  In this paper we denonstrate that the use of the system of 2-adic numbers
provides a new insight to some problems of genetics, in particular, generacy of
the genetic code and the structure of the PAM matrix in bioinformatics. The
2-adic distance is an ultrametric and applications of ultrametrics in
bioinformatics are not surprising. However, by using the 2-adic numbers we
match ultrametric with a number theoretic structure. In this way we find new
applications of an ultrametric which differ from known up to now in
bioinformatics.
  We obtain the following results. We show that the PAM matrix A allows the
expansion into the sum of the two matrices A=A^{(2)}+A^{(\infty)}, where the
matrix A^{(2)} is 2-adically regular (i.e. matrix elements of this matrix are
close to locally constant with respect to the discussed earlier by the authors
2-adic parametrization of the genetic code), and the matrix A^{(\infty)} is
sparse. We discuss the structure of the matrix A^{(\infty)} in relation to the
side chain properties of the corresponding amino acids.
