Fbw7 Repression by Hes5 Creates a Feedback Loop That Modulates Notch-Mediated Intestinal and Neural Stem Cell Fate Decisions

A novel intracellular positive feedback loop connects Fbw7 and Notch: while Fbw7 down-regulates the stability of NICD protein, it is also itself transcriptionally down-regulated by NICD target Hes5.


Introduction
FBW7 belongs to the family of SCF (Skp1, Cul1, F-box)-E3 ligases, which degrades several oncoproteins that function in cellular growth and division pathways, including c-MYC, CYCLIN-E, c-JUN, and Notch proteins. Three FBW7 isoforms have been identified (FBW7a, FBW7b, FBW7c), each with an isoform-specific first exon, linked to 10 shared exons. Each isoform is expressed from its own promoter allowing isoform-specific transcriptional regulation and tissue-specific expression. Whether FBW7 isoforms show preferential degradation of substrates is still controversial, although studies have shown that c-MYC, CY-CLIN-E, and PIN1 are degraded specifically by FBW7a [1][2][3]. FBW7b, however, has remained more enigmatic, partly due to its lower absolute mRNA abundance in several cell lines and tissues, when compared to Fbw7a [2,4]. A further level of complexity of FBW7 function is added by the fact that different substrates are regulated in a tissue-specific manner by FBW7 [4][5][6].
Intestinal stem cells are located in the crypt base where they produce rapidly proliferating daughter cells, transit amplifying (TA) cells, which fill the crypts and gradually lose their progenitor identity to differentiate into the two main epithelial lineages upon reaching the crypt-villus junction. The absorptive lineage comprises all enterocytes, while the secretory lineage is composed of goblet cells (secreting protective mucins), enteroendocrine cells (secreting hormones like serotonin or secretin), and Paneth cells (secreting bactericidal proteins, and restricted to the bottom of the crypt in the small intestine [7]). TA cells inevitably encounter a binary decision point that will determine whether they differentiate along an absorptive or a secretory pathway [8,9]. The Notch pathway is a key regulator of this choice. RBP-Jk conditional knockout mice or treatment of mice with a c-secretase inhibitor results in secretory cell expansion [10]. Conversely, in transgenic mice expressing the activated form of Notch1 (NICD1), goblet cells are absent and the proliferative compartment is expanded [11]. FBW7 has proven to be a critical regulator of intestinal stem cell differentiation, as its deletion in the gut significantly increased NICD1 protein levels and reduced goblet cell numbers [5].
Another example demonstrating the importance of FBW7 in Notch biology and function is that of neural stem cells (NSCs). At the beginning of neurogenesis, neuroepithelial stem cells give rise to radial glial stem cells (RGCs), which represent the major population of NSCs at later stages of embryonic cortex development [12]. Notch activity is very high in RGCs, and needs to be downregulated for neuronal differentiation to occur [13]. Overexpression of NICD1 has been shown to be sufficient to promote radial glial identity during embryogenesis, while abrogation of Notch signalling leads to depletion of RGCs [14,15]. In line with these observations, we have shown that absence of Fbw7 in NSCs causes severely impaired RGC stem cell differentiation, accompanied by accumulation of the FBW7 substrate NICD1 [4].
The Notch signalling pathway is a highly conserved pathway that is not only involved in the development and stem cell biology of the mammalian intestine and brain, but controls cell differentiation decisions in a wide range of metazoan species, in a broad range of cell types within a single organism, and at different steps during cell lineage progression.
Mammals have 4 Notch receptors (Notch1-4), 3 Delta-like ligands (Dll1, 3,4), and 2 Serrate-like ligands termed Jagged (Jagged1 and 2). Ligand binding triggers a complex proteolytic cascade involving ADAM proteases and an intramembranous enzyme complex called c-secretase, which results in the release of the cytoplasmic domain of Notch proteins from the plasma membrane. The Notch intracellular domain (NICD) shuttles all the way from the cell membrane to the nucleus, where it binds to RBP-Jk and other proteins, and establishes an activator complex, leading to the expression of target genes. In mammals, the bestcharacterized Notch target genes belong to the Hes (Hairy Enhancer of Split) and Herp/Hey (Hes-related repressor proteins with Y-box) family of basic helix-loop-helix (bHLH) transcriptional repressors [16,17].
An important function of the Notch pathway is in lateral inhibition-an interaction between equal adjacent cells that serves to drive them towards different final states. The basic principle of lateral inhibition is that activation of Notch represses production of the Notch ligand. Consequently, the cell with lower Notch activity produces more ligand, and this activates Notch signalling in the neighbouring cell, which results in reduced ligand production. This in turn enables the cell with lower Notch activity to increase its ligand production even further, because it receives a weakened inhibitory signal back from its neighbours. The effect of this feedback loop is that any initial difference in Notch activity between them, whether stochastic or genetically controlled, is amplified to drive the neighbouring cells into opposite Notch-level status and hence into different developmental pathways [18].
In this manuscript we describe the identification of a novel intracellular positive feedback loop that connects Fbw7 and Notch: FBW7 not only downregulates stability of NICD protein, as previously established, but is also itself transcriptionally downregulated by NICD (via the action of NICD on Hes5). We demonstrate that FBW7 is haploinsufficient for Notch-dependent physiological functions, as Fbw7 D/+ heterozygous mice show impaired differentiation of intestinal goblet cells and NSCs. This haploinsufficiency is greatly dependent on the newly identified negative transcriptional regulation of the Fbw7b promoter by Hes5 protein. We can further show for the first time a pronounced isoform-specific function of FBW7b in driving Notch1 intracellular domain (NICD1) degradation. Genetic rescue experiments and computer modelling of Notch signalling suggest that the FBW7b/ NICD/HES5 feedback loop modulates Notch-dependent cell fate decisions and underlies Fbw7 haploinsufficiency.

Haploinsufficient Fbw7 Function in Intestinal and NSC Fate Decisions
We have previously used conditional gut-specific knock-out mice allowing for deletion of Fbw7 specifically in the intestinal tissue to investigate Fbw7 function in gut biology and tumourigenesis. Mice harbouring an Fbw7 allele in which exon5 was flanked by two loxP sites were crossed to villin-cre transgenic mice, previously shown to provide efficient gut-specific Cre activity [19]. Deletion of exon 5, which encodes most of the F-box, an essential domain of FBW7, disrupts the Fbw7 open reading frame and prevents production of detectable FBW7 protein [20]. Monoallelic FBW7 mutations are frequently observed in human colorectal cancer (CRC) and we described that also in the mouse Fbw7 heterozygosity greatly increased intestinal tumour number in the APC Min/+ mouse model [5], indicating that FBW7 haploinsufficiency in intestinal tumour formation is conserved between mouse and human. Fbw7 f/+ ; villin-cre heterozygous (Fbw7 DG/+ ) mice showed a significant decrease in goblet cell differentiation, suggesting that FBW7 is a haploinsufficient regulator of goblet cell fate decisions in the gut (Figure 1a,b). FBW7 controls the stability of several proteins with well-documented functions in the intestine such as NICD [21], N-terminally phosphorylated c-JUN [22], c-MYC [1], and CYCLIN-E [23]. We next determined to what extent protein levels of these substrates were deregulated by heterozygous Fbw7 inactivation. Western blot analysis revealed an increase in NICD1, but the protein levels of N-terminally phosphorylated c-JUN, c-MYC, and CYCLIN-E were less affected in Fbw7 DG/+ mice (Figure 1c, Figure S1a). To have a more quantitative measure for NOTCH and c-JUN activity, we performed q-PCR analysis of classical target genes of both transcription factors (Figure 1d,

Author Summary
The Notch signalling pathway is a highly conserved system that controls cell differentiation decisions in a wide range of animal species and cell types, and at different steps during cell lineage progression. An important function of the Notch pathway is in lateral inhibition-an interaction between equal adjacent cells that drives them towards different final states. The basic principle of lateral inhibition is that activation of the Notch cell surface receptor represses production of the Notch ligand (also borne on the cell surface). Consequently, cells expressing less Notch produce more Notch ligand that can activate the Notch pathway in neighboring cells and thereby amplify the differences between these cells. However, the additional regulatory circuits required to fine-tune this delicate process have so far remained elusive. Here we describe the identification of a novel intracellular positive feedback loop that connects Fbw7 (the ubiquitin ligase responsible for targeting Notch for degradation) and Notch itself. We show that Fbw7 reduces the stability of Notch intracellular domain (NICD) protein, as previously established, but also that the fbw7 gene is itself transcriptionally downregulated by the Notch effector Hes5. Thus we conclude that increased Notch activity causes NICD stabilisation. Further, we demonstrate that perturbation of this regulatory loop is responsible for the Fbw7 haploinsufficiency observed for Notch-dependent functions in intestine and brain stem cells.
Figure S1d-e). In agreement with the western blot analysis, c-Jun and c-Myc mRNA levels were unaffected in Fbw7 DG/+ intestines, while Hes5 mRNA was significantly increased (Figure 1d). Thus only NICD1, but none of the other substrates tested, was increased in Fbw7 heterozygous mice.
To further investigate FBW7 haploinsufficiency in a second tissue, we analysed NSCs from FBW7 wild-type and heterozygous animals.
We generated conditional brain-specific knock-out mice allowing the deletion of Fbw7 specifically in the brain. The aforementioned Fbw7 f/+ mice were crossed to Nestin:Cre transgenic mice previously shown to provide efficient brain-specific Cre activity [4].
NSCs were prepared from E13.5 embryos and maintained as an adherent monolayer culture. These cultures were induced to differentiate by withdrawing growth factors, and 3 d after the induction of differentiation, the percentage of remaining Nestinpositive NSCs was determined. A significantly higher number of Fbw7 DN/+ NSCs retained Nestin expression as compared to the wild-type controls (Figure 1e, 1f), which coincided with elevated NICD1 protein levels in Fbw7 DN/+ NSCs (Figure 1g, Figure S1b). Consequently, mRNA levels of Hes5, but not c-Jun or c-Myc, were significantly elevated in Fbw7 DN/+ NSCs (Figure 1h, Figure S1c).
Thus Fbw7 is haploinsufficient for Notch degradation during both goblet cell and NSC differentiation.

Distinct Regulation of the Fbw7b Locus
To understand the haploinsufficiency of FBW7 function, we explored the possibility of feedback regulation and investigated the expression of Fbw7 in Fbw7 f/+ control and Fbw7 DG/+ heterozygous intestine and Fbw7 DN/+ heterozygous NSCs. The Fbw7 locus encodes three different Fbw7 isoforms (Fbw7a, Fbw7b, Fbw7c) that are not generated by alternative splicing; rather, each isoform has its unique 59UTR and is transcribed from an isoform-specific promoter (Figure 2a) [24]. We have previously shown that the a and b Fbw7 isoforms are expressed in the intestine and the brain, whereas the c isoform was undetectable [4,5]. Using quantitative qPCR analysis we show that the Fbw7a isoform is 170-and 10-fold more abundant than the Fbw7b isoform in the intestine and NSCs, respectively ( Figure S2). To circumvent a potential alteration in mRNA stability of the Fbw7D allele, we used Q-PCR primers located in exon5, which is missing in the Fbw7D allele ( Figure 2a). Thus using this approach exactly 50% of the normal amount of Fbw7 mRNA is expected in Fbw7 D/+ heterozygous cells. However, Fbw7 mRNA levels in Fbw7 DG/+ intestine and Fbw7 DN/+ NSC were only 30% of controls, a reduction of about 40% from the expected expression of the intact allele ( Figure 2b). Q-PCR analysis using isoform-specific primers, which detect both the wildtype and the DFbw7 alleles (Figure 2a), showed that Fbw7a mRNA levels were only slightly reduced in control Fbw7 f/+ and Fbw7 DG/+   intestines as well as in Fbw7 DN/+ NSCs. In contrast, expression of Fbw7b mRNA was greatly reduced in Fbw7 DG/+ intestines and Fbw7 DN/+ NSCs (Figure 2b). Mono-allelic (i.e., heterozygous) FBW7 mutations are frequently observed in human CRC, and Fbw7 heterozygosity greatly increases intestinal tumour number in the APC Min/+ mouse model [5]. Similarly, a reduction in Fbw7b mRNA was observed in tumours from APC Min/+ ; Fbw7 DG/+ mice compared to APC Min/+ ; Fbw7 f/+ tumours (Figure 2c).
To gain insights into the mechanism of Fbw7 transcriptional regulation, we performed an in silico transcription factor binding site analysis of the genomic Fbw7 locus. This revealed the presence of putative N-box sites, the consensus binding element recognized by HES transcription factors, in the promoters of both Fbw7a and Fbw7b ( Figure 2d). Our attempts to perform Chromatin immunoprecipitation (ChIP) analysis on endogenous HES5 failed as we were unable to identity a suitable Hes5-specific antibody ( Figure  S3). For this reason Flag-HES5 was overexpressed in HCT116 colon cancer cells and ChIP performed using Flag antibody. This revealed binding of HES5 protein to the N-box in the neurogenin3 promoter (NGN3), a known HES target gene [25], which served as a positive control. However, we also observed some unspecific DNA binding of FLAG-HES5 relative to control vector transfected cells at the GAPDH, b-ACTIN, and CYCLIND1 promoters, which all served as negative controls. HES5 bound to predicted Nbox elements present in the FBW7a and FBW7b promoters to a similar extent to NGN3, but did not bind significantly to a putative N-box in exon1 of FBW7b (Figure 2e).
Together these data point very strongly to a specific role for HES5 in regulating FBW7 transcription.

Hes5 Represses Fbw7b Transcription
To further validate FBW7 as a direct transcriptional target of HES5, NICD1 was ectopically expressed in HCT116 colon cancer cells. NICD1 expression resulted in increased HES5 mRNA levels, but had no effect on HES1. Moreover, FBW7b and to a lesser extent FBW7a mRNA levels were strongly repressed (Figure 3a). shRNA-mediated knock-down of HES5 reversed the repression of FBW7a and FBW7b expression (Figure 3b). Similar results were obtained in NSCs ( Figure S4a,b).
The direct repression of FBW7b expression, and to a lesser extent, of FBW7a, by HES5 implies that NICD1, HES5, and FBW7 are connected through a feedback loop. This leads to the unexpected prediction that overexpression of HES5 should result in a cell-autonomous increase in NICD1 protein levels (Figure 3c), but that this increase should be impaired in cells deleted for the E3 ligase (that is, FBW7) regulating NICD turnover. To test this hypothesis, we used a set of human colon cancer HCT116 cell lines that have homozygous isoform-specific FBW7-null mutations [2].
GFP-tagged-HES5 or GFP alone was overexpressed in HCT116 FBW7-wt, FBW7a-null, and FBW7b-null cells followed by intracellular NICD staining and FACS analysis. FACS analysis on GFP+ gated cells revealed that NICD1 protein levels in HCT116 are not uniform, rather that there are two distinct subpopulations with different NICD1 levels. This resembles the bistability observed when lateral inhibition operates, and thus should be affected by the intracellular NICD-.Hes5 -| Fbw7 -| NICD positive feedback loop. In line with this, the majority of FBW7-wt cells were in the low-NICD state, while a greater proportion of FBW7b-null cells were in the high-NICD state (Figures S5a-c and S6a). Expression of HES5-GFP shifted these proportions, leading to a marked cell-autonomous increase in the percentage of cells in the high-NICD1 state in FBW7-wt and FBW7a-null cells, but this increase was drastically impaired in FBW7b-null cells (Figure 3c and Figure S5). Conversely, silencing HES5 (sh-HES5-GFP) led to a cell-autonomous reduction in the percentage of cells in a high-NICD state in FBW7-wt and FBW7anull cells, which was compromised in FBW7b-null cells (Figure 3d and Figure S5). These data imply that FBW7b is the predominant isoform involved in the NICD1/HES5/FBW7 feedback loop.
To formally show that FBW7b regulates NICD degradation, we performed cycloheximide chase experiments for NICD turnover in FBW7-wt, FBW7a-null, and FBW7b-null cells. We found that NICD turnover was reduced in FBW7b-null cells by comparison with FBW7-wt and FBW7a-null cells (Figure 3e, 3f). Accordingly, we observed less ubiquitylation of NICD in FBW7b-null cells ( Figure S8c). Q-PCR analysis performed in the same set of Fbw7mutant cell lines confirmed that only loss of FBW7b resulted in increased HES5 mRNA levels ( Figure S6b). Together, these data demonstrate a crucial role of FBW7b in regulation of NICD turnover.

Fbw7 Haploinsufficiency Requires Hes5 Function
To further investigate HES5 function in our proposed loop, we characterized the phenotype of Hes5-deficent mice in the intestine and NSCs. Hes5 2/2 mice are viable, but mutant phenotypes in various organ systems such as the eye, inner ear, and nervous system have been described [26][27][28]. However, the function of HES5 in the intestine and in NSCs has not been analysed. The absence of HES5 led to a significant increase in intestinal goblet cell number by approximately 50% (Figure 4a,b). Q-PCR analysis revealed increased Fbw7b expression, and also the mRNA levels of the HES target gene Dll1 and the goblet cell marker Muc2 were augmented while Fbw7a transcript levels remained unchanged (Figure 4c). Loss of HES5 in the brain caused no obvious phenotypic abnormalities, consistent with previous observations [29]. However, NSCs cultured from Hes5 2/2 animals showed significant premature differentiation of Nestin-positive cells with a concomitant mild increase of Map2 positive neurons (Figure 4d,e). Deletion of Hes5 in NSCs also led to a significant increase in Fbw7b and Dll1 expression (Figure 4f).

Mathematical Modelling of the Effects of the Fbw7 Feedback Loop in the Delta-Notch Lateral Inhibition Circuit
Our experiments imply that, overlaid on the standard gene regulatory circuit of Delta-Notch-mediated lateral inhibition, there is an intracellular feedback loop involving Fbw7: NICD stimulates expression of Hes5; Hes5 represses Fbw7b; and Fbw7b drives degradation of NICD. The net action of this NICD-.Hes5 -| Fbw7 -| NICD feedback loop is positive: it tends to amplify the effect of any change in any of the three components. This can explain why Fbw7 is haploinsufficient, in the sense that loss of just one allele of the gene is enough to cause a marked shift in the ratio of secretory (low NICD) to absorptive (high NICD) cells in the gut, or of neurons to progenitors in the brain.
Intuitive arguments are, however, untrustworthy when applied to systems with feedback. We have therefore investigated a mathematical model of the Delta-Notch lateral inhibition circuitry incorporating the intracellular Fbw7 feedback loop, to see whether pCMV6-Gfp or pCMV6-Hes5-gfp plasmid (histograms represent the levels of NICD on GFP+ gated cells). (d) FACS analysis of intracellular NICD in HCT116-Wt, HCT116-Fbw7-a-null, or HCT116-Fbw7-b-null cells transfected with either sh-control-Gfp or sh-Hes5-gfp plasmid (histograms represent the levels of NICD on GFP+ gated cells). (e) Western blot analysis of NICD and ACTIN in HCT116-Wt, HCT116-Fbw7-a-null, or HCT116-Fbw7-b-null cells after treatment with cycloheximide for the indicated time points. (f) Quantification of NICD levels normalized to actin in HCT116-Wt, HCT116-Fbw7-anull, or HCT116-Fbw7-b-null cells after treatment with cycloheximide for the indicated time points. doi:10.1371/journal.pbio.1001586.g003 it can indeed give rise to the observed phenomena. In Figure 6, we compare the predicted multicellular patterns of differentiation under four conditions, corresponding to the genotypes Fbw7 +/+ ; Hes5 +/+ (b), Fbw7 +/2 ;Hes +/+ (c), Fbw7 +/+ ;Hes5 2/2 (d), and Fbw7 +/2 ;Hes5 2/2 (e). In (d), where Hes5 is absent, the proportion of secretory cells is increased; in (c), where Hes5 is present but one of the two Fbw7 gene copies is defective, we see the opposite effect, reflecting haploinsufficiency of Fbw7; and in (e), where both types of mutation are present, their effects cancel out, restoring the normal ratio of secretory to absorptive cells. These results depend, of course, on the values assumed for the parameters in the model, for many of which we can only make rough guesses. The results of the modelling should therefore be viewed not so much as quantitative predictions, but rather as a demonstration that the experimental observations (Figures 1a, 4a, and 5a) are indeed consistent with a mechanism of the type proposed.
Intuitively, it seems that the Fbw7 loop superimposed on the standard lateral-inhibition circuitry should tend to amplify the differences between neighbouring cells and perhaps speed up the creation of a salt-and-pepper pattern. Moreover, as we have argued, it could explain why loss of a single Fbw7 gene copy has an unexpectedly large effect on the ratio of differentiated cell types in this final pattern.

Discussion
Notch signalling is a key pathway that controls differentiation decisions in a vast number of cell types. SCF(Fbw7) is an important negative regulator of NICD function [30,31], and many, though not all, of the phenotypes observed in Fbw7 mutant animals can be attributed to deregulation of Notch activity [4,5,21,[32][33][34]. In this study we show that FBW7b is the isoform responsible for NICD degradation and also reveal that the functional relationship between FBW7b and Notch is not unidirectional, but that FBW7b and NICD are connected through a double-negative, i.e. positive, feedback loop.
We propose that the NICD/HES5/FBW7b feedback loop functions to refine the classical lateral inhibition mechanism (Figure 6a). Notch signalling represses transcription of Notch ligands, which leads to unequal levels of Notch signalling in neighbouring cells. We propose here that increasing levels of Notch activity results in reduced expression of Fbw7b, which in turn will lead to a further increase in NICD1 protein levels. Similarly, attenuation of Notch signalling will decrease NICD1 levels, as Fbw7b will be more highly expressed. Whereas NICD/ Notch ligand regulation operates non-cell-autonomously, the NICD/HES5/FBW7b loop results in a cell-autonomous amplification of inequalities in Notch activity. This mechanism will help the cell to stably attain a Notch-high or Notch-low state, thereby solidifying cell fate decisions.
NICD1 stands out among all the SCF(Fbw7) substrates as it is the only substrate that is noticeably increased in Fbw7 D/+ heterozygous cells. Mechanistically, this is explained by the positive feedback causing repression of the wild-type Fbw7 allele in Fbw7 D/+ heterozygous cells. Thus, instead of being reduced to just 50% of normal, Fbw7 mRNA levels are reduced even further.   Figures 4b and 5b). (In comparing the model with the real tissue, note that in the gut, the future absorptive cells continue dividing after the secretory cells have stopped [9], scaling up the observed numbers of absorptive cells relative to secretory cells in all genotypes.) See Materials and Methods and Data S1 for details of the modelling. doi:10.1371/journal.pbio.1001586.g006 Absolute quantification of Fbw7 mRNA abundance in the intestine and NSCs has shown that the reduction in total Fbw7 mRNA in heterozygous animals cannot be accounted for solely by the reduction in levels of the Fbw7b isoform. We believe that the small but consistent reduction of the more abundant Fbw7a mRNA (reflecting its moderate regulation by Hes5; see Figure 3a,b) contributes to the overall regulation of total Fbw7 mRNA levels in heterozygous cells.
Previous reports have generated Fbw7b-specific knockout mice, which are viable, but comprehensive analyses of Notch-mediated phenotypes in brain or gut were not performed [35]. The same holds true for Hes5 2/2 mice, which had not been reported to have abnormalities in intestinal or NSC differentiation. In our analysis we have clearly shown that decreased levels of Fbw7b or loss of Hes5 have a profound effect on patterns of differentiation in the intestine and in NSCs.
There are various reports regarding the localisation of FBW7b and its contribution to substrate turnover. Some accounts report that FBW7b localises to the cytosol [1,36], whereas others have found it in the ER and Golgi [35]. Also in the cells we studied FBW7b localised predominantly in the cytoplasm but some nuclear localisation could also be observed, especially in response to proteasome inhibitor treatment ( Figure S7a-c). Conversely FBW7b is able to interact with both endogenous NICD and overexpressed NICD (Figure S8a,b) and the ubiquitylation of overexpressed NICD is severely impaired in HCT116-FBW7b-null cells ( Figure S8c). The cytoplasmic presence of FBW7b might even explain why the observed haploinsufficiency of Fbw7 D/+ animals is restricted to NICD1. Many Fbw7 substrates are predominantly nuclear, whereas NICD shuttles from the cytoplasm into the nucleus, and is thus present in both subcellular compartments. On a similar note, Ye et al. have shown that FBW7b is the predominant isoform responsible for CYCLIN-E turnover, which is primarily nuclear, but shuttles between cytoplasm and nucleus, like NICD [37].
A recent study, using homozygous isoform-specific FBW7-null mutations in human colon cancer HCT116 cells, has shown that FBW7a is the major isoform contributing to c-MYC and SREBP degradation [2]. We have used those cells to show that FBW7b is the isoform regulating NICD degradation. While our data suggest that Fbw7b is the major isoform regulating NICD degradation, Fbw7a possibly also contributes to the proposed feedback loop. Further, we can confirm previous studies showing that c-MYC is primarily degraded by FBW7a ( Figure S6c) and [2]. The difference in substrate specificity and absolute abundance of the Fbw7 isoforms, together with their heterogeneous tissue distribution, could also possibly explain the varying penetrance of Fbw7 deletion in different organs.
FBW7 is frequently mutated in a large variety of human tumours [24]. In particular, loss-of-function mutations in FBW7 are very commonly found in human CRC [38]. Interestingly, about 70% of FBW7 mutations are mono-allelic, and only about 30% of the colorectal tumours with FBW7 mutations show loss-ofheterozygosity (LOH) [39,40]. FBW7 mRNA levels are significantly lower in human CRC tumour tissues than in normal intestinal tissue, and low FBW7 expression correlates with poor prognosis [41]. In a mouse model for human CRC, it was clearly shown that Hes5 expression was upregulated in tumours carrying FBW7 heterozygous mutations when compared to tumours wildtype for FBW7 [5]. Thus FBW7 heterozygosity results in increased Hes5 expression both in human colorectal tumours and in the APC min ;Fbw7 DG/+ mouse model, suggesting that the NICD/HES5/ FBW7b positive feedback loop is the molecular mechanism that underlies FBW7 haploinsufficiency in tumour suppression.
Thus the feedback loop created through repression of Fbw7b by NICD plays a crucial part in Notch-regulated cell fate decisions, not only in normal tissues but also in the evolution of a large class of cancers.
For differentiation, growth factors were withdrawn from the medium and 10% NeuroCult Differentiation Supplement (Stem-Cell Technologies) was added. Under differentiation conditions, cells were plated on poly-L-ornithine (0.01% solution; Sigma; diluted 1:10 in 150 mM disodium tetraborate; Sigma) coated cover slips.
For transfection, NSCs were plated at subconfluence and transfected with Lipofectamine 2000 according to the manufacturer's protocol (Invitrogen).

Histological Analysis
Mice were euthanized by cervical dislocation and the small intestines prepared for histology as described before [48]. Sections were cut at 4 mm for Haematoxylin & Eosin staining and PAS/AB staining. To quantify goblet cells, AB/PAS+ cells were quantified from at least 100 villi from comparable intestinal regions from at least 5 mice from each genotype and the data represented as the mean 6 SEM.

Intracellular Staining and FACS Analysis
HCT116 cells transfected with the indicated plasmids were fixed for 10 min in 1% PFA, permeabilized in PBS+0.5% Triton for 10 min at RT, and blocked in PBS+2% FCS for 30 min. After blocking, cells were incubated with anti-NICD antibody (1:500 dilution in PBS+2% FCS) for 30 min. Cells were washed in PBS+2% FCS and incubated with donkey-anti-rabbit-Alexa647 secondary antibody (1:1000 in PBS+2% FCS) for 30 min in the dark at RT. Cells were analysed in an LSRII cytometer. Overlay Histograms (Hes-GFP or sh-Hes5-GFP versus their controls) were represented as NICD-Alexa-647 versus cell numbers on GFP+ gated cells. The number of GFP+ cells quantified for each individual sample, the single histograms, and the percentage of cells in high-NICD and low-NICD state are indicated in Figure  S5.

Mathematical Modelling
To describe the Delta-Notch-Fbw7-Hes gene regulatory circuit, we adapted a standard simple Delta-Notch lateral-inhibition model, adding the Fbw7 feedback loop as in Figure 6a. We represented the dynamics by a set of differential equations, which we solved numerically using Mathematica to determine the final state of a two-dimensional array of cells. The model assumes that there are two relevant Hes genes, HesX and Hes5, where HesX stands for one (or more) of the many other members of the Hes/ Hey family that are expressed in gut and CNS. HesX (by itself) represses Delta, while HesX and Hes5 act in parallel to repress Fbw7. Loss of functional Hes5 thus leads roughly to a doubling of Fbw7 expression and can be compensated by a halving of the Fbw7 gene dosage. With our chosen model parameters, the Fbw7 positive feedback loop gives rise to bistability, allowing a cell exposed to a given level of Delta signalling from its neighbours (above a certain low Delta threshold) to exist in either a low-or a high-NICD state (as suggested by the data; see Figures 3c,d and S5a). This biases the outcome of Delta-Notch-mediated lateral inhibition. In the version of the model used to compute Figure 6, we postulate molecular lifetimes such that the dynamics of the Fbw7 loop are fast compared with the dynamics of the Delta-Notch loop. Each cell then moves rapidly to a low-or high-NICD state, with a relative probability dependent on the starting conditions and genotype, creating an initial random multicellular pattern that is subsequently adjusted by lateral inhibition. The adjustments follow a simple rule: thanks to bistability, low-NICD cells can persist regardless of the states of their neighbours, but any high-NICD cell that is entirely surrounded by other high-NICD cells is eventually converted to a low-NICD state. This is because high NICD entails a near-zero level of Delta production, and the high-NICD state becomes unstable when levels of Delta signalling from neighbours fall very low.
The model assumes that cells all start in an approximately similar state but with some small random variation from cell to cell, reflecting genetic noise, whose consequences are amplified through the Fbw7 and Delta-Notch feedback loops to give a final pepper-and-salt pattern. Results of the computation are shown for a 10610 hexagonal array of cells, with cyclic boundary conditions.
Mathematical details of the model and values of the parameters are given in Data S1. The Mathematica program is available on request from julian.lewis@cancer.org.uk.

Statistical Analysis
Statistical evaluation was performed by Student's unpaired t test. Data are presented as mean 6 SEM. *p#0.05 was considered statistically significant. **p#0.01 was considered highly statistically significant. ***p#0.001 was considered very highly statistically significant.

Supporting Information
Data S1 Mathematical model.