Ofer Rahat

Cluster conservation as a novel tool for studying protein-protein interactions evolution.

Protein–protein interactions networks has come to be a buzzword associated with nets containing edges that represent a pair of interacting proteins (e.g. hormone‐receptor, enzyme‐inhibitor, antigen‐antibody, and a subset of multichain biological machines). Yet, each such interaction composes its own unique network, in which vertices represent amino acid residues, and edges represent atomic contacts. Recent studies have shown that analyses of the data encapsulated in these detailed networks may impact predictions of structure–function correlation. Here, we study homologous families of protein–protein interfaces, which share the same fold but vary in sequence. In this context, we address what properties of the network are shared among relatives with different sequences (and hence different atomic interactions) and which are not. Herein, we develop the general mathematical framework needed to compare the modularity of homologous networks. We then apply this analysis to the structural data of a few interface families, including hemoglobin α–β, growth hormone‐receptor, and Serine protease‐inhibitor. Our results suggest that interface modularity is an evolutionarily conserved property. Hence, protein–protein interfaces can be clustered down to a few modules, with the boundaries being evolutionarily conserved along homologous complexes. This suggests that protein engineering of protein–protein binding sites may be simplified by varying each module, but retaining the overall modularity of the interface. Proteins 2008.

Understanding hydrogen-bond patterns in proteins using network motifs

UNLABELLED Protein structures can be viewed as networks of contacts (edges) between amino-acid residues (nodes). Here we dissect proteins into sub-graphs consisting of six nodes and their corresponding edges, with an edge being either a backbone hydrogen bond (H-bond) or a covalent interaction. Six thousand three hundred and twenty-two such sub-graphs were found in a large non-redundant dataset of high-resolution structures, from which 35 occur much more frequently than in a random model. Many of these significant sub-graphs (also called network motifs) correspond to sub-structures of alpha helices and beta-sheets, as expected. However, others correspond to more exotic sub-structures such as 3(10) helix, Schellman motif and motifs that were not defined previously. This topological characterization of patterns is very useful for producing a detailed differences map to compare protein structures. Here we analyzed in details the differences between NMR, molecular dynamics (MD) simulations and X-ray structures for Lysozyme, SH3 and the lambda repressor. In these cases, the same structures solved by NMR and simulated by MD showed small but consistent differences in their motif composition from the crystal structures, despite a very small root mean square deviation (RMSD) between them. This may be due to differences in the pair-wise energy functions used and the dynamic nature of these proteins. AVAILABILITY A web-based tool to calculate network motifs is available at http://bioinfo.weizmann.ac.il/protmot/.

Complexity of Error-Correcting Codes Derived from Combinatorial Games

The main result of the present paper is to establish an algorithm for computing a linear error-correcting code called lexicode in O(n d − 1) steps, where n and d are the size and distance of the code, respectively. This is done by using the theory of combinatorial games, specifically, two-player cellular automata games. Previous algorithms were exponential in n.

Rediscovering secondary structures as network motifs---an unsupervised learning approach

MOTIVATION Secondary structures are key descriptors of a protein fold and its topology. In recent years, they facilitated intensive computational tasks for finding structural homologues, fold prediction and protein design. Their popularity stems from an appealing regularity in patterns of geometry and chemistry. However, the definition of secondary structures is of subjective nature. An unsupervised de-novo discovery of these structures would shed light on their nature, and improve the way we use these structures in algorithms of structural bioinformatics. METHODS We developed a new method for unsupervised partitioning of undirected graphs, based on patterns of small recurring network motifs. Our input was the network of all H-bonds and covalent interactions of protein backbones. This method can be also used for other biological and non-biological networks. RESULTS In a fully unsupervised manner, and without assuming any explicit prior knowledge, we were able to rediscover the existence of conventional alpha-helices, parallel beta-sheets, anti-parallel sheets and loops, as well as various non-conventional hybrid structures. The relation between connectivity and crystallographic temperature factors establishes the existence of novel secondary structures.

Infinite Cyclic Impartial Games

We define the family of locally path-bounded digraphs, which is a class of infinite digraphs, and show that on this class it is relatively easy to compute an optimal strategy (winning or nonlosing); and realize a win, when possible, in a finite number of moves. This is done by proving that the Generalized Sprague-Grundy function exists uniquely and has finite values on this class.