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Strong Comma-Free Codes in Genetic Information.

Elena Fimmel1, Christian J Michel2, Lutz Strüngmann1

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

Bulletin of Mathematical Biology
|June 24, 2017
PubMed
Summary
This summary is machine-generated.

Strong comma-free codes, a new class of circular codes, efficiently detect frameshifts in biological translation. These codes reveal novel properties of the genetic code and its evolution, with each amino acid coded by at least one such code.

Keywords:
-propertyEnumerationGenetic codeMaximalitySelf-complementarityStrong comma-free codes

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Area of Science:

  • Combinatorics
  • Bioinformatics
  • Genetics

Background:

  • Comma-free codes are a well-studied class of circular codes.
  • Recent graph theory approaches have led to the identification of new circular code types.
  • Frameshift detection is crucial in biological translation processes.

Purpose of the Study:

  • To introduce and define a new class of circular codes: strong comma-free codes.
  • To explore the combinatorial properties of these codes, including enumeration, maximality, self-complementarity, and the [Formula: see text]-property.
  • To investigate the implications of strong comma-free codes for understanding the standard genetic code and its evolution.

Main Methods:

  • Utilizing graph theory for the study of circular codes.
  • Applying combinatorial analysis to strong comma-free codes.
  • Examining the structure of the standard genetic code in relation to these codes.

Main Results:

  • Strong comma-free codes are identified, capable of detecting frameshifts after a reading window of at most two nucleotides.
  • Several combinatorial properties of strong comma-free codes are described and analyzed.
  • Each amino acid in the standard genetic code is shown to be encoded by at least one strong comma-free code of size 1.
  • A subset of 9 amino acids (S) is identified for which their synonymous trinucleotide sets form strong comma-free codes.
  • The primeval comma-free RNY code is characterized as a self-complementary [Formula: see text]-code and the union of two complementary strong comma-free codes.

Conclusions:

  • Strong comma-free codes offer a novel framework for understanding error detection in biological translation.
  • The combinatorial properties of these codes provide new insights into the structure and evolution of the genetic code.
  • The findings suggest a fundamental role for strong comma-free codes in the efficiency and robustness of the genetic code.