Studies of genomes based on linguistic approaches date a few decades back [Brendel et al. 1986; Pevzner et al. 1989; Searls 1992 The aim of the present Letter is to draw attention to simple treatments of nucleotide sequences in viral RNAs by means of new parameters, which can be immediately extracted from genome data. We expect that such parameters can be potentially used as an auxiliary tool in the classification of viruses, cf, in particular, [Wang 2013 ]. The idea of this study is linked to the recent COVID-19 outbreak, and the analysis started from comparing human coronaviruses [Su et al. 2016; Wu et al. 2020 ] and some other viruses. To achieve relative homogeneity of the material, we restrict our sample to single-stranded RNA viruses only. Both positive-and negative-sense RNAs are considered. For future reference, we also include two retroviruses, HIV-1 and HIV-2.
The paper is organized as follows. Summary of data and description of methods are given in Section 2. Results are presented in Section 3. Finally, brief discussion is given in Section 4. Detailed tables of numerical results are placed in the Appendix.
The viral genomes are taken from the databases of the National Center for Biotechnology Information (NCBI, https://www.ncbi.nlm.nih.gov); the complete list is given in We use two approaches to define nucleotide sequences. The first one is based on cutting an RNA genome into chunks of equal length of n nucleotides. The second approach is rooted in linguistics, so that the most frequent nucleotide is treated as a "space" dividing a RNA into "words" of different lengths [Rovenchak 2018]. Note also distantly related units applied in the analysis of the human DNA, so called motifs [Liang 2014 ].
To demonstrate the first approach, with equal-length chunks, let us consider the Ebolavirus genome, starting with the following nucleotide sequence:
Choosing the chunk length n = 4, we obtain: GGAC ACAC AAAA AGAA AGAA GAAT TTTT AGGA TCTT TTGT . . . .
(2) Eventually, for RNA length not being multiples of four, the last chunk can have one to three nucleotides. Obviously, the number of all possible 4-nucleotide combinations is 4 4 = 256. Note that longer chunks would yield much higher variety of combinations with frequencies being distributed very smoothly. On the other hand, we would like to avoid studies of shorter chunks, like threenucleotide sequences corresponding to codons. So, the length n = 4 seems optimal for our analysis.
In the second approach, the same Ebolavirus sequence (]refeq1) can be split using the most frequent nucleotide -adenine -as a "space" into the following:
The "X" stands for a zero-length element inserted between two consecutive "A"s.
We have also applied peculiar treatment of the Influenza A virus (H1N1) by adding spaces between each of eight segments of its RNA in the first and second approaches.
In both approaches, we calculate the frequencies of obtained nucleotide chunks within a given genome split in the respective manner and compile the rank-frequency distributions. The latter are obtained in a standard manner as follows: the most frequent item has rank 1, the second most frequent one has rank 2 and so on. Items with equal frequencies are given consecutive ranks in a random order, which is not relevant.
The rank-frequency distributions obtained using the first approach -with 4nucleotide chunks -were analyzed using a special software, AltmannFitter 2.1 [Altmann 2000 ]. We found that two discrete distributions describe the obtained data with the highest precision, so called 1-displaced negative hypergeometric distribution [Grzybek 2007; Wilson 2013] :
and Pólya distribution [Wimmer & Altmann 1999; Johnson et al. 2005] :
Absolute frequencies are obtained by multiplying p r by the sample size N . In most cases, the discrepancy coefficient C = χ 2 /N is smaller than 0.02, which is considered a good fit [Mačutek 2008 ]. Typical rank-frequency distributions and respective fits are shown in Figure 1 . Complete data are summarized in Table 3 in the Appendix and visualized in Figure 2 . The first immediate observation from Figure 2 is that the length of genomes has no special influence on the fitting parameters. Indeed, both the shortest Hepatitis D genome and two longest -Ball python nidovirus and Planidovirus -genomes have close values of M or s parameters. On the other hand, for genomes of similar lengths (coronaviruses) a clear separation is seen with respect to M and p parameters. It is even more pronounced in the former case corresponding to the negative hypergeometric distribution: lower values for HCoV viruses (229E, HKU1, NL63, and OC43) and higher ones for MERS, SARS, and SARS-CoV-2.
Rank-frequency distributions were also compiled for nucleotide "words" obtained using the second approach and used to calculate certain parameters, like entropy, mean length (first central moment), length dispersion (second central moment) and some others. Previous studies [Rovenchak 2018 ] showed that entropy and mean lengths of nucleotide sequences in the mitochondrial DNA can be used to distinguish species and genera of mammals. It appears, however, that even better results are achieved with the "entropy -length dispersion" pair of variables, cf. Figure 3 .
The parameters are defined as follows. Entropy is given by
where the upper summation limit corresponds to the total number of different "words" in the list and relative frequencies p r are
and f r are absolute frequencies at rank r. Mean length and length dispersion are
where the summations run over all the "words" of the analyzed genome. Lengths x i of a particular word are counted as the number of nucleotides except for "X" having length zero. One should note that from similarity of species one can expect proximity of points but not vice versa: it would be too bold to expect species distinguishability from only two parameters.
This second approach can be divided into two sub-branches: (a) adenine, which is the most frequent nucleotide in most species studied in the present work, is used as a "space"; (b) the most frequent nucleotide is used as a "space". The latter is mostly relevant for RNAs, where low frequencies of adenine yield too long "words" thus significantly distorting the expected dependencies. The respective results are shown in Figures 4-6. All the data are summarized in Table 4 .
In Figure 6 , we can observe in particular that α-coronaviruses, HCoV-229E and HCoV-NL63, have very close values of the parameters (the respective point nearly overlap). A similar situation is with β-corovaniruses HCoV-OC43 and HCoV-HKU1. Two other β-corovaniruses, SARS and SARS-CoV-2, are located close to HCoV-OC43 and HCoV-HKU1, while MERS occupies an intermediate position. The latter virus also significantly differs in the entropy value, see Figure 5 . On the other hand, calculations with the most frequent nucleotide used as a space (T for the analyzed coronaviruses) do not exhibit such a grouping, see Figure 4 . When looking in detail into the rank-frequency distributions corresponding to coronaviruses we have discovered the following pattern: the first rank is always occupied by "X" followed by three single-nucleotide "words" with ranks 2-4, while the fifth ranks are occupied by a two-nucleotide sequence with either the same (4-same) or different (4-diff) nucleotides, see Table 2 . Curiously, different nucleotides correspond to coronaviruses causing much more severe diseases. This observation is yet to be extended onto a wider material, but the preliminary data for the analyzed human viruses are as follows: Three other viruses, Hepatitis D, Yellow fever, and Zika, do not follow either pattern having a two-nucleotide sequence with as low ranks as 3 or 4. Table 2 Top-ranked nucleotide sequences in the genomes of the human coronaviruses.
HCoV-HKU1 HCoV-NL63 HCoV-OC43 r "word" fr "word" fr "word" fr "word" fr "word" fr "word" fr "word" fr 
We have presented several possible approaches to simple parametrization of RNA viruses based on the analysis of nucleotide sequences in viral genomes. They are based on discrete distributions (negative hypergeometric and Pólya) for equal-length (4-nucleotide) chunks and on the pair "entropy -length dispersion" for distributions of sequences separated by adenine or another most frequent nucleotide. Related viruses are characterized by close values of the calculated parameters. In some cases, similar values are also obtained for unrelated viruses. This is not surprising as representing viruses on a plane means a two-parametric projection of points that are certainly described by more than two variables. We consider our study as preliminary steps in discovering such variables.
Observations regarding peculiarities of rank-frequency distributions, with the fourth most frequent sequence containing two either the same or different nucleotides (4-same vs 4-diff), support the fact that 4-diff cases correspond to viruses causing potentially more severe diseases when dealing with seven human coronaviruses. This tendency is generally preserved if the analyzed set is expanded by other viruses studied in this work. Some precautions concern, in particular, the two HIV types, which fall into the 4-same category while certainly being extremely dangerous. However, HIV are not strictly RNA viruses but retroviruses, so we suggest that the reported peculiarities might be specific for RNA viruses only. "False-positive" alerts (cf. Norovirus in the 4-diff category) are not problematic, but the rate of "false-negative" results (severe diseases in the 4-same category) is yet to be identified. Expansion of the analyzed material in future studies would help to clarify the relevance of this observation. To establish relations between peculiarities of the rank-frequency distributions in virus genomes and disease severity, a formalization of the latter is required. Initially we planned using the case fatality rate (CFR) indicator [Reich et al. 2012 ; Kim et al. 2020] but where not able to find a study with data for different viruses based on a unified approach, similar, e.g., to [GBD 2017 ].
The main expected outcome of our reported analysis is a call for collaboration to expand the dataset and consistently classify diseases caused by RNA viruses, in particular with respect to severity and contagiousness. If some simple patterns could be established in the nucleotide distributions, this might help alerting healthcare systems, which seems to become a very topical issue from this year on.
The authors, Mykola Husev and Andrij Rovenchak, declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors. 