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Pathogenic bacteria encounter various stressors while residing in the host. They respond through intricate mechanisms of gene expression regulation, ensuring their survival and adaptation. Understanding how bacteria adapt to different stress conditions through regulatory processes of specific genes requires exploring complex transcriptional responses using gene co-expression networks. We employed a large transcriptome data set comprising 32 diverse human bacterial pathogens exposed to the same 11 host-mimicking stress conditions. Using the weighted gene co-expression network analysis algorithm, we generated bacterial gene co-expression networks. By associating modular eigengene expression with specific stress conditions, we identified gene co-expression modules and stress-specific stimulons, including genes with unique expression patterns under specific stress conditions. Suggesting a new potential role of the frm operon in responding to bile stress in enteropathogenic bacteria demonstrates the effectiveness of our approach. We also revealed the regulation of streptolysin S genes, involved in the production, processing, and export of streptolysin S, a toxin responsible for the beta-hemolytic phenotype of group A Streptococcus. In a comparative analysis of stress responses in three Escherichia coli strains from the core transcriptome, we revealed shared and unique expression patterns across the strains, offering insights into convergent and divergent stress responses. To help researchers perform similar analyses, we created the user-friendly web application Co-PATHOgenex. This tool aids in deepening our understanding of bacterial adaptation to stress conditions and in deciphering complex transcriptional responses of bacterial pathogens.IMPORTANCEUnveiling gene co-expression networks in bacterial pathogens has the potential for gaining insights into their adaptive strategies within the host environment. Here, we developed Co-PATHOgenex, an interactive and user-friendly web application that enables users to construct networks from gene co-expressions using custom-defined thresholds (https://avicanlab.shinyapps.io/copathogenex/). The incorporated search functions and visualizations within the tool simplify the usage and facilitate the interpretation of the analysis output. Co-PATHOgenex also includes stress stimulons for various bacterial species, which can help identify gene products not previously associated with a particular stress condition. Unveiling gene co-expression networks in bacterial pathogens has the potential for gaining insights into their adaptive strategies within the host environment. Here, we developed Co-PATHOgenex, an interactive and user-friendly web application that enables users to construct networks from gene co-expressions using custom-defined thresholds (https://avicanlab.shinyapps.io/copathogenex/). The incorporated search functions and visualizations within the tool simplify the usage and facilitate the interpretation of the analysis output. Co-PATHOgenex also includes stress stimulons for various bacterial species, which can help identify gene products not previously associated with a particular stress condition.

Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using Gaussian graphical models, requiring regularization to sparsify the models. Acknowledging that the modular structure of these inferred networks is often studied, we suggest module-based regularization to balance under- and overfitting. Compared with the graphical lasso, a standard approach using the Gaussian log-likelihood for estimating the regularization strength, this approach better recovers and infers modular structure in noisy synthetic and real data. The module-based regularization technique improves the usefulness of Gaussian graphical models in the many applications where they are employed.

Rapid metabolic responses to pathogens are essential for plant survival and depend on numerous transcription factors. Mediator is the major transcriptional co-regulator for integration and transmission of signals from transcriptional regulators to RNA polymerase II. Using four Arabidopsis Mediator mutants, med16, med18, med25 and cdk8, we studied how differences in regulation of their transcript and metabolite levels correlate to their responses to Pseudomonas syringae infection. We found that med16 and cdk8 were susceptible, while med25 showed increased resistance. Glucosinolate, phytoalexin and carbohydrate levels were reduced already before infection in med16 and cdk8, but increased in med25, which also displayed increased benzenoids levels. Early after infection, wild type plants showed reduced glucosinolate and nucleoside levels, but increases in amino acids, benzenoids, oxylipins and the phytoalexin camalexin. The Mediator mutants showed altered levels of these metabolites and in regulation of genes encoding key enzymes for their metabolism. At later stage, mutants displayed defective levels of specific amino acids, carbohydrates, lipids and jasmonates which correlated to their infection response phenotypes. Our results reveal that MED16, MED25 and CDK8 are required for a proper, coordinated transcriptional response of genes which encode enzymes involved in important metabolic pathways for Arabidopsis responses to Pseudomonas syringae infections.

Analyzing relational data consisting of multiple samples or layers involves critical challenges: How many networks are required to capture the variety of structures in the data? And what are the structures of these representative networks? We describe efficient nonparametric methods derived from the minimum description length principle to construct the network representations automatically. The methods input a population of networks or a multilayer network measured on a fixed set of nodes and output a small set of representative networks together with an assignment of each network sample or layer to one of the representative networks. We identify the representative networks and assign network samples to them with an efficient Monte Carlo scheme that minimizes our description length objective. For temporally ordered networks, we use a polynomial time dynamic programming approach that restricts the clusters of network layers to be temporally contiguous. These methods recover planted heterogeneity in synthetic network populations and identify essential structural heterogeneities in global trade and fossil record networks. Our methods are principled, scalable, parameter-free, and accommodate a wide range of data, providing a unified lens for exploratory analyses and preprocessing large sets of network samples.

Inland waters play a critical role in the carbon cycle by emitting significant amounts of land-exported carbon to the atmosphere. While carbon gas emissions from individual aquatic systems have been extensively studied, how networks of connected streams and lakes regulate integrated fluxes of organic and inorganic forms remain poorly understood. Here, we develop a process-based model to simulate the fate of terrestrial dissolved organic carbon (DOC) and carbon dioxide (CO₂) in artificial inland water networks with variable topology, hydrology, and DOC reactivity. While the role of lakes is highly dependent on DOC reactivity, we find that the mineralization of terrestrial DOC is more efficient in lake-rich networks. Regardless of typology and hydrology, terrestrial CO₂ is emitted almost entirely within the network boundary. Consequently, the proportion of exported terrestrial carbon emitted from inland water networks increases with the CO₂ versus DOC export ratio. Overall, our results suggest that CO₂ emissions from inland waters are governed by interactions between the relative amount and reactivity of terrestrial DOC and CO₂ inputs and the network configuration of recipient lakes and streams.

New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with alluvial diagrams, which visualize community splits and merges between networks. However, alluvial diagrams were developed for networks with regular nodes assigned to non-overlapping flat communities. How should they be defined for nodes in layers, state nodes, or hyperedges? How can they depict multilevel, overlapping communities? Here we generalize alluvial diagrams to map change in higher-order networks and provide an interactive tool for anyone to generate alluvial diagrams. We use the alluvial diagram generator in three case studies to illustrate significant changes in the organization of science, the effect of modeling network flows with memory in a citation network and distinguishing multidisciplinary from field-specific journals, and the effects of multilayer representation of a collaboration hypergraph.

Correlation networks derived from multivariate data appear in many applications across the sciences. These networks are usually dense and require sparsification to detect meaningful structure. However, current methods for sparsifying correlation networks struggle with balancing overfitting and underfitting. We propose a module-based cross-validation procedure to threshold these networks, making modular structure an integral part of the thresholding. We illustrate our approach using synthetic and real data and find that its ability to recover a planted partition has a step-like dependence on the number of data samples. The reward for sampling more varies non-linearly with the number of samples, with minimal gains after a critical point. A comparison with the well-established WGCNA method shows that our approach allows for revealing more modular structure in the data used here.

To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two flow-based community-detection methods Markov stability and the map equation identify such communities based on different principles and search algorithms. But how similar are the resulting communities? We explain both methods’ machinery applied to hypergraphs and compare them on synthetic and real-world hypergraphs using various hyperedge-size biased random walks and time scales. We find that the map equation is more sensitive to time-scale changes and that Markov stability is more sensitive to hyperedge-size biases.

To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as degree centrality, betweenness centrality, or PageRank neglect the community structure found in real-world networks. To study node importance based on network flows from a mesoscopic perspective, we analytically derive a community-aware information-theoretic centrality score based on network flow and the coding principles behind the map equation: map equation centrality. Map equation centrality measures how much further we can compress the network's modular description by not coding for random walker transitions to the respective node, using an adapted coding scheme and determining node importance from a network flow-based point of view. The information-theoretic centrality measure can be determined from a node's local network context alone because changes to the coding scheme only affect other nodes in the same module. Map equation centrality is agnostic to the chosen network flow model and allows researchers to select the model that best reflects the dynamics of the process under study. Applied to synthetic networks, we highlight how our approach enables a more fine-grained differentiation between nodes than node-local or network-global measures. Predicting influential nodes for two different dynamical processes on real-world networks with traditional and other community-aware centrality measures, we find that activating nodes based on map equation centrality scores tends to create the largest cascades in a linear threshold model.