TY - JOUR
T1 - The Hidden Geometries of the Arabidopsis thaliana Epidermis
AU - Staff, Lee
AU - Hurd, Patricia
AU - Reale, Lara
AU - Seoighe, Cathal
AU - Rockwood, Alyn
AU - Gehring, Christoph A
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2012/9/11
Y1 - 2012/9/11
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/325307
UR - https://dx.plos.org/10.1371/journal.pone.0043546
UR - http://www.scopus.com/inward/record.url?scp=84866302151&partnerID=8YFLogxK
U2 - 10.1371/journal.pone.0043546
DO - 10.1371/journal.pone.0043546
M3 - Article
C2 - 22984433
SN - 1932-6203
VL - 7
SP - e43546
JO - PLoS ONE
JF - PLoS ONE
IS - 9
ER -