A fractal scaling analysis of the SARS-CoV-2 genome sequence

An approach based on fractal scaling analysis to characterize the organization of the SARS-CoV-2 genome sequence was used. The method is based on the detrended fluctuation analysis (DFA) implemented on a sliding window scheme to detect variations of long-range correlations over the genome sequence regions. The nucleotides sequence is mapped in a numerical sequence by using four different assignation rules: amino-keto, purine-pyrimidine, hydrogen-bond and hydrophobicity patterns. The originally reported sequence from Wuhan isolates (Wuhan Hu-1) was considered as a reference to contrast the structure of the 2002-2004 SARS-CoV-1 strain. Long-range correlations, quantified in terms of a scaling exponent, depended on both the mapping rule and the sequence region. Deviations from randomness were attributed to serial correlations or anti-correlations, which can be ascribed to ordered regions of the genome sequence. It was found that the Wuhan Hu-1 sequence was more random than the SARS-CoV-1 sequence, which suggests that the SARS-CoV-2 possesses a more efficient genomic structure for replication and infection. In general, the virus isolated in the early 2020 months showed slight correlation differences with the Wuhan Hu-1 sequence. However, early isolates from India and Italy presented visible differences that led to a more ordered sequence organization. It is apparent that the increased sequence order, particularly in the spike region, endowed some early variants with a more efficient mechanism to spreading, replicating and infecting. Overall, the results showed that the DFA provides a suitable framework to assess long-term correlations hidden in the internal organization of the SARS-CoV-2 genome sequence.