Continuum modelling of structure formation of biosilica patterns in diatoms
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RESEARCH ARTICLE
BMC Materials Open Access
Continuum modelling of structure formation of biosilica patterns in diatoms Manfred Bobeth1, Arezoo Dianat1 , Rafael Gutierrez1* , David Werner3, Hongliu Yang1, Hagen Eckert1 and Gianaurelio Cuniberti1,2
Abstract 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. Keywords: Diatoms, Biosilica formation, Phase separation, Cahn–Hilliard equation, Reaction–diffusion equations
Introduction The formation of various beautiful silica structures of diatoms is a very fascinating example of biomineralization. In recent years, considerable progress has been made in elucidating the chemical and biological processes, which are involved in the silica morphogenesis of diatom valves (cf. for example [1–5]). Summaries of very recent findings have been given in [6, 7]. So far, only relatively few works have dealt with the very challenging theoretical modeling of the morphogenesis of diatom valves [8–13]. Early models were based on diffusion-limited aggregation *Correspondence: rafael.gutierrez@tu‑dresden.de 1 Institute for Materials Science and Max Bergmann Center of Biomaterials, Dresden University of Technology, 01062 Dresden, Germany Full list of author information is available at the end of the article
of silica nanoparticles, which are imported into the silica deposition vesicle (SDV) at its leading edge [9, 11]. Corresponding computer simulations were able to describe the formation of the radial rib structure of valves. On the basis of diffusion-reaction mechanisms, the formation of various nano-sized pore patterns within larger pores of silica valves has also been addressed in [12, 13]. A special computer evolution model of the morphogenesis of raphid pennate diatoms was
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