New dimension indices for the characterization of the solvent-accessible surface

Valence Topological Charge-Transfer Indices for Dipole Moments

New valence topological charge-transfer indices are applied to the calculation of dipole moments. The algebraic and vector semisum charge-transfer indices are defined. The combination of the charge-transfer indices allows the estimation of the dipole moments. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moments of a homologous series of phenyl alcohols. Linear and non-linear correlation models are obtained. The new charge-transfer indices improve the multivariable non-linear regression equations for the dipole moment. When comparing with previous results, the variance decreases 92%. No superposition of the corresponding G_k–J_k and – pairs is observed. This diminishes the risk of co-linearity. Inclusion of the oxygen atom in the π-electron system is beneficial for the description of the dipole moment, owing to either the role of the additional p orbitals provided by the heteroatom or the role of steric factors in the π-electron conjugation. Linear and non-linear correlations between the fractal dimension and various descriptors point not only to a homogeneous molecular structure but also to the ability to predict and tailor drug properties.

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 spⁿ 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 sp². Comparison of the proteins with a Gaussian chain is interpreted in terms of steric repulsion.