A 3D view of the Genetic Code
Quaternary Mathematics
The DNA/RNA is completely optimized, non-random and since billions of years without changes to the underlying principles. It certainly did not appear out of nowhere as a "All 64 set". What was the starter kit? Here is a new reasoning with logic and observations.
From 0 to 63, from GGG to UUU, from 000 to 333
G level 0-15, A level 16-31, C level 32-47 and U level 48-63.
About this page
My name is Bernhard Pfennigschmidt. I like to discuss this very very specialized area of research on "how did the DNA happen”.
Reading up on DNA research for over 40 years, I designed 20 years ago The CUBE, a better RNA codon table with more sense than the normal RNA codon tables of the Genetic-Code. You see The CUBE on the left.
This statistic analysis blew my mind completely: Origin and evolution of the genetic code: The universal enigma, but for this work I was less concerned with the quantitative analysis, instead I treated it as a mathematical and logical challenge. The linked article qualifies the non-randomness of the 20 Amino acids. Wonderful. I could not agree more.
Nature always simplifies: Chaos theory confirms that any system with more than 3 attractors becomes chaotic: "The DNA appears to be a programming language operating with quaternary mathematics limited to three digits."
The decimal numbers from 0 to 63 in quarternary mathematics.
Digit 0 is last letter, digit 1 is middle letter, digit 2 is the first letter.
A 3D representation of the RNA
Introduction
The RNA uses four functional entities called nucleotides. The letters G A C and U are all it takes to encode the complete building plan of every living being on this planet. Three of the four letters grouped in a triplet are called a codon. There are a total of 64 codons. These codons are used to describe complete gene sequences. The whole purpose of the RNA is to transform these gene sequences, strings with different codons, into functional proteins and release them into the body.
Abstract
The numerical approach taken translates the four nucleotide letters into the numbers 0-3 and uses a matrix operation to create 16 elements and a second one to obtain 64 elements. This paper visualizes the resulting four level grid The CUBE, a 3D representation of the genetic code showing relations and similarities between the individual amino acid codons.
Definition 1
Density of the DNA/RNA nucleotides
I wanted an oscillation based gradient map of the four nucleotides.
To get them in the right order, we can do that with the inverse density assigned to integers.
Purines
G = 2.2 g/cm3
A = 1.6 g/cm3
Pyrimidines
C = 1.55 g/cm3
U = 1.32 g/cm3
T = 1.223 g/cm3
G = 0, A = 1, C = 2, T/U = 3
There are other distinct reasons confirming this specific letter order but that explanation would be distracting at this point.
Definition 2
Combine & combine again
Doing a m-by-n matrix operation with these four expressions creates a 16 element grid representing the second and third letter of codon triplets. ID 0-15.
Doing another matrix operation with these four expressions and the 16 element grid, we obtain a cube with four stacked grids. 4 x 4 x 4 = 64.
Counting the codon IDs cell by cell and row by row, we start with 0 and end at 63.
Hypothesis 1
Change any one of the three letters. Similarities in 3 directions.
The DNA appears to employ a three dimensional address system for the 64 codons. The quarternary address space needs only 3 digits to express 000 to 333.
Moving from one cell in this cube to an ajacent cell requires only to change one of the three letters of the codon.
To navigate around the cube:
Changing planes adds or subtracts 16 to/from the cell value. Changing a row in the grid adds or subtracts 4, changing a cell adds or subtracts 1.
Changing planes is done with the first letter. Changing rows with the second letter. Changing cells with the last letter.
Hypothesis 2
Null is null and leading zeros don't matter.
Observing the incrementing numerical values of the codons in quarternal mathematics, we can see that we have four codons with two leading zeros, represented by the first and second letter. 000 001 002 003 or simply 0 1 2 and 3.
Except for the special case GGG, which is NULL, the other three codons are like single letter on, expressed by the lowest value codons GGA GGC and GGT ( 1-3 ), but knowing that G is zero, we could also just say these codons are the pure expressions of A, C, and T. All encode for Gly.
Those three and GGG as NULL could be "little versions" of the four triple letter codons, the maximum in-character expression, GGG = Gly, AAA = Lys, CCC = Pro, and UUU = Phe respectively.
On the G level there are also the other 12 codons with one leading zero. The same logic applies, they are somewhat basic expressions of the higher level combinations in the matrix.
The special G level: The first 16 codon grid.
We are prefixing the respective first letter on each level to the quaternary number of this grid to complete the three letters of each codon.
Hypothesis 3
Master expression, master function Amino Acid?
Because we use the density gradient on all three axis of the cube, we can observe a continuously incrementing value or oscillation represented by the ID.
There are the four master codons encoding for specific amino acids ( AA ), each one with a different job.
GGG = Gly, is used in the DNA synthesis, purine skeleton, hemoglobin, growth hormons and neuro transmitter inhibitors. Lowest id #0, also the master NULL, FALSE and NOT.
AAA = Lys, is used to make bones and connective tissues. #21
CCC = Pro, is used to build collagen and fibers and to make repairs. #42
UUU = Phe is making neurotransmitters, brains. highest id. #63
Can you see the trend?
All other codon expressions are matrix combinations of the AA expression of these four masters.
The codon's first, middle and last digit present together a triple sound, three oscillations on different octaves.
Pure mathematics.
Discussion
Am I completely off or do I have valid arguments?
Any associations that came to mind while reading this article?
Can this weighted, visual arrangement of the codons explain still unsolved RNA questions?
Can we build a programming language with an architecture of 20 words like the DNA? I wish that to happen so badly.
Review The CUBE