Imperfect Turing Patterns: Diffusiophoretic Assembly of Hard Spheres via Reaction-Diffusion Instabilities

TL;DR

This paper introduces a new model of Turing patterns incorporating diffusiophoretic assembly and intercellular interactions, capturing natural pattern imperfections and multi-scale structures beyond classical single-scale formulations.

Contribution

It develops a framework that integrates diffusiophoretic assembly with reaction-diffusion instabilities, accounting for imperfections and multi-scale features in biological patterns.

Findings

Reproduces natural pattern features with structural variations

Identifies key control parameters like Péclet number and cell size

Demonstrates pattern imperfections such as breakups and thickness variations

Abstract

Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic length scale that balances reaction and diffusion, making them overly simplistic for describing biological patterns, which often exhibit multi-scale structures, grain-like textures, and inherent imperfections. Here, we integrate diffusiophoretically-assisted assembly of finite-sized cells, driven by a background chemical gradient in a Turing pattern, while also incorporating intercellular interactions. This framework introduces key control parameters, such as the P\'{e}clet number, cell size distribution, and intercellular interactions, enabling us to reproduce strikingly similar structural features observed in natural patterns. We report imperfections, including spatial variations in pattern thickness, packing limits, and pattern breakups. Our model not only deepens our understanding but also opens a new line of inquiry into imperfect Turing patterns that deviate from the classical formulation in significant ways.