A mathematical Model for Inter-Cellular Inductive


In vertebrate limb, a group of specialized epithelial cells called Apical Ectodermal Ridge (AER) form at the boundary of dorsal and ventral limb ectoderm. Recent experiments suggest that AER forms at the boundary of Fringe expressing and Fringe non-expressing cells by a specific type of receptor-ligand interaction called as inductive signaling, involving the transmembrane proteins Notch, Serrate and Delta. Experiments conducted on Drosophila wing disc have shown that Fringe inhibits the binding ability of Serrate ligand to Notch and enhances that of Delta to Notch. Although several of the signaling elements have been identified experimentally, it remains unclear how the inter-cellular interactions can give rise to such a boundary of specialized cells. Here we present an ordinary differential equation (ODE) model involving Delta→Notch and Serrate→Notch interactions between juxtaposed Fringe expressing and Fringe nonexpressing cells. When simulated in a compartmentalized set up, this model gives rise to high Notch levels at the boundary of Fringe expressing and Fringe non-expressing cells.

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J. Srividhya, "A mathematical Model for Inter-Cellular Inductive," Computational Molecular Bioscience, Vol. 2 No. 3, 2012, pp. 102-107. doi: 10.4236/cmb.2012.23010.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] E. R. Andersson, R. Sandberg and U. Lendahl, “Notch Signaling: Simplicity in Design, Versatility in Function,” Development, Vol. 138, No. 17, 2011, pp. 3593-3612. doi:10.1242/dev.063610
[2] N. Haines and K. D. Irvine, “Glycosylation Regulates Notch Signalling,” Nature Reviews Molecular Cell Biology, Vol. 4, No. 10, 2003, pp. 786-797.
[3] S. J. Bray, “Notch Signalling: A Simple Pathway Becomes Complex,” Nature Reviews Molecular Cell Biology, Vol. 7, No. 9, 2006, pp. 678-689. doi:10.1038/nrm2009
[4] S. S. Blair, “Limb development: Marginal Fringe Benefits,” Current Biology, Vol. 7, No. 11, 1997, pp. R686-R690. doi:10.1016/S0960-9822(06)00356-3
[5] K. D. Irvine and T. F. Vogt, “Dorsal—Ventral Signaling in Limb Development,” Current Opinion in Cell Biology, Vol. 9, No. 6, 1997, pp. 867-876. doi:10.1016/S0955-0674(97)80090-7
[6] V. Hamburger and H. L. Hamilton, “A Series of Normal Stages in the Development of the Chick Embryo,” Developmental Dynamics, Vol. 195, No. 4, 1992, pp. 231-272. doi:10.1002/aja.1001950404
[7] B. A. Parr and A. P. McMahon, “Dorsalizing Signal Wnt-7a Required for Normal Polarity of D-V and A-P Axes of Mouse Limb,” Nature, Vol. 374, No. 6520, 1995, pp. 350-353. doi:10.1038/374350a0
[8] R. D. Riddle, et al., “Induction of the LIM Homeobox Gene Lmx1 by WNT6a Establishes Dorsoventral Pattern in the Vertebrate Limb,” Cell, Vol. 83, No. 4, 1995, pp. 631-640. doi:10.1016/0092-8674(95)90103-5
[9] C. Rodriguez-Esteban, et al., “Radical Fringe Positions the Apical Ectodermal Ridge at the Dorsoventral Boundary of the Vertebrate Limb,” Nature, Vol. 386, No. 6623, 1997, pp. 360-366. doi:10.1038/386360a0
[10] T. Klein and A. M. Arias, “Interactions among Delta, Serrate and Fringe Modulate Notch Activity during Drosophila Wing Development,” Development, Vol. 125, No. 15, 1998, pp. 2951-2962.
[11] C. Rauskolb, T. Correia and K. D. Irvine, “Fringe-Dependent Separation of Dorsal and Ventral Cells in the Drosophila Wing,” Nature, Vol. 401, No. 6752, 1999, pp. 476-480. doi:10.1038/46786
[12] E. Laufer, et al., “Expression of Radical Fringe in Limb-Bud Ectoderm Regulates Apical Ectodermal Ridge Formation,” Nature, Vol. 386, No. 6623, 1997, pp. 366-373. doi:10.1038/386366a0
[13] K. D. Irvine and E. Wieschaus, “Fringe, a Boundary-Specific Signaling Molecule, Mediates Interactions between Dorsal and Ventral Cells during Drosophila Wing Development,” Cell, Vol. 79, No. 4, 1994, pp. 595-606. doi:10.1016/0092-8674(94)90545-2
[14] M. Milan and S. M. Cohen, “A Re-Evaluation of the Contributions of Apterous and Notch to the Dorsoventral Lineage Restriction Boundary in the Drosophila Wing,” Development, Vol. 130, No. 3, 2003, pp. 553-562. doi:10.1242/dev.00276
[15] S. Koelzer and T. Klein, “Regulation of Expression of Vg and Establishment of the Dorsoventral Compartment Boundary in the Wing Imaginal Disc by Suppressor of Hairless,” Developmental Biology, Vol. 289, No. 1, 2006, pp. 77-90. doi:10.1016/j.ydbio.2005.10.008
[16] J. F. de Celis and S. Bray, “Feed-Back Mechanisms Affecting Notch Activation at the Dorsoventral Boundary in the Drosophila Wing,” Development, Vol. 124, No. 17, 1997, pp. 3241-3251.
[17] J.R. Collier, et al., “Pattern Formation by Lateral Inhibition with Feedback: A Mathematical Model of Delta-Notch Intercellular Signalling,” Journal of Theoretical Biology, Vol. 183, No. 4, 1996, pp. 429-446. doi:10.1006/jtbi.1996.0233
[18] H.M. Sauro, et al., “Next Generation Simulation Tools: The Systems Biology Workbench and BioSPICE Integration,” OMICS: A Journal of Integrative Biology, Vol. 7, No. 4, 2003, pp. 355-372. doi:10.1089/153623103322637670

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