Nonlinear dimensionality reduction on 3-D protein image analysis

A new perspective to investigate protein structures was introduced by applying Isomap algorithm on the protein 3-D structures. Through representing the location of each amino acid in the protein by its C alpha atom, the protein 3D structure was described as a set of points in 3D space. The reasonable nearest neighbors were defined through statistical amino acids contacts information and protein structure analysis interests. The lsomap algorithm on the 3D protein structure generated the meaningful protein geodesic structure. The residual variance analysis demonstrated that the best dimensionality for representing protein geodesic structure is 3D, but the computational results also showed that there is a nearly linear relationship between the geodesic shortest distance in original 3D and the Euclidean distance in the 2D constructed by the first two of Isomap's coordinates. The 2D protein geodesic representations can be used to measure the protein similarity and the analysis of the 2D protein geodesic representation image reveals the different protein secondary structures having different patterns. The lsomap's global coordinates provided a new approach to analyze the protein structures.