Quantitative analysis of cellular networks: cell cycle entry (original) (raw)
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Stochastic E2F activation and reconciliation of phenomenological cell-cycle models
2010
The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.
BMC bioinformatics, 2009
Background: The cell cycle is a complex process that allows eukaryotic cells to replicate chromosomal DNA and partition it into two daughter cells. A relevant regulatory step is in the G 0 / G 1 phase, a point called the restriction (R) point where intracellular and extracellular signals are monitored and integrated. Subcellular localization of cell cycle proteins is increasingly recognized as a major factor that regulates cell cycle transitions. Nevertheless, current mathematical models of the G 1 /S networks of mammalian cells do not consider this aspect. Hence, there is a need for a computational model that incorporates this regulatory aspect that has a relevant role in cancer, since altered localization of key cell cycle players, notably of inhibitors of cyclin-dependent kinases, has been reported to occur in neoplastic cells and to be linked to cancer aggressiveness.
A Model of Cell Cycle Behavior Dominated by Kinetics of a Pathway Stimulated by Growth Factors
Bulletin of Mathematical Biology, 1999
A modified version of a previously developed mathematical model [Obeyesekere et al., Cell Prolif. (1997)] of the G1-phase of the cell cycle is presented. This model describes the regulation of the G1-phase that includes the interactions of the nuclear proteins, RB, cyclin E, cyclin D, cdk2, cdk4 and E2F. The effects of the growth factors on cyclin D synthesis under saturated or unsaturated growth factor conditions are investigated based on this model. The solutions to this model (a system of nonlinear ordinary differential equations) are discussed with respect to existing experiments. Predictions based on mathematical analysis of this model are presented. In particular, results are presented on the existence of two stable solutions, i.e., bistability within the G1-phase. It is shown that this bistability exists under unsaturated growth factor concentration levels. This phenomenon is very noticeable if the efficiency of the signal transduction, initiated by the growth factors leading to cyclin D synthesis, is low. The biological significance of this result as well as possible experimental designs to test these predictions are presented.
Network calisthenics Control of E2F dynamics in cell cycle entry
Stimulation of quiescent mammalian cells with mitogens induces an abrupt increase in E2F1-3 expression just prior to the onset of DNA synthesis, followed by a rapid decline as replication ceases. This temporal adaptation in E2F facilitates a transient pattern of gene expression that reflects the ordered nature of DNA replication. The challenge to understand how E2F dynamics coordinate molecular events required for high-fidelity DNA replication has great biological implications. Indeed, precocious, prolonged, elevated or reduced accumulation of E2F can generate replication stress that culminates in either arrest or death. Accordingly, temporal characteristics of E2F are regulated by several network modules that include feedforward and autoregulatory loops. In this review, we discuss how these network modules contribute to "shaping" E2F dynamics in the context of mammalian cell cycle entry.
The dynamics of cell cycle regulation
BioEssays, 2002
Major events of the cell cycle-DNA synthesis, mitosis and cell division-are regulated by a complex network of protein interactions that control the activities of cyclin-dependent kinases. The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. Computer simulations are necessary for detailed quantitative comparisons between theory and experiment, but they give little insight into the qualitative dynamics of the control system and how molecular interactions determine the fundamental physiological properties of cell replication. To that end, bifurcation diagrams are a useful analytical tool, providing new views of the dynamical organization of the cell cycle, the role of checkpoints in assuring the integrity of the genome, and the abnormal regulation of cell cycle events in mutants. These claims are demonstrated by an analysis of cell cycle regulation in fission yeast.
Mathematical modeling as a tool for investigating cell cycle control networks
Methods, 2007
Although not a traditional experimental ''method,'' mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.
Studying Irreversible Transitions in a Model of Cell Cycle Regulation
Electronic Notes in Theoretical Computer Science, 2009
Cells life follows a cycling behaviour which starts at cell birth and leads to cell division through a number of distinct phases. The transitions through the various cell cycle phases are controlled by a complex network of signalling pathways. Many cell cycle transitions are irreversible: once they are started they must reach completion. In this study we investigate the existence of conditions which lead to cases when irreversibility may be broken. Specifically, we characterise the elements of the cell cycle signalling network that are responsible for the irreversibility and we determine conditions for which the irreversible transitions may become reversible. We illustrate our results through a formal approach in which stochastic simulation analysis and model checking verification are combined. Through probabilistic model checking we provide a quantitative measure for the probability of irreversibility in the "Start" transition of the cell cycle.
The role of modelling in identifying drug targets for diseases of the cell cycle
Journal of The Royal Society Interface, 2006
The cell cycle is implicated in diseases that are the leading cause of mortality and morbidity in the developed world. Until recently, the search for drug targets has focused on relatively small parts of the regulatory network under the assumption that key events can be controlled by targeting single pathways. This is valid provided the impact of couplings to the wider scale context of the network can be ignored. The resulting depth of study has revealed many new insights; however, these have been won at the expense of breadth and a proper understanding of the consequences of links between the different parts of the network. Since it is now becoming clear that these early assumptions may not hold and successful treatments are likely to employ drugs that simultaneously target a number of different sites in the regulatory network, it is timely to redress this imbalance. However, the substantial increase in complexity presents new challenges and necessitates parallel theoretical and experimental approaches. We review the current status of theoretical models for the cell cycle in light of these new challenges. Many of the existing approaches are not sufficiently comprehensive to simultaneously incorporate the required extent of couplings. Where more appropriate levels of complexity are incorporated, the models are difficult to link directly to currently available data. Further progress requires a better integration of experiment and theory. New kinds of data are required that are quantitative, have a higher temporal resolution and that allow simultaneous quantitative comparison of the concentration of larger numbers of different proteins. More comprehensive models are required and must accommodate not only substantial uncertainties in the structure and kinetic parameters of the networks, but also high levels of ignorance. The most recent results relating network complexity to robustness of the dynamics provide clues that suggest progress is possible.
On the cell cycle and its switches
Nature, 2008
For the cell-division cycle to progress, hundreds of genes and proteins must be coordinately regulated. Systems-level studies of this cycle show that positive-feedback loops help to keep events in sync. The cell cycle is a complex but orderly sequence of events that culminates in the production of two cells from one. In eukaryotes, the cycle is divided into four phases: cell growth in G1 phase, DNA replication in S phase, more growth in G2 phase, and cell division in mitosis or M phase. The system of regulators that drives transitions between phases is centred on the cyclin-dependent kinases (CDKs), enzymes that are activated when regulatory proteins called cyclins bind to them. The CDK network directly or indirectly orchestrates coordinated regulation of proteins and genes involved in essentially every aspect of cell function. The complexity of these regulatory events raises the question of what systems-level strategies keep the process temporally coherent-how does the maestro of the cell cycle generate a definitive downbeat? Writing in this issue, Skotheim et al. 1 and Holt et al. 2 examine different phases of the cell cycle in the budding yeast Saccharomyces cerevisiae, and their findings converge on the same answer: positive feedback. In budding yeast, the cell cycle begins with the synthesis of the initiator cyclin Cln3, which binds to and activates Cdk1. Substrates of the Cln3-Cdk1 complex include the SBF and MBF gene transcription factors (activated through phosphorylation), and the transcriptional inhibitor Whi5, which is translocated out of the nucleus (and so inactivated) after phosphorylation. The reciprocal regulation of SBF/MBF and Whi5 brings about the transcription of hundreds of genes that collectively constitute the G1/S regulon. Among the targets of SBF/MBF are the genes that encode the G1 cyclins Cln1 and Cln2. Like Cln3, these two cyclins can activate Cdk1. And like Cln3-Cdk1, Cln1/2-Cdk1 complexes can activate SBF/MBF and inhibit Whi5. Thus, the Cdk1 system has a pair of interlinked positivefeedback loops that could, in principle, function as an irreversible, bistable trigger, with Cln1 and Cln2 promoting their own accumulation in an ever-accelerating cycle (Fig. 1a). The 'explosive' kinetics of the positive-feedback system could provide the definitive downbeat that keeps the G1/S regulon coherent. This attractive idea was tested more than a decade ago in cell populations 3,4 and found to be (apparently) incorrect: cells lacking the CLN1 and CLN2 genes (cln1Δ cln2Δ cells) seemed to activate the promoter sequence for CLN2 just as quickly as normal cells. But sometimes studying individual cells can reveal things that are masked by averaging over a population, and Skotheim et al. 1 (page 291) show that this is the case here. Examining normal cells individually by live-cell fluorescence microscopy, these authors find that Whi5 can abruptly translocate out of the nucleus some 40-50 minutes after the start of the G1 phase, and that the CLN2 promoter is turned on at about the same time. By contrast, in cln1Δ cln2Δ cells, the redistribution of Whi5 to the cytoplasm occurs slowly and gradually,