The Multiple Common Point Set Problem and Its Application to Molecule Binding Pattern Detection

Abstract

Recognition of binding patterns common to a set of protein structures is important for recognition of function, prediction of binding, and drug design. We consider protein binding sites represented by a set of 3D points with assigned physico-chemical and geometrical properties important for protein-ligand interactions. We formulate the multiple binding site alignment problem as detection of the largest common set of such 3D points. We discuss the computational problem of multiple common point set detection and, particularly, the matching problem in K-partite-epsilon graphs, where K partitions are associated with K structures and edges are defined between epsilon-close points. We show that the K-partite-epsilon matching problem is NP-hard in the Euclidean space with dimension larger than one. Consequently, we show that the largest common point set problem between three point sets is NP-hard. On the practical side, we present a novel computational method, MultiBind, for recognition of binding patterns common to a set of protein structures. It performs a multiple alignment between protein binding sites in the absence of overall sequence, fold, or binding partner similarity. Despite the NP-hardness results, in our applications, we practically overcome the exponential number of multiple alignment combinations by applying an efficient branchand- bound filtering procedure. We show applications of MultiBind to several biological targets. The method recognizes patterns which are responsible for binding small molecules, such as estradiol, ATP/ANP, and transition state analogues.

Superposition and Alignment of Labeled Point Clouds

“…The concept of a labeled point cloud, appears to be a quite natural representation for biological structures [33,34]. In comparison to other approaches, such as the prevalent graph-based methods, the modeling step is hence simplified and does not involve any complex transformations.…”

“…Another interesting approach, namely geometric hashing, allows for calculating a partial alignment between point clouds [34,3,26,25,42,27]. First, k-tuples are drawn from a point cloud and stored in a hash table.…”

“…Another interesting way to obtain a multiple alignment in one step is proposed in [34], were a kpartite pivot graph is used instead of a bipartite graph. Since the problem to find a matching on that graph is NP-hard, the authors make use of a simple greedy heuristic.…”

SEGA: Semiglobal Graph Alignment for Structure-Based Protein Comparison

“…A similar representation is used by SiteEngine [32] and MultiBind [9], albeit with slightly different rules for the assignment of these properties. SiteEngine employs geometric hashing for the comparison of protein binding sites, whereas CavBase again utilizes graph theory.…”

“…Many approaches to the functional analysis of proteins already exist, either on the sequence level [1,2] or on the structural level [3,4,5,6,7,8,9]. However, these methods typically aim at the comparison of whole protein structures, some of them for example based on representations on a folding level, such as the well-known DALI approach [4].…”