A frustule is the hard and porous cell wall or external layer belonging to diatoms. The frustule is composed almost purely of silica, made from silicic acid, and is coated with a layer of organic substance, sometimes pectin, a fiber most commonly found in cell walls of plants.

The frustule's structure is composed of two overlapping sections: the epitheca overlaps the hypotheca. This overlapping feature allows for the diatom to achieve limited movement. Also the overlapping allows for additional internal growth room and during the reproduction process, as the cell splits each new cell retains one half of the frustule. The frustules structure also contains many pores and slits that provide the diatom access to the external environment for process such as waste removal and mucilage secretion. The long slit where the epitheca and hypotheca overlap is called the raphe.

Diatoms

Diatoms are single celled organisms that micro organisms that live in ocean and freshwater environments. Diatoms usually rely on ocean current and wind to keep them in the upper oceanic levels as their cell wall is denser than water they would naturally sink otherwise. However, in some species one function of the raphe is to secrete mucilage, which if attached to a surface will allow the diatom to move in an oozing or gliding motion, similar to that of an amoeba.

Diatom skeletons and their uses

When diatoms die and the organic material decomposes, the frustules sink to the bottom of aquatic environments. This left over material is called diatomite and used commercially as filter, mineral fillers, in insulation material, anti-caking agents and as a fine abrasive. There is also current research regarding the use of diatom frustules and their properties for the field of optics, along with other cells, such as those in butterfly scales.

Mathematics of frustules

Due to the wide variety of shapes and formations that a frustule can take, certain fields of mathematics have attempted to derive a formula that can produce all of different frustules shapes observed in diatoms. One theory is that Johan Gielis’ Superformula can be applied to frustules due to its ability to produce a wide variety of shapes with relatively few parameters.

Frustule formation

As the diatom prepares to separate it undergoes several processes in order to start the production of either a new hypotheca or new epitheca. Once each cell is completely separate they then have similar protection and the ability to continue frustule production.

A brief and extremely simplified version can be explained as:

1. The newly formed nucleus and the pre-existing nucleus each move to the side of the diatom where the new hypotheca will be formed.
2. A vesicle known as the silica deposition vesicle forms near the plasma membrane.
3. This forms the center of the pattern and silica despostion can continue outward from that point, till the frustule is produced.

External links

• Frustule on Britannica
• diatom frustule on astrographics.com
• Geometry and Pattern in Nature 1: Exploring the shapes of diatom frustules with Johan Gielis' Superformula, by Christina Brodie, UK
• http://www.nature.com/nnano/journal/v2/n6/full/nnano.2007.152.html
• Exploring Bioinorganic Pattern Formation in Diatoms. A Story of Polarized Trafficking on plantphysiol.org

Regarding the Super formula

• Exploring the miniature world on microscopy-uk.org.uk
• Superellipse And Superellipsoid, A Geometric Primitive for Computer Aided Design, by Paul Bourke, January 1990
• Supershapes (Superformula) by Paul Bourke, March 2002

References