Fractal analisys of tandem repeats protein
Proteins are biopolymers essential to life, constituted by a long amino acid sequence. They may be formed from up to 20 different kinds of amino acids. A significant portion of these proteins, about 14\% \textit{et all} [1,2], they have repeated segments of amino acids. These repetitions occur when in tandem trigger regular tertiary structures, exactly by a plurality of different sizes and functions resulting in different classifications repeat protein family. Repeat proteins have the advantage of the folding pathways that are likely to be schematized. In this article were selected in 1213 proteins deposited in the Brookhaven Protein Data Bank suggested by Andrade and collaborators [3], divided into six tandem repeat class with different lengths from 20 to 50 residues, wherein we investigate characteristics of fractal geometry. Using the Mean Field Theory of Flory, the mass-size scale exponent analysis shows that the exponent is $\delta=2.15$. The average packing density tends to $\rho=0.86 a.u./A^3$ with $q$-Gaussian distribution to the masses of proteins with entropic index $q =1.90$. The findings indicate self-organized criticality as to the explanation protein folding and no hydrophobicity scale can be relevant to these proteins. Therefore, the fractal geometry behaves between a two-dimensional wire crumpled and packed spheres randomly in the percolation threshold.
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