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There are two phases of Wnt signalling in early vertebrate embryogenesis: very early, maternal Wnt signalling promotes dorsal development, and slightly later, zygotic Wnt signalling promotes ventral and lateralmesoderm induction. However, recent molecular biology analysis has revealed more complexity among the direct Wnt target genes, with at least five classes. Here in order to test the logic and the dynamics of a new Gene Regulatory Network model suggested by these discoveries we use mathematical modelling based on ordinary differential equations (ODEs). Our mathematical modelling of this Gene Regulatory Network reveals that a simplified model, with one "super-gene" for each class is sufficient to a large extent to describe the regulatory behaviour previously observed experimentally.
Fig. 1. A gene regulatory network built to represent dorsoventral axis induction in Xenopus tropicalis embryos, with certain genes chosen from each of five classes of direct Wnt target genes. The first class of Wnt target genes (nodal and siamois) are regulated by maternal Wnt/-catenin signalling and maternal nodal/TGF signalling. The second class of Wnt target genes (frzb, chordin, goosecoid and lefty) are regulated by early maternal Wnt/-catenin signalling and products of the first class of Wnt target genes (i.e., SIAMOIS and NODAL) in a coherent, feed-forward regulatory loop manner. The third class of Wnt target genes (axin2) is regulated by both early maternal Wnt/-catenin signalling and zygotic Wnt8a/-catenin signalling. The fourth class of Wnt target genes (msx1) are co-regulated by zygotic BMP signalling and zygotic WNT8a/-catenin signalling. The fifth class of Wnt target genes (cdx2) is co-regulated by zygotic FGF signalling and zygotic Wnt8a/-catening signalling. Model constructed using BioTapestry.
Fig. 2. Protein concentrations as a function of time for a mathematical model representing dorsoventral axis induction in Xenopus, for modelling ventraltissue. The units for both concentration and time are arbitrary. Note that the modelling results in simulated high expression of msx1 and cdx and that plots for genes with similar regulation mechanisms (frzb, chordin, goosecoid and lefty) are difficult to distinguish.
Fig. 3. Protein concentrations as a function of time for a mathematical model representing dorsoventral axis induction in Xenopus, for modelling dorsal tissue. Initial NODAL concentration is set to 0.1 while initial -CATENIN concentration is set to 1. The units for both concentration and time are arbitrary. Note that the modelling results in simulated high expression of frzb, chordin, goosecoid and lefty but plots for genes with similar regulation mechanisms are difficult to distinguish.
Fig. 4. A simplified gene regulatory network with only one âsuper-geneâ per class. Model constructed using BioTapestry.
Fig. 5. Protein concentrations as a function of time for a simplified mathematical model with only one “super-gene†per class, in ventraltissue. The units for both concentration and time are arbitrary. Note that the modelling results in simulated high expression of msx1 and cdx.
Fig. 6. Protein concentrations as a function of time for a simplified mathematical model with only one “super-gene†per class, in dorsal tissue. Initial NODAL concentration is set to 0.1 while initial B-CATENIN concentration is set to 1. The units for both concentration and time are arbitrary. Note that the modelling results in simulated high expression of the FrzB/Chordin/Goosecoid/Lefty “super geneâ€.
Fig. 7. Simulation of the over-expression of NS by setting initial NS concentration to 1 while keeping initial B-CATENIN at 0. Note that the modelling results in simulated high expression of the FrzB/Chordin/Goosecoid/Lefty âsuper geneâ.
Fig. 8. Simulation of the knock-down of Class II genes by setting with high initial NS and -CATENIN concentration.
Fig. 9. Simulation of the experimental over-activation of Class II genes by setting initial âFCGLâ concentration to 1 while keeping initial NS and B-CATENIN at 0. Note the high level of FCGL product.
Fig. 10. Simulation of the experimental over-activation of BMP by setting its initial concentration to 1 with initial NODAL and B-CATENIN at 1. Note that modelling essentially simulates a dorsal response with high expression of the FrzB/Chordin/Goosecoid/Lefty “super gene†despite some expression of msx1.
Fig. 11. Simulation of the experimental over-activation of FGF by setting its initial concentration to 1 with initial NODAL and B-CATENIN at 1. Note that modelling results in a mixed response with high expression of the FrzB/Chordin/Goosecoid/Lefty “super gene†and cdx.
