Informational Approach for the Study of Cis-Regulatory Elements and Dna Binding Proteins

Nishihama, Mutsuko; Sakatsuji, Yukako; Arinami, Atsushi; Miyazaki, Satoru

doi:10.1142/9789812793171_0028

Cited by 2 publications

(3 citation statements)

References 4 publications

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“…We remark that the use of ultrametric is not surprising in bioinformatics, see e.g. [12,13,14,15] for review. The main novelty of our approach is the use of locally constant clustering functions and consideration of this approach as a generalization of the group-theoretic approach.…”

Section: Introductionmentioning

confidence: 99%

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2-Adic clustering of the PAM matrix

Khrennikov

Козырев

2009

Journal of Theoretical Biology

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In this paper we demonstrate that the use of the system of 2-adic numbers provides a new insight to some problems of genetics, in particular, degeneracy of the genetic code and the structure of the PAM matrix in bioinformatics. The 2-adic distance is an ultrametric and applications of ultrametric 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((infinity)), 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((infinity)) is sparse. We discuss the structure of the matrix A((infinity)) in relation to the side chain properties of the corresponding amino acids. We introduce the family of substitution matrices A(alpha,beta)=alpha A((2))+beta A((infinity)), alpha,beta>or=0 which should allow to vary the alignment procedure in order to take into account the different chemical and geometric properties of the amino acids.

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Section: Introductionmentioning

confidence: 99%

“…2-adic arithmetic operations are continuous with respect to this metric 3. We remark that to appeal to hierarchical structures is quite common in genetics and bioinformatics in general, see, e.g [14],[15]…”

mentioning

confidence: 99%

2-Adic clustering of the PAM matrix

Khrennikov

Козырев

2009

Journal of Theoretical Biology

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“…Various clustering procedures play a crucial role in bioinformatics, in particular, genetics, see, e.g., [1,2] or [3]. An important class of such procedures is based on introduction of various metrics on the space information strings, see e.g.…”

Section: Introductionmentioning

confidence: 99%

p-Adic numbers in bioinformatics: from genetic code to PAM-matrix

Khrennikov,

Kozyrev

2009

Preprint

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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 (∞) , 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 (∞) is sparse. We discuss the structure of the matrix A (∞) in relation to the side chain properties of the corresponding amino acids.

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Informational Approach for the Study of Cis-Regulatory Elements and Dna Binding Proteins

Cited by 2 publications

References 4 publications

2-Adic clustering of the PAM matrix

2-Adic clustering of the PAM matrix

p-Adic numbers in bioinformatics: from genetic code to PAM-matrix

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