Phyllotactic Patterns: A Biophysical Mechanism for their Origin

Abstract

The patterns seen in plant shoots and flowers, 'phyllotaxis', originate in an annular region. They are typically propagated inward from this ring-like area. We show here that an initial undulating periodic pattern (a 'whorl' of hump-like organs) can arise in a flat unstructured annulus. The pattern arises not from pre-localized pushes from below, but rather as a spontaneous physical response of the expanding surface to lateral constraint. Physical properties of a uniform formative layer (tunica) and a uniform substratum (corpus) provide the wavelength of the undulation and hence the number of organs. Establishment of the parameters for this buckling, as well as the follow-through of organ development, is biological. We propose, however, that at the moment of periodic pattern initiation the plant tissue simply manifests the spontaneous but complex properties of a two-layered inanimate sheet.