Topological data analysis of truncated contagion maps

The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space. Specifically, one can use the activation times of threshold contagions to construct contagion maps as a manifold-learning approach. One drawback of contagion maps is their high computational cost. Here, we demonstrate that a truncation of the threshold contagions may considerably speed up the construction of contagion maps. Finally, we show that contagion maps may be used to find an insightful low-dimensional embedding for single-cell RNA-sequencing data in the form of cell-similarity networks and so reveal biological manifolds. Overall, our work makes the use of contagion maps as manifold-learning approaches on empirical network data more viable

Quantifying the ‘end of history’ through a Bayesian Markov-chain approach

Political regimes have been changing throughout human history. After the apparent triumph of liberal democracies at the end of the twentieth century, Francis Fukuyama and others have been arguing that humankind is approaching an ‘end of history’ (EoH) in the form of a universality of liberal democracies. This view has been challenged by recent developments that seem to indicate the rise of defective democracies across the globe. There has been no attempt to quantify the expected EoH with a statistical approach. In this study, we model the transition between political regimes as a Markov process and—using a Bayesian inference approach—we estimate the transition probabilities between political regimes from time-series data describing the evolution of political regimes from 1800 to 2018. We then compute the steady state for this Markov process which represents a mathematical abstraction of the EoH and predicts that approximately 46% of countries will be full democracies. Furthermore, we find that, under our model, the fraction of autocracies in the world is expected to increase for the next half-century before it declines. Using random-walk theory, we then estimate survival curves of different types of regimes and estimate characteristic lifetimes of democracies and autocracies of 244 years and 69 years, respectively. Quantifying the expected EoH allows us to challenge common beliefs about the nature of political equilibria. Specifically, we find no statistical evidence that the EoH constitutes a fixed, complete omnipresence of democratic regimes

Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material

Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio

Functional module detection through integration of single-cell RNA sequencing data with protein–protein interaction networks

Funder: Novo Nordisk; doi: http://dx.doi.org/10.13039/501100004191Abstract: Background: Recent advances in single-cell RNA sequencing have allowed researchers to explore transcriptional function at a cellular level. In particular, single-cell RNA sequencing reveals that there exist clusters of cells with similar gene expression profiles, representing different transcriptional states. Results: In this study, we present scPPIN, a method for integrating single-cell RNA sequencing data with protein–protein interaction networks that detects active modules in cells of different transcriptional states. We achieve this by clustering RNA-sequencing data, identifying differentially expressed genes, constructing node-weighted protein–protein interaction networks, and finding the maximum-weight connected subgraphs with an exact Steiner-tree approach. As case studies, we investigate two RNA-sequencing data sets from human liver spheroids and human adipose tissue, respectively. With scPPIN we expand the output of differential expressed genes analysis with information from protein interactions. We find that different transcriptional states have different subnetworks of the protein–protein interaction networks significantly enriched which represent biological pathways. In these pathways, scPPIN identifies proteins that are not differentially expressed but have a crucial biological function (e.g., as receptors) and therefore reveals biology beyond a standard differential expressed gene analysis. Conclusions: The introduced scPPIN method can be used to systematically analyse differentially expressed genes in single-cell RNA sequencing data by integrating it with protein interaction data. The detected modules that characterise each cluster help to identify and hypothesise a biological function associated to those cells. Our analysis suggests the participation of unexpected proteins in these pathways that are undetectable from the single-cell RNA sequencing data alone. The techniques described here are applicable to other organisms and tissues

President\u27s Note

<p>Black lines indicate best linear fit to the data (dashed) and model (solid) networks. In panel <i>(B)</i>, the parameter values used for the affinity model are the following: , , and .</p

Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges—for example, due to airline transportation or communication media—allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct ‘contagion maps’ that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks

Cell lineage-specific mitochondrial resilience during mammalian organogenesis

Mitochondrial activity differs markedly between organs, but it is not known how and when this arises. Here we show that cell lineage-specific expression profiles involving essential mitochondrial genes emerge at an early stage in mouse development, including tissue-specific isoforms present before organ formation. However, the nuclear transcriptional signatures were not independent of organelle function. Genetically disrupting intra-mitochondrial protein synthesis with two different mtDNA mutations induced cell lineage-specific compensatory responses, including molecular pathways not previously implicated in organellar maintenance. We saw downregulation of genes whose expression is known to exacerbate the effects of exogenous mitochondrial toxins, indicating a transcriptional adaptation to mitochondrial dysfunction during embryonic development. The compensatory pathways were both tissue and mutation specific and under the control of transcription factors which promote organelle resilience. These are likely to contribute to the tissue specificity which characterizes human mitochondrial diseases and are potential targets for organ-directed treatments

Generalised networks for protein interaction analysis

Protein interaction networks (PINs) are mathematical representations of interactions between proteins within organisms. Studying their properties can give insights into biological functions and the importance of proteins, and it can therefore aid in drug- discovery. Graphs are the most common mathematical object used to represent PINs. In this thesis, we investigate generalised mathematical representations of PINs. In particular, we examine multilayer networks (MLNs) and node-weighted networks. These mathematical objects allow the construction of temporal PINs and tissue-specific PINs by combining gene-expression data with PINs. We introduce promiscuity as an information-theoretical measure of a nodeâs distribution of neighbours across different layers in MLNs. We examine promiscuity in synthetic networks and tissue-specific PINs and find that the vast majority of proteins are not cell-type specific. Integrating temporal gene-expression data with PINs allows us to create temporal PINs in the form of MLNs. We investigate an eigenvector-based temporal centrality in a temporal PIN of yeast during the cell cycle. We thereby examine the change of proteinsâ importance over time, which reflects their activity during the cell cycle. We then discuss the detection of community structure in node-weighted networks. For synthetic networks, we show that considering node weights can alter detected community structure. We combine a human PIN with gene-expression data to construct tissue-specific PINs and investigate their community structure. Comparing the detected communities with gene-ontology information, we find some tissue-specific functions of these PINs. Overall, the case studies in this thesis suggest that MLN and node-weighted networks are suitable for the integration of protein-interaction data with other biological data sets.</p

Generalised networks for protein interaction analysis

Protein interaction networks (PINs) are mathematical representations of interactions between proteins within organisms. Studying their properties can give insights into biological functions and the importance of proteins, and it can therefore aid in drug- discovery. Graphs are the most common mathematical object used to represent PINs. In this thesis, we investigate generalised mathematical representations of PINs. In particular, we examine multilayer networks (MLNs) and node-weighted networks. These mathematical objects allow the construction of temporal PINs and tissue-specific PINs by combining gene-expression data with PINs. We introduce promiscuity as an information-theoretical measure of a node’s distribution of neighbours across different layers in MLNs. We examine promiscuity in synthetic networks and tissue-specific PINs and find that the vast majority of proteins are not cell-type specific. Integrating temporal gene-expression data with PINs allows us to create temporal PINs in the form of MLNs. We investigate an eigenvector-based temporal centrality in a temporal PIN of yeast during the cell cycle. We thereby examine the change of proteins’ importance over time, which reflects their activity during the cell cycle. We then discuss the detection of community structure in node-weighted networks. For synthetic networks, we show that considering node weights can alter detected community structure. We combine a human PIN with gene-expression data to construct tissue-specific PINs and investigate their community structure. Comparing the detected communities with gene-ontology information, we find some tissue-specific functions of these PINs. Overall, the case studies in this thesis suggest that MLN and node-weighted networks are suitable for the integration of protein-interaction data with other biological data sets.</p