New invariant of DNA sequences.

For a DNA sequence with n bases, one can always associate it with an n x n nonnegative real symmetric matrix whose diagonal entries are zero. Once the matrix is given, its leading eigenvalue is usually calculated and used as an invariant to characterize the DNA sequence. Let M be such a matrix, and lambda1 its leading eigenvalue. Then (1/n)//M//m1 and sqrt [(n-1)/n]//M//F are the lower and upper bounds of lambda1, respectively. Since their arithmetic average is an approximate value of lambda1 and simpler for calculation, we can use it as an alternative invariant to characterize the DNA sequence. The utility of the new parameter is illustrated on the DNA sequences of five species: human, chimpanzee, mouse, rat, and gallus.