What Is the Meaning of the Square Root of the Number Three in Biochemistry?

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1. Introduction and Calculation of the Square Root of Three Numbers from Decimal Base System (10) to Binary Base System (2) and Binary Base System (2) to Decimal Base System (10)

The relationships between numbers and genetic codes are not only researched with velocity of light numbers [2] but also researched with the golden ratio numbers, too [3] . The name of this relationship research is called Quantum Perspective Model by Kevser Köklü [4] . Then, the relationships between the square root of the number two and the genetic codes are researched by Tahir ÖLMEZ [5] . Now, as per this model, this paper attempts to search the relationships between the square root of the number three and the genetic codes (see Table 1).

2. Methods and Discussion

The chemical structures of bases include Carbon(C), Nitrogen (N), Oxygen (O), and Hydrogen (H). Calculation of bases with chemical atoms (See also Table 2) (Ölmez T, 2020) [3] .

The atomic numbers of them: Carbon (C): 6, Nitrogen (N): 7, Oxygen (O): 8, Hydrogen (H): 1 (Wieser E M et al., 2013) [6] . The chemical structures of bases (A, T, C, G, and U) are shown below (Ölmez T, 2020) [3] .

Table 1. The representation of decimal numbers in the binary base and vice versa.

Table 2. Representation of nucleotide bases (A, T, C, G and U) in chemical atoms.

(A) Adenine: C_{5}H_{5}N_{5}: 70;

(T) Thymine: C_{5}H_{6}N_{2}O_{2}: 66,

(C) Cytosine: C_{4}H_{5}N_{3}O_{1}: 64,

(G) Guanine: C_{5}H_{5}N_{5}O_{1}: 78, and

(U) Uracil: C_{4}H_{4}N_{2}O_{2}: 58

(Lodish H et al., 2018) [7] .

Before this work, the fourteen group of Pi number can be shown as: Continuous UTA’s by Kevser Köklü [4] . Secondly, another favorite sample of this research is done with velocity of light numbers by Kevser Köklü again [2] . This relationship between the numbers and genetic codes is called Quantum Perspective Model by Kevser Köklü [4] . Thirdly, in another article with identical cis regulatory elements examined the links between the Golden Ratio numbers [3] . Fourthly, there is a connection between Euler numbers and the Fibonacci series. When the numbers of Euler after the comma were converted from a decimal (10) number-based system to a binary (2) number-based system, they corresponded to the number “55” in the Fibonacci series [2] . Fifthly, there is a link between the square root of two [5] and the genetic codes. This can be shown as: [GGATGTCTATTGAGTGACAA] [5] . After all these studies, the square root of the number three and the genetic codes are now being investigated in relation to the Quantum Perspective Model.

3. Calculation of the Square Root of Three Numbers and Genetic Codes

The first two hundred digits of the square root of three [1] after the comma are here:

The square root of three = 1.73205080756887729352744634150587236694280525381038062805580697945193301690880003708114618675724857567562614141540670302996994509499895247881165551209437364852809323190230558206797482010108467492326501531234326690332288665067225466892183797122704713166036786158801904998653737985938946765034750657605075661834812960610094760218

At first, the first two digits after the comma were taken each time. For example, 73, 20, 50, 80, 75, 68, 87, 72 … and so on. Then these numbers are found in the binary number system in Table 1. (For instance, “73”, 1001001 and so on). Secondly, convert these binary numbers to decimal number base (For instance, “73” 1001001; 100 = 4, 100 = 4 and 1 = 1).Thirdly, all decimal numbers are subjected to the addition process, respectively. (4 + 4 + 1 = 6). All of the first result of the addition is “77”. Just like as in Guanine (G): 78 (See also Table 1).

This sequence can be shown as [GGATGACTACGGGTTTAGAAA]. Let me try to explain this sequence with the “Quantum Perspective Model.” For example, The first groups of the square root of three after comma equal to Guanine (G): 77 with the lack of one “1” Hydrogen bond (H: 1). (Remember, See Table 2; Guanine (G): 78) This result may mean the sequence of the square root of three in groups [GGATGACTACGGGTTTAGAAA]. The fourth groups of the square root of three after the comma is regarded as Thymine (T) with the lack of one Hydrogen bond (H: 1). (Remember, See Table 2; Thymine (T): 66) (Because the deviations in the calculation of the square root of three numbers can be derived from the Adenine (A) - Thymine (T) Hydrogen bonds because of Adenine (A) pairs with Thymine (T) by two hydrogen bonds. Cytosine (C) - Guanine (G) pairs with by three hydrogen bonds [4] . The reason for the lack of hydrogen bonds: Hydrogen bonding is a very versatile attraction (Ölmez T, 2020) [3] . Hydrogen bonds are relatively weak and easily broken by increasing hardness (Farrell R E, 2010) [8] .

4. Results

After searching the square root of the three numbers with the National Biotechnology Information Center (NCBI) databases, some conceptual relationships with bony fish can ultimately be found. Types of bony fishes are based on DENTICLE HERRING (See Figure 1). Types of other living creatures are Barber pole worm, human chromosome 15, golden spiny mouse and bacterium [9] (See Figure 2).

Figure 1. The NCBI (National Biotechnology Information Center) result for nucleotide sequence “GGATGACTACGGGTTTAGAAA” [9] .

Figure 2. The NCBI (National Biotechnology Information Center) result blast tree view widget for “GGATGACTACGGGTTTAGAAA” nucleotide sequence [9] .

5. Conclusions

Although the most widely used number digit system today is the decimal system, in this study, the square root of the number three is expressed as a binary number base system instead of a decimal base system [10] . When the numbers of Euler after the comma were converted from the decimal (10) number base system to the binary (2) number base system, they corresponded to the number “55” in the Fibonacci series (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…) [11] . In the same way, the binary (2) number-based system was used in this research. The alphabet of DNA and RNA is associated with binary numbers [12] . However, almost all the studies so far into perception of irrational numbers have focused on numbers, on the other hands, future studies should be studied in detail later in the perspective of genetic codes.

Firstly, the result of this research can be summarized as the expression of the numbers of three roots after commas by chemical formulas in genetic codes. Secondly, both 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. Because these results include both bony fish and especially DENTICLE HERRING. The common feature of pi numbers [4] and Euler numbers [13] along with the square of the speed of light is that the NCBI results are bony fish [2] [3] . Let alone this result, NCBI result for CAAT Box also consists of bony fishes, especially DENTICLE HERRING [3] . Denticle Herring is the most primitive living clupeiform [14] . Here is the consequence of how a single amino acid change on fish can have a major impact on ecological adaptation which is described [15] . Therefore, in the calculation of the golden ratio numbers, triplet codons were also used to express cis-regulatory elements (TATA Box, CAAT Box and GC box) [3] . Thirdly, with the genetic codes of the square root of two, the genetic codes of the square root of three consist of the same gene sequence in the following sequence: [GGATGACT] [5] . Finally, the results of calculating the square root of three numbers with genetic codes can be expressed by: [(A) Adenine, (T) Thymine, (C) Cytosine, (G) Guanine and (U) Uracil]. So, these can be associated with both Biochemistry and Mathematics. Namely, the square root numbers of the three after the comma can be attributed not only to numbers in mathematics, but also to genetic codes and chemical formulas in Biochemistry. In summary, researching this interesting connection in terms of the Quantum Perspective Model basically reveals the comparability of small units of analysis of the sciences, as in genetic codes and mathematical numbers.

References

[1] https://apod.nasa.gov/htmltest/gifcity/sqrt3.1mil

[2] Köklü, K. (2019) Is Relativity Theory Also Valid in Biogenetics and Mathematics? NeuroQuantology, 17, 53-58. https://doi.org/10.14704/nq.2019.17.3.1999

[3] Ölmez, T. (2020) Is There an Aesthetics in Golden Ratio as Regards to the Common Cis-Regulatory Elements versus to Atomic Numbers of Elements with Respect to Quantum Perspective Model? Neurology and Neuroscience Reports, 3, 1-4.

[4] Köklü, K. (2019) A Quantum Perspective Model to Genetic Codes through Various Sciences. NeuroQuantology, 17, 15-18. https://doi.org/10.14704/nq.2019.17.3.1974

[5] Ölmez, T. (2021) According to the Binary Number Base System, Are the Square Roots of Two Numbers Also Significant in Biochemistry?

[6] Wieser, E.M., Holden, N., Coplen, B.T., Böhlke, J.K., Berglund, M., Brand, W.A., et al. (2013) Atomic Weights of the Elements 2011. Pure and Application Chemistry, 85, 1047-1078.

https://doi.org/10.1351/PAC-REP-13-03-02

[7] Lodish, H., Berk, A., Zipursky, S.L., Matsudaira, P., Baltimore, D. and Darnell, J. (2018) Molecular Cell Biology. 6th Edition, Translation: Geçkil, H., Özmen, M., Yeşilada, Ö., Palme Publishing, New York, 294-302.

[8] Farrell, R.E. (2010) RNA Methodologies A Laboratory Guide for Isolation and Characterization. 4th Edition, Elsevier Academic Press, Amsterdam, 704-710.

[9] Basic Local Alignment Search Tool.
https://blast.ncbi.nlm.nih.gov/Blast.cgi

[10] Brind, S. (2019) Alternative Number Systems: What Are Binary Numbers?

https://owlcation.com/stem/Binary-Numbers

[11] Ölmez, T. (2021) Is There a Similarity between Fibonacci Sequence and Euler’s Number with Respect to Quantum Perspective Model? Global Journal of Science Frontier Research, 20, 33.

https://doi.org/10.34257/GJSFRFVOL20IS9PG35

[12] Sergey, P. (2019) The Genetic Code, Algebraic Codes and Double Numbers.

https://doi.org/10.20944/preprints201911.0301.v1

[13] Ölmez, T. (2021) With Respect to Quantum Perspective Model, Can Euler Numbers Be Related to Biochemistry? Global Journal of Science Frontier Research, 20, 7-14.

https://doi.org/10.34257/GJSFRFVOL20IS9PG7

[14] https://www.britannica.com/animal/Denticipitidae

[15] Hill, J., et al. (2019) Recurrent Convergent Evolution at Amino Acid Residue 261 in Fish Rhodopsin. PNAS, 116, 18473-18478.
https://www.pnas.org/content/116/37/18473