Informational Macromolecules

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The Genetic Code

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Fun with Numbers

Permutations are the possible rearrangements of things when order is important. Combinations apply when order is not important. The principle behind the math of permutations is quite simple, though actual numbers grow exponentially.

Taking the letters caug, for example, yields the following permutations
caug augc ugca gcau
cuag uagc agcu gcua
gauc aucg ucga cgau
guac uacg acgu cgua
aguc guca ucag cagu
ucga cgau gauc aucg

That is, 24 permutations arise from the ordered rearrangement of 4 letters. This number is much more easily worked out by the formula:
4! = 4.3.2.1 = 24

So, if we started with 7a's 8c's 6u's and 5g's, we would have 26! = 26.25.24....1 = 4.032914611266056e+26, which approximates to 11^26 permutations.

e= Euler's number = base of natural logarithms = 2.71828 18284 59045 23536 02874 7135...)

In more general terms, n! = n.(n-1).(n-2)...1

Of course, we might have started with different combinations of 'caug' totalling 26, for example 8a's 7c's 6u's and 5g's, and for each combination we would have 26! = 11^26.

Here, the total number of combinations of 4 letters assembled into total groups of 26 is 14,950 = 26! divided by 22!

This brings the grand total number of permutations to 14,950 x 11^26. This simplifies to about 1.7 x 10^29 -- that is 1.7 followed by 29 zeros.
permutation-combination calculator

Why these letters? The letters are the symbols for the bases in RNA = CAUG = cytosine, adenine, uracil, and guanine. The minimal genome is calculated to be about 260 genes – thousands of bases, so exponentially more permutations.

Idists employ such numbers in their effort to demonstrate that the genetic code for a particular protein – determined by the order of bases in the nucleic acid chain – could not arise by chance. Proids ignore, or are ignorant of, several important features of the genome and proteome when they employ such numbers, and talk of monkeys typing Shakespeare.

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