Fractals for hybrid orbitals in protein models

The concept of fractal has been applied to a number of properties of proteins. The structure and shape of the polypeptide chain of proteins are determined by the hybridized states of atomic orbitals in the molecular chain. The fractal dimension in the range of short distances (1-10 /spl Aring/) of the tertiary structures of some proteins covering various structural classes of protein molecules have been analyzed and compared with a Gaussian chain. The interpretation is given in terms of steric repulsion. The calculated s ratio in the sp/sup n/ hybrid orbitals is computed from the fractal dimension. A mean value of about 0.29 predicts sp/sup 2.46/ hybrid orbitals, half-way between planar sp/sup 2/ orbitals and tetrahedral sp/sup 3/ hydrids. The /spl beta/ proteins are distinguished quantitatively from other classes. They show a higher s ratio (about 0.32) which predicts about sp/sup 2.1/ hybrid orbitals, very similar to planar sp/sup 2/ orbitals.