Turing Biology 2005 Albert Harris   How can chemical reactions create geometrical patterns This is related to the examples on page 21 of the textbook; and it isn't actually known whether embryos use these mechanisms. Reaction-Diffusion Systems (proposed by Alan Turing) Suppose that two chemicals exist , chemical A and chemical B (the textbook calls them P and S, but that's confusing) 1) Suppose that A somehow causes the synthesis of more A , and that A also cause the synthesis of more B. (in other words, the rates of synthesis of A and B at each place are proportional to the local concentration of A each place. 2) Suppose that B cause the destruction or removal of A and B. (in other words, both A and B decrease in proportion to the local concentration of B at each location. 3) Suppose that B diffuses faster than A. What will happen, if these 3 rules are obeyed?? Answer: it makes spontaneous peaks and valleys of alternating higher and lower concentrations of both chemicals. (The one that inhibits has to diffuse faster) Diagram 1.2B implies that it needs to start off with lots of random variations in concentration, but that is a mistaken idea. The variables "A" and "B" do not have to be chemical concentrations A could be the population density of cells. B could be mechanical tension produced by cell traction. B doesn't have to diffuse faster than A; it just needs to act at longer range . (diffusing faster is one way of having a longer range effect) An applied mathematician friend of mine even wrote a paper about what would happen if A and B were populations of animals; with species B eating species A, and B migrating faster. The stable wave-length of the pattern varies according to the ratio of the two diffusion constants (or the ratios of range at which they act) relative to rates of the chemical reactions of synthesis & destuction. This is not the only combination of reaction rules that make patterns. (but don't memorize these rules; instead memorize the other set, above) Another sub-category would obey the following 5 rules : 1) A made at a constant rate 2) B is destroyed at a constant rate 3) A catalyses conversion of B to A 4) B catalyses conversion of A to B 5) B diffuses faster (This is closer to Turing's original idea) http://www.bio.unc.edu/faculty/harris/Courses/biol166/automata.html this site describes different kinds of computer pattern generation; and Reaction-Diffusion mechanisms come second, so scroll down a way. SIMPLE COMPUTER PROGRAMS CAN BE WRITTEN THAT WILL SHOW YOU WHAT WILL HAPPEN FOR ANY SET OF RULES. This is called "computer modeling" It is a way of finding out what would result from different rules. Notice that modeling DOES NOT tell you whether animals and plants really use those particular rules to make stripes, etc. Modeling tells you whether the rules COULD work, and helps design experiments to distinguish possiblities. Some researchers synthesized some real chemicals that obey one of Turing's sets of rules; and published this in Science years ago. The main problem was the large differences in diffusion rates; it's very unusual for one chemical to diffuse 5 times faster than another.< A completely different set of (actual) chemical reactions makes waves that propagate (move) in regular patterns. These were invented in Russia by Beloussov & Zhabotinski. (But this is not the same Beloussov who is an embryologist) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Another completely different example of pattern-generation by reaction & diffusion is called "Liesegang's Rings" (but these can be stripes or spots or bands, just as well as rings) These were discovered in the late 1800s in Austria during experiments about how to improve photography. Make a gelatin gel with potassium bichromate dissolved in water Put a few crystals of silver nitrate on the surface of this gel. Silver bichromate is much less soluble than either silver nitrate or potassium bichromate, so crystals of silver bichromate form. The surprising thing is that the silver bichromate precipitates in stripes, with clear gaps between them. Why this happens is not known for sure (= scientists disagree) Regarding Liesegang Rings: The first theory suggested goes like this: Saturation, and therefore precipitation of a salt occurs where the concentration of one dissolved ion multiplied by the concentration of some other dissolved ion i.e. [Ag+] multiplied by [Bichromate-] is larger than "the solubility product" for this particular salt. However, super-saturation often occurs where no crystals of precipitate have formed yet. In other words, the concentrations of the two ions can get considerably larger than is supposed to result in precipitation of silver bichromate crystals (which is how much of the ions would exist dissolved in equilibrium with crystals). But there is some higher threshold level, at which new crystals can form even where there were none before. I wrote computer simulatons of this hypothetical mechanism (originally in BASIC on an Apple II computer) and later in Turbo-Pascal for Macintosh, to see if this mechanism would make patterns that look like the ones that form in a petri dish when you put the silver nitrate on the gel. Testing what invented mechanisms would do if they were true. In this case, the computer simulations accurately predicted many facts 1) the widening distances between rings farther from the silver nitrate, 2) the broadening of these rings 3) their slower rate of formation. I was so impressed by the accuracy of these "reverse predictions" that I re-did the chemical experiments by which Ostwald had supposedly disproved this super-saturation mechanism to make rings. This experiment was to add many small crystals of pre-formed silver bichromate to the gel, before putting the silver nitrate crystals there. Super-saturation is impossible where crytals of the salt already are. Ostwald had claimed that such pre-made crystals did NOT block later formation of Liesegang Rings. But my experiments turned out the opposite: they did prevent rings Also, I made a gradient of population density of silver bichromate crystals, and there was a perfect inverse correllation with ring formation!! I have never published these results in any journal or book, although I have shown my photos & other data at meetings. If somebody wanted to do a Bio 98 project on this, I would be glad to sponsor them and to fund the experiments.< Some real embryological problems to be solved are: (in reverse order) (these are really difficult questions, that no one has been able to answer) 1) By which chemical or physical mechanisms do developing zebra fish form stripes?....or how do Zebras form their stripes? etc. for every species of fish, snake, butterfly, mammal, bird etc. 2) Invent experiments to test which (if any) of the kinds of pattern-generating reaction-diffusion mechanism is the true cause of the color patterns (or other anatomical geometry) for zebra fish, etc. For #2 above, notice the reasoning of our textbook, on page 22, and in the cited research paper by Asai et a.. 1999 Mech. Dev 89: 87-92 a) Mutations in a certain ("leopard") gene were observed to cause xebra fish to form spots, instead of stripes. b) Changing one of the variables in a computer simulation also caused spots to be formed instead of stripes. c) The intermediate geometries between stripes and spots look alike. THEREFORE WHAT CAN WE CONCLUDE FROM THIS? x) This mutation alters a chemical used in a Turing-like mechanism? y) It is not impossible that "x" is true? z) We should invent some better experiments, that could test between different kinds of reaction-diffusion systems q) We should write computer programs that can systematically scan the actual color patterns of real animals and match these with alternative categories of pattern-generating mechanisms. (roughly analogous to how "Fourier Transforms" detect each wave-length in a complex spatial pattern) r) How else will anybody ever discover what embryological mechanisms cause the formation of zebra stripes, zebra fish stripes, and finger prints? s) How would it be possible to identify the different chemicals, and which ones stimulate their own synthesis, which ones stimulate breakdown, and what their diffusion rates are? t) Suppose that somebody isolated genetic mutant zebra fish with abnormal skin color patterns, trying to find as many different geometrically different patterns as possible: What if all of these mutant patterns could be generated on a computer simulation of one of Turing's reaction-diffusion systems by one or another changed combinations of rates of synthesis, breakdown and diffusion? In other words, let's assume that many conceivable geometric patterns could NOT be generated by any possible fiddling of the various reaction rates and diffusion rates, but that none of these "Turing-Impossible" patterns would ever show up in the skin of any mutant line of zebra fish! Would THAT then be supporting evidence? Embryologists can't decide. So don't worry if you can't. Could you imagine constructing a system of defining categories of reaction-diffusion mechanism, in which the key defining property of each one would be which geometric patterns it COULD NOT produce? Please all members of the class vote on this next question: Given the choice between discovering one or other of the following, which would you prefer to discover? A) What are the specific proteins or other chemicals whose diffusions and reaction create zebra-fish color patterns? B) Which category of reaction-diffusion mechanism do these chemicals obey? Which of these questions would probably need to be solved first , to provide a basis for experiments about the answer to the other question? Which question does the author of our textbook think will be answered before the other question. Which answer would he publish in the next edition, if both answers were discovered? Both? Only A? Only B? Neither? Maybe we should write him and ask.

 

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