Introduction Studying neutral and selective evolution by the analyses of the distribution of bases in genomes and in dinucleotides whose bases were separated by 0, 1, 2, K nucleotides sites, I discovered that neutral evolution was impossible [1-7]. The studies of dinucleotides constructed a matrix where columns describe the distance to randomness of the distribution of both bases of a dinucleotide (measured by a chi-square test) and selective values, and rows the number of nucleotide sites separations between both bases of a dinucleotide. The study of selective profiles of the 16 possible dinucleotides shows in procaryotes (double stranded DNA) a great selective similitude between an Index (Ind) dinucleotide with its 5’-3’ Antiparallel (a-Par) dinucleotide, but a large difference between this Index and its Parallel (Par) dinucleotide [8,9].

In single stranded virus there is a small or none similitude between the index dinucleotide and their a-Par dinucleotide and a smaller similitude with its Par dinucleotide. Now I present a new analysis founded in a matrix where columns show selective values of the 16 dinucleotides and rows the number of site separations. GENOMES, METHOD AND RATIONALE Genomes and Method As in previous studies [2,9], we collected from Genbank genomes of the Human chromosome 21, a bacterium, one Archaea and some double and single stranded viruses. In the present Study genomes are: H. sapiens Chromosome 21 (HCh21) NC_000021.9 GRCh38.p7, 46,709,983 bp, double stranded (ds) DNA; M. Smithii (Archaea) NC_009515.1, strain ATCC 35061, 1,853,160 bp, dsDNA; Human cytomegalovirus (also Human herpesvirus 5, HHV-5), X17403.0 strain AD169, 229,354 bp, dsDNA; Phi X 174 phage of E.

coli, NC_001422, 5,386 b, ssDNA; SARS-CoV-2 virus, LR757998.1Wuhan, 29,903 b, ssRNA: HIV-1 MN691959.1, isolate ACH2-NFLMDA13 B1 (USA), 9,493 bp, ssRNA; E. coli genome, NZ_CP124398.1, strain AVSO967, 5,097,505 bp, dsDNA (processed for this program, I could not find this reference in the present information). Note: the number of nucleotides is approximate, it varies with strains and time since some variants are replaced; the collection of these genomes began more than 15 years ago. Also, there are few clerical errors (in relation to previous articles). The number of actual bases that are analyzed is less than the total number of sites that GenBank provides (sites without assigned bases). However, if the number and the chi-square value may vary, the structure of data is maintained almost equal.

In single stranded nucleic acids, I used b instead of bp. For these genomes I constructed the set of dinucleotides separated by 0, 1, 2, …100 dinucleotide sites. In these set of dinucleotides, I estimated the distance to randomness of the distribution of their both bases by a chi-square (χ2 ) test with 9 degrees of freedom (d.f.) for the total value, and with a χ2 test for each dinucleotide. This is the result of the matrix of four columns and four rows given by the four nucleotides: adenine (A), thymine (T), guanine (G) and cytosine (C). The selective value for each dinucleotide is given by the expected (random) and observed values (Obsi -Expi )/Expi where i goes from 1 to 16, the ordered dinucleotides are: AA, AT, AG, AC, TA, TT, TG, TC, GA, GT, GG, GC, CA, CT, CG, and CC.

This conforms a table where columns are the dinucleotides with their respective selective values and their distances to randomness measure by the χ2 (described in Table 1 but not analyzed here) and rows given by the separation of bases by K nucleotide sites from 0 to 100 as shown in Table 1. The χ2 is obtained by (Obsi -Expi )2 / Expi where i goes from 1 to 16. This table was shortened and shows, in columns, the first 2 dinucleotides and the last 2 dinucleotides, and in rows the first 16 separations and the last 9 separations. Rationale Dinucleotides, in double stranded DNA or RNA, present obligatory complementary and concatenated behavior with their related dinucleotides given the double stranded and the complementary constitution of nucleic acid.

An index dinucleotide in the 5’-3’ strand have complementary parallel (Par) and anti-parallel (a-Par) dinucleotides in the complementary strand and a reverse (Rev) dinucleotide in the same strand. Thus, the coefficient of selection of, for example, AG as the index dinucleotide with 5’-3’ sense (the published strand) is expected correlated with its Par TC (3’-5’ sense) or the a-Par CT (5’-3’ sense) dinucleotides, respectively, in the complementary strand of the original DNA. These dinucleotides are tested in the index strand only in the 5’-3’ sense. In the single stranded DNA or RNA none of these relationships are possible. Thus, it is necessary to restrict the comparisons to those more discriminant ones.

I presented in previous articles three categories of dinucleotides in double stranded DNA or RNA. I) those (Index) dinucleotides with the same Par and a-Par dinucleotides: AA-TT and GG-CC = 4 dinucleotides; II) those dinucleotides with a different Par and equal a-Par: AT (or vice versa TA) with TA (Par) and AT (a-Par), and GC (or vice versa CG) with GC (Par) and CG (a-Par) = 4 dinucleotides; those dinucleotides with different Par and a-Par dinucleotides (the reader will easily construct their Par and a-Par dinucleotides): AG, AC, TG, TC, GA, GT, CA, CT = 8 dinucleotides. The rationale of the following analyses is founded in the assumption of similarity in selection of dinucleotides according to the complementary rule of bases and the direction of the synthesis 5’- 3’ or 3’-5’ of nucleic acids.

I assume that both strands are equally selected. Given that we use a 5’-3’ strand of DNA (index dinucleotides from GenBank) or RNA, if mutation occurs preferentially in the transcription process and is selected in the following life processes it is expected that either the 5’-3’ (A-Par) dinucleotide or the 3’-5’ (Par) dinucleotide to the index (5’-3’) has more similarities with the index dinucleotide. It is expected that in single stranded viruses this relationship be less evident or does not exist. I must prevent the reader this study is not based in the single or double stranded condition of viruses in their virion state, which is probably the weakest evolutionary instance.

The rationale is based in the idea that viruses exist, during their reproductive cycle, either in the single or double stranded form. The typification here of a single or double stranded virus depends on their relative existence of these two stranded forms during the life cycle of the virus. The time is evolutionary time because some stages have a larger density of evolutionary events such as mutation or selection. Double stranded DNA organisms have single stranded stages, but their existence is so ephemeral that they do not have known evolutionary transcendence.

Results The nuclear data were collected in the matrix of the 16 dinucleotides where columns have the dinucleotide with its deviation from the random expectancy of the distribution of the two bases (χ2 ), and its selection coefficient. The description is presented in Table 1 for H. cytomegalovirus, a big double stranded DNA virus with near 230,000 bp, that can insert in the host DNA. In this table the initial 2 dinucleotides and the terminal 2 dinucleotides, and the initial 15 and the terminal 9 separations are described. The minimal significant value for a χ2 (all the dinucleotides) is 16.92 (P = 0.05) and it is 3.84 for the individual (dinucleotide) χ2 , thus a great deal of tests is significant.

Each dinucleotide has 100 selective values corresponding to the 100 separations (from 0 to 99). It is remarkable the periodicity of the value of the χ2 and also that of the individual χ2 values. Even though only four dinucleotides are presented they are not completely homogeneous for their periodicity. This periodicity continues until separation 99 (not the aim of this article). Table 1. Selective parameters according to separation in H. cytomegalovirus. First two and last two dinucleotides Adenine-Adenine Adenine-Thymine … Cytosine-Guanine Cytosine-Cytosine Sep χ2 Din χ2 Sel Din χ2 Sel … Din χ2 Sel Din χ2 Sel 0 2981.2 AA[+] 183.8 0.131 AT[-] 83.2 -0.089 … CG[+] 666.97 0.189 CC[-] 348.97 -0.138 1 1581.4 AA[+] 419.7 0.198 AT[-] 515.0 -0.221 … CG[+] 32.72 0.042 CC[-] 0.04 -0.001 2 3808.1 AA[+] 591.0 0.235 AT[+] 0.2 0.004 … CG[-] 9.28 -0.022 CC[+] 656.13 0.189 3 379.9 AA[+] 50.1 0.069 AT[-] 0.9 -0.009 … CG[+] 94.01 0.071 CC[-] 22.15 -0.035 4 308.8 AA[+] 5.0 0.022 AT[-] 127.8 -0.110 … CG[-] 12.5 -0.026 CC[-] 0.67 -0.006 5 2660.8 AA[+] 365.7 0.185 AT[+] 19.3 0.043 … CG[-] 1.04 -0.007 CC[+] 389.65 0.146 6 112.8 AA[+] 4.9 0.022 AT[+] 1.5 0.012 … CG[+] 1.86 0.010 CC[+] 11.86 0.025 7 61.6 AA[+] 2.1 0.014 AT[-] 12.7 -0.035 … CG[-] 3.84 -0.014 CC[+] 5.92 0.018 8 2419.4 AA[+] 306.7 0.170 AT[+] 31.5 0.055 … CG[+] 0.59 0.006 CC[+] 364.06 0.141 9 47.1 AA[+] 1.5 0.012 AT[+] 2.8 0.016 … CG[+] 4.88 0.016 CC[+] 0.13 0.003 10 112.0 AA[+] 2.1 0.014 AT[-] 15.3 -0.038 … CG[-] 11.92 -0.025 CC[+] 2.42 0.011 11 2530.4 AA[+] 341.2 0.179 AT[+] 36.6 0.059 … CG[-] 1.18 -0.008 CC[+] 348.95 0.138 12 107.7 AA[+] 20.4 0.044 AT[+] 0.0 0.001 … CG[+] 4.54 0.016 CC[+] 3.4 0.014 13 51.7 AA[+] 8.2 0.028 AT[-] 11.9 -0.034 … CG[-] 0.92 -0.007 CC[+] 0.18 0.003 14 1978.6 AA[+] 258.8 0.156 AT[+] 53.2 0.071 … CG[+] 0.69 0.006 CC[+] 266.25 0.120 .

. . . . . . . … . . . . . . . . . . . . . . … . . . . . . 91 87.3 AA[+] 0.1 0.003 AT[-] 4.2 -0.020 … CG[-] 22.13 -0.034 CC[+] 2.13 0.011 92 1174.2 AA[+] 167.7 0.125 AT[+] 20.2 0.044 … CG[+] 11.5 0.025 CC[+] 114.31 0.079 93 75.7 AA[+] 1.9 0.013 AT[+] 5.9 0.024 … CG[+] 7.59 0.020 CC[+] 2.75 0.012 94 43.9 AA[+] 1.0 0.010 AT[-] 15.0 -0.038 … CG[-] 2.37 -0.011 CC[+] 0.1 0.002 95 1052.8 AA[+] 125.4 0.108 AT[+] 46.0 0.066 … CG[+] 10.75 0.024 CC[+] 86.99 0.069 96 69.3 AA[+] 1.7 0.013 AT[+] 2.8 0.016 … CG[+] 0.53 0.005 CC[+] 2.01 0.010 97 53.9 AA[+] 0.0 0.002 AT[-] 8.4 -0.028 … CG[-] 0.65 -0.006 CC[-] 0.2 -0.003 98 1104.4 AA[+] 147.9 0.118 AT[+] 28.1 0.052 … CG[+] 11.06 0.024 CC[+] 94.48 0.072 99 57.9 AA[+] 0.3 0.005 AT[+] 3.5 0.018 … CG[+] 5.21 0.017 CC[+] 2.41 0.011 Sep = separation; χ2 = total chi square with 9 d.f.; Din = dinucleotide with its sign of selection; Sel = selection coefficient.

χ2 = individual (for each nucleotide) chi square with 1 d.f. The following analysis was by means of the Pearson’s correlation coefficient between the selection coefficients of dinucleotide couples: AA-AA (r = 1.0); AA-AT; AA-AG; AA-AC; … CT-CG; CT-CC; CG-CC; CC-CC (r = 1.0) = 128 pairs of correlations between selection coefficients of dinucleotides from which 16 pairs are of the same dinucleotide (with correlation 1.0). For example (Table 1), excluding the first five separations, the selection coefficients of AA are highly correlated with the selection coefficients of CC; this is directly seen by the chi-square values that present equal periodicities, this indicates a high correlation as it is seen in Table 2.

Table 2. correlations between selection coefficients of dinucleotides. H. cytomegalovirus AA AT AG AC TA TT TG TC GA GT GG GC CA CT CG CC AA 1,000 0,460 -0,791 -0,868 0,542 0,991 -0,939 -0,792 -0,798 -0,848 0,814 0,373 -0,920 -0,744 0,403 0,803 AT 1,000 -0,781 -0,718 0,582 0,458 -0,619 -0,472 -0,448 -0,728 0,700 0,031 -0,639 -0,744 0,219 0,700 AG 1,000 0,720 -0,361 -0,779 0,766 0,521 0,519 0,722 -0,687 -0,137 0,772 0,974 -0,642 -0,676 AC 1,000 -0,817 -0,865 0,957 0,873 0,861 0,983 -0,951 -0,339 0,946 0,712 -0,096 -0,947 TA 1,000 0,537 -0,728 -0,881 -0,863 -0,826 0,806 0,438 -0,719 -0,317 -0,269 0,785 TT 1,000 -0,940 -0,799 -0,789 -0,854 0,817 0,364 -0,914 -0,794 0,387 0,809 TG 1,000 0,835 0,829 0,951 -0,940 -0,278 0,983 0,757 -0,214 -0,928 TC 1,000 0,975 0,874 -0,814 -0,625 0,808 0,509 -0,006 -0,795 GA 1,000 0,843 -0,788 -0,667 0,777 0,509 -0,045 -0,754 GT 1,000 -0,963 -0,313 0,947 0,686 -0,066 -0,949 GG 1,000 0,114 -0,940 -0,653 -0,051 0,992 GC 1,000 -0,210 -0,151 0,260 0,072 CA 1,000 0,743 -0,200 -0,940 CT 1,000 -0,668 -0,658 CG 1,000 -0,060 CC 1,000 These correlations are presented in Table 2 for H.

cytomegalovirus. With 100 pairs, correlations are significantly different from 0.0 (index r), for a two tailed z test (P ≤ 0.05), when r = ± 0.275. The comparison between two correlations is significant depending on the values of r. If one correlation is ± 0.5, significant correlations with larger absolute value of r, are with r ≥ 0.681 for positive r and ≤ -0.681 for negative r; and with smaller absolute value of r with r ≤ 0.261 for positive r and r ≥ -0.261 for negative r. If the index correlation to compare is r = ± 0.75, significant values are found with r ≥ 0.85 and r ≤ 0.599 for positive r, and with r ≤ -0.85 and r ≥ -0.599 for negative r.

With index r = 0.25 significances occur with r ≥ 0.495 and r ≤ -0.026, for larger and smaller r values, respectively. With index r -0.25 significant values occur with r ≤ -0.495 and r ≥ 0.026. These figures allow interpret Table 2. Let us remember that double stranded DNA are: M. smithi (archaea), H. cytomegalovirus (virus), H. sapiens and E. coli (bacterium). The phage of E. coli, Phi X 174 is a single stranded DNA virus that may integrate the host DNA after a transformation in a double stranded DNA; SARS-CoV-2 is a single stranded lytic RNA virus and HIV-1 is a single stranded RNA retrovirus that can integrate into the host DNA.

The most critical correlations are presented in Table 3. I) Among the dinucleotides with equal Par and a-Par dinucleotides, AA- TT and GG-CC, the discriminant power of the test is evident. Double stranded DNA present a very high correlation (over 0.9) for both type of dinucleotide pairs. The other correlations are significant with lower significance than those found in organisms with dsDNA with the exception of Phi X 174 for AA-TT. II) Among dinucleotides with different Par and a-Par, with a-Par equal to the index dinucleotide (AT-TA; GC-CG) dsDNA presented higher correlations (in absolute values) with the exception of SARS- CoV-2 in both AT-TA (0.66) and GC-CG (-0.55) pairs. HIV showed non-significant correlations.

III) Among dinucleotides with Par and a-Par different from the Index dinucleotide. In general, with few exceptions a-Par dinucleotides shows. Table 3. Critical selective correlations in double and single stranded nucleic acids. M. smithi Coli pX174 H Cytomeg SARS-CoV-2 HIV-1 H. sapiens E. coli dsDNA ssDNA dsDNA ssRNA ssRNA dsDNA dsDNA Equal Parallel and Anti-Parallel Dinucleotide; both different to Index dinucleotide AA-TT 0.98245 0.85556 0.99069 0.38501 0.35952 0.94605 0.99899 GG-CC 0.99934 0.40174 0.99170 0.69554 0.46313 0.91909 0.99927 Different Parallel and Anti-Parallel Dinucleotide; Anti-Parallel equal to Index dinucleotide AT-TA 0.54821 0.30705 0.58173 0.66171 -0.25841 0.78944 -0.76046 GC-CG -0.70511 -0.06223 -0.05052 -0.55469 -0.24668 0.08654 0.31400 Index, Parallel and Anti-Parallel Dinucleotides are different AG-CT 0.94486 -0.37320 0.97364 -0.32252 0.42950 0.87042 0.99826 AG-TC -0.71539 0.56141 0.52069 0.45469 -0.45748 0.35616 -0.09087 AC-GT 0.98432 -0.38395 0.98330 0.04884 0.35999 0.86769 0.99878 AC-TG 0.57925 -0.06202 0.95679 0.28188 0.34009 -0.31221 0.20667 TG-CA 0.98664 -0.28970 0.98287 0.14781 -0.16202 0.95469 0.99893 TC-GA 0.95956 -0.32028 0.97490 -0.33411 0.32342 0.77378 0.99767 GA-CT -0.76752 0.63999 0.50948 0.38763 -0.12491 0.37300 -0.09300 GT-CA 0.59263 -0.13609 0.94696 0.05596 0.03653 -0.25719 0.40646 Coli pX174 = phi X174 phage of E.

coli; H Cytomeg = H. cytomegalovirus. higher correlations than Par dinucleotides with index dinucleotides. The values of correlations among ssDNA or ssRNA are significatively lower than correlations among dsDNA with the exception of Par-Index correlation (AG-TC, and GA-CT) in Phi X 174. It is remarkable the positive and high correlations of H. Cytomegalovirus either with the Par or a-Par dinucleotides. It is interesting that Phi X 174 presented higher correlations between Par-Index pairs and negative correlations between a-Par-Index pairs; this contrasts with the dsDNA organisms particularly with M. smithi (at its left side). I found unexplainable correlations, among them, those of non-related bases by complementarity. Table 4 shows these correlations.

The AA-TT and GG-CC are repeated from Table 3 to contrast these comparisons. It is remarkable that all these correlations are positive. Table 4. Correlations between dinucleotides of one base: AA, TT, GG, CC M. smithi Coli fX174 H Cytomeg SARS-CoV-2 HIV H. sapiens E. coli dsDNA ssDNA dsDNA ssRNA ssRNA dsDNA dsDNA AA-TT 0.98245 0.85556 0.99069 0.38501 0.35952 0.94605 0.99899 AA-GG 0.96572 0.74596 0.81403 0.29006 0.42631 0.76498 0.71051 AA-CC 0.96787 0.36017 0.80274 0.19690 0.23965 0.77114 0.70991 TT-GG 0.91177 0.88266 0.81723 0.95409 0.45717 0.73310 0.70405 TT-CC 0.91677 0.46229 0.80887 0.70175 0.41910 0.79453 0.70325 GG-CC 0.99934 0.40174 0.99170 0.69554 0.46313 0.91909 0.99927 Nomenclature as in Table 3. It is remarkable that all correlations in double stranded DNA are over 0.70.

Several correlations among single stranded viruses, all in HIV, are under 0.5. Correlations AA-CC are very critical, while dsDNA show correlations over 0.7, ssDNA or ss- RNA show correlations under 0.37; all these differences are highly significant.

Discussion Data show a clear discrimination between double and single stranded DNA or RNA. It is also clear that single stranded viral DNA or RNA are not so single as they are found in the virion particle. Along their life cycle these viruses exist in double or single stranded forms that undergo mutational or selective events in different frequencies, and very probable, mostly during the replication process. During replication they are mostly in double stranded state. These results confirm those found in previous articles [8,9]. It is remarkable the results found in Index dinucleotides with different Par and a-Par complementary dinucleotides that is in agreement with the 5’-3’ sense of replication.

In present results the a-Par dinucleotide has a high correlation with its Index dinucleotide as it was found in previous studies [8,9]. However, in those studies and in this one, Phi X 174 shows that Par dinucleotides are selectively more similar to their Index dinucleotides than the a-Par dinucleotide. This is very probably due to the existence of a negative or reverse strand needed in replication in this bacteriophage of E. coli [10]. The biochemical and molecular study is out of the scope of this article but it is in the current virological knowledge. These studies may be a useful tool for molecular studies of viral replication and evolution and open a big road of research in several fields of biology.

By the way, one of the most significant selection coefficients was found in H cytomegalovirus. It was CpG with positive selection. This is, contradictory, because CpG was negatively selected in H sapiens and its parasitic viruses HIV-1 and SARS-CoV-2, and in the archaea M. smithi that is a commensal of H. sapiens. The negative selection is very probable due to their epigenetic condition of shutting down DNA [11]. In H cytomegalovirus it seems positive CpG protects the virus from the host immune system (out of the scope of this article) [12]. This is another property of this analysis, to discover functional evolutionary hidden relationships. Genetic drift or any random process are not mentioned since the demonstration that the found deviations are incompatible with any drift process.

In the literature there is a confusion between contingent and random processes. According to our results contingent processes that are always causal processes do exist; random processes, as multicausal processes leading to fluctuation of frequencies of genetic forms of unknown origin, do exist in our analyses or models, but at last all of them are produced by precise causal events. As the synthetic evolutionary theory proposes drift is not a directional (causal) factor of evolution [5-7,9,13]

Conclusions These analyses confirm that the study of selection coefficients of dinucleotides whose bases are separated by 0, 1, 2 … K nucleotide sites allows to determine the proportion of the existence of a nucleic acid in single or double stranded condition along its life cycle. The analyses open a great deal of new properties of genomes hidden to previous current analyses. Acknowledgments I am indebted to my professors of population genetics Francesco Scudo and Ching Chung Li, and to my colleagues. Funding No extraordinary funds were used in this research Conflicts of Interest The author declares no conflicts of interest Availability of data and methods Genomes are freely found in GenBank, even though most of the original genomes may not be found at present, because they were replaced by actualized genomes.

The methods and analyses can be generated by any researcher or student that know statistics, genomes, and a computational language.

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