Robustness of morphogen gradients with ``bucket brigade'' transport through membrane-associated non-receptors (Q1948824)

The paper is devoted to a mathematical analysis of a model of morphogen gradient formation in the presence of non-receptors with both diffusion of free morphogens and the movement of morphogens bound to non-receptors. A functional boundary value problem is introduced and existence, uniqueness and linear stability of a biologically acceptable steady-state solution is proven. The robustness of this steady-state solution with respect to significant changes in the morphogen synthesis rate is analyzed. It is proven that the model is able to produce robust biological morphogen gradients when production and degradation rates of morphogens are large enough and non-receptors are abundant. The results in this paper provide mathematical and biological insight to a mechanism of achieving stable robust long distance morphogen gradients.