Abstract
A previously investigated basic model (System B) for the study of signaling morphogen gradient formation that allows for reversible binding of morphogens (aka ligands) with signaling receptors, degradation of bound morphogens and diffusion of unbound morphogens is extended to include the effects of membrane-bound non-signaling molecules (or non-receptors for short) such as proteoglycans that bind reversibly with the same morphogens and degrade them. Our main goal is to delineate the effects of the presence of non-receptors on the existence and properties of the steady-state concentration gradient of signaling ligand–receptor complexes. Stability of the steady-state morphogen gradients is established and the time to reach steady-state behavior after the onset of morphogen production will be analyzed. The theoretical findings offer explanations for observations reported in several previous experiments on Drosophila wing imaginal discs.
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Lander, A.D., Nie, Q. & Wan, F.Y.M. Membrane-Associated Non-Receptors and Morphogen Gradients. Bull. Math. Biol. 69, 33–54 (2007). https://doi.org/10.1007/s11538-006-9152-2
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DOI: https://doi.org/10.1007/s11538-006-9152-2