Critical Point in Self-Organized Tissue Growth

TL;DR

This paper develops a theory of pattern formation in growing tissues, identifying a critical point where growth and pattern scaling are proportionally linked, with applications to fruit fly wing development.

Contribution

It introduces a novel theoretical framework for understanding how tissue growth influences pattern formation through feedback mechanisms, highlighting a critical point in this process.

Findings

Identification of a critical point in tissue growth dynamics

Proportional scaling of patterns with tissue length

Quantitative validation in Drosophila wing development

Abstract

We present a theory of pattern formation in growing domains inspired by biological examples of tissue development. Gradients of signaling molecules regulate growth, while growth changes these graded chemical patterns by dilution and advection. We identify a critical point of this feedback dynamics, which is characterized by spatially homogeneous growth and proportional scaling of patterns with tissue length. We apply this theory to the biological model system of the developing wing of the fruit fly \textit{Drosophila melanogaster} and quantitatively identify signatures of the critical point.