**12. Definitive universal equations**

In the normalization of nucleotide contents (G + C + A + T = 1), as (G = C) and (A = T) based on Chargaff's parity rules, (2G + 2A = 1) is obtained. This equation is altered to (A = 0.5 – G) and then (A – G = 0.5 – 2G). Finally, G – A = 2G – 0.5. The relationship between (G – A) and (G) is linear when both (G) and (A) are expressed by linear functions. In animal mitochondria, only the correlations between the two purines (A versus G) or the two pyrimidines (C versus T) are linear, while the correlations between purines and pyrimidines (A or G versus T or C) are weak or not correlated at all [62]. For example, when plotting (G – C), (G – T), (G – A), (C – T), (C – A), and (T – C) against G content, only (G – A) versus G content was linear in vertebrate mitochondria [59]. In invertebrate mitochondria, plotting nucleotide content differences against G content was weakly linear.

Plotting (X – Y)/(X + Y) against (X – Y), the following linear relationship was obtained in mitochondria, chloroplasts, and chromosomes (**Figure 12**): (X – Y)/ (X + Y) = a (X – Y) + b, where X and Y are nucleotide contents, and (a) and (b) are constants. As (b) was almost null and (a) was ~2.0, (X – Y)/(X + Y) ≈ 2.0 (X – Y). In these genome analyses, which are independent of Chargaff's parity rules, the values of (a) for (G, C), (G, A), (G, T), (C, T), (C, A), and (A, T) were 2.5858, 1.85558, 1.9908, 1.9771, 1.9968, and 1.5689, respectively, in our previous results [53, 54]. Based on these results, (G + C), (G + A), (G + T), (C + A), (C + T), and (A + T) were 0.39, 0.54, 0.50, 0.51, 0.50, and 0.64, respectively. In virus genome analyses [53, 54], the constant values for (a) were 1.9–2.1, and the values for (X + Y) were 0.47–0.53. In contrast, in the normalization of nucleotide contents (G + C + A + T = 1), as (G = C) and (A = T) based on Chargaff's parity rules, (2G + 2A = 1) is obtained. This equation is altered to (G + A = 0.5). This value is consistent with the value obtained above from genome analyses. Similarly, (G + T = 0.5), (C + A = 0.5), and (C + T = 0.5), although (G + C) and (A + T) cannot be determined. Therefore, the four nucleotide contents are expressed by the following regression lines, plotted against G content: A = 0.5 – G, T = 0.5 – G, C = G, and G = G. Lines G and C overlap, as do lines A and T, and the former line is symmetrical to the latter against line (y = 0.25). The intercepts of lines G and C are close to the origin, while those of lines A and T are close to 0.5 at the vertical and horizontal axes. All organisms from bacteria to *H. sapiens* are located on the

#### *Cheminformatics and Its Applications*

diagonal lines of a 0.5 square, termed the "Diagonal Genome Universe," using the normalized values that obey Chargaff's first parity rule [12]. These relationships lead to (G or C) + (A or T) = 0.5. The present results indicate that a linear regression line equation, (X – Y)/(X + Y) = a (X – Y) + b, universally represents all normalized values, including the values deviating from Chargaff's parity rules. This newly discovered equation clearly reflects not only Chargaff's first parity rules, based on hydrogen bonding between two nucleotides, but also natural rule.

#### **Figure 12.**

*Universal rules. The following genome samples were examined: mitochondria of vertebrates (65), invertebrates (54), and non-animals (42), chloroplasts (28), prokaryote chromosomes (21), and eukaryote chromosomes (15). Left side: relationship between (X – Y) and (X – Y)/(X + Y) and right side: relationship between (X/Y) and (X – Y)/(X + Y).*

**25**

**Acknowledgements**

computer analyses.

*Visible Evolution from Primitive Organisms to* Homo sapiens

A linear regression line was not obtained when using randomly chosen value (**Figure 12A**). Furthermore, plotting (X – Y)/(X + Y) against (X/Y), the following logarithmic function was obtained for all tested genomes as well as when using randomly chosen values (**Figure 12B**): (X – Y)/(X + Y) = a ln (X/Y) + b. As (b) was almost null and (a) was ~0.5, (X – Y)/(X + Y) ≈ 0.5 ln (X/Y). The ratio between two values, (X/Y), can be expressed by a logarithmic function, ~0.5 ln (X/Y) ≈ (X – Y)/(X + Y). Plotting the GC skew vs. G content, animal mitochondria were classified into two groups: high and low C/G [59]. This fact indicates that the ratio C/G and the GC skew are evolutionarily related to each other. Any change can be expressed universally by a definitive logarithmic function, (X – Y)/(X + Y) = a ln (X/Y) + b. The present results indicate that cellular organelle evolution is strictly controlled under these characteristic rules, although nonanimal mitochondria, chloroplasts, and chromosomes are controlled under Chargaff 's parity rules [12, 14]. The present study clearly shows that biological evolution, which seems to be based on complicated processes, is governed by

The ratios of amino acids to the total amino acids or of nucleotides to total nucleotides predicted from complete genomes consisting of huge number of nucleotides can characterize a whole organism. In addition, as these values are independent of species and genome size, these indexes are very useful for genome research, as well as single gene research. The validity of these indexes is clearly based on the homogeneity of genomic structures. In addition, patternalization of values after simple calculations based on large data sets can provide an intuitive picture and provide useful insights, revealing the homogeneity of genomic structures followed by synchronous alterations over the genome. In addition, any change between two values, X and Y, including biological evolution can be expressed definitively by a linear regression line equation, (X – Y)/ (X + Y) = a (X – Y) + b, where X and Y are nucleotide contents, and (a) and (b) are constants, and by a logarithmic function, (X – Y)/(X + Y) = a′ ln (X/Y) + b′, where (a′) and (b′) are constants. As the present review is based on the endeavors and data of numerous scientists from all over the world, the author would like to express finally his following feeling as one of scientists. (Human being is an organism of huge numbers of organisms on the Earth, and we are not ranked as a special species above all organisms as a result of long evolution.) However, we have made the present modern civilization based on fossil energy usage which seems to induce climate changes. Thus, we must be responsible to establish sustainable development not only for Human being but also for other organisms.

The author greatly acknowledges President Hiroyuki Okada of Shinko Sangyo, Co. Ltd., Takasaki, Gunma, Japan for his financial support and Dr. Teiji Okayasu who was one of collaborators in Dokkyo Medical University for his excellent

The Earth is for all organisms, not only for Human being.

*DOI: http://dx.doi.org/10.5772/intechopen.91170*

simple universal equations.

**13. Conclusions**

*Visible Evolution from Primitive Organisms to* Homo sapiens *DOI: http://dx.doi.org/10.5772/intechopen.91170*

A linear regression line was not obtained when using randomly chosen value (**Figure 12A**). Furthermore, plotting (X – Y)/(X + Y) against (X/Y), the following logarithmic function was obtained for all tested genomes as well as when using randomly chosen values (**Figure 12B**): (X – Y)/(X + Y) = a ln (X/Y) + b. As (b) was almost null and (a) was ~0.5, (X – Y)/(X + Y) ≈ 0.5 ln (X/Y). The ratio between two values, (X/Y), can be expressed by a logarithmic function, ~0.5 ln (X/Y) ≈ (X – Y)/(X + Y). Plotting the GC skew vs. G content, animal mitochondria were classified into two groups: high and low C/G [59]. This fact indicates that the ratio C/G and the GC skew are evolutionarily related to each other. Any change can be expressed universally by a definitive logarithmic function, (X – Y)/(X + Y) = a ln (X/Y) + b. The present results indicate that cellular organelle evolution is strictly controlled under these characteristic rules, although nonanimal mitochondria, chloroplasts, and chromosomes are controlled under Chargaff 's parity rules [12, 14]. The present study clearly shows that biological evolution, which seems to be based on complicated processes, is governed by simple universal equations.
