essay I describe my personal journey from reductionist to systems cell biology and describe how this in turn led to a 3-year sea voyage to explore complex ocean communities. In describing this journey, I hope to convey some important principles that I gleaned along the way. I realized that cellular functions emerge from multiple molecular interactions and that new approaches borrowed from statistical physics are required to understand the emergence of such complex systems. Then I wondered how such interaction networks developed during evolution. Because life first evolved in the oceans, it became a natural thing to start looking at the small organisms that compose the plankton in the world's oceans, of which 98% are … individual cells—hence the Tara Oceans voyage, which finished on 31 March 2012 in Lorient, France, after a 60,000-mile around-the-world journey that collected more than 30,000 samples from 153 sampling stations.

A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system perturbations

Background

Eukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network’s dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation.

Results

The model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes.

Conclusions

This study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes.

A dynamical model of the spindle position checkpoint

The spindle position checkpoint (SPOC) is an important surveillance mechanism in the budding yeast cell cycle. An integrated approach, combining quantitative experimental cell biology with mathematical modeling, reveals how the SPOC inhibits mitotic exit at the molecular level.

We used fluorescence microscopy to quantify the number of molecules of Bfa1, Bub2 and Tem1 at the spindle pole bodies, and the size of the GAP-dependent and -independent Tem1 pools that coexist during mitosis.

We constructed a dynamical model of Tem1 regulation by Bfa1–Bub2.

Based on in-silico evidence supported by in-vivo data, we propose that cytoplasmic regulation of Tem1 by the GAP complex is critical for robust spindle position checkpoint arrest.

Our model also indicates the necessity of additional mechanisms of GAP inhibition for checkpoint silencing after spindle realignment.

The orientation of the mitotic spindle with respect to the polarity axis is crucial for the accuracy of asymmetric cell division. In budding yeast, a surveillance mechanism called the spindle position checkpoint (SPOC) prevents exit from mitosis when the mitotic spindle fails to align along the mother-to-daughter polarity axis. SPOC arrest relies upon inhibition of the GTPase Tem1 by the GTPase-activating protein (GAP) complex Bfa1–Bub2. Importantly, reactions signaling mitotic exit take place at yeast centrosomes (named spindle pole bodies, SPBs) and the GAP complex also promotes SPB localization of Tem1. Yet, whether the regulation of Tem1 by Bfa1–Bub2 takes place only at the SPBs remains elusive. Here, we present a quantitative analysis of Bfa1–Bub2 and Tem1 localization at the SPBs. Based on the measured SPB-bound protein levels, we introduce a dynamical model of the SPOC that describes the regulation of Bfa1 and Tem1. Our model suggests that Bfa1 interacts with Tem1 in the cytoplasm as well as at the SPBs to provide efficient Tem1 inhibition.

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.

An integrative model links multiple inputs and signaling pathways to the onset of DNA synthesis in hepatocytes

During liver regeneration, quiescent hepatocytes re-enter the cell cycle to proliferate and compensate for lost tissue. Multiple signals including hepatocyte growth factor, epidermal growth factor, tumor necrosis factor α, interleukin-6, insulin and transforming growth factor β orchestrate these responses and are integrated during the G₁ phase of the cell cycle. To investigate how these inputs influence DNA synthesis as a measure for proliferation, we established a large-scale integrated logical model connecting multiple signaling pathways and the cell cycle. We constructed our model based upon established literature knowledge, and successively improved and validated its structure using hepatocyte-specific literature as well as experimental DNA synthesis data. Model analyses showed that activation of the mitogen-activated protein kinase and phosphatidylinositol 3-kinase pathways was sufficient and necessary for triggering DNA synthesis. In addition, we identified key species in these pathways that mediate DNA replication. Our model predicted oncogenic mutations that were compared with the COSMIC database, and proposed intervention targets to block hepatocyte growth factor-induced DNA synthesis, which we validated experimentally. Our integrative approach demonstrates that, despite the complexity and size of the underlying interlaced network, logical modeling enables an integrative understanding of signaling-controlled proliferation at the cellular level, and thus can provide intervention strategies for distinct perturbation scenarios at various regulatory levels.

How do control-based approaches enter into biology?

Control is intrinsic to biological organisms, whose cells are in a constant state of sensing and response to numerous external and self-generated stimuli. Diverse means are used to study the complexity through control-based approaches in these cellular systems, including through chemical and genetic manipulations, input-output methodologies, feedback approaches, and feed-forward approaches. We first discuss what happens in control-based approaches when we are not actively examining or manipulating cells. We then present potential methods to determine what the cell is doing during these times and to reverse-engineer the cellular system. Finally, we discuss how we can control the cell's extracellular and intracellular environments, both to probe the response of the cells using defined experimental engineering-based technologies and to anticipate what might be achieved by applying control-based approaches to affect cellular processes. Much work remains to apply simplified control models and develop new technologies to aid researchers in studying and utilizing cellular and molecular processes.

Landscape and global stability of nonadiabatic and adiabatic oscillations in a gene network

We quantify the potential landscape to determine the global stability and coherence of biological oscillations. We explore a gene network motif in our experimental synthetic biology studies of two genes that mutually repress and activate each other with self-activation and self-repression. We find that in addition to intrinsic molecular number fluctuations, there is another type of fluctuation crucial for biological function: the fluctuation due to the slow binding/unbinding of protein regulators to gene promoters. We find that coherent limit cycle oscillations emerge in two regimes: an adiabatic regime with fast binding/unbinding and a nonadiabatic regime with slow binding/unbinding relative to protein synthesis/degradation. This leads to two mechanisms of producing the stable oscillations: the effective interactions from averaging the gene states in the adiabatic regime; and the time delays due to slow binding/unbinding to promoters in the nonadiabatic regime, which can be tested by forthcoming experiments. In both regimes, the landscape has a topological shape of the Mexican hat in protein concentrations that quantitatively determines the global stability of limit cycle dynamics. The oscillation coherence is shown to be correlated with the shape of the Mexican hat characterized by the height from the oscillation ring to the central top. The oscillation period can be tuned in a wide range by changing the binding/unbinding rate without changing the amplitude much, which is important for the functionality of a biological clock. A negative feedback loop with time delays due to slow binding/unbinding can also generate oscillations. Although positive feedback is not necessary for generating oscillations, it can make the oscillations more robust.

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

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

Identifying a static nonlinear structure in a biological system using noisy, sparse data

When part of a biological system cannot be investigated directly by experimentation, we face the problem of structure identification: how can we construct a model for an unknown part of a mostly known system using measurements gathered from its input and output? This problem is especially difficult to solve when the measurements available are noisy and sparse, i.e. widely and unevenly spaced in time, as is common when measuring biological quantities at the cellular level. Here we present a procedure to identify a static nonlinearity embedded between two dynamical systems using noisy, sparse measurements. To reduce the level of error caused by measurement noise, we introduce the concept of weighted-sum predictability. If we make the input and output subsystems weighted-sum predictable and normalize the measurements to their weighted sum, we achieve better noise reduction than through normalizing to a loading control. We then interpolate the normalized measurements to obtain continuous input and output signals, with which we solve directly for the input-output characteristics of the unknown static nonlinearity. We demonstrate the effectiveness of this structure identification procedure by applying it to identify a model for ergosterol sensing by the proteins Sre1 and Scp1 in fission yeast. Simulations with this model produced outputs consistent with experimental observations. The techniques introduced here will provide researchers with a new tool by which biological systems can be identified and characterized.

The genetic control of growth rate: a systems biology study in yeast

BACKGROUND

Control of growth rate is mediated by tight regulation mechanisms in all free-living organisms since long-term survival depends on adaptation to diverse environmental conditions. The yeast, Saccharomyces cerevisiae, when growing under nutrient-limited conditions, controls its growth rate via both nutrient-specific and nutrient-independent gene sets. At slow growth rates, at least, it has been found that the expression of the genes that exert significant control over growth rate (high flux control or HFC genes) is not necessarily regulated by growth rate itself. It has not been determined whether the set of HFC genes is the same at all growth rates or whether it is the same in conditions of nutrient limitation or excess.

RESULTS

HFC genes were identified in competition experiments in which a population of hemizygous diploid yeast deletants were grown at, or close to, the maximum specific growth rate in either nutrient-limiting or nutrient-sufficient conditions. A hemizygous mutant is one in which one of any pair of homologous genes is deleted in a diploid, These HFC genes divided into two classes: a haploinsufficient (HI) set, where the hemizygous mutants grow slower than the wild type, and a haploproficient (HP) set, which comprises hemizygotes that grow faster than the wild type. The HI set was found to be enriched for genes involved in the processes of gene expression, while the HP set was enriched for genes concerned with the cell cycle and genome integrity.

CONCLUSION

A subset of growth-regulated genes have HFC characteristics when grown in conditions where there are few, or no, external constraints on the rate of growth that cells may attain. This subset is enriched for genes that participate in the processes of gene expression, itself (i.e. transcription and translation). The fact that haploproficiency is exhibited by mutants grown at the previously determined maximum rate implies that the control of growth rate in this simple eukaryote represents a trade-off between the selective advantages of rapid growth and the need to maintain the integrity of the genome.

Interplay of transcriptional and proteolytic regulation in driving robust cell cycle progression

Complex biological systems, such as the cell cycle control network, are shown to be robust against various perturbations. It is crucial to identify the interactions of the network that can contribute towards robust cell cycle behaviour. The proteins in the cell cycle control network are regulated at the level of synthesis, degradation and activity. A closer examination of the network reveals that most of the proteins are subjected to all three types of regulation. Such multiple layers of regulation most probably contribute towards the robust cell cycle behaviour against perturbations. In this work, we investigate such a hypothesis by subjecting our budding yeast cell cycle model to global parameter perturbations using pre-defined viability criteria. We systematically tested the global role of regulated transcription and targeted degradation of proteins in driving robust cell cycle oscillations. We demonstrate that targeted degradation of proteins in the budding yeast cell cycle model makes the cell cycle oscillations robust against perturbations even in the absence of regulated transcription. We show that regulated transcription plays a major role in controlling the period of the cell cycle oscillations which is argued to be important for balanced cell growth and division. We show that both regulated transcription and degradation are part of feedback loops in the network which ensure robust function against parametric variations that can arise from the mutations and/or variations in protein levels.

Implicit methods for qualitative modeling of gene regulatory networks

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

Modelling Gene Regulatory Networks Using Computational Intelligence Techniques

This chapter presents modelling gene regulatory networks (GRNs) using probabilistic causal model and the guided genetic algorithm. The problem of modelling is explained from both a biological and computational perspective. Further, a comprehensive methodology for developing a GRN model is presented where the application of computation intelligence (CI) techniques can be seen to be significantly important in each phase of modelling. An illustrative example of the causal model for GRN modelling is also included and applied to model the yeast cell cycle dataset. The results obtained are compared for providing biological relevance to the findings which thereby underpins the CI based modelling techniques.

Genetic network analyzer: a tool for the qualitative modeling and simulation of bacterial regulatory networks

Genetic Network Analyzer (GNA) is a tool for the qualitative modeling and simulation of gene regulatory networks, based on so-called piecewise-linear differential equation models. We describe the use of this tool in the context of the modeling of bacterial regulatory networks, notably the network of global regulators controlling the adaptation of Escherichia coli to carbon starvation conditions. We show how the modeler, by means of GNA, can define a regulatory network, build a model of the network, determine the steady states of the system, perform a qualitative simulation of the network dynamics, and analyze the simulation results using model-checking tools. The example illustrates the interest of qualitative approaches for the analysis of the dynamics of bacterial regulatory networks.

Molecular systems biology of Sic1 in yeast cell cycle regulation through multiscale modeling

Cell cycle control is highly regulated to guarantee the precise timing of events essential for cell growth, i.e., DNA replication onset and cell division. Failure of this control plays a role in cancer and molecules called cyclin-dependent kinase (Cdk) inhibitors (Ckis) exploit a critical function in cell cycle timing. Here we present a multiscale modeling where experimental and computational studies have been employed to investigate structure, function and temporal dynamics of the Cki Sic1 that regulates cell cycle progression in Saccharomyces cerevisiae. Structural analyses reveal molecular details of the interaction between Sic1 and Cdk/cyclin complexes, and biochemical investigation reveals Sic1 function in analogy to its human counterpart p27(Kip1), whose deregulation leads to failure in timing of kinase activation and, therefore, to cancer. Following these findings, a bottom-up systems biology approach has been developed to characterize modular networks addressing Sic1 regulatory function. Through complementary experimentation and modeling, we suggest a mechanism that underlies Sic1 function in controlling temporal waves of cyclins to ensure correct timing of the phase-specific Cdk activities.

An integrated framework to model cellular phenotype as a component of biochemical networks

Identification of regulatory molecules in signaling pathways is critical for understanding cellular behavior. Given the complexity of the transcriptional gene network, the relationship between molecular expression and phenotype is difficult to determine using reductionist experimental methods. Computational models provide the means to characterize regulatory mechanisms and predict phenotype in the context of gene networks. Integrating gene expression data with phenotypic data in transcriptional network models enables systematic identification of critical molecules in a biological network. We developed an approach based on fuzzy logic to model cell budding in Saccharomyces cerevisiae using time series expression microarray data of the cell cycle. Cell budding is a phenotype of viable cells undergoing division. Predicted interactions between gene expression and phenotype reflected known biological relationships. Dynamic simulation analysis reproduced the behavior of the yeast cell cycle and accurately identified genes and interactions which are essential for cell viability.

Overexpression limits of fission yeast cell-cycle regulators in vivo and in silico

Cellular systems are generally robust against fluctuations of intracellular parameters such as gene expression level. However, little is known about expression limits of genes required to halt cellular systems. In this study, using the fission yeast Schizosaccharomyces pombe, we developed a genetic 'tug-of-war' (gTOW) method to assess the overexpression limit of certain genes. Using gTOW, we determined copy number limits for 31 cell-cycle regulators; the limits varied from 1 to >100. Comparison with orthologs of the budding yeast Saccharomyces cerevisiae suggested the presence of a conserved fragile core in the eukaryotic cell cycle. Robustness profiles of networks regulating cytokinesis in both yeasts (septation-initiation network (SIN) and mitotic exit network (MEN)) were quite different, probably reflecting differences in their physiologic functions. Fragility in the regulation of GTPase spg1 was due to dosage imbalance against GTPase-activating protein (GAP) byr4. Using the gTOW data, we modified a mathematical model and successfully reproduced the robustness of the S. pombe cell cycle with the model.

Software for systems biology: from tools to integrated platforms

Understanding complex biological systems requires extensive support from software tools. Such tools are needed at each step of a systems biology computational workflow, which typically consists of data handling, network inference, deep curation, dynamical simulation and model analysis. In addition, there are now efforts to develop integrated software platforms, so that tools that are used at different stages of the workflow and by different researchers can easily be used together. This Review describes the types of software tools that are required at different stages of systems biology research and the current options that are available for systems biology researchers. We also discuss the challenges and prospects for modelling the effects of genetic changes on physiology and the concept of an integrated platform.

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.

Dynamic gene network reconstruction from gene expression data in mice after influenza A (H1N1) infection

BACKGROUND

The immune response to viral infection is a temporal process, represented by a dynamic and complex network of gene and protein interactions. Here, we present a reverse engineering strategy aimed at capturing the temporal evolution of the underlying Gene Regulatory Networks (GRN). The proposed approach will be an enabling step towards comprehending the dynamic behavior of gene regulation circuitry and mapping the network structure transitions in response to pathogen stimuli.

RESULTS

We applied the Time Varying Dynamic Bayesian Network (TV-DBN) method for reconstructing the gene regulatory interactions based on time series gene expression data for the mouse C57BL/6J inbred strain after infection with influenza A H1N1 (PR8) virus. Initially, 3500 differentially expressed genes were clustered with the use of k-means algorithm. Next, the successive in time GRNs were built over the expression profiles of cluster centroids. Finally, the identified GRNs were examined with several topological metrics and available protein-protein and protein-DNA interaction data, transcription factor and KEGG pathway data.

CONCLUSIONS

Our results elucidate the potential of TV-DBN approach in providing valuable insights into the temporal rewiring of the lung transcriptome in response to H1N1 virus.

Chemical reaction systems with toric steady states

Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to have toric steady states. Furthermore, we analyze the capacity of such a system to exhibit positive steady states and multistationarity. Examples of systems with toric steady states include weakly-reversible zero-deficiency chemical reaction systems. An important application of our work concerns the networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism.

Computational modeling of the cell cycle

This Teaching Resource provides lecture notes, slides, and a problem set for introducing graduate-level students to computational biology through a simple mathematical model of the cell cycle. The model simulates interactions between cyclin B and cyclin-dependent kinase 1, proteins that together form the mitosis-promoting factor (MPF), which initiates the processes leading to mitosis. The lecture begins with a biological background describing the importance of MPF for mitosis, the components of MPF, and the changes in cellular MPF observed during different phases of the cell cycle. The model is compared with newer, more mechanistically detailed models of the same process, which allows for a discussion of the insights that can be gained even from simplified models. The lecture concludes with a demonstration of how this model can be implemented in the scientific programming language MATLAB and includes a problem set.

A method for zooming of nonlinear models of biochemical systems

BACKGROUND

Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.

RESULTS

In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.

CONCLUSIONS

We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.

Systems-biology approaches for predicting genomic evolution

Is evolution predictable at the molecular level? The ambitious goal to answer this question requires an understanding of the mutational effects that govern the complex relationship between genotype and phenotype. In practice, it involves integrating systems-biology modelling, microbial laboratory evolution experiments and large-scale mutational analyses - a feat that is made possible by the recent availability of the necessary computational tools and experimental techniques. This Review investigates recent progresses in mapping evolutionary trajectories and discusses the degree to which these predictions are realistic.

Cell growth and cell cycle in Saccharomyces cerevisiae: basic regulatory design and protein-protein interaction network

In this review we summarize the major connections between cell growth and cell cycle in the model eukaryote Saccharomyces cerevisiae. In S. cerevisiae regulation of cell cycle progression is achieved predominantly during a narrow interval in the late G1 phase known as START (Pringle and Hartwell, 1981). At START a yeast cell integrates environmental and internal signals (such as nutrient availability, presence of pheromone, attainment of a critical size, status of the metabolic machinery) and decides whether to enter a new cell cycle or to undertake an alternative developmental program. Several signaling pathways, that act to connect the nutritional status to cellular actions, are briefly outlined. A Growth & Cycle interaction network has been manually curated. More than one fifth of the edges within the Growth & Cycle network connect Growth and Cycle proteins, indicating a strong interconnection between the processes of cell growth and cell cycle. The backbone of the Growth & Cycle network is composed of middle-degree nodes suggesting that it shares some properties with HOT networks. The development of multi-scale modeling and simulation analysis will help to elucidate relevant central features of growth and cycle as well as to identify their system-level properties. Confident collaborative efforts involving different expertises will allow to construct consensus, integrated models effectively linking the processes of cell growth and cell cycle, ultimately contributing to shed more light also on diseases in which an altered proliferation ability is observed, such as cancer.

Replication origins and timing of temporal replication in budding yeast: how to solve the conundrum?

Similarly to metazoans, the budding yeast Saccharomyces cereviasiae replicates its genome with a defined timing. In this organism, well-defined, site-specific origins, are efficient and fire in almost every round of DNA replication. However, this strategy is neither conserved in the fission yeast Saccharomyces pombe, nor in Xenopus or Drosophila embryos, nor in higher eukaryotes, in which DNA replication initiates asynchronously throughout S phase at random sites. Temporal and spatial controls can contribute to the timing of replication such as Cdk activity, origin localization, epigenetic status or gene expression. However, a debate is going on to answer the question how individual origins are selected to fire in budding yeast. Two opposing theories were proposed: the "replicon paradigm" or "temporal program" vs. the "stochastic firing". Recent data support the temporal regulation of origin activation, clustering origins into temporal blocks of early and late replication. Contrarily, strong evidences suggest that stochastic processes acting on origins can generate the observed kinetics of replication without requiring a temporal order. In mammalian cells, a spatiotemporal model that accounts for a partially deterministic and partially stochastic order of DNA replication has been proposed. Is this strategy the solution to reconcile the conundrum of having both organized replication timing and stochastic origin firing also for budding yeast? In this review we discuss this possibility in the light of our recent study on the origin activation, suggesting that there might be a stochastic component in the temporal activation of the replication origins, especially under perturbed conditions.

Multistationarity in mass action networks with applications to ERK activation

Ordinary Differential Equations (ODEs) are an important tool in many areas of Quantitative Biology. For many ODE systems multistationarity (i.e. the existence of at least two positive steady states) is a desired feature. In general establishing multistationarity is a difficult task as realistic biological models are large in terms of states and (unknown) parameters and in most cases poorly parameterized (because of noisy measurement data of few components, a very small number of data points and only a limited number of repetitions). For mass action networks establishing multistationarity hence is equivalent to establishing the existence of at least two positive solutions of a large polynomial system with unknown coefficients. For mass action networks with certain structural properties, expressed in terms of the stoichiometric matrix and the reaction rate-exponent matrix, we present necessary and sufficient conditions for multistationarity that take the form of linear inequality systems. Solutions of these inequality systems define pairs of steady states and parameter values. We also present a sufficient condition to identify networks where the aforementioned conditions hold. To show the applicability of our results we analyse an ODE system that is defined by the mass action network describing the extracellular signal-regulated kinase (ERK) cascade (i.e. ERK-activation).

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.

A low number of SIC1 mRNA molecules ensures a low noise level in cell cycle progression of budding yeast

The budding yeast genome comprises roughly 6000 genes generating a number of about 10 000 mRNA copies, which gives a general estimation of 1-2 mRNA copies generated per gene. What does this observation implicate for cellular processes and their regulation? Whether the number of mRNA molecules produced is important for setting the amount of proteins implicated in a particular function is at present unknown. In this context, we studied cell cycle control as one of the highly fine tuned processes that guarantee the precise timing of events essential for cell growth. Here, we developed a stochastic model that addresses the effect of varying the mRNA amount of Sic1, inhibitor of the Cdk1-Clb5 kinase activity, and the resulting noise on Sic1/Clb5 balance at the G1/S transition. We considered a range of SIC1 transcripts number according to our experimental data derived from the MS2 mRNA tagging system. Computational simulation revealed that an increased amount of SIC1 mRNAs lead to an amplified dispersion of Sic1 protein levels, suggesting mRNA control being critical to set timing of Sic1 downregulation and, therefore, S phase onset. Moreover, Sic1/Clb5 balance is strongly influenced by Clb5 production in both daughter and mother cells in order to maintain the characteristic time of S phase entry overall the population. Furthermore, CLB5 mRNA molecules calculated to reproduce temporal dynamics of Sic1 and Clb5 for daughter and mother cells agree with recent data obtained from more complex networks. Thus, the results presented here provide novel insights into the influence that the mRNA amount and, indirectly, the transcription process exploit on cell cycle progression.

Dynamic modelling of oestrogen signalling and cell fate in breast cancer cells

Cancers of the breast and other tissues arise from aberrant decision-making by cells regarding their survival or death, proliferation or quiescence, damage repair or bypass. These decisions are made by molecular signalling networks that process information from outside and from within the breast cancer cell and initiate responses that determine the cell's survival and reproduction. Because the molecular logic of these circuits is difficult to comprehend by intuitive reasoning alone, we present some preliminary mathematical models of the basic decision circuits in breast cancer cells that may aid our understanding of their susceptibility or resistance to endocrine therapy.

Rising cyclin-CDK levels order cell cycle events

Background

Diverse mitotic events can be triggered in the correct order and time by a single cyclin-CDK. A single regulator could confer order and timing on multiple events if later events require higher cyclin-CDK than earlier events, so that gradually rising cyclin-CDK levels can sequentially trigger responsive events: the “quantitative model” of ordering.

Methodology/Principal Findings

This ‘quantitative model’ makes predictions for the effect of locking cyclin at fixed levels for a protracted period: at low cyclin levels, early events should occur rapidly, while late events should be slow, defective, or highly variable (depending on threshold mechanism). We titrated the budding yeast mitotic cyclin Clb2 within its endogenous expression range to a stable, fixed level and measured time to occurrence of three mitotic events: growth depolarization, spindle formation, and spindle elongation, as a function of fixed Clb2 level. These events require increasingly more Clb2 according to their normal order of occurrence. Events occur efficiently and with low variability at fixed Clb2 levels similar to those observed when the events normally occur. A second prediction of the model is that increasing the rate of cyclin accumulation should globally advance timing of all events. Moderate (<2-fold) overexpression of Clb2 accelerates all events of mitosis, resulting in consistently rapid sequential cell cycles. However, this moderate overexpression also causes a significant frequency of premature mitoses leading to inviability, suggesting that Clb2 expression level is optimized to balance the fitness costs of variability and catastrophe.

Conclusions/Significance

We conclude that mitotic events are regulated by discrete cyclin-CDK thresholds. These thresholds are sequentially triggered as cyclin increases, yielding reliable order and timing. In many biological processes a graded input must be translated into discrete outputs. In such systems, expression of the central regulator is likely to be tuned to an optimum level, as we observe here for Clb2.

Network news: innovations in 21st century systems biology

A decade ago, seminal perspectives and papers set a strong vision for the field of systems biology, and a number of these themes have flourished. Here, we describe key technologies and insights that have elucidated the evolution, architecture, and function of cellular networks, ultimately leading to the first predictive genome-scale regulatory and metabolic models of organisms. Can systems approaches bridge the gap between correlative analysis and mechanistic insights?

Modeling the cell cycle: why do certain circuits oscillate?

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations.

Image processing and classification algorithm for yeast cell morphology in a microfluidic chip

The study of yeast cell morphology requires consistent identification of cell cycle phases based on cell bud size. A computer-based image processing algorithm is designed to automatically classify microscopic images of yeast cells in a microfluidic channel environment. The images were enhanced to reduce background noise, and a robust segmentation algorithm is developed to extract geometrical features including compactness, axis ratio, and bud size. The features are then used for classification, and the accuracy of various machine-learning classifiers is compared. The linear support vector machine, distance-based classification, and k-nearest-neighbor algorithm were the classifiers used in this experiment. The performance of the system under various illumination and focusing conditions were also tested. The results suggest it is possible to automatically classify yeast cells based on their morphological characteristics with noisy and low-contrast images.

System-level feedbacks make the anaphase switch irreversible

The mitotic checkpoint prevents a eukaryotic cell from commencing to separate its replicated genome into two daughter cells (anaphase) until all of its chromosomes are properly aligned on the metaphase plate, with the two copies of each chromosome attached to opposite poles of the mitotic spindle. The mitotic checkpoint is exquisitely sensitive in that a single unaligned chromosome, 1 of a total of ~50, is sufficient to delay progression into anaphase; however, when the last chromosome comes into alignment on the metaphase plate, the mitotic checkpoint is quickly satisfied, and the replicated chromosomes are rapidly partitioned to opposite poles of the dividing cell. The mitotic checkpoint is also curious in the sense that, before metaphase alignment, chromosomes that are not being pulled in opposite directions by the mitotic spindle activate the checkpoint, but during anaphase, these same tensionless chromosomes can no longer activate the checkpoint. These and other puzzles associated with the mitotic checkpoint are addressed by a proposed molecular mechanism, which involves two positive feedback loops that create a bistable response of the checkpoint to chromosomal tension.

External control of the GAL network in S. cerevisiae: a view from control theory

While there is a vast literature on the control systems that cells utilize to regulate their own state, there is little published work on the formal application of control theory to the external regulation of cellular functions. This paper chooses the GAL network in S. cerevisiae as a well understood benchmark example to demonstrate how control theory can be employed to regulate intracellular mRNA levels via extracellular galactose. Based on a mathematical model reduced from the GAL network, we have demonstrated that a galactose dose necessary to drive and maintain the desired GAL genes' mRNA levels can be calculated in an analytic form. And thus, a proportional feedback control can be designed to precisely regulate the level of mRNA. The benefits of the proposed feedback control are extensively investigated in terms of stability and parameter sensitivity. This paper demonstrates that feedback control can both significantly accelerate the process to precisely regulate mRNA levels and enhance the robustness of the overall cellular control system.