Tip and whorl morphogenesis in Acetabularia by calcium-regulated strain fields

Abstract

Using tip and whorl formation in the marine alga Acetabularia mediterranea as an example, we investigate the nature of the spatial ordering which arises from Ca2+ regulation of the viscoelastic properties of the cell cortex. From a survey of the empirical information available on the effect of free Ca2+ on the elastic and viscous properties of the cell cortex, and on the mechanisms of strain-induced Ca2+ release, we derive a set of coupled, non-linear equations using first order theory of elastic and viscous response to stress fields, in effect extending previous work of Odell et al. (1981) and Oster & Odell (1985) in this regard. Calculations assuming one-dimensional geometries show that bifurcations to relevant spatial patterns can occur in the strain field in the cortical cytoplasm. The secondary effects of such patterns and the experimental implications of the proposed mechanisms are discussed. Finally, some remarks are made relating to a comparison of the strain field approach and that using diffusion-reaction mechanisms.