Fractal Geometry Study of DNA Binding Proteins

The main aim of this paper is to search for three-dimensional structure homology between DNA-binding proteins. The run of a proteinʹs main chain is depicted by a sequence, which is constituted by the fractal indices, where each index describes how twisted or extended a partial protein segment is. Two proteins are compared by constructing a dot matrix between two such sequences, and the matrix is searched for dot-concentrated rectangles which is an indication of tertiary homology. This new method is applied to DNA-binding proteins which are selected from Brookhaven Protein Data Bank, among which most contain a helix-turn-helix motif. The dot-matrix shows that there is tertiary homology between two motifs. Other interesting results are also presented in this paper.