Cluster protein structures using recurrence quantification analysis on coordinates of alpha-carbon atoms of proteins

The 3-dimensional coordinates of alpha-carbon atoms of proteins are used to distinguish the protein structural classes based on recurrence quantification analysis (RQA). We consider two independent variables from RQA of coordinates of alpha-carbon atoms, %determ1 and %determ2, which were defined by Webber et al. [C.L. Webber Jr., A. Giuliani, J.P. Zbilut, A. Colosimo, Proteins Struct. Funct. Genet. 44 (2001) 292]. The variable %determ2 is used to define two new variables, %determ21 and %determ22. Then three variables %determ1, %determ21 and %determ22 are used to construct a 3-dimensional variable space. Each protein is represented by a point in this variable space. The points corresponding to proteins from the α, β  , α+βα+β and α/βα/β structural classes position into different areas in this variable space. In order to give a quantitative assessment of our clustering on the selected proteins, Fisher's discriminant algorithm is used. Numerical results indicate that the discriminant accuracies are very high and satisfactory.