System-Level Feedbacks Control Cell Cycle Progression

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FEBS Letters 583 (2009) 3992–3998

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Review System-level feedbacks control cell cycle progression

Orsolya Kapuy a, Enuo He a, Sandra López-Avilés b, Frank Uhlmann b, John J. Tyson c, Béla Novák a,*

a Oxford Centre for Integrative Systems Biology, Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, UK b Chromosome Segregation Laboratory, Cancer Research UK London Research Institute, 44 Lincoln’s Inn Fields, London WC2A 3PX, UK c Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

article info abstract

Article history: Repetitive cell cycles, which are essential to the perpetuation of life, are orchestrated by an under- Received 25 June 2009 lying biochemical reaction network centered around cyclin-dependent protein kinases (Cdks) and Revised 27 July 2009 their regulatory subunits (cyclins). Oscillations of Cdk1/CycB activity between low and high levels Accepted 13 August 2009 during the cycle trigger DNA replication and mitosis in the correct order. Based on computational Available online 22 August 2009 modeling, we proposed that the low and the high kinase activity states are alternative stable steady Edited by Johan Elf states of a bistable Cdk-control system. Bistability is a consequence of system-level feedback (positive and double-negative feedback signals) in the underlying control system. We have also argued that bistability underlies irreversible transitions between low and high Cdk activity states and Keywords: Cell cycle thereby ensures directionality of cell cycle progression. Bistability Ó 2009 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved. Irreversibility Feedback Start Mitotic exit

1. Introduction activate and inhibit particular cell cycle events, and this dual control is crucial for proper progression through the cell cycle [2]. All cells arise by the division of preexisting cells. Successful cell The Cdk/cyclin complexes that initiate S phase and mitosis are division requires that the cell first replicate its DNA (during the conveniently called S phase promoting factor (SPF) and M phase period called S phase), and then partition the replicated chromo- promoting factor (MPF), respectively [3]. Higher eukaryotes have somes evenly to the two incipient progeny cells in mitosis (M many different Cdks (Cdk1, Cdk2, etc.) and multiple cyclins (CycA, phase). During cell proliferation, chromosome replication and CycB, etc.); however, only Cdk1 is essential [4]. In higher eukary- segregation should happen once and only once between two otes the Cdk subunits of SPF and MPF are Cdk1 and Cdk2, respec- successive divisions and in the correct order: S phase followed by tively; while lower eukaryotes employ Cdk1 in both SPF and M phase. The timing and ordering of chromosome replication, MPF. The cyclin partners in SPF and MPF are usually different: CycA segregation and cell division (in eukaryotes) is controlled by and CycB in higher eukaryotes, and two different CycBs in lower cyclin-dependent protein kinases (Cdks) and their counter-acting eukaryotes. phosphatases. Cdks in complex with activatory subunits (called SPF activity rises at the G1/S transition and triggers DNA repli- cyclins) phosphorylate their target proteins on specific amino acid cation, while MPF activity peaks later and brings about M phase. residues, while phosphatases reverse these modifications [1]. Since both SPF and MPF block further replication of already repli- These target proteins are responsible for executing particular cated chromosomes, re-replication of the genome is impossible cell cycle events. Hence the proper ordering of these events as long as these activities are present. At the end of mitosis both depends on the timely activation (or possibly inactivation) of SPF and MPF activities disappear because their cyclin subunits Cdk-target proteins. Because Cdk-dependent phosphorylation are degraded [5]. During G1 phase of the following cell cycle, when events may either activate or inhibit target proteins, Cdks can both both SPF and MPF activities are low [6], origins of replication can be relicensed for another round of DNA synthesis [7,8]. Lumping together SPF and MPF activities, we can define two Abbreviations: Cdk, cyclin-dependent-kinase; APC, anaphase promoting com- fundamental states of the cell cycle: G1, when Cdk activity is low plex; CKI, cyclin-dependent kinase inhibitor; SPF, S phase promoting factor; MPF, M and chromosomes are unreplicated, and S + G2 + M, when Cdk phase promoting factor * Corresponding author. Fax: +44 (0) 1865 613213. activity is high and chromosomes are being replicated and segre- E-mail address: [email protected] (B. Novák). gated. Two fundamental transitions define the boundaries between

0014-5793/$36.00 Ó 2009 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.febslet.2009.08.023 O. Kapuy et al. / FEBS Letters 583 (2009) 3992–3998 3993 these two states: the G1/S transition (sometimes called ‘Start’) and the cell cycle are two alternative steady states of the underlying the M/G1 transition (often called ‘Exit from mitosis’). The two fun- Cdk-control network (see [22] for review). damental cell cycle states must be stable, and the transitions be- Switching between these two stable states, which must occur at tween them must be irreversible. An accidental transition from the G1/S and M/G1 transitions, is promoted by ‘helper proteins’ one state to the other can compromise the order of cell cycle (see Fig. 1). Helper proteins are not part of these feedback loops, events. If, for example, the cell loses SPF and MPF activities before but they can push the bistable switch in one direction or the other. it has completed mitosis, then the next activation of SPF will trig- The helper proteins for the G1/S transition are starter kinases (SK, ger another round of S phase and increase the ploidy of the cell [9]. usually Cdk/cyclin complexes other than SPF and MPF) that are Hence, the underlying mechanisms that provide stability to the resistant to the inhibitors of SPF and MPF and are not dependent low- and high-Cdk states and irreversibility to the transitions be- on the activators of SPF and MPF. By inhibiting the inhibitors of tween these states are crucial for unidirectional progression SPF and MPF (or activating their activators), the starter kinases through the cell cycle. destabilize the G1 state of the cycle and promote entry into S The cyclin components of both SPF and MPF are abruptly de- phase. ‘Exit proteins’ (EP) work in the opposite way to destabilize graded at the end of mitosis [10], and this observation provided the high Cdk activity state and promote exit from mitosis. a simple, intuitive explanation for the irreversibility of mitotic exit: Since Start and Exit flip the switch in opposite directions, the since protein degradation is a thermodynamically irreversible pro- helper proteins for one transition are inhibitory for the other. cess, a dividing cell cannot revert to M phase [11]. Tim Hunt’s dis- Therefore, the helper proteins must be present only transiently covery of cyclin degradation became a paradigm for understanding during the Start and Exit transitions. This transiency is achieved cell cycle progression, as many other cell cycle regulators were by negative feedback loops in the control system. The starter ki- found to be abruptly degraded in specific phases of the cycle. nases are down-regulated by high SPF and MPF activities after Therefore, it is commonplace now to explain all cell cycle transi- the G1/S transition takes place. In contrast, the activities of exit tions by the irreversibility of protein degradation [11]. proteins are dependent on high SPF and/or MPF activity, and, But there is a flaw in this simple, appealing view: in a living cell, hence, they turn off after mitotic exit. As a consequence of these protein degradation is counteracted by protein synthesis. negative feedback loops, after each transition a cycling cell returns Consequently, although protein degradation is thermodynamically to a neutral state of the control system (no starter kinases and no irreversible, the concentration of a cellular protein may rise or fall exit proteins). In the neutral state, the control system is bistable. It reversibly with the shifting kinetic balance between protein locks into the high Cdk activity state after the G1/S transition and synthesis and degradation [12]. As an alternative to the paradigm into the low activity state after the M/G1 transition. Consequently, that ‘protein degradation provides directionality to the cell cycle’, this bistable switch with two negative feedback loops drives the Novak and Tyson have been arguing for many years that the irre- cell cycle control system (Fig. 1) in a clockwise direction like a versibility of cell cycle transitions is an emergent property of feed- ratchet. This ratcheting effect (which engineers call ‘hysteresis’) back circuits in the molecular mechanism of Cdk control [13–15]. ensures strict alternation between the low and high Cdk activity states, thereby guaranteeing the correct order of cell cycle events. Progression around this hysteresis loop is also controlled by 2. Systems view of cell cycle control checkpoint mechanisms. These surveillance mechanisms keep the control system in one of the stable states until certain conditions Cdk subunits are usually present in a cell at high concentrations, and the cell modulates the availability of cyclin subunits as one means of controlling Cdk activities. Cyclin levels are modulated by controls on both cyclin synthesis and degradation. Rates of cyclin synthesis are regulated by transcription factors. Cyclin degradation is initiated by ubiquitination of cyclin subunits by the Anaphase Promoting Complex (APC; also called the ‘Cyclosome’) [16]. The rate of cyclin ubiquitination can be modulated by phosphorylation and dephosphorylation of the APC and its associated proteins, Cdc20 and Cdh1. Besides the regulation of cyclin levels, eukaryotes control SPF and MPF kinase activities by other mechanisms. For example, most cells in G1 phase have stoichiometric inhibitors (CKIs) that bind to and inhibit Cdk/cyclin complexes [17–19]. In addition, reversible phosphorylation of the Cdk1 subunit may be used to inhibit MPF activity, especially in cells with a long G2 phase [20]. With the exception of cyclin synthesis, all the processes men- tioned above have a negative effect on SPF and MPF activities. In addition, all the proteins regulating SPF and MPF activities are among the target proteins of SPF and MPF as well. Therefore, feedback loops are created in the cell cycle control system, and these Fig. 1. Alternative, stable states in the eukaryotic cell cycle. SPF and MPF are loops entail dynamic properties not evident in the individual involved in positive and double-negative feedback loops with their regulators. components. These feedback loops can persist in either one of two stable states: G1 with low activities of SPF and MPF, and S/G2/M with high activities. These two stable states In most cases, SPF and MPF down-regulate their inhibitory pro- are represented by continuous lines on the diagram, and they are separated by a teins, creating a double-negative (‘antagonistic’) feedback loop. locus of unstable steady states indicated by the dashed line. Starter kinases (SK) When they are activating their positive regulators, a positive feed- destabilize the G1 state by inhibiting the antagonists of SPF and MPF (and possibly back loop is established. Importantly, both of these network motifs by activating their activators). Exit proteins (EP) have the opposite effect on the regulators of SPF and MPF regulators, thereby promoting return to the G1 state. can potentially create a bistable system with alternative stable Eukaryotic cells move clockwise around this bistable switch, as indicated by the steady states [21]. Based on physiological arguments, we have pro- blue trajectory (often referred to as a ‘hysteresis loop’) and the typical cytological posed that the low- and high-activity states of Cdk observed during stages of the cell cycle surrounding the diagram. 3994 O. Kapuy et al. / FEBS Letters 583 (2009) 3992–3998 are satisfied. The spindle-assembly checkpoint [23] stabilizes the initiated by phosphorylation, which makes it recognizable by a high Cdk activity state (M) by inhibiting activation of EPs until ubiquitinating enzyme [33]. Since both SPF and MPF phosphorylate all the chromosomes are properly attached to the bipolar spindle. CKI, double-negative feedback loops are established. The mutual The G1 steady state is stabilized by a ‘size control’ mechanism inhibition between MPF and CKI is strengthened by MPF inhibition [24] which blocks the activation of SKs until cells grow to a critical of Swi5, the transcription factor for Sic1 [34]. Since both SPF and size. This mechanism coordinates cell growth with DNA replication MPF activities are low in G1, the CKI level is high [17,19]. Degrada- and mitosis, the events controlled by the bistable switching mech- tion of CKI is initiated by starter kinases (Cln/Cdk1 complexes), anism. This coordination is necessary because cytoplasmic growth which become activate when budding yeast cells grow to a critical is usually the rate-limiting step for cell cycle progression [25].By size [35]. Starter kinases also activate the transcription factor delaying the transition out of the G1 steady state, a cell can extend (MBF) responsible for production of S phase cyclin (Clb5). When its cycle time up to the time required to double its size. Mathemat- MPF activity rises, it shuts off production of starter cyclins (Clns), ical models with size-controlled bistable switching mechanisms which accounts for the transient appearance of Cln-dependent ki- have been built for budding yeast [26–28], fission yeasts [13,14] nase activity in the budding yeast cell cycle [36]. and mammalian cells [29]. The bistable mechanism is pretty robust The APC requires either Cdc20 or Cdh1 to catalyze ubiquitina- against molecular noise if the number of participating molecules is tion of S and M cyclins [37]. Both SPF and MPF inhibit Cdh1 by more than 100 [30] and its stochastic extension provides a reason- phosphorylation, because phosphorylated Cdh1 cannot bind to able description of ‘noise’ in cycle time and cell size distributions the APC [37]. Since Clb2 is a Cdh1/APC substrate, MPF inhibits its [31]. own degradation (double-negative feedback [13]). In the following sections we will summarize some experimental A positive feedback loop on Clb2 production is established by evidences for bistability in cell cycle progression, using examples the fact that MPF phosphorylates and activates its own transcrip- from the budding yeast cell cycle. We will support the arguments tion factor, Mcm1. with computational modeling. The two exit proteins are Cdc20 and Cdc14. Cdc20 binds to the APC and promotes degradation of the cyclin components of SPF 3. Feedbacks in the budding yeast cell cycle control network and MPF. Unlike Cdh1, the activity of Cdc20/APC depends on MPF, creating a negative feedback loop on this exit protein. The In budding yeast SPF and MPF are complexes of Cdk1 with two other exit protein, Cdc14, is a phosphatase that dephosphorylates different B-type cyclins, Clb5 and Clb2, respectively [32]. The feed- and activates proteins, like Swi5 [38], that are antagonists of SPF back loops controlling SPF and MPF activities are shown in Fig. 2. and MPF. Cdc14 activity is promoted by Cdc20 and opposed by The stoichiometric inhibitor (CKI, called Sic1 in budding yeast) Cdh1. binds to and inhibits both SPF and MPF. Degradation of CKI is To illustrate bistability in the Cdk-control system of budding yeast, we present (in Supplementary material) a simple mathematical model based on Fig. 2. The equations are written for the rate of change of the number of molecules of each cell cycle regulator. All reactions are described by the law of mass action; hence, the model is suitable for both deterministic and stochastic simulations. We have ignored the regulation of Cdh1, Cdc20 and Cln-dependent kinase, because these feedbacks are not important for our story. For Swi5, we take into account that the protein is multi-phosphorylated (which introduces important nonlinearity into the mechanism) and phosphorylation inhibits its biological activity. The qualitative features of these nonlinear differential equations can be conveniently illustrated in a coordinate system 1 spanned by CKI and Clb2total (Fig. 3). By assuming that all regulatory molecules are in steady state except CKI and Clb2, we can reduce the dimension of the system to two. It is instructive to plot

the ‘balance curves’ for Clb2total and CKI: along a balance curve the rate of synthesis of a particular component (in our case, Clb2total or CKI) is exactly balanced by its rate of degradation. Fig. 3A illustrates the balance curves for a G1-phase budding yeast cell in the ‘neutral’ state (no starter kinase, no exit proteins,

and also no Clb5). The Clb2total balance curve (yellow) is Z-shaped, and the CKI balance curve (red) is inverse N-shaped. To the left of the yellow curve, Clb2 is increasing, while to the right to the yellow curve, Clb2 is decreasing. Similarly, below the red curve, CKI is rising, and above the red curve it is dropping. The ‘folded’ character of these balance curves is a consequence of the feedback loops that regulate the production and degradation of Clb2 and CKI. The two balance curves intersect at three points which repre- Fig. 2. Feedback loops in the cyclin/Cdk-control network of budding yeast. SPF and sent steady states for the whole control system. The stable steady MPF activities are provided by Clb5/Cdk1 and Clb2/Cdk1 complexes, respectively. Both SPF and MPF promote degradation of CKI (Sic1), which inhibits their activities. state with high CKI level and low Clb2 level represents G1 phase of The transcription factors of Clb2 (Mcm1) and CKI (Swi5) are activated and inhibited the cell cycle. The other stable steady state, with high Clb2 level by MPF, respectively, creating other positive and double-negative feedback loops. and low CKI level, represents G2/M phase of the cell cycle. The Negative feedback loops control the starter kinase (Cln/Cdk1) and the exit protein (Cdc20). Cdh1 is also involved in a double-negative feedback loop with MPF. These last three feedback loops are ignored in the model (Supplementary material) 1 We use the level of mitotic cyclin (Clb2), rather than the cumulative Clb5 + Clb2 because they are not operative in the experimental protocol of Lopez-Aviles et al. level, as a dynamic variable because Clb2 was monitored in the experiments [40]. described below. O. Kapuy et al. / FEBS Letters 583 (2009) 3992–3998 3995

Fig. 3. Phase plane analysis of bistability in budding yeast cell cycle. Balance curves for Clb2total (yellow) and CKI (red) are plotted in different cell cycle stages based on the kinetic model in Supplementary material. Grey arrows and dashed curves show the rate vectors and the trajectories of the system. (A) The neutral state (low starter kinase (Cln = 200) and no exit protein: APC. Cdh1CA = 0) is bistable with S phase (Clb5) cyclin (ksclb5 = 0). (B) G1/S transition: a 10-fold increase in the starter kinase level (Cln = 2000) eliminates the stable G1 state and the controls systems moves in the direction of the other stable state following the grey trajectory. (C) The neutral state is also bistable with S phase cyclin (Clb5): the same as (A) except Clb5 is present (ksclb5 = 0.01). Tiny differences in the initial conditions (Ã) lead to completely different final cell cycle states. (D) M/G1 transition: the stable G2/M state disappears above Cdh1CA level over 500 (APC = 1). The trajectory (dashed grey curve) was calculated with 43.6 and 43.7 min long continuous Cdh1CA synthesis (kscdh1 = 0.02) starting from the G2/M state. The end points of these simulations were used as initial conditions in Fig. 3Cto calculate the yellow and red trajectories. intermediate (unstable) steady state is a ‘saddle point’, which rep- alternative stable states. Which steady state wins depends on resents a ‘dividing of the ways’, as we shall shortly see. whether the system lands below or above the unstable steady state This picture, which is based on a reasonable description of the in the neutral position (the open circle in Fig. 1). Where it lands biochemical kinetics of Cdk control in budding yeast, is equivalent will be determined by how much SPF+MPF activity accumulates to the ‘cartoon’ in Fig. 1. In the cartoon, we are imagining the ef- during the starter kinase pulse. fects of helper proteins on the bistable switch. Here we view the Cross et al. [39] found that, as predicted, after a short pulse of control system as an antagonism between MPF and CKI; the helper starter kinase the majority of cells stayed unbudded, could not proteins will influence the shape and position of the balance accumulate Clb2, and returned to the stable G1 phase. After a long- curves. er pulse most of the cells moved to the stable mitotic state. Fig. 1 is just a cartoon to illustrate the basic ideas of dynamic 4. Probing for bistability from G1 phase of the cycle reversibility and irreversibility. More precise simulations of Cross’s experiments are presented in Fig. 3B. Since starter kinase promotes Cross et al. [39] have blocked cells in G1 phase of the cell cycle degradation of CKI, the CKI balance curve (red) is pushed down into by depriving all starter kinases (Cln/Cdk1), which are required for the corner of the diagram. The stable G1 state has disappeared, and the G1/S transition. These cells are blocked in the steady state la- the only steady state available to the system left is the high-Clb2 beled G1 in Figs. 1 and 3. Blocked cells were then induced to syn- mitotic state. Therefore, the system moves from the right to the left thesize one of the starter cyclins (Cln3) for different periods of (CKI gets degraded) in Fig. 3B, sneaks between the two balance time. At the end of this period Cln3 synthesis was turned off and curves and then moves upward (Clb2 synthesis) toward the one of the exit proteins (Cdc14) was inactivated, to prevent mitotic S + G2 + M state. When starter kinase induction is terminated, the exit. From the viewpoint of the bistable model (Fig. 1), starter-ki- CKI balance curve recovers to its original position (Fig. 3A), which nase induction pushes the system transiently to the left, causing reestablishes the G1 steady state. If, at this time, the system has a rise of SPF + MPF activity once starter kinase activity exceeds not yet accumulated much Clb2 (the lower Ã in the corner of the threshold. When starter kinase (SK) induction and exit protein Fig. 1A), then CKI will increase faster than Clb2, and the G1 state (EP) activity are turned off at the end of the treatment, the system will recover. If the system has accumulated a little more Clb2 moves to the right (in Fig. 1) to the neutral position (SK = EP = 0). In (the upper Ã in Fig. 1A), then Clb2 will increase faster than CKI, the neutral position the system must decide between the two and the system will move on to the mitotic state. It should be clear 3996 O. Kapuy et al. / FEBS Letters 583 (2009) 3992–3998 from Fig. 1A that the dynamics close to the unstable saddle point promote exit from mitosis (spindle disassembly and some re-accu- determines this ‘dividing of the ways’. Although the unstable stea- mulation of CKI). However, this degree of ‘exit’ was still reversible, dy state is unachievable (as a distinct state of the control system), because inactivation of the APC after 50 min allowed Clb2 to re- it has very noticeable physiological consequences. accumulate and drive CKI back to its low (mitotic) level. Slightly longer treatment (60 min of Cdh1CA/APC-dependent Clb2 degrada- 5. Probing for bistability from M phase of the cycle tion) renders mitotic exit irreversible, even after APC inactivation (Fig. 4B). Complementing Cross et al. [39] who tested bistability on the The experiment simulated in Fig. 4A shows that cyclin degrada- left-hand side of Fig. 1, Lopez-Aviles et al. [40] recently provided tion is not sufficient to make mitotic exit irreversible. Irreversibil- evidence (in budding yeast) for bistability on the right-hand side ity of mitotic exit, in this experimental situation, requires of the diagram. To explain their results, we carried out stochastic accumulation of CKI above a threshold (Fig. 4B) rather than cyclin simulations of these experiments (Fig. 4A and B) based on the degradation per se. In order to illustrate this point we consult the model in Supplementary materials. To block cells in M phase high phase-plane diagrams in Fig. 3.InFig. 3C, the two balance curves SPF and MPF levels, Lopez-Aviles et al. [40] deprived cells of Cdc20 are drawn for a cell blocked at metaphase by Cdc20 deprivation. (an essential exit protein). For cells blocked in metaphase, cyclin At the beginning of the experiment, the cell is in the upper left CA degradation was turned on for different periods of time. Some steady state (M phase). Induction of Cdh1 pushes the Clb2 bal- experimental details are relevant here. Lopez-Aviles et al. used a ance curve down, and the mitotic steady state disappears constitutively active form of Cdh1 (Cdh1CA) in which all Cdk1 phos- (Fig. 3D). The system must move toward the G1 steady state, first phorylation sites are mutated to non-phosphorylable amino acids by a drop in Clb2 level, followed by CKI accumulation at low Clb2/ [37]. (Because Clb2 cannot inactivate Cdh1CA, the constitutively ac- Cdk1 activity (Fig. 3D). When the APC is inactivated by a tempera- tive form of Cdh1 works like an exit protein rather than a feedback ture shift, the balance curves are reinstated as in Fig. 3C. The sub- loop component.) The strain used also carried a temperature-sen- sequent evolution of the control system depends on how much CKI CA sitive APC mutation, which allowed the experimenters to termi- has accumulated in the meantime. After a Cdh1 -treatment of nate Cdh1/APC-dependent cyclin degradation by inactivating the 43.6 min (Fig. 3C, yellow dashed trajectory), the control system APC. Cdh1CA induction caused efficient degradation of Clb2 but passes up and to the left of the saddle point and returns to the mi- not of Clb5. Fifty minutes of Cdh1CA/APC activity (see Fig. 4A) totic steady state (reversible exit, despite nearly complete degrada- was sufficient to degrade Clb2 to undetectable levels and to tion of Clb2). After a 43.7 min treatment (Fig. 3C, red dashed

Fig. 4. Stochastic simulations of mitotic exit in the Lopez-Aviles experiments. (A) The protocol for ‘reversible mitotic exit’ is used: the synthesis of Cdh1CA and the activity of APC are turned off at 30 and 50 min, respectively (Cdh1off = 30 and APCoff = 50 in the model). (B) The protocol for ‘irreversible mitotic exit’ is used: the synthesis of Cdh1CA is not turned off and APC are inactivated 60 min (Cdh1off > 150 and APCoff = 60 in the model). In both (A) and (B) the number of molecules are plotted in time for a single cell (except for Mcm1 which molecular number is divided by 10). The temporal changes in distribution of Clb2 (C) and CKI (D) molecular numbers during reversible mitotic exit protocol. Stochastic simulations were run 100 times with conditions in Fig. 4A. In all panels, inactive APC has 2% residual activity (APClow = 0.02). O. Kapuy et al. / FEBS Letters 583 (2009) 3992–3998 3997 trajectory), the control system passes below the saddle point and experimental evidences for bistability and feedback-dependent continues on to the G1 steady state (irreversible exit, for exactly irreversibility appeared in the literature. the same extent of degradation of Clb2).2 We have summarized the available experimental evidence from This analysis clearly shows that irreversible mitotic exit de- budding yeast for bistability of cell cycle phases and for the associ- pends on reaching a critical CKI level. The threshold level of CKI ation of irreversible transitions to system-level feedback rather is determined roughly by the lower corner (the ‘knee’) of the than to protein degradation per se. We have described in detail Clb2 balance curve (see Fig. 3C). Experiments confirm this predic- the evidence, coming from a recent paper by Lopez-Aviles et al. tion by showing that mitotic exit, in the Lopez-Aviles protocol, is [40], that cyclin degradation is neither necessary nor sufficient always reversible in the absence of CKI [40]. It is important to men- for irreversible exit from mitosis. We have simulated these exper- tion, that the essential role of CKI for irreversible mitotic exit is a iments with a stochastic model based on a reasonable molecular consequence of the inactivation of the APC in this experimental mechanism of the feedback loops in the budding-yeast control sys- set-up. Under other circumstances, either CKI or Cdh1/APC is able tem, and we have provided a dynamical understanding of the oper- to stabilize the low MPF activity state and make mitotic exit ation of the network by classical phase-plane analysis. irreversible.) There is other strong experimental support in the literature that Of course, the outcome of the Lopez-Aviles experiment is so pre- irreversibility of cell cycle transitions does not depend on proteol- dictable only for a perfectly deterministic system. In real cells, with ysis of cell cycle regulators, e.g. [43–45]. We highlight another con- molecular noise arising from small number of molecules, the out- vincing experiment that irreversible mitotic exit is not a come is less predictable. To illustrate this point we have run sto- consequence cyclin degradation per se. Although the APC, whose chastic simulations 100 times under conditions which conclude job is to degrade cyclins and other proteins in anaphase, is an with reversible mitotic exit in a deterministic system (Fig. 4A). essential component of the cell cycle machinery, its requirement The results of these stochastic simulations are presented in proba- can be bypassed. Thornton and Toczyski [46], by deleting two sub- bility plots for Clb2 and CKI levels in Fig. 4C and D. The majority strates (Clb5 and securin), could make apcÀ mutants viable with a (90%) of cells resynthesize Clb2 and down-regulate CKI after simultaneous 10-fold overexpression of the stoichiometric Cdk APC inactivation at 50 mins, but others escape to a G1 state. This inhibitor, Sic1. These mutants exit mitosis not by degrading cyclins splitting behavior in the population of individual cells is the conse- but by up-regulating Sic1 level as a consequence of Cdc14 phos- quence of APC inactivation close to the saddle point (see Fig. 4A). As phatase activation [46,47]. Furthermore, cyclin degradation is not a consequence of ‘dividing the ways’ behavior the distribution of necessary for irreversible mitotic exit degradation (see more de- both Clb2 and CKI are bimodal at the end of the experiment. tails in Lopez-Aviles et al. [40]). All the evidences presented in this paper come from budding 6. Conclusions yeast cells, which obviously have some unusual features compared to higher eukaryotes. Therefore, we must ask how relevant are our In this paper we have briefly summarized our system-level view conclusions for higher eukaryotes? In particular, are irreversible of cell cycle control in eukaryotes. The center piece of this view is transitions in the replication-division cycles of mammalian cells bistability, a consequence of feedback signals in the Cdk-control caused by protein degradation or by system-level feedback loops? network that create two alternative, stable states. These stable Since all living cells are dynamical systems [48] and our arguments states correspond to the pre-replicative (G1) and the replicative/ about bistability, hysteresis and irreversibility are based on general post-replicative (S/G2/M) phases of the cell cycle.3 They are properties of dynamical systems, we maintain that our conclusions stabilized by system-level feedback signals, which are resistant to must be true for mammalian cells as well as for yeast cells. None- molecular noise as long as the participating molecules are present theless, it is still argued and believed that mitotic exit in mamma- in 100 copies or more per cell [39,41]. The existence of two alter- lian cells is made irreversible by cyclin degradation [49]. This native stable states of the cell cycle implies that the cell must make conclusion is based on an experiment in which cyclin degradation irreversible transitions from one state to the other and back again, as is blocked by a proteasome inhibitor (MG132) and then mitotic it progresses through a complete replication-division cycle. These exit is induced by transient inhibition of Cdk activity; when the irreversible transitions occur as the cell enters S phase and as it exits Cdk inhibitor is removed, the cells return to a mitotic state. To be M phase. Close to the transition points, stochastic fluctuations in sure, these investigators observed reversible mitotic exit in the ab- number of molecules may determine exactly when a cell makes sence of cyclin degradation, but that does not imply that cyclin the transition and, hence, may introduce some variability in cell degradation makes mitotic exit irreversible. Indeed, after a more cycle progression among individual cells. lengthy inhibition of Cdk activity, mitotic exit becomes irreversible We hope it is clear from this paper that ‘system-level feedback’, because of inhibitory tyrosine phosphorylation of Cdk1 [50]. Since ‘bistability’ and ‘irreversible transitions’ are all intimately con- the enzymes responsible for tyrosine phosphorylation of Cdk1 nected concepts. Feedback (positive or double-negative) creates (Wee1 and Myt1) are themselves inhibited by phosphorylation bistability (alternative stable states) which makes transitions irre- by Cdk1/CycB, there exists between these antagonistic kinases a versible (hysteretic) [12]. Although the feedback loops have been double-negative feedback loop that is analogous to the double- known to molecular biologists for years, few of them have recog- negative feedback loop between CKI (Sic1) and Cdk1/CycB. Hence, nized their significance in creating alternative stable steady states the mitotic-exit experiments of Potapova et al. [50] on mammalian and in enforcing irreversibility of progression through the cell cycle cells are entirely analogous to the mitotic-exit experiments of Lo- (a notable exception being Nasmyth [32,42]). Only recently have pez-Aviles et al. [40] on budding yeast cells. We interpret both sets of experiments in the same way: irreversibility of mitotic exit is not dependent on cyclin degradation but on the existence of feed- 2 Both of the trajectories in Fig. 3C and D were calculated with continuous Cdh1CA synthesis (‘irreversible mitotic exit’ protocol of Lopez-Aviles et al. [40]) which back loops that create a bistable system with hysteretic transitions. explains why reversible mitotic exit is terminated earlier than in Fig. 4. These Whether mitotic exit is reversible or irreversible depends on subtle calculations also show that the different outcome after Cdh1CA pulse is not the timing details of the experiment that determine whether the sys- consequence of the different protocols used by Lopez-Aviles et al. [40]. tem’s dynamical trajectory passes to one side or another of an 3 Actually, there is another bistable switch in most eukaryotic organisms, which unstable saddle point. A full appreciation of the phenomena of irre- splits the S/G2/M state into two separate phases (S/G2 and M). This switch is also controlled by system-level feedback signals, but further discussion of this switch is versible cell cycle transitions requires a full systems-level, dynamic beyond the focus of this article. view of molecular regulatory networks. 3998 O. Kapuy et al. / FEBS Letters 583 (2009) 3992–3998

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