Some results on more flexible versions of Graph Motif

The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a vertex-colored graph. Due to the high rate of noise in the biological data, more flexible definitions of the problem have been outlined. We present in this paper two inapproximability results for two different optimization variants of Graph Motif: one where the size of the solution is maximized, the other when the number of substitutions of colors to obtain the motif from the solution is minimized. We also study a decision version of Graph Motif where the connectivity constraint is replaced by the well known notion of graph modularity. While the problem remains NP-complete, it allows algorithms in FPT for biologically relevant parameterizations

Probability Models for Degree Distributions of Protein Interaction Networks

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad-hoc fashion, with clear power-law like behaviour often only extending over a limited range of connectivities. Here we apply formal model selection techniques to decide which probability distribution best describes the degree distributions of protein interaction networks. Contrary to previous studies this well defined approach suggests that the degree distribution of many molecular networks is often better described by distributions other than the popular power-law distribution. This, in turn, suggests that simple, if elegant, models may not necessarily help in the quantitative understanding of complex biological processes.

Structural modeling and functional analysis of the essential ribosomal processing protease Prp from Staphylococcus aureus

In Firmicutes and related bacteria, ribosomal large subunit protein L27 is encoded with a conserved N-terminal extension that is removed to expose residues critical for ribosome function. Bacteria encoding L27 with this N-terminal extension also encode a sequence-specific cysteine protease, Prp, which carries out this cleavage. In this work, we demonstrate that L27 variants with an un-cleavable N-terminal extension, or lacking the extension (pre-cleaved), are unable to complement an L27 deletion in Staphylococcus aureus. This indicates that N-terminal processing of L27 is not only essential but possibly has a regulatory role. Prp represents a new clade of previously uncharacterized cysteine proteases, and the dependence of S. aureus on L27 cleavage by Prp validates the enzyme as a target for potential antibiotic development. To better understand the mechanism of Prp activity, we analyzed Prp enzyme kinetics and substrate preference using a fluorogenic peptide cleavage assay. Molecular modeling and site-directed mutagenesis implicate several residues around the active site in catalysis and substrate binding, and support a structural model in which rearrangement of a flexible loop upon binding of the correct peptide substrate is required for the active site to assume the proper conformation. These findings lay the foundation for the development of antimicrobials that target this novel, essential pathway

Spectral Sequence Motif Discovery

Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance are required to process the big datasets produced by new high-throughput sequencing technologies. Most existing algorithms are computationally demanding and often cannot support the large size of new experimental data. We present a new motif discovery algorithm that is built on a recent machine learning technique, referred to as Method of Moments. Based on spectral decompositions, this method is robust under model misspecification and is not prone to locally optimal solutions. We obtain an algorithm that is extremely fast and designed for the analysis of big sequencing data. In a few minutes, we can process datasets of hundreds of thousand sequences and extract motif profiles that match those computed by various state-of-the-art algorithms.Comment: 20 pages, 3 figures, 1 tabl

Coarse-Graining and Self-Dissimilarity of Complex Networks

Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units (CGU) as connectivity patterns which can serve as the nodes of a coarse-grained network, and present algorithms to detect them. We use this approach to systematically reverse-engineer electronic circuits, forming understandable high-level maps from incomprehensible transistor wiring: first, a coarse-grained version in which each node is a gate made of several transistors is established. Then, the coarse-grained network is itself coarse-grained, resulting in a high-level blueprint in which each node is a circuit-module made of multiple gates. We apply our approach also to a mammalian protein-signaling network, to find a simplified coarse-grained network with three main signaling channels that correspond to cross-interacting MAP-kinase cascades. We find that both biological and electronic networks are 'self-dissimilar', with different network motifs found at each level. The present approach can be used to simplify a wide variety of directed and nondirected, natural and designed networks.Comment: 11 pages, 11 figure