A simple probabilistic model of submicroscopic diatom morphogenesis

Abstract

Unicellular algae called diatoms morph biomineral compounds into tough exoskeletons via complex intracellular processes about which there is much to be learned. These exoskeletons feature a rich variety of structures from submicroscale to milliscale, many that have not been reproduced in vitro. In order to help understand this complex miniature morphogenesis, here we introduce and analyse a simple model of biomineral kinetics, focusing on the exoskeleton's submicroscopic patterned planar structures called pore occlusions. The model reproduces most features of these pore occlusions by retuning just one parameter, thereby indicating what physio-biochemical mechanisms could sufficiently explain morphogenesis at the submicroscopic scale: it is sufficient to identify a mechanism of lateral negative feedback on the biomineral reaction kinetics. The model is nonlinear and stochastic; it is an extended version of the threshold voter model. Its mean-field equation provides a simple and, as far as the authors are aware, new way of mapping out the spatial patterns produced by lateral inhibition and variants thereof.