Effect of positive feedback loops on the robustness of oscillations in the network of cyclin-dependent kinases driving the mammalian cell cycle

The transitions between the G(1) , S, G(2) and M phases of the mammalian cell cycle are driven by a network of cyclin-dependent kinases (Cdks), whose sequential activation is regulated by intertwined negative and positive feedback loops. We previously proposed a detailed computational model for the Cdk network, and showed that this network is capable of temporal self-organization in the form of sustained oscillations, which govern ordered progression through the successive phases of the cell cycle [Gérard and Goldbeter (2009) Proc Natl Acad Sci USA106, 21643-21648]. We subsequently proposed a skeleton model for the cell cycle that retains the core regulatory mechanisms of the detailed model [Gérard and Goldbeter (2011) Interface Focus1, 24-35]. Here we extend this skeleton model by incorporating Cdk regulation through phosphorylation/dephosphorylation and by including the positive feedback loops that underlie the dynamics of the G(1) /S and G(2) /M transitions via phosphatase Cdc25 and via phosphatase Cdc25 and kinase Wee1, respectively. We determine the effects of these positive feedback loops and ultrasensitivity in phosphorylation/dephosphorylation on the dynamics of the Cdk network. The multiplicity of positive feedback loops as well as the existence of ultrasensitivity promote the occurrence of bistability and increase the amplitude of the oscillations in the various cyclin/Cdk complexes. By resorting to stochastic simulations, we further show that the presence of multiple, redundant positive feedback loops in the G(2) /M transition of the cell cycle markedly enhances the robustness of the Cdk oscillations with respect to molecular noise.     

Mitotic progression becomes irreversible in prometaphase and collapses when Wee1 and Cdc25 are inhibited

Mitosis requires precise coordination of multiple global reorganizations of the nucleus and cytoplasm. Cyclin-dependent kinase 1 (Cdk1) is the primary upstream kinase that directs mitotic progression by phosphorylation of a large number of substrate proteins. Cdk1 activation reaches the peak level due to positive feedback mechanisms. By inhibiting Cdk chemically, we showed that, in prometaphase, when Cdk1 substrates approach the peak of their phosphorylation, cells become capable of proper M-to-G1 transition. We interfered with the molecular components of the Cdk1-activating feedback system through use of chemical inhibitors of Wee1 and Myt1 kinases and Cdc25 phosphatases. Inhibition of Wee1 and Myt1 at the end of the S phase led to rapid Cdk1 activation and morphologically normal mitotic entry, even in the absence of G2. Dampening Cdc25 phosphatases simultaneously with Wee1 and Myt1 inhibition prevented Cdk1/cyclin B kinase activation and full substrate phosphorylation and induced a mitotic "collapse," a terminal state characterized by the dephosphorylation of mitotic substrates without cyclin B proteolysis. This was blocked by the PP1/PP2A phosphatase inhibitor, okadaic acid. These findings suggest that the positive feedback in Cdk activation serves to overcome the activity of Cdk-opposing phosphatases and thus sustains forward progression in mitosis.     

Rapid cycling and precocious termination of G1 phase in cells expressing CDK1AF

In Xenopus embryos, the cell cycle is driven by an autonomous biochemical oscillator that controls the periodic activation and inactivation of cyclin B1-CDK1. The oscillator circuit includes a system of three interlinked positive and double-negative feedback loops (CDK1 -> Cdc25 -> CDK1; CDK1 -/ Wee1 -/ CDK1; and CDK1 -/ Myt1 -/ CDK1) that collectively function as a bistable trigger. Previous work established that this bistable trigger is essential for CDK1 oscillations in the early embryonic cell cycle. Here, we assess the importance of the trigger in the somatic cell cycle, where checkpoints and additional regulatory mechanisms could render it dispensable. Our approach was to express the phosphorylation site mutant CDK1AF, which short-circuits the feedback loops, in HeLa cells, and to monitor cell cycle progression by live cell fluorescence microscopy. We found that CDK1AF-expressing cells carry out a relatively normal first mitosis, but then undergo rapid cycles of cyclin B1 accumulation and destruction at intervals of 3-6 h. During these cycles, the cells enter and exit M phase-like states without carrying out cytokinesis or karyokinesis. Phenotypically similar rapid cycles were seen in Wee1 knockdown cells. These findings show that the interplay between CDK1, Wee1/Myt1, and Cdc25 is required for the establishment of G1 phase, for the normal approximately 20-h cell cycle period, and for the switch-like oscillations in cyclin B1 abundance characteristic of the somatic cell cycle. We propose that the HeLa cell cycle is built upon an unreliable negative feedback oscillator and that the normal high reliability, slow pace and switch-like character of the cycle is imposed by a bistable CDK1/Wee1/Myt1/Cdc25 system.     

Mitotic exit in two dimensions

Metaphase of mitosis is brought about in all eukaryotes by activation of cylin-dependent kinase (Cdk1), whereas exit from mitosis requires down-regulation of Cdk1 activity and dephosphorylation of its target proteins. In budding yeast, the completion of mitotic exit requires the release and activation of the Cdc14 protein-phosphatase, which is kept inactive in the nucleolus during most of the cell cycle. Activation of Cdc14 is controlled by two regulatory networks called FEAR (Cdc fourteen early anaphase release) and MEN (mitotic exit network). We have shown recently that the anaphase promoting protease (separase) is essential for Cdc14 activation, thereby it makes mitotic exit dependent on execution of anaphase. Based on this finding, we have proposed a new model for mitotic exit in budding yeast. Here we explain the essence of the model by phaseplane analysis, which reveals two underlying bistable switches in the regulatory network. One bistable switch is caused by mutual activation (positive feedback) between Cdc14 activating MEN and Cdc14 itself. The mitosis-inducing Cdk1 activity inhibits the activation of this positive feedback loop and thereby controlling this switch. The other irreversible switch is generated by a double-negative feedback (mutual antagonism) between mitosis inducing Cdk1 activity and its degradation machinery (APC(Cdh1)). The Cdc14 phosphatase helps turning this switch in favor of APC(Cdh1) side. Both of these bistable switches have characteristic thresholds, the first one for Cdk1 activity, while the second for Cdc14 activity. We show that the physiological behaviors of certain cell cycle mutants are suggestive for those Cdk1 and Cdc14 thresholds. The two bistable switches turn on in a well-defined order. In this paper, we explain how the activation of Cdc20 (which causes the activation of separase and a decrease of Cdk1 kinase activity) provides an initial trigger for the activation of the MEN-Cdc14 positive feedback loops, which in turn, flips the second irreversible Cdk-APC(Cdh1) switch on the APC(Cdh1) side).     

Human Cdc14A regulates Wee1 stability by counteracting CDK-mediated phosphorylation

The activity of Cdk1–cyclin B1 mitotic complexes is regulated by the balance between the counteracting activities of Wee1/Myt1 kinases and Cdc25 phosphatases. These kinases and phosphatases must be strictly regulated to ensure proper mitotic timing. One masterpiece of this regulatory network is Cdk1, which promotes Cdc25 activity and suppresses inhibitory Wee1/Myt1 kinases through direct phosphorylation. The Cdk1-dependent phosphorylation of Wee1 primes phosphorylation by additional kinases such as Plk1, triggering Wee1 degradation at the onset of mitosis. Here we report that Cdc14A plays an important role in the regulation of Wee1 stability. Depletion of Cdc14A results in a significant reduction in Wee1 protein levels. Cdc14A binds to Wee1 at its amino-terminal domain and reverses CDK-mediated Wee1 phosphorylation. In particular, we found that Cdc14A inhibits Wee1 degradation through the dephosphorylation of Ser-123 and Ser-139 residues. Thus the lack of phosphorylation of these two residues prevents the interaction with Plk1 and the consequent efficient Wee1 degradation at the onset of mitosis. These data support the hypothesis that Cdc14A counteracts Cdk1–cyclin B1 activity through Wee1 dephosphorylation.     

Switches and latches: a biochemical tug-of-war between the kinases and phosphatases that control mitosis

Activation of the cyclin-dependent kinase (Cdk1) cyclin B (CycB) complex (Cdk1:CycB) in mitosis brings about a remarkable extent of protein phosphorylation. Cdk1:CycB activation is switch-like, controlled by two auto-amplification loops--Cdk1:CycB activates its activating phosphatase, Cdc25, and inhibits its inhibiting kinase, Wee1. Recent experimental evidence suggests that parallel to Cdk1:CycB activation during mitosis, there is inhibition of its counteracting phosphatase activity. We argue that the downregulation of the phosphatase is not just a simple latch that suppresses futile cycles of phosphorylation/dephosphorylation during mitosis. Instead, we propose that phosphatase regulation creates coherent feed-forward loops and adds extra amplification loops to the Cdk1:CycB regulatory network, thus forming an integral part of the mitotic switch. These network motifs further strengthen the bistable characteristic of the mitotic switch, which is based on the antagonistic interaction of two groups of proteins: M-phase promoting factors (Cdk1:CycB, Cdc25, Greatwall and Endosulfine/Arpp19) and interphase promoting factors (Wee1, PP2A-B55 and a Greatwall counteracting phosphatase, probably PP1). The bistable character of the switch implies the existence of a CycB threshold for entry into mitosis. The end of G2 phase is determined by the point where CycB level crosses the CycB threshold for Cdk1 activation.     

Ultrasensitivity in the Regulation of Cdc25C by Cdk1

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Highlights? The response of Cdc25C to Cdk1 in Xenopus egg extracts is ultrasensitive ? The Hill coefficient for the response is astronomical (～11–32) ? Multisite phosphorylation accounts for some of the ultrasensitivity ? The Cdc25C and Wee1A responses account for the bistability of the mitotic trigger     

Synthetic conversion of a graded receptor signal into a tunable,reversible switch

The ability to engineer an all‐or‐none cellular response to a given signaling ligand is important in applications ranging from biosensing to tissue engineering. However, synthetic gene network ‘switches’ have been limited in their applicability and tunability due to their reliance on specific components to function. Here, we present a strategy for reversible switch design that instead relies only on a robust, easily constructed network topology with two positive feedback loops and we apply the method to create highly ultrasensitive (n_H>20), bistable cellular responses to a synthetic ligand/receptor complex. Independent modulation of the two feedback strengths enables rational tuning and some decoupling of steady‐state (ultrasensitivity, signal amplitude, switching threshold, and bistability) and kinetic (rates of system activation and deactivation) response properties. Our integrated computational and synthetic biology approach elucidates design rules for building cellular switches with desired properties, which may be of utility in engineering signal‐transduction pathways.     

Gauchos and ochos: a Wee1-Cdk tango regulating mitotic entry

The kinase Wee1 has been recognized for a quarter century as a key inhibitor of Cyclin dependent kinase 1 (Cdk1) and mitotic entry in eukaryotes. Nonetheless, Wee1 regulation is not well understood and its large amino-terminal regulatory domain (NRD) has remained largely uncharted. Evidence has accumulated that cyclin B/Cdk1 complexes reciprocally inhibit Wee1 activity through NRD phosphorylation. Recent studies have identified the first functional NRD elements and suggested that vertebrate cyclin A/Cdk2 complexes also phosphorylate the NRD. A short NRD peptide, termed the Wee box, augments the activity of the Wee1 kinase domain. Cdk1/2-mediated phosphorylation of the Wee box (on T239) antagonizes kinase activity. A nearby region harbors a conserved RxL motif (RxL1) that promotes cyclin A/Cdk2 binding and T239 phosphorylation. Mutation of either T239 or RxL1 bolsters the ability of Wee1 to block mitotic entry, consistent with negative regulation of Wee1 through these sites. The region in human somatic Wee1 that encompasses RxL1 also binds Crm1, directing Wee1 export from the nucleus. These studies have illuminated important aspects of Wee1 regulation and defined a specific molecular pathway through which cyclin A/Cdk2 complexes foster mitotic entry. The complexity, speed, and importance of regulation of mitotic entry suggest that there is more to be learned.     

Dual Phosphorylation of Cdk1 Coordinates Cell Proliferation with Key Developmental Processes in Drosophila

Eukaryotic organisms use conserved checkpoint mechanisms that regulate Cdk1 by inhibitory phosphorylation to prevent mitosis from interfering with DNA replication or repair. In metazoans, this checkpoint mechanism is also used for coordinating mitosis with dynamic developmental processes. Inhibitory phosphorylation of Cdk1 is catalyzed by Wee1 kinases that phosphorylate tyrosine 15 (Y15) and dual-specificity Myt1 kinases found only in metazoans that phosphorylate Y15 and the adjacent threonine (T14) residue. Despite partially redundant roles in Cdk1 inhibitory phosphorylation, Wee1 and Myt1 serve specialized developmental functions that are not well understood. Here, we expressed wild-type and phospho-acceptor mutant Cdk1 proteins to investigate how biochemical differences in Cdk1 inhibitory phosphorylation influence Drosophila imaginal development. Phosphorylation of Cdk1 on Y15 appeared to be crucial for developmental and DNA damage-induced G2-phase checkpoint arrest, consistent with other evidence that Myt1 is the major Y15-directed Cdk1 inhibitory kinase at this stage of development. Expression of non-inhibitable Cdk1 also caused chromosome defects in larval neuroblasts that were not observed with Cdk1(Y15F) mutant proteins that were phosphorylated on T14, implicating Myt1 in a novel mechanism promoting genome stability. Collectively, these results suggest that dual inhibitory phosphorylation of Cdk1 by Myt1 serves at least two functions during development. Phosphorylation of Y15 is essential for the premitotic checkpoint mechanism, whereas T14 phosphorylation facilitates accumulation of dually inhibited Cdk1–Cyclin B complexes that can be rapidly activated once checkpoint-arrested G2-phase cells are ready for mitosis.     

Molecular titration and ultrasensitivity in regulatory networks

Protein sequestration occurs when an active protein is sequestered by a repressor into an inactive complex. Using mathematical and computational modeling, we show how this regulatory mechanism (called “molecular titration”) can generate ultrasensitive or “all-or-none” responses that are equivalent to highly cooperative processes. The ultrasensitive nature of the input-output response is mainly determined by two parameters: the dimer dissociation constant and the repressor concentration. Because in vivo concentrations are tunable through a variety of mechanisms, molecular titration represents a flexible mechanism for generating ultrasensitivity. Using physiological parameters, we report how details of in vivo protein degradation affect the strength of the ultrasensitivity at steady state. Given that developmental systems often transduce signals into cell-fate decisions on timescales incompatible with steady state, we further examine whether molecular titration can produce ultrasensitive responses within physiologically relevant time intervals. Using Drosophila somatic sex determination as a developmental paradigm, we demonstrate that molecular titration can generate ultrasensitivity on timescales compatible with most cell-fate decisions. Gene duplication followed by loss-of-function mutations can create dominant negatives that titrate and compete with the original protein. Dominant negatives are abundant in gene regulatory circuits, and our results suggest that molecular titration might be generating an ultrasensitive response in these networks.     

A kinetic model of the cyclin E/Cdk2 developmental timer in Xenopus laevis embryos

Early cell cycles of Xenopus laevis embryos are characterized by rapid oscillations in the activity of two cyclin-dependent kinases. Cdk1 activity peaks at mitosis, driven by periodic degradation of cyclins A and B. In contrast, Cdk2 activity oscillates twice per cell cycle, despite a constant level of its partner, cyclin E. Cyclin E degrades at a fixed time after fertilization, normally corresponding to the midblastula transition. Based on published data and new experiments, we constructed a mathematical model in which: (1) oscillations in Cdk2 activity depend upon changes in phosphorylation, (2) Cdk2 participates in a negative feedback loop with the inhibitory kinase Wee1; (3) cyclin E is cooperatively removed from the oscillatory system; and (4) removed cyclin E is degraded by a pathway activated by cyclin E/Cdk2 itself. The model's predictions about embryos injected with Xic1, a stoichiometric inhibitor of cyclin E/Cdk2, were experimentally validated.     

A Bifunctional Regulatory Element in Human Somatic Wee1 Mediates Cyclin A/Cdk2 Binding and Crm1-Dependent Nuclear Export

Sophisticated models for the regulation of mitotic entry are lacking for human cells. Inactivating human cyclin A/Cdk2 complexes through diverse approaches delays mitotic entry and promotes inhibitory phosphorylation of Cdk1 on tyrosine 15, a modification performed by Wee1. We show here that cyclin A/Cdk2 complexes physically associate with Wee1 in U2OS cells. Mutation of four conserved RXL cyclin A/Cdk binding motifs (RXL1 to RXL4) in Wee1 diminished stable binding. RXL1 resides within a large regulatory region of Wee1 that is predicted to be intrinsically disordered (residues 1 to 292). Near RXL1 is T239, a site of inhibitory Cdk phosphorylation in Xenopus Wee1 proteins. We found that T239 is phosphorylated in human Wee1 and that this phosphorylation was reduced in an RXL1 mutant. RXL1 and T239 mutants each mediated greater Cdk phosphorylation and G₂/M inhibition than the wild type, suggesting that cyclin A/Cdk complexes inhibit human Wee1 through these sites. The RXL1 mutant uniquely also displayed increased nuclear localization. RXL1 is embedded within sequences homologous to Crm1-dependent nuclear export signals (NESs). Coimmunoprecipitation showed that Crm1 associated with Wee1. Moreover, treatment with the Crm1 inhibitor leptomycin B or independent mutation of the potential NES (NESm) abolished Wee1 nuclear export. Export was also reduced by Cdk inhibition or cyclin A RNA interference, suggesting that cyclin A/Cdk complexes contribute to Wee1 export. Somewhat surprisingly, NESm did not display increased G₂/M inhibition. Thus, nuclear export of Wee1 is not essential for mitotic entry though an important functional role remains likely. These studies identify a novel bifunctional regulatory element in Wee1 that mediates cyclin A/Cdk2 association and nuclear export.Despite broad progress in studies of cell cycle control in eukaryotes, advanced models are lacking for the regulation of mitotic entry in human cells. This regulation is pivotal in cell cycle control, and a better understanding of it may be crucial to improving cytotoxic cancer chemotherapy, the mainstay of cancer treatment. Models of mitotic entry in higher eukaryotes revolve around activation of the cyclin B/Cdk1 (cyclin-dependent kinase 1 or Cdc2) complex, which drives the major events of mitosis. A rise in the cyclin B level triggers mitotic entry in Xenopus egg extracts but not in mammalian cells (15, 47). Inhibitory phosphorylation of Cdk1 on the ATP-binding site residue tyrosine 15 (Y15) has been recognized as a key constraint throughout eukaryotes (29, 42). Wee1 and Myt kinases perform this phosphorylation in vertebrate cells, where Wee1 appears to be dominant (34). Kim and Ferrell and others have recently developed an elegant model for ultrasensitive, switch-like inactivation of Wee1 by cyclin B/Cdk1 in a positive feedback loop that contributes to mitotic entry in Xenopus egg extracts (27).Although cyclin A(A2)/Cdk2 is traditionally omitted from models of mitotic entry, accumulating evidence from several different approaches suggests that cyclin A/Cdk complexes play roles. Cyclin A levels rise during S phase and peak in G₂ before falling abruptly in prometaphase of mitosis (60). Microinjection of cyclin A/Cdk2 complexes in human G₂ phase cells was observed to drive mitotic entry (14). Conversely, microinjection of antibodies directed against cyclin A in S-phase cells inhibited mitotic entry without an apparent effect on bulk DNA synthesis (45). In complementary approaches that supported biochemical analyses, cyclin A RNA interference (RNAi) or induction of a dominant negative mutant of Cdk2 (Cdk2-dn), the major cyclin A binding partner, inhibited mitotic entry (13, 15, 21, 37). In these settings, cyclin B/Cdk1 complexes accumulated in inactive, Y15-phosphorylated forms (13, 21, 37). Cdc25 phosphatases, which can reverse this phosphorylation, show reduced activity in this context (37), but increased Cdc25 activity could not readily overcome the arrest (13). RNAi-mediated knockdown of Wee1 was found capable of overriding the arrest mediated by cyclin A RNAi, suggesting that Wee1 is a key rate-limiting factor (13). However, whether and by what mechanisms cyclin A complexes might regulate Wee1 and drive Cdk1 dephosphorylation and mitotic entry have remained unclear.Recently, genetic studies in mice have reinforced these observations while providing evidence for some cell type differences (24). Although Cdk2 is not essential, in its absence Cdk1 binds more cyclin A and E and provides redundant functions (4, 25, 44). Deletion of the cyclin A gene is lethal for embryos and adults (24). Gene deletion in fibroblasts in vitro did not completely abrogate their proliferation but caused S and G₂/M delays. In this setting cyclin E was upregulated, and combined deletion of cyclin E yielded arrest in G₁, S, and G₂/M phases. Cyclin A gene deletion was alone sufficient to block proliferation of hematopoietic stem cells, suggesting that cyclin A is essential for their proliferation.Wee1 is regulated on multiple levels, including inhibitory phosphorylation in the amino-terminal regulatory domain (NRD), residues 1 to 292. This region is predicted to be intrinsically disordered (56), and few functional elements have been identified in it. The cyclin B/Cdk1 complex has been thought to be the principal or exclusive kinase responsible for NRD phosphorylation (18, 27, 28). Two sites in the Xenopus embryonic Wee1 NRD, Thr 104 and Thr 150 (referred to here by the homologous residue, T239, in human somatic Wee1), have been identified as Cdk phosphorylation sites that inhibit Wee1 activity (28). Recent studies of Xenopus somatic Wee1 suggest that T239 phosphorylation may antagonize the function of a surrounding motif, dubbed the Wee box (43). This small, conserved region appears to augment the activity of the carboxy-terminal kinase domain.We show here that cyclin A/Cdk2 complexes directly bind Wee1 as a substrate in human cells. In particular, a conserved cyclin A/Cdk binding RXL motif in the Wee1 NRD is required for efficient T239 phosphorylation. Further analysis revealed that RXL1 is located within a Crm1 binding site that mediates Wee1 export during S and G₂ phases. Cyclin A/Cdk2 activity appears to foster Wee1 export, but this export is not essential for mitotic entry. These findings further define roles of cyclin A/Cdk complexes in regulating Wee1 and mitotic entry in human cells and dissect the mechanisms and consequences of Wee1 redistribution during the run-up to mitosis.     

A phosphatase threshold sets the level of Cdk1 activity in early mitosis in budding yeast

Entry into mitosis is initiated by synthesis of cyclins, which bind and activate cyclin-dependent kinase 1 (Cdk1). Cyclin synthesis is gradual, yet activation of Cdk1 occurs in a stepwise manner: a low level of Cdk1 activity is initially generated that triggers early mitotic events, which is followed by full activation of Cdk1. Little is known about how stepwise activation of Cdk1 is achieved. A key regulator of Cdk1 is the Wee1 kinase, which phosphorylates and inhibits Cdk1. Wee1 and Cdk1 show mutual regulation: Cdk1 phosphorylates Wee1, which activates Wee1 to inhibit Cdk1. Further phosphorylation events inactivate Wee1. We discovered that a specific form of protein phosphatase 2A (PP2A(Cdc55)) opposes the initial phosphorylation of Wee1 by Cdk1. In vivo analysis, in vitro reconstitution, and mathematical modeling suggest that PP2A(Cdc55) sets a threshold that limits activation of Wee1, thereby allowing a low constant level of Cdk1 activity to escape Wee1 inhibition in early mitosis. These results define a new role for PP2A(Cdc55) and reveal a systems-level mechanism by which dynamically opposed kinase and phosphatase activities can modulate signal strength.     

Spatial positive feedback at the onset of mitosis

Mitosis is triggered by the activation of Cdk1-cyclin B1 and its translocation from the cytoplasm to the nucleus. Positive feedback loops regulate the activation of Cdk1-cyclin B1 and help make the process irreversible and all-or-none in character. Here we examine whether an analogous process, spatial positive feedback, regulates Cdk1-cyclin B1 redistribution. We used chemical biology approaches and live-cell microscopy to show that nuclear Cdk1-cyclin B1 promotes the translocation of Cdk1-cyclin B1 to the nucleus. Mechanistic studies suggest that cyclin B1 phosphorylation promotes nuclear translocation and, conversely, nuclear translocation promotes cyclin B1 phosphorylation, accounting for the feedback. Interfering with the abruptness of Cdk1-cyclin B1 translocation affects the timing and synchronicity of subsequent mitotic events, underscoring the functional importance of this feedback. We propose that spatial positive feedback ensures a rapid, complete, robust, and irreversible transition from interphase to mitosis and suggest that bistable spatiotemporal switches may be widespread in biological regulation.     

Artemis links ATM to G2/M checkpoint recovery via regulation of Cdk1-cyclin B

Artemis is a phospho-protein that has been shown to have roles in V(D)J recombination, nonhomologous end-joining of double-strand breaks, and regulation of the DNA damage-induced G(2)/M cell cycle checkpoint. Here, we have identified four sites in Artemis that are phosphorylated in response to ionizing radiation (IR) and show that ATM is the major kinase responsible for these modifications. Two of the sites, S534 and S538, show rapid phosphorylation and dephosphorylation, and the other two sites, S516 and S645, exhibit rapid and prolonged phosphorylation. Mutation of both of these latter two residues results in defective recovery from the G(2)/M cell cycle checkpoint. This defective recovery is due to promotion by mutant Artemis of an enhanced interaction between unphosphorylated cyclin B and Cdk1, which in turn promotes inhibitory phosphorylation of Cdk1 by the Wee1 kinase. In addition, we show that mutant Artemis prevents Cdk1-cyclin B activation by causing its retention in the centrosome and inhibition of its nuclear import during prophase. These findings show that ATM regulates G(2)/M checkpoint recovery through inhibitory phosphorylations of Artemis that occur soon after DNA damage, thus setting a molecular switch that, hours later upon completion of DNA repair, allows activation of the Cdk1-cyclin B complex. These findings thus establish a novel function of Artemis as a regulator of the cell cycle in response to DNA damage.     

Ultrasensitivity in Phosphorylation-Dephosphorylation Cycles with Little Substrate

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with phosphosites, we find an upper bound of the Hill number of , and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate''s phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells.

Authors Summary

Dose-response curves are said to be ultrasensitive when they are sigmoidal rather than hyperbolic and often underlay cellular decision-making circuits. Zero-order ultrasensitivity is a well-known mechanism to generate sigmoidal curves in phosphorylation cycles, but one of its assumptions often implies that the substrate is more abundant than the modifying enzymes. We show that this assumption is unlikely to always hold in vivo, and we present a general model that generates ultrasensitivity when the enzymes are in excess of their substrate. The model combines conformational allosteric transitions of the substrate with two-stage binding of the enzymes: the enzymes bind first to a docking site on the substrate and then to the substrate''s phosphosites. Ultrasensitivity is generated because the kinase can bind to the fully phosphorylated form of the substrate (at its docking site) and sequester the substrate away from the phosphatase and, similarly, the phosphatase can bind to the fully dephosphorylated form of the substrate and sequester the substrate away from the kinase. The number of kinase-phosphatase competitions for the substrate determines the degree of ultrasensitivity. Finally, we show that this model can generate non-monotonic responses that peak at intermediate levels of input.     

Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements

Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero-order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.