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.

不同硅藻种类规则结构的硅质壳的形成是生物矿化中一个特别引人入胜的现象。人们已经进行了大量深入的研究以阐明硅藻壳结构的形成机制。特定种类有机分子的相分离被认为参与了图案形成，其中不断演化的有机分子结构作为硅质形成的模板。在本研究中，我们采用连续介质方法，研究在相分离模型中高度规则的硅质结构能够形成的条件。鉴于先前报道的硅质形成的体外实验揭示了磷酸根离子在有机分子自组装中的重要作用，我们提出了一个相分离与化学反应耦合的模型。我们分析了磷酸根离子与有机分子的反应对有机模板所呈现形态的影响。给出了规则稳定图案形成的二维和三维模拟。还探讨了受限几何形状以及有机分子与壁的相互作用对图案形成的影响。我们期望我们的方法将对旨在在受控的体外条件下诱导结构形成的实验研究具有参考价值。