Various physical properties such as dipole moment, heat of formation and energy of the most stable formation of nucleotides and bases were calculated by PM3 (modified neglect of diatomic overlap, parametric method number 3) and AM1 (Austin model 1) methods. As distinct from previous calculations, for nucleotides the interaction with neighbours is taken into account up to gradient of convergence equaling 1. The dependences of these variables from the place in the codon and the determinative degree were obtained. The difference of these variables for codons and anticodons is shown.
It is well-known from the genetic code structure that there exists a connection between codons and physical and chemical amino acid properties (Lewin, 1983). Codon properties in turn are defined by physical properties of the nucleotides from which they are compounded (Ratner, 1985;2000). The most important properties of nucleotides as complex three-dimensional molecules are their dipole moment, heat of formation and energy of the most stable conformation (Schneider and Berman, 1995;Zheltovsky et al., 1989;Govorun et al., 1992). This work is devoted to theoretical calculation of these parameters depending on the nucleotide position in the codon and on the characteristics descriptions of different bases specificity-the nucleotides determinative degree introduced in (Duplij and Duplij, 2000;2001;Duplij et al., 2000).
Various physical properties, such as total energy, heat of formation, dipole moment and ionization potential of canonical isolated nucleotides were calculated in (Zheltovsky et al., 1989;Govorun et al., 1992) by AM1 (austin model 1) method and in (Sponer et al., 1996) by MP2 (second-order Moller-Plesset perturbational method). Here we use PM3 (modified neglect of diatomic overlap, parametric method number 3) method which is a modified AM1 method with many more parameters (Stewart, 1990;Dewar et al., 1985).
It is known that the bases in the genetic code triplets play different roles related to amino acid determination. For example, first base doublet in a codon determines certain amino acid’s formation to a greater degree than third base doublet in codon. Hence half of all triplets (32 codons) have full degeneration by third base doublet, so that an amino acid is entirely specified by the first two nucleotides independently of the third one (Lewin, 1983;Singer and Berg, 1991). Nearly two thirds of all DNA bases have almost constant properties in every organ-ism-those are the bases being in the first or second positions in a triplet. Sixteen of possible doublets may be described as two octets. The first eight doublets (“strong”) code amino acids independently of the third codon’s nucleotide base and another eight doublets (“weak”) determine the codon by third nucleotide base. So it is possible to arrange nucleotides in decreasing order of their ability of amino acid one-to-one determination in such a way: C, G, T, A (Rumer, 1968). In the works (Duplij and Duplij, 2000;Duplij et al., 2000) an abstract characteristics of nucleotides-the determinative degree (d x )-was introduced and used for numerical description of the “strength” of nucleotides. It was proposed so as shown as follows:
It allows us to follow from the qualitative description of the genetic code structure (relative to ability of coding amino acids) to its quantitative description. We suppose that the first approximation determinative degree of codons is additive, that is for doublet x, y we have d xy =d x +d y . So the rhombic doublets structure can be presented as follows:
which corresponds to the rhombic version of the genetic dictionary (Karasev and Sorokin, 1997;Karasev, 1976), and is related to the “strength” of every doublet so that horizontal rows of this structure consist of doublets with equal “strength”. The additivity proposition for triplets gives the possibility to calculate their “strength” by the formula d xyz =d x +d y +d z and to examine the symmetry of the cubic codon matrix.
Next we deal with physical properties of nucleotides depending on the abstract characteristics-their determinative degree d.
AM1 is a modified MNDO (modified neglect of differential overlap method) method. PM3 is a reparametrization of AM1 which is based on the ignoring of diatomic differential overlap (NDDO) approximation (Stewart, 1990). NDDO retains all one-center differential overlap terms when coulomb and exchange integrals are computed. PM3 differs from AM1 only in the values of the parameters (Dewar et al., 1985). The parameters for PM3 were derived by comparing a much larger number and wider variety of experimental versus computed molecular properties. The elements of the Fock matrix based on the NDDO approximation are described below. When orbitals φ µ and φ ν are on different centers, the off-diagonal elements of the Fock matrix are
where λ is index of orbitals on atom A and σ is index of orbitals on atom B , and α and β desribe two different sets of spatial molecular orbitals-those that hold electrons with spin up and those that hold electrons with spin down, respectively. The diagonal elements of the Fock matrix are
where P α+β =P α +P β and P is the effective number of electrons occupying the atomic orbital. The terms involved in the above equations are described below.
The MNDO method has 22 unique two-center two-electron integrals for each pair of heavy (non-hydrogen)
The two-center two-electron repulsion integrals µν|λσ represent the energy of interaction between the charge distributions (φ µ φ ν ) in atom A and (φ λ φ σ
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