Protein gradients in single cells induced by their coupling to "morphogen"-like diffusion

TL;DR

This paper proposes a new mechanism for forming protein concentration gradients within single cells by coupling proteins to a morphogen-like molecule called a pronogen, leading to stable steady-state gradients.

Contribution

It introduces a novel model where proteins couple with a pronogen to form stable gradients, expanding understanding beyond traditional differential diffusion models.

Findings

Gradients are linearly stable to perturbations.

The model predicts steady-state protein concentration profiles.

Coupling with pronogens enables gradient formation without large diffusion ratios.

Abstract

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.