# Robustness of spatial patterns in buffered reaction-diffusion systems and its reciprocity with phase plasticity

## TL;DR

This paper introduces a buffered reaction-diffusion model that enhances pattern robustness and reveals a reciprocal relationship between pattern wavelength stability and phase plasticity, with implications for biological systems.

## Contribution

It proposes a novel buffered reaction-diffusion system demonstrating how buffer molecules confer pattern robustness and uncovers a reciprocal link with phase plasticity.

## Key findings

- Robustness of pattern wavelength is achieved through buffer molecule dynamics.
- Scaling properties explain the robustness and reciprocity in the system.
- Relevance of the reciprocity to biological developmental processes.

## Abstract

Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigated, little is known about a general mechanism for achieving robustness in reaction-diffusion systems. Here, we propose a buffered reaction-diffusion system, in which active states of chemicals mediated by buffer molecules contribute to reactions, and demonstrate that robustness of the pattern wavelength is achieved by the dynamics of the buffer molecule. This robustness is analytically explained as a result of the scaling properties of the buffered system, which also lead to a reciprocal relationship between the wavelength's robustness and the plasticity of the spatial phase upon external perturbations. Finally, we explore the relevance of this reciprocity to biological systems.