Self-similarity and the maximum entropy principle in the genetic code

• Published in: Theory in biosciences = Theorie in den Biowissenschaften Vol. 142; no. 3; pp. 205 - 210
• Main Author: Kak, Subhash
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023; Springer Nature B.V
• Subjects: Amino acids; Bioinformatics; Biology; Biomedical and Life Sciences; Codons; Coevolution; Complex Systems; Entropy; Evolutionary Biology; Gene mapping; Genetic code; Genetic transformation; Life Sciences; Mathematical and Computational Biology; Original Article; Philosophy of Biology; Theoretical Ecology/Statistics; Genetic code; Error-correction coding; Maximum entropy principle; Information efficiency
• ISSN: 1431-7613; 1611-7530; 1611-7530
• DOI: 10.1007/s12064-023-00396-y

This paper addresses the relationship between information and structure of the genetic code. The code has two puzzling anomalies: First, when viewed as 64 sub-cubes of a 4 × 4 × 4 cube, the codons for serine (S) are not contiguous, and there are amino acid codons with zero redundancy, which goes counter to the objective of error correction. To make sense of this, the paper shows that the genetic code must be viewed not only on stereochemical, co-evolution, and error-correction considerations, but also on two additional factors of significance to natural systems, that of an information-theoretic dimensionality of the code data, and the principle of maximum entropy. One implication of non-integer dimensionality associated with data dimensions is self-similarity to different scales, and it is shown that the genetic code does satisfy this property, and it is further shown that the maximum entropy principle operates through the scrambling of the elements in the sense of maximum algorithmic information complexity, generated by an appropriate exponentiation mapping. It is shown that the new considerations and the use of maximum entropy transformation create new constraints that are likely the reasons for the non-uniform codon groups and codons with no redundancy.