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The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modeled as an elongating path or series of segments, without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2014
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3899046/ https://www.ncbi.nlm.nih.gov/pubmed/24465607 http://dx.doi.org/10.1371/journal.pone.0085585 |
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author | Bucksch, Alexander Turk, Greg Weitz, Joshua S. |
author_facet | Bucksch, Alexander Turk, Greg Weitz, Joshua S. |
author_sort | Bucksch, Alexander |
collection | PubMed |
description | Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modeled as an elongating path or series of segments, without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by expanding the area around the completed elongated path. Modeling expansion in this way can lead to contradictions in the physical plausibility of the resulting surface and to uncertainty about how the object reached certain regions of space. Here, we introduce fiber walks as a self-avoiding random walk model for tip-driven growth processes that includes lateral expansion. In 2D, the fiber walk takes place on a square lattice and the space occupied by the fiber is modeled as a lateral contraction of the lattice. This contraction influences the possible subsequent steps of the fiber walk. The boundary of the area consumed by the contraction is derived as the dual of the lattice faces adjacent to the fiber. We show that fiber walks generate fibers that have well-defined curvatures, and thus enable the identification of the process underlying the occupancy of physical space. Hence, fiber walks provide a base from which to model both the extension and expansion of physical biological objects with finite thickness. |
format | Online Article Text |
id | pubmed-3899046 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-38990462014-01-24 The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion Bucksch, Alexander Turk, Greg Weitz, Joshua S. PLoS One Research Article Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modeled as an elongating path or series of segments, without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by expanding the area around the completed elongated path. Modeling expansion in this way can lead to contradictions in the physical plausibility of the resulting surface and to uncertainty about how the object reached certain regions of space. Here, we introduce fiber walks as a self-avoiding random walk model for tip-driven growth processes that includes lateral expansion. In 2D, the fiber walk takes place on a square lattice and the space occupied by the fiber is modeled as a lateral contraction of the lattice. This contraction influences the possible subsequent steps of the fiber walk. The boundary of the area consumed by the contraction is derived as the dual of the lattice faces adjacent to the fiber. We show that fiber walks generate fibers that have well-defined curvatures, and thus enable the identification of the process underlying the occupancy of physical space. Hence, fiber walks provide a base from which to model both the extension and expansion of physical biological objects with finite thickness. Public Library of Science 2014-01-22 /pmc/articles/PMC3899046/ /pubmed/24465607 http://dx.doi.org/10.1371/journal.pone.0085585 Text en © 2014 Bucksch et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Bucksch, Alexander Turk, Greg Weitz, Joshua S. The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion |
title | The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion |
title_full | The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion |
title_fullStr | The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion |
title_full_unstemmed | The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion |
title_short | The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion |
title_sort | fiber walk: a model of tip-driven growth with lateral expansion |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3899046/ https://www.ncbi.nlm.nih.gov/pubmed/24465607 http://dx.doi.org/10.1371/journal.pone.0085585 |
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