New invariant of DNA sequences

Area of Science:

• Bioinformatics
• Computational Biology
• Genomics

Background:

• DNA sequences can be represented by n x n nonnegative real symmetric matrices with zero diagonal entries.
• The leading eigenvalue of these matrices is a common invariant for DNA sequence characterization.

Purpose of the Study:

• To introduce a novel, computationally simpler invariant for characterizing DNA sequences.
• To evaluate the utility of this new invariant as an alternative to leading eigenvalues.

Main Methods:

• Association of DNA sequences with n x n nonnegative real symmetric matrices (M).
• Calculation of lower bound ((1/n)||M||_m1) and upper bound (sqrt[(n-1)/n]||M||_F) for the leading eigenvalue (lambda1).
• Using the arithmetic average of these bounds as an alternative invariant.

Main Results:

• The arithmetic average of the derived bounds provides a simpler approximation of the leading eigenvalue.
• This new parameter effectively characterizes DNA sequences.

Conclusions:

• The proposed arithmetic average serves as a practical and simpler alternative invariant for DNA sequence characterization.
• The method's utility is demonstrated across diverse species including human, chimpanzee, mouse, rat, and gallus.