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Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems

Vascular tissue in plants provides a resource distribution network for water and nutrients that exhibits remarkable diversity in patterning among different species. In many succulent plants, the vascular network includes longitudinally-oriented supplemental vascular bundles (SVBs) in the central cor...

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Autor principal: Hearn, David J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6715405/
https://www.ncbi.nlm.nih.gov/pubmed/31339881
http://dx.doi.org/10.1371/journal.pone.0219055
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author Hearn, David J.
author_facet Hearn, David J.
author_sort Hearn, David J.
collection PubMed
description Vascular tissue in plants provides a resource distribution network for water and nutrients that exhibits remarkable diversity in patterning among different species. In many succulent plants, the vascular network includes longitudinally-oriented supplemental vascular bundles (SVBs) in the central core of the succulent stems and roots in addition to the more typical zone of vascular tissue development (vascular cambium) in a cylinder at the periphery of the succulent organ. Plant SVBs evolved in over 38 plant families often in tandem with evolutionary increases in stem and root parenchyma storage tissue, so it is of interest to understand the evolutionary-developmental processes responsible for their recurrent evolution and patterning. Previous mathematical models have successfully recreated the two-dimensional vascular patterns in stem and root cross sections, but such models have yet to recreate three-dimensional vascular patterning. Here, a stochastic reaction-diffusion model of plant vascular bundle patterning is developed in an effort to highlight a potential mechanism of three dimensional patterning–Turing pattern formation coupled with longitudinal efflux of a regulatory molecule. A relatively simple model of four or five molecules recreated empirical SVB patterns and many other common vascular arrangements. SVBs failed to develop below a threshold width of parenchymatous tissues, suggesting a mechanism of evolutionary character loss due to changes in the spatial context in which development takes place. Altered diffusion rates of the modeled activator and substrate molecules affected the number and size of the simulated SVBs. This work provides a first mathematical model employing a stochastic Turing-type mechanism that recreates three dimensional vascular patterns seen in plant stems. The model offers predictions that can be tested using molecular-genetic approaches. Evolutionary-developmental ramifications concerning evolution of diffusion rates, organ size and geometry are discussed.
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spelling pubmed-67154052019-09-10 Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems Hearn, David J. PLoS One Research Article Vascular tissue in plants provides a resource distribution network for water and nutrients that exhibits remarkable diversity in patterning among different species. In many succulent plants, the vascular network includes longitudinally-oriented supplemental vascular bundles (SVBs) in the central core of the succulent stems and roots in addition to the more typical zone of vascular tissue development (vascular cambium) in a cylinder at the periphery of the succulent organ. Plant SVBs evolved in over 38 plant families often in tandem with evolutionary increases in stem and root parenchyma storage tissue, so it is of interest to understand the evolutionary-developmental processes responsible for their recurrent evolution and patterning. Previous mathematical models have successfully recreated the two-dimensional vascular patterns in stem and root cross sections, but such models have yet to recreate three-dimensional vascular patterning. Here, a stochastic reaction-diffusion model of plant vascular bundle patterning is developed in an effort to highlight a potential mechanism of three dimensional patterning–Turing pattern formation coupled with longitudinal efflux of a regulatory molecule. A relatively simple model of four or five molecules recreated empirical SVB patterns and many other common vascular arrangements. SVBs failed to develop below a threshold width of parenchymatous tissues, suggesting a mechanism of evolutionary character loss due to changes in the spatial context in which development takes place. Altered diffusion rates of the modeled activator and substrate molecules affected the number and size of the simulated SVBs. This work provides a first mathematical model employing a stochastic Turing-type mechanism that recreates three dimensional vascular patterns seen in plant stems. The model offers predictions that can be tested using molecular-genetic approaches. Evolutionary-developmental ramifications concerning evolution of diffusion rates, organ size and geometry are discussed. Public Library of Science 2019-07-24 /pmc/articles/PMC6715405/ /pubmed/31339881 http://dx.doi.org/10.1371/journal.pone.0219055 Text en © 2019 David J. Hearn http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Hearn, David J.
Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
title Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
title_full Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
title_fullStr Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
title_full_unstemmed Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
title_short Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
title_sort turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6715405/
https://www.ncbi.nlm.nih.gov/pubmed/31339881
http://dx.doi.org/10.1371/journal.pone.0219055
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