Diffusible ligand and lateral inhibition dynamics for pattern formation

Abstract

Equivalent cells interact and become distinct, creating periodic patterns of different cell types during organism development. Interactions between neighbouring cells can be mediated by the binding of two different proteins, receptors and ligands, each anchored in a different cell membrane. After binding, a signal arises within the cell harbouring the receptor. Hence, when all cells can produce receptors and ligands, communication between cells can be bidirectional. Lateral inhibition occurs when the signal inhibits the production of the ligand and theoretical studies have shown that it can drive the spontaneous formation of patterns. There is experimental evidence pointing to soluble ligands that diffuse and signal. In this work, we study what the effect is of an additional diffusible ligand on the appearance of a pattern. Our results show that diffusion of the ligand has both positive and negative roles when it is coupled to lateral inhibition dynamics. Diffusion tends to destroy the pattern by stabilizing the homogeneous solution in a larger region of the parameter space and by reducing the difference between the cell types being formed. However, diffusion helps to create patterns with an exact periodicity.