Fractal genomics of SOD1 evolution
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ORIGINAL ARTICLE
Fractal genomics of SOD1 evolution Mohammad Saeed1 Received: 11 September 2020 / Accepted: 28 October 2020 / Published online: 25 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract To understand the fundamental processes of gene evolution such as the impact of point mutations and segmental duplications on statistical topography, superoxide dismutase-1 (SOD1) orthologous sequences (n = 50) are studied. These demonstrate scale invariant self-similarity patterns and long-range correlations (LRCs) indicating fractal organization. Phylogenetic hierarchies change when SOD1 orthologs are grouped according to fractal measures, indicating that statistical topographies can be used to study gene evolution. Sliding window k-mer analysis show that majority of k-mers across all SOD1 orthologs are unique, with very few duplications. Orthologs from simpler species contribute minimally ( 0.5). There is moderate degree of concordance between DFA and RDA (R2 = 0.66), indicating that the two algorithms measure fractality differently. Neither measure correlate with gene length (DFA R2 = 0.48; RDA R2 = 0.41) or taxonomic order (DFA R2 = 0.49; RDA R2 = 0.38). Small gene sequences from simpler organisms such as Caenorhabditis elegans (174141) and Apis mellifera (409398) with length of ~ 1200 nucleotides show correlations (α = 0.60 and 0.67; D = 1.47 and 1.34, respectively). Hence, short-range correlations are present as well (Table S1). Exons of human SOD1 (NM_000454.5) also show some degree of LRC (alpha = 0.533, D = 1.33).
Diagrammatic self‑similarity of SOD1 sequences To be consistent with fractals, SOD1 sequences should form scale invariant patterns within a given SOD1 ortholog (Albrecht-Buehler, 2012). These patterns may not be exact; however, their features should repeat across a range of sizes. Hence, the SOD1 sequences are graphed in proportional window sizes to visually evaluate self-similarity, as in zoomed-in photographs. To allow uniform comparison of patterns across different sizes, the SOD1 sequence of length
Immunogenetics (2020) 72:439–445
2n nucleotides is allowed to weave across the plane in all four directions. When the sequence approaches the window borders it wraps across, so as to continue within the window frame. Moreover, the window sizes are determined by the RDA principle to be 2 n+3 to allow sufficient space for uniform pattern development. This photographic method is intuitively sensitive as pattern discernment is a fundamental ability of human vision. As shown in Fig. 1, there is sufficient self-similarity (3–5 orders of magnitude) in the SOD1 sequences to be considered as fractals. Further examples of the various degrees of self-similarity are depicted in Fig. S1, and a complete list of images of SOD1 orthologs can be viewed at GeneFractals SOD1 Images.
Phylogenetic sequence reconstruction of SOD1 Frequency matching of k-mer oligonucleotides show that lower organisms contribute minimally ( 90%) unique k-mer sequences. Point mutations were thought to i
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