Degradation of Ndd1 by APC/CCdh1 generates a feed forward loop that times mitotic protein accumulation

Ndd1 activates the Mcm1–Fkh2 transcription factor to transcribe mitotic regulators. The anaphase-promoting complex/cyclosome activated by Cdh1 (APC/CCdh1) mediates the degradation of proteins throughout G1. Here we show that the APC/CCdh1 ubiquitinates Ndd1 and mediates its degradation, and that APC/CCdh1 activity suppresses accumulation of Ndd1 targets. We confirm putative Ndd1 targets and identify novel ones, many of them APC/CCdh1 substrates. The APC/CCdh1 thus regulates these proteins in a dual manner—both pretranscriptionally and post-translationally, forming a multi-layered feedforward loop (FFL). We predict by mathematical modelling and verify experimentally that this FFL introduces a lag between APC/CCdh1 inactivation at the end of G1 and accumulation of genes transcribed by Ndd1 in G2. This regulation generates two classes of APC/CCdh1 substrates, early ones that accumulate in S and late ones that accumulate in G2. Our results show how the dual state APC/CCdh1 activity is converted into multiple outputs by interactions between its substrates. Ndd1 activates the transcription of mitotic regulators. Here the authors show that the ubiquitin ligase complex APC/CCdh1ubiquitinates Ndd1 as well as Ndd1 target genes, creating a feedforward loop that generates an early class of substrates that accumulate at S phase and a late class that accumulate at G2.

T he anaphase-promoting complex/cyclosome (APC/C) was discovered almost 20 years ago as the ubiquitin ligase, which mediates the degradation of mitotic cyclins 1,2 . The APC/C is a very large complex comprising more than a dozen subunits totalling about 1.5 mD, which is highly conserved in all eukaryotes 3 . The APC/C is activated in metaphase by the adaptor protein Cdc20 (refs 4,5). The degradation of Pds1/Securin 6 and mitotic cyclins mediated by APC/C Cdc20 specific ubiquitination is essential for sister chromatid separation and completion of cell division 7,8 . The APC/C Cdc20 degrades multiple additional mitotic proteins in a well-defined order 9 and is the target of the mitotic checkpoint that prevents premature entry into mitosis 10 Cdc20 activates the APC/C only during the short mitotic window and is replaced by Cdh1 in late mitosis 4,11,12 . The APC/ C Cdh1 remains active throughout G1 until the onset of S phase 13 and is constitutively active in metazoan cells in G0 as well as in differentiated cells 14 . The budding yeast APC/C Cdh1 has more than 20 known substrates (Table 1), and this might be only the tip of the iceberg. Some of these substrates are also degraded by APC/C Cdc20 , but many are unique to APC/C Cdh1 . In spite of this large number of substrates, Cdh1 is not essential in yeast; however, cdh1D cells are sensitive to different types of stress and have a longer cell cycle 15 . In addition to Cdc20 and Cdh1, the APC/C is activated by Ama1, a third, meiosis-specific, activator 16,17 .
The increasing number of APC/C substrates discovered in recent years led us 18 , as well as the Solomon lab 19,20 , to devise systematic screens to map the entire APC/C 'degradome'. These screens had an initial bioinformatic step to define a group of candidate genes, followed by various experimental approaches to identify and verify putative substrates. While yielding multiple interesting new APC/C substrates, these screens were limited by the initial biofinformatic step to proteins with a specific transcriptional pattern and degradation box [18][19][20] . We thus set up an unbiased screen designed to probe the entire yeast proteome. During the pilot stage of this screen, we identified Ndd1, an essential protein, which activates the Mcm1-Fkh2 G2-specific transcription factor [21][22][23][24] . We show here that Ndd1 is an APC/C Cdh1 substrate and that the APC/C Cdh1 is a major regulator of the cell cycle-specific oscillations of Ndd1. We demonstrate that the activities of Ndd1 and the APC/C Cdh1 reciprocally counteract each other. We used these counteracting activities to verify putative, and identify novel, Ndd1 targets. We tested 16 APC/C Cdh1 substrates and found nine of them to be transcribed by Ndd1. The observation that the APC/C Cdh1 regulates the level of Ndd1, which transcribes many of the APC/C Cdh1 substrates, implies a multi-layered feedforward loop (FFL) that involves both transcriptional and post-translational regulations. We use mathematical modelling to simulate the effect of this Ndd1/APC/C Cdh1 FFL on the timing of accumulation and level of APC/C Cdh1 substrates. The model predicts that Ndd1 degradation delays the accumulation of these proteins in comparison with APC/C Cdh1 substrates that are not transcribed by Ndd1. Live-cell imaging confirms these predictions, and shows that substrates regulated by the Ndd1/APC/C Cdh1 FFL accumulate in G2, while those only regulated by the APC/C Cdh1 accumulate already in early S phase.

Results
Ndd1 degradation is mediated by the APC/C Cdh1 . We set up a screen to identify novel APC/C Cdh1 substrates in budding yeast. We mated the yeast TAP library 25 with a strain expressing constitutively active Cdh1 m11 from an inducible GAL promoter 26 . The library was plated out into 96-well plates with Cdh1 m11 induced or uninduced in alternating rows. Protein was extracted from the cultures in each well, dot-blotted on nitrocellulose membranes and immunoblotted with anti-TAP antibodies (Fig. 1a). Using this method, we identified the transcription activator Ndd1 (refs 21,27) as a putative APC/C Cdh1 substrate (Fig. 1b). Ndd1 is the activator of the Mcm1-Fkh2 transcription factor complex [21][22][23][24] . The protein levels of Ndd1 oscillate periodically and it has been previously speculated 28 that it might be degraded by the APC/C. It was further recently shown 17 that Ndd1 is degraded in meiosis by the APC/C Ama1 .
We used several approaches to verify that Ndd1 degradation is indeed mediated by the APC/C Cdh1 . Figure 2a shows that the endogenous TAP-tagged Ndd1 protein was degraded on activation of Cdh1 m11 without reducing the level of its mRNA. Figure 2b shows that Ndd1 accumulated like Clb2 in unsynchronized or mitotic wild-type cells and was virtually absent when these cells were arrested with a factor. In contrast, Ndd1 levels remained high in a factor-arrested cdh1D cells.
We further used a GAL promoter to induce the expression of GST-tagged Ndd1 in wild-type and in cdh1D cells. Once transcription of GST-Ndd1 was turned off by the addition of glucose, Ndd1 was degraded within less than an hour in wild-type cells. In cdh1D cells in contrast, Ndd1 levels remained constant for the duration of the experiment (2 h; Fig. 2c).
The activity of the APC/C Cdh1 can be inhibited by inducible expression of Acm1 (refs 29-31). Figure 2d shows that once Acm1 was activated, Ndd1 accumulated at the same rate as that of the known APC/C Cdh1 substrate Cdc5. The fact that the Ndd1 levels rise with similar kinetics to those of Cdc5 strongly suggests Previously reported Not tested þ 9,70 that its stabilization is a direct consequence of APC/C Cdh1 inactivation. If Ndd1 accumulation would have been a downstream event of stabilization of another APC/C Cdh1 substrate, its accumulation would have been delayed compared with Cdc5 accumulation. Cdh1D cells proliferate relatively normally. We thus did not anticipate that Cdh1 inhibition by Acm1 overexpression would lead to cell cycle arrest. Indeed, fluorescence-activated cell sorting (FACS) analysis showed that Acm1 induction did not significantly perturb the cell cycle ( Fig. 2d bottom).
Most APC/C Cdh1 substrates require an RxxL 32 or KEN 33 type 'destruction box' to be targeted for ubiquitination and degradation. Ndd1 has five RxxL sequences and no KEN box. According to the GPS-ARM programme 34 the 265 RTPL 268 and the 318 RTPL 321 rank highest as candidates for a genuine destruction box. We mutated the 318 RTPL 321 to 318 KTPA 321 and as shown in Fig. 2e, this mutation significantly stabilized Ndd1. It is rare to obtain complete stabilization by mutagenesis of a single or of even multiple destruction boxes of APC/C substrates in yeast. Indeed, even mutagenesis of all five RxxL sequences did not completely abrogated degradation of Ndd1 by the APC/C Ama1 in meiosis 17 . While all these experiments strongly suggest that Ndd1 is a substrate of the APC/C Cdh1 , it is not possible to completely exclude the possibility that Ndd1 degradation is an indirect downstream event of APC/C Cdh1 activity. We therefore expressed GST-Ndd1 in bacteria and tested its ubiquitination in vitro using APC/C purified from HeLa cells. Figure 2f shows that addition of human Cdh1, expressed by baculovirus and purified from 5B cells to this APC/C, lead to significant monoubiquitination (and more modest polyubiquitination) of Ndd1. We thus conclude that Ndd1 is an APC/C Cdh1 ubiquitination substrate.
The APC/C Cdh1 regulate Ndd1 levels throughout the cell cycle. Given our observations that Ndd1 is degraded by the APC/C Cdh1 in G1, as well as by the APC/C Ama1 in meiosis 17 , we wondered whether Ndd1 is also degraded by the APC/C Cdc20 in mitosis. We overexpressed Cdc20 from a GAL promoter in cdh1D cells arrested in mitosis with nocodazole. Figure 3a shows that the massive overexpression activated the APC/C Cdc20 and led to the degradation of Clb2. Ndd1, on the other hand, remained stable. Ndd1 is thus, like Cdc5, Cdc20 and many other G1-specific APC/C Cdh1 substrates, not targeted by the APC/C Cdc20 .
We next sought to follow the level of Ndd1 during the cell cycle and to establish when the APC/C Cdh1 is regulating its levels. Ideally, this should have been done in real time in unsynchronized cells. The level of endogenous Ndd1, which is a transcription factor, is however too low to be detected and followed by tagging with a fluorescent protein. We therefore synchronized cells, expressing endogenous TAP-tagged Ndd1 by alpha factor arrest and release. Figure 3b shows that cells start to accumulate Ndd1 20 min after release from alpha factor arrest on initiation of budding. Clb2 accumulation seems to be slightly delayed compared with Ndd1 accumulation, apparently, as will be discussed below, because Ndd1 is required for the transcription of Clb2. Clb2 is degraded on cell division by the APC/C Cdc20 and subsequently by APC/C Cdh1 . The reduction in Ndd1 levels on cell division seems to be slower and less complete, probably due to the fact that it is not degraded by the APC/C Cdc20 (Fig. 3a) and also due to loss of synchronization.
The levels of Ndd1 and Clb2 were followed in a similar fashion in cdh1D cells (Fig. 3c). Ndd1 levels hardly change in these cells during the cell cycle, indicating that the APC/C Cdh1 is the major regulator of Ndd1 levels throughout the cell cycle. As expected, Clb2 levels are higher in cdh1D cells and present throughout the entire cell cycle. Clb2 levels still oscillate, presumably due to its degradation by APC/C Cdc20 in mitosis.
The activities of Ndd1 and APC/C Cdh1 reciprocally counteract. Ndd1 mediates the transcription of mitotic regulators like Clb2 (ref. 27) and Cdc5 (ref. 35), which are degraded by the APC/C Cdh1 . We thus speculated that Ndd1 could counteract the activity of the APC/C Cdh1 . To probe the functional interactions between Ndd1 and APC/C Cdh1 in vivo, we used GAL-inducible overexpression of Ndd1, as well as of constitutively active Cdh1 m11 . Figure 4a shows that Ndd1 overexpression impairs growth. Live-cell imaging of these cells shows that they stopped to divide after three to four cycles and extensively grew in size (Fig. 4b). Expression of Cdh1 m11 led to cell cycle arrest and to growth of extremely elongated buds (Fig. 4b) 36 . Strikingly, co-expression of Ndd1 and Cdh1 m11 almost eliminated the elongated bud phenotype caused by Cdh1 m11 observed after 2 h and greatly reduced it by 24 h (Fig. 4b,c). These observations suggest reciprocal interactions between Ndd1 and the APC/C Cdh1 -not only does the APC/C Cdh1 mediate the degradation of Ndd1 (Fig. 2)   Ndd1 leads to a cell cycle arrest with elongated buds and replicated DNA 27 , which is strikingly similar to the phenotype caused by Cdh1 m11 expression.
We hypothesized that the reciprocal effect of Ndd1 and the APC/C Cdh1 is caused by the induction of Ndd1-mediated transcription of proteins degraded by the APC/C Cdh1 . Indeed, Fig. 4d shows that induced expression of Ndd1 rescues the expression of Clb2 and Cdc20, known to be activated by Ndd1 transcriptionally 27,37 and degraded by the APC/C Cdh1 (ref. 38), even in the presence of constitutively active Cdh1 m11 .

APC/C Cdh1 activation represses Ndd1-specific transcription.
Our observation that the activities of Ndd1 and of the APC/C Cdh1 phenotypically counteract (Fig. 4) suggested that APC/C Cdh1 activation inhibits the transcription of Ndd1 targets. We thus wondered whether overexpression of Ndd1 and activation of APC/C Cdh1 individually and in combination could be used to identify Ndd1 targets. We extracted RNA from cells overexpressing Ndd1, Cdh m11 and Ndd1 þ Cdh m11 and subjected it to real-time PCR. We initially tested the mRNA levels of genes reported to be transcribed by Ndd1 (CLB1, CLB2, SWI5 (ref. 27), CDC5 (ref. 35) and ACE2 (ref. 39) as well as putative targets whose promoter is bound by Ndd1 (ref. 37; CDC20, SPO12, BUD4 and RAX2). Figure 5a shows that the overexpression of Ndd1 led to significant increase in the mRNA levels of these genes. In contrast, constitutive activation of the APC/C Cdh1 led to a significant decrease in their mRNA levels. This decrease is conceivably due to the degradation of the endogenous Ndd1, depleting its activity as a transcriptional activator. Indeed, the combined expression of Ndd1 and Cdh1 m11 resulted in an increase of mRNA levels of these genes, but to a lesser extent than when Ndd1 was overexpressed on its own.
Interestingly, approximately half of these genes are encoding APC/C Cdh1 substrates (CLB1, CLB2, CDC5, CDC20 and SPO12), while the rest (RAX2, BUD4, ACE2 and SWI5) are not. We thus expected to find additional novel Ndd1 targets among genes encoding APC/C Cdh1 substrates. We tested the effects of overexpression of Ndd1, Cdh1 m11 and Ndd1 þ Cdh1 m11 on 11 genes encoding APC/C Cdh1 substrates, none of which has previously been associated with Ndd1. Figure 5b shows that four of these genes (ASE1, IQG1, NRM1 and YPH1) were both activated by Ndd1 and repressed by Cdh1 m11 , as described above, suggesting that they are Ndd1 targets. The mRNA levels of five other genes encoding APC/C Cdh1 substrates (CIN8, KIP1, HSL1, PDS1 and RNH202) were neither increased by Ndd1 nor reduced by Cdh1 m11 , suggesting that they are not transcribed by Ndd1. The mRNA levels of two genes encoding APC/C Cdh1 substrates (CIK1 and FIN1) was increased by Ndd1 but not reduced by Cdh1 m11 . As these two genes did not conform to our stringent dual (a) Cdh1D cells expressing gal-inducible Cdc20 were grown to mid-log phase in raffinose. Cells were subsequently arrested by nocodazole for 2 h in mitosis, treated with galactose to induce Cdc20 and sampled at the indicated time points. Cdc20 is as expected strongly induced leading to degradation of Clb2, but not to degradation of Ndd1. Mid-log populations of wild-type (b) or cdh1D (c) cells were arrested with alpha factor for two hours, released and sampled at 10-min intervals.  criterion of activation by Ndd1 and repression by Cdh1 m11 , we do not define them as Ndd1 targets. It is possible that they are indirect targets or transcribed by Ndd1 as well as by an additional factor. Indeed CIK1 is known to be transcribed by Kar4 (ref. 40), as well as Hcm1 (ref. 41). Finally, we tested the effect of Ndd1 and Cdh1 m11 on mRNA levels of HOF1, a CLB2 cluster gene whose protein is not degraded by the APC/C 42 . Figure 5c shows that HOF1 mRNA level is strongly induced by Ndd1 overexpression and reduced by Cdh1 m11 expression suggesting that HOF1 is transcribed by Ndd1. Table 1 summarizes the results of these experiments and shows that we identified five novel Ndd1 targets (ASE1, IQG1, NRM1, YPH1 and HOF1), validated four putative ones (CDC20, SPO12, BUD4 and RAX2) and confirmed five previously reported ones (CLB1, CLB2, CDC5, ACE2 and SWI5). Interestingly, the majority of the Ndd1 targets are regulated by the APC/C Cdh1 , and about half of the APC/C Cdh1 substrates we tested are transcribed by Ndd1 (Fig. 5d).
Ndd1 and the APC/C Cdh1 generate an FFL. The observation that the APC/C Cdh1 exerts a dual effect on some of its substrates, degrading both the proteins themselves and the transcription activator responsible for their synthesis (Fig. 6a), suggests a multilayered FFL 43,44 . We hypothesized that APC/C Cdh1 substrates subject to the regulation at both levels will have a different pattern of expression compared with APC/C Cdh1 substrates regulated only by proteolysis. We reasoned that degradation of the transcription activator mediating transcription of the gene should postpone the reappearance of the translated protein to G2. It should require more time to sequentially synthesize the transcription activator, which subsequently transcribes its target. In contrast, the synthesis of those APC/C Cdh1 substrates that are not transcribed by Ndd1 but by another transcription factor could accumulate, depending on the activity of this factor, earlier, already in S phase. We used mathematical modelling and simulations (see Methods) to follow the temporal variation in the levels of shared targets that are regulated by both the APC/ C Cdh1 and Ndd1 through the wild-type FFL structure (Fig. 6b). These were compared with the target levels obtained when either APC/C Cdh1 -Ndd1 or APC/C Cdh1 -target interaction was impaired. The former mimics a situation where the targets are regulated by a transcription factor that is independent of APC/C Cdh1 . The latter mimics a situation where the targets are substrates of another E3 ligase. Figure 6b shows the oscillations of a protein regulated dually by Ndd1 and APC/C Cdh1 (bottom panel-blue) in relation to APC/C Cdh1 activity pattern (top panel). When regulation of Ndd1 by the APC/C Cdh1 was abolished, amounting to Ndd1 stabilization, the substrate accumulated earlier (bottom panelturquoise). On the other hand, when the generic substrate was regulated only by Ndd1 and not by the APC/C Cdh1 , its accumulation remained late and unchanged (bottom panelmagenta). The timing of its degradation depends on the E3 mediating its ubiquitination. This situation describes the   Table 1. RT-PCR, reverse transcription-PCR.
presumed fate of proteins like Hof1 and other proteins transcribed by Ndd1 and not degraded by the APC/C Cdh1 . The model further predicts that the steady-state levels of substrates dually regulated will be lower than those regulated by either mode independently.
We set out to test the model by following the accumulation of proteins subjected to dual and individual regulations by either APC/C Cdh1 or Ndd1, or by both of them together. Fortunately, Iqg1 (APC/C Cdh1 and Ndd1), Hsl1 (APC/C Cdh1 only) and Hof1 (Ndd1 only) have a highly defined and identical localization to the bud neck facilitating comparison of their accumulation and degradation in real time. We used cells with a carboxyl-terminal GFP (green fluorescent protein)-tagged endogenous gene of each of these three proteins 45 and followed asynchronous logarithmic cultures by confocal microscopy. Figure 6c,d shows that the accumulation patterns of these proteins strongly support our mathematical model. Iqg1 (Supplementary Movie 1) regulated by both APC/C Cdh1 and Ndd1 accumulates late (44 min after budding). Hsl1 (Supplementary Movie 2), regulated only by the APC/C Cdh1 accumulates considerably earlier (16 min after budding). As predicted, both proteins are degraded at exactly the same time (52 min after budding). Hof1 (Supplementary Movie 3), transcribed by Ndd1 and degraded by the SCF Grr1 ubiquitin ligase 42 and not by the APC/C Cdh1 , accumulates, as predicted, at the same time as Iqg1. As Hof1 degradation does not depend on the APC/C Cdh1 , it takes place later than that of Iqg1 and Hsl1.
Our model further predicted that the elimination of APC/C Cdh1 activity would change the time of accumulation of Ndd1 targets. As Iqg1 and Hsl1 are APC/C Cdh1 substrates, elimination of APC/C Cdh1 leads to their stabilization throughout the cell cycle precluding the possibility to follow their accumulation. However, Hof1 degradation does not depend on APC/C Cdh1 and indeed in cdh1D cells, where Ndd1 is stabilized, Hof1 accumulates significantly earlier than in wild-type cells (20 min compared with 44 min after budding; Fig. 6c,d and Supplementary Movie 4). Interestingly, this observation matches a report by Blondel et al. 42 who replaced the endogenous Hof1 promoter with constitutive CYC1 or ADH promoters and observed that Hof1 started to accumulate shortly after budding, much earlier than when it was expressed from its endogenous promoter. In the experiment we describe here (Fig. 6c bottom panels), we obtained exactly the same effect by deleting CDH1 thereby stabilizing Ndd1. Moreover, as predicted in the model (Fig. 6b turquoise), the level of Hof1 is apparently higher as it is not fully eliminated from previous bud scars (asterisk).

Discussion
The APC/C, which is active from metaphase to the onset of S phase, mediates the ubiquitination and degradation of dozens of proteins. On the background of this crude 'wholesale' destruction mechanism, different substrates achieve highly specific temporal patterns of degradation and accumulation. Some of this finetuning is achieved via the two activators Cdc20 and Cdh1 that sequentially activate the APC/C 46 . Recent studies have revealed intricate mechanisms that regulate the temporal pattern of degradation by the APC/C Cdc20 . Different substrates are degraded at different times, sometimes only minutes apart 3,9,47 . While the timing of degradation is obviously critical, especially for highly complex events during mitosis, we still know little about what happens at the other end-reaccumulation of these ARTICLE proteins during the S and G2 phases. After an APC/C substrate has been degraded, its accumulation will depend on the time the APC/C is inactivated, as well as on its synthesis. The APC/C Cdh1 is turned off at the end of G1 by inactivating phosphorylation of multiple Cdh1 phosphosites 26 . The inactivation of the APC/C Cdh1 at the onset of S phase however does not lead to instantaneous accumulation of all of its substrates, many of which are required only in mitosis. Indeed, most of the substrates regulated by both Ndd1 and the APC/C Cdh1 are mitotic proteins.
On the other hand, APC/C Cdh1 substrates that are not transcribed by Ndd1 may, depending on their respective transcription factor, be expressed either earlier or later. Interestingly, several of these genes are transcribed by the Hcm1 transcription factor 41 (Table 1), which is active in S phase before Ndd1 and which also transcribes NDD1. The FFL generated by the ubiquitin ligase APC/C Cdh1 , the transcription factor Ndd1, and their shared targets presents an intriguing regulatory circuit. While FFLs comprising two transcription factors were studied previously 44 , the interaction we describe here is a multi-layered FFL that involves both transcriptional and post-translational regulations. Mathematical simulation of this FFL highlighted two features. The first, which we already discussed, concerns the timing of accumulation of the target proteins in G2 rather than in S. The second effect concerns the extent of substrate repression during G1. Our simulation shows that the steady-state levels of substrates regulated by the FFL are reduced in G1, compared with reduction achieved by any of the regulations on their own. This could be of importance in generating maximal oscillations of activity of these proteins, as well as for achieving effective and rapid repression during G1.
The model in Fig. 6a shows only the basic FFL and has intentionally been stripped of any other interactions. The most relevant interaction is the activating phosphorylation of Ndd1 by Clb1/2 (ref. 48) and Cdc5 (ref. 35). This activation forms in effect an activating positive feedback loop whereby the kinases activate their transcriptional activator.
Ndd1 is degraded during meiosis by the meiotic APC/C Ama1 complex and this degradation is required for maintenance of the extended meiotic prophase 17 . Interestingly, the function of the degradation during the mitotic cycle we describe here seems to be quite different, highlighting how distinct, yet related, ubiquitin ligases can regulate the same protein for diverse purposes during the mitotic and meiotic phases of the cell cycle.
Strikingly, inactivation of Cdh1 eliminates the cell cycle periodicity of the Ndd1 protein (Fig. 3c). This is interesting in view of the periodic transcription by Hcm1 (ref. 41). In the absence of APC/C Cdh1 activity, the Ndd1 protein is apparently stable enough so that the periodic transcription has little effect on its level. Cin8, which is also periodically transcribed by Hcm1 (ref. 41) and degraded by the APC/C Cdh1 also loses its periodicity on APC/C Cdh1 inactivation 49 .
Ndd1 is the transcriptional activator of Mcm1-Fkh2 in yeast. Mammals, which have a much more complex Forkhead transcription factor network 50 , lack a direct Ndd1 orthologue. However, in mammals the FoxM1 transcription factor, which transcribes many mitotic genes 51 including many APC/C Cdh1 substrates, is degraded by the APC/C Cdh1 like Ndd1 in budding yeast, and this degradation is critical for entry into S-phase 52,53 . The apparent evolutionary conservation of this FFL thus confirms its importance for cell cycle regulation.
Yeasts were grown overnight in synthetic defined (SD) medium, diluted 10 Â and grown for 2 h to mid-log phase at 30°C. When proteins were expressed from GAL promoter, cells were grown overnight and diluted in SD raffinose (2%) medium. Protein expression was induced by the addition of galactose (2%). Strains with plasmids were grown at the same conditions but in SD-ura medium.
For obtaining cells at defined cell cycle stages, exponentially growing cells were arrested with 5 mg ml À 1 alpha factor (Zymo Research) for 75 min and treated with an additional portion of 5 mg ml À 1 alpha factor for 45 min. Cells were either harvested immediately or washed and released into fresh medium and harvested at the indicated time points. Mitotic cells were obtained by treating exponentially growing cells with 15 mg ml À 1 Nocodozole (Sigma) for 2 h. Cell samples for FACS analysis were collected simultaneously and processed and analysed as described by Nash et al. 56 on a FACSAriaIII (BD Biosciences). For budding, index samples were fixed in 12.5% formaldehyde and washed with double-distilled water before counting. At least 200 cells were counted for each sample.
RNA analysis. Total was RNA extracted using the RNeasy mini kit (Qiagen). One microgram RNA from each sample was used for Oligo (dT) 20 -primed reverse transcription (Invitrogen) and quantitative reverse transcriptase-PCR reactions were performed using powerSYBR green PCR mix (ABI). Each sample was analysed in duplicates. RNA loading of all samples was normalized for TFC1 levels 59 . Primers (Supplementary Table 1) were designed using ProbeFinder software, Universal Probe Library for yeast (www.roche-applied-science.com).
Mathematical model. The analyses of the FFL module, composed of Cdh1 that regulates its targets both directly and indirectly via Ndd1, were carried out using a deterministic model, based on rate equations. The model consists of a set of coupled ordinary differential equations, where each equation evaluates the time derivative of the number of one type of molecule.
The rate equations describe the following processes: Cdh1 mRNA (m x ) is transcribed at rate g mx and degraded at rate d mx . Cdh1 protein (P x ) is translated at rate g Px and degraded at rate d Px . Cdh1 is transformed into its active form (P Ã x ) at rate p, and is degraded at rate d P Ã x . Ndd1 mRNA (m y ) is transcribed at rate g my and degraded at rate d my . Ndd1 protein (P y ) is translated at rate g Py and degraded at rate d Py . Ndd1 is bound and degraded by Cdh1 active protein at rate b xy . In addition, Ndd1 binds the promoter of its target gene at rate b z and unbinds the promoter at rate u z . The average number of bound Ndd1 proteins to the target promoter is denoted by B z . The target mRNA (m z ) is transcribed at rate g mz B z , reflecting its transcriptional activation by Ndd1, and it is degraded at rate d mz .
The target protein (P z ) is translated at rate g Pz and degraded at rate d Pz . The target protein is bound and degraded by Cdh1 active protein at rate b xz . The rate equations describing these processes take the form: x dm y dt ¼ g my À d my m y dP y dt ¼ g Py m y À b xy P Ã x P y À b z P y 1 À B z ð ÞÀu z B z Â Ã À d Py P y dB z dt ¼ b z P y 1 À B z ð ÞÀu z B z dm z dt ¼ g mz B z À d mz m z dP z dt ¼ g Pz m z À b xz P Ã x P z À d Pz P z This basic FFL module was tweaked in two ways. To reflect a module without Cdh1-Ndd1 regulation, b xy was set to 0. Similarly, in a module without Cdh1-target regulation, b xz ¼ 0.
The equations were implemented in MATLAB (MathWorks) and integrated using its built-in solver ode45.
Live imaging. Cells were plated on conA-coated chambered coverglasses (Mattek) and imaged by an Olympus FV1000 confocal microscope with a 488-nm Argon ion laser equipped with an automated stage, auto-focus device (Z-drift compensation, ZDC) and an environmental chamber (LIS, Switzerland). A Â 60 1.4 NA oil immersion objective was used, temperature was maintained at 30°C and frames were captured every 5 min. The various strains were filmed in parallel in the different wells in the same experiment to ensure identical conditions. Differential interference contrast images were also captured. Data analysis was performed using ImageJ (NIH).