As you know DNA is composed of strings of 4 letters. I am wondering if the number 4 here has any significance? Any property of 4 that makes using 4 letters more advantageous over more (or less) letters to encode information?
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8$\begingroup$ I'm no expert, but I would expect the answer to be chemistry or biology and not mathematics. The four letters correspond to certain acids, and so it's not simply an encoding, but also has a functional part. $\endgroup$– HelgeCommented Jul 18, 2010 at 10:49
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2$\begingroup$ I'm no expert either, but to me this looks a lot more like numerology than biology or chemistry, let alone mathematics. $\endgroup$– Franz LemmermeyerCommented Jul 18, 2010 at 12:02
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2$\begingroup$ Also, there are technically more than four bases - there are less common modified bases, such as m5C. See en.wikipedia.org/wiki/Nucleobase. $\endgroup$– Thomas BloomCommented Jul 18, 2010 at 12:10
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1$\begingroup$ If you believe in the RNA world, this probably originated as some sort of compromise between having a minimally complex chemistry with sufficiently interesting enzymatic/catalytic behavior. $\endgroup$– Rob GreyCommented Jul 18, 2010 at 12:49
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1$\begingroup$ There might also be a genome-compactness/efficiency vs. chemical complexity/difficulty-of-error-correction argument. $\endgroup$– Rob GreyCommented Jul 18, 2010 at 12:52
2 Answers
A short (and not entirely correct) answer is: redundancy. There is a very nice article on this in Brian Hayes' book, Group Theory in the Bedroom. The precursor of the chapter appeared in the American Scientist: "The Invention of the Genetic Code". One interesting aspect of the story is that George Gamov proposed several clever triplet genetic codes of great abstract beauty. Other physicists and mathematicians (Feynman, Teller, Golomob) also made suggestions. But nature chose its own path.
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$\begingroup$ I'm pretty sure his name is Brian, not Barry. :) I read his blog bit-player.org quite often. In fact, since this is CW, I'm just going to in and edit it. BTW I highly, highly recommend Group Theory in the Bedroom. $\endgroup$ Commented Jul 18, 2010 at 14:24
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$\begingroup$ @Willie: Thanks for the correction! $\endgroup$ Commented Jul 18, 2010 at 14:57
A 1993 PRL by Hornos and Hornos suggested that the evolution of the genetic code manifests itself through symmetry breaking. According to them the basic symmetry is supposed to be $SU(2)^{\otimes 3}$ (three nucleotides per codon).
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$\begingroup$ It's an interesting idea, but the paper reads more like pattern fitting than actual a priori derivation. Then again, I am no expert in biophysics. $\endgroup$ Commented Jul 18, 2010 at 14:21