Fuzzy Modeling of Labeled Point Cloud Superposition for the Comparison of Protein Binding Sites

Abstract — Geometric objects are often represented approximately in terms of a finite set of points in three-dimensional Euclidean space. In this paper, we extend this representation to what we call labeled point clouds. A labeled point cloud is a finite set of points, where each point is not only associated with a position in three-dimensional space, but also with a discrete class label that represents a specific property. This type of model is especially suitable for modeling biomolecules such as proteins and protein binding sites, where a label may represent an atom type or a physicochemical property. Proceeding from this representation, we address the question of how to compare two labeled points clouds in terms of similarity. Using fuzzy modeling techniques, we develop a suitable similarity measure as well as an efficient evolutionary algorithm to compute it. Finally, an application study is presented in which the approach is used to classify protein binding sites