Modern coding sequences are in the periodic-to-chaotic transition.

Area of Science:

• Genomics
• Bioinformatics
• Molecular Biology

Background:

• Coding sequences exhibit complex dynamics, often near a periodic-to-chaotic transition.
• The alpha A-crystallin gene is crucial for lens transparency and is a model for studying sequence evolution.

Purpose of the Study:

• To analyze the evolutionary dynamics of the chicken alpha A-crystallin coding sequence.
• To investigate the proposed decay of periodicity governed by the golden mean (4, 7, 11 rule).

Main Methods:

• Sequence analysis of the chicken alpha A-crystallin coding sequence.
• Identification of repeating units and their hierarchical organization.
• Application of number theory principles (golden mean) to describe sequence patterns.

Main Results:

• The initial tetrameric periodicity (CCTG) of the alpha A-crystallin sequence is decaying.
• This decay follows a specific pattern related to the golden mean, described by the 4, 7, 11 rule.
• The tetramer is incorporated into recurring heptamers, which in turn form 11-base-long repeating units.

Conclusions:

• The chicken alpha A-crystallin coding sequence demonstrates a transition towards chaotic behavior.
• The golden mean-based 4, 7, 11 rule provides a mathematical framework for understanding this sequence evolution.
• Hierarchical repeating units emerge as periodicity decays, suggesting a mechanism for sequence diversification.