The plasmids encoding the armadillo (ARM) repeat domain of human β-catenin (residues 134–671) and APC were kind gifts from Prof. W. I. Weis and Dr. S. H. McLaughlin, respectively. The R3 region of APC and fragments thereof (Figure 1) and shorter constructs of APC were produced by PCR, and mutations were introduced using site-directed mutagenesis. All plasmids used for expression were cloned into a modified pRSET vector where the His-tag has been replaced by a GST-tag and a thrombin cleavage site introduced between the GST and the protein of interest; after cleavage this leaves two amino acids, GS, at the N-terminus of the protein. All proteins were expressed in E. coli C41 cells (Miroux and Walker, 1996). Transformed cells were grown in 2TY media with appropriate antibiotic until OD600 of 0.6 at 37°C was reached, the temperature was then lowered to 25°C and the cells induced with 0.2 mM IPTG after a further 18 h the cells were harvested at 5,000 g for 7 min at 4°C. The cells were resuspended in 50 mM Tris-HCl buffer pH7.5, 150 mM NaCl, 1 mM DTT containing protease inhibitors and lysed using an Emusiflex C5 (Avestin) at 10,000 psi. The lysed cells were centrifuged at 35,000 g for 35 min at 4°C. The proteins were purified using glutathione-Sepharose 4B beads (Cytiva). The GST was cleaved from the target protein on the resin using thrombin and the protein eluted.

β-catenin was further purified using a Mono-Q column (Cytiva) equilibrated in 50 mM Tris-HCl buffer pH 8.9, 50 mM NaCl, 1 mM DTT and eluted with a linear NaCl gradient to 1M NaCl. Fractions containing greater than 95% β-catenin were pooled, flash frozen, lyophilised, and stored at −80°C (Supplementary Figure S1). Further purification of the APC constructs was achieved by removing high molecular weight impurities using differential filtration; the samples were centrifuged through a centrifugal concentrator with a 30 kD molecular weight cut-off (MWCO) membrane, and the flow through was concentrated using a 3 kD MWCO centrifugal concentrator (Supplementary Figure S2). The purified protein was then flash frozen and stored at −80°C. The identities of all proteins were confirmed by MALDI mass spectrometry performed by Dr. Len Packman (University of Cambridge PNAC Facility). β-catenin concentration was calculated from its extinction coefficient at 280 nm obtained from ProtParam (Gasteiger et al., 2005), and APC concentration was measured using the Pierce™ BCA protein Assay Kit (ThermoFisher).

APC constructs were labelled at the single cysteine residue located at position 1,501, which was retained in all of the fragments made here. Proteins were buffered exchanged into PBS containing 1 mM TCEP and labelled with either fluorescein-maleimide or Alexa Fluor™ 488 C5 maleimide. Fluorescein-maleimide was added at a 5-fold molar excess concentration to protein and incubated for 1 h at room temperature; excess dye was removed by acetone precipitation of the APC construct (Vivès and Lebleu, 2003); the labelled protein was resuspended in PBS, 1 mM DTT. A 2-fold molar excess of Alexa Fluor™ 488 C5 maleimide was added to the protein for 2 h at room temperature and excess dye was removed using Pierce™ Dye Removal Columns (ThermoFisher). The labelling efficiency was determined from the ratio of the concentration of the fluorescein/Alexa Fluor™ 488 moiety to the protein concentration, and additionally the number of sites labelled per molecule was assessed by MALDI mass spectrometry (performed by Dr. Len Packman, University of Cambridge PNAC Facility). This analysis showed that all of the APC constructs were labelled at >90% and at the single intended site (Cysteine 1501). Labelled APC was flash frozen and stored at −80°C.

The binding of fluorescent labelled APC constructs to β-catenin was monitored either by fluorescence or by fluorescence anisotropy using a LS55 fluorimeter (Perkin Elmer). All proteins were buffer exchanged into PBS, 1 mM DTT, and measurements were made at 25°C. Excitation and emission wavelengths were 495 and 519 nm, respectively, and slit widths were 5 nm. APC_bc labelled at Cys 1501 with Alexa-488 was used in a competition fluorescence assay to measure the IC₅₀ values of the phosphomimetic APC_bc variants for β-catenin. In these experiments, a solution of 20 nM Alexa-488-APC and 200 nM β-catenin was incubated in the cuvette at 25°C for 30 min prior to titration of unlabelled APC_bc variants using a Microlab 500C dispenser (Hamilton). After addition of each aliquot, the sample was stirred for 30 s and equilibrated for a further 60 s before measurement. The IC₅₀ was calculated using the following equation: F = F f + Δ F ( 1 + ( [ U ] I C 50 ) ) (1) where F is the measured fluorescence, F _f is the fluorescence of the free ligand, ΔF is the change in fluorescence between the free and bound form, and U is the concentration of the competing APC ligand.

All other APC constructs were labelled with fluorescein, and the dissociation constants were measured by fluorescence anisotropy. In these experiments, aliquots of β-catenin were titrated into a cuvette containing 10 nM fluorescein-labelled APC, and the sample was stirred and equilibrated before measurement (as described above). Both fluorescence anisotropy and fluorescence intensity were measured at 15°C. As there was a difference in the fluorescence intensity of bound and unbound APC, the fluorescence anisotropy was adjusted using the following equation: R a d j   = ( R − R f R b − R ) ( Q f Q b ) R b + R f 1 + ( R − R f R b − R ) ( Q f Q b ) (2) where Q is the measured fluorescence and R is the measured anisotropy. The subscripts f and b denote the unbound (free) and saturated bound forms of labelled APC. The adjusted anisotropy data were then fitted using a single-state Hill plot to derive the K _d and Hill coefficient, h: R = R h P h K d h + P h (3) where P is the APC concentration

To calculate the Gibbs free energy of binding from the K _d, Equation 4 was used: Δ G= R T  ln  K d (4) where R is the gas constant and T is the temperature in Kelvin.

Stopped-flow fluorescence was used to measure the kinetics of binding with a SX-19 stopped-flow fluorimeter (Applied Photophysics). The excitation wavelength was 495 nm, and a cut-off filter of 515 nm was used to measure the emission. The slit widths were 2 nm for both excitation and emission. All proteins were prepared in PBS buffer, 1 mM DTT, and the experiments were performed at 15°C. The β-catenin concentrations used were at least ten times higher than that of the APC to ensure pseudo first-order conditions; a fixed concentration of fluorescein-labelled APC (25 nM) was rapidly mixed with varying concentrations of unlabelled β-catenin (between 250 and 2,000 nM) in a 1:1 volume ratio, and the change in fluorescence intensity was recorded. For dissociation experiments, the complex of β-catenin and labelled APC was pre-formed by mixing the two proteins in a 1:1 molar ratio (200 nM) and incubated for 1 h at 15°C in the dark. The pre-formed complex was then mixed in a 1:1 volume ratio with 10 times molar excess of the same APC construct, and the change in fluorescence intensity was measured. A minimum of five traces was collected and averaged. The averaged trace was plotted using GraphPad Prism 5 (GraphPad Software, Ltd.) and fitted to either a single exponential phase or the sum of two exponential phases. For the association experiments, the observed rate constant, k _obs , was plotted against the concentration of β-catenin, and k _on was calculated from the linear fit: k o b s = k o n [ β catenin ] + k o f f (5)

It is important to note that in the crystal structures of β-catenin-APC and β-catenin-E-cadherin complexes, both of which show similar contacts between β-catenin and the phosphorylation sites of the respective ligands, there appears to be no interaction between β-catenin and these residues in their unphosphorylated forms (Huber and Weis, 2001; Ha et al., 2004). In addition to the β-catenin contacts made by the phosphorylated sites of APC spanning residues 1,487–1,510, there are other contacting residues, notably within 1,510–1,529 that folds back onto 1,487–1,510 (Figure 2). With an APC construct comprising subdomains b and c (residues 1,483–1,533), referred to as APC_bc, the five phosphorylation sites were mutated to the phosphomimetic glutamate either individually or in combination [T1487E (T1), S1504E (S1), S1505E (S2), S1507E (S3), S1510E (S4)], and the IC50s were measured by competition fluorescence assay using APC_bc labelled with Alexa-488 at Cys 1,501 (Figure 3).

Mutation of any one of these residues to the phosphomimetic increases the affinity for β-catenin between 4-fold and 30-fold, with S1507E showing the greatest increase; in the crystal structure of the complex, phospho-S1507 (S3) is tightly coordinated and fixed in a specific orientation by three β-catenin residues and therefore would be predicted to have the tightest binding affinity of the five phosphorylated residues. Phospho-S1505 (S2) does not appear to make any contacts with β-catenin in the crystal structure of the complex, but the phosphomimetic mutation at this site nevertheless increased the binding affinity 5-fold. This could be as result of the interaction of E1505 with R1523 within the short helix formed by this region of APC, which could stabilise its interaction with β-catenin. Alternatively, it may reflect a “fuzzy” behaviour of the APC-β-catenin interaction, in which the interface, and the interactions formed by specific residues, in solution is different from the static structure captured in the crystallography. Constructs containing four or more phosphomimetics showed a ∼150-fold increase in affinity.

The affinity of the full-length R3 domain, APC_abc containing all five phosphomimetics (referred to subsequently as pAPC), was also measured by fluorescence anisotropy, (see next section), and the K _d determined to be 5.3 nM (Table 1; Figure 4). This value is similar to K _d values obtained in previous studies using an APC R3 construct that had been phosphorylated using CK1-ε and GSK3-β (Ha et al., 2004; Xing et al., 2004; Choi et al., 2006; Liu et al., 2006), indicating that glutamate serves as a good phosphomimetic.

We next looked at APC R3 constructs comprising each of the three different β-catenin binding interfaces either alone or in combination (Figure 1B), and the affinities were measured by fluorescence anisotropy using APC labelled at residue 1,501 with fluorescein (Figure 4; Table 1). Domains b and c could be expressed in isolation, but domain a could not. The binding of the phosphodomain c was only detectable in the phosphomimetic form, p-c (K _d of 160 nM), suggesting that this region only interacts with β-catenin in the cell when phosphorylated, which is consistent with what is observed in the crystal structures (as discussed above). The lysine-binding domain b has a dissociation constant of 246 nM, which is similar to that of p-c; when domain b is combined with unphosphorylated domain c (bc), the affinity shows only a small increase (196 nM) relative to b alone, again consistent with the weak interaction of unphosphorylated c with β-catenin. When domain b is combined with domain a (ab) the affinity increases approximately 2.5-fold relative to b alone (90 nM versus 246 nM). The entire unphosphorylated APC fragment comprising all three domains (abc) has a 12-fold higher affinity than bc and a 5-fold higher affinity than ab. The increase in affinity upon adding unphosphorylated c to ab is somewhat surprising given the very small increase in affinity observed upon adding unphosphorylated c to b. Adding p-c to ab (i.e., the entire phosphorylated APC fragment, p-abc) results in the largest increase in affinity of adding any single domain (∼18-fold, 5.3 nM versus 90 nM).

Differences were observed in the shapes of the binding curves, indicating that there is cooperative binding of the subdomains for some of the APC constructs but not others. Cooperativity was observed for pAPC, as indicated by a Hill coefficient of 2, but not for the unphosphorylated APC or for any of the phosphorylated or unphosphorylated fragments (Hill coefficient of 1 within error) (Figure 5 and Table 1). This result suggests that the binding of the phosphorylated domain c results in an increase in affinity of the other domains, presumably due to the tethering of one domain bringing the other domains into proximity.

Because the lysine-binding domain b is the middle domain, it cannot be deleted in the same way as the helical domain a and phospho domain c. However, its affinity for β-catenin can be dramatically weakened by mutation of the lysine-interacting residues D1486 and E1494 (Xing et al., 2003; Ha et al., 2004; Kohler et al., 2008). The mutation D1486S lowered the affinity of unphosphorylated APC by more than 100-fold (2 μM vs 16 nM). (E1494T reduces the affinity to below the detection limit of the experiment (>5 μM)). This result suggests that domain a cannot bind to β-catenin in the absence of sufficient contacts made by domains b and c. D1486S lowered the affinity of pAPC 7.5-fold (30 nM vs. 5 nM). The affinity of pAPC_abc D1486S is higher than the affinity of p-c alone (160 nM), suggesting that some contacts of domain a with β-catenin are retained when domain c is bound; alternatively there may be some fraying of the β-catenin interface in the isolated p-c fragment, meaning that p-c does not effectively recapitulate the interactions present in the full p-abc and p-abc D1486S constructs.

We also investigated the contributions of the three domains of APC to the kinetics of β-catenin binding by stopped-flow fluorescence measurements of the fluorescein-labelled APC (Figure 5). (The kinetics of abc were also measured using Alexa 488-labelled APC, and similar kinetics were observed to those obtained using fluorescein-labelled APC). Two phases could be detected in the dissociation kinetics, a fast phase (∼35% amplitude) and a slow phase (∼65%). Deletion of domains a and c (constructs bc and ab, respectively) results in small (∼3-fold) decreases in the association rate and small (2-fold) increases in the dissociation rate (Table 1; Figure 4). Only one dissociation phase could be detected for bc, but given that for many of the variants there is a relatively small difference in the rates of the two phases, it could be that they are too similar in bc to distinguish. The introduction of the phosphomimetics (p-abc), which strengthens the interaction of domain c with β-catenin, has a small effect on the association kinetics (4-fold) and a larger effect on the dissociation kinetics than on the association kinetics, decreasing the fast dissociation phase 6-fold and the slow dissociation phase 50-fold. In contrast, the introduction of the D1486S mutation, which weakens the interaction of domain b with β-catenin, has negligible effect on the association kinetics of p-abc but a large effect on the dissociation kinetics, decreasing the fast phase 40-fold and the slow phase 200-fold. The association and dissociation kinetics of (unphosphorylated) abc D1486S could not be measured due to the very low binding affinity of this construct.

To further probe the relationships between the three binding interfaces within APC, linkers were inserted at two different sites where there are no visible contacts with β-catenin in the crystal structures (Ha et al., 2004; Xing et al., 2004) (Figures 2, 6). The first site was between domains a and b (between residues 1,478 and 1,479) at the C-terminus of the α-helix. The second site was between domains b and c (between residues 1,500 and 1,501). This region of APC is four amino acids in length and is not visible in the crystal structure of the complex, suggesting that it is highly dynamic. Three types of linkers were used: one flexible linker and two rigid linkers (Figure 6). The linkers were all designed to be of similar length (16–19 amino acids) and have similar charge properties. The flexible linker (FL) is based on the (SG)₄ linker between tandem immunoglobulin domains but also includes lysine and glutamate residues to aid solubility (Chen et al., 2013). The rigid linker RL forms an α-helix stabilised by glutamate-lysine salt bridges (Marqusee and Baldwin, 1987; Arai, 2021). The polyproline linker forms an extended left-handed helix and is regarded as a rigid “molecular ruler” (Schuler et al., 2005; Adzhubei et al., 2013). This linker is expected to be longer (∼4 nm) than the RL linker (∼1.8 nm).

Insertion of either the rigid or the flexible linker at 1,500 between domains b and c into either APC_abc or pAPC_abc reduced the affinity ∼1.5–2-fold indicating that most of the contacts with β-catenin were not disrupted (Table 1; Figure 6). A reduction in affinity even without any disruption of contacts is expected due to the greater entropy cost of closing the longer loop formed by the linker upon binding to β-catenin. Insertion of the polyproline linker into pAPC_abc reduced the affinity three-fold (16.4 nM versus 5.3 nM). The affinity was similar to that of unphosphorylated APC_abc (16.5 nM) that has a weakened c domain and pAPC_abc D1486S (30 nM) that has a weakened b domain, suggesting that the polyproline linker disrupts the interface and prevents domains b and c either side of it from binding to β-catenin simultaneously. Only the flexible linker was inserted at 1,478 (between domains a and b), and it did not change the binding affinity of APC_abc but reduced the affinity of pAPC_abc 5-fold, suggesting disruption of contacts in domains a and/or b.

As observed at equilibrium, the linker insertions at 1,500 (between b and c) had only small effects on the association rate, decreasing it ∼2-fold for both APC_abc and pAPC_abc. There were also small increases (∼2.5-fold) in the dissociation rates. Insertion of the polyproline linker into pAPC_abc had a larger effect on the dissociation kinetics, increasing the rate of the fast dissociation phase 6-fold to a value similar to that of APC; the rate of the slow dissociation phase was increased 9-fold but it was still much slower than constructs APC_abc and pAPC_abc D1486S with weakened c/b domain. Interestingly, insertion of the flexible linker at 1,478 (between a and b) increased the association rate of APC_abc 2-fold. This result could be due to some steric stress between binding interfaces of the two domains that is relieved upon linker insertion.

The Hill coefficient was ∼1 for APC_abc with either the flexible or rigid linker inserted at bc, indicating a single binding event. In contrast, for pAPC_abc with the flexible or rigid linker inserted at the same position the Hill coefficient was ∼2, indicating that cooperativity between b and c is maintained upon linker insertion. Insertion of the polyproline linker into bc in pAPC_abc gave a Hill coefficient of 1, consistent with this linker preventing the binding of b and p-c simultaneously. From these results and the results for the truncations showing that the Hill coefficient is 1 for constructs ab and abc lacking the high-affinity p-c domain, we can conclude that a and b are not independent domains but rather form one contiguous binding surface.