One of the many ways cells transmit information within their volume is through steady spatial gradients of different proteins. However, the mechanism through which  such single-cell gradients form is not yet fully understood. We first demonstrate that one of the models for  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 then introduce an alternative for gradient formation via the coupling of the proteins within a single cell with a molecule  whose action is similar to that of morphogens in multi-cell assemblies ; the "morphogen" 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 "morphogen" dynamics within the cell ; it is the non-linearity that 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.
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.
A
proteins without any sources or sinks form
D
form
R
We first demonstrate that one
One
A
such
R
then introduce an alternative
introduce a novel mechanism
A
, that we call a "pronogen",
R
; the "morphogen"
, the pronogen
R
"morphogen"
pronogen
R
; it is the non-linearity that
, which
R
steady state
steady-state