# Group Theory applied to DNA nucleotides to describe proteins behavior

Summary:
https://proteinproteininteractions.net/

I have a mathematical model to represent proteins. Their properties like interactions and structure derive from the math properties associated to the description, based on Group Theory.

I am looking for someone willing to get this model and use it to explore the possible applications and the limit of validity.

Full Description:
DNA can be represented with a mathematical Group of 5th order: 4 elements and one neuter element to describe DNA, amino acids and proteins properties. In fact In DNA we have four objects into two separate classes with two elements each, two purines (AG) and two pyrimidines (CT or CU).

The best application for this model is in new drugs development for Biotech or Pharmaceutical companies. It is possible to describe the interactions, and the interaction regions can be created ad hoc/ enabled/ disabled.

My idea to investigate in this direction started from the empirical observation that blood groups behave as a mathematical group.
Blood types A, B, AB and 0 are the elements of the group and the composition low is the way a group can be transfused to a patient. 0 is the neuter element of the group: it can be donated to any other group (any element is invariant if combined with the neuter one).

Starting from this, my main hypothesis is that also in biology there are precise mathematical rules governing bio behaviors.
I investigated the possibility that a mathematical description based on group theory can describe the universal genetic code and codon sequences behavior, and consequently protein interactions. The properties of the proteins are at nucleotide level, and not at amino acids level.

Applying Group Theory to DNA/Proteins structure and following precise mathematical rules it is possible to explain the mechanism that regulates binding regions.
The structure of a protein also finds correspondences in the codon sequence properties described with the 5th order Group. But I didn’t investigate deeply the structure, so far I focused mainly in the interaction properties.

The model is protected by US patent application #17/247,845

Claims of the Patent:
1. a mathematical model that describe proteins properties using the rules of a 5th Order Group including:
a. 2 equivalence classes formed by 2 DNA nucleotides each
b. the 2 equivalence classes are formed by Purines and Pyrimidines
c. to represent the group it is used the unidimensional representation table.
d. the composition law is formed by the double condition:
i. two elements of the group can be combined only forming the DNA double helix pairs AT and GC
ii. Pairs must join and generate the neuter element (in this case 5), therefore the only possible combinations are 1-4 and 2-3.

2. The use of 5th Order Group applied to nucleotides for the description, prediction, creation and deactivation of regions for protein-protein interaction
3. The use of 5th Order Group applied to nucleotides to describe and find a solution for the genetic mutations known as SNP Single Nucleotide Polymorphism
4. The use of 5th Order Group applied to nucleotides to generate ad hoc binding regions for specific targets
5. The use of 5th Order Group applied to nucleotides to disable specific binding regions in any kind of protein.
6. The use of 5th Order Group applied to nucleotides to describe protein structures.

Protein interactions and properties

Auxiliary products or services for sale:
https://proteinproteininteractions.net/

Available for consultation? Yes

Invention #12382
Date posted: 2021-03-27

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