Continuum modelling of structure formation of biosilica patterns in diatoms

Formation of regularly structured silica valves of various diatom species is a particularly fascinating phenomenon in biomineralization. Intensive investigations have been devoted to elucidate the formation mechanisms of diatom valve structures. Phase-separation of species-specific organic molecules has been proposed to be involved in pattern formation, where the evolving organic molecule structures serve as template for silica formation. In the present work, using a continuum approach, we investigate the conditions under which silica structures of high regularity can develop within a phase separation model. In relation to previously reported in vitro experiments of silica formation, which revealed the important role of phosphate ions in the self-assembly of organic molecules, we propose a model where phase separation is coupled with a chemical reaction. We analyze the impact of the reaction of phosphate ions with organic molecules on the appearing morphology of the organic template. Two- and three-dimensional simulations of the development of regular stationary patterns are presented. The influence of a confined geometry and an interaction of organic molecules with the walls on pattern formation is also addressed. We expect that our approach will be relevant for experimental studies aiming at inducing structure formation under controlled in vitro conditions.