Arrangement of cells in vegetable tissues

Abstract

The authors study the arrangement of cells in undifferentiated vegetable tissues of five different species. The distribution of the number of sides, the average area (an), perimeter (pn) and side length (ln) of n-sided cells are determined as well as the correlation between the number of sides of a cell and of its neighbours. The results show that vegetable cellular nets obey Aboav-Weaire's law. They also discuss Lewis' law and a possible relation between (pn) and n. The analysis of these structures provides a different example of random cellular structures and helps to show general aspects of the ideal one.

On the Aboav–Weaire law

“…In 2D when the Euler's rule holds: (15) and recognizing that n lok does not depend on moments higher than the second, for simplicity we can write σ instead of σ 2 :…”

“…The parameter a versus parameter σ from the literature[2,4,7,[15][16][17][18][19][20][21][22][23][24][25][26].…”

Glass transition in self-organizing cellular patterns

“…Although the micro-dynamics we have considered is idealized and chosen for minimalist study, it is interesting to compare our results with those observed in nature. Most undifferentiated biological tissues are space-filling assemblies of cells where the side distribution is centered around n = 6 and the second moment µ 2 takes values between 0.5 and 1.2; for instance, µ 2 = 0.53 in human epidermis [12], 0.6 ≤ µ 2 ≤ 1.1 in vegetable leaves [13], µ 2 = 0.68 in cucumber epithelia and µ 2 = 1.00 in human amnion [1].…”

Geometrical properties of the Potts model during the coarsening regime

“…Systems as diverse as soap froths [6][7][8], cellular tissues and other natural tilings [9,10], magnetic grains or polycrystalline structures [11][12][13][14][15], type I superconductors [16], etc., are, in a statistical sense, geometrically similar. Their overall morphology and growth properties are well described by simple spin models with multiple ground states.…”