A systematic evaluation of the influence of macrophage phenotype descriptions on inflammatory dynamics.

Macrophages play a wide range of roles in resolving the inflammatory damage that underlies many medical conditions, and have the ability to adopt different phenotypes in response to different environmental stimuli. Categorising macrophage phenotypes exactly is a difficult task, and there is disparity in the literature around the optimal nomenclature to describe these phenotypes; however, what is clear is that macrophages can exhibit both pro- and anti-inflammatory behaviours dependent upon their phenotype, rendering mathematical models of the inflammatory response potentially sensitive to their description of the macrophage populations that they incorporate. Many previous models of inflammation include a single macrophage population with both pro- and anti-inflammatory functions. Here, we build upon these existing models to include explicit descriptions of distinct macrophage phenotypes and examine the extent to which this influences the inflammatory dynamics that the models emit. We analyse our models via numerical simulation in Matlab and dynamical systems analysis in XPPAUT, and show that models that account for distinct macrophage phenotypes separately can offer more realistic steady state solutions than precursor models do (better capturing the anti-inflammatory activity of tissue resident macrophages), as well as oscillatory dynamics not previously observed. Finally, we reflect on the conclusions of our analysis in the context of the ongoing hunt for potential new therapies for inflammatory conditions, highlighting manipulation of macrophage polarisation states as a potential therapeutic target.

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 miRNet2.0 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.

Structure-function clustering in weighted brain networks.

Functional networks, which typically describe patterns of activity taking place across the cerebral cortex, are widely studied in neuroscience. The dynamical features of these networks, and in particular their deviation from the relatively static structural network, are thought to be key to higher brain function. The interactions between such structural networks and emergent function, and the multimodal neuroimaging approaches and common analysis according to frequency band motivate a multilayer network approach. However, many such investigations rely on arbitrary threshold choices that convert dense, weighted networks to sparse, binary structures. Here, we generalise a measure of multiplex clustering to describe weighted multiplexes with arbitrarily-many layers. Moreover, we extend a recently-developed measure of structure-function clustering (that describes the disparity between anatomical connectivity and functional networks) to the weighted case. To demonstrate its utility we combine human connectome data with simulated neural activity and bifurcation analysis. Our results indicate that this new measure can extract neurologically relevant features not readily apparent in analogous single-layer analyses. In particular, we are able to deduce dynamical regimes under which multistable patterns of neural activity emerge. Importantly, these findings suggest a role for brain operation just beyond criticality to promote cognitive flexibility.

Spatial considerations in the resolution of inflammation: Elucidating leukocyte interactions via an experimentally-calibrated agent-based model.

Many common medical conditions (such as cancer, arthritis, chronic obstructive pulmonary disease (COPD), and others) are associated with inflammation, and even more so when combined with the effects of ageing and multimorbidity. While the inflammatory response varies in different tissue types, under disease and in response to therapeutic interventions, it has common interactions that occur between immune cells and inflammatory mediators. Understanding these underlying inflammatory mechanisms is key in progressing treatments and therapies for numerous inflammatory conditions. It is now considered that constituent mechanisms of the inflammatory response can be actively manipulated in order to drive resolution of inflammatory damage; particularly, those mechanisms related to the pro-inflammatory role of neutrophils and the anti-inflammatory role of macrophages. In this article, we describe the assembly of a hybrid mathematical model in which the spatial spread of inflammatory mediators is described through partial differential equations, and immune cells (neutrophils and macrophages) are described individually via an agent-based modelling approach. We pay close attention to how immune cells chemotax toward pro-inflammatory mediators, presenting a model for cell chemotaxis that is calibrated against experimentally observed cell trajectories in healthy and COPD-affected scenarios. We illustrate how variations in key model parameters can drive the switch from resolution of inflammation to chronic outcomes, and show that aberrant neutrophil chemotaxis can move an otherwise healthy outcome to one of chronicity. Finally, we reflect on our results in the context of the on-going hunt for new therapeutic interventions.

The role of node dynamics in shaping emergent functional connectivity patterns in the brain.

The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure-function issue, treating a system of Jansen-Rit neural mass nodes with heterogeneous structural connections estimated from diffusion MRI data provided by the Human Connectome Project. Via direct simulations we determine the similarity of functional (inferred from correlated activity between nodes) and structural connectivity matrices under variation of the parameters controlling single-node dynamics, highlighting a nontrivial structure-function relationship in regimes that support limit cycle oscillations. To determine their relationship, we firstly calculate network instabilities giving rise to oscillations, and the so-called 'false bifurcations' (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring beyond this onset. We highlight that functional connectivity (FC) is inherited robustly from structure when node dynamics are poised near a Hopf bifurcation, whilst near false bifurcations, and structure only weakly influences FC. Secondly, we develop a weakly coupled oscillator description to analyse oscillatory phase-locked states and, furthermore, show how the modular structure of FC matrices can be predicted via linear stability analysis. This study thereby emphasises the substantial role that local dynamics can have in shaping large-scale functional brain states.

Identification of novel genes associated with longevity in Drosophila melanogaster - a computational approach.

Despite a growing number of studies on longevity in Drosophila, genetic factors influencing lifespan are still poorly understood. In this paper we propose a conceptually new approach for the identification of novel longevity-associated genes and potential target genes for SNPs in non-coding regions by utilizing the knowledge of co-location of various loci, governed by the three-dimensional architecture of the Drosophila genome. Firstly, we created networks between genes/genomic regions harboring SNPs deemed to be significant in two longevity GWAS summary statistics datasets using intra- and inter-chromosomal interaction frequencies (Hi-C data) as a measure of co-location. These networks were further extended to include regions strongly interacting with previously selected regions. Using various network measures, literature search and additional bioinformatics resources, we investigated the plausibility of genes found to have genuine association with longevity. Several of the newly identified genes were common between the two GWAS datasets and these possessed human orthologs. We also found that the proportion of non-coding SNPs in borders between topologically associated domains is significantly higher than expected by chance. Assuming co-location, we investigated potential target genes for non-coding SNPs. This approach therefore offers a stepping stone to identification of novel genes and SNP targets linked to human longevity.

Predicting novel genomic regions linked to genetic disorders using GWAS and chromosome conformation data - a case study of schizophrenia.

Genome-wide association studies identified numerous loci harbouring single nucleotide polymorphisms (SNPs) associated with various human diseases, although the causal role of many of them remains unknown. In this paper, we postulate that co-location and shared biological function of novel genes with genes known to associate with a specific phenotype make them potential candidates linked to the same phenotype ("guilt-by-proxy"). We propose a novel network-based approach for predicting candidate genes/genomic regions utilising the knowledge of the 3D architecture of the human genome and GWAS data. As a case study we used a well-studied polygenic disorder ‒ schizophrenia ‒ for which we compiled a comprehensive dataset of SNPs. Our approach revealed 634 novel regions covering ~398 Mb of the human genome and harbouring ~9000 genes. Using various network measures and enrichment analysis, we identified subsets of genes and investigated the plausibility of these genes/regions having an association with schizophrenia using literature search and bioinformatics resources. We identified several genes/regions with previously reported associations with schizophrenia, thus providing proof-of-concept, as well as novel candidates with no prior known associations. This approach has the potential to identify novel genes/genomic regions linked to other polygenic disorders and provide means of aggregating genes/SNPs for further investigation.

Differences in anatomical connections across distinct areas in the rodent prefrontal cortex.

Prefrontal cortex (PFC) network structure is implicated in a number of complex higher-order functions and with a range of neurological disorders. It is therefore vital to our understanding of PFC function to gain an understanding of its underlying anatomical connectivity. Here, we injected Fluoro-Gold and Fluoro-Ruby into the same sites throughout rat PFC. Tracer injections were applied to two coronal levels within the PFC (anterior +4.7 mm to bregma and posterior +3.7 mm to bregma). Within each coronal level, tracers were deposited at sites separated by approximately 1 mm and located parallel to the medial and orbital surface of the cortex. We found that both Fluoro-Gold and Fluoro-Ruby injections produced prominent labelling in temporal and sensory-motor cortex. Fluoro-Gold produced retrograde labelling and Fluoro-Ruby largely produced anterograde labelling. Analysis of the location of these connections within temporal and sensory-motor cortex revealed a consistent topology (as the sequence of injections was followed mediolaterally along the orbital surface of each coronal level). At the anterior coronal level, injections produced a similar topology to that seen in central PFC in earlier studies from our laboratory (i.e. comparing equivalently located injections employing the same tracer), this was particularly prominent within temporal cortex. However, at the posterior coronal level this pattern of connections differed significantly, revealing higher levels of reciprocity, in both temporal cortex and sensory-motor cortex. Our findings indicate changes in the relative organization of connections arising from posterior in comparison to anterior regions of PFC, which may provide a basis to determine how complex processes are organized.

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 oversimplification of 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 environments displayed increased levels of robustness and topological complexity.

A geometric network model of intrinsic grey-matter connectivity of the human brain.

Network science provides a general framework for analysing the large-scale brain networks that naturally arise from modern neuroimaging studies, and a key goal in theoretical neuroscience is to understand the extent to which these neural architectures influence the dynamical processes they sustain. To date, brain network modelling has largely been conducted at the macroscale level (i.e. white-matter tracts), despite growing evidence of the role that local grey matter architecture plays in a variety of brain disorders. Here, we present a new model of intrinsic grey matter connectivity of the human connectome. Importantly, the new model incorporates detailed information on cortical geometry to construct 'shortcuts' through the thickness of the cortex, thus enabling spatially distant brain regions, as measured along the cortical surface, to communicate. Our study indicates that structures based on human brain surface information differ significantly, both in terms of their topological network characteristics and activity propagation properties, when compared against a variety of alternative geometries and generative algorithms. In particular, this might help explain histological patterns of grey matter connectivity, highlighting that observed connection distances may have arisen to maximise information processing ability, and that such gains are consistent with (and enhanced by) the presence of short-cut connections.

The topology of connections between rat prefrontal and temporal cortices.

Understanding the structural organization of the prefrontal cortex (PFC) is an important step toward determining its functional organization. Here we investigated the organization of PFC using different neuronal tracers. We injected retrograde (Fluoro-Gold, 100 nl) and anterograde [Biotinylated dextran amine (BDA) or Fluoro-Ruby, 100 nl] tracers into sites within PFC subdivisions (prelimbic, ventral orbital, ventrolateral orbital, dorsolateral orbital) along a coronal axis within PFC. At each injection site one injection was made of the anterograde tracer and one injection was made of the retrograde tracer. The projection locations of retrogradely labeled neurons and anterogradely labeled axon terminals were then analyzed in the temporal cortex: area Te, entorhinal and perirhinal cortex. We found evidence for an ordering of both the anterograde (anterior-posterior, dorsal-ventral, and medial-lateral axes: p < 0.001) and retrograde (anterior-posterior, dorsal-ventral, and medial-lateral axes: p < 0.001) connections of PFC. We observed that anterograde and retrograde labeling in ipsilateral temporal cortex (i.e., PFC inputs and outputs) often occurred reciprocally (i.e., the same brain region, such as area 35d in perirhinal cortex, contained anterograde and retrograde labeling). However, often the same specific columnar temporal cortex regions contained only either labeling of retrograde or anterograde tracer, indicating that PFC inputs and outputs are frequently non-matched.

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 underlying 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 networks.

The topology of connections between rat prefrontal, motor and sensory cortices.

The connections of prefrontal cortex (PFC) were investigated in the rat brain to determine the order and location of input and output connections to motor and somatosensory cortex. Retrograde (100 nl Fluoro-Gold) and anterograde (100 nl Biotinylated Dextran Amines, BDA; Fluorescein and Texas Red) neuronanatomical tracers were injected into the subdivisions of the PFC (prelimbic, ventral orbital, ventrolateral orbital, dorsolateral orbital) and their projections studied. We found clear evidence for organized input projections from the motor and somatosensory cortices to the PFC, with distinct areas of motor and cingulate cortex projecting in an ordered arrangement to the subdivisions of PFC. As injection location of retrograde tracer was moved from medial to lateral in PFC, we observed an ordered arrangement of projections occurring in sensory-motor cortex. There was a significant effect of retrograde injection location on the position of labelled cells occurring in sensory-motor cortex (dorsoventral, anterior-posterior and mediolateral axes p < 0.001). The arrangement of output projections from PFC also displayed a significant ordered projection to sensory-motor cortex (dorsoventral p < 0.001, anterior-posterior p = 0.002 and mediolateral axes p < 0.001). Statistical analysis also showed that the locations of input and output labels vary with respect to one another (in the dorsal-ventral and medial-lateral axes, p < 0.001). Taken together, the findings show that regions of PFC display an ordered arrangement of connections with sensory-motor cortex, with clear laminar organization of input connections. These results also show that input and output connections to PFC are not located in exactly the same sites and reveal a circuit between sensory-motor and PFC.

Spreading dynamics on spatially constrained complex brain networks.

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way.

On the use of stabilizing transformations for detecting unstable periodic orbits in high-dimensional flows.

We explore the possibility of extending the stabilizing transformations approach [J. J. Crofts and R. L. Davidchack, SIAM J. Sci. Comput. (USA) 28, 1275 (2006)]. to the problem of locating large numbers of unstable periodic orbits in high-dimensional flows, in particular those that result from spatial discretization of partial differential equations. The approach has been shown to be highly efficient when detecting large sets of periodic orbits in low-dimensional maps. Extension to low-dimensional flows has been achieved by the use of an appropriate Poincare surface of section [D. Pingel, P. Schmelcher, and F. K. Diakonos, Phys. Rep. 400, 67 (2004)]. For the case of high-dimensional flows, we show that it is more efficient to apply stabilizing transformations directly to the flows without the use of the Poincare surface of section. We use the proposed approach to find many unstable periodic orbits in the model example of a chaotic spatially extended system-the Kuramoto-Sivashinsky equation. The performance of the proposed method is compared against other methods such as Newton-Armijo and Levenberg-Marquardt algorithms. In the latter case, we also argue that the Levenberg-Marquardt algorithm, or any other optimization-based approach, is more efficient and simpler in implementation when applied directly to the detection of periodic orbits in high-dimensional flows without the use of the Poincare surface of section or other additional constraints.

A weighted communicability measure applied to complex brain networks.

Recent advances in experimental neuroscience allow non-invasive studies of the white matter tracts in the human central nervous system, thus making available cutting-edge brain anatomical data describing these global connectivity patterns. Through magnetic resonance imaging, this non-invasive technique is able to infer a snapshot of the cortical network within the living human brain. Here, we report on the initial success of a new weighted network communicability measure in distinguishing local and global differences between diseased patients and controls. This approach builds on recent advances in network science, where an underlying connectivity structure is used as a means to measure the ease with which information can flow between nodes. One advantage of our method is that it deals directly with the real-valued connectivity data, thereby avoiding the need to discretize the corresponding adjacency matrix, i.e. to round weights up to 1 or down to 0, depending upon some threshold value. Experimental results indicate that the new approach is able to extract biologically relevant features that are not immediately apparent from the raw connectivity data.