A Model for Self-Organized Growth, Branching, and Allometric Scaling of the Planarian Gut

TL;DR

This paper combines experimental and theoretical approaches to understand how the branched structure of the planarian gut scales with organism size, revealing power-law relationships and a self-organized growth model.

Contribution

It introduces a novel theoretical framework linking interface dynamics and reaction-diffusion processes to organ scaling, supported by experimental data on planarian gut morphology.

Findings

Gut properties scale with organism size according to power laws

A shape instability of the interface leads to self-organized branching patterns

The model reproduces observed scaling laws of the planarian gut

Abstract

The growth and scaling of organs is a fundamental aspect of animal development. However, how organs grow to the right size and shape required by physiological demands, remains largely unknown. Here, we provide a framework combining theory and experiment to study the scaling of branched organs. As a biological model, we focus on the branching morphogenesis of the planarian gut, which is a highly branched organ responsible for the delivery of nutrients. Planarians undergo massive body size changes requiring gut morphology to adapt to these size variations. Our experimental analysis shows that various gut properties scale with organism size according to power laws. We introduce a theoretical framework to understand the growth and scaling of branched organs. Our theory considers the dynamics of the interface between organ and surrounding tissue to be controlled by a morphogen and illustrates how a shape instability of this interface can give rise to the self-organized formation and growth of complex branched patterns. Considering the reaction-diffusion dynamics in a growing domain representative of organismal growth, we show that a wide range of scaling behaviors of the branching pattern emerges from the interplay between interface dynamics and organism growth. Our model can recapitulate the scaling laws of planarian gut morphology that we quantified and also opens new directions for understanding allometric scaling laws in various other branching systems in organisms.