Critical Point in Self-Organized Tissue Growth

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.

arXiv comment5 pages, 3 figures

References in corpus (2)

• Robust formation of morphogen gradients
• Scaling and regeneration of self-organized patterns

Cited by in corpus (8)

• Theory of mechano-chemical patterning in biphasic biological tissues
• Universality of biochemical feedback and its application to immune cells
• Mechanical Feedback in Regulating the Size of Growing Multicellular Spheroids
• Non-reciprocal hidden degrees of freedom: A unifying perspective on memory, feedback, and activity
• The role of topology and mechanics in uniaxially growing cell networks
• Stability of pattern formation in systems with dynamic source regions
• Hyperdisordered cell packing on a growing surface
• Dimensionality-Reduction in the Drosophila Wing as Revealed by Landmark-Free Measure-ments of Phenotype