Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming

Disposition of Federally Owned Surpluses

PDZ domains are scaffolding modules in protein-protein interactions that mediate numerous physiological functions by interacting canonically with the C-terminus or non-canonically with an internal motif of protein ligands. A conserved carboxylate-binding site in the PDZ domain facilitates binding via backbone hydrogen bonds; however, little is known about the role of these hydrogen bonds due to experimental challenges with backbone mutations. Here we address this interaction by generating semisynthetic PDZ domains containing backbone amide-to-ester mutations and evaluating the importance of individual hydrogen bonds for ligand binding. We observe substantial and differential effects upon amide-to-ester mutation in PDZ2 of postsynaptic density protein 95 and other PDZ domains, suggesting that hydrogen bonding at the carboxylate-binding site contributes to both affinity and selectivity. In particular, the hydrogen-bonding pattern is surprisingly different between the non-canonical and canonical interaction. Our data provide a detailed understanding of the role of hydrogen bonds in protein-protein interactions

Design principles for riboswitch function

Scientific and technological advances that enable the tuning of integrated regulatory components to match network and system requirements are critical to reliably control the function of biological systems. RNA provides a promising building block for the construction of tunable regulatory components based on its rich regulatory capacity and our current understanding of the sequence–function relationship. One prominent example of RNA-based regulatory components is riboswitches, genetic elements that mediate ligand control of gene expression through diverse regulatory mechanisms. While characterization of natural and synthetic riboswitches has revealed that riboswitch function can be modulated through sequence alteration, no quantitative frameworks exist to investigate or guide riboswitch tuning. Here, we combined mathematical modeling and experimental approaches to investigate the relationship between riboswitch function and performance. Model results demonstrated that the competition between reversible and irreversible rate constants dictates performance for different regulatory mechanisms. We also found that practical system restrictions, such as an upper limit on ligand concentration, can significantly alter the requirements for riboswitch performance, necessitating alternative tuning strategies. Previous experimental data for natural and synthetic riboswitches as well as experiments conducted in this work support model predictions. From our results, we developed a set of general design principles for synthetic riboswitches. Our results also provide a foundation from which to investigate how natural riboswitches are tuned to meet systems-level regulatory demands

The Overlap of Small Molecule and Protein Binding Sites within Families of Protein Structures

Protein–protein interactions are challenging targets for modulation by small molecules. Here, we propose an approach that harnesses the increasing structural coverage of protein complexes to identify small molecules that may target protein interactions. Specifically, we identify ligand and protein binding sites that overlap upon alignment of homologous proteins. Of the 2,619 protein structure families observed to bind proteins, 1,028 also bind small molecules (250–1000 Da), and 197 exhibit a statistically significant (p<0.01) overlap between ligand and protein binding positions. These “bi-functional positions”, which bind both ligands and proteins, are particularly enriched in tyrosine and tryptophan residues, similar to “energetic hotspots” described previously, and are significantly less conserved than mono-functional and solvent exposed positions. Homology transfer identifies ligands whose binding sites overlap at least 20% of the protein interface for 35% of domain–domain and 45% of domain–peptide mediated interactions. The analysis recovered known small-molecule modulators of protein interactions as well as predicted new interaction targets based on the sequence similarity of ligand binding sites. We illustrate the predictive utility of the method by suggesting structural mechanisms for the effects of sanglifehrin A on HIV virion production, bepridil on the cellular entry of anthrax edema factor, and fusicoccin on vertebrate developmental pathways. The results, available at http://pibase.janelia.org, represent a comprehensive collection of structurally characterized modulators of protein interactions, and suggest that homologous structures are a useful resource for the rational design of interaction modulators

Computational Fragment-Based Binding Site Identification by Ligand Competitive Saturation

Fragment-based drug discovery using NMR and x-ray crystallographic methods has proven utility but also non-trivial time, materials, and labor costs. Current computational fragment-based approaches circumvent these issues but suffer from limited representations of protein flexibility and solvation effects, leading to difficulties with rigorous ranking of fragment affinities. To overcome these limitations we describe an explicit solvent all-atom molecular dynamics methodology (SILCS: Site Identification by Ligand Competitive Saturation) that uses small aliphatic and aromatic molecules plus water molecules to map the affinity pattern of a protein for hydrophobic groups, aromatic groups, hydrogen bond donors, and hydrogen bond acceptors. By simultaneously incorporating ligands representative of all these functionalities, the method is an in silico free energy-based competition assay that generates three-dimensional probability maps of fragment binding (FragMaps) indicating favorable fragment∶protein interactions. Applied to the two-fold symmetric oncoprotein BCL-6, the SILCS method yields two-fold symmetric FragMaps that recapitulate the crystallographic binding modes of the SMRT and BCOR peptides. These FragMaps account both for important sequence and structure differences in the C-terminal halves of the two peptides and also the high mobility of the BCL-6 His116 sidechain in the peptide-binding groove. Such SILCS FragMaps can be used to qualitatively inform the design of small-molecule inhibitors or as scoring grids for high-throughput in silico docking that incorporate both an atomic-level description of solvation and protein flexibility

Assessing the druggability of protein-protein interactions by a supervised machine-learning method

<p>Abstract</p> <p>Background</p> <p>Protein-protein interactions (PPIs) are challenging but attractive targets of small molecule drugs for therapeutic interventions of human diseases. In this era of rapid accumulation of PPI data, there is great need for a methodology that can efficiently select drug target PPIs by holistically assessing the druggability of PPIs. To address this need, we propose here a novel approach based on a supervised machine-learning method, support vector machine (SVM).</p> <p>Results</p> <p>To assess the druggability of the PPIs, 69 attributes were selected to cover a wide range of structural, drug and chemical, and functional information on the PPIs. These attributes were used as feature vectors in the SVM-based method. Thirty PPIs known to be druggable were carefully selected from previous studies; these were used as positive instances. Our approach was applied to 1,295 human PPIs with tertiary structures of their protein complexes already solved. The best SVM model constructed discriminated the already-known target PPIs from others at an accuracy of 81% (sensitivity, 82%; specificity, 79%) in cross-validation. Among the attributes, the two with the greatest discriminative power in the best SVM model were the number of interacting proteins and the number of pathways.</p> <p>Conclusion</p> <p>Using the model, we predicted several promising candidates for druggable PPIs, such as SMAD4/SKI. As more PPI data are accumulated in the near future, our method will have increased ability to accelerate the discovery of druggable PPIs.</p

Designing Focused Chemical Libraries Enriched in Protein-Protein Interaction Inhibitors using Machine-Learning Methods

Protein-protein interactions (PPIs) may represent one of the next major classes of therapeutic targets. So far, only a minute fraction of the estimated 650,000 PPIs that comprise the human interactome are known with a tiny number of complexes being drugged. Such intricate biological systems cannot be cost-efficiently tackled using conventional high-throughput screening methods. Rather, time has come for designing new strategies that will maximize the chance for hit identification through a rationalization of the PPI inhibitor chemical space and the design of PPI-focused compound libraries (global or target-specific). Here, we train machine-learning-based models, mainly decision trees, using a dataset of known PPI inhibitors and of regular drugs in order to determine a global physico-chemical profile for putative PPI inhibitors. This statistical analysis unravels two important molecular descriptors for PPI inhibitors characterizing specific molecular shapes and the presence of a privileged number of aromatic bonds. The best model has been transposed into a computer program, PPI-HitProfiler, that can output from any drug-like compound collection a focused chemical library enriched in putative PPI inhibitors. Our PPI inhibitor profiler is challenged on the experimental screening results of 11 different PPIs among which the p53/MDM2 interaction screened within our own CDithem platform, that in addition to the validation of our concept led to the identification of 4 novel p53/MDM2 inhibitors. Collectively, our tool shows a robust behavior on the 11 experimental datasets by correctly profiling 70% of the experimentally identified hits while removing 52% of the inactive compounds from the initial compound collections. We strongly believe that this new tool can be used as a global PPI inhibitor profiler prior to screening assays to reduce the size of the compound collections to be experimentally screened while keeping most of the true PPI inhibitors. PPI-HitProfiler is freely available on request from our CDithem platform website, www.CDithem.com

Identification of hot-spot residues in protein-protein interactions by computational docking

<p>Abstract</p> <p>Background</p> <p>The study of protein-protein interactions is becoming increasingly important for biotechnological and therapeutic reasons. We can define two major areas therein: the structural prediction of protein-protein binding mode, and the identification of the relevant residues for the interaction (so called 'hot-spots'). These hot-spot residues have high interest since they are considered one of the possible ways of disrupting a protein-protein interaction. Unfortunately, large-scale experimental measurement of residue contribution to the binding energy, based on alanine-scanning experiments, is costly and thus data is fairly limited. Recent computational approaches for hot-spot prediction have been reported, but they usually require the structure of the complex.</p> <p>Results</p> <p>We have applied here normalized interface propensity (<it>NIP</it>) values derived from rigid-body docking with electrostatics and desolvation scoring for the prediction of interaction hot-spots. This parameter identifies hot-spot residues on interacting proteins with predictive rates that are comparable to other existing methods (up to 80% positive predictive value), and the advantage of not requiring any prior structural knowledge of the complex.</p> <p>Conclusion</p> <p>The <it>NIP </it>values derived from rigid-body docking can reliably identify a number of hot-spot residues whose contribution to the interaction arises from electrostatics and desolvation effects. Our method can propose residues to guide experiments in complexes of biological or therapeutic interest, even in cases with no available 3D structure of the complex.</p

A Dual Receptor Crosstalk Model of G-Protein-Coupled Signal Transduction

Macrophage cells that are stimulated by two different ligands that bind to G-protein-coupled receptors (GPCRs) usually respond as if the stimulus effects are additive, but for a minority of ligand combinations the response is synergistic. The G-protein-coupled receptor system integrates signaling cues from the environment to actuate cell morphology, gene expression, ion homeostasis, and other physiological states. We analyze the effects of the two signaling molecules complement factors 5a (C5a) and uridine diphosphate (UDP) on the intracellular second messenger calcium to elucidate the principles that govern the processing of multiple signals by GPCRs. We have developed a formal hypothesis, in the form of a kinetic model, for the mechanism of action of this GPCR signal transduction system using data obtained from RAW264.7 macrophage cells. Bayesian statistical methods are employed to represent uncertainty in both data and model parameters and formally tie the model to experimental data. When the model is also used as a tool in the design of experiments, it predicts a synergistic region in the calcium peak height dose response that results when cells are simultaneously stimulated by C5a and UDP. An analysis of the model reveals a potential mechanism for crosstalk between the Gαi-coupled C5a receptor and the Gαq-coupled UDP receptor signaling systems that results in synergistic calcium release