Feedback in the β-catenin destruction complex imparts bistability and cellular memory

Wnt/β-catenin signaling is involved in organism development, stem cell maintenance, and is misregulated in human disease. At the core of this, signaling pathway is the β-catenin destruction complex, comprised of the kinases glycogen synthase kinase 3 (GSK3) and casein kinase 1 alpha, and the scaffolding proteins Axin and adenomatous polyposis coli (APC). In the absence of Wnt ligands, phosphorylation of the transcriptional co-activator β-catenin within the destruction complex targets β-catenin for ubiquitin-mediated proteasomal degradation, thereby maintaining low levels of cytoplasmic and nuclear β-catenin. Wnt signaling inhibits phosphorylation of β-catenin to block its turnover; accumulated β-catenin subsequently enters the nucleus to mediate a Wnt-specific transcriptional program required for animal development and tissue homeostasis (1).

Although Wnt ligands are considered classical morphogens, Wnt gradients are dispensable for proper patterning during development in some contexts (2–4). To better understand the biochemical function of the β-catenin destruction complex and to assess how critical steps within the complex impact behavior of the Wnt pathway, we performed biochemical reconstitutions of the destruction complex with Xenopus egg extracts and purified proteins. Based on these measurements, we developed mathematical simulations of destruction complex dynamics and validated our model by performing single-cell analyses of β-catenin behavior.

Previous studies in cultured mammalian cells and in vitro reconstitution have shown that the scaffold protein Axin is a direct target of GSK3 (5, 6). Because Xenopus egg extracts are readily amenable to biochemical studies and faithfully recapitulate signaling dynamics that control β-catenin turnover (7), we examined the regulation of Axin by GSK3 in extracts (Fig. 1A). Consistent with previous studies (5), inhibition of GSK3 with LiCl induced Axin turnover (Fig. 1 B and C). Axin stability was decreased by mutating the two GSK3 phosphorylation sites (Ser 322 and Ser 326) to alanines, and by deleting its GSK3-binding site (Fig. 1C) (8).

As Axin is the limiting component of the destruction complex, overexpression of Axin promotes β-catenin degradation and inhibits Wnt signaling even in the absence of APC (9, 10). The limiting concentration of Axin provides a simple means for insulating a discrete pool of GSK3 that specifically targets β-catenin for phosphorylation (10). In addition, given its role as a scaffold, Axin is ideally positioned to regulate the activity of GSK3, thereby promoting both Axin stability and β-catenin degradation. We initially examined GSK3 activity in Xenopus egg extracts using a phospho-specific antibody that recognizes GSK3β phosphorylation at serine 9 (pS9 GSK3), which limits GSK3β activity. The addition of recombinant maltose-binding protein-Axin chimera expressed in bacteria to extracts resulted in a marked reduction in pS9 GSK3 (Fig. 1D). The requirement for a phosphatase in β-catenin degradation has been reported (11). Thus, we tested the effect of the phosphatase inhibitor okadaic acid (OA) on pS9 GSK3. We found that OA prevented the Axin-mediated reduction of pS9 GSK3 in Xenopus extracts (Fig. 1D), suggesting an OA-sensitive phosphatase requirement at this regulatory step.

To identify Axin regions that bind co-factors necessary for pS9 GSK3 dephosphorylation, we performed domain deletion analysis by expressing Axin mutants in HEK 293 cells (Fig. 1E). As expected, full-length Axin promoted loss of the inhibitory phosphorylation of GSK3, and OA blocked this effect, suggesting phosphatase dependence of GSK3 activation. Similarly, the deletion of the GSK3-binding site (GBS) or the phosphatase 2A (PP2A) domains of Axin prevented Axin-mediated inhibition of GSK3 phosphorylation, suggesting these regions are essential for GSK3 activation by Axin. In contrast, Axin lacking its β-catenin-binding site (βcat-BS), APC-binding site (RGS), or DIX domain still promoted the removal of the inhibitory serine 9 phosphorylation on GSK3; thus, these sites are not required for Axin-mediated removal of serine 9 phosphorylation on GSK3. Additionally, Axin was recently shown to contain a short linear motif (SLiM) that interacts with the B56 subunit of PP2A (12, 13). We made alanine mutants of this conserved SLiM sequence (SI Appendix, Fig. S1) and found that SLiM 4A Axin mutants could not remove pS9 on GSK3 (Fig. 1F).

To test if PP2A could directly act on pS9 GSK3, we performed in vitro reconstitution using purified components of the destruction complex. We found that PP2A exhibited a preference for pS9 GSK3 (Fig. 1G) versus the β-catenin sites phosphorylated by GSK3 (phospho-serine 33, serine 37, and threonine 41; Fig. 1H). Based on these findings, we propose the following model: the majority of cytoplasmic GSK3 is in or fluctuating as the pS9 GSK3 state, which normally limits its activity. Upon pS9 GSK3 binding to Axin, pS9 GSK3 is targeted for dephosphorylation by Axin-bound PP2A. Dephosphorylated GSK3 is active and phosphorylates Axin to promote its stabilization. Active, dephosphorylated GSK3 and phosphorylated Axin (bound to APC) comprise a destruction complex state that is “fully activated” to phosphorylate β-catenin, targeting it for ubiquitin-mediated proteasomal degradation.

We built a theoretical model based on our biochemical observations to better understand the reaction kinetics within the β-catenin destruction complex (Fig. 2A). GSK3 concentration was kept constant as it is predicted to be degraded at a relatively slow rate (10). Rates of Axin synthesis and degradation were based on our Xenopus extract data and previous work (10). We translated our model (Fig. 2A) into a set of ordinary differential equations (SI Appendix, Table S1) and solved them numerically and analytically in steady-state conditions (SI Appendix, Fig. S2). The reaction rates and rate constants used in the model are listed in SI Appendix, Tables S2 and S3, respectively. As shown in Fig. 2A, our model is based on a positive feedback loop between Axin and GSK3.

The function of the destruction complex is to promote the phosphorylation and subsequent ubiquitin-mediated degradation of β-catenin. When Axin^p and GSK3 are high, β-catenin is low, and the pathway is “off.” When Axin^P and GSK3 are low (e.g., via Wnt activation), cytoplasmic and nuclear β-catenin is high, and the pathway is “on.” Consistent with previous work, we modeled the Wnt signal to act on the active, destruction complex-bound GSK3 by directly increasing the inhibitory rate (k₁) (14) and calculated the steady-state concentration of β-catenin. To model pathway activation, we started initially with a low value of k₁, which was followed by a gradual increase. For each k₁ value, the β-catenin concentration was determined and plotted as “naive.” As shown in Fig. 2B, β-catenin levels are small for k₁ < 0.85, and then β-catenin abruptly accumulates above this threshold. Additionally, we solved the equations with decreasing values of k_1, starting with a high value, and referred to this as “pre-activated.” In this case (Fig. 2B), β-catenin level remains high even if k₁ is reduced to 0. The model predicts that β-catenin can be turned on by increasing Wnt signaling above a threshold but cannot be turned back off be decreasing Wnt, even to 0. In contrast, when dephosphorylation of GSK3 by Axin^P was omitted from the model, the effect of k1 was identical for naïve and pre-activated states (Fig. 2C).

Our modeling suggests the β-catenin destruction complex has two stable states, off and on. This bistability may result from self-perpetuating states such as positive feedback or double-negative feedback (15). A bistable system is characterized by two alternative steady states, an off-state and an on-state, without intermediate states (Fig. 3A) (15). In a population of cells, the inflection point of the switching will be set by subtle variation in the concentrations and rates of pathway components. This is why, in a uniform sheet of cells, one often observes a salt-and-pepper phenotype rather than perfect collective switching. To simulate the heterogeneous response of a population of cells, we ran the simulation for 2,000 cells where we randomly selected a k₁ value for each cell from a normal distribution (SI Appendix, Fig. S3). We then plotted the distribution of β-catenin with an increase in the mean value of k₁ (Fig. 3B) that demonstrates the expectation for β-catenin response in a noisy tissue culture system.

We then validated whether the positive feedback between Axin and GSK3 observed in Xenopus egg extracts can lead to a bistable response in mammalian cells activated by Wnt ligands. Accurate single-cell quantification of soluble β-catenin has been challenging due to the high concentrations of non-signaling β-catenin at adherens junctions. We combined automated imaging with custom cell-identification software (Fig. 3C) to analyze primary, immortalized human colonic epithelial cells (HCECs) (16). By varying concentrations of purified, recombinant Wnt3a, and measuring nuclear β-catenin, we found that at low Wnt3a concentrations, signaling is in the off-state (nuclear β-catenin is absent), whereas, at high Wnt concentrations, signaling is in the on-state (nuclear β-catenin is present) (Fig. 3D). At intermediate Wnt3a doses, we found a mixed population of cells that were either in the off- or the on-state, with a bistable range between 2 and 6 nM Wnt3a. The β-catenin response to increasing Wnt3a exhibited a Hill exponent of ~6. Such large Hill exponents are commonly attributed to high cooperativity among signaling molecules, but another possibility is the all-or-none response of individual cells, associated with bistability (as in Fig. 2B), conflated with cell-to-cell variability of biochemically noisy cells in culture (SI Appendix, Fig. S4).

For a system to be genuinely bistable, it must exhibit hysteresis, i.e., the concentration of Wnt needed to maintain a given response (after Wnt exposure) is lower than the concentration of Wnt required to mediate the initial response (15, 17). An alternative possibility for the salt-and-pepper β-catenin phenotype we observed is the existence of a monostable transcritical bifurcation, a mechanism often found in phase separation settings, in which a two-state system switches states at a single inflection point (i.e., turning on and turning off occur at the same ligand concentration) (18, 19). To test this, we fully activated cells with high concentrations of Wnt ligand and then measured the concentrations of Wnt needed to maintain the on-state (Fig. 4A). Importantly, after stimulating cells, Wnt must be completely removed to insure residual Wnt/receptor complexes are not contributing to a sustained β-catenin response. We immunoblotted for Wnt3a immediately after stimulating for 1.5 h and 3 h after thorough Wnt3a washout and did not detect Wnt3a after washout (Fig. 4B). We observed that cells that were previously treated with a high concentration of Wnt maintained nuclear β-catenin throughout the experiment (Fig. 4 C and D) and that this hysteretic behavior persisted several hours after the initial Wnt3a treatment (SI Appendix, Figs. S5 and S6A). We confirmed these findings in RKO cells, a colon carcinoma cell line that lacks E-cadherin, making soluble β-catenin easier to detect, yet the Wnt pathway is presumed to be intact (SI Appendix, Fig. S7 A and B). Together, our Wnt stimulation and washout experiments suggest that bistability allows maintenance of elevated β-catenin concentrations hours after Wnt ligands are gone.

We next tested whether the bistable response observed in HCEC cells in response to Wnt3a treatment was due to positive feedback between Axin and GSK3 revealed in our biochemical experiments (Fig. 1). Our modeling suggested bistability was lost by removing the function of Axin^p in the dephosphorylation of GSK3 (Fig. 5 A and B). Wnt ligand-mediated activation of the Wnt pathway occurs via a mechanism involving inhibition of GSK3-mediated β-catenin phosphorylation (14, 20, 21). We predict, however, that direct inhibition of GSK3 with a small molecule inhibitor that targets its ATP catalytic pocket would break the biochemical GSK3/Axin feedback loop by being insensitive to Axin^p-dependent dephosphorylation of pS9 GSK3 (Fig. 5C). We treated HCEC and RKO cells with the GSK3 inhibitor CHIR99021 (GSK3i) (22) and found that, in contrast with the Wnt3a treatment regimen, activation of the pathway with GSK3i treatment failed to promote the bistable behavior of nuclear β-catenin (Fig. 5D and SI Appendix, Fig. S7C). Unlike Wnt3a, the effects of GSK3i on β-catenin nuclear accumulation were readily reversible, and the nuclear β-catenin signal was lost rapidly (without any observable evidence of hysteresis) after the removal of GSK3i (SI Appendix, Fig. S6B). Hence, for all GSK3i experiments, we used time points for which we observed a steady-state response after GSK3i treatment, i.e., a minimum of 6 h treatment (SI Appendix, Fig. S8A), but we could not wash out the inhibitor because β-catenin levels rapidly reset to baseline (SI Appendix, Fig. S8B). Finally, we observed that GSK3i caused cells to respond in a monostable, graded manner (Fig. 5D and SI Appendix, Fig. S9). These experimental findings further support the conclusion from our biochemical reconstitution and mathematical model: bistability and hysteresis in Wnt signaling are driven by positive feedback between Axin and GSK3.

These experiments demonstrate that a biochemical feedback loop between GSK3 and Axin maintains the β-catenin destruction complex in a stable off- or on-state. This switch-like behavior requires the mutual activation of GSK3 and Axin via antagonistic behaviors of an additional kinase and phosphatase (Fig. 2A). We also provided evidence (Fig. 1D) that PP2A removes the inhibitory phosphorylation on serine 9 of GSK3 in an Axin-dependent process. Modeling of these biochemical events suggested that cells would respond in a binary manner to Wnt pathway stimulation, which was supported by our experiments in HCECs. Additionally, these cells displayed memory to Wnt stimulation, and β-catenin remained in the nucleus even after Wnt ligands had been removed. These results suggest the β-catenin destruction complex displays robustness by existing in two self-sustaining attractor states of active and inactive, which provides a mechanism for suppressing potentially deleterious fluctuations in concentrations and activities of pathway components.

Whether serine 9/21 phosphorylation of GSK3 affects Wnt signaling has been controversial (23–27). Though we demonstrate serine 9/21 phosphorylation removal via Axin and PP2a, this does not necessary imply that phosphorylation of serine 9/21 is the primary mechanism for GSK3 inhibition upon Wnt receptor activation. Axin and PP2a may have the capacity to remove serine 9/21 phosphorylation as a way to put free cytosolic GSK3 molecules that become sequestered by Axin in a precise active conformation; a way to “clean up” random GSK3 molecules, inhibited by other kinases, as they enter the destruction complex. Upon Wnt stimulation, GSK3 could be inhibited by many mechanisms—LRP6 binding (21, 28–30), GSK3 sequestration (31), PP2a regulation, GSK3 disassociation from the destruction complex, or Ser9/21 phosphorylation. Presuming all these scenarios lead to reduced GSK3 toward β-catenin and Axin, these molecular events would produce a similar bistable response.

The existence of bistability in Wnt signal transduction has implications for our understanding of Wnt as a classical morphogen that can produce apparent concentration-dependent gene expression. In vivo, Wnt signaling gradients could be due to a true β-catenin gradient forming from a lack of Axin/GSK3-positive feedback and switch-like signaling in certain tissues. One could imagine cells where Axin does not degrade upon Wnt signaling (as we modeled in 2C) as being more graded. This would be a simple mechanism for tissue-specific control of graded or switch-like control of Wnt signaling. An alternative possibility is that the lack of high-resolution single cells studies capturing space and time have limited our abilities to decipher all-or-none or graded signaling in vivo. Gradients of mRNA transcripts could exist because of a previous parental stem cell in the fully “wnt on” state and expressing the mRNA transcript that then gets diluted in concentration as the daughter cells grow and divide—dilution through cell division. Alternatively, the low resolution of in situ hybridization could make a salt-and-pepper expression pattern look graded. Additional studies in developmental and stem cell systems are required to decipher when Wnt/β-catenin signaling elicits a graded or bistable response.

Bistability has emerged as a foundational principle in signal transduction (32), yet its existence has been elusive in the Wnt pathway. Beyond suppressing noise within the Wnt pathway, positive feedback in the β-catenin destruction complex provides a mechanism to insulate a pool of GSK3 required in the complex from the total cellular GSK3, thereby preventing crosstalk with other GSK3-regulating pathways such as PI3K/AKT and MAPK (23, 24). Furthermore, the existence of both bistable and graded responses could explain why long-range Wnt morphogen activity is dispensable in certain in vivo contexts but essential in others (33). The phenomena described herein shed light on a foundational structure of the Wnt/β-catenin pathway that instills robustness and, when perturbed, could lead to vulnerabilities in the accurate processing of Wnt signals.

We are grateful to Dr. Jerry Shay of U.T. Southwestern Medical Center for providing us with the HCEC line. Funding: M.J.C. was supported by the Cancer Biology Training Grant CA T32009213-40. E.A. was supported by the Sidney Hopkins, Mayola B. Vail, and Patricia Ann Hanson Postdoctoral Fellowship. This work was supported by NIH grants GM122516 (E.L.) and CA224188 (E.L. and Y.A.), GM136233 (Y.A.), GM119455 (A.N.K.), DK103126, GM147128 (C.A.T.), GM134207 (K.D.), and Robert A. Welch Foundation I-1950-20180324 (K.D.).