Fractal Analysis of Tertiary Structure of Protein Molecule

Abstract

The tertiary structures of 43 proteins selected so as to cover the five structural classes of protein molecule are analyzed with a geometrical theory called fractal theory with the intention of devising a new tool for quantitative description of the tertiary structure of protein. A brief introduction to the fractal theory is given in the text. It is demonstrated that the principles dictating the folding of the local backbone structure and the global backbone structure are well characterized in terms of the representation of the fractal theory. Comparison of the fractal character of protein molecules with that of the ideal Gaussian chain revealed several characters of these principles. It is also shown that the proteins in the structural class of β type are distinguished quantitatively from other classes with this representation. A curious discovery that several proteins take the fractal dimension greater than two is reported and discussed.