Diffusiophoretic assembly of finite-size cells via reaction-diffusion chemical signal: imperfect Turing patterns

Turing patterns, central to biophysics, emerge from the nonequilibrium interactions between diffusive and reactive components, governed by short-range self-enhancement and long-range inhibition. However, classical Turing models are often too simplistic to capture multiscale and imperfect nature of biological patterns, as they rely on a single length scale balancing the reaction and diffusion properties. We present a framework that couples the diffusiophoretic assembly of finite-size cells with background chemical gradients arising from a reaction–diffusion system, while accounting for intercellular interactions. This formulation introduces additional control parameters such as the Péclet number, cell size distribution, and intercellular forces, which together allow us to recreate the complex structural features observed in natural systems, such as the skin patterns of the Ornate Boxfish. Our study highlights imperfections such as variable pattern thickness, packing constraints, and inconsistencies in the pattern. The current framework extends classical Turing theory by integrating colloidal physics and is also relevant to the other systems, including intracellular phase separation, bioinspired engineering, and soft-material design.