Kinetic Responses of β-Catenin Specify the Sites of Wnt Control

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Science  07 Dec 2012:
Vol. 338, Issue 6112, pp. 1337-1340
DOI: 10.1126/science.1228734


Despite more than 30 years of work on the Wnt signaling pathway, the basic mechanism of how the extracellular Wnt signal increases the intracellular concentration of β-catenin is still contentious. Circumventing much of the detailed biochemistry, we used basic principles of chemical kinetics coupled with quantitative measurements to define the reactions on β-catenin directly affected by the Wnt signal. We conclude that the core signal transduction mechanism is relatively simple, with only two regulated phosphorylation steps. Their partial inhibition gives rise to the full dynamics of the response and subsequently maintains a steady state in which the concentration of β-catenin is increased.

Kinetic analysis of chemical pathways at steady state can order the steps of a reaction sequence and identify points of control (1, 2). Whether such analysis can be as successful for signaling pathways as it is for mass conversion is unclear. We applied this approach to the canonical Wnt pathway, a fundamental circuit in development and adult homeostasis. Wnt leads to stabilization and accumulation of β-catenin, which then activates transcriptional targets. β-catenin is constantly synthesized but is normally maintained at a low cytoplasmic concentration by degradation. Degradation is mediated by casein kinase 1α (CK1α) and glycogen synthase kinase 3 (GSK3), which sequentially phosphorylate β-catenin, creating a phosphodegron (3, 4). The interaction between the kinases and β-catenin is mediated by two scaffold proteins, Axin1 and adenomatous polyposis coli (APC), forming the so-called destruction complex.

The mechanism by which Wnt inhibits the degradation of β-catenin is still open to debate. Because phosphorylated β-catenin decreases after Wnt stimulation, it is thought that Wnt inhibits phosphorylation of β-catenin, thereby blocking its degradation (35). Inhibition has been proposed to occur by interfering with GSK3 (6, 7), CK1α (4), or Axin (8, 9). Wnt is also proposed to inhibit ubiquitylation, rather than phosphorylation (10). Moreover, the proposed mechanisms do not explain how β-catenin is maintained at an elevated steady-state level and what prevents it from accumulating indefinitely.

To understand how Wnt controls β-catenin, we examined cultured cells, in which the β-catenin dynamics could be accurately measured. Our analysis focused on sequential β-catenin modifications across two phases: (i) a transient phase of β-catenin accumulation and (ii) a final phase at which β-catenin concentration reaches a new, higher steady state. From a basic conservation law of enzyme kinetics, we deduced the point of Wnt action and revealed a simple core mechanism that couples the Wnt signal to the steady-state amount of β-catenin.

Continuous stimulation of cells by Wnt-3A led to distinct dynamic changes in phosphorylated and total β-catenin (Fig. 1A and fig. S1). The total amount of β-catenin increased 15 to 30 min after exposure to Wnt and reached a steady state in 2 hours that was maintained for several hours. In human colon carcinoma RKO cells, β-catenin concentration increased by a factor of 6 (from 8 ± 1 nM to 52 ± 7 nM) (Fig. 1B). By contrast, the amount of GSK3-phosphorylated β-catenin (phospho T41/S37/S33) decreased 80 ± 20% 15 to 30 min after Wnt stimulation and then returned to its initial concentration in 2 hours (Fig. 1, A and D). The amount of CK1α-phosphorylated β-catenin (phospho S45) showed little or no decrease over the first 30 min and then increased above its initial concentration (Fig. 1A). Similar results were observed in all cell lines tested (fig. S1).

Fig. 1

Dynamics of β-catenin during the Wnt response. (A to D) Total, GSK3- and CK1α-phosphorylated β-catenin after Wnt stimulation. α-tubulin: loading control. (B) shows absolute concentration of total β-catenin. (E) Accumulation rate of β-catenin [the derivative of (C)]. In (C) to (E), lines show fits to the kinetic model described in Fig. 2. (F) Accumulation of β-catenin in Wnt-stimulated RKO cells treated with proteasome inhibitor MG132. (G and H) Response of phosphorylated β-catenin to Wnt stimulation after inhibition by LiCl or various shRNAs. (I) Ratio of GSK3-phosphorylated β-catenin to total β-catenin relative to initial levels [calculated from (C) and (D)]. Error bars, mean ± SD (N = 3 replicates).

The amount of GSK3-phosphorylated β-catenin showed a strong negative correlation with the rate of β-catenin accumulation (Pearson correlation R = –0.93) (Fig. 1, C to E). When phosphorylation decreased to a minimum, the rate of β-catenin accumulation was at a maximum (arrows, Fig. 1, C to E). This correlation supports the view that Wnt inhibits phosphorylation to increase β-catenin concentration. When phosphorylation increased and returned to the initial amount, the β-catenin accumulation rate decreased to zero; thereafter, β-catenin was maintained at a high concentration. In this new steady state, degradation must occur because synthesis of the protein remains unchanged during Wnt stimulation (11) (fig. S2). These observations suggest that recovery of phosphorylation restores degradation.

We therefore tested whether β-catenin is still degraded during Wnt stimulation. Treatment of Wnt-stimulated cells with a proteasome inhibitor increased β-catenin abundance within 1 hour (Fig. 1F), confirming that β-catenin was being degraded. From Fig. 1B, we calculated that Wnt increases β-catenin lifetime from 16 to 104 min (see supplementary materials), still lower by a factor of 10 than the average protein lifetime (12). To determine whether the destruction complex is responsible for mediating degradation after Wnt stimulation, we first blocked GSK3 activity with lithium chloride (LiCl) or silenced APC, Axin1, or CK1α with short hairpin RNA (shRNA) and then added Wnt. Under these conditions, β-catenin phosphorylation dropped but did not fully recover (Fig. 1, G and H, and fig S3). Thus, the destruction complex functions both in the absence and presence of Wnt. However, in the presence of Wnt, the destruction complex must be only partially active because the ratio of GSK3-phosphorylated β-catenin to total β-catenin drops and remains low (Fig. 1I). Inhibition of the destruction complex is not inconsistent with the full recovery of GSK3-phosphorylated β-catenin to its original concentration because the concentration of β-catenin has increased. Therefore, Wnt partially inhibits the destruction complex; recovery of phosphorylation halts the rise in β-catenin, restoring degradation and establishing a new steady state.

These conclusions shape basic features of the Wnt response, but they leave open a number of questions regarding the full dynamics. To determine whether partial inhibition of phosphorylation explains the entire response, or whether Wnt might act elsewhere to inhibit degradation, we used the laws of chemical kinetics to identify constraints on the system behavior. In the simplest model, a protein X (β-catenin) is synthesized with a rate S and degraded by an enzyme E. The protein concentration ([X]) is constant only if it is degraded with a flux kdeg[X] that equals the synthesis rate, which remains unchanged during Wnt stimulation. In the Michaelis-Menten approximation for an unsaturated enzyme, kdeg = kcat[E]/KM. Degradation can be inhibited by lowering the enzyme concentration [E] or its intrinsic catalytic rate kcat, or by lowering the affinity (1/KM). If the enzyme is inhibited by any of these means, kdeg is reduced and, as a result, the degradation flux, kdeg[X] initially decreases. The protein concentration then increases until the flux equals S once again. The same principle of flux conservation holds when more than one enzymatic step is required for degradation, as for β-catenin (Fig. 2A) (2, 13), and when the reactions do not conform to the Michaelis-Menten approximation (supplementary materials, section S-I). At steady state, the net flux through each step equals S irrespective of the point of inhibition.

Fig. 2

Flux analysis of the points of Wnt action on β-catenin degradation. (A) The β-catenin life cycle. (B) The three possible qualitative behaviors of phosphorylated β-catenin in response to Wnt, as predicted by flux analysis. (C) Quantification of total, GSK3-, and CK1α-phosphorylated β-catenin in Wnt-stimulated RKO cells. (D and E) The abundance of ubiquitylated phospho-β-catenin during Wnt stimulation in human embryonic kidney HEK293T (D) and RKO (E) cells. (F and G) The rates of GSK3- and CK1α-mediated phosphorylation, calculated from the measurements in (C) (supplementary materials, section S-IV). Gray curves show bounds on the CK1α phosphorylation rate: If β-catenin dephosphorylation is rare, the rate is described by the lower bound; if dephosphorylation occurs at a higher rate than phosphorylation and ubiquitylation, the upper bound holds. The black curve shows the dynamics if dephosphorylation and phosphorylation occur at comparable rates. Error bars, mean ± SD (N = 3 replicates).

We use this conservation principle to identify the point of Wnt action. All possible mechanisms lead to just three dynamical outcomes for GSK3-phosphorylated β-catenin (supplementary materials, sections S-I to S-III): First, if inhibition occurs downstream of phosphorylation (Fig. 2A), then GSK3-phosphorylated β-catenin should accumulate to restore the degradation flux (Fig. 2B, black curve). With kdeg describing the degradation rate of the phosphorylated protein, its concentration adapts from S/kdeg(0) to S/kdeg(Wnt) with kdeg(Wnt) < kdeg(0). Second, if inhibition occurs at the phosphorylation steps, or upstream of them (Fig. 2A), the concentration of GSK3-phosphorylated β-catenin should drop transiently because the influx to that state would be inhibited. Ultimately, the amount of GSK3-phosphorylated β-catenin would return precisely to the initial level because the influx recovers to S, whereas the stability of the phosphorylated protein is unchanged, kdeg(Wnt) = kdeg(0) (Fig. 2B, red curve). Third, if inhibition occurs both upstream and downstream of phosphorylation, then GSK3-phosphorylated β-catenin levels should first drop (or appear unchanged) until the influx matches S. The protein would then accumulate above its original concentration, reflecting its increased stability with kdeg(Wnt) < kdeg(0) again (Fig. 2B, blue curve). This three-fold classification resembles the crossover theorem first used to identify control points in the electron transport chain (2, 14).

These dynamic responses derive from basic laws of enzyme kinetics with no particular assumptions about molecular mechanism. The same dynamics also occur if there were feedback on the destruction complex activity (supplementary materials, section S-I). Similarly, the same dynamic responses could occur through activation of the reverse reactions (dephosphorylation or deubiquitylation) (supplementary materials, section S-II). There are two exceptions to the three cases: If β-catenin were degraded independently of phosphorylation, phosphorylated β-catenin should drop without recovering to its initial concentration (supplementary materials, section S-VI). Second, if Wnt causes complete inhibition or saturation of the destruction complex, the degradation flux would not recover, giving an uncontrolled accumulation of β-catenin (supplementary materials, section S-V).

From this analysis, the observed dynamics of GSK3-phosphorylated β-catenin (Figs. 1D and 2C) are consistent with Wnt inhibiting β-catenin degradation at, or upstream, of phosphorylation (Fig. 2B, red curve). We can exclude all other points of inhibition. This mode of inhibition predicts that every intermediate downstream of phosphorylation shows the same dip and full recovery. We confirmed this prediction for ubiquitylated β-catenin in cells stimulated with Wnt (Fig. 2, D and E). Thus, partial inhibition of phosphorylation entirely explains the observed dynamics. Full recovery can occur through mass action alone and does not require feedback. Saturation of the destruction complex has been proposed as a mechanism of Wnt action (10), but the dynamics refute this explanation.

To determine how Wnt might affect the individual phosphorylation steps, we applied the same analysis (Fig. 2B). We asked whether Wnt inhibits at or upstream of the priming phosphorylation at S45 by CK1α, or downstream of it, or both. For this analysis, we showed that the majority (80 ± 5%) of CK1α-phosphorylated β-catenin is not phosphorylated by GSK3 (fig. S4). If Wnt only inhibits the GSK3-dependent step, then CK1α-phosphorylated β-catenin should behave similarly to total β-catenin. If Wnt only inhibits the CK1α-dependent step, then CK1α-phosphorylated β-catenin should behave like GSK3-phosphorylated β-catenin. Neither of these occurs. Instead, the accumulation of CK1α-phosphorylated β-catenin is entirely explained by Wnt inhibiting both phosphorylation steps, leading to an initial drop and later accumulation over the initial amount (Fig. 2, B and C). We calculated that the GSK3 and CK1α phosphorylation rates drop in response to Wnt to 24 ± 11% (mean ± SD, N = 3) and 16 to 58% (lower/upper bounds) of their initial value, respectively (Fig. 2, F and G) (supplementary materials, section S-IV). Although Wnt might affect the two kinases independently, it seems more likely that Wnt affects a common property of the destruction complex, such as its state of assembly.

It has been suggested that signaling activity may reflect the phosphorylation state, rather than the abundance of β-catenin (15). According to this view, β-catenin not phosphorylated by GSK3, called “active” β-catenin, is the transcriptionally active form (15); without Wnt, it constitutes 1% of cytoplasmic and nuclear β-catenin (16). On addition of Wnt, “active” β-catenin would accumulate massively. For example, a six-fold increase in total β-catenin (Fig. 1B) would translate into a 600-fold increase in “active” β-catenin. Instead, we found that the increase in dephosphorylated β-catenin was comparable to that of total β-catenin (Fig. 3A). Furthermore, in the absence of Wnt, “active” β-catenin was the predominant form (80 ± 5%), as determined by dephosphorylating β-catenin or immunodepleting the GSK3-phosphorylated form (Fig. 3, B and C, and fig. S5). The notion of “active” β-catenin is inconsistent with the observation that almost all β-catenin is unphosphorylated even in the absence of Wnt.

Fig. 3

The size of the unphosphorylated fraction of β-catenin. (A) Abundance of nonphospho β-catenin during Wnt stimulation in RKO cells. (B) Dephosphorylation of RKO cell lysates with protein phosphatase from bacteriophage λ increased the signal of unphosphorylated β-catenin by 5 ± 5%. (C) Immunodepletion of GSK3-phosphorylated β-catenin decreased the signal of total β-catenin by 20 ± 5%. (A) and (B) show qualitative immunoblots; fractions (mean ± SD; N = 3 replicates) were determined by quantitative immunoblots (see supplementary materials).

Depictions of signaling pathways have grown exponentially complex with the inclusion of multiple ligands, receptors, extracellular modulators, and downstream targets. Despite this complexity, the core behavior of pathways could be relatively simple. Kinetic analysis of systems, particularly at steady state, provides a powerful strategy to interrogate complex mechanisms; it can provide strong predictions while being insensitive to mechanistic details. In Wnt signaling, β-catenin is subject to a conservation law on the protein flux that permits a few kinetic analyses to resolve long-standing debates about the point of Wnt action. The basic regulatory feature of the pathway is a partial inhibition of two sequential phosphorylation steps without perturbing downstream reactions. Partial inhibition alone establishes the entire dynamics of the β-catenin response. Because a steady state is achieved without saturating the destruction machinery, there in principle can be rapid and facile control of the abundance of β-catenin by tuning its degradation rate through a number of modulators, internal or external to the cell. With a clarification of these central features of the Wnt pathway, we can turn more confidently to its perturbation by drugs and by mutation and to its pathology and pharmacology in different settings.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S6

References (1725)

References and Notes

  1. Acknowledgments: We thank J. Gerhart, M. Springer, X. He, W. Fontana, J. Gunawardena, J. Gray, F. Cong, and R. Deibler for discussions and comments on the manuscript; Y. Ben-Neriah for plasmids; and the Novartis Institutes for Biomedical Research for support of this work. A.M.K. holds a Career Award at the Scientific Interface from the Burroughs Welcome Fund. M.W.K. serves as a paid consultant on the scientific review board of Novartis.
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