Families of protein with similar total structure identified using statistical geometry

Two quantities, herein defined as the displacement and the uniqueness, describe quantitatively the total structural difference between two proteins. All possible pairs of protein chains in the Brookhaven database are characterized in terms of these quantities. Pairs of proteins with small values of both displacement and uniqueness, in secondary and super-secondary configuration spaces, have similar total structure. Proteins related in this fashion are grouped into 158 families of similar total structure. The radial displacement function is herein defined to characterize the relative displacement of a residue from the center of the mass of its protein. In addition, the residue backbone structure function is also defined to characterize the local configuration of the protein main chain in the vicinity of the residue. The values of polynomial convolutions of these two functions are characteristic of a particular tertiary structure type. These polynomial convolutions, together with other structural parameters, are used to verify the structural similarity of proteins belonging to the families indicated above. Variations in these polynomial convolutions illustrate the amount and sequence location of structural deviations between proteins of the same family.