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    The Hidden Geometries of the Arabidopsis thaliana Epidermis

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    Type
    Article
    Authors
    Staff, Lee
    Hurd, Patricia
    Reale, Lara
    Seoighe, Cathal
    Rockwood, Alyn
    Gehring, Christoph A cc
    KAUST Department
    Biological and Environmental Sciences and Engineering (BESE) Division
    Bioscience Program
    Molecular Signalling Group
    Visual Computing Center (VCC)
    Date
    2012-09-11
    Permanent link to this record
    http://hdl.handle.net/10754/325307
    
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    Abstract
    The quest for the discovery of mathematical principles that underlie biological phenomena is ancient and ongoing. We present a geometric analysis of the complex interdigitated pavement cells in the Arabidopsis thaliana (Col.) adaxial epidermis with a view to discovering some geometric characteristics that may govern the formation of this tissue. More than 2,400 pavement cells from 10, 17 and 24 day old leaves were analyzed. These interdigitated cells revealed a number of geometric properties that remained constant across the three age groups. In particular, the number of digits per cell rarely exceeded 15, irrespective of cell area. Digit numbers per 100 ?m2 cell area reduce with age and as cell area increases, suggesting early developmental programming of digits. Cell shape proportions as defined by length:width ratios were highly conserved over time independent of the size and, interestingly, both the mean and the medians were close to the golden ratio 1.618034. With maturity, the cell area:perimeter ratios increased from a mean of 2.0 to 2.4. Shape properties as defined by the medial axis transform (MAT) were calculated and revealed that branch points along the MAT typically comprise one large and two small angles. These showed consistency across the developmental stages considered here at 140° (± 5°) for the largest angles and 110° (± 5°) for the smaller angles. Voronoi diagram analyses of stomatal center coordinates revealed that giant pavement cells (?500 ?m2) tend to be arranged along Voronoi boundaries suggesting that they could function as a scaffold of the epidermis. In addition, we propose that pavement cells have a role in spacing and positioning of the stomata in the growing leaf and that they do so by growing within the limits of a set of 'geometrical rules'. © 2012 Staff et al.
    Citation
    Staff L, Hurd P, Reale L, Seoighe C, Rockwood A, et al. (2012) The Hidden Geometries of the Arabidopsis thaliana Epidermis. PLoS ONE 7: e43546. doi:10.1371/journal.pone.0043546.
    Publisher
    Public Library of Science (PLoS)
    Journal
    PLoS ONE
    DOI
    10.1371/journal.pone.0043546
    PubMed ID
    22984433
    PubMed Central ID
    PMC3439452
    ae974a485f413a2113503eed53cd6c53
    10.1371/journal.pone.0043546
    Scopus Count
    Collections
    Articles; Biological and Environmental Science and Engineering (BESE) Division; Bioscience Program; Visual Computing Center (VCC)

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