Fractal Hybrid Orbitals Analysis of the Tertiary Structure of Protein Molecules†

The structure and shape of the polypeptide chains of proteins are determined by the hybridized states of the atomic orbitals in the molecular chain. The calculated s ratio in the sp(n) hybrid orbitals is computed from the fractal dimension D of the tertiary structures of 43 proteins selected to cover the five structural classes of protein molecules. A brief introduction to fractal theory is given in the text. It is demonstrated that the principles dictating the folding of the local and global backbone structures are well characterized in terms of the representation given by fractal theory. Comparison of the fractal character of protein molecules with that of the ideal Gaussian chain revealed several features of these principles. It is also shown that proteins in the β type structural class are distinguished quantitatively from those in other classes with this representation. They show a higher s ratio (0.32) in sp(2.20) hybrids, rather similar to planar sp(2). Comparison of the proteins with a Gaussian chain is interpreted in terms of steric repulsion.