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

Christian Hanauer1, Amrutha Palavalli2, Baiqun An2, Efe Ilker1,*, Jochen C. Rink2,3,†, and Frank Jülicher1,4,5,‡

  • *Contact author: efe.ilker@inserm.fr
  • †Contact author: jochen.rink@mpinat.mpg.de
  • ‡Contact author: julicher@pks.mpg.de
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PRX Life 4, 013014 – Published 3 February, 2026

DOI: https://doi.org/10.1103/n8n9-gptw

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.

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PRX Life 4, 013014– Published 3 February, 2026
  • Received 31 January 2025
  • Accepted 22 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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