Reaction-Diffusion Systems Feb. 3, 2012

Inorganic chemical reactions that break displacement symmetry

Diffusion of a chemical can create geometric patterns more complicated than linear gradients, when two or more chemicals are diffusing and also reacting with each other.

Three examples, each one of which is a category that includes many different specific examples. (In other words, it's not just certain chemicals that can create geometric patterns.)

The connection to embryology is NOT that any animal color pattern is caused by inorganic chemicals, And not even that anatomical patterns are formed by these particular abstract rules, that make the patterns shown here.

Maybe we can call it "The American Flag" problem, as a counter argument to Wolpert's French flag: What different methods can make stripes, or make stars, or other more complex patterns?

It turns out that many alternative sets of rules can make complex patterns.

The following are three possibilities - that MIGHT occur in embryos.
How to prove or disprove whether any of these 3 kinds of mechanism works in real embryos is an experimental answer that can only be solved by people who have first learned about these possibilities.

#1) The Belousov-Zhabotinsky reaction (Wikipedia article).
Take a look at the moving video! This is a combination of chemical reactions that produces waves that move. Therefore, it is less relevant to anatomical patterns and animal color patterns and more relevant to heart contractions (especially of the pathological kind called "fibrillations") and peristaltic contractions of smooth muscles contractions. Maybe also muscle spasms in victems of slipped disks? The moving waves are also strikingly similar to the waves of increasing and decreasing concentrations of calcium ions that occur in tissue culture monolayers of brain glial cells, that might be how memory is achieved.
B. P. Belousov is not the same person as the famous Russian embryologist Lev Beloussov.

#2) Liesegang rings (also called Liesegang bands. Discovered in the late 1800s, during photography experiments by a man named Liesegang. Over four thousand research papers have been published about this phenomenon. The true explanation has not yet been discovered/invented. Several mechanisms have been invented which could work, in the sense that computer simulations of the invented hypotheses prove that animals could use that invented mechanism, whether or not it works the same way as the chemical interactions that Liesegang observed. The Wikipedia article has what seem to me to be a few mistakes, but is a good introduction to the topic.

If the salt potassium chromate ( warning: chromate ions are a serious, cumulative poison for humans and other animals, so always be very careful with it, and dispose of it properly) is dissolved in water, and gelatin is also dissolve in that water (by heating) , and this is poured into a petri dish, then a thin, pale yellow gel will be formed.

Next, put a few small crystals of silver nitrate on the top of this gel. ( Another warning: Silver ions will stain skin and clothes black, and can't be washed out no matter what you do. Be especially careful not to get any silver salt or solution in your eyes.) The black color is lots of very, very tiny pieces of silver metal, strange to say.

Although silver nitrate is very soluble in water, and potassium chromate is also very soluble in water, and potassium nitrate is very, very soluble in water - silver chromate is very INSOLUBLE. Therefore it is no surprise that crystals of silver chromate precipitate out of solution. They are bright red-orange, which is why people use these salts in preference to others. The original discovery of the phenomenon was made using gelatin, potassium chromate and silver nitrate.

You can also get geometric patterns using calcium salts instead of chromate salts, and using agar instead of gelatin or even using silicate gels (or even using very narrow glass tubes, and no gel)

The interesting phenomenon is that silver chromate precipitates in a series of bands, with clear areas between them, arranged somewhat like the pattern on an archery target.

The circumferential clear areas are what is interesting. You can also get interference patterns, in the sense of clear areas along the bands of precipitate.

#3) Reaction-Diffusion Systems, of which the first examples were invented by Alan Turing, and were independently invented by 2 Germans: Alfred Gierer and Hans Meinhardt.

Please read the three following articles, which are available free on the web:

page from last year's Biology 441 course

Wired Science page on Turing

An Interview with Hans Meinhardt


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