Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs

SUMMARY: Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns that occur much more frequently than in randomized networks with the same degree sequence. Network motifs were demonstrated to play key information processing roles in biological regulation networks. Existing algorithms for detecting network motifs act by exhaustively enumerating all subgraphs with a given number of nodes in the network. The runtime of such algorithms increases strongly with network size. Here, we present a novel algorithm that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size. This algorithm is based on random sampling of subgraphs. Network motifs are detected with a surprisingly small number of samples in a wide variety of networks. Our method can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms. We present results for high-order motifs in several biological networks and discuss their possible functions. AVAILABILITY: A software tool for estimating subgraph concentrations and detecting network motifs (mfinder 1.1) and further information is available at http://www.weizmann.ac.il/mcb/UriAlon/     

SLIDER: a generic metaheuristic for the discovery of correlated motifs in protein-protein interaction networks

Correlated motif mining (cmm) is the problem of finding overrepresented pairs of patterns, called motifs, in sequences of interacting proteins. Algorithmic solutions for cmm thereby provide a computational method for predicting binding sites for protein interaction. In this paper, we adopt a motif-driven approach where the support of candidate motif pairs is evaluated in the network. We experimentally establish the superiority of the Chi-square-based support measure over other support measures. Furthermore, we obtain that cmm is an np-hard problem for a large class of support measures (including Chi-square) and reformulate the search for correlated motifs as a combinatorial optimization problem. We then present the generic metaheuristic slider which uses steepest ascent with a neighborhood function based on sliding motifs and employs the Chi-square-based support measure. We show that slider outperforms existing motif-driven cmm methods and scales to large protein-protein interaction networks. The slider-implementation and the data used in the experiments are available on http://bioinformatics.uhasselt.be.     

Perspective: network-guided pattern formation of neural dynamics

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain''s network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatio-temporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.     

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.     

Dynamic network rewiring determines temporal regulatory functions in Drosophila melanogaster development processes

The identification of network motifs has been widely considered as a significant step towards uncovering the design principles of biomolecular regulatory networks. To date, time‐invariant networks have been considered. However, such approaches cannot be used to reveal time‐specific biological traits due to the dynamic nature of biological systems, and hence may not be applicable to development, where temporal regulation of gene expression is an indispensable characteristic. We propose a concept of a “temporal sequence of network motifs”, a sequence of network motifs in active sub‐networks constructed over time, and investigate significant network motifs in the active temporal sub‐networks of Drosophila melanogaster . Based on this concept, we find a temporal sequence of network motifs which changes according to developmental stages and thereby cannot be identified from the whole static network. Moreover, we show that the temporal sequence of network motifs corresponding to each developmental stage can be used to describe pivotal developmental events.     

Complex recombination events at the hypermutable minisatellite CEB1 (D2S90).

Some minisatellite structures are the site of high rates of DNA recombination in non-pathological situations, with an excess of motif insertion events and a locus-dependent sex-specific mutation bias. We previously reported the cloning of the hypermutable minisatellite locus CEB1 (D2S90), remarkable for its 13% mutation rate in the male germline (compared to approximately 0.4% in female). We have sought to analyse the mechanisms underlying the addition or deletion of motifs at this locus using the minisatellite variant repeat mapping technique. This is possible with a high precision due to the extreme sequence polymorphism seen between different motifs. No crossing-over event was observed among 38 informative neomutations. Four of the 19 informative mutant alleles with an addition of motifs are interallelic events, the others are intra-allelic. Overall, the insertion and deletion mutations are spread along the alleles, although the subset of interallelic events shows clustering towards the analysed end. The apparently complex recombination events observed can all be interpreted as a succession of elementary duplications-deletions of inter- as well as intra-chromosomal origin, suggesting a model in which sister chromatid as well as conversion-like exchanges are involved in these mutation processes.     

Quantitative self-organizing maps for clustering electron tomograms

Tomography emerges as a powerful methodology for determining the complex architectures of biological specimens that are better regarded from the structural point of view as singular entities. However, once the structure of a sufficiently large number of singular specimens is solved, quite possibly structural patterns start to emerge. This latter situation is addressed here, where the clustering of a set of 3D reconstructions using a novel quantitative approach is presented. In general terms, we propose a new variant of a self-organizing neural network for the unsupervised classification of 3D reconstructions. The novelty of the algorithm lies in its rigorous mathematical formulation that, starting from a large set of noisy input data, finds a set of "representative" items, organized onto an ordered output map, such that the probability density of this set of representative items resembles at its possible best the probability density of the input data. In this study, we evaluate the feasibility of application of the proposed neural approach to the problem of identifying similar 3D motifs within tomograms of insect flight muscle. Our experimental results prove that this technique is suitable for this type of problem, providing the electron microscopy community with a new tool for exploring large sets of tomogram data to find complex patterns.     

Finding biological process modifications in cancer tissues by mining gene expression correlations

Background  

Through the use of DNA microarrays it is now possible to obtain quantitative measurements of the expression of thousands of genes from a biological sample. This technology yields a global view of gene expression that can be used in several ways. Functional insight into expression profiles is routinely obtained by using Gene Ontology terms associated to the cellular genes. In this paper, we deal with functional data mining from expression profiles, proposing a novel approach that studies the correlations between genes and their relations to Gene Ontology (GO). By using this "functional correlations comparison" we explore all possible pairs of genes identifying the affected biological processes by analyzing in a pair-wise manner gene expression patterns and linking correlated pairs with Gene Ontology terms.     

A network of conserved co-occurring motifs for the regulation of alternative splicing

Cis-acting short sequence motifs play important roles in alternative splicing. It is now possible to identify such sequence motifs as conserved sequence patterns in genome sequence alignments. Here, we report the systematic search for motifs in the neighboring introns of alternatively spliced exons by using comparative analysis of mammalian genome alignments. We identified 11 conserved sequence motifs that might be involved in the regulation of alternative splicing. These motifs are not only significantly overrepresented near alternatively spliced exons, but they also co-occur with each other, thus, forming a network of cis-elements, likely to be the basis for context-dependent regulation. Based on this finding, we applied the motif co-occurrence to predict alternatively skipped exons. We verified exon skipping in 29 cases out of 118 predictions (25%) by EST and mRNA sequences in the databases. For the predictions not verified by the database sequences, we confirmed exon skipping in 10 additional cases by using both RT–PCR experiments and the publicly available RNA-Seq data. These results indicate that even more alternative splicing events will be found with the progress of large-scale and high-throughput analyses for various tissue samples and developmental stages.     

CLICK and EXPANDER: a system for clustering and visualizing gene expression data

MOTIVATION: Microarrays have become a central tool in biological research. Their applications range from functional annotation to tissue classification and genetic network inference. A key step in the analysis of gene expression data is the identification of groups of genes that manifest similar expression patterns. This translates to the algorithmic problem of clustering genes based on their expression patterns. RESULTS: We present a novel clustering algorithm, called CLICK, and its applications to gene expression analysis. The algorithm utilizes graph-theoretic and statistical techniques to identify tight groups (kernels) of highly similar elements, which are likely to belong to the same true cluster. Several heuristic procedures are then used to expand the kernels into the full clusters. We report on the application of CLICK to a variety of gene expression data sets. In all those applications it outperformed extant algorithms according to several common figures of merit. We also point out that CLICK can be successfully used for the identification of common regulatory motifs in the upstream regions of co-regulated genes. Furthermore, we demonstrate how CLICK can be used to accurately classify tissue samples into disease types, based on their expression profiles. Finally, we present a new java-based graphical tool, called EXPANDER, for gene expression analysis and visualization, which incorporates CLICK and several other popular clustering algorithms. AVAILABILITY: http://www.cs.tau.ac.il/~rshamir/expander/expander.html     

Efficient parameter estimation for spatio-temporal models of pattern formation: case study of Drosophila melanogaster

MOTIVATION: Diffusable and non-diffusable gene products play a major role in body plan formation. A quantitative understanding of the spatio-temporal patterns formed in body plan formation, by using simulation models is an important addition to experimental observation. The inverse modelling approach consists of describing the body plan formation by a rule-based model, and fitting the model parameters to real observed data. In body plan formation, the data are usually obtained from fluorescent immunohistochemistry or in situ hybridizations. Inferring model parameters by comparing such data to those from simulation is a major computational bottleneck. An important aspect in this process is the choice of method used for parameter estimation. When no information on parameters is available, parameter estimation is mostly done by means of heuristic algorithms. RESULTS: We show that parameter estimation for pattern formation models can be efficiently performed using an evolution strategy (ES). As a case study we use a quantitative spatio-temporal model of the regulatory network for early development in Drosophila melanogaster. In order to estimate the parameters, the simulated results are compared to a time series of gene products involved in the network obtained with immunohistochemistry. We demonstrate that a (mu,lambda)-ES can be used to find good quality solutions in the parameter estimation. We also show that an ES with multiple populations is 5-140 times as fast as parallel simulated annealing for this case study, and that combining ES with a local search results in an efficient parameter estimation method.     

Efficient detection of network motifs

Motifs in a given network are small connected subnetworks that occur in significantly higher frequencies than would be expected in random networks. They have recently gathered much attention as a concept to uncover structural design principles of complex networks. Kashtan et al. [Bioinformatics, 2004] proposed a sampling algorithm for performing the computationally challenging task of detecting network motifs. However, among other drawbacks, this algorithm suffers from a sampling bias and scales poorly with increasing subgraph size. Based on a detailed analysis of the previous algorithm, we present a new algorithm for network motif detection which overcomes these drawbacks. Furthermore, we present an efficient new approach for estimating the frequency of subgraphs in random networks that, in contrast to previous approaches, does not require the explicit generation of random networks. Experiments on a testbed of biological networks show our new algorithms to be orders of magnitude faster than previous approaches, allowing for the detection of larger motifs in bigger networks than previously possible and thus facilitating deeper insight into the field     

Mixture models with multiple levels, with application to the analysis of multifactor gene expression data

Model-based clustering is a popular tool for summarizing high-dimensional data. With the number of high-throughput large-scale gene expression studies still on the rise, the need for effective data- summarizing tools has never been greater. By grouping genes according to a common experimental expression profile, we may gain new insight into the biological pathways that steer biological processes of interest. Clustering of gene profiles can also assist in assigning functions to genes that have not yet been functionally annotated. In this paper, we propose 2 model selection procedures for model-based clustering. Model selection in model-based clustering has to date focused on the identification of data dimensions that are relevant for clustering. However, in more complex data structures, with multiple experimental factors, such an approach does not provide easily interpreted clustering outcomes. We propose a mixture model with multiple levels, , that provides sparse representations both "within" and "between" cluster profiles. We explore various flexible "within-cluster" parameterizations and discuss how efficient parameterizations can greatly enhance the objective interpretability of the generated clusters. Moreover, we allow for a sparse "between-cluster" representation with a different number of clusters at different levels of an experimental factor of interest. This enhances interpretability of clusters generated in multiple-factor contexts. Interpretable cluster profiles can assist in detecting biologically relevant groups of genes that may be missed with less efficient parameterizations. We use our multilevel mixture model to mine a proliferating cell line expression data set for annotational context and regulatory motifs. We also investigate the performance of the multilevel clustering approach on several simulated data sets.     

Spread of porcine circovirus associated disease (PCVAD) in Ontario (Canada) swine herds: Part I. Exploratory spatial analysis

Background  

The emergence of porcine circovirus associated disease (PCVAD) was associated with high mortality in swine populations worldwide. Studies performed in different regions identified spatial, temporal, and spatio-temporal trends as factors contributing to patterns of the disease spread. Patterns consistent with spatial trend and spatio-temporal clustering were already identified in this dataset. On the basis of these results, we have further investigated the nature of local spread in this report. The primary objective of this study was to evaluate risk factors for incidence cases of reported PCVAD.     

Structural characterization of naturally occurring RNA single mismatches

RNA is known to be involved in several cellular processes; however, it is only active when it is folded into its correct 3D conformation. The folding, bending and twisting of an RNA molecule is dependent upon the multitude of canonical and non-canonical secondary structure motifs. These motifs contribute to the structural complexity of RNA but also serve important integral biological functions, such as serving as recognition and binding sites for other biomolecules or small ligands. One of the most prevalent types of RNA secondary structure motifs are single mismatches, which occur when two canonical pairs are separated by a single non-canonical pair. To determine sequence–structure relationships and to identify structural patterns, we have systematically located, annotated and compared all available occurrences of the 30 most frequently occurring single mismatch-nearest neighbor sequence combinations found in experimentally determined 3D structures of RNA-containing molecules deposited into the Protein Data Bank. Hydrogen bonding, stacking and interaction of nucleotide edges for the mismatched and nearest neighbor base pairs are described and compared, allowing for the identification of several structural patterns. Such a database and comparison will allow researchers to gain insight into the structural features of unstudied sequences and to quickly look-up studied sequences.