Clustering of protein structures using hydrophobic free energy and solvent accessibility of proteins

The hydrophobic free energy and solvent accessibility of amino acids are used to study the relationship between the primary structure and structural classification of large proteins. A measure representation and a Z curve representation of protein sequences are proposed. Fractal analysis of the measure and Z curve representations of proteins and multifractal analysis of their hydrophobic free energy and solvent accessibility sequences indicate that the protein sequences possess correlations and multifractal scaling. The parameters from the fractal and multifractal analyses on these sequences are used to construct some parameter spaces. Each protein is represented by a point in these spaces. A method is proposed to distinguish and cluster proteins from the alpha, beta, alpha+beta, and alpha/beta structural classes in these parameter spaces. Fisher's linear discriminant algorithm is used to give a quantitative assessment of our clustering on the selected proteins. Numerical results indicate that the discriminant accuracies are satisfactory. In particular, they reach 94.12% and 88.89% in separating beta proteins from {alpha,alpha+beta,alpha/beta} proteins in a three-dimensional space.