Effects of multistability, absorbing boundaries and growth on Turing pattern formation

Turing patterns are a fundamental concept in developmental biology, describing how homogeneous tissues develop into self-organized spatial patterns. However, the classical Turing mechanism, which relies on linear stability analysis, often fails to capture the complexities of real biological systems, such as multistability, non-linearities, growth, and boundary conditions. Here, we explore the impact of these factors on Turing pattern formation, contrasting linear stability analysis with numerical simulations based on a simple reaction-diffusion model, motivated by synthetic gene-regulatory pathways. We demonstrate how non-linearities introduce multistability, leading to unexpected pattern outcomes not predicted by the traditional Turing theory. The study also examines how growth and realistic boundary conditions influence pattern robustness, revealing that different growth regimes and boundary conditions can disrupt or stabilize pattern formation. Our findings are critical for understanding pattern formation in both natural and synthetic biological systems, providing insights into engineering robust patterns for applications in synthetic biology.