Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

EGIA–evolutionary optimisation of gene regulatory networks, an integrative approach

Quantitative modelling of gene regulatory networks (GRNs) is still limited by data issues such as noise and the restricted length of available time series, creating an under-determination problem. However, large amounts of other types of biological data and knowledge are available, such as knockout experiments, annotations and so on, and it has been postulated that integration of these can improve model quality. However, integration has not been fully explored, to date. Here, we present a novel integrative framework for different types of data that aims to enhance model inference. This is based on evolutionary computation and uses different types of knowledge to introduce a novel customised initialisation and mutation operator and complex evaluation criteria, used to distinguish between candidate models. Specifically, the algorithm uses information from (i) knockout experiments, (ii) annotations of transcription factors, (iii) binding site motifs (expressed as position weight matrices) and (iv) DNA sequence of gene promoters, to drive the algorithm towards more plausible network structures. Further, the evaluation basis is also extended to include structure information included in these additional data. This framework is applied to both synthetic and real gene expression data. Models obtained by data integration display both quantitative and qualitative improvement

From Nonspecific DNA–Protein Encounter Complexes to the Prediction of DNA–Protein Interactions

©2009 Gao, Skolnick. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.doi:10.1371/journal.pcbi.1000341DNA–protein interactions are involved in many essential biological activities. Because there is no simple mapping code between DNA base pairs and protein amino acids, the prediction of DNA–protein interactions is a challenging problem. Here, we present a novel computational approach for predicting DNA-binding protein residues and DNA–protein interaction modes without knowing its specific DNA target sequence. Given the structure of a DNA-binding protein, the method first generates an ensemble of complex structures obtained by rigid-body docking with a nonspecific canonical B-DNA. Representative models are subsequently selected through clustering and ranking by their DNA–protein interfacial energy. Analysis of these encounter complex models suggests that the recognition sites for specific DNA binding are usually favorable interaction sites for the nonspecific DNA probe and that nonspecific DNA–protein interaction modes exhibit some similarity to specific DNA–protein binding modes. Although the method requires as input the knowledge that the protein binds DNA, in benchmark tests, it achieves better performance in identifying DNA-binding sites than three previously established methods, which are based on sophisticated machine-learning techniques. We further apply our method to protein structures predicted through modeling and demonstrate that our method performs satisfactorily on protein models whose root-mean-square Ca deviation from native is up to 5 Å from their native structures. This study provides valuable structural insights into how a specific DNA-binding protein interacts with a nonspecific DNA sequence. The similarity between the specific DNA–protein interaction mode and nonspecific interaction modes may reflect an important sampling step in search of its specific DNA targets by a DNA-binding protein

Protein docking by Rotation-Based Uniform Sampling (RotBUS) with fast computing of intermolecular contact distance and residue desolvation

<p>Abstract</p> <p>Background</p> <p>Protein-protein interactions are fundamental for the majority of cellular processes and their study is of enormous biotechnological and therapeutic interest. In recent years, a variety of computational approaches to the protein-protein docking problem have been reported, with encouraging results. Most of the currently available protein-protein docking algorithms are composed of two clearly defined parts: the sampling of the rotational and translational space of the interacting molecules, and the scoring and clustering of the resulting orientations. Although this kind of strategy has shown some of the most successful results in the CAPRI blind test <url>http://www.ebi.ac.uk/msd-srv/capri</url>, more efforts need to be applied. Thus, the sampling protocol should generate a pool of conformations that include a sufficient number of near-native ones, while the scoring function should discriminate between near-native and non-near-native proposed conformations. On the other hand, protocols to efficiently include full flexibility on the protein structures are increasingly needed.</p> <p>Results</p> <p>In these work we present new computational tools for protein-protein docking. We describe here the RotBUS (Rotation-Based Uniform Sampling) method to generate uniformly distributed sets of rigid-body docking poses, with a new fast calculation of the optimal contacting distance between molecules. We have tested the method on a standard benchmark of unbound structures and we can find near-native solutions in 100% of the cases. After applying a new fast filtering scheme based on residue-based desolvation, in combination with FTDock plus pyDock scoring, near-native solutions are found with rank ≤ 50 in 39% of the cases. Knowledge-based experimental restraints can be easily included to reduce computational times during sampling and improve success rates, and the method can be extended in the future to include flexibility of the side-chains.</p> <p>Conclusions</p> <p>This new sampling algorithm has the advantage of its high speed achieved by fast computing of the intermolecular distance based on a coarse representation of the interacting surfaces. In addition, a fast desolvation scoring permits the screening of millions of conformations at low computational cost, without compromising accuracy. The protocol presented here can be used as a framework to include restraints, flexibility and ensemble docking approaches.</p

A Dimer of the Toll-Like Receptor 4 Cytoplasmic Domain Provides a Specific Scaffold for the Recruitment of Signalling Adaptor Proteins

The Toll-like receptor 4 (TLR4) is a class I transmembrane receptor expressed on the surface of immune system cells. TLR4 is activated by exposure to lipopolysaccharides derived from the outer membrane of Gram negative bacteria and forms part of the innate immune response in mammals. Like other class 1 receptors, TLR4 is activated by ligand induced dimerization, and recent studies suggest that this causes concerted conformational changes in the receptor leading to self association of the cytoplasmic Toll/Interleukin 1 receptor (TIR) signalling domain. This homodimerization event is proposed to provide a new scaffold that is able to bind downstream signalling adaptor proteins. TLR4 uses two different sets of adaptors; TRAM and TRIF, and Mal and MyD88. These adaptor pairs couple two distinct signalling pathways leading to the activation of interferon response factor 3 (IRF-3) and nuclear factor κB (NFκB) respectively. In this paper we have generated a structural model of the TLR4 TIR dimer and used molecular docking to probe for potential sites of interaction between the receptor homodimer and the adaptor molecules. Remarkably, both the Mal and TRAM adaptors are strongly predicted to bind at two symmetry-related sites at the homodimer interface. This model of TLR4 activation is supported by extensive functional studies involving site directed mutagenesis, inhibition by cell permeable peptides and stable protein phosphorylation of receptor and adaptor TIR domains. Our results also suggest a molecular mechanism for two recent findings, the caspase 1 dependence of Mal signalling and the protective effects conferred by the Mal polymorphism Ser180Leu

Characterizing Protein-Protein Interactions with the Fragment Molecular Orbital Method

Proteins are vital components of living systems, serving as building blocks, molecular machines, enzymes, receptors, ion channels, sensors, and transporters. Protein-protein interactions (PPIs) are a key part of their function. There are more than 645,000 reported disease-relevant PPIs in the human interactome, but drugs have been developed for only 2% of these targets. The advances in PPI-focused drug discovery are highly dependent on the availability of structural data and accurate computational tools for analysis of this data. Quantum mechanical approaches are often too expensive computationally, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. FMO provides essential information for PPI drug discovery, namely, identification of key interactions formed between residues of two proteins, including their strength (in kcal/mol) and their chemical nature (electrostatic or hydrophobic). In this chapter, we have demonstrated how three different FMO-based approaches (pair interaction energy analysis (PIE analysis), subsystem analysis (SA) and analysis of protein residue networks (PRNs)) have been applied to study PPI in three protein-protein complexes

Crystal structures of the CusA efflux pump suggest methionine-mediated metal transport

Gram-negative bacteria, such as Escherichia coli, frequently utilize tripartite efflux complexes in the resistance-nodulation-cell division (RND) family to expel diverse toxic compounds from the cell.1,2 The efflux system CusCBA is responsible for extruding biocidal Cu(I) and Ag(I) ions.3,4 No prior structural information was available for the heavy-metal efflux (HME) subfamily of the RND efflux pumps. Here we describe the crystal structures of the inner membrane transporter CusA in the absence and presence of bound Cu(I) or Ag(I). These CusA structures provide important new structural information about the HME sub-family of RND efflux pumps. The structures suggest that the metal binding sites, formed by a three-methionine cluster, are located within the cleft region of the periplasmic domain. Intriguingly, this cleft is closed in the apo-CusA form but open in the CusA-Cu(I) and CusA-Ag(I) structures, which directly suggests a plausible pathway for ion export. Binding of Cu(I) and Ag(I) triggers significant conformational changes in both the periplasmic and transmembrane domains. The crystal structure indicates that CusA has, in addition to the three-methionine metal binding site, four methionine pairs - three located in the transmembrane region and one in the periplasmic domain. Genetic analysis and transport assays suggest that CusA is capable of actively picking up metal ions from the cytosol, utilizing these methionine pairs/clusters to bind and export metal ions. These structures suggest a stepwise shuttle mechanism for transport between these sites

FitEM2EM—Tools for Low Resolution Study of Macromolecular Assembly and Dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top

Protein tyrosine phosphatases expression during development of mouse superior colliculus

Protein tyrosine phosphatases (PTPs) are key regulators of different processes during development of the central nervous system. However, expression patterns and potential roles of PTPs in the developing superior colliculus remain poorly investigated. In this study, a degenerate primer-based reverse transcription-polymerase chain reaction (RT-PCR) approach was used to isolate seven different intracellular PTPs and nine different receptor-type PTPs (RPTPs) from embryonic E15 mouse superior colliculus. Subsequently, the expression patterns of 11 PTPs (TC-PTP, PTP1C, PTP1D, PTP-MEG2, PTP-PEST, RPTPJ, RPTPε, RPTPRR, RPTPσ, RPTPκ and RPTPγ) were further analyzed in detail in superior colliculus from embryonic E13 to postnatal P20 stages by quantitative real-time RT-PCR, Western blotting and immunohistochemistry. Each of the 11 PTPs exhibits distinct spatiotemporal regulation of mRNAs and proteins in the developing superior colliculus suggesting their versatile roles in genesis of neuronal and glial cells and retinocollicular topographic mapping. At E13, additional double-immunohistochemical analysis revealed the expression of PTPs in collicular nestin-positive neural progenitor cells and RC-2-immunoreactive radial glia cells, indicating the potential functional importance of PTPs in neurogenesis and gliogenesis