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First-order patterning transitions on a sphere as a route to cell morphology

arXiv.org, 2016-05

2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;http://arxiv.org/licenses/nonexclusive-distrib/1.0 ;EISSN: 2331-8422 ;DOI: 10.48550/arxiv.1603.00557

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  • Title:
    First-order patterning transitions on a sphere as a route to cell morphology
  • Author: Lavrentovich, Maxim O ; Horsley, Eric M ; Radja, Asja ; Sweeney, Alison M ; Kamien, Randall D
  • Subjects: Defects ; Eggs ; Free energy ; Grains ; Hexagons ; Insects ; Mathematical morphology ; Patterning ; Phase transitions ; Phenomenology ; Physics - Biological Physics ; Physics - Soft Condensed Matter ; Physics - Statistical Mechanics ; Pollen ; Reproducibility ; Spores ; Topology ; Variations
  • Is Part Of: arXiv.org, 2016-05
  • Description: We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an individual pattern is robustly reproducible by a single species and a similar set of developmental stages produces a variety of patterns. We argue that the pattern diversity and reproducibility may be explained by interpreting the pattern development as a first-order phase transition to a spatially modulated phase. Brazovskii showed that for such transitions on a flat, infinite sheet, the patterns are uniform striped or hexagonal. Biological objects, however, have finite extent and offer different topologies, such as the spherical surfaces of pollen grains. We consider Brazovskii transitions on spheres and show that the patterns have a richer phenomenology than simple stripes or hexagons. We calculate the free energy difference between the unpatterned state and the many possible patterned phases, taking into account fluctuations and the system's finite size. The proliferation of variety on a sphere may be understood as a consequence of topology, which forces defects into perfectly ordered phases. The defects are then accommodated in different ways. We also argue that the first-order character of the transition is responsible for the reproducibility and robustness of the pattern formation.
  • Publisher: Ithaca: Cornell University Library, arXiv.org
  • Language: English
  • Identifier: EISSN: 2331-8422
    DOI: 10.48550/arxiv.1603.00557
  • Source: arXiv.org
    AUTh Library subscriptions: ProQuest Central
    Open Access: Freely Accessible Journals by multiple vendors
    ROAD: Directory of Open Access Scholarly Resources
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