Toward a quantitative understanding of the Wnt/β‐catenin pathway through simulation and experiment

(a) Wnt signaling pathways. Different combinations of Wnt ligands and receptor at the cell surface can initiate specific Wnt pathways. The ‘canonical’ β‐catenin/TCF (T‐cell factor) pathway is the best described (C), with the Ca2+ pathway (A) and planar cell polarity (PCP) pathway (B) also downstream of Frizzled receptors. Ryk and Ror are tyrosine kinase receptors also implicated in mediating Wnt signaling (pathways D and E). (b) Wnt/β‐catenin signaling pathway. ‘OFF’ state: ZNRF3 acts as a ubiquitin ligase to promote Frizzled and low‐density lipoprotein receptor protein 6 (LRP6) turnover. β‐Catenin is held in the destruction complex where it is phosphorylated and targeted for degradation by the proteasome in the absence of Wnt ligand. TCF transcription factors are complexed with transcriptional inhibitors such as Transducer like Enhancer of split/Groucho, and target genes are not transcribed. ‘ON’ state: Rspo promotes ZNRF3 turnover by binding to ZNRF3 and LGR4, leading to stabilization of LRP6 and Frizzled and potentiation of Wnt signaling. Wnt binding causes disassociation of the complex in a Dvl‐dependent manner, allowing the nuclear translocation of β‐catenin and displacement of Groucho. Additional transcriptional co‐activators and histone modifiers such as Brg1, CBP, Bcl9, and Pygopus are recruited to activate transcription of target genes.

Wnt signaling and the cell cycle. Recent studies have elucidated many mechanisms that link Wnt signaling to events during the mitotic cell cycle. The Wnt target genes, CyclinD1 and Myc, are key regulators of G1, while Axin2 has been suggested to have a pro‐proliferative role at G2/M. Dvl, Axin, β‐catenin GSK3, and APC have been shown to associate with centrosomes and/or kinetochores during mitosis, with Wnt signaling also reported to regulate the orientation of the mitotic spindle. The G2/M‐dependent induction of CyclinY activates the CDK14 kinase, leading to increased levels of LRP6 phosphorylation, which enhances Wnt signaling and β‐catenin accumulation. The increased levels of β‐catenin may, via effects at G1/S and G2/M, allow progression through cell cycle checkpoints. Red arrows represent canonical Wnt/β‐catenin pathway signaling, black arrows represent responses that result from cell cycle‐dependent changes and dashed arrows represent further molecular binding/phosphorylation interactions.

Modeling—state of the art. Mathematical models of Wnt signaling may be classified according to the scale at which they are built: biochemical, subcellular, cellular, and tissue. Different aspects of Wnt signaling biology is highlighted within each of the different scales, with circular boxes indicating biological complexity that has yet to be modeled in the mathematical studies indicated above.