Scorpion venom complexity fractal analysis. Its relevance for comparing venoms

We analyzed the venom elution pattern of 15 scorpions species. Data were scanned at 1 Hz and stored digitally. Approximate fractal dimension (D) [Sevcik (1998)] was calculated for minutes 0-60 of the elutions. D was calculated for either the whole time range, or calculated using a window of 500 points, which was displaced by one time increment recursively, and stored [(t_i,D_i) sets]. We avoid the term complexity as much as possible since defining complexity is difficult; instead we propose the term contortedness and represent it by the variable Q=D−1. To compare venom contortednesses of different species, a phase plot with their (t_i,Q_i) sets was constructed and determination coefficient (d_s) were calculated squaring the Spearman rank correlation coefficient. (t_i,Q_i) sets of several elutions of the same specie were averaged and compared with other species finding that some were amazingly similar (Tityus clathratus vs Tityus caripitensis, d_s = 0.813). Tityus discrepans was similar to 6 of 8 species of the same genus (d_s ranging from 0.23 to 0.49), and also similar to Centruroides gracilis and Chactas laevipes (d_s 0.54 and 0.49, respectively). Serendipitously,T. discrepans was chosen many years ago to produce anti-Tityus antivenom in Venezuela; perhaps the clinical success in neutralizing the venom of the other known Venezuelan Tityus, stems from the mimetism of this venom with the remaining species’ venom.