Are Irrational Numbers (Like the Square Root of the Number Seven) Applicable to Genetic Sequences? ()
1. Introduction and Calculation of the Square Root of Seven numbers
1.1. Introduction
The relationships between numbers and genetic codes are not only research with the square root of the number two [1] and but also researched with the square root of the number three [2] and the square root of the number five [3], too from the Quantum Perspective Model [4], this paper attempts to search the relationships between the square root of the number seven and the genetic codes.
1.2. Calculating the Square Root of Seven
The square root of seven =
2.645751311064590590501615753639260425710259183082450180368334459201068823;
2302836277603928864745436106150645783384974630957435298886272147844273905;
558801077227171507297283238922996895948650872607009780542037238280237159;
4110034193911600157852559630594574103515239680271640737379907404158151990440347431;
945367139973059700505139969223754561609711902737815499163328828770400065757;
0674651963497752083793818114613090876473786595624330579947981281632307054 [5].
2. Methods and Discussion
2.1. Methods
The chemical structures of bases include Carbon (C), Nitrogen (N), Oxygen (O), and Hydrogen (H). Calculation of bases with chemical atoms (See also Table 1) (Ölmez T, 2020) [6].
The atomic numbers of them: Carbon (C): 6, Nitrogen (N): 7, Oxygen (O): 8, Hydrogen (H): 1 (Wieser E M et al., 2013) [7]. The chemical structures of bases (A, T, C, G, and U) are shown below (Ölmez T, 2020) [6].
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Table 1. Representation of nucleotide bases (A, T, C, G and U) in chemical atoms.
(A) Adenine: C5H5N5: 70; (T) Thymine: C5H6N2O2: 66, (C) Cytosine: C4H5N3O1: 58, (G) Guanine: C5H5N5O1: 78, and (U) Uracil: C4H4N2O2: 58 (Lodish H et al., 2018) [8].
2.2. Discussion
Every cell in our body contains genes, but only a certain subset of them is “turned on” or expressed in every cell. The amount of protein in each cell is controlled by a series of different processes. Now, if we analyze the genetic languages with the lowest level of information processing, it is the language of DNA and RNA with four nucleotide base alphabets and the language of proteins with twenty amino acid alphabets (Jonathan S, 2005) [9]. Genetic information is stored in DNA, the mobile messenger nucleic acid is transcribed into RNA and translated into amino acid sequences, which are then folded into proteins. Now, if we look at the Quantum Perspective Model starting from the amino acid class in the genetic code; The universal triplet has significant degeneration in genetic codes, with 64 codons (Penrose R et al., 2008) [10]. The reason it’s called the QUANTUM PERSPECTIVE MODEL, which evokes quantum mechanics, implies that the universe is effectively computing not only at the most microscopic level but also at larger scales (Penrose R et al., 2008) [10].
3. Calculation of the Square Root of Seven Numbers and Genetic Codes
The first four hundred and fifty digits of the square root of seven after the comma are here:
2.645751311064590590501615753639260425710259183082450180368334459201068823;
2302836277603928864745436106150645783384974630957435298886272147844273905;
558801077227171507297283238922996895948650872607009780542037238280237159;
4110034193911600157852559630594574103515239680271640737379907404158151990440347431;
945367139973059700505139969223754561609711902737815499163328828770400065757;
0674651963497752083793818114613090876473786595624330579947981281632307054 [5].
At first, the first group of the square root numbers of seven after comma was taken. For example, 6, 4, 5, 7, 5, 1, 3, 1, 1, 0, 6, 4, 5, 9, 0, 5, 9, 0, 5, 0, 1, …and so on. Secondly, all decimal numbers are subjected to the addition process, respectively. (6+4+5+7+5+1+3+1+1+0+6+4+5+9+0+5+9+0+5+0+1 = 77). The sum of the first group of the root square numbers of seven after comma is “77”. Just like as in (G) Guanine: 78 (See also Table 1).
The first group of the root square numbers of seven after comma:
6+4+5+7+5+1+3+1+1+0+6+4+5+9+0+5+9+0+5+0+1 = 77 (G) Guanine: 78
The second group of the root square numbers of seven after comma:
6+1+5+7+5+3+6+3+9+2+6+0+4+2+5+7 = 70 (A) Adenine: 70
The third group of the root square numbers of seven after comma:
1+0+2+5+9+1+8+3+0+8+2+4+5+0+1+8+0+3+6 = 66 (T) Thymine: 66
The fourth group of the root square numbers of seven after comma:
8+3+3+4+4+5+9+2+0+1+0+6+8+8+2+3 = 66 (T) Thymine: 66
The fifth group of the root square numbers of seven after comma:
2+3+0+2+8+3+6+2+7+7+6+0+3+9 = 58 (U) Uracil: 58
The sixth group of the root square numbers of seven after comma:
2+8+8+6+4+7+4+5+4+3+6+1+0+6+1+5 = 70 (A) Adenine: 70
The seventh group of the root square numbers of seven after comma:
0+6+4+5+7+8+3+3+8+4+9+7+4 = 68 (A) Adenine: 70
The eighth group of the root square numbers of seven after comma:
6+3+0+9+5+7+4+3+5+2+9+8+8 = 69 (A) Adenine: 70
The ninth group of the square numbers of seven after comma:
8+6+2+7+2+1+4+7+8+4+4+2+7+3+9+0+5 = 79 (G) Guanine: 78
The tenth group of the root square numbers of seven after comma:
5+5+8+8+0+1+0+7+7+2+2+7+1+7 = 60 (U) Uracil: 58
The eleventh group of the root square numbers of seven after comma:
1+5+0+7+2+9+7+2+8+3+2+3+8+9 = 66 (T) Thymine: 66
The twelfth group of the root square numbers of seven after comma:
2+2+9+9+6+8+9+5+9+4+8 = 71 (A) Adenine: 70
The thirteenth group of the root square numbers of seven after comma:
6+5+0+8+7+2+6+0+7+0+0+9+7+8+0+5 = 70 (A) Adenine: 70
The fourteenth group of the root square numbers of seven after comma:
4+2+0+3+7+2+3+8+2+8+0+2+3+7+1+5+9 = 66 (T) Thymine:66
The fifteenth group of the root square numbers of seven after comma:
4+1+1+0+0+3+4+1+9+3+9+1+1+6+0+0+1+5+7+8+5+2 = 71 (A) Adenine: 70
The sixteenth group of the root square numbers of seven after comma:
5+5+9+6+3+0+5+9+4+5+7+4+1+0+3 = 66 (T) Thymine: 66
The seventh group of the root square numbers of seven after comma:
5+1+5+2+3+9+6+8+0+2+7+1+6+4+0+7 = 66 (T) Thymine: 66
The eighteenth group of the root square numbers of seven after comma:
3+7+3+7+9+9+0+7+4+0+4+1+5+8+1 = 68 (A) Adenine: 70
The nineteenth group of the root square numbers of seven after comma:
5+1+9+9+0+4+4+0+3+4+7+4+3+1 = 58(U) Uracil: 58
The twentieth group of the root square numbers of seven after comma:
9+4+5+3+6+7+1+3+9+9+7+3 = 66 (T) Thymine: 66
The twenty-first group of the root square numbers of seven after comma:
0+5+9+7+0+0+5+0+5+1+3+9+9+6+9+2 = 70 (A) Adenine: 70
The twenty-second group of the root square numbers of seven after comma:
2+3+7+5+4+5+6+1+6+0+9+7+1+1+9+0+2+7+3 = 78 (G) Guanine: 78
The twenty-thirdgroup of the root square numbers of seven after comma:
7+8+1+5+4+9+9+1+6+3+3+2+8 = 66 (T) Thymine: 66
The twenty-fourth group of the root square numbers of seven after comma:
8+2+8+7+7+0+4+0+0+0+6+5+7+5+7 = 66 (T) Thymine: 66
The twenty-fifth group of the root square numbers of seven after comma:
0+6+7+4+6+5+1+9+6+3+4+9+7 = 67 (T) Thymine: 66
The twenty-sixth group of the root square numbers of seven after comma:
7+5+2+0+8+3+7+9+3+8+1+8+1+1+4+6+1+3 = 77 (G) Guanine: 78
The twenty-seventh group of the root square numbers of seven after comma:
0+9+0+8+7+6+4+7+3+7+8+6+5 = 70 (A) Adenine: 70
The twenty-eighth group of the root square numbers of seven after comma:
9+5+6+2+4+3+3+0+5+7+9+9+4 = 66 (T) Thymine: 66
The twenty-ninth group of the root square numbers of seven after comma:
7+9+8+1+2+8+1+6+3+2+3+0+7+0+5+4 = 66 (T) Thymine: 66
This sequence can be shown as [GATTUAAGUTAATATTAUTAGTTTGATT]. Let me try to explain this sequence with the “Quantum Perspective Model”. For example, The first group of the square root of seven after comma is equal to Guanine (G): 77 with the lack of one “1” Hydrogen bond (H:1) (Remember, See Table 1; Guanine (G): 78). This result may mean the sequence of the square root of seven in groups [GATTUAAGUTAATATTAUTAGTTTGATT]. The fifteenth group of the square root of seven after the comma is regarded as Adenine (A) with one more Hydrogen bond (H:1); Adenine: 71. (Remember, See Table 1; (A) Adenine:70) (Because the deviations in the calculation of the square root of seven numbers can be derived from the Cytosine (C)―Guanine (G) Hydrogen bonds because of Cytosine (C)―Guanine (G) pairs with by three hydrogen bonds. Adenine (A) pairs with Thymine (T) by two hydrogen bonds [6]. The reason for the lack/more of hydrogen bonds: Hydrogen bonding is a very versatile attraction (Ölmez T, 2020) [6]. Hydrogen bonds are relatively weak and easily broken by increasing hardness (Farrell R E, 2010) [11].
4. Results
After searching the square root of the number seven with the National Biotechnology Information Center (NCBI) databases [12], some conceptual relationships with bony fishes can ultimately be found. Types of bony fishes are based on Danio rerio (zebrafish) (See Figure 1). Types of other living creatures are eudicots, walking sticks, Danio aesculapii, flies beetles, moths, butterflies, lice, bivalves, roaches, hawks and eagles, caddisflies, Timema tahoe, Timema bartmani and carnivores. Another interesting result of NCBI is Timema shepardi, an animal that has not engaged in sexual reproduction for many years and has the longest known asexual period [11] (See Figure 2).
5. Conclusions
At first, the result of this research can be summarized as the expression of root
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Figure 1. The NCBI (National Center for Biotechnology Information) result for nucleotide sequence “GATTUAAGUTAATATTAUTAGTTTGATT” [13]. (https://blast.ncbi.nlm.nih.gov/Blast.cgi?PROGRAM=blastn&PAGE_TYPE=BlastSearch&LINK_LOC=blasthome)
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Figure 2. The NCBI (National Center for Biotechnology Information) result blast tree view widget for “GATTUAAGUTAATATTAUTAGTTTGATT” nucleotide sequence [14]. (https://www.ncbi.nlm.nih.gov/blast/treeview/treeView.cgi?request=page&blastRID=32WBVGR8016&queryID=lcl|Query_51663&entrezLim=&ex=&exl=&exh=&ns=100)
seven numbers after commas by genetic codes. Secondly, digits after the comma were thought to be an indicator of genetic codes. As a common feature of Biochemistry and Mathematical sciences, NCBI blasts are obtained [12]. Because these results include both bony fishes and especially Danio Rerio (zebrafish) (See Figure 1), some genetic stem cells have also been studied in zebrafish (Danio rerio) in studies with functional macrophages (Takahashi K, 2001) [15]. Zebrafish not only have muscarinic in their nervous system but also, receptor isoforms not previously identified in other species are present in zebrafish (Nuckels R J, 2006) [16] and (Abrams P et al. 2006) [17]. Although there are no specific subtypes of muscarinic acetylcholine receptors, detected in the zebrafish retina. An enzyme was studied in the developing zebrafish brain and retina. But more work may be needed to confirm the studies and experiment with zebrafish (Nuckels R J, 2006).
In biology-related experiments and gene sequencing, it is an excellent favorite example [18]. The common feature of pi numbers [4] and Euler numbers [19] [20] along with the square of the speed of light is that the NCBI results are bony fish [21] [22]. Let alone this result, NCBI result for CAAT Box also consists of bony fishes, too [6]. Thirdly, the genetic codes of the square root of two [1] and the genetic codes of the square root of three consist of the same NCBI blast results as the same as bony fishes [2]. Fourthly, although there is no periodic sequence of irrational numbers, in this paper a periodic sequence is obtained in terms of genetic sequences, just as in “GAT” and “UTA”. Remember, this sequence can be shown as [GATTUAAGUTAATATTAUTAGTTTGATT]. Finally, the results of calculating the square root of seven numbers with genetic codes can be expressed by chemical formulas of nucleotide bases. It is stated by Steward that life is between genes and Mathematics (Stewart I, 1999) [23]. Indeed, the relationships between Mathematics and Genetics have been described by a molecular-genetic alphabet matrix. According to the quantum perspective model, just like this matrix, is it possible to define the square root of the number seven as genetic sequences? (Petoukhov S V, 2011) [24].