  One of the many ways cells transmit information within their volume is
through steady spatial gradients of different proteins. However, the mechanism
through which proteins without any sources or sinks form such single-cell
gradients is not yet fully understood. One of the models for such gradient
formation, based on differential diffusion, is limited to proteins with large
ratios of their diffusion constants or to specific protein-large molecule
interactions. We introduce a novel mechanism for gradient formation via the
coupling of the proteins within a single cell with a molecule, that we call a
"pronogen", whose action is similar to that of morphogens in multi-cell
assemblies, the pronogen is produced with a fixed flux at one side of the cell.
This coupling results in an effectively non-linear diffusion degradation model
for the pronogen dynamics within the cell, which leads to a steady-state
gradient of the protein concentration. We use a stability analysis to show that
these gradients are linearly stable with respect to perturbations.
