Integrality gaps of integer knapsack problems

We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a “typical” knapsack problem is drastically smaller than the integrality gap that occurs in a worst case scenario

A novel method to compare protein structures using local descriptors

<p>Abstract</p> <p>Background</p> <p>Protein structure comparison is one of the most widely performed tasks in bioinformatics. However, currently used methods have problems with the so-called "difficult similarities", including considerable shifts and distortions of structure, sequential swaps and circular permutations. There is a demand for efficient and automated systems capable of overcoming these difficulties, which may lead to the discovery of previously unknown structural relationships.</p> <p>Results</p> <p>We present a novel method for protein structure comparison based on the formalism of local descriptors of protein structure - DEscriptor Defined Alignment (DEDAL). Local similarities identified by pairs of similar descriptors are extended into global structural alignments. We demonstrate the method's capability by aligning structures in difficult benchmark sets: curated alignments in the SISYPHUS database, as well as SISY and RIPC sets, including non-sequential and non-rigid-body alignments. On the most difficult RIPC set of sequence alignment pairs the method achieves an accuracy of 77% (the second best method tested achieves 60% accuracy).</p> <p>Conclusions</p> <p>DEDAL is fast enough to be used in whole proteome applications, and by lowering the threshold of detectable structure similarity it may shed additional light on molecular evolution processes. It is well suited to improving automatic classification of structure domains, helping analyze protein fold space, or to improving protein classification schemes. DEDAL is available online at <url>http://bioexploratorium.pl/EP/DEDAL</url>.</p

Drug Discovery Using Chemical Systems Biology: Identification of the Protein-Ligand Binding Network To Explain the Side Effects of CETP Inhibitors

Systematic identification of protein-drug interaction networks is crucial to correlate complex modes of drug action to clinical indications. We introduce a novel computational strategy to identify protein-ligand binding profiles on a genome-wide scale and apply it to elucidating the molecular mechanisms associated with the adverse drug effects of Cholesteryl Ester Transfer Protein (CETP) inhibitors. CETP inhibitors are a new class of preventive therapies for the treatment of cardiovascular disease. However, clinical studies indicated that one CETP inhibitor, Torcetrapib, has deadly off-target effects as a result of hypertension, and hence it has been withdrawn from phase III clinical trials. We have identified a panel of off-targets for Torcetrapib and other CETP inhibitors from the human structural genome and map those targets to biological pathways via the literature. The predicted protein-ligand network is consistent with experimental results from multiple sources and reveals that the side-effect of CETP inhibitors is modulated through the combinatorial control of multiple interconnected pathways. Given that combinatorial control is a common phenomenon observed in many biological processes, our findings suggest that adverse drug effects might be minimized by fine-tuning multiple off-target interactions using single or multiple therapies. This work extends the scope of chemogenomics approaches and exemplifies the role that systems biology has in the future of drug discovery

SIMPLE ZEROS OF MAASS L-FUNCTIONS

We show that one simple zero of a Maass L-function implies infinitely many simple zeros of the L-function. Since Strombergsson found simple zeros of three different even Maass L-functions, we know that there are at least three Maass L-functions having infinitely many simple zerosope