A representation of DNA primary sequences by random walk

Area of Science:

• Bioinformatics
• Computational Biology
• Genomics

Background:

• DNA primary sequences present complex data.
• Analyzing sequence similarity and dissimilarity is crucial for evolutionary and functional studies.

Purpose of the Study:

• To develop a novel method for describing and analyzing DNA primary sequences.
• To introduce new invariants for characterizing DNA sequences.
• To compare beta-globin gene sequences across species using these invariants.

Main Methods:

• Describing DNA primary sequences using random walk models.
• Generating two random sequences, {Y(m)} and {X(n)}, from DNA sequences.
• Proving that {Y(m)} and {X(n)} are Markov chains.
• Utilizing transition probability distributions and numerical characterizations.
• Introducing new DNA sequence invariants.

Main Results:

• Demonstrated that the derived random sequences {Y(m)} and {X(n)} are Markov chains.
• Introduced novel invariants for DNA primary sequences based on Markov chain properties.
• Successfully compared exon 1 sequences of beta-globin genes from nine species, analyzing similarities and dissimilarities.

Conclusions:

• The random walk and Markov chain approach provides a robust framework for DNA sequence analysis.
• The newly introduced invariants offer valuable tools for quantitative comparison of genetic sequences.
• This method facilitates a deeper understanding of evolutionary relationships and functional conservation among genes.