A minimum-surface mechanism to account for the organization of cells into columns in the mammalian epidermis.

It has recently been discovered that the stratum corneum and superficial living epidermis of mammalian skin are organized into neat vertical columns of interdigitating cells. The mechanism for this organization has not yet been determined. This study shows that the stacked organization is not unique to the epidermis but also occurs in cork cambium and the pith of woody plant stems. The structural and spatial organization of the stacked cells in these tissues were compared and found to approximate closely the shape of Kelvin's minimum-surface polygon, the tetrakaidecahedron. Paper models of flattened tetrakaidecahedra were constructed and found to stack columns of interdigitating units which are consistent with all of the structural details seen in stacked cells observed under the light and the scanning electron microscopes. Indeed, only polygons of this type are capable of aggregating without interstices in the manner of the stacked cells. A study of stacked arrays of these models has revealed a mechanism by which the epidermis might become organized in columns of stacked and interdigitating cells. The proposed mechanism assumes that cells within an array seek the smallest possible surface-to-volume ratio and, under appropriate conditions, form stacked tetrakaidecahedra.