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Construction of Dinucleotide Circular Codes Based on Nucleotide Probabilities.

Elena Fimmel1, Christian J Michel2, Lutz Strüngmann1

  • 1Institute of Mathematical Biology, Faculty for Computer Sciences, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.

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|December 29, 2025
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Summary
This summary is machine-generated.

This study reveals how primitive dinucleotide circular codes, essential for gene reading frames, may arise from basic nucleotide statistics. Two universal codes were identified, supporting a model for the genetic code

Keywords:
ClassesConstructionDinucleotide circular codesGenetic codeNucleotide probabilityTransitive codes

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Area of Science:

  • Genetics and Genomics
  • Bioinformatics and Computational Biology
  • Origin of Life Research

Background:

  • The origin of circular codes, crucial for gene reading frame recovery, remains an open problem, especially in primitive biological systems.
  • Previous work identified trinucleotide circular codes but generated only a subset using probabilistic methods.
  • A gap exists in understanding how these codes might emerge from fundamental nucleotide properties.

Purpose of the Study:

  • To explore the generation of dinucleotide circular codes using a nucleotide probability product model.
  • To investigate the theoretical basis for the emergence of circular codes from primitive nucleotide distributions.
  • To identify universal dinucleotide circular codes across different domains of life.

Main Methods:

  • Development and application of a nucleotide probability product model (Construction 2) for generating dinucleotide circular codes.
  • Introduction and theoretical characterization of transitive dinucleotide codes, including theorems on circularity and comma-free properties.
  • Analysis of codon usage data from bacteria, archaea, and eukaryotes to identify observed dinucleotide codes.

Main Results:

  • Demonstrated the generation of various dinucleotide circular codes via the probabilistic model.
  • Identified two universal maximal dinucleotide circular codes ([Formula: see text] and [Formula: see text]) in bacterial, archaeal, and eukaryotic codon usage.
  • Showed that a specific dinucleotide code ([Formula: see text]) generated by Construction 2 matches an observed universal code, supporting a statistical origin.

Conclusions:

  • Dinucleotide circular codes can be generated from statistical properties of primitive nucleotide distributions.
  • The findings support a theoretical model for the emergence of circular codes, potentially offering insights into the origin of the genetic code.
  • The identified universal codes suggest underlying principles governing genetic code structure.