arXiv subjects
Publications and source records attributed to Miloje M. Rakocevic.
In several previous works, I presented the mirror symmetry in the set of protein amino acids, expressed through the number of atoms. Here, however, the same thing is shown but over the number of nucleons and molecules mass. Compared to the previous version of the paper, minimal changes have been made, and Display 2 as well as Figures 3 and 4 have been added.
In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict distinction in Genetic Code Table (GCT) into some different quantums: 20, 23, 61 amino acid molecules. These molecules distinction is followed by specific balanced atom number and/or nucleon number distinctions within those molecules. In this second version two appendices are added; also a new version of Periodic system of numbers, whose first verson is given in arXiv:1107.1998 [q-bio.OT].
In the paper a new generalization of the Golden mean, as a further generalization in relation to Stakhov (1989) and to Spinadel (1999), is presented. Also it is first observed that the Euler divine equation represents a possible generalization of Golden mean. In this fourth version Figure A1 and Tables A3-A10 are added.
The paper represents three supplements to the source paper, q-bio/0610044 [q-bio.OT], with three new series of harmonic structures of the genetic code, determined by Gauss arithmetical algorithm; by Table of Minimal Adding, as in (Rakocevic, 2011a: Table 4; 2011b: Table 4); all structures in relation to Binary-code tree (Rakocevic, 1998). The determination itself is realized through atom and nucleon number balancing and nuancing of molekular polarity. In the first supplement the word is about some additional harmonic structures in relation to a previous our paper (Rakocevic, 2004); in the second one about the relation that structures with the polarity of protein amino acids. In the third supplement we give new ideas about the genetic code by an inclusion of the notions cipher of the genetic code and the key of that cipher.
It is shown that there is a sense in splitting Genetic Code Table (GCT) into three parts using the harmonic mean, calculated by the formula H (a, b) = 2ab / (a + b), where a = 63 and b = 31.5. Within these three parts, the amino acids (AAs) are positioned on the basis of the validity of the evident regularities of key parameters, such as polarity, hydrophobicity and enzyme-mediated amino acid classification. In addition, there are obvious balances of the number of atoms in the nucleotide triplets and corresponding amino acid groups and/or classes.
This paper presents, for the first time, four diversity types of protein amino acids. The first type includes two amino acids (G, P), both without standard hydrocarbon side chains; the second one four amino acids, as two pairs [(A, L), (V, I)], all with standard hydrocarbon side chains; the third type comprises the six amino acids, as three pairs [(F, Y), (H, W), (C, M)], two aromatic, two hetero aromatic and two "hetero" non-aromatic); finally, the fourth type consists of eight amino acids, as four pairs [(S, T), (D, E), (N, Q), (K, R)], all with a functional group which also exists in amino acid functional group (wholly presented: H2N-ĊH-COOH; separately: OH, COOH, CONH2, NH2). The insight into existence of four types of diversity was possible only after an insight into the existence of some very new arithmetical regularities, which were so far unknown. Also, as for showing these four types was necessary to reveal the relationships between several key harmonic structures of the genetic code (which we presented in our previous works), this paper is also a review article of the author's researches of the genetic code. By this, the review itself shows that the said harmonic structures are connected through the same (or near the same) chemically determined amino acid pairs, 10 pairs out of the 190 possible.
It is presented that the positions of amino acids within Genetic Code Table follow from strict their physical and chemical properties as well as from a pure formal determination by the Golden mean.
This note represents the further progress in understanding the determination of the genetic code by Golden mean (Rakocevic, 1998). Three classes of amino acids that follow from this determination (the 7 "golden" amino acids, 7 of their complements, and 6 non-complements) are observed now together with two further possible splittings into 4 x 5 and 5 x 4 amino acids.
In this paper it is shown that within a Combined Genetic Code Table, realized through a combination of Watson-Crick Table and Codon Path Cube it exists, without an exception, a strict distinction between two classes of enzymes aminoacyl-tRNA synthetases, corresponding two classes of amino acids and belonging codons. By this, the distinction itself is followed by a strict balance of atom number within two subclasses of class I as well as two subclasses of class II of amino acids.
In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict AAs positions; more exactly, with AAs ordinal number in three variants; first variant 00-19, second 00-21 and third 00-20. The ordinal number follows from the positions of belonging codons, i.e. their digrams (or doublets). The reading itself is a reading in quaternary numbering system if four bases possess the values within a specific logical square: A = 0, C = 1, G = 2, U = 3. By this, all splittings, distinctions and classifications of AAs appear to be in accordance to atom and nucleon number balance as well as to the other physico-chemical properties, such as hydrophobicity and polarity.
In this work it is shown that three pairs of the factors appear to be the key, i.e. main factors of a natural classification of protein (canonical) amino acids within the amino acid (genetic) code. First pair: the factors of the habit of an amino acid molecule (size and polarity). Second pair: the factors of the association (type of the amino acid/enzyme reactivity and degree of the hydrophobicity/hydrophilicity of an amino acid molecule). Third pair: the factors of the dissociation (degree of the acidity-basicity, over acidic group, COOH and degree of the basicity/acidity over the basic group, NH2). As a result of the influence and interdependence of all six factors (measured through correspondent valid parameters) it appears still one natural classification into polar and non-polar amino acids, where polar amino acids possess negative and non-polar, the positive values of hydropathy index.
In a certain way, this paper presents the continuation of the previous one which discussed the harmonic structure of the genetic code (Rakocevic, 2004). Several new harmonic structures presented in this paper, through specific unity and coherence, together with the previously presented (Rakocevic, 2004), show that it makes sense to understand genetic code as a set of several different harmonic structures. Thereby, the harmonicity itself represents a specific unity and coherence of physico-chemical properties of amino acid molecules and the number of atoms and/or nucleons in the molecules themselves (in the form of typical balances). A specific Gauss' arithmetical algorithm has the central position among all these structures and it corresponds to the patterns of the number of atoms within the side chains of amino acid molecules in the following sense: G+V = 11; P+I = 21; S+T+L+A+G = 31; D+E+M+C+P = 41; K+R+Q+N+V = 61; F+Y+W+H+I = 71; (L+M+Q+W) + (A+C+N+H) = 81; (S+D+K+F) + (T+E+R+Y) = 91; (F+L+M+S+P) = (T+A+Y+H+I) = (Q+N+K+D+V) = (E+C+W+R+G) = 51. Bearing in mind all these regularities it make sense to talk about genetic code as a harmonic system. On the other hand, such an order provides new evidence supporting the hypothesis established in the previous paper (Rakocevic, 2004) that genetic code has been complete from the very beginning and as such was the condition for the origin and evolution of life.