Examination of effects of GSK3β phosphorylation, βcatenin phosphorylation, and βcatenin degradation on kinetics of Wnt signaling pathway using computational method
 YingChieh Sun^{1}Email author
DOI: 10.1186/17424682613
© Sun; licensee BioMed Central Ltd. 2009
Received: 22 April 2009
Accepted: 22 July 2009
Published: 22 July 2009
Abstract
Background
Recent experiments have explored effects of activities of kinases other than the wellstudied GSK3β, in wnt pathway signaling, particularly at the level of βcatenin. It has also been found that the kinase PKA attenuates βcatenin degradation. However, the effects of these kinases on the level and degradation of βcatenin and the resulting downstream transcription activity remain to be clarified. Furthermore, the effect of GSK3β phosphorylation on the βcatenin level has not been examined computationally. In the present study, the effects of phosphorylation of GSK3β and of phosphorylations and degradation of βcatenin on the kinetics of the wnt signaling pathway were examined computationally.
Methods
The wellknown computational LeeHeinrich kinetic model of the wnt pathway was modified to include these effects. The rate laws of reactions in the modified model were solved numerically to examine these effects on βcatenin level.
Results
The computations showed that the βcatenin level is almost linearly proportional to the phosphorylation activity of GSK3β. The dependence of βcatenin level on the phosphorylation and degradation of free βcatenin and downstream TCF activity can be analyzed with an approximate, simple function of kinetic parameters for added reaction steps associated with effects examined, rationalizing the experimental results.
Conclusion
The phosphorylations of βcatenin by kinases other than GSK3β involve free unphorphorylated βcatenin rather than GSK3βphosphorylated βcatenin*. In order to account for the observed enhancement of TCF activity, the βcatenin dephosphorylation step is essential, and the kinetic parameters of βcatenin phosphorylation and degradation need to meet a condition described in the main text. These findings should be useful for future experiments.
Background
The Wnt/βcatenin signaling pathway (named wnt pathway hereafter for simplicity) plays a significant role in cell proliferation, differentiation, and apoptosis. These have implications for aspects of cell development, stem cells and cancer [1]. Many characteristics of this pathway and its role in cell signaling have been revealed in experimental studies (for review, see for example [1], and references therein and the literature listed at http://www.stanford.edu/~rnusse/wntwindow.html). Briefly, wnt signaling enhances the level of the output signal protein, unphosphorylated βcatenin, which then binds with TCF to induce associated gene expression in the nucleus. At steady state (SS), the level of βcatenin is balanced by its synthesis and degradation. The socalled destruction cycle is a major mechanism of degradation, in which phosphorylation of βcatenin by GSK3b is a key step [2]. When the wnt signal acts on cell, wnt recruits several proteins to attenuate the reaction rate of this key step, slowing down the degradation. Therefore, βcatenin accumulates, enhancing the level of TCF/βcatenin complex and the resulting associated gene expression.
Recent advances have further illustrate how phosphorylation and dephosphorylation of major components in the wnt pathway affect the stability of βcatenin and its TCF transcription activity [3–7]. It has been found that LRP6 phosphorylates GSK3β and regulates βcatenin independently of the axin pathway [3]. PKA phosphorylates GSK3β and affects the βcatenin level in Saos2 cells [4]. βcatenin is also phosphorylated by AKT at Ser552, promoting TCF activity [4]. Furthermore, PKA phosphorylates Ser552 and Ser675 of βcatenin but this does not affect the βcatenin level in COS7 cells [5]. Moreover, CK1 phosphorylates not only axin and APC but also GSK3β and βcatenin [6]. A newly identified component, PP1, dephosphorylates axin [6]. In addition, phosphorylation of βcatenin at Ser675 by PKA attenuates βcatenin degradation, stabilizing βcatenin and enhancing TCF activity in the cells investigated [7]. In aspects of pathology, βcatenin has a role in carcinogenesis although the extent of its effect varies among cancers [8]. For example, the effect on colorectal cancer is more significant than on lung cancer. In a recent study [9], a derivative of celecoxib, derivatives of which have been extensively examined for anticancer treatment, was found to have potential for treating lung cancer. Proteomics examination showed that PKA activity has a significant effect on the wnt signaling pathway and in differentiating lung from normal cells.
In addition to the LeeHeinrich model of the wnt pathway itself, this model has been used and extended to examine the effect of Apc mutations on the wnt signaling pathway [10], crosstalk with the ERK pathway [11], and the interaction of axin2 proteins with the wnt pathway [12]. While many characteristics of this pathway have been elucidated both experimentally and computationally, much of its role in cell signaling and the means by which it interacts with other pathways remain to be explored.
In the present study, in the light of the recent experimental studies described above [3–7], I aimed to examine the effects of GSK3β phosphorylation, βcatenin phosphorylation by kinases other than GSK3β (referred to as βcatenin nonGSK3β phosphorylation hereafter), and βcatenin degradation on the kinetics of the wnt pathway using a computational method based on the LeeHeinrich model. These effects were not included explicitly in the LeeHeinrich model, and to my knowledge, they have not previously been examined computationally. The present computational study should elucidate how these effects affect the wnt pathway. The reaction steps of GSK3β phosphorylation, βcatenin nonGSK3β phosphorylation, and βcatenin degradation were added to the LeeHeinrich model (see added reaction steps in blue in Figure 1). The dependence of SS concentrations on the associated kinetic parameters of interest in these reaction steps was examined. Control coefficients of selected parameters and time courses of selected components with wnt signalling were calculated and examined as well. The method is described in Section II. Section III presents the results and discussion. Conclusions are given in the final section.
Methods
Steadystate concentrations of selected components in the LeeHeinrich and modified models
Concentration (nM)  

component  LeeHeinrich model  modified model  Fold change 
Dsh_{a}  0  0  
(APC*/axin*/GSK3β)  0.00966  0.004742  0.491 
(APC/axin/GSK3β)  0.00483  0.002362  0.489 
(βcatenin*/APC*/axin*/GSK3β)  0.00202  0.001991  0.986 
βcatenin*  1.00  0.983341  0.983 
βcatenin  25.1  50.3766  2.007 
Axin  0.000493  0.000492  0.998 
GSK3β  50  25  0.500 
GSK3β*  25  
βcatenin_{+}  5.03766 
The forward/backward reaction rate constants of GSK3β and βcatenin phosphorylations are denoted k_{G}/k_{G}' and k_{β}/k_{β}', respectively. The rate constant of βcatenin degradation is denoted k_{βdeg}. For simplicity, these kinetic parameters were all set equal to 1 min^{1} except in some cases (see Section III). The parameters of interest were then varied to examine their effects on the kinetics of the wnt pathway. Initial concentrations were values of SS concentrations used in the LeeHeinrich model [2] with additional components, GSK3β_{+}, βcatenin_{+}, and βcatenin*_{+}, with initial concentrations all set at zero. The superscript * denotes phosphorylation by GSK3β. Other phosphorylations are denoted by the subscript_{+}. The differential equations were solved for 20000 minutes, or as long as 40000 minutes, to ensure they reached SS.
where βcat is concentration of βcatenin and k is the parameter of interest. This coefficient was calculated numerically by varying the associated parameters by 1% and solving the kinetic equations over enough time to obtain SS concentrations, in order to calculate control coefficients as in [2]. Finally, the wnt signaling effect in a modified model (see below) was also examined with constant wnt signaling and transient wnt signaling separately, as in [2]. Initial concentrations in the modified model were obtained from computations for SS concentrations. Computed results are presented and discussed in the next section.
Results and discussion
Effects of GSK3β phosphorylation and βcatenin phosphorylations
Initially, I examined these two effects without including the βcatenin degradation step (step 20 in Figure 1) in computing βcatenin concentration, and assumed that βcatenin nonGSK3β phosphorylation involves βcatenin only (reaction step 19 in lower part of Figure 1). Computed SS concentrations of selected components and their fold changes are listed in Table 1, along with values in the original LeeHeinrich model [2]. The concentration of GSK3β was reduced to half its original value. The values of complexes with APC and axin were also reduced to approximately half their original values while βcatenin*/APC*/axin*/GSK3β, βcatenin*, and axin remained approximately the same. The unphosphorylated βcatenin shows a twofold change and significant enhancement in its absolute concentration because of its high concentration compared with most of the other components.
Steadystate concentrations of total and unphosphorylated βcatenin (in nM) under conditions of different k_{G}/k_{G}' ratios
k_{G}/k_{G}' ratio  SS concentration of βcatenin in total  SS concentration of unphosphorylated βcatenin 

10  342.1747  280.744 
2  101.1289  75.8736 
1  69.83185  50.3766 
0.5  53.8597  37.6965 
0.1  40.78498  27.5907 
0.01  37.78723 34.94785^{a}  25.3219 25.0699^{a} 
In addition to the effects of GSK3β phosphorylation, the effect of βcatenin nonGSK3β phosphorylation was examined. I first examined this effect in free unphosphorylated βcatenin (lower part of Figure 1). Analysis of pathway fluxes showed that no SS concentrations of components are affected by the k_{β}/k_{β}' ratio, excepting concentrations of βcatenin_{+}. This was confirmed by computations with several values of k_{β}/k_{β}'. This is because βcatenin is one of two components, in addition to axin, that have flux turnovers in the pathway. Because of this, addition of reaction step 19 to the LeeHeinrich model does not change the fluxin or fluxout at SS. This is in contrast to phosphorylation of GSK3β, when the k_{G}/k_{G}' ratio does affect the concentrations of components at SS. This is because the total amount of GSK3β is conserved and has no turnover. Therefore, reaction step 18 decreases the level of unphosphorylated GSK3β and increases the level of βcatenin. This shows that phosphorylation of GSK3β has a significant effect on the βcatenin, but βcatenin nonGSK3b phosphorylation has no significant effect on concentrations of components in the destruction cycle in this model. In addition to this calculation examining the effect of nonGSK3β phosphorylation of free unphosphorylated βcatenin, I also considered this effect as taking place separately at the βcatenin* shown in the upper part of Figure 1. Because the pattern of reaction steps is similar, similar results for the dependence of βcatenin*_{+} level on the kinetic parameter k_{β}/k_{β}' were expected and obtained in the computations.
Control coefficients of βcatenin (concentration in total) with respect to selected kinetic parameters.
Control coefficient for βcatenin  

Kinetic parameter  LeeHeinrich model  modified model 
k_{4}  0.89  0.89786 
k_{5}  0.89  0.906281 
v_{12}  0.929  0.949923 
k_{G}  0.453225 
Effect of wnt signal
Steadystate concentrations of selected components without and with constant wnt signaling in the LeeHeinrich and the present modified model
W = 0  W = 1  

Components  LeeHeinrich model  Modified model  LeeHeinrich model  Modified model 
Dsh_{a}  0  0  90.9091  90.9091 
(APC*/axin*/GSK3β)  0.00966  0.004742  0.001461  0.000656 
(APC/axin/GSK3β)  0.00483  0.002362  0.000728  0.000327 
(βcatenin*/APC*/axin*/GSK3β)  0.00202  0.001991  0.001862  0.001672 
βcatenin*  1.00  0.983341  0.920076  0.825947 
βcatenin  25.1  50.3766  153.028  305.759 
Axin  0.000493  0.000492  0.000492  0.000492 
GSK3β  50  25  50  25 
GSK3β_{+}  25  25  
βcatenin_{+}  5.03766  30.5759 
Effect of βcatenin degradation
To test this analysis further, computations with varied k_{β} values, which make the term k_{β}/(1+k_{β}'/k_{βdeg}) smaller or larger than k_{13}, were carried out as well. When k_{β} was equal to or 1 order smaller than k_{13}, the level of unphosphorylated βcatenin did not change significantly when the βcatenin_{+} degradation constant, k_{βdeg}, was varied (shown in the dashed line in Figure 5), consistent with the above analysis. When k_{β} was increased, the term k_{β}/(1+k_{β}'/k_{βdeg}) gradually dominates over k_{13}. The k_{β} value was increased up to 1.0. In the range of 0.5–1.0, a significant change in the unphosphorylated βcatenin level due to varying k_{βdeg}was seen, as shown in Figure 5 (thin solid line with open circles). The TCF/βcatenin level varied by about 1 order within the range examined in Figure 5 (thin solid line with solid circles). The TCF/βcatenin complex varied less than βcatenin because of the rapid equilibrium of the reaction βcatenin + TCF ↔ βcatenin/TCF with dissociation constant 30 nM; the total concentration of TCF was 15 nM [2]. The results then account for the observed, significant change in TCF activity described above. It is noted here that nonGSK3β phosphorylation of βcatenin by PKA takes place at Ser675 of βcatenin, which is distinct from the sites of phosphorylation by GSK3β [7]. Mutation of Ser675 to alanine stabilizes βcatenin, attenuates inhibition of βcatenin degradation, and enhances TCF activity [7]. On the basis of these observations, reaction step 20 was added to the LeeHeinrich model and is a degradation channel for βcatenin additional to those in the LeeHeinrich model. PKA was assumed to inhibit degradation at reaction step 20 only. The above analysis of Eqs. (1) and (2) is based on these assumptions. Furthermore, to examine whether the added reactions at βcatenin*_{+} affect the added reactions at βcatenin_{+} and the level of unphosphorylated βcatenin, computations with both added reaction parts present in the model were also carried out. Variations of both degradation rate constants in the added reaction steps, which may change the level of βcatenin significantly, showed that the computed results are similar to those obtained with each part computed separately in the model as shown in Figure 5. This is because, in the model, one key assumption is the rapid equilibration of reaction step 8, βcatenin/APC*/Axin*/GSK3β ↔ APC*/Axin*/GSK3β + βcatenin, with dissociation equilibrium constant of 120 nM [2]. Because of the low level of Axin and APC*/Axin*/GSK3β, on the 10^{4} and 10^{2} nM scales, respectively, the level of unphosphorylated βcatenin (on the tens of nM scale) is roughly 4 and 1–2 orders higher than the APC*/Axin*/GSK3β/βcatenin complex and the downstream phosphorylated βcatenin, βcatenin*, respectively. Therefore, the presence of the added reaction steps at βcatenin*_{+} has no significant effect on the SS level of components in the added reaction step at βcatenin_{+} or the unphosphorylated βcatenin. The added reaction steps at βcatenin_{+} alone can describe the parameter dependence of βcatenin level due to nonGSK3β phosphorylation, the succeeding degradation, and the resulting TCF activity. Finally, to verify the findings in the present computational study, it is suggested that the following be investigated in future experiments: (1) to seek the phosphatase of βcatenin_{+} and obtain its kinetic rate constant, k_{β}'. (2) to obtain the kinetic constants, k_{β} and k_{βdeg}, of the added reaction steps 19 and 20, respectively, associated with nonGSK3β phosphorylation of βcatenin. In the longrun, the model will be extended to include more unexamined effects caused by other components in the course of wnt signaling pathway research in order to draw a more complete picture.
Conclusion
The present computational study gave the following results: (1) Phosphorylation of GSK3β increases the level of βcatenin in an approximately linear fashion. (2) βcatenin nonGSK3β phosphorylation is more likely to take place at free unphorphorylated βcatenin rather than GSK3βphosphorylated βcatenin*, thus accounting for the observed enhancement of TCF activity. (3) To account for the effects of kinases such as PKA, which phosphorylates βcatenin and inhibits βcatenin degradation at the same time, the dephosphorylation step is essential. In addition, the kinetic parameters of the reactions taking place at the unphosphorylated βcatenin site need to meet the conditions described above in describing the simplified mathematical functions (1) and (2). Finally, the qualitative behaviors found in the present study should be useful for future experiments in charactering how the effects of GSK3β phosphorylation, βcatenin nonGSK3β phosphorylations, and βcatenin degradation, affect the kinetics of the wnt pathway, and can be verified in future experiments.
List of abbreviations
 GSK3:

Glycogen synthase kinase 3
 PKA:

Protein kinase A
 TCF:

Tcell factor.
Declarations
Acknowledgements
The author thanks NSC and NTNU (Top Research Grant) for providing support. My gratitude also goes to the Academic Paper Editing Clinic, NTNU.
Authors’ Affiliations
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