{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T08:58:22Z","timestamp":1776675502445,"version":"3.51.2"},"reference-count":51,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T00:00:00Z","timestamp":1776470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China National Science Foundation Program","award":["31860304"],"award-info":[{"award-number":["31860304"]}]},{"name":"China National Science Foundation Program","award":["62401300"],"award-info":[{"award-number":["62401300"]}]},{"name":"Natural Science Foundation of Inner Mongolia Autonomous Region of China","award":["2024MS03054"],"award-info":[{"award-number":["2024MS03054"]}]},{"name":"Fundamental Research Funds for Inner Mongolia University of Science & Technology","award":["2023QNJS080"],"award-info":[{"award-number":["2023QNJS080"]}]},{"name":"Research Program of science and technology at Universities of Inner Mongolia","award":["NJZY23086"],"award-info":[{"award-number":["NJZY23086"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>Given the rapid mutation and high transmissibility of coronaviruses, especially SARS-CoV-2, comparative genomic studies are crucial for understanding viral evolution, transmission dynamics, and therapeutic development. In prior work, we analyzed and compared the spectral distribution patterns of various k-mer subsets across 920 genome sequences, spanning from primates to prokaryotes. This revealed an evolutionary mechanism in genome sequences, indicating the presence of both CG and TA-specific selection modes. In the present study, we further investigate the specific selection modes in coronavirus genomic sequences by examining the intrinsic distribution rules of 32 XYi 6-mer subset spectra. Our results show that coronavirus genomes exhibit only the CG-specific selection mode, with no evidence of TA-specific selection. Using the CG-specific selection mode, we identified CG1 6-mers as the fundamental subset underlying coronavirus genome evolution. To validate the CG1 subset, we constructed phylogenetic relationships for a set of coronaviruses and SARS-CoV-2 variant genomes. Comparative analysis confirmed that the resulting phylogenetic relationships align more closely with established knowledge. This study thus provides a theoretical framework for inferring phylogenetic relationships at the whole-genome level.<\/jats:p>","DOI":"10.3390\/ijms27083604","type":"journal-article","created":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T08:24:23Z","timestamp":1776673463000},"page":"3604","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Deciphering 6-mer Spectra Distribution Rules in Coronavirus Genomes: Application to Comparative Genomic Analysis"],"prefix":"10.3390","volume":"27","author":[{"given":"Zhenhua","family":"Yang","sequence":"first","affiliation":[{"name":"School of Economics and Management, Inner Mongolia University of Science & Technology, Baotou 014010, China"},{"name":"Inner Mongolia Industrial Informatization and Industrial Innovation Research Center, Inner Mongolia University of Science & Technology, Baotou 014010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6819-3038","authenticated-orcid":false,"given":"Hong","family":"Li","sequence":"additional","affiliation":[{"name":"Laboratory of Theoretical Biophysics, School of Physical Science & Technology, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, Inner Mongolia Agriculture University, Hohhot 010018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guojun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Life Science and Technology, Inner Mongolia University of Science & Technology, Baotou 014010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, Q., Shah, T., Wang, B., Qu, L., Wang, R., Hou, Y., Baloch, Z., and Xia, X. (2023). Cross-species transmission, evolution and zoonotic potential of coronaviruses. Front. Cell. Infect. Microbiol., 12.","DOI":"10.3389\/fcimb.2022.1081370"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"D708","DOI":"10.1093\/nar\/gkx932","article-title":"Virus taxonomy: The database of the International Committee on Taxonomy of Viruses (ICTV)","volume":"46","author":"Lefkowitz","year":"2018","journal-title":"Nucleic Acids Res."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Akbari Rokn Abadi, S., Mohammadi, A., and Koohi, S. (2023). A new profiling approach for DNA sequences based on the nucleotides\u2019 physicochemical features for accurate analysis of SARS-CoV-2 genomes. BMC Genom., 24.","DOI":"10.1186\/s12864-023-09373-7"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"104650","DOI":"10.1016\/j.compbiomed.2021.104650","article-title":"Classification of SARS-CoV-2 and non-SARS-CoV-2 using machine learning algorithms","volume":"136","author":"Singh","year":"2021","journal-title":"Comput. Biol. Med."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Pechlivanis, N., Togkousidis, A., Tsagiopoulou, M., Sgardelis, S., Kappas, I., and Psomopoulos, F. (2021). A Computational Framework for Pattern Detection on Unaligned Sequences: An Application on SARS-CoV-2 Data. Front. Genet., 12.","DOI":"10.3389\/fgene.2021.618170"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"59597","DOI":"10.1109\/ACCESS.2021.3073728","article-title":"Deep Learning for SARS COV-2 Genome Sequences","volume":"9","author":"Whata","year":"2021","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/j.jiph.2022.07.002","article-title":"A comprehensive genomic study, mutation screening, phylogenetic and statistical analysis of SARS-CoV-2 and its variant omicron among different countries","volume":"15","author":"Ahmad","year":"2022","journal-title":"J. Infect. Public Health"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"40712","DOI":"10.1038\/srep40712","article-title":"Viral Phylogenomics Using an Alignment-Free Method: A Three-Step Approach to Determine Optimal Length of k-mer","volume":"7","author":"Zhang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s12275-024-00112-5","article-title":"Genomic Evolution and Recombination Dynamics of Human Adenovirus D Species: Insights from Comprehensive Bioinformatic Analysis","volume":"62","author":"Park","year":"2024","journal-title":"J. Microbiol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"e01336-20","DOI":"10.1128\/mSphere.01336-20","article-title":"k-mer-Based Metagenomics Tools Provide a Fast and Sensitive Approach for the Detection of Viral Contaminants in Biopharmaceutical and Vaccine Manufacturing Applications Using Next-Generation Sequencing","volume":"6","author":"MacDonald","year":"2021","journal-title":"mSphere"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2092","DOI":"10.1097\/CM9.0000000000003182","article-title":"Enhancing antimicrobial resistance detection with MetaGeneMiner: Targeted gene extraction from metagenomes","volume":"137","author":"Liu","year":"2024","journal-title":"Chin. Med. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1093\/bib\/bbaa231","article-title":"A computational toolset for rapid identification of SARS-CoV-2, other viruses and microorganisms from sequencing data","volume":"22","author":"Chen","year":"2021","journal-title":"Brief. Bioinform."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Saha, I., Ghosh, N., Maity, D., Seal, A., and Plewczynski, D. (2021). COVID-DeepPredictor: Recurrent Neural Network to Predict SARS-CoV-2 and Other Pathogenic Viruses. Front. Genet., 12.","DOI":"10.3389\/fgene.2021.569120"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4673","DOI":"10.1093\/nar\/22.22.4673","article-title":"CLUSTAL W: Improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice","volume":"22","author":"Thompson","year":"1994","journal-title":"Nucleic Acids Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3059","DOI":"10.1093\/nar\/gkf436","article-title":"MAFFT: A novel method for rapid multiple sequence alignment based on fast Fourier transform","volume":"30","author":"Katoh","year":"2002","journal-title":"Nucleic Acids Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1792","DOI":"10.1093\/nar\/gkh340","article-title":"MUSCLE: Multiple sequence alignment with high accuracy and high throughput","volume":"32","author":"Edgar","year":"2004","journal-title":"Nucleic Acids Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5114","DOI":"10.1038\/s41467-018-07641-9","article-title":"High throughput ANI analysis of 90K prokaryotic genomes reveals clear species boundaries","volume":"9","author":"Jain","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"12826","DOI":"10.1073\/pnas.0905115106","article-title":"Whole-proteome phylogeny of large dsDNA virus families by an alignment-free method","volume":"106","author":"Wu","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.ygeno.2015.04.004","article-title":"Repetitive element signature-based visualization, distance computation, and classification of 1766 microbial genomes","volume":"106","author":"Lee","year":"2015","journal-title":"Genomics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105106","DOI":"10.1016\/j.meegid.2021.105106","article-title":"Alignment-free sequence comparison for virus genomes based on location correlation coefficient","volume":"96","author":"He","year":"2021","journal-title":"Infect. Genet. Evol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2607","DOI":"10.1007\/s11517-023-02837-8","article-title":"ViralVectors: Compact and scalable alignment-free virome feature generation","volume":"61","author":"Ali","year":"2023","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Solis-Reyes, S., Avino, M., Poon, A., and Kari, L. (2018). An open-source k-mer based machine learning tool for fast and accurate subtyping of HIV-1 genomes. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0206409"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Randhawa, G.S., Soltysiak, M.P.M., El Roz, H., De Souza, C.P.E., Hill, K.A., and Kari, L. (2020). Machine learning using intrinsic genomic signatures for rapid classification of novel pathogens: COVID-19 case study. PLoS ONE, 15, Erratum in PLoS ONE 2021, 16, e0246465.","DOI":"10.1371\/journal.pone.0246465"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1089\/cmb.2021.0536","article-title":"kmer2vec: A Novel Method for Comparing DNA Sequences by word2vec Embedding","volume":"29","author":"Ren","year":"2022","journal-title":"J. Comput. Biol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"195263","DOI":"10.1109\/ACCESS.2020.3031387","article-title":"Classification of COVID-19 and Other Pathogenic Sequences: A Dinucleotide Frequency and Machine Learning Approach","volume":"8","author":"Dlamini","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","first-page":"31","article-title":"Visualization of K-tuple distribution in procaryote complete genomes and their randomized counterparts","volume":"Volume 1","author":"Xie","year":"2002","journal-title":"Proceedings IEEE Computer Society Bioinformatics Conference"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"011908","DOI":"10.1103\/PhysRevE.72.011908","article-title":"Model for the distributions of k-mers in DNA sequences","volume":"72","author":"Chen","year":"2005","journal-title":"Phys. Rev. E Stat. Nonlin. Soft Matter Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"R108","DOI":"10.1186\/gb-2009-10-10-r108","article-title":"Genomic DNA k-mer spectra: Models and modalities","volume":"10","author":"Chor","year":"2009","journal-title":"Genome Biol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Yang, Z., Li, H., Jia, Y., Zheng, Y., Meng, H., Bao, T., Li, X., and Luo, L. (2020). Intrinsic laws of k-mer spectra of genome sequences and evolution mechanism of genomes. BMC Evol. Biol., 20.","DOI":"10.1186\/s12862-020-01723-3"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, X., Li, H., Yang, Z., Wu, Y., and Zhang, M. (2023). Exploring objective feature sets in constructing the evolution relationship of animal genome sequences. BMC Genom., 24.","DOI":"10.1186\/s12864-023-09747-x"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, X., Li, H., Yang, Z., and Wang, L. (2024). Distribution rules of 8-mer spectra and characterization of evolution state in animal genome sequences. BMC Genom., 25.","DOI":"10.1186\/s12864-024-10786-1"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"e00265-18","DOI":"10.1128\/JVI.00265-18","article-title":"Discovery and Sequence Analysis of Four Deltacoronaviruses from Birds in the Middle East Reveal Interspecies Jumping with Recombination as a Potential Mechanism for Avian-to-Avian and Avian-to-Mammalian Transmission","volume":"92","author":"Lau","year":"2018","journal-title":"J. Virol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"8638","DOI":"10.1128\/JVI.01055-13","article-title":"Genetic characterization of Betacoronavirus lineage C viruses in bats reveals marked sequence divergence in the spike protein of pipistrellus bat coronavirus HKU5 in Japanese pipistrelle: Implications for the origin of the novel Middle East respiratory syndrome coronavirus","volume":"87","author":"Lau","year":"2013","journal-title":"J. Virol."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Usserbayev, B., Zhugunissov, K., Smekenov, I., Akmyrzayev, N., Abdykalyk, A., Abeuov, K., Zhumadil, B., Melisbek, A., Shirinbekov, M., and Zhaksylyk, S. (2025). Alpha- and Beta-Coronaviruses in Humans and Animals: Taxonomy, Reservoirs, Hosts, and Interspecies Transmission. Microorganisms, 14.","DOI":"10.3390\/microorganisms14010043"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"104933","DOI":"10.1016\/j.meegid.2021.104933","article-title":"Exploration of hosts and transmission traits for SARS-CoV-2 based on the k-mer natural vector","volume":"93","author":"Zhang","year":"2021","journal-title":"Infect. Genet. Evol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1093\/molbev\/msaa094","article-title":"Extreme Genomic CpG Deficiency in SARS-CoV-2 and Evasion of Host Antiviral Defense","volume":"37","author":"Xia","year":"2020","journal-title":"Mol. Biol. Evol."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Konishi, T. (2020). Principal component analysis of coronaviruses reveals their diversity and seasonal and pandemic potential. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0242954"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Greenbaum, B.D., Levine, A.J., Bhanot, G., and Rabadan, R. (2008). Patterns of evolution and host gene mimicry in influenza and other RNA viruses. PLoS Pathog., 4.","DOI":"10.1371\/journal.ppat.1000079"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"veaa057","DOI":"10.1093\/ve\/veaa057","article-title":"Intra-genome variability in the dinucleotide composition of SARS-CoV-2","volume":"6","author":"Digard","year":"2020","journal-title":"Virus Evol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"e01337-19","DOI":"10.1128\/JVI.01337-19","article-title":"CpG Dinucleotides Inhibit HIV-1 Replication through Zinc Finger Antiviral Protein (ZAP)-Dependent and -Independent Mechanisms","volume":"94","author":"Ficarelli","year":"2020","journal-title":"J. Virol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e12735","DOI":"10.7554\/eLife.12735","article-title":"Elevation of CpG frequencies in influenza A genome attenuates pathogenicity but enhances host response to infection","volume":"5","author":"Gaunt","year":"2016","journal-title":"Elife"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/978-1-0716-1884-4_14","article-title":"Generation of CpG-Recoded Zika Virus Vaccine Candidates","volume":"Volume 2410","author":"Trus","year":"2022","journal-title":"Vaccine Design: Methods and Protocols, Volume 1. Vaccines for Human Diseases; Methods in Molecular Biology"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"msac029","DOI":"10.1093\/molbev\/msac029","article-title":"The Slowing Rate of CpG Depletion in SARS-CoV-2 Genomes Is Consistent with Adaptations to the Human Host","volume":"39","author":"Kumar","year":"2022","journal-title":"Mol. Biol. Evol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"7039","DOI":"10.1128\/JVI.03273-12","article-title":"A case for the ancient origin of coronaviruses","volume":"87","author":"Wertheim","year":"2013","journal-title":"J. Virol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3995","DOI":"10.1128\/JVI.06540-11","article-title":"Discovery of seven novel Mammalian and avian coronaviruses in the genus deltacoronavirus supports bat coronaviruses as the gene source of alphacoronavirus and betacoronavirus and avian coronaviruses as the gene source of gammacoronavirus and deltacoronavirus","volume":"86","author":"Woo","year":"2012","journal-title":"J. Virol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1099\/jgv.0.001494","article-title":"Analysis of partial sequences of the RNA-dependent RNA polymerase gene as a tool for genus and subgenus classification of coronaviruses","volume":"101","author":"Wilkinson","year":"2020","journal-title":"J. Gen. Virol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"veae074","DOI":"10.1093\/ve\/veae074","article-title":"Comprehensive detection and dissection of interlineage recombination events in the SARS-CoV-2 pandemic","volume":"10","author":"Li","year":"2024","journal-title":"Virus Evol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"veab059","DOI":"10.1093\/ve\/veab059","article-title":"Recombinant SARS-CoV-2 genomes circulated at low levels over the first year of the pandemic","volume":"7","author":"VanInsberghe","year":"2021","journal-title":"Virus Evol."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Fang, L., Xu, J., Zhao, Y., Fan, J., Shen, J., Liu, W., and Cao, G. (2023). The effects of amino acid substitution of spike protein and genomic recombination on the evolution of SARS-CoV-2. Front. Microbiol., 14.","DOI":"10.3389\/fmicb.2023.1228128"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"ovae074","DOI":"10.1093\/lambio\/ovae074","article-title":"The nuts and bolts of recombination in the generation of SARS-CoV-2 variants; from XA to XBB","volume":"77","author":"Karim","year":"2024","journal-title":"Lett. Appl. Microbiol."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"bbac513","DOI":"10.1093\/bib\/bbac513","article-title":"VirusRecom: An information-theory-based method for recombination detection of viral lineages and its application on SARS-CoV-2","volume":"24","author":"Zhou","year":"2023","journal-title":"Brief. Bioinform."}],"container-title":["International Journal of Molecular Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1422-0067\/27\/8\/3604\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T08:26:21Z","timestamp":1776673581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1422-0067\/27\/8\/3604"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,18]]},"references-count":51,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["ijms27083604"],"URL":"https:\/\/doi.org\/10.3390\/ijms27083604","relation":{},"ISSN":["1422-0067"],"issn-type":[{"value":"1422-0067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,18]]}}}