| Abstract | Patterning by morphogens is the predominant model by which cells acquire positional information during animal development. However, how cells respond to morphogen gradients that change with time, or how and when concentration thresholds are interpreted to form reproducible patterns of gene expression is largely unknown. Although recent studies have highlighted the importance of morphogen gradient dynamics, how these transient gradients contribute to developmental patterning has not been explored in detail, in part because the difficulty of isolating transient from steady-state effects. Here we present a mathematical method to identify perturbations on the gene networks controlling developmental patterning that affect the transient, but leave invariant the shape of the steady-state morphogen gradient. The set of these perturbations defines a geometric object in parameter space named Steady-State Invariant Manifold (SSIM). In many systems, SSIMs can be obtained analytically providing a tool to study the role of transient gradients in developmental pattern formation. As a case study, we demonstrate how this theoretical approach can be used to study the dynamic properties of Hedgehog signaling in the wing disc of the fruitfly Drosophila melanogaster. Finally, we discuss how this method can be employed to design experiments that permit to assay the function of morphogen gradients dynamics in a more general way. |
|---|
