RESEARCH ARTICLE Open Access Analysis of Wnt signaling β ... · of the pathway, however a...

Tan et al. BMC Systems Biology 2014, 8:44http://www.biomedcentral.com/1752-0509/8/44

RESEARCH ARTICLE Open Access

Analysis of Wnt signaling β-catenin spatialdynamics in HEK293T cellsChin Wee Tan1,2,3,4*, Bruce S Gardiner5, Yumiko Hirokawa1,3, David W Smith5 and Antony W Burgess1,2,3,6

Abstract

Background: Wnt/β-catenin signaling is involved in different stages of mammalian development and implicated invarious cancers (e.g. colorectal cancer). Recent experimental and computational studies have revealed characteristicsof the pathway, however a cell-specific spatial perspective is lacking. In this study, a novel 3D confocal quantitationprotocol is developed to acquire spatial (two cellular compartments: nucleus and cytosol-membrane) and temporalquantitative data on target protein (e.g. β-catenin) concentrations in Human Epithelial Kidney cells (HEK293T) duringperturbation (with either cycloheximide or Wnt3A). Computational models of the Wnt pathway are constructed andinterrogated based on this data.

Results: A single compartment Wnt pathway model is compared with a simple β-catenin two compartment modelto investigate Wnt3A signaling in HEK293T cells. When protein synthesis is inhibited, β-catenin decreases at thesame rate in both cellular compartments, suggesting diffusional transport is fast compared to β-catenin degradationin the cytosol. With Wnt3A stimulation, the total amount of β-catenin rises throughout the cell, however theincrease is initially (~first hour) faster in the nuclear compartment. While both models were able to reproducethe whole cell changes in β-catenin, only the compartment model reproduced the Wnt3A induced changes inβ-catenin distribution and it was also the best fit for the data obtained when active transport was includedalongside passive diffusion transport.

Conclusions: This integrated 3D quantitation imaging protocol and computational modeling approach allowedcell-specific compartment models of the signaling pathways to be constructed and analyzed. The Wnt modelsconstructed in this study are the first for HEK293T and have suggested potential roles of inter-compartmenttransport to the dynamics of signaling.

Keywords: Wnt signaling, HEK293T, β-catenin, Computational model, Compartmentalization, Confocal microscopy,Systems biology

Backgroundβ-catenin is a multi-functional protein involved in cell ad-hesion, cell migration and gene transcription associatedwith cell survival, proliferation and differentiation [1-3].The primary function of the Wnt/β-catenin pathway ap-pears to be the regulation of the β-catenin concentrationwithin the cell [4,5]. It has been proposed previously that inthe absence of Wnt signaling, β-catenin forms a complexwith the scaffold proteins Axin and Adenomatous Polyposis

* Correspondence: [email protected] Biology Division, The Walter and Eliza Hall Institute of MedicalResearch, Parkville, VIC, Australia2Department of Medical Biology, University of Melbourne, Parkville, VIC,AustraliaFull list of author information is available at the end of the article

© 2014 Tan et al.; licensee BioMed Central LtdCommons Attribution License (http://creativecreproduction in any medium, provided the orDedication waiver (http://creativecommons.orunless otherwise stated.

Coli (APC, itself a multi-functional protein) to form the so-called degradation complex [6,7]. The degradation complexfacilitates the phosphorylation of β-catenin by glycogensynthase kinase-3-β (GSK3β) [8], targeting phosphorylatedβ-catenin for degradation via the proteasome pathway [9].Activation of the Wnt/β-catenin pathway by Wnt ligandsbrings about the disruption of the degradation complexand a consequent reduction in β-catenin degradationwithin the cytoplasm [10,11]. Increased β-catenin con-centrations in the cell lead to the formation of the β-catenin: T-Cell Factor complex (TCF, transcription co-factor) in the cell nucleus. The β-catenin-TCF complexactivates gene transcription promoting cellular functionswhich include cell proliferation, survival and cell fate deci-sions [2,12,13]. However, this general description of the

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Wnt pathway typically does not take into account thecompartment concentrations of proteins, crosstalk withother signaling pathways (e.g. with the cell-cell adhesionpathway) or modulation of pathway behavior due to se-questration to binding partners. Further, this Wnt pathwaydescription has recently been challenged by evidence ofAPC-independent β-catenin degradation [14,15], APC-associated phosphorylation of β-catenin independent ofAxin (and surprisingly mediated by β-catenin itself ) [16],Wnt activation of different phospho-forms of β-catenin[17,18] and β-catenin ubiquitination [19]. Clearly theregulation of β-catenin is more complex than the trad-itional account of Wnt Signaling, so much so that thepathways controlling cytosolic/membrane β-catenin con-centrations need to be revisited.The computational-experimental model developed by

Lee and colleagues [20] is still arguably the leading system-atic study of Wnt signaling. They studied β-catenin signal-ing in Xenopus oocyte cytosolic extracts and developed asingle compartment computational model to interpret theirexperimental system under a range of perturbations. Thissystem has many advantages, the foremost of which is thesimplicity introduced by focusing on a single homogeneouscompartment i.e. the removal of spatial dependencies. Ingeneral, more recent models of the Wnt signaling pathwayhave been based on the Lee model [21-24], as discussed inrecent reviews [25,26]. However, to understand the Wntsignaling pathway for human cells, it is logical to want toprogress the existing Xenopus Wnt signaling model to onewhich is parameterized for a mammalian cell system [27].Even better, to the development of an experimental-computational model of an intact mammalian cell system.However there is only limited mammalian data on the pro-tein concentrations for Wnt signaling components. Tobegin to overcome data limitations, we recently measuredthe concentrations of several key Wnt signaling pathwayproteins, namely β-catenin, Axin, APC and GSK3β in fivemammalian cell-lines [27]. Our results show significantdifferences between the Xenopus extracts and the proteinconcentration in mammalian cells. For example in Xen-opus, Axin was found to be at low concentrations relativeto other pathway proteins, whereas in the mammalian celllines, it was APC that was at low concentrations. Indeedwe have measured the rate of β-catenin degradation inmammalian cell-free extracts (see Additional file 1: Figure S1)and our results indicate that the degradation of mam-malian β-catenin is much slower than in the Xenopusoocyte cell-free extracts [20]. These issues highlight theneed for caution when extrapolating pathway behaviorbetween cell systems.Recent Wnt signaling models have progressed towards

spatial multi-compartmental models [25,28-31] takinginto account spatial complexity of cellular signaling [32].Schmitz et al. [29,30] developed ODE models, based on

a two compartment (nucleus and cytoplasm) model, tostudy the influence of nucleo-cytoplasmic shuttling ofAPC and β-catenin on Wnt signaling [29]. Subsequentlythey extended the model [30] to investigate the impactof nucleo-cytoplasmic shuttling of β-catenin with itscomponent binding partners in the degradation com-plex. Another study by van Leeuwen et al. [28] in 2007developed an ODE model of Wnt signaling incorpo-rating different β-catenin pools and three functional‘compartments’ (i.e. nucleus, cytoplasm and membrane).Another approach to model cellular compartments wastaken by Basan and co-workers [31] and involved usinga reaction–diffusion model of membrane and cytoplas-mic compartments to investigate roles of cytoplasmic β-catenin and α-catenin on cell adhesion and contactinhibition. What was clear from these studies was theneed for more quantitative spatial data. The current limi-tation to multi-scale and multi-compartment modelling isthe lack of quantitative spatial and temporal data on thekey signaling proteins and complexes (this was also thecase for van Leeuwen et al.) [25]. Clearly we need morequantitative data on the Wnt Pathway in mammalian cellsystems [27], particularly quantitative spatial temporaldata. High-resolution quantitative microscopy techniquesenable cellular compartments to be distinguished andquantified, presenting a valuable opportunity for captu-ring dynamic spatial data of key signaling proteins [25].The aim of this study was to interrogate the Wnt path-

way in HEK293T cells (a human kidney epithelial cellline [33]). HEK293T cells were used in this study, asthese cells respond to Wnt3A stimulation (the only cellsto do so in the panel of cell lines analyzed in our previ-ous quantitative study [27]) and have no known muta-tions in the proteins associated with Wnt signaling(therefore providing a comparatively complete systemfor studying the Wnt signaling mechanism). Specificallywe examined the dynamics of the Wnt signaling path-way in structurally intact mammalian HEK293T cells byquantifying changes in the spatial concentration of β-catenin as a result of Wnt3A stimulation or in the pres-ence of cycloheximide. To achieve this aim, a novel 3Dconfocal quantitative imaging technique was developed.Two theoretical models of the Wnt signaling pathway inHEK293T were constructed with different structuresand compartment compositions. The first model is anextension to the single compartment Lee et al. model[20], to include HEK293T data and additional interac-tions between the key pathway components, and thesecond model is a simple two compartment model ofβ-catenin dynamics in the nucleus and cytosol-membranecompartments. A two compartment model was developedto simulate our quantitative compartment data (nucleiand cytosol-membrane). This two-compartment modelis structurally similar to the theoretical model published

Figure 1 3D view of a typical acquired image stack forHEK293T cells. An angled 3D volumetric view with microspheres ingreen isolated at both corners. Overlayed fluorescent stains: DAPI(nucleus, blue), β-catenin (green) and N-cadherin (red). Co-localizationof β-catenin and N-cadherin at cell junctions observed as strong yellow(green + red) fluorescent bands. The image was generated with Imarisx64 Version 7.0.0 (Bitplane AG).


by Schmitz et al. [30] with key differences in the trans-port mechanisms and data used (see Discussions). Cur-rent limitations in image processing methods andmembrane markers limit the advancement to a threecompartment model. In time, advances in image pro-cessing techniques and fluorescent markers will over-come this limitation.

ResultsThe 3D confocal microscopy protocol employed in thisstudy was adapted from the confocal compartment cellvolume measurement protocol established previously [27].Specifically, the technique was extended to analyze intactadherent cell cultures stained with fluorescent markers tospecifically identify the nuclei region with DAPI and thecell with N-cadherin antibodies. The temporal and spatialperturbations of β-catenin following application of theWnt pathway activator (Wnt3A ligand) or an inhibitorof protein biosynthesis (cycloheximide) were examinedquantitatively. To standardize the intensity levels betweensamples and time points, 0.3% rated InSpeck™ micro-spheres were selected as intensity calibration standards, soenabling quantitative microscopy. The selection of micro-spheres was based on flow cytometry (FACS Calibur) andconfocal microscopy analysis (see Additional file 1: Text,Figure S3 and Table S1 for details). This analysis also con-firmed that the InSpeck™ intensity microspheres have astable and specific fluorescent intensity.

3D confocal image acquisition of HEK293TThree sets of independent experiments were performedfor the two types of perturbation (Wnt3A or CHX), eachexperiment having 4 time points (0, 1, 2 or 4 hours).Figure 1 shows the 3D volume view of a typical imagestack with overlaying fluorescent channels for the nucleusin blue (DAPI), β-catenin in green and N-cadherin in red(cell boundary), together with isolated InSpeck™ micro-spheres. Figures 2 and 3 show 2D sectional images of theimage stack revealing the effects of CHX inhibition andWnt3A stimulation on β-catenin levels with time.Qualitatively, the 2D images (Figure 2) suggested that

endogenous β-catenin levels decreased with time underthe influence of CHX, whereas the total endogenous β-catenin levels increased under the influence of Wnt3A(Figure 3). Visual inspection of a representative 2Dimage would be misleading if it is used to determine thechange in β-catenin in different regions of the cell (nu-cleus, cytosol and membrane) for each time point. Simi-larly, the total β-catenin of a 3D image stack could notbe accurately inferred from a single 2D image. Combin-ing intensities from all 2D images comprising the 3Dsignals (entire stack of images) gave a clearer estimation.Therefore, the extent of changes in β-catenin levelsin the different compartments (nucleus and cytosol-

membrane) were quantified using computational andimage processing techniques (see Additional file 1: Text,Figures S4 and S5 for details) and the results of the ana-lysis are shown in Figure 4. The quantitative results wereconsistent with the visual observations. The total con-centration of β-catenin in the whole cell for Wnt3Atreatment increased with time (45 ± 22% of t0 in 4 hours,p-value,T0-T240 p = 0.02) whereas during CHX treatmentβ-catenin levels decreased (26 ± 15% of t0 in 4 hours,p-value,T0-T240 p = 0.14). Under Wnt3A stimulation(Figure 4B), the β-catenin level increased in both the nu-cleus and the cytosol-membrane compartments, how-ever, during the first hour of incubation, the rate ofincrease in the nuclear compartment was greater thanthat of the cytosol-membrane compartment (p-value,T0-T60 N: p < 0.01, CM: p = 0.04). After this initial rapid riseof nuclear β-catenin in the nuclear compartment, therate of increase in the nuclear compartment concentra-tion of β-catenin reduced (p-value, T60-T240 N: p = 0.28)and appeared to be similar to the rate of change in theconcentration in the cytosol-membrane compartment(p-value, T60-T240 CM: p = 0.16). For CHX inhibition, adecrease in β-catenin levels was observed in the nuclearcompartment (p-value, T0-T240 N: p < 0.01), with poten-tially an oscillation observed. For the cytosolic-membranecompartment, the decrease in β-catenin was non-significant during the duration of the experiment (p-value, T0-T240 CM: p = 0.22).This redistribution of β-catenin between compart-

ments was quantified using the ratio of the β-cateninlevel in the nucleus (N) compartment and cytosol-membrane (CM) compartment (the N:CM ratio). An N:

Figure 2 2D confocal images of CHX inhibited HEK293T cells. HEK293T cells stimulated for 0, 1, 2 or 4 hours with CHX; showing DAPI (blue),β-catenin (green), N-cadherin (red) and 3 channel overlay. One (of three) independently conducted confocal quantification experiments is shown.


CM ratio > 1.0 implies greater nucleus β-catenin concen-tration than that in the cytosol-membrane compartment.In Figure 4C, the normalized N:CM with respect to T0

(ΔNCM) was plotted, indicating the shift in β-cateninbetween the compartments due to the specific perturba-tions in time (i.e. a greater ΔNCM implies a shift of β-catenin levels to the nuclei compartment as compared toT0). Wnt3A stimulation increased the ΔNCM by 0.22 ±0.04 (p-value,T0-T60 p < 0.01) within the first hour andwas followed by a steady rate of β-catenin increment inboth compartments as indicated by a constant ΔNCM ofapproximately 1.2 (p-value,T60-T240 p = 0.82). For CHX in-hibition, the ΔNCM decreased over the 4 hours of CHXincubation (p-value,T0-T240 p = 0.02), indicating a gradualshift of β-catenin to the cytosol-membrane compartment.At the onset of Wnt3A stimulation the analyses showeda rapid increase of β-catenin concentration in the nu-cleus and with CHX inhibition, a slow gradual decreaseof β-catenin in both compartments. These observationsdemonstrated the ability of the protocol to successfullyquantify and monitor (in 3D) the concentration of a

specific target protein and its localization in intracellularcompartments.Visual inspection of 2D images (Figures 2 and 3) for

endogenous N-cadherin in HEK293T cells, in the pres-ence of either Wnt3A or CHX, showed no change withtime (up to 4 hours). β-catenin and N-cadherin appearedto be co-located near the membrane, as seen from theyellow overlapping (green and red) signal predominantlyat the cell surface. Quantitation of the concentration oftotal N-cadherin was investigated (Figure 4D). For totalN-cadherin, results indicated that Wnt3A stimulationled to an increase of 13 ± 3% after 4 hours (p-value,T0-T240 p = 0.05). In the presence of CHX, total N-cadherindecreased 17 ± 10% after 1 hour and then remainedstable (±1.7%) over the remaining 4 hours (p-value,T0-T240 p = 0.39).

Comparison of 3D microscopy quantitation with westernblot quantitationTo validate the results of the above 3D quantificationtechnique, quantitative Western blots were performed

Figure 3 2D confocal images of Wnt3A stimulated HEK293T cells. HEK293T cells stimulated for 0, 1, 2 or 4 hours with Wnt3A CM; showingDAPI (blue), β-catenin (green), N-cadherin (red) and 3 channel overlay. One (of three) independently conducted confocal quantification experi-ments is shown.


under the same perturbation and culture conditions (asdescribed in the Methods section). Five sets of inde-pendent quantitative Western blot experiments wereconducted with HEK293T cells. β-tubulin was used asthe loading control in these experiments and as a refer-ence for normalization between the samples. Extractsfrom cells incubated with either Wnt3A or CHX for 0,1, 2 or 4 hours were loaded onto the gels as shown inFigure 5. Each membrane was immunoblotted for β-catenin and β-tubulin. Upon visual inspection, it couldbe seen that qualitatively, the levels of total β-catenin in-creased with Wnt3A incubation and decreased withCHX incubation. The intensities for each band werequantified and normalized. Results of these independentexperiments were compared with results obtained usingthe confocal 3D quantification (as shown in Figure 5C).The two sets of results, that is, the Western blots andthe 3D confocal imaging technique, were consistent.This independent validation experiment demonstratedthat the 3D confocal quantification technique developed

in this study can be used to accurately and reproduciblyquantify and monitor the levels of target proteins (in thiscase β-catenin) in HEK293T cells at different time afterstimulation. This allows for confident quantification andanalysis of the spatial localization, distribution and levelsof the target proteins using quantitative 3D microscopy.

Computational modeling of whole cell experimental dataThere are two types of experimental data presented inthis study. First, we had whole cell data in which spatialinformation was hidden by summing up the changes inβ-catenin within subcellular compartments (see Figure 4A).Secondly we had compartmental data in which β-catenin concentration was monitored in two subcellu-lar compartments (see Figure 4B and C). By removingspatial dependencies, the whole cell data set resembledthe single homogeneous system developed by Lee et al.It was then logical, as a first step, to fit a one compart-ment Wnt model strongly based on the Lee model tothis data. This extended the Lee model and is referred to

Figure 4 Quantification of β-catenin and N-cadherin in stimulated/inhibited HEK293T cells. HEK293T cells were stimulated with Wnt3A CMor inhibited by CHX for 0, 1, 2, or 4 hours. (A) Relative change in β-catenin concentration intensity (in terms of % of T0); (B) Relative change inβ-catenin compartment concentration intensity (in terms of % of T0); (C) β-catenin Nucleus/Cytosol-membrane intensity ratio (normalized to T0);(D) Relative change in N-cadherin concentration intensity (in terms of % of T0); Error Bars: (A and D) Standard deviations, (B and C) Standard Errorof the Mean. n = 3; each data point has≥ 3 image sets. A single factor analysis of variance (ANOVA) test was applied to test for differences be-tween data points for each perturbation, specifically between T0-T240, T0-T60 and T60-T240.


here as Model 1. However, to interpret the compartmentdata required the development of a multi-compartmentmodel which included inter-compartment transport.Hence, a new simple two compartment β-catenin model,referred to as Model 2 was developed. The results forModel 1 based on whole cell data are presented below.Our single compartment model (Model 1, Figure 6)

was optimized (for selected parameters, see Additionalfile 1: Table S6) using the steady state total protein con-centrations of the key Wnt signaling proteins (i.e. β-catenin, Axin, APC and GSK3β), as measured in ourprevious study [27], and then fitted to the β-catenin deg-radation and Wnt3A stimulation dynamics data obtainedin this study (Figure 4A). A poor correlation of steadystate Axin concentration for Model 1 with the data wasobserved before optimization (see Additional file 1:Figure S2). During the optimization of the Wnt stimula-tion data, the Wnt receptor signaling components ad-justed included the protein elements Wnt and both(active and inactive) forms of dishevelled. The resulting

optimized Wnt model (Figure 7A and see Additional file 1:Figure S2) fitted the experimental data reasonably wellwith a R2 of 0.775 (Figure 4A). The optimization modelprocess and the optimized parameters are described in theMethods section as well as in Additional file 1, Textsection 1.6 and Tables S2-S5.It should be noted, that the optimization of the model

came at a ‘cost’, in the form of substantial parametric ad-justments (with adjustments of 0.1 to 15000 times theoriginal parameter values from Lee et al., see Additionalfile 1: Table S6). On further inspection of the protein/complex redistribution profiles during the steady stateanalysis (Figure 7B), it appeared that the low concentra-tion of the degradation complex (Axin:APC:GSK3β) wasthe limiting factor in the model when modulating thedegradation of β-catenin in the degradation cycle. In Leeet al.’s work, Axin was the component controlling thelevel of this degradation complex. However in thecurrent study, as the concentration of APC is very lowin HEK293T cells [27], the limiting component was

Figure 5 Confocal 3D quantitation technique validation withquantitative Western blot for HEK293T Whole Cell Lysates.Western blots for β-catenin:(A) Wnt3A stimulation; (B) CHX inhibitionfor 0, 1, 2 or 4 hours; (C) Comparison between the results of confocalquantification and Western blot validation. P-values for both Wnt3Aand CHX are greater than p = 0.05. (Error Bars: Standard deviation.Selected blots showing non-continuous lanes, replicates are labeledas A or B with β-tubulin used as a loading control.)


APC. In particular, the levels of free APC appeared to bevery low at steady state [27].The perturbation experimental data obtained in this

study were a measure of the total β-catenin proteinlevels for the whole cells (Figure 4A). In Model 1 theonly β-catenin-containing component that was clearlypresent in the nuclear compartment was the β-catenin/TCF complex. The change in the compartment ratio be-tween the nuclear (N, i.e. β-catenin/TCF complex) andnon-nuclear compartment (CM, i.e. the rest of the sys-tem components) β-catenin intensity was calculated (N:CM, Figure 4C). The predicted N:CM ratio from Model1 was significantly lower than that of the experiment.Having TCF as the only nuclear compartment bindingpartner of β-catenin was a likely limitation, as was havingthe TCF concentration fixed (during model optimization)at the values provided by Lee et al.Model 1, with parameters optimized to reproduce the

whole cell data, was a one compartment, i.e. whole cellmodel. It was therefore not surprising that optimizationto the compartment data was not very successful.However, it did highlight the limitation of the one-compartment model for understanding cell compart-ment dynamics and a need for developing new modelsthat included multiple cell compartments. In the nextsection we consider a multi-compartment model (i.e.Model 2).

Two compartment β-catenin modelHere we show that once diffusion and active transportmechanisms between compartments are included (Referto Table 1 and Table 2 as well as see Additional file 1 fordetails of model composition, numerical analysis), the ex-perimental compartment data can be reproduced using arelatively simple two compartment model for β-catenin(Model 2, Figure 6). Various reports [34-41] have sug-gested transport of β-catenin between the nucleus andcytosol. In this study, a generic active transport mechan-ism was assumed without specifying the identity of trans-port protein(s) involved. The model consists of twocompartments, one to represent the cell nucleus andanother compartment for the cytoplasm-membrane.Note that this two-compartment model correspondedto the spatial resolution of our data. In each compartmentit was assumed that β-catenin had a binding partner. This

Figure 6 Schematic diagrams of Computational Models. (A) Model 1 is a Wnt signaling pathway whole cell model based on the full ODEreconstruction of the Lee et al. (2003) model with alternative binding partners not included and updates on binding affinities for mammaliancells. (B) Model 2 is a simple β-catenin compartment model with nuclear and non-nuclear compartments. Model 2 includes a binding partner forβ-catenin and considers diffusion and/or active transport mechanisms. (C) Schematic of computational modelling stages/phases implemented inthis study. Two stages were conducted, each having two phases with the experimental data used during optimization for each phase (1A, 1B, 2Aand 2B). (Bottom inset) Phase A, steady state analysis where proteins were distributed among the complexes and Phase B, transient analysis dueto specific perturbations.


assumption aims to represent the net binding of β-cateninto all possible ligands. The exception to this assumptionwas the degradation pathway which was treated as a singlestep via the free (unbound) β-catenin in the cytosol-membrane compartment. We assumed that β-catenindegradation and synthesis only occur in the cytosol-membrane compartment. The free β-catenin was assumedto be transported between compartments by a diffusion-like process (i.e. proportional to concentration differencebetween compartments) and/or actively (i.e. the rate oftransport is independent of the concentration differencebetween the compartments). The equations describingthis model were:

dBc

dt¼ Bsynthesis−kdegradationBc þ kCRC

C−kCF BcLc

−kdiffusion BC−BN

� �þ kCactiveBC−kNactiveB

N

VC

ð1Þ

dBN

dt¼ kNR C

N−kNF BNLN

þ kdiffusion BC−BN� �þ kCactiveB

C−kNactiveBN

VN ð2Þ

dLc

dt¼ kcRC

c−kcFBc LcT−C

c� � ð3Þ

dCc

dt¼ −kcRC

c þ kcFBc LcT−C

c� � ð4Þ

dLN

dt¼ kNR C

N−kNF BN LNT −C

N� � ð5Þ

dCN

dt¼ −kNR C

N þ kNF BN LNT −C

N� � ð6Þ

where: the superscripts denote either cytosol-membrane(C) or nuclear (N) compartments. LN

T and LNT were thetotal ligand concentrations in either compartment (C orN). BC and BN were the free β-catenin concentrations ineither compartment (C or N), CC and CN were thebound β-catenin-ligand complex concentrations in eithercompartment (C or N) and LC and LN were the free lig-and concentrations in either compartment (C or N). kNFand kCF were the forward rate constants between β-catenin and ligand in either compartment (C or N), withkNR and kCR the corresponding reverse rate constants.Bsynthesis was the β-catenin synthesis rate, kdegradation was

Figure 7 HEK293T cell model simulations, optimization andresults. Computational optimization of Model 1 for the totalβ-catenin data obtained using quantitative confocal microscopy(shown in Figure 5). Specifically, (A) the model was fitted to thedegradation (cycloheximide inhibition experiments in red circles)and Wnt perturbation (blue diamonds) dynamics of total β-catenin.Results show a reasonable correlation between Model 1 and theexperiment. (B) Redistribution of Wnt signaling pathway proteinsand the interacting protein complexes during the steady state usingthe optimized whole cell Model 1 (log scale). It should be notedthat concentrations of protein and complexes in the degradationcomplex (in red box) are significantly lower than the other proteins(and complexes) in the model.

Table 1 Steady state concentrations obtained for optimized M

Component

- -

Cytosol-membrane β-catenin BC0

Cytosol-membrane Ligand LC0

Cytosol-membrane complex CC0

Nuclear β-catenin BN0

Nuclear ligand LC0

Nuclear complex CN0


the β-catenin degradation rate, kdiffusion was the diffusionrate constant and included contributions of the nuclearmembrane surface area, effective membrane thicknessand diffusion coefficient on the mass flux between com-partments by passive diffusion. Finally, active transportbetween compartments was described using the con-stants kCactive and kNactive where the superscript related tothe compartment from which β-catenin was being trans-ported (‘C’ cytosol-membrane and ‘N’ nucleus).At steady state the two compartment model required

BC0 ¼ Bsynthesis

kdegradationð7Þ

and that

kdiffusion BC0 −B

N0

� �þ kCactiveBC0 −k

NactiveB

N0 ¼ 0 ð8Þ

In the absence of active transport at steady state, i.e.prior to perturbing the system with Wnt3A or CHX,Equation (8) could only be satisfied if BC

0 ¼ BN0 , i.e. the

free β-catenin at steady state needed to be the same ineach compartment. However active transport enabled adifference in free β-catenin to be maintained at steadystate. Whether or not free β-catenin was higher in thenucleus or cytosol at steady state, depends on the activetransporters and the affinity of the binding partnerswithin each compartment. From our earlier studies [27],initially HEK293T cells had an average total β-cateninconcentration of 490nM, using the compartment distri-bution of β-catenin measured in this study (N:CM of1.05, Figure 4C at t0), the total β-catenin concentrationin the cytosol-membrane compartment was calculatedas 465.5nM and in the nucleus as 515.8nM. Therefore,in the absence of active transporters, there was a lowerbound β-catenin steady state concentration CC

0

� �in the

cytosol-membrane compartment than in the nucleusCN

0

� �i:e: CC

0 < CN0

� �. Note, to achieve BC

0 ¼ BN0 while

CC0 ¼ CN

0 did not restrict the relative binding affinity ortotal ligand concentration in the cytosol and nucleus. Inour model we assumed an excess of β-catenin binding

odel 2 with and without active transport

Steady state concentration (nM)

With active transport Without active transport

46.6 70.8

581.1 605.3

418.9 394.7

32.6 61.8

516.8 546.0

483.2 454.0

Table 2 Change in model parameters for Models 2 after optimization

Parameters Initial conditions Optimized with active transport Fold change Optimized without active transport Fold change

- Steady state CHX WNT - CHX WNT -

Bsynthesis 1.306 0 1.306 - 0 1.306 -

Kdegradation 0. 0163 0.0163 0 - 0.0163 0 -

kR_cyto 0.0026 0.000647 0.25 0.00109 0.42

kF_cyto 0.00001 0.00001 - 0.00001 -

kR_nuclear 0.003 0.00349 1.16 0.00743 2.48

kF_nuclear 0.0001 0.0001 - 0.0001 -

kdiffusion 36 39.13 1.09 1354.1 37.6

kCactive 4.5 4.5 1 0 -

kNactive 2 17.16 8.58 0 -

Figure 8 Role of β-catenin active transport into the nucleus in regulating protein distribution/dynamics in HEK293T cells. Simulationresults from the optimization of the simple two compartment model for β-catenin (Model 2) indicate the critical role of active transport inregulating the compartmental distribution and dynamics of β-catenin in HEK293T cells. Model 2 was optimized for the relative change in totalβ-catenin concentrations (A and B) relative changes in β-catenin compartment concentrations (C and D) and relative change in nuclear/cyto-membraneconcentration ratios (data not shown). Simulations are conducted with either active transport switch on (A and C) or switched off (B and D).Simulations with active transport clearly show an improved correlation and fit to the experimental data when compared with simulationswithout active transport.



ligands in both the cytosol-membrane and nuclearcompartments.We next consider the transient perturbation data. Our

aim was to simulate the compartmental β-catenin changesunder CHX inhibition or Wnt3A stimulation using thesame model parameters, except with Bsynthesis = 0 for CHXinhibition and kdegradation = 0 for Wnt3A stimulation. Wetested both conditions with (active) or without (passive)active transport and attempted to calibrate the model ineach case. Unlike the single compartment model, our opti-mal solutions (Tables 1 and 2) for both forms of the trans-port model (passive or active transport), were able toreproduce the Wnt3A and CHX experiments (Figure 8).In the case of active transport, not only was a closereproduction of the experimental compartment resultsobtained, the efflux diffusion rate for β-catenin from thenucleus was also maintained after optimization (Table 2).This was in contrast to the conditions required to achievethe optimal condition for the passive transport model,where the diffusion rate constant was over 37 times theinitial estimated value (see Table 2). Our results suggestthat Model 2 with active transport was the better modelfor Wnt signaling in HEK293T cells.

DiscussionIn previous studies, various mechanisms of Wnt pathwaysignaling (e.g. the APC-independent β-catenin degrad-ation mechanism) [14,16] as well as cell type specific pro-tein concentration and dynamics have been suggested[27]. There is also an increasing awareness that signalingpathways function across several cellular compartmentsand so their operation must be understood in this context.Consequently, there is a growing emphasis for recordingthe spatial localization of proteins and to account for theprotein distribution when modeling biological systems[33]. This is evident from the increasing number of multi-compartment and multi-scale computational models ofWnt signaling published in recent years [28-31]. The add-itional spatial aspect inevitably increases the complexity ofthe modeling problem; there is an increased number ofpotential interactions and a requirement for additionaldata to inform model parameters. At present, this quanti-tative data is either incomplete or unavailable.In order to bridge the gaps in the existing data on the

cellular distribution of protein components, a protocolusing immunofluorescence, confocal microscopy was de-veloped and validated for analysis of the 3D sub-cellularlocalization of target proteins in whole cells. This protocolallowed the concentrations of target proteins in differentcompartments of the cells to be determined and changesin concentrations to be analyzed under specific perturba-tions at different times.It is difficult to use transfection of fluorescently-

tagged proteins (β-catenin in this case), as often the

levels, distribution and turnover of the recombinant formscan be quite different to the endogenous proteins. Unlessit can be validated that an introduced recombinant proteinbehaves in a similar manner to the endogenous protein,the use of live cell imaging has limited utility for the studyof signaling systems. Therefore, individual formaldehydefixed samples at specific time points were used. In thiscase it was essential to have a reference fluorescence probeto normalize the results between the different samplesand different time points. We used the InSpeck™ Greenbeads in each sample as intensity markers.This imaging quantitation technique provided insights

previously unavailable from the cellular extract experi-ments, in particular protein localization under differentperturbations in intact cells. Critically, we observed adistinctly different dynamic behavior for the Wnt signal-ing proteins in HEK293T mammalian cells than for theXenopus oocyte cell-free extract. In particular, the rateof β-catenin degradation in HEK293T cells was relativeslow (15% decrease in 1 hour compared to a 50%decrease for Xenopus cell free extracts). From the ana-lysis of the transient change in compartment β-cateninconcentrations, Wnt stimulation increased the β-cateninconcentrations in both the nucleus and cytosol-membranecompartments. Although over 4 hours the rate of increaseappeared to be similar in both compartments, an initialrapid increase in β-catenin concentration was observedfor the nuclear compartment. This was reflected in the ob-served rapid increase in the normalized N:CM ratio(ΔNCM) in the first hour, before stabilizing at ~1.2 for theduration of the experiment. These results suggest thatthere is an active transport mechanism, stimulated byWnt, which concentrates β-catenin in the nuclearcompartment. One possibility is that Wnt stimulationincreases the activity of potential transporter proteins(e.g. Pygopus, legless/BCL9-2 [34,40], TCF-4 or Menin[35,41]). This increased activity could occur either by achange in the levels or affinity of the transporter pro-teins or by a change in the affinity of a pool of β-catenin for these transporter proteins (e.g. via specificWnt associated phosphorylation of β-catenin [18]).Another possibility (which does not require activetransport) is that Wnt induces a relative change in affinityfor β-catenin for its ligands in the two compartments, thuschanging the relative free diffusible β-catenin concentra-tions (higher in the cytoplasm-membrane compartmentthan nuclear compartment) and driving β-catenin trans-port to the nucleus down its concentration gradient. Aswe were only measuring total (bound and unbound) β-catenin in this study, a change in the ratio of bound andunbound β-catenin was not determined. In any case thesimilar rate of concentration increment in both nucleusand the cytosol-membrane compartments after 1 hoursuggested that drivers for β-catenin transport into the


nucleus were balanced by an opposite (passive) diffusiontransport out of the nucleus. Note also that under the in-fluence of cycloheximide the rate of loss of β-catenin wasthe same in both compartments, suggesting that rate oftransport between compartments or the rate of release ofβ-catenin from ligands in each compartment were not thelimiting rates for removing β-catenin from the cell. Onemechanism to achieve an initial increase in the ΔNCM β-catenin ratio, i.e. a two compartment model, was exam-ined briefly in this study (see below). Our adoption of thetwo-compartment model does not imply this is the onlyexplanation for the rapid nuclear influx of β-catenin. Dif-ferent reports have further implicated roles of nucleo-cytoplasmic shuttling of β-catenin and/or its degradationcomplex binding partners in regulating β-catenin nuclearlocalization [36-39,41,42]. Firstly, β-catenin has been re-ported to translocate into the nucleus without having thenuclear localization signal (NLS) sequence, independentlyof cellular nuclear import mechanisms [36,41]. Secondly,it has been proposed that the APC’s nuclear export signal(NES) allows it to shuttle between the nucleus and cyto-plasm, controlling the compartment levels of β-catenin[38,39]. Likewise, it has been reported that a direct inter-action of Axin (another β-catenin binding partner) withthe CRM1 receptor facilitated its shuttling between thenucleus and cytoplasm [42]. GSK3 has also been reportedto have a NLS and binds to FRAT for nuclear export in aCRM1-dependent manner [37]. Interestingly, it has alsobeen reported that GSK3 down-regulates β-catenin activ-ity in the nucleus [43] and that the nucleocytoplasmic dis-tribution of β-catenin is regulated by retention rather thantransport [44]. This active transport mechanism andthe other possibilities need to be investigated furtherin subsequent publications. One technique for measur-ing nucleo-cytoplasmic transport dynamics of proteinsis the use of 3D confocal microscopy introduced in thisstudy. Another approach would be to conduct FRAP ex-periments [44], looking at the recovery of fluorescent-tagged proteins moving back into selectively photo-bleached regions, thus providing data on the motility andrate of movement of these proteins.Computationally, the total β-catenin kinetic data ob-

tained here were integrated into a previously availableWnt signaling model (Xenopus extract Wnt model fromLee et al. in 2003 [20]) with the aim of developing aWnt model more representative of mammalian cells(HEK293T). Although in this optimized HEK293T Wntmodel (Model 1) dynamics correlated well with thewhole cell experimental data, substantial changes tomodel parameters were required (see Table 1) and thismodel was unable to capture the compartment data. Itwas clear that to advance the whole cell model to aspatial compartment model of the Wnt signaling path-way, structural changes and transport mechanisms had

to be taken into consideration. To test this hypothesis, asimple two compartment β-catenin model (Model 2)was developed which replicated the experimentally ob-served β-catenin dynamics. Our results emphasize theimportance of creating an appropriate structure for themodel, in this case a second cellular compartment is re-quired. While this β-catenin model does not take intoaccount other Wnt signaling components, it provides agood platform for developing a more complete compart-ment model of the Wnt signaling pathway in HEK293Tcells. Moving forward, these predictions will serve as themotivation for specific experiments to be conducted tomeasure realistic parameter values or bounds/limits forfurther refinement of the models.One of the critical decisions when developing the com-

putational models for biological systems was the choice ofmodel parameters. Often experimental measures of theseparameters are unavailable, which presents significant ob-stacles for modeling. Thus the significance of havingquantitative measurement techniques such as the one pre-sented in this paper. In cases where no information is dir-ectly available, estimations had to be made. In Model 1,the whole cell model, optimization was conducted on pa-rameters that were initially estimated rather than mea-sured experimentally (6 of 21 reactions, Table 1). InModel 2, the two-compartment model, one of these opti-mized parameters was kdiffusion, which corresponds to thetransport between the intracellular compartments viadiffusion. As no diffusion rate constant (kdiffusion) forHEK293T was available, the initial value (kdiffusion =36 m∙min−1) was estimated using information from theliterature and physics (See Additional file 1, Section1.8 for details) and based on the transport propertiesof nuclear pore complexes for proteins [36,45]. Whencomparing the optimized models in the case of activetransport versus diffusion only transport, althoughboth models fit the compartment data, only the activetransport model did so without significant changesfrom our initial model parameter estimates. Speci-fically it was found that the active transport case hadan optimized kdiffusion = 39.13 m∙min−1 (i.e. minimalchange from the initial estimates) whereas in the caseof no active transport kdiffusion = 1354 m∙min−1 (i.e. ~37times larger than initial estimates). This suggests thatactive transport is likely to be involved in determining thecompartment distribution of β-catenin in HEK293T cellsunder Wnt stimulation. For both conditions of Model 2,the model’s initial response to Wnt3A was too slow. Thiswas evidenced by both sets of simulations missing the nu-clear β-catenin concentration data point at 60 minutes forWnt3A stimulation. The other major change in parame-ters is that the β-catenin equilibrium constant in the nu-cleus for both simulations increases (Table 2). The initialvalue used in this study was inferred from work by Lee


et al. [20] for TCF/β-catenin interactions in the Xenopusoocyte. Further validation with experimental data frommammalian sources will be needed to validate this newequilibrium constant to further constraint the model.These simulation results indicated a closely coupled

relationship between the diffusion and active transportrate in the control of β-catenin compartmentalization inthis cellular system. We do not discount the possibilitythat there was likely to be sequestering effects of otherpartner proteins on β-catenin (e.g. E-cadherin) that willmodulate its levels in specific compartments. The simula-tions presented in this study suggest that a multi-compartment model, in contrast to the homogeneous Leeet al. whole cell model of Wnt signaling (that takes intoaccount compartments and active transport mechanisms)was needed to understand the Wnt3A signaling pathway.Although Model 2 did not take into account the variety ofpotential binding proteins found in Model 1, using a gen-eric binding partner instead, this simplified β-cateninmodel provides a good platform for advancing a Wnt sig-naling model which is more representative of real lifesystems.The schematic illustrating Model 2 is similar to that re-

cently proposed by Schmitz et al. [30]. Schmitz and col-leagues consolidated the components of the degradationcomplex (i.e. APC, Axin and GSK3β) into a single speciesknown as AAG and constrained its shuttling rate (v2) withrespect to that of the free β-catenin shuttling rate (v1). Inthis study, Model 2 assumes shuttling of free β-catenin bya diffusion-like or active transport, but no transporterprotein is defined explicitly. Another difference betweenSchmitz et al. [30] and Model 2 is that Model 2 was cali-brated with mammalian spatial data. Model 2 was de-signed to test the need for a multi-compartment approachand whether it might provide further insights on compart-ment specific Wnt signaling in mammalian cell systems,thus overcoming the limitations of the single compart-ment models. The Schmitz et al. [30] model was built spe-cifically to study the effect of nucleo-cytoplasmic shuttlingon Wnt signaling and as a consequence, they performed aparametric study to explore the possible states of thesystem. Model 2 primarily aimed to simulate the com-partmental dynamic data generated in this study usingquantitative 3D confocal microscopy.One approach for constraining computational models

of biological systems is to acquire and optimize for bothspatial and temporal data for the signaling components.In most studies, either spatial data or temporal data areavailable, but seldom are both acquired together. This wasone of the key objectives of the methods introduced inthis study, to acquire both spatial (compartments) andtemporal (time-course) data using immunofluorescence.Computationally, the typical approach has been to use or-dinary differential equations and generic rate constants to

approximate and optimize these data for simulating com-plex biological pathways. However, in a biological system,cell growth causes volume changes which could changethe associated rate constants in time [46]. As more ad-vanced models starts to incorporate cellular compart-ments in the time domain, even more approximationswould have to be made. In this study, we approximatedcompartment volumes as the population averages over asteady state population [27] and assumed these volumesdo not change in time. Furthermore, we assumed that therate constants do not change with time. Nonetheless, withthe increasing abundance of temporal and spatial data,these considerations would have to be addressed (i.e.time-dependent rate constants and cellular volumes) dur-ing the development of the computational models.Computationally, the optimization process to find the

best solution for a complex signaling network is notsimple. As the number of parameters in a model in-crease, the number of permutations to be considered foroptimization increases exponentially. As an example, inour study, each model includes four flux terms (two eachfor Axin and β-catenin) so four unique sequences wouldrequire 24 permutations. Approximating each simulationhaving 1000 random starting points, each search typicallyrequires 100 iterations, a total of 2,400,000 simulationcycles are required. Thus the computational require-ments and time will be considerable and constraining.The use of a topological analysis approach (see Additionalfile 1) helped to reduce the number of iterations neededby making logical deductions when selecting parametersand parametric adjustments. Efforts had been made bymany research groups to remove the computationalconstraints and limitation caused by network size, e.g.by using a rule-based modeling [47,48]. Rule basedmodeling has the potential to speed up the computa-tional analysis processes involved with pathway simula-tions and should be explored further as we developcompartmentalized models.One potential limitation of our experimental system is

the number of available confocal channels that can be usedfor each analysis. Current available microscopes had threeto four fluorescent channels, which were shared amongmonitoring target proteins as well as markers for specificcompartments. This study used three channels for bothcompartment probes and target protein identification. Tomonitor more target proteins, the procedure had to be re-peated for each additional protein of interest. The numberof compartments which can be analyzed depends not onlyon the availability of confocal channels, but also on the suit-ability/specificity of the marker probes which define thecompartments. In this study, two compartments (the nucleiand cytosol-membrane compartment) were identified andanalyzed quantitatively. For the study of epithelial cellsmonolayer or aggregates, it would have been ideal to be


able to analyze the membrane compartments separately.Unfortunately, efficient isolation of the membrane fluores-cence was limited by membrane marker suitability. Despitemany attempts to effectively distinguish and isolate themembrane fluorescence from the cytosol, we were unableto resolve the boundaries between neighboring adherentcells at various depths in 3D space. Consequently, ourstudy is limited to two compartments, but with further in-vestigation into image processing techniques and improvedmembrane markers, it should be possible in subsequentstudies to analyze three compartments (nucleus, cytosoland membrane) for each cell in a monolayer or even an ag-gregate of cells.We note that the compartment concentration distri-

bution of β-catenin reported here does not correlatewith our previously reported β-catenin distributionsusing sub-cellular fractionation technique [27]. The sub-cellular fractionation procedures applied in the previousstudy recovered the majority of the compartment pro-teins (well fractionated), but there were inevitable lossesassociated in each step of the process. Loss was associ-ated with pipetting, washing and mechanical disruptionsof the cell and transfer of fluids. In particular cytoplas-mic proteins were lost during the isolation of the othercompartments. In contrast, the microscopy techniquewas able to give a more accurate quantitation of the pro-tein concentrations as it measures the proteins concentra-tions “in situ” without external intervention or cellulardisruptions. In comparison to sub-cellular fractionation,the confocal imaging quantitation technique thereforeprovides a more realistic and accurate measurements ofthe protein concentrations in each compartment.Other components of the cell also modulate the dis-

tribution and function of β-catenin. For example, theCadherin family proteins are key adhesion partners of β-catenin in the cell-cell adhesion processes [49,50]. Theseinteractions will influence the distribution of β-cateninwithin the cell. From the immunofluorescence images, itwas clear that a substantial amount of β-catenin was local-ized at the membrane (presumably with a cadherin). Thisobservation, coupled with recent reports of differingmodes of action of Wnt signaling on β-catenin (e.g. mod-ulates ubiquitination of β-catenin [19]) as well as distinctpools of Wnt induced β-catenin isoforms at different loca-tions in the cell [17,18], provides further incentive to de-velop a multi-compartmental experimental and modelingconfiguration to describe the signaling processes within acellular network.

ConclusionsIn this study, we have developed and applied an inte-grated experimental computational approach to investi-gate the spatial and temporal dynamics of Wnt signalingin HEK293T cells. A 3D quantitation protocol using 3D

confocal microscopy, immunofluorescence and imageprocessing was developed to acquire quantitative cellularcompartment (nucleus and cytosol-membrane) and tem-poral data for target protein β-catenin concentrationsunder different signaling perturbations. Our results sug-gest that β-catenin diffusion between compartments isfaster than β-catenin degradation in the cytosol and thatWnt stimulation increases total β-catenin throughoutthe cell. Initially (~first hour), there is a faster incrementof β-catenin in the nucleus. This experimental data wasused to parameterize mathematical models of Wnt sig-naling in HEK293T cells. Computational analysis com-paring a single and a two compartments model wereconducted. Both models were able to reproduce wholecell changes in β-catenin. However, only the two com-partment model could reproduce the Wnt3A induced β-catenin changes, and the best reasonable fit was ob-tained with the inclusion of an active transport compo-nent alongside passive diffusion to account for the rateof transfer of β-catenin to the nucleus. This suggested arole of active transport and compartmentalization inregulating both the spatial and temporal dynamics of β-catenin when HEK293T cells are stimulated by Wnt3A.

MethodsAntibodies, reagents and intensity standardsThe antibodies used in this study were: mouse monoclo-nal anti-β-catenin (BD Transduction Laboratories, BDBiosciences, San Jose, CA, cat#610153) and mouse mono-clonal anti-N-cadherin (BD Transduction Laboratories, BDBiosciences, San Jose, CA, cat#610921). The anti-β-cateninmarks the target protein endogenous β-catenin in the cellwhile the N-cadherin was used both as a marker to outlinethe whole cell as well as to stain the endogenous N-cadherin protein in the cell. The fluorescent stain 4, 6-diamidino-2-phenyl indole Nucleic Acid Stain (DAPI,cat# D1306 Molecular Probes Inc, Eugene, OR, Invitro-gen) was used to stain the nuclei. The secondary fluor-escent dyes used were Alexa Fluor ®488 goat anti-rabbitIgG (H + L) (Molecular Probes Inc, Eugene, OR, Invitro-gen cat#A-11034) and Alexa Fluor® 546 goat anti-rabbitIgG (H + L) (Probes Inc, Eugene, OR, Invitrogen cat#A-11030).Perturbation of the Wnt pathway was conducted using a

known activator/stimulator of the Wnt signaling pathway[51], Wnt3A (Wnt3A CM, in the form of L-cell condi-tioned media containing the Wnt3A ligand was acquiredfrom L-cells producing and secreting the recombinantWnt3A protein, LWnt3A cell (ATCC#CRL-2647, [52,53]).A known inhibitor of protein biosynthesis, cycloheximide(CHX, Sigma-Aldrich Corporation, St. Louis, MO 63103USA cat#C7698 [54]) was purchased from Sigma-Aldrich.4% formaldehyde (Formaldehyde solution min. 37% freefrom acid, cat#103999, 64293 Darmstadt, Germany) in


phosphate buffered saline (PBS) was used as a fixationagent to preserve the sub-structures of the cells (physicallyand chemically) for microscopy.InSpeck™ Microscope Image Intensity Calibration Kits,

specifically 6.0 μm InSpeck™ Green (cat#I-14785, MolecularProbes Inc, Eugene, Oregon), were utilized as the intensityreference for confocal microscopy. 0.3% rated microsphereswere identified for use in these experiments based on aselection criteria outlined in Additional file 1 main text,Figure S3 and Table S1.

Cell culture, sample preparation and treatmentsHEK293T, a human kidney epithelial cell line [33] wasused in this study as these cells are responsive to Wnt3Astimulation and have no known mutations among theproteins associated with Wnt signaling. The cells weregrown in Dulbecco’s modified Eagle’s medium (DMEM)supplemented with 10% fetal calf serum (FCS) on glasscover slips. For Wnt pathway investigations, the respectivecover slips of cells were incubated with either Wnt3A con-ditioned media (40% in DMEM+ 10% FCS) or cyclohexi-mide (CHX, 100 μg/ml in DMEM+ 10% FCS) for 0, 1, 2or 4 hours selectively at 37˚C. Wnt3A is an activator ofthe Wnt pathway which has been reported to increase thelevels of target protein β-catenin in the cell [51], whileCHX is a protein synthesis inhibitor [54] which allows formonitoring of the degradation of existing pool of β-catenin protein in the cell in the absence of new synthesis.At the end of the respective incubation periods, the coverslips of cells were fixed with 4% formaldehyde (Formalde-hyde solution min. 37% free from acid, cat#103999, 64293Darmstadt, Germany) in PBS. The fixed cell samples werethen immuno-stained with primary anti-β-catenin andanti-N-cadherin antibodies, secondary antibodies AlexaFluor® 488 and Alexa Fluor® 594 and fluorescent dye DAPIfor immunofluorescent studies under the confocal micro-scope. The stained samples were stored in HT-PBS at 4°Cuntil just before confocal imaging.

3D confocal imaging and quantitative compartmentalanalysisThe fixed and stained cell samples were mounted ontoSykes Moore Chambers (Bellco Glass Inc., Vineland, NJ)with an aliquot of InSpeck™ intensity microspheres PBSmixture and allowed to settle. As this was a fixed time-course system with independent samples of cells on adifferent cover slip, the InSpeck™ intensity microsphereswere used as the intensity reference to facilitate compar-isons between the samples (see Additional file 1: Textand Figure S4 for details).An Olympus FV1000 confocal microscope with a 60x

water immersion lens was used to acquire 3D imagestacks of the stained cells which were then processedusing Metamorph Premier image processing software

into image data files. DAPI, β-catenin and N-cadherinfluorophores on the antibodies were excited with the405 nm, 488 and 594 nm laser lines respectively and theemission captured at wavelengths 405 nm, 473 nm and559 nm, respectively. Image analysis procedures forInSpeck™ intensity calibration and compartmental ana-lysis were performed on the resulting data files (inMatlab version R2007a (The Mathworks Inc.)) to obtainthe resultant β-catenin measurements for each sample.In this study, either Wnt3A or the inhibitor CHX wasadded to the cells and spatial 3D image stacks acquired0, 1, 2 or 4 hours after adding the reagent.Note that for compartmental analysis, only two sub-

cellular compartments (nuclei and cytosol-membrane)are defined. Experimentally it was not possible to distin-guish the membrane compartment from the cytosol, pri-marily due to interferences from neighboring cells in 3Dspace. With improved image processing and membranemarkers, subsequent studies will be aimed at progressingto a three compartment model.

Validation of total whole cell β-catenin confocal measure-ments using quantification western blotsQuantitative western blots were conducted to validatethe 3D microscope fluorescence intensity quantitationtechnique. Specifically, HEK293T cell cultures were platedin 6 well plates with DMEM+ 10% FCS and culturedovernight (until about 70 ~ 80% confluent). The mediawas removed and replaced with new media containingWnt3A (40% Wnt3a L-cell CM in DMEM+ 10% FCS) orCHX (100 μg/ml) for respective wells at predefined times.The cells were incubated for the required time intervals(0, 1, 2 or 4 hours at 37˚C). HEK293T cultures had beenincubated with either Wnt3A or CHX for the 0, 1, 2 or4 hours at 37°C (i.e. similar to confocal quantificationexperiments).At the end of incubation, the cells were harvested,

lysed in lysis buffer on ice containing 1% triton-X100and 1% deoxycholate, and the debris spun down at13000 rpm for 10 minutes at 4°C. The cell extract wascollected as the whole cell lysate and stored at −20˚C.Quantitative SDS-PAGE was conducted with SDS samplebuffer (4x, NuPAGE LDS Sample Buffer Cat#NP0007,Invitrogen) and DTT using NuPAGE 4-12% Bis-Tris Gels.In the analysis, recombinant β-catenin proteins wereloaded in the same gel to form the standard curve forquantitation.Proteins were transferred to Nitrocellulose or PVDF

membranes and immuno-blotted with primary mousemonoclonal anti-β-catenin, mouse monoclonal anti-β-tubulin antibodies (BD PharMingen™, BD Biosciences,USA, cat#560381) and secondary antibody (Goat anti-mouse IRDye® 800CW, Li-COR Biosciences, and USAcat #926-32210). The resulting blot was scanned using


the Odyssey infra-red scanner at 800 μm and results an-alyzed using the LI-COR Odyssey™ application software(version 3.0, LI-COR, Inc., Lincoln, NE, USA), quantify-ing the protein band intensities and normalizing withthe respective β-tubulin intensities (as control). Thequantitative western blots results were compared to theconfocal 3D-measurements.

Computational modelsThe computational models developed in this study arereferred to as Models 1 and 2 (Figure 6A and B). Model1 was a single compartment model (Figure 6A), devel-oped using a full ODE reconstruction model of Lee et al.2003 Xenopus Wnt signaling model [21] and extendedby including additional protein complexes not found inthe Lee et al. model. Model 2 (Figure 6B) was a simpli-fied two compartment β-catenin model, with one com-partment representing the cell nucleus and the secondcompartment representing everything else and was re-ferred to as the cytosol-membrane compartment.

Model 1: single compartment Wnt pathway modelModel 1 extends the Lee et al. model to also account foradditional potential permutations of the key proteinscomplexes (specifically APC:β-catenin, Axin:β-catenin,GSK3β:β-catenin and GSK3β:Axin). The following reac-tions had been added, V18: binding of GSK3β with APC(see Additional file 1: Text and Table S2), V19: bindingof β-Catenin with Axin [7,55], V20: binding of β-Cateninwith GSK3β (see Additional file 1: Text and Table S2),V21: binding of GSK3β with Axin [6,55]. Furthermore,two reactions (V17: binding of β-Catenin with APC,V18: binding of β-catenin with TCF) have been updatedusing recently obtained unpublished mammalian bindingaffinity data (see Additional file 1: Text and Table S2).For the SBML file, see Additional file 2.

Model 2: two compartment β-catenin modelTo describe the two compartment imaging data detailingchanges in β-catenin concentration under Wnt andCHX, we developed a simplified model of this system.The aim was not to develop a complex Wnt signalingmodel containing all the potential protein-protein inter-actions and transport, synthesis and degradation pro-cesses. A common criticism of this approach has beenthat with so many unknown adjustable parameters it caneasily fit any experimental data. Instead, we use a simpli-fied model which groups multiple processes into genericinteractions and use this system to guide us towards un-derstanding what general processes need to occur withinthe cell and within the Wnt pathway for models to re-produce the experimental data. However simply stated,the model consists of a nuclear and a cytosol-membranecompartment. Each compartment has β-catenin interacting

reversibly with a single binding partner. β-catenin is syn-thesized and degraded only in the cytosol-membranecompartment, however it can be transported betweencompartments by passive diffusion and active transport.The schematic of the equations are as shown in Figure 6and see Additional file 3 for the SBML file. (Details ofmodel equations, numerical solutions and simulations areas described in the Tables 1 and 2, Additional file 1: Textand Table S7).

Model parameter calibrationThe computational models were constructed in the full‘ODE’ (ordinary differential equation) form and solved inMatlab version R2007a (The Mathworks Inc.) using thestiff solver ‘ode23s’ [56]. Model optimization was con-ducted using Matlab’s cost-minimization function ‘pat-ternsearch’ with a cost function based on the coefficientof determination, R2. Experimental and computationalintegration involved two stages (Figure 6C). Stage onewas the optimization of model parameters to a set of ex-perimental data calibrations (both steady state and tran-sient data). After the model calibration, stage two involvedthe validation of the calibrated model using a set of testtransient experimental data.Each stage required two modeling phases (see Figure 6C)

as described previously in ref [27]. Phase A calibrated themodel for the conservation of total protein concentrationduring protein redistribution into various protein com-plexes. Using experimentally measured steady state totalprotein concentrations as inputs, this phase obtains astable initial steady state for modeling. In this study, steadystate protein concentrations of key Wnt proteins from ref[27] were used for Phase A. Phase B optimized the modelto reproduce the transient behavior of the system ob-served experimentally.In Stage 1A of this study, the model calibration used the

total protein concentration as the initial and objectiveconcentrations, while the Stage 1B model optimizationused the transient β-catenin degradation from CHX per-turbation (either whole cell data (Figure 4A) or 2 compart-ment data (Figure 4B)). Stage two (model validation)required both Phase 1A and 1B to be optimized for thecalibration data (set as a prerequisite). In Stage 2A and 2B,using the optimized model, validation was conducted withthe transient Wnt3A perturbation data (either whole celldata (Figure 4A) or two compartment data (Figure 4B)).Based on the results of the validation, further calibrationand optimization of the model was carried out (repeatingboth stages) in order for the model to be consistent withthe experimental data (total protein concentrations andboth transient perturbation datasets).In Phase B, for β-catenin degradation, protein synthe-

sis rates were set to zero, while for Wnt perturbation,Wnt concentrations and inactive dishevelled were set to


the initial concentrations of 1nM and 100nM respect-ively (as per Lee et al. (2003) [20]). In order to identifythe best possible parameters for adjustments, sensitivity,steady state and topological, analyses were applied insupport of the optimization (see Additional file 1).

Additional files

Additional file 1: Supplementary Materials. This file provides furtherdetails of confocal imaging protocols and computational processinganalysis utilized in this study. Documentation includes SupplementaryText sections 1.1-1.10, Tables S1-S7 and Figures S1-S5.

Additional file 2: SBML file for Model 1. The SBML file Model1.xml canbe browsed using JDesigner of the Systems Biology Workbench. Pleasedownload JDesigner at http://sbw.sourceforge.net/, install it, and openthe SBML file Model1.xml to browse the Wnt signaling model.

Additional file 3: SBML file for Model 2. The SBML file Model2.xml canbe browsed using JDesigner of the Systems Biology Workbench. Pleasedownload JDesigner at http://sbw.sourceforge.net/, install it, and openthe SBML file Model2.xml to browse the Wnt signaling model. Use the‘Manage Parameter Sets’ option to switch between parameters for Model2 (active) and Model 2 (passive).

Competing interestsThe authors have declared that no competing interests exist.

Authors’ contributionsCT, YH and AWB conceived and designed the experiments. CT and YHperformed the experiments. CT, YH and AWB analyzed and interpreted theexperimental data. CT and BSG conducted the computational modeling. CT,BSG and DWS evaluated the computational model results. CT drafted themanuscript. CT, BSG, DWS and AWB participated in revising the paper. Allauthors have read and approved the manuscript.

AcknowledgementsThe authors wish to thank Dr Maree Faux, Dr Meredith Layton and MrCameron Nowell for their thoughtful discussions and assistance renderedand Dr Bruno Catimel (Ludwig Institute for Cancer Research (Austin), Victoria,Australia) for providing binding affinity data used during this study. Wethank the School of Engineering, University of Melbourne and the LudwigInstitute for Cancer Research, Melbourne-Parkville Branch (Victoria, Australia)for supporting CT.This work is also supported by National Health and Medical Research Council(NHMRC) Project Grants #542531, Program Grant #487922 and by funds fromthe Operational Infrastructure Support Program provided by the VictorianGovernment, Australia. The funders had no role in study design, datacollection and analysis, decision to publish, or preparation of the manuscript.Additionally the manuscript is solely the responsibility of the institutions andindividual authors and does not reflect the views of NHMRC.

Author details1Structural Biology Division, The Walter and Eliza Hall Institute of MedicalResearch, Parkville, VIC, Australia. 2Department of Medical Biology, Universityof Melbourne, Parkville, VIC, Australia. 3Ludwig Institute for Cancer Research,Melbourne-Parkville Branch, Parkville, VIC, Australia. 4Department ofInfrastructure Engineering, University of Melbourne, Parkville, VIC, Australia.5School of Computer Science and Software Engineering, The University ofWestern Australia, Perth, WA, Australia. 6Department of Surgery, University ofMelbourne, Parkville, VIC, Australia.

Received: 29 November 2013 Accepted: 31 March 2014Published: 8 April 2014

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doi:10.1186/1752-0509-8-44Cite this article as: Tan et al.: Analysis of Wnt signaling β-catenin spatialdynamics in HEK293T cells. BMC Systems Biology 2014 8:44.

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