Symmetry in encoding genetic information in DNA
- PDF / 91,518 Bytes
- 7 Pages / 595.276 x 793.701 pts Page_size
- 84 Downloads / 168 Views
SYMMETRY IN ENCODING GENETIC INFORMATION IN DNA1 I. V. Sergienko,a† A. M. Gupal,a‡ and A. A. Vagisa
UDC 519.217.2
Abstract. It is shown that two types of symmetry are possible for pairs of bases; however, only one, more efficient method of encoding and decoding information is implemented in nature. It is proved that the symmetry of short sequences including separate bases follows from the symmetry of sequences of bases. A model of Markov chains is used to show that the symmetry of sequences of bases follows from the symmetry of pairs of bases. Keywords: bases, complementarity, symmetry, Markov chain, transition probabilities. INTRODUCTION Complementarity, or symmetry relations in encoding of bases along one strand in DNA chromosomes were studied in [1–3] (see [1] for bibliography). Symmetry relations are presented in [2, 3] as short formulas, which makes understanding of these results much simpler and provides a basis to develop a mathematical apparatus in order to obtain new results. Statistical analysis has proved that symmetry relations hold for genomes of bacteria, plants, higher organisms (about hundred genomes), including human DNA [2, 3]. Thus, there is obvious symmetry in genetic information encoded in DNA; however, the reasons that explain this phenomenon are not revealed yet. In the paper, we will derive new rules in base decoding along one strand in DNA chromosomes and will prove that the symmetry of short sequences, including isolated bases, follows from the symmetry of sequences of bases. Two forms of symmetry are possible for pairs of bases; however, one, more efficient way of encoding and decoding of information is implemented in the nature. We will use a model of a homogeneous Markov chain to show that the symmetry for triples, quadruples, and short sequences of bases follows from the symmetry of pairs of bases. SYMMETRY OF BASES DNA has the form of a double helix, information is encoded in a four-letter alphabet of bases: adenine (A), cytosine (C), guanine (G), and timine (T). C — G and A — T are known to be complementary pairs of bases that link two strands. Chromosomes are indivisible segments of DNA, they contain information about thousands of genes; therefore, calculations were performed at the level of the whole chromosome, not an isolated gene. The bases of the first and second complementary strands of DNA chromosome are encoded and decoded from left to right in the 5¢ ® 3¢ direction and from right to left in the 5¢ ® 3¢ direction, respectively (Fig. 1). In what follows, the relationships are usually approximate. 1
The study was carried out within the framework of the project of the NAS of Ukraine and Russian Fund for Basic Research for 2010–2011 and was sponsored by the Presidium of the NAS of Ukraine. a
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]; ‡[email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 88–94, May–June 2011. Original article submitted January 11, 2011. †
408
1060-0396
Data Loading...
