How much does the cell boundary contract in a monolayered cell sheet?

The method is developed to know how much the cell boundary contracts in a pattern consisting of convex polygonal cells with no gaps nor overlaps; when a cellular pattern is given, we can make it into another pattern whose total boundary length becomes shorter than the original, without reducing the area of each cell. By repetition of such procedure, (1) it can predict the hypothetical cellular pattern whose boundary length has approximated to the shortest possible and, (2) it can estimate the s value, which indicates the degree of lack of boundary shortening of the cellular pattern. The method is applied to several cellular and artificial patterns; cultured epithelial cells in monolayers from lung and pigment retina, epidermis of plant leaf, two-dimensional arrangement of soap bubbles, etc. The results are discussed in relation to recent knowledge on contractile microfilaments in organized cells.