Tissue growth constrains root organ outlines into an isometrically scalable shape

Motohiro Fujiwara,Keiji Nakajima,Hidehiro Fukaki,Koichi Fujimoto,Satoru Tsugawa,Tatsuaki Goh

doi:10.1242/dev.196253

Motohiro Fujiwara, Keiji Nakajima + Show 4 more

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https://doi.org/10.1242/dev.196253

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Abstract

ABSTRACTOrgan morphologies are diverse but also conserved under shared developmental constraints among species. Any geometrical similarities in the shape behind diversity and the underlying developmental constraints remain unclear. Plant root tip outlines commonly exhibit a dome shape, which likely performs physiological functions, despite the diversity in size and cellular organization among distinct root classes and/or species. We carried out morphometric analysis of the primary roots of ten angiosperm species and of the lateral roots (LRs) of Arabidopsis, and found that each root outline was isometrically scaled onto a parameter-free catenary curve, a stable structure adopted for arch bridges. Using the physical model for bridges, we analogized that localized and spatially uniform occurrence of oriented cell division and expansion force the LR primordia (LRP) tip to form a catenary curve. These growth rules for the catenary curve were verified by tissue growth simulation of developing LRP development based on time-lapse imaging. Consistently, LRP outlines of mutants compromised in these rules were found to deviate from catenary curves. Our analyses demonstrate that physics-inspired growth rules constrain plant root tips to form isometrically scalable catenary curves.

Highlights

Plant and animal organ forms are defined by size and shape
Despite the morphological diversity of root tip in size and internal cellular organization (Fig. S5) (Clowes, 2000; Hamamoto et al, 2006; Heimsch and Seago, 2008), our morphometric analysis revealed that the outlines of the primary roots (PRs) of ten angiosperm species and Arabidopsis lateral roots (LRs) commonly fitted to a catenary curve and its essentially equivalent curve, a catenary-closest ellipse (Fig. 2A; Figs S3,S4,S6)
The catenary curve is seen in free-hanging chains and bridges (Fig. 2B), and has several interesting features in mathematics, physics and architecture, such as (1) being represented by a simple mathematical function with a single catenary parameter

Summary

Introduction

Plant and animal organ forms (i.e. outline morphologies of organs) are defined by size and shape. Received 23 August 2020; Accepted 11 January 2021 diversity, organ outlines can collapse onto a single common shape across species by rescaling of individual size [e.g. cannon bones of ox, sheep and giraffe (Thompson, 1917), and beaks of songbirds (Abzhanov, 2017; Campas et al, 2010)]. The scaling of songbird beaks is imposed by developmental programs shared among species (Abzhanov, 2017; Campas et al, 2010; Fritz et al, 2014). The scaling of organ size (e.g. proportionality and allometry to body size) has been extensively studied (Niklas, 1994; Schmidt-Nielsen, 1984), quantitative assessments on the shape scaling and underlying developmental constraints have only been reported in a limited number of cases, as mentioned above

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