Hypergraph models of metabolism

In this paper, we employ a directed hypergraph model to investigate the extent to which environmental variability influences the set of available biochemical reactions within a living cell. Such an approach avoids the limitations of the usual complex network formalism by allowing for the multilateral relationships (i.e. connections involving more than two nodes) that naturally occur within many biological processes. More specifically, we extend the concept of network reciprocity to complex hyper-networks, thus enabling us to characterise a network in terms of the existence of mutual hyper-connections, which may be considered a proxy for metabolic network complexity. To demonstrate these ideas, we study 115 metabolic hyper-networks of bacteria, each of which can be classified into one of 6 increasingly varied habitats. In particular, we found that reciprocity increases significantly with increased environmental variability, supporting the view that organism adaptability leads to increased complexities in the resultant biochemical networks

Network motif frequency vectors reveal evolving metabolic network organisation

At the systems level many organisms of interest may be described by their patterns of interaction, and as such, are perhaps best characterised via network or graph models. Metabolic networks, in particular, are fundamental to the proper functioning of many important biological processes, and thus, have been widely studied over the past decade or so. Such investigations have revealed a number of shared topological features, such as a short characteristic path-length, large clustering coefficient and hierarchical modular structure. However, the extent to which evolutionary and functional properties of metabolism manifest via this under- lying network architecture remains unclear. In this paper, we employ a novel graph embedding technique, based upon low-order network motifs, to compare metabolic network structure for 383 bacterial species categorised according to a number of biological features. In particular, we introduce a new global significance score which enables us to quantify important evolutionary relationships that exist between organisms and their physical environments. Using this new approach, we demonstrate a number of significant correlations between environmental factors, such as growth conditions and habitat variability, and network motif structure, providing evidence that organism adaptability leads to increased complexities in the resultant metabolic network

Complexity and robustness in hypernetwork models of metabolism

Metabolic reaction data is commonly modelled using a complex network approach, whereby nodes represent the chemical species present within the organism of interest, and connections are formed between those nodes participating in the same chemical reaction. Unfortunately, such an approach provides an inadequate description of the metabolic process in general, as a typical chemical reaction will involve more than two nodes, thus risking over-simplification of the the system of interest in a potentially significant way. In this paper, we employ a complex hypernetwork formalism to investigate the robustness of bacterial metabolic hypernetworks by extending the concept of a percolation process to hypernetworks. Importantly, this provides a novel method for determining the robustness of these systems and thus for quantifying their resilience to random attacks/errors. Moreover, we performed a site percolation analysis on a large cohort of bacterial metabolic networks and found that hypernetworks that evolved in more variable enviro nments displayed increased levels of robustness and topological complexity

Can linear collocation ever beat quadratic?

Computational approaches are becoming increasingly important in neuroscience, where complex, nonlinear systems modelling neural activity across multiple spatial and temporal scales are the norm. This paper considers collocation techniques for solving neural field models, which typically take the form of a partial integro-dfferential equation. In particular, we investigate and compare the convergence properties of linear and quadratic collocation on both regular grids and more general meshes not fixed to the regular Cartesian grid points. For regular grids we perform a comparative analysis against more standard techniques, in which the convolution integral is computed either by using Fourier based methods or via the trapezoidal rule. Perhaps surprisingly, we find that on regular, periodic meshes, linear collocation displays better convergence properties than quadratic collocation, and is in fact comparable with the spectral convergence displayed by both the Fourier based and trapezoidal techniques. However, for more general meshes we obtain superior convergence of the convolution integral using higher order methods, as expected

A numerical simulation of neural fields on curved geometries

Despite the highly convoluted nature of the human brain, neural field models typically treat the cortex as a planar two-dimensional sheet of neurons. Here, we present an approach for solving neural field equations on surfaces more akin to the cortical geometries typically obtained from neuroimaging data. Our approach involves solving the integral form of the partial integro-differential equation directly using collocation techniques alongside efficient numerical procedures for determining geodesic distances between neural units. To illustrate our methods, we study localised activity patterns in a two-dimensional neural field equation posed on a periodic square domain, the curved surface of a torus, and the cortical surface of a rat brain, the latter of which is constructed using neuroimaging data. Our results are twofold: Firstly, we find that collocation techniques are able to replicate solutions obtained using more standard Fourier based methods on a flat, periodic domain, independent of the underlying mesh. This result is particularly significant given the highly irregular nature of the type of meshes derived from modern neuroimaging data. And secondly, by deploying efficient numerical schemes to compute geodesics, our approach is not only capable of modelling macroscopic pattern formation on realistic cortical geometries, but can also be extended to include cortical architectures of more physiological relevance. Importantly, such an approach provides a means by which to investigate the influence of cortical geometry upon the nucleation and propagation of spatially localised neural activity and beyond. It thus promises to provide model-based insights into disorders like epilepsy, or spreading depression, as well as healthy cognitive processes like working memory or attention

Towards In Silico identification of genes contributing to similarity of patients’ multi-omics profiles: a case study of acute myeloid leukemia

We propose a computational framework for selecting biologically plausible genes identified by clustering of multi-omics data that reveal patients' similarity, thus giving researchers a more comprehensive view on any given disease. We employ spectral clustering of a similarity network created by fusion of three similarity networks, based on mRNA expression of immune genes, miRNA expression and DNA methylation data, using SNF_v2.1 software. For each cluster, we rank multi-omics features, ensuring the best separation between clusters, and select the top-ranked features that preserve clustering. To find genes targeted by DNA methylation and miRNAs found in the top-ranked features, we use chromosome-conformation capture data and miRNet 2.0 software, respectively. To identify informative genes, these combined sets of target genes are analyzed in terms of their enrichment in somatic/germline mutations, GO biological processes/pathways terms and known sets of genes considered to be important in relation to a given disease, as recorded in the Molecular Signature Database from GSEA. The protein-protein interaction (PPI) networks were analyzed to identify genes that are hubs of PPI networks. We used data recorded in The Cancer Genome Atlas for patients with acute myeloid leukemia to demonstrate our approach, and discuss our findings in the context of results in the literature

Synchrony in directed connectomes

Synchronisation plays a fundamental role in a variety of physiological functions, such as visual perception, cognitive function, sleep and arousal. The precise role of the interplay between local dynamics and directed cortical topology on the propensity for cortical structures to synchronise, however, remains poorly understood. Here, we study the impact that directed network topology has on the synchronisation properties of the brain by considering a range of species and parcellations, including the cortex of the cat and the Macaque monkey, as well as the nervous system of the C. elegans round worm. We deploy a Kuramoto phase model to simulate neural dynamics on the aforementioned connectomes, and investigate the extent to which network directionality influences distributed patterns of neural synchrony. In particular, we find that network directionality induces both slower synchronisation speeds and more robust phase locking in the presence of network delays. Moreover, in contrast to large-scale connectomes, we find that recently observed relations between resting state directionality patterns and network structure appear to break down for invertebrate networks such as the C. elegans connectome, thus suggesting that observed variations in directed network topology at different scales can significantly impact patterns of neural synchrony. Our results suggest that directionality plays a key role in shaping network dynamics and moreover that its exclusion risks simplifying neural activation dynamics in a potentially significant way

Complete Ascertainment of Intragenic Copy Number Mutations (CNMs) in the CFTR Gene and its Implications for CNM Formation at Other Autosomal Loci

Over the last 20 years since the discovery of the cystic fibrosis transmembrane conductance regulator (CFTR) gene, more than 1,600 different putatively pathological CFTR mutations have been identified. Until now, however, copy number mutations (CNMs) involving the CFTR gene have not been methodically analyzed, resulting almost certainly in the under-ascertainment of CFTR gene duplications compared with deletions. Here, high-resolution array comparative genomic hybridization (averaging one interrogating probe every 95 bp) was used to analyze the entire length of the CFTR gene (189 kb) in 233 cystic fibrosis chromosomes lacking conventional mutations. We succeeded in identifying five duplication CNMs that would otherwise have been refractory to analysis. Based upon findings from this and other studies, we propose that deletion and duplication CNMs in the human autosomal genome are likely to be generated in the proportion of approximately 2-3:1. We further postulate that intragenic gene duplication CNMs in other disease loci may have been routinely underascertained. Finally, our analysis of +/-20 bp flanking each of the 40 CFTR breakpoints characterized at the DNA sequence level provide support for the emerging concept that non-B DNA conformations in combination with specific sequence motifs predispose to both recurring and nonrecurring genomic rearrangements. Hum Mutat 31:421-428, 2010. (C) 2010 Wiley-Liss, Inc

Long homopurine•homopyrimidine sequences are characteristic of genes expressed in brain and the pseudoautosomal region

Homo(purine•pyrimidine) sequences (R•Y tracts) with mirror repeat symmetries form stable triplexes that block replication and transcription and promote genetic rearrangements. A systematic search was conducted to map the location of the longest R•Y tracts in the human genome in order to assess their potential function(s). The 814 R•Y tracts with ≥250 uninterrupted base pairs were preferentially clustered in the pseudoautosomal region of the sex chromosomes and located in the introns of 228 annotated genes whose protein products were associated with functions at the cell membrane. These genes were highly expressed in the brain and particularly in genes associated with susceptibility to mental disorders, such as schizophrenia. The set of 1957 genes harboring the 2886 R•Y tracts with ≥100 uninterrupted base pairs was additionally enriched in proteins associated with phosphorylation, signal transduction, development and morphogenesis. Comparisons of the ≥250 bp R•Y tracts in the mouse and chimpanzee genomes indicated that these sequences have mutated faster than the surrounding regions and are longer in humans than in chimpanzees. These results support a role for long R•Y tracts in promoting recombination and genome diversity during evolution through destabilization of chromosomal DNA, thereby inducing repair and mutation