Construction and Experimental Validation of a Petri Net Model of Wnt/β-Catenin Signaling

The Wnt/β-catenin signaling pathway is important for multiple developmental processes and tissue maintenance in adults. Consequently, deregulated signaling is involved in a range of human diseases including cancer and developmental defects. A better understanding of the intricate regulatory mechanism and effect of physiological (active) and pathophysiological (hyperactive) WNT signaling is important for predicting treatment response and developing novel therapies. The constitutively expressed CTNNB1 (commonly and hereafter referred to as β-catenin) is degraded by a destruction complex, composed of amongst other AXIN1 and GSK3. The destruction complex is inhibited during active signaling leading to β-catenin stabilization and induction of β-catenin/TCF target genes. In this study we investigated the mechanism and effect of β-catenin stabilization during active and hyperactive WNT signaling in a combined in silico and in vitro approach. We constructed a Petri net model of Wnt/β-catenin signaling including main players from the plasma membrane (WNT ligands and receptors), cytoplasmic effectors and the downstream negative feedback target gene AXIN2. We simulated the model with active (i.e. WNT stimulation) and hyperactive (i.e. GSK3 inhibition) signaling, which led to the following observations: 1) A dose- and time-dependent response was observed for both WNT stimulation and GSK3 inhibition. 2) The Wnt-pathway activity was 2-fold higher for GSK3 inhibition compared to WNT stimulation. Both of these observations were corroborated by TCF/LEF luciferase reporter assays. Using this experimentally validated model we simulated the effect of the negative feedback regulator AXIN2 upon WNT stimulation and observed an attenuated β-catenin stabilization. We furthermore simulated the effect of APC inactivating mutations, yielding a stabilization of β-catenin levels comparable to the Wnt-pathway activities observed in colorectal and breast cancer. Our model can be used for further investigation and viable predictions of the role of Wnt/β-catenin signaling in oncogenesis and development. Author Summary Deregulated Wnt/β-catenin signaling is implicated in cancer and developmental defects. In this study we combined in silico and in vitro efforts to investigate the behavior of physiological and pathophysiological WNT signaling. We created a model of Wnt/β-catenin signaling that describes the core interactions: receptor activation, inhibition of downstream effectors and an important negative feedback mechanism. Simulations with the model demonstrated the expected dose- and time-dependent response for both conditions, and the Wnt-pathway activity was significantly higher for pathophysiological compared to physiological signaling. These observations were experimentally validated, which allowed us to investigate and predict the effect of the negative feedback and an inactivating cancer mutation on the Wnt-pathway activity. Our model provides mechanistic insight on the different conditions and can easily be extended and used to answer other questions on Wnt/β-catenin signaling in the area of cancer research and regenerative medicine.

[1]  Christof Niehrs,et al.  Wnt Induces LRP6 Signalosomes and Promotes Dishevelled-Dependent LRP6 Phosphorylation , 2007, Science.

[2]  K. Basler,et al.  β-Catenin hits chromatin: regulation of Wnt target gene activation , 2009, Nature Reviews Molecular Cell Biology.

[3]  Paul Polakis,et al.  Stabilization of β-Catenin by Genetic Defects in Melanoma Cell Lines , 1997, Science.

[4]  M. Berridge,et al.  Calcium signaling : a subject collection from Cold Spring Harbor perspectives in biology , 2012 .

[5]  M. Bienz,et al.  The function of BCL9 in Wnt/β-catenin signaling and colorectal cancer cells , 2008, BMC Cancer.

[6]  W. Birchmeier,et al.  Wnt signalling and its impact on development and cancer , 2008, Nature Reviews Cancer.

[7]  Hans Clevers,et al.  Armadillo Coactivates Transcription Driven by the Product of the Drosophila Segment Polarity Gene dTCF , 1997, Cell.

[8]  Jana Wolf,et al.  Mathematical modelling of Wnt/β-catenin signalling. , 2010, Biochemical Society transactions.

[9]  Michael Kühl,et al.  Functional interaction of β-catenin with the transcription factor LEF-1 , 1996, Nature.

[10]  W. Birchmeier,et al.  Functional interaction of an axin homolog, conductin, with beta-catenin, APC, and GSK3beta. , 1998, Science.

[11]  Akira Kikuchi,et al.  Axin, a negative regulator of the Wnt signaling pathway, forms a complex with GSK‐3β and β‐catenin and promotes GSK‐3β‐dependent phosphorylation of β‐catenin , 1998 .

[12]  David I. Smith,et al.  Mutations in AXIN2 cause colorectal cancer with defective mismatch repair by activating beta-catenin/TCF signalling (vol 26, pg 146, 2000) , 2000 .

[13]  J. Hurley,et al.  The molecular genetics of colorectal cancer , 2013, Frontline Gastroenterology.

[14]  Wei Hsu,et al.  The Mouse Fused Locus Encodes Axin, an Inhibitor of the Wnt Signaling Pathway That Regulates Embryonic Axis Formation , 1997, Cell.

[15]  Hans Clevers,et al.  Wnt Signaling through Inhibition of β-Catenin Degradation in an Intact Axin1 Complex , 2012, Cell.

[16]  Kirk W. Johnson,et al.  Selective glycogen synthase kinase 3 inhibitors potentiate insulin activation of glucose transport and utilization in vitro and in vivo. , 2003, Diabetes.

[17]  Yusuke Nakamura,et al.  AXIN1 mutations in hepatocellular carcinomas, and growth suppression in cancer cells by virus-mediated transfer of AXIN1 , 2000, Nature Genetics.

[18]  Hans Clevers,et al.  Activation of β-Catenin-Tcf Signaling in Colon Cancer by Mutations in β-Catenin or APC , 1997, Science.

[19]  Reinhart Heinrich,et al.  The Roles of APC and Axin Derived from Experimental and Theoretical Analysis of the Wnt Pathway , 2003, PLoS biology.

[20]  Mark Peifer,et al.  Decisions, decisions: beta-catenin chooses between adhesion and transcription. , 2005, Trends in cell biology.

[21]  D. Piwnica-Worms,et al.  Real-time imaging of β-catenin dynamics in cells and living mice , 2007, Proceedings of the National Academy of Sciences.

[22]  Kathleen R. Cho,et al.  Activation of AXIN2 expression by beta-catenin-T cell factor. A feedback repressor pathway regulating Wnt signaling. , 2002, The Journal of biological chemistry.

[23]  Yuri Kogan,et al.  A new validated mathematical model of the Wnt signalling pathway predicts effective combinational therapy by sFRP and Dkk. , 2012, The Biochemical journal.

[24]  Xi He,et al.  Wnt/beta-catenin signaling: components, mechanisms, and diseases. , 2009, Developmental cell.

[25]  F. Fagotto,et al.  The ins and outs of APC and β‐catenin nuclear transport , 2002 .

[26]  Jörg Stappert,et al.  β‐catenin is a target for the ubiquitin–proteasome pathway , 1997 .

[27]  Michael Kühl,et al.  Extended analyses of the Wnt/β‐catenin pathway: Robustness and oscillatory behaviour , 2007, FEBS letters.

[28]  Helen M Byrne,et al.  Toward a quantitative understanding of the Wnt/β‐catenin pathway through simulation and experiment , 2013, Wiley interdisciplinary reviews. Systems biology and medicine.

[29]  W. Weis,et al.  The β-catenin destruction complex. , 2013, Cold Spring Harbor perspectives in biology.

[30]  R. Moon,et al.  WNT signalling pathways as therapeutic targets in cancer , 2012, Nature Reviews Cancer.

[31]  J. Wolf,et al.  Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions , 2013, Front. Physiol..

[32]  C. Malbon,et al.  Abundance, complexation, and trafficking of Wnt/β-catenin signaling elements in response to Wnt3a , 2007, Journal of molecular signaling.

[33]  Paul Polakis,et al.  Wnt signaling in cancer. , 2012, Cold Spring Harbor perspectives in biology.

[34]  Walter Birchmeier,et al.  Hot papers in cell biology - J. Behrens, J.P. von Kries, M. Kuehl, L. Bruhn, D. Wedlich, R. Grosschedl, W. Birchmeier: "Functional interaction of beta-catenin with the transcription factor LEF-1" - Comments by Walter Birchmeier , 1999 .

[35]  Manisha Sharma,et al.  Targeting the β-catenin nuclear transport pathway in cancer. , 2014, Seminars in cancer biology.

[36]  Helen M Byrne,et al.  Elucidating the interactions between the adhesive and transcriptional functions of beta-catenin in normal and cancerous cells. , 2007, Journal of theoretical biology.

[37]  Hans Clevers,et al.  XTcf-3 Transcription Factor Mediates β-Catenin-Induced Axis Formation in Xenopus Embryos , 1996, Cell.

[38]  Luay Nakhleh,et al.  The Signaling Petri Net-Based Simulator: A Non-Parametric Strategy for Characterizing the Dynamics of Cell-Specific Signaling Networks , 2008, PLoS Comput. Biol..

[39]  Owen J. Sansom,et al.  Genetic Dissection of Differential Signaling Threshold Requirements for the Wnt/β-Catenin Pathway In Vivo , 2010, PLoS genetics.

[40]  K. Cadigan,et al.  Celebrating 30 Years of Wnt Signaling , 2012, Science Signaling.

[41]  Ajamete Kaykas,et al.  Zebrafish Prickle, a Modulator of Noncanonical Wnt/Fz Signaling, Regulates Gastrulation Movements , 2003, Current Biology.

[42]  Henri E. Bal,et al.  Executing multicellular differentiation: quantitative predictive modelling of C.elegans vulval development , 2009, Bioinform..

[43]  Chin Wee Tan,et al.  Wnt Signalling Pathway Parameters for Mammalian Cells , 2012, PloS one.

[44]  W. Blankesteijn,et al.  β‐Galactosidase enzyme fragment complementation for the measurement of Wnt/β‐catenin signaling , 2010, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[45]  C. Petri.  Kommunikation mit Automaten , 1962 .

[46]  F. Costantini,et al.  Mouse Axin and Axin2/Conductin Proteins Are Functionally Equivalent In Vivo , 2005, Molecular and Cellular Biology.

[47]  B. Doble,et al.  The ground state of embryonic stem cell self-renewal , 2008, Nature.

[48]  Bernhard G Herrmann,et al.  Segmentation in vertebrates: clock and gradient finally joined. , 2004, Genes & development.

[49]  Ioannis Xenarios,et al.  Hard-wired heterogeneity in blood stem cells revealed using a dynamic regulatory network model , 2013, Bioinform..

[50]  Hans Clevers,et al.  Negative Feedback Loop of Wnt Signaling through Upregulation of Conductin/Axin2 in Colorectal and Liver Tumors , 2002, Molecular and Cellular Biology.

[51]  Choun-Ki Joo,et al.  Wnt/β-Catenin/Tcf Signaling Induces the Transcription of Axin2, a Negative Regulator of the Signaling Pathway , 2002, Molecular and Cellular Biology.

[52]  Mark Peifer,et al.  Wnt signaling from development to disease: insights from model systems. , 2009, Cold Spring Harbor perspectives in biology.

[53]  Christof Niehrs,et al.  Casein kinase 1 γ couples Wnt receptor activation to cytoplasmic signal transduction , 2005, Nature.

[54]  W. J. Meek,et al.  THE FEDERATION OF AMERICAN SOCIETIES FOR EXPERIMENTAL BIOLOGY. , 1938, Science.

[55]  Wolfgang Reisig,et al.  Lectures on Petri Nets I: Basic Models , 1996, Lecture Notes in Computer Science.

[56]  Jeremy Nathans,et al.  A new member of the frizzled family from Drosophila functions as a Wingless receptor , 1996, Nature.

[57]  Mariann Bienz,et al.  Dynamic recruitment of axin by Dishevelled protein assemblies , 2007, Journal of Cell Science.

[58]  B. Cheyette,et al.  Dact1 presomitic mesoderm expression oscillates in phase with Axin2 in the somitogenesis clock of mice , 2006, Developmental dynamics : an official publication of the American Association of Anatomists.

[59]  E. Kuipers,et al.  Colorectal Cancers Choosing Sides , 2011 .

[60]  Xi He,et al.  A dual-kinase mechanism for Wnt co-receptor phosphorylation and activation , 2005, Nature.

[61]  David I. Smith,et al.  Mutations in AXIN2 cause colorectal cancer with defective mismatch repair by activating β-catenin/TCF signalling , 2000, Nature Genetics.

[62]  Ryoichiro Kageyama,et al.  Control of Hes7 Expression by Tbx6, the Wnt Pathway and the Chemical Gsk3 Inhibitor LiCl in the Mouse Segmentation Clock , 2013, PloS one.

[63]  Yoichi Kato,et al.  LDL-receptor-related proteins in Wnt signal transduction , 2000, Nature.

[64]  Kwang-Hyun Cho,et al.  Wnt pathway mutations selected by optimal β‐catenin signaling for tumorigenesis , 2006 .

[65]  Hans Clevers,et al.  Wnt/β-Catenin Signaling and Disease , 2012, Cell.

[66]  Henri E. Bal,et al.  Design Issues for Qualitative Modelling of Biological Cells with Petri Nets , 2008, FMSB.

[67]  R. Nusse,et al.  Lentiviral Vectors to Probe and Manipulate the Wnt Signaling Pathway , 2010, PloS one.

[68]  Weiqi Zhang,et al.  Generation of iPSCs from mouse fibroblasts with a single gene, Oct4, and small molecules , 2011, Cell Research.

[69]  E. Fearon,et al.  AXIN1 and AXIN2 variants in gastrointestinal cancers. , 2014, Cancer letters.

[70]  Matthias Mann,et al.  Axin-mediated CKI phosphorylation of beta-catenin at Ser 45: a molecular switch for the Wnt pathway. , 2002, Genes & development.