Diffusiophoresis-Enhanced Turing Patterns

Turing patterns are essential in biophysics, emerging from short-range activation and long-range inhibition processes in reaction-diffusion systems. However, their paradigm is based on diffusive transport processes, which yields Turing patterns that are less sharp than the ones observed in nature. A complete physical description of why the Turing patterns observed in nature are significantly sharper than state-of-the-art models remains unknown. Here, we propose a novel solution to this phenomenon by investigating the role of diffusiophoresis in Turing patterns. The inclusion of diffusiophoresis enables one to generate patterns of colloidal particles with significantly finer length scales than the accompanying chemical patterns. Further, diffusiophoresis enables a degree of control that allows for robust modeling of fish patterns which would otherwise require ad hoc techniques. We present a scaling analysis indicating that chromatophores, ubiquitous in biological pattern formation, are likely diffusiophoretic, and that their Péclet number controls the pattern enhancement. Our theoretical results are strongly supported by the recent experiments on diffusiophoretic pattern formation and sharpening of biomolecules in the MinDE protein system of extit{E. coli} and we illustrate qualitative agreement between the two. This discovery suggests important features of biological pattern formation can be explained with a universal mechanism that is quantified straightforwardly from the fundamental physics of colloids and inspires future exploration of adaptive materials, lab-on-a-chip devices, and tumorigenesis. Alessio and Gupta (2023): arXiv:2305.11372