Meiotic prophase requires proteolysis of M phase regulators mediated by the meiosis-specific APC/CAma1.

Whereas proliferating cells enter M phase shortly after DNA replication, the first M phase of meiosis is preceded by an extended prophase in which homologous chromosomes undergo recombination. Exit from prophase I is controlled by the recombination checkpoint (RC), which, in yeast, represses the meiosis-specific transcription factor Ndt80 required for the expression of B-type cyclins and other M phase regulators. We show that an extended prophase I additionally requires the suppression of latent, mitotic cell-cycle controls by the anaphase-promoting complex (APC/C) and its meiosis-specific activator Ama1, which trigger the degradation of M phase regulators and Ndd1, a subunit of a mitotic transcription factor. ama1Δ mutants exit from prophase I prematurely and independently of the RC, which results in recombination defects and chromosome missegregation. Thus, control of prophase I by meiotic mechanisms depends on the suppression of the alternative, mitotic mechanisms by a meiosis-specific form of the APC/C.

The oscillation of mitotic kinase governs cell cycle latches in mammalian cells.

The mammalian cell cycle alternates between two phases - S-G2-M with high levels of A- and B-type cyclins (CycA and CycB, respectively) bound to cyclin-dependent kinases (CDKs), and G1 with persistent degradation of CycA and CycB by an activated anaphase promoting complex/cyclosome (APC/C) bound to Cdh1 (also known as FZR1 in mammals; denoted APC/C:Cdh1). Because CDKs phosphorylate and inactivate Cdh1, these two phases are mutually exclusive. This 'toggle switch' is flipped from G1 to S by cyclin-E bound to a CDK (CycE:CDK), which is not degraded by APC/C:Cdh1, and from M to G1 by Cdc20-bound APC/C (APC/C:Cdc20), which is not inactivated by CycA:CDK or CycB:CDK. After flipping the switch, cyclin E is degraded and APC/C:Cdc20 is inactivated. Combining mathematical modelling with single-cell timelapse imaging, we show that dysregulation of CycB:CDK disrupts strict alternation of the G1-S and M-G1 switches. Inhibition of CycB:CDK results in Cdc20-independent Cdh1 'endocycles', and sustained activity of CycB:CDK drives Cdh1-independent Cdc20 endocycles. Our model provides a mechanistic explanation for how whole-genome doubling can arise, a common event in tumorigenesis that can drive tumour evolution.

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells.

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

Cyclin A triggers Mitosis either via the Greatwall kinase pathway or Cyclin B.

Two mitotic cyclin types, cyclin A and B, exist in higher eukaryotes, but their specialised functions in mitosis are incompletely understood. Using degron tags for rapid inducible protein removal, we analyse how acute depletion of these proteins affects mitosis. Loss of cyclin A in G2-phase prevents mitotic entry. Cells lacking cyclin B can enter mitosis and phosphorylate most mitotic proteins, because of parallel PP2A:B55 phosphatase inactivation by Greatwall kinase. The final barrier to mitotic establishment corresponds to nuclear envelope breakdown, which requires a decisive shift in the balance of cyclin-dependent kinase Cdk1 and PP2A:B55 activity. Beyond this point, cyclin B/Cdk1 is essential for phosphorylation of a distinct subset of mitotic Cdk1 substrates that are essential to complete cell division. Our results identify how cyclin A, cyclin B and Greatwall kinase coordinate mitotic progression by increasing levels of Cdk1-dependent substrate phosphorylation.

Human chromosome segregation involves multi-layered regulation of separase by the peptidyl-prolyl-isomerase Pin1.

Ring-shaped cohesin keeps sister chromatids paired until cleavage of its Scc1/Rad21 subunit by separase triggers chromosome segregation in anaphase. Vertebrate separase is held inactive by mutually exclusive binding to securin or Cdk1-cyclin B1 and becomes unleashed only upon ubiquitin-dependent degradation of these regulators. Although most separase is usually found in association with securin, this anaphase inhibitor is dispensable for murine life while Cdk1-cyclin B1-dependent control of separase is essential. Here, we show that securin-independent inhibition of separase by Cdk1-cyclin B1 in early mitosis requires the phosphorylation-specific peptidyl-prolyl cis/trans isomerase Pin1. Furthermore, isomerization of previously securin-bound separase at the metaphase-to-anaphase transition renders it resistant to re-inhibition by residual securin. At the same time, isomerization also limits the half-life of separase's proteolytic activity, explaining how cohesin can be reloaded onto telophase chromatin in the absence of securin and cyclin B1 without being cleaved.

The BEG (PP2A-B55/ENSA/Greatwall) pathway ensures cytokinesis follows chromosome separation.

Cytokinesis follows separase activation and chromosome segregation. This order is ensured in budding yeast by the mitotic exit network (MEN), where Cdc14p dephosphorylates key conserved Cdk1-substrates exemplified by the anaphase spindle-elongation protein Ase1p. However, in metazoans, MEN and Cdc14 function is not conserved. Instead, the PP2A-B55α/ENSA/Greatwall (BEG) pathway controls the human Ase1p ortholog PRC1. In this pathway, PP2A-B55 inhibition is coupled to Cdk1-cyclin B activity, whereas separase inhibition is maintained by cyclin B concentration. This creates two cyclin B thresholds during mitotic exit. Simulation and experiments using PRC1 as a model substrate show that the first threshold permits separase activation and chromosome segregation, and the second permits PP2A-B55 activation and initiation of cytokinesis. Removal of the ENSA/Greatwall (EG) timer module eliminates this second threshold, as well as associated delay in PRC1 dephosphorylation and initiation of cytokinesis, by uncoupling PP2A-B55 from Cdk1-cyclin B activity. Therefore, temporal order during mitotic exit is promoted by the metazoan BEG pathway.

A comprehensive model for the proliferation-quiescence decision in response to endogenous DNA damage in human cells.

Human cells that suffer mild DNA damage can enter a reversible state of growth arrest known as quiescence. This decision to temporarily exit the cell cycle is essential to prevent the propagation of mutations, and most cancer cells harbor defects in the underlying control system. Here we present a mechanistic mathematical model to study the proliferation-quiescence decision in nontransformed human cells. We show that two bistable switches, the restriction point (RP) and the G1/S transition, mediate this decision by integrating DNA damage and mitogen signals. In particular, our data suggest that the cyclin-dependent kinase inhibitor p21 (Cip1/Waf1), which is expressed in response to DNA damage, promotes quiescence by blocking positive feedback loops that facilitate G1 progression downstream of serum stimulation. Intriguingly, cells exploit bistability in the RP to convert graded p21 and mitogen signals into an all-or-nothing cell-cycle response. The same mechanism creates a window of opportunity where G1 cells that have passed the RP can revert to quiescence if exposed to DNA damage. We present experimental evidence that cells gradually lose this ability to revert to quiescence as they progress through G1 and that the onset of rapid p21 degradation at the G1/S transition prevents this response altogether, insulating S phase from mild, endogenous DNA damage. Thus, two bistable switches conspire in the early cell cycle to provide both sensitivity and robustness to external stimuli.

Design principles of biochemical oscillators.

Cellular rhythms are generated by complex interactions among genes, proteins and metabolites. They are used to control every aspect of cell physiology, from signalling, motility and development to growth, division and death. We consider specific examples of oscillatory processes and discuss four general requirements for biochemical oscillations: negative feedback, time delay, sufficient 'nonlinearity' of the reaction kinetics and proper balancing of the timescales of opposing chemical reactions. Positive feedback is one mechanism to delay the negative-feedback signal. Biological oscillators can be classified according to the topology of the positive- and negative-feedback loops in the underlying regulatory mechanism.

Dilution and titration of cell-cycle regulators may control cell size in budding yeast.

The size of a cell sets the scale for all biochemical processes within it, thereby affecting cellular fitness and survival. Hence, cell size needs to be kept within certain limits and relatively constant over multiple generations. However, how cells measure their size and use this information to regulate growth and division remains controversial. Here, we present two mechanistic mathematical models of the budding yeast (S. cerevisiae) cell cycle to investigate competing hypotheses on size control: inhibitor dilution and titration of nuclear sites. Our results suggest that an inhibitor-dilution mechanism, in which cell growth dilutes the transcriptional inhibitor Whi5 against the constant activator Cln3, can facilitate size homeostasis. This is achieved by utilising a positive feedback loop to establish a fixed size threshold for the Start transition, which efficiently couples cell growth to cell cycle progression. Yet, we show that inhibitor dilution cannot reproduce the size of mutants that alter the cell's overall ploidy and WHI5 gene copy number. By contrast, size control through titration of Cln3 against a constant number of genomic binding sites for the transcription factor SBF recapitulates both size homeostasis and the size of these mutant strains. Moreover, this model produces an imperfect 'sizer' behaviour in G1 and a 'timer' in S/G2/M, which combine to yield an 'adder' over the whole cell cycle; an observation recently made in experiments. Hence, our model connects these phenomenological data with the molecular details of the cell cycle, providing a systems-level perspective of budding yeast size control.

Protein phosphatase 2A controls the order and dynamics of cell-cycle transitions.

Bistability of the Cdk1-Wee1-Cdc25 mitotic control network underlies the switch-like transitions between interphase and mitosis. Here, we show by mathematical modeling and experiments in Xenopus egg extracts that protein phosphatase 2A (PP2A), which can dephosphorylate Cdk1 substrates, is essential for this bistability. PP2A inhibition in early interphase abolishes the switch-like response of the system to Cdk1 activity, promoting mitotic onset even with very low levels of Cyclin, Cdk1, and Cdc25, while simultaneously inhibiting DNA replication. Furthermore, even if replication has already initiated, it cannot continue in mitosis. Exclusivity of S and M phases does not depend on bistability only, since partial PP2A inhibition prevents replication without inducing mitotic onset. In these conditions, interphase-level mitotic kinases inhibit Cyclin E-Cdk2 chromatin loading, blocking initiation complex formation. Therefore, by counteracting both Cdk1 activation and activity of mitotic kinases, PP2A ensures robust separation of S phase and mitosis and dynamic transitions between the two states.

PP2A/B55 and Fcp1 regulate Greatwall and Ensa dephosphorylation during mitotic exit.

Entry into mitosis is triggered by activation of Cdk1 and inactivation of its counteracting phosphatase PP2A/B55. Greatwall kinase inactivates PP2A/B55 via its substrates Ensa and ARPP19. Both Greatwall and Ensa/ARPP19 are regulated by phosphorylation, but the dynamic regulation of Greatwall activity and the phosphatases that control Greatwall kinase and its substrates are poorly understood. To address these questions we applied a combination of mathematical modelling and experiments using phospho-specific antibodies to monitor Greatwall, Ensa/ARPP19 and Cdk substrate phosphorylation during mitotic entry and exit. We demonstrate that PP2A/B55 is required for Gwl dephosphorylation at the essential Cdk site Thr194. Ensa/ARPP19 dephosphorylation is mediated by the RNA Polymerase II carboxy terminal domain phosphatase Fcp1. Surprisingly, inhibition or depletion of neither Fcp1 nor PP2A appears to block dephosphorylation of the bulk of mitotic Cdk1 substrates during mitotic exit. Taken together our results suggest a hierarchy of phosphatases coordinating Greatwall, Ensa/ARPP19 and Cdk substrate dephosphorylation during mitotic exit.

Cell cycle control by a minimal Cdk network.

In present-day eukaryotes, the cell division cycle is controlled by a complex network of interacting proteins, including members of the cyclin and cyclin-dependent protein kinase (Cdk) families, and the Anaphase Promoting Complex (APC). Successful progression through the cell cycle depends on precise, temporally ordered regulation of the functions of these proteins. In light of this complexity, it is surprising that in fission yeast, a minimal Cdk network consisting of a single cyclin-Cdk fusion protein can control DNA synthesis and mitosis in a manner that is indistinguishable from wild type. To improve our understanding of the cell cycle regulatory network, we built and analysed a mathematical model of the molecular interactions controlling the G1/S and G2/M transitions in these minimal cells. The model accounts for all observed properties of yeast strains operating with the fusion protein. Importantly, coupling the model's predictions with experimental analysis of alternative minimal cells, we uncover an explanation for the unexpected fact that elimination of inhibitory phosphorylation of Cdk is benign in these strains while it strongly affects normal cells. Furthermore, in the strain without inhibitory phosphorylation of the fusion protein, the distribution of cell size at division is unusually broad, an observation that is accounted for by stochastic simulations of the model. Our approach provides novel insights into the organization and quantitative regulation of wild type cell cycle progression. In particular, it leads us to propose a new mechanistic model for the phenomenon of mitotic catastrophe, relying on a combination of unregulated, multi-cyclin-dependent Cdk activities.

Role for regulated phosphatase activity in generating mitotic oscillations in Xenopus cell-free extracts.

Although current textbook explanations of cell-cycle control in eukaryotes emphasize the periodic activation of cyclin-dependent protein kinases (CDKs), recent experimental observations suggest a significant role for the periodic activation and inactivation of a CDK-counteracting protein phosphatase 2A with a B55δ subunit (PP2A:B55δ), during mitotic cycles in frog-egg extracts and early embryos. In this paper, we extend an earlier mathematical model of embryonic cell cycles to include experimentally motivated roles for PP2A:B55δ and its regulation by Greatwall kinase. Our model is consistent with what is already known about the regulation of CDK and PP2A:B55δ in frog eggs, and it suggests a previously undescribed role for the Greatwall-PP2A:B55δ interaction in creating a toggle switch for activation of the anaphase-promoting complex as embryonic cells exit mitosis and return to interphase.

Models in biology: lessons from modeling regulation of the eukaryotic cell cycle.

In this essay we illustrate some general principles of mathematical modeling in biology by our experiences in studying the molecular regulatory network underlying eukaryotic cell division. We discuss how and why the models moved from simple, parsimonious cartoons to more complex, detailed mechanisms with many kinetic parameters. We describe how the mature models made surprising and informative predictions about the control system that were later confirmed experimentally. Along the way, we comment on the 'parameter estimation problem' and conclude with an appeal for a greater role for mathematical models in molecular cell biology.

A model for the epigenetic switch linking inflammation to cell transformation: deterministic and stochastic approaches.

Recently, a molecular pathway linking inflammation to cell transformation has been discovered. This molecular pathway rests on a positive inflammatory feedback loop between NF-κB, Lin28, Let-7 microRNA and IL6, which leads to an epigenetic switch allowing cell transformation. A transient activation of an inflammatory signal, mediated by the oncoprotein Src, activates NF-κB, which elicits the expression of Lin28. Lin28 decreases the expression of Let-7 microRNA, which results in higher level of IL6 than achieved directly by NF-κB. In turn, IL6 can promote NF-κB activation. Finally, IL6 also elicits the synthesis of STAT3, which is a crucial activator for cell transformation. Here, we propose a computational model to account for the dynamical behavior of this positive inflammatory feedback loop. By means of a deterministic model, we show that an irreversible bistable switch between a transformed and a non-transformed state of the cell is at the core of the dynamical behavior of the positive feedback loop linking inflammation to cell transformation. The model indicates that inhibitors (tumor suppressors) or activators (oncogenes) of this positive feedback loop regulate the occurrence of the epigenetic switch by modulating the threshold of inflammatory signal (Src) needed to promote cell transformation. Both stochastic simulations and deterministic simulations of a heterogeneous cell population suggest that random fluctuations (due to molecular noise or cell-to-cell variability) are able to trigger cell transformation. Moreover, the model predicts that oncogenes/tumor suppressors respectively decrease/increase the robustness of the non-transformed state of the cell towards random fluctuations. Finally, the model accounts for the potential effect of competing endogenous RNAs, ceRNAs, on the dynamics of the epigenetic switch. Depending on their microRNA targets, the model predicts that ceRNAs could act as oncogenes or tumor suppressors by regulating the occurrence of cell transformation.

Irreversibility of mitotic exit is the consequence of systems-level feedback.

The eukaryotic cell cycle comprises an ordered series of events, orchestrated by the activity of cyclin-dependent kinases (Cdks), leading from chromosome replication during S phase to their segregation in mitosis. The unidirectionality of cell-cycle transitions is fundamental for the successful completion of this cycle. It is thought that irrevocable proteolytic degradation of key cell-cycle regulators makes cell-cycle transitions irreversible, thereby enforcing directionality. Here we have experimentally examined the contribution of cyclin proteolysis to the irreversibility of mitotic exit, the transition from high mitotic Cdk activity back to low activity in G1. We show that forced cyclin destruction in mitotic budding yeast cells efficiently drives mitotic exit events. However, these remain reversible after termination of cyclin proteolysis, with recovery of the mitotic state and cyclin levels. Mitotic exit becomes irreversible only after longer periods of cyclin degradation, owing to activation of a double-negative feedback loop involving the Cdk inhibitor Sic1 (refs 4, 5). Quantitative modelling suggests that feedback is required to maintain low Cdk activity and to prevent cyclin resynthesis. Our findings demonstrate that the unidirectionality of mitotic exit is not the consequence of proteolysis but of systems-level feedback required to maintain the cell cycle in a new stable state.

Bistability, oscillations, and traveling waves in frog egg extracts.

Mathematical modeling is a powerful tool for unraveling the complexities of the molecular regulatory networks underlying all aspects of cell physiology. To support this claim, we review our experiences modeling the cyclin-dependent kinase (CDK) network that controls events of the eukaryotic cell cycle. The model was derived from classic experiments on the biochemistry and molecular genetics of CDKs and their partner proteins. Because the dynamical properties of CDK activity depend in large part on positive and negative feedback loops in the regulatory network, it is difficult to predict its behavior by intuitive reasoning alone. Mathematical modeling is the correct tool for reliably determining the properties of the network in comparison with observed properties of dividing cells and for predicting the behavior of the control system under novel conditions. In this review, we describe six unexpected predictions of our 1993 model of the CDK control system in frog egg extracts and the remarkable experiments, performed much later, that verified all six predictions. The dynamical properties of the CDK network are consequences of feedback signals and ultrasensitive responses of regulatory proteins to CDK activity, and we describe the experimental evidence for the predicted ultrasensitivity. This case study illustrates the novel insights that mathematical modeling, analysis, and simulation can provide cell physiologists, and it points the way to a new "dynamical perspective" on molecular cell biology.

Multisite phosphoregulation of Cdc25 activity refines the mitotic entrance and exit switches.

Cyclin-dependent kinase 1 (Cdk1) kinase dephosphorylation and activation by Cdc25 phosphatase are essential for mitotic entry. Activated Cdk1 phosphorylates Cdc25 and other substrates, further activating Cdc25 to form a positive feedback loop that drives the abrupt G2/mitosis switch. Conversely, mitotic exit requires Cdk1 inactivation and reversal of Cdk1 substrate phosphorylation. This dephosphorylation is mediated, in part, by Clp1/Cdc14, a Cdk1-antagonizing phosphatase, which reverses Cdk1 phosphorylation of itself, Cdc25, and other Cdk1 substrates. Thus, Cdc25 phosphoregulation is essential for proper G2-M transition, and its contributions to cell cycle control have been modeled based on studies using Xenopus and human cell extracts. Because cell extract systems only approximate in vivo conditions where proteins interact within dynamic cellular environments, here, we use Schizosaccharomyces pombe to characterize, both experimentally and mathematically, the in vivo contributions of Cdk1-mediated phosphorylation of Cdc25 to the mitotic transition. Through comprehensive mapping of Cdk1 phosphosites on Cdc25 and characterization of phosphomutants, we show that Cdc25 hyperphosphorylation by Cdk1 governs Cdc25 catalytic activation, the precision of mitotic entry, and unvarying cell length but not Cdc25 localization or abundance. We propose a mathematical model that explains Cdc25 regulation by Cdk1 through a distributive and disordered phosphorylation mechanism that ultrasensitively activates Cdc25. We also show that Clp1/Cdc14 dephosphorylation of Cdk1 sites on Cdc25 controls the proper timing of cell division, a mechanism that is likely due to the double negative feedback loop between Clp1/Cdc14 and Cdc25 that controls the abruptness of the mitotic exit switch.

A general G1/S-phase cell-cycle control module in the flowering plant Arabidopsis thaliana.

The decision to replicate its DNA is of crucial importance for every cell and, in many organisms, is decisive for the progression through the entire cell cycle. A comparison of animals versus yeast has shown that, although most of the involved cell-cycle regulators are divergent in both clades, they fulfill a similar role and the overall network topology of G1/S regulation is highly conserved. Using germline development as a model system, we identified a regulatory cascade controlling entry into S phase in the flowering plant Arabidopsis thaliana, which, as a member of the Plantae supergroup, is phylogenetically only distantly related to Opisthokonts such as yeast and animals. This module comprises the Arabidopsis homologs of the animal transcription factor E2F, the plant homolog of the animal transcriptional repressor Retinoblastoma (Rb)-related 1 (RBR1), the plant-specific F-box protein F-BOX-LIKE 17 (FBL17), the plant specific cyclin-dependent kinase (CDK) inhibitors KRPs, as well as CDKA;1, the plant homolog of the yeast and animal Cdc2⁺/Cdk1 kinases. Our data show that the principle of a double negative wiring of Rb proteins is highly conserved, likely representing a universal mechanism in eukaryotic cell-cycle control. However, this negative feedback of Rb proteins is differently implemented in plants as it is brought about through a quadruple negative regulation centered around the F-box protein FBL17 that mediates the degradation of CDK inhibitors but is itself directly repressed by Rb. Biomathematical simulations and subsequent experimental confirmation of computational predictions revealed that this regulatory circuit can give rise to hysteresis highlighting the here identified dosage sensitivity of CDK inhibitors in this network.

Phosphorylation network dynamics in the control of cell cycle transitions.

Fifteen years ago, it was proposed that the cell cycle in fission yeast can be driven by quantitative changes in the activity of a single protein kinase complex comprising a cyclin - namely cyclin B - and cyclin dependent kinase 1 (Cdk1). When its activity is low, Cdk1 triggers the onset of S phase; when its activity level exceeds a specific threshold, it promotes entry into mitosis. This model has redefined our understanding of the essential functional inputs that organize cell cycle progression, and its main principles now appear to be applicable to all eukaryotic cells. But how does a change in the activity of one kinase generate ordered progression through the cell cycle in order to separate DNA replication from mitosis? To answer this question, we must consider the biochemical processes that underlie the phosphorylation of Cdk1 substrates. In this Commentary, we discuss recent findings that have shed light on how the threshold levels of Cdk1 activity that are required for progression through each phase are determined, how an increase in Cdk activity generates directionality in the cell cycle, and why cell cycle transitions are abrupt rather than gradual. These considerations lead to a general quantitative model of cell cycle control, in which opposing kinase and phosphatase activities have an essential role in ensuring dynamic transitions.