Fractal signature of coronaviruses related to severe acute respiratory syndrome
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Fractal signature of coronaviruses related to severe acute respiratory syndrome Thiago de Salazar e Fernandes 1
&
Jonas Sérgio de Oliveira Filho 1 & Isvania Maria Serafim da Silva Lopes 1
Received: 13 April 2020 / Accepted: 27 May 2020 # Sociedade Brasileira de Engenharia Biomedica 2020
Abstract Purpose The aim of this work was to investigate the genome of SARS-CoV, MERS-CoV, and SARS-CoV-2 by the paradigm of chaos theory and fractal geometry. Coronavirus is the agent that causes the severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS) and emergent infections such as the present pandemic of COVID-19. Understanding its genome pattern is important for developing new and faster ways of testing for identifying the genome of the virus and also for better understanding of its origin and evolution. Methods For that, it was calculated the alpha coefficient by detrended fluctuation analysis (DFA) for the sequences of these genomes converted to binary numbers in order to determine if it is a chaotic or a random series of data. Also, it applied the random walking for obtaining a fractal map of the whole genome and calculated the fractal dimension (FD) by box-counting of this map by two different software. Results With this, it was found that the alpha coefficient of the first SARS viruses was > 0.5, indicating that the series is chaotic or fractal, and has a persistent long-range memory or self-similarity along its sequence. This is not the case for MERS virus, which showed to have a completely random sequence (α < 0.5). For the fractal dimension, SARS viruses presented a FD around 1.5, and for MERS the fractal dimension decreases (FD < 1.5). Conclusion The images generated by random walking of the entire RNA genome are by itself a fractal signature of the virus, which may be applied for studying its origin and for faster diagnostic of COVID-19. Keywords Fractal analysis . Random walking . Deterministic chaos . Coronavirus . COVID-19
Introduction A high incidence of flu in adults and children are caused by coronavirus. The SARS-CoV-2 virus is the cause of COVID19, a severe acute respiratory syndrome (SARS). In 2002, a pathogenic coronavirus caused the first SARS, and 10 years later, MERS-CoV caused the Midle East respiratory syndrome (MERS) (Chen 2020). Previous studies have shown that SARS-CoV during the epidemic of 2002 has passed through mutations to better bind to the
* Thiago de Salazar e Fernandes [email protected] 1
Departamento de Biofísica e Radiobiologia, Universidade Federal de Pernambuco, Avenida Moraes Rego, 1235, Cidade Universitária, Recife, PE 50670-901, Brazil
human cellular receptor ACE-2 in order to replicate, increasing its virulence (Cui et al. 2019). Therefore, viruses change its genome from time to time originating emergent infections. But understanding the dynamics and pattern of these mutations and its consequences for the entire RNA genome of these viruses requires also a new paradigm in science, based not on classical methods. T
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