Understanding of Genetic Code Degeneracy and New Way of Classifying of Protein Family - A Mathematical Approach

Oct 12, 2026

Uploaded by dawugda

The genetic code maps DNA/RNA triplet codons to protein amino-acid sequences, creating a degeneracy problem because multiple codons can encode the same amino acid. This manuscript presents a mathematical explanation of genetic-code degeneracy using a parameter called “Impression.” It further introduces a graph-theoretic method for classifying protein families, motivated by the biochemical similarity of proteins within a class and its relevance to drug design.

LanguageEnglish

CategoryGeneral

FormatPDF

Pages5

Reading Time2 min

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I. INTRODUCTION

II. METHODS AND MATERIALS

Encoding into ternary numbers and the “Impression” parameter

Graph building using “Impression”

III. RESULTS AND DISCUSSION

Degeneracy of the codon table

Classification of the Iron protein family

CONCLUSION

Understanding of Genetic Code Degeneracy and New Way of Classifying of Protein Family: A Mathematical Approach Jayanta Kumar Das 1, Atrayee Majumder2, Pabitra Pal Choudhury3 Applied Statistics Unit Indian Statistical Institute Kolkata-700108, India [1](1dasjayantakumar89@gmail.com)[dasjayantakumar89@gmail.com](1dasjayantakumar89@gmail.com) , [atu.tua@gmail.com](atu.tua@gmail.com2)[2](atu.tua@gmail.com2), [pabitrapalchoudhury@gmail.com](pabitrapalchoudhury@gmail.com3)[3](pabitrapalchoudhury@gmail.com3) Abstract— The genetic code is the set of rules by which information encoded in genetic material (DNA or RNA sequences) is translated into proteins (amino acid sequences) by living cells. The code defines a mapping between tri-nucleotide sequences, called codons, and amino acids. Since there are 20 amino acids and 64 possible tri-nucleotide sequences, more than one among these 64 triplets can code for a single amino acid which incorporates the problem of degeneracy. This manuscript explains the underlying logic of degeneracy of genetic code based on a mathematical point of view using a parameter named“Impression”. Classification of protein family is also a longstanding problem in the field of Bio-chemistry and Genomics. Proteins belonging to a particular class have some similar biochemical properties which are of utmost importance for new drug design. Using the same parameter “Impression” and using graph theoretic properties we have also devised a new way of classifying a protein family. Index Terms- Encoding, Impression, Order pair Graph, Degeneracy, Classification etc. I. INTRODUCTION Biological functionality of every living organism is regulated by proteins [1] which, in turn, can be viewed as sequences of amino acids. There are many methods for information processing that can be used for the analysis of proteins (sequence of amino acids) [2, 3] . There are 25 amino acids among which 20 are standard and 5 are non-standard amino acids. All of them can be represented by their respective unique symbols in ternary notation following an encoding scheme. The main problem is how to make the digital coding of amino acids for better distinguishability which can be done in various ways [4] . Here encoding is done based on molecular weight of amino acid. The question may arise why as such encoding schemes are required. From biochemical point of view, amino acids have some properties (polar, non-polar, charged etc.) with the help of which we can categorize them into different groups. But when we want to study these groups from a mathematical point of view we need to define parameters which can uniquely represent these 25 amino acids without any ambiguity. Therefore we have to transform each amino acid to some other notable symbols so that we can formulate a new parameter to study the properties of the group mathematically. For this reason, encoding or transformation of amino acids into ternary numbers get suitable notation and best fitted without loss of generality. The code in which genetic instructions are written, using an alphabet based on the four bases in DNA and RNA: adenine (A), cytosine (C), guanine (G), and thymine (T) (for DNA) or uracil (U) (for RNA) . Each triplet of bases indicates a particular kind of amino acid which is tobe synthesized. Since there are 20 amino acids and 64 possible triplets, more than one triplet can code for a particular amino acid [5] . The code is non-overlapping; the triplets are read end-to-end in sequence (e.g. UUU = phenylalanine, UUA = leucine, CCU = proline); and there are three triplets not translated into amino acid, indicating chain termination called stop codon. The code is universal and applies to all species with some exceptions. Theoretically, there are 43 = 64 different codon combinations possible with a triplet codon of three nucleotides. In reality, all 64 codons of the standard genetic code are assigned for either amino acids or stop signals during translation.

FAQs

What does the manuscript mean by genetic code degeneracy?

Degeneracy refers to the fact that among 64 possible codon triplets, multiple triplets can correspond to a single amino acid in the translation process.

How is the parameter “Impression” used in the study?

“Impression” is defined as a mathematical parameter of an amino acid on ternary numbers in triplet form, and it is used to explain codon degeneracy and support protein-family classification.

How does the paper classify a protein family?

After encoding and defining “Impression,” the work constructs a graph-theoretic model to classify proteins, specifically the Iron protein family, and relates the resulting classes to biological properties.

Oct 12, 2026

Uploaded by dawugda