Superposition and Alignment of Labeled Point Clouds

Abstract

Geometric objects are often represented approximately in terms of a finite set of points in threedimensional 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 physico-chemical property. Proceeding from this representation, we address the question of how to compare two labeled points clouds in terms of their similarity. Using fuzzy modeling techniques, we develop a suitable similarity measure as well as an efficient evolutionary algorithm to compute it. Moreover, we consider the problem of establishing an alignment of the structures in the sense of a one-to-one correspondence between their basic constituents. From a biological point of view, alignments of this kind are of great interest, since mutually corresponding molecular constituents offer important information about evolution and heredity, and can also serve as a means to explain a degree of similarity. In this paper, we therefore develop a method for computing pairwise or multiple alignments of labeled point clouds. To this end, we proceed from an optimal superposition of the corresponding point clouds and construct an alignment which is as much as possible in agreement with the neighborhood structure established by this superposition. We apply our methods to the structural analysis of protein binding sites.

Experimental Analysis of Optimization Algorithms: Tuning and Beyond

“…SPOT was successfully applied in the fields of bioinformatics [79,33,32], environmental engineering [48,30], shipbuilding [72], fuzzy logic [82], multimodal optimization [68], statistical analysis of algorithms [50,78], multicriteria optimization [80], genetic programming [51], particle swarm optimization [9,49], automated and manual parameter tuning [31,74,42,43], graph drawing [77,65], aerospace and shipbuilding industry [63], mechanical engineering [56], and chemical engineering [39]. Bartz-Beielstein [3] collects publications related to the sequential parameter optimization.…”

GPU-Based Point Cloud Superpositioning for Structural Comparisons of Protein Binding Sites

“…Moreover, we would like to emphasize that the problem of comparing two protein binding sites is more difficult than the problem of comparing protein structures (e.g., at the fold level). Only relatively few works focus on the comparison of protein binding sites, which can be subdivided into feature-based [25], [26], [27], graphbased [8], [28], [29], [30], [31], [32] and geometric approaches [33], [34], [35], [36]. Geometric approaches are particularly powerful, since they do not rely on a lossy transformation from a set of points in Euclidean space to graphs or features, in contrast to the other approaches.…”

“…A promising geometric approach is labeled point cloud superpositioning [35], [36]. This approach is based on op-timizing a multimodal real-valued problem by means of an evolution strategy (ES) [37].…”

“…For this purpose, we propose a parallel ES that operates on large population sizes, but nevertheless requires low runtimes. The basic idea of the parallel ES is to leverage principles derived from the comparison of chemical compounds using labeled point cloud superpositioning [36] and implement the resulting ES on a General Purpose Computation on Graphics Processing Units (GP-GPU or GPU) platform.…”

“…The performance of the proposed parallel ES is compared to the previously proposed CPU-based sequential approach for labeled point cloud superpositioning [35], [36], indicating that the GPU-based parallel ES leads to qualitatively better results and significantly shorter runtimes, with speed improvements of up to a factor of 1,500 for large populations. Binary classification tests based on the ATP, FAD, and NADH protein subsets of CavBase, a database containing putative binding sites, show average classification rate improvements from about 92% (CPU) to 96% (GPU).…”