[Charles]

I am continuing my discussion of the DNA Code. If I simply posted the networks it would mean much less to you, without some explanation. Also, don't forget the concept of "don't cares". This concept is fleshed out in the workings of the cell through the fact that in human cells only about 30 of the potential codons and anti-codons (tRNA's) are ever used. Thus fully 34 codons (34 inputs) are never used. They become in a sense the "don't cares" of the Code and the "don't cares" of the cell.

In biochemistry texts you will see this type of notation: ACU, ACC, ACA, ACG = Thr. What this means is these 4 codons each code for the amino acid Threonine.

Now let's write this expression in a more elegant Boolean expression:

Thr = ACU + ACC + ACA + ACG where each codon is a minterm and the "+" is the logical sum operator of Boolean algebra.

Thus the amino acid Threonine becomes equal to a minterm sum.

In fact, every amino acid and stop codon can be expressed this way, i.e. as a
minterm sum.

It is a fact of Boolean algebra that a minterm sum can be simplified to become a Boolean logic equation/function.

Thus each amino acid equals a Boolean logic equation or function.


Since there are 20 amino acids and a stop codon, the 21 outputs of the network for the Universal Code will equal these 21 Boolean logic functions, each logic function equaling one amino acid and one logic function for the stop codon. The inputs are the codons of the DNA Code. For any given cell only about 30 or so codons are ever used.

In order to create these logic functions and networks (I also have a network for the Code incorporating Selenium, known as the 21st amino acid, and also a network for the Mitochondrial Code), we must assign 2-bits to each nucleotide (A, G, C, U). U = the nucleotide Uracil. There are 4! or 24 ways to assign 2-bits to these 4 nucleotides. Each bit assignment results in a different assignment of minterms to each amino acid and stop codon.

For any Boolean network it is desirable to have the simplest most elegant network possible. Therefore we must create 24 networks composed of these logic functions and determine the number of gates necessary to create each network.

Each of these 24 networks represents about 20 minterm sums. Each minterm sum is composed of terms that are 6 variables each. Each minterm equals one codon. The minterm that is assigned to the codon changes according to the bit assignment but the codons assigned to each amino acid do not. They are fixed by the Code in nature. Without going into the details, this a truly daunting math problem but it is solvable. With considerable help I solved it.

Next, we then look at the 24 networks in terms of the number of gates and discover the one with the fewest number of gates. This network will have a bit assignment associated with it. This bit assignment should be the optimum bit assignment for the DNA Code.

Since there are 3 Codes: Universal, Universal with Selenium, and Mitochondrial, we must determine the optimum bit assignment for each Code by doing a similar analysis.

I hope that you can appreciate the complexity of this problem. A question arises: will the optimum bit assignment be identical for all three Codes? Will it be optimum for Transcription and Replication? in other words is the bit assignment as universal for Life as are the Codes?

I'm going to stop here. I just received a large batch of pics. Nevertheless, I will post the networks and optimum bit assignment on Sunday. Then I will continue on with some considerable explanation. I will also attempt to explain the "minterm". Basically, a minterm is a special one term (hence the phrase "min") Boolean logic function with amazing properties. I will elaborate by giving some examples but I want to get the networks and solution to the bit assignment posted first.