Counting the "Letters" in DNA

An article describing the work of Jean Claude Perez written by a colleague of Perez. There are some mathematical mistakes in it, but I think it provides quite a clear description of Perez's work, so I am including it on my website.

reference : http://www.cosmicfingerprints.com/blog/mathematics-of-dna/

Computers use something called a “checksum” to detect data errors. It turns out DNA uses checksums too. But DNA’s checksum is not only able to detect missing data; sometimes it can even calculate what’s missing. Here’s how it works.

In English, the letter E appears 12.7% of the time. The letter Z appears 0.7% of the time. The other letters fall somewhere in between. So it’s possible to detect data errors in English just by counting letters.

In DNA, some letters also appear a lot more often (like E in English) and some much less often. But… unlike English, how often each letters appears in DNA is controlled by an exact mathematical formula that is hidden within the genetic code table.

When cells replicate, they count the total number of letters in the DNA strand of the daughter cell. If the letter counts don’t match certain exact ratios, the cell knows that an error has been made. So it abandons the operation and kills the new cell.

Failure of this checksum mechanism causes birth defects and cancer.

Dr. Jean-Claude Perez started counting letters in DNA. He discovered that these ratios are highly mathematical and based on “Phi”, the Golden Ratio 1.618. This is a very special number, sort of like Pi. Perez’ discovery was published in the scientific journal Interdisciplinary Sciences / Computational Life Sciences in September 2010.

Jean-Claude Perez discovered an evolutionary mathematical matrix in DNA, based on the Golden Ratio 1.618

Before I tell you about it, allow me to explain just a little bit about the genetic code.

DNA has four symbols, T, C, A and G. These symbols are grouped into letters made from combinations of 3 symbols, called triplets.  There are 4×4x4=64 possible combinations.

So the genetic alphabet has 64 letters. The 64 letters are used to write the instructions that make amino acids and proteins.

Perez somehow figured out that if he arranged the letters in DNA according to a T-C-A-G table, an interesting pattern appeared when he counted the letters.

He divided the table in half as you see below. He took single stranded DNA of the human genome, which has 1 billion triplets. He counted the population of each triplet in the DNA and put the total in each slot:

When he added up the letters, the ratio of total white letters to black letters was 1:1. And this turned out to not just be roughly true. It was exactly true, to better than one part in one thousand, i.e. 1.000:1.000.

Then Perez divided the table this way:

Perez discovered that the ratio of white letters to black letters is exactly 0.690983, which is (3-Phi)/2. Phi is the number 1.618, the “Golden Ratio.”

He also discovered the exact same ratio, 0.690983, when he divided the table the following two alternative ways:

Again, the total number of white letters divided by the total number of black letters is 0.6909, to a precision of better than one part in 1,000.

Perez discovered two more symmetries:

Above: Total ratio of white:black letters = 1:1



Again, total ratio of white:black letters = 1:1

So for three ways of dividing the table, the ratio of white to black is 1.000:1.000.

And for the other three ways of dividing it, the ratio is 0.690983 or (3-Phi)/2.

When you overlay these 6 symmetries on top of each other, you get a set of mathematical stairs with 32 golden steps. Then an absolutely fascinating geometrical pattern emerges: The “Dragon Curve” which is well known in fractal geometry. Here it is, labeled with DNA letters in descending frequency:

You can see other non-DNA, computer generated versions of this same curve here.
 

Other interesting facts:

• Similar patterns with variations on these same rules are seen across a range of 20 different species. From the AIDS virus to bacteria, primates and humans
• Each character in DNA occurs a precise number of times, and each has a twin. TTT and AAA are twins and appear the most often; they’re the DNA equivalent of the letter E.
• This pattern creates a stair step of 32 frequencies, a specific frequency for each pair.
• The number of triplets that begin with a T is precisely the same as the number of triplets that begin with A (to within 0.1%).
• The number of triplets that begin with a C is precisely the same as the number of triplets that begin with G.
• The genetic code table is fractal - the same pattern repeats itself at every level. The micro scale controls conversion of triplets to amino acids, and it’s in every biology book. The macro scale, newly discovered by Dr. Perez, checks the integrity of the entire organism.
• Perez is also discovering additional patterns within the pattern.

Think of the genetic code as a chessboard consisting of 64 squares (8 x 8). Each square represents one of the 64 codons. What Perez found was that

• half = 32 codons ---------the ratio between the even half and the odd half  = 1
• quartile = 16 codons -----the ratio between even quartiles and odd quartiles =  0.691457
• octant = 8 codons --------the ratio between even octants and odd octants = 1
• square = 4 codons -------the ratio between even squares and odd squares = 0.691457
• binome = 2 codons ------the ratio between even binomes and odd binomes = 1
• codon = 1 codon --------the ratio between even codons and odd codons = 0.691457

It is one thing for the genome to come about by chance and possess just the right functions to support life. It is quite another thing for the elements of the genome to also be in proportions that follow pure mathematical pattern through and through.
 

Here is the Wiki on Perez -http://creationwiki.org/Jean-claude_Perez
 

Perez's papers can be seen here -

http://www.resurgence.be/pdf/ADN-perez.pdf

http://www.matematicasmisticas.com/Descargas/IS-2010-0006jcPerezLastRevisedPaperInterdisciplinaryScience.pdf