Cellular patterns in Arabidopsis root epidermis emerge from gene regulatory network and diffusion dynamical feedback.

We propose a system biology approach to understand how GRNs' dynamical feedback with diffusion of some molecular components underlie the emergence of spatial cellular patterns. We use experimental data on the GRN underlying cell differentiation and spatial arrangement in the root epidermis of WT and mutant Arabidopsis phenotypes to validate our proposal. We test a generalized model of reaction-diffusion, which includes cell-to-cell interaction through lateral inhibition dynamics. The GRN corresponds to the reactive part, and diffusion involves two of its components. The Arabidopsis thaliana root epidermis has a distinct interspersed spatial pattern of hair and non-hair cells. Central to this process is the diffusion of CPC and GL3/EGL3 proteins, which drive lateral inhibition to coordinate cell identity. Existing models have shown a limited predictive power due to incomplete GRN topologies and the lack of explicit diffusion dynamics. Here, we introduce a diffusion-coupled meta-GRN model that integrates positive and negative feedback loops to simulate root epidermal pattern formation in wild-type and mutant lines under varying diffusion levels. By explicitly simulating CPC and GL3/EGL3 protein diffusion, in addition to recovering 28 single and multiple loss-of-function mutant phenotypes, as well as capturing trichoblast and atrichoblast spatial distributions relative to cortex cells, this study presents a 2-D morphospace or phenotypic landscape for epidermis patterning depending on diffusion levels. The findings highlight the critical role of protein diffusion and its dynamic feedback loops with complex GRN in shaping cellular spatial configurations and offer new insights into an extended reaction-diffusion dynamic patterning mechanism that is surely at play in other biological systems.