the hidden geometries of the arabidopsis thaliana epidermis拟南芥表皮的隐藏的几何图形.pdf

The Hidden Geometries of the Arabidopsis thaliana Epidermis 1 1 2 3 1 4 Lee Staff , Patricia Hurd , Lara Reale , Cathal Seoighe , Alyn Rockwood , Chris Gehring * 1 Geometric Modeling and Scientific Visualization Centre, King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia, 2 Department of Applied Biology, University of Perugia, Perugia, Italy, 3 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland, 4 Division of Chemistry, Life Science and Engineering, King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia 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 mm2 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 i