The large-scale organization of metabolic networks

Integration of multi-omics data for survival prediction of lung adenocarcinoma

BACKGROUND AND OBJECTIVE

The morbidity of lung adenocarcinoma (LUAD) has been increasing year by year and the prognosis is poor. This has prompted researchers to study the survival of LUAD patients to ensure that patients can be cured in time or survive after appropriate treatment. There is still no fully valid model that can be applied to clinical practice.

METHODS

We introduced struc2vec-based multi-omics data integration (SBMOI), which could integrate gene expression, somatic mutations and clinical data to construct mutation gene vectors representing LUAD patient features. Based on the patient features, the random survival forest (RSF) model was used to predict the long- and short-term survival of LUAD patients. To further demonstrate the superiority of SBMOI, we simultaneously replaced scale-free gene co-expression network (FCN) with a protein-protein interaction (PPI) network and a significant co-expression network (SCN) to compare accuracy in predicting LUAD patient survival under the same conditions.

RESULTS

Our results suggested that compared with SCN and PPI network, the FCN based SBMOI combined with RSF model had better performance in long- and short-term survival prediction tasks for LUAD patients. The AUC of 1-year, 5-year, and 10-year survival in the validation dataset were 0.791, 0.825, and 0.917, respectively.

CONCLUSIONS

This study provided a powerful network-based method to multi-omics data integration. SBMOI combined with RSF successfully predicted long- and short-term survival of LUAD patients, especially with high accuracy on long-term survival. Besides, SBMOI algorithm has the potential to combine with other machine learning models to complete clustering or stratificational tasks, and being applied to other diseases.

Guest-induced narcissistic self-sorting in water via imine formation

Two anionic tetrahedral cages were self-assembled as the only observable products in weakly basic water via imine condensation. The success of the high-yielding formation of the cages in water relies on (i) multivalency enhancing the stability of the imine bond and affording these cages water compatibility and (ii) a guest template with a complementary size and geometry that provides a hydrophobic driving force by occupying the corresponding cage cavity. When all four precursors, namely two trisaldehydes and two trisamines, were combined in water, narcissistic self-sorting occurred when both guest templates were present. In organic media where the hydrophobic effect is absent, narcissistic self-sorting did not occur in the analogous cage systems, confirming the importance of guest templates.

Network approach reveals preferential T-cell and macrophage association with α-linked β-cells in early stage of insulitis in NOD mice

One of the challenges in studying islet inflammation - insulitis - is that it is a transient phenomenon. Traditional reporting of the insulitis progression is based on cumulative, donor-averaged values of leucocyte density in the vicinity of pancreatic islets, that hinders intra- and inter-islet heterogeneity of disease progression. Here, we aimed to understand why insulitis is non-uniform, often with peri-insulitis lesions formed on one side of an islet. To achieve this, we demonstrated applicability of network theory in detangling intra-islet multi-cellular interactions during insulitis. Specifically, we asked the question "what is unique about regions of the islet which interact with immune cells first". This study utilized the non-obese diabetic mouse model of type one diabetes and examined the interplay among α-, β-, T-cells, myeloid cells, and macrophages in pancreatic islets during the progression of insulitis. Disease evolution was tracked based on T/β cell ratio in individual islets. In the early stage, we found that immune cells are preferentially interacting with α-cell-rich regions of an islet. At the islet periphery α-linked β-cells were found to be targeted significantly more compared to those without α-cell neighbors. Additionally, network analysis revealed increased T-myeloid, and T-macrophage interactions with all β-cells.

A study of correlations between cephalometric measurements in Koreans with normal occlusion by network analysis

Analyzing the correlation between cephalometric measurements is important for improving our understanding of the anatomy in the oral and maxillofacial region. To minimize bias resulting from the design of the input data and to establish a reference for malocclusion research, the aims of this study were to construct the input set by integrating nine cephalometric analyses and to study the correlation structure of cephalometric variables in Korean adults with normal occlusion. To analyze the complex correlation structure among 65 cephalometric variables, which were based on nine classical cephalometric analyses, network analysis was applied to data obtained from 735 adults (368 males, 367 females) aged 18-25 years with normal occlusion. The structure was better revealed through weighted network analysis and minimum spanning tree. Network analysis revealed cephalometric variable clusters and the inter- and intra-correlation structure. Some metrics were divided based on their geometric interpretation rather than their clinical significance. It was confirmed that various classical cephalometric analyses primarily focus on investigating nine anatomical features. Investigating the correlation between cephalometric variables through network analysis can significantly enhance our understanding of the anatomical characteristics in the oral and maxillofacial region, which is a crucial step in studying malocclusion using artificial intelligence.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

Tetrahydrofolate levels influence 2-aminoacrylate stress in Salmonella enterica

In Salmonella enterica, the absence of the RidA deaminase results in the accumulation of the reactive enamine 2-aminoacrylate (2AA). The resulting 2AA stress impacts metabolism and prevents growth in some conditions by inactivating a specific target pyridoxal 5'-phosphate (PLP)-dependent enzyme(s). The detrimental effects of 2AA stress can be overcome by changing the sensitivity of a critical target enzyme or modifying flux in one or more nodes in the metabolic network. The catabolic L-alanine racemase DadX is a target of 2AA, which explains the inability of an alr ridA strain to use L-alanine as the sole nitrogen source. Spontaneous mutations that suppressed the growth defect of the alr ridA strain were identified as lesions in folE, which encodes GTP cyclohydrolase and catalyzes the first step of tetrahydrofolate (THF) synthesis. The data here show that THF limitation resulting from a folE lesion, or inhibition of dihydrofolate reductase (FolA) by trimethoprim, decreases the 2AA generated from endogenous serine. The data are consistent with an increased level of threonine, resulting from low folate levels, decreasing 2AA stress.IMPORTANCERidA is an enamine deaminase that has been characterized as preventing the 2-aminoacrylate (2AA) stress. In the absence of RidA, 2AA accumulates and damages various cellular enzymes. Much of the work describing the 2AA stress system has depended on the exogenous addition of serine to increase the production of the enamine stressor. The work herein focuses on understanding the effect of 2AA stress generated from endogenous serine pools. As such, this work describes the consequences of a subtle level of stress that nonetheless compromises growth in at least two conditions. Describing mechanisms that alter the physiological consequences of 2AA stress increases our understanding of endogenous metabolic stress and how the robustness of the metabolic network allows perturbations to be modulated.

Reassessing the modularity of gene co-expression networks using the Stochastic Block Model

Finding communities in gene co-expression networks is a common first step toward extracting biological insight from these complex datasets. Most community detection algorithms expect genes to be organized into assortative modules, that is, groups of genes that are more associated with each other than with genes in other groups. While it is reasonable to expect that these modules exist, using methods that assume they exist a priori is risky, as it guarantees that alternative organizations of gene interactions will be ignored. Here, we ask: can we find meaningful communities without imposing a modular organization on gene co-expression networks, and how modular are these communities? For this, we use a recently developed community detection method, the weighted degree corrected stochastic block model (SBM), that does not assume that assortative modules exist. Instead, the SBM attempts to efficiently use all information contained in the co-expression network to separate the genes into hierarchically organized blocks of genes. Using RNA-seq gene expression data measured in two tissues derived from an outbred population of Drosophila melanogaster, we show that (a) the SBM is able to find ten times as many groups as competing methods, that (b) several of those gene groups are not modular, and that (c) the functional enrichment for non-modular groups is as strong as for modular communities. These results show that the transcriptome is structured in more complex ways than traditionally thought and that we should revisit the long-standing assumption that modularity is the main driver of the structuring of gene co-expression networks.

An integrative dynamical perspective for graph theory and the analysis of complex networks

Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis methods, which allows for their comparison. Here, we challenge the widespread idea that graph theory is a universal analysis tool, uniformly applicable to any kind of network data. Instead, we show that many classical graph metrics-including degree, clustering coefficient, and geodesic distance-arise from a common hidden propagation model: the discrete cascade. From this perspective, graph metrics are no longer regarded as combinatorial measures of the graph but as spatiotemporal properties of the network dynamics unfolded at different temporal scales. Once graph theory is seen as a model-based (and not a purely data-driven) analysis tool, we can freely or intentionally replace the discrete cascade by other canonical propagation models and define new network metrics. This opens the opportunity to design-explicitly and transparently-dedicated analyses for different types of real networks by choosing a propagation model that matches their individual constraints. In this way, we take stand that network topology cannot always be abstracted independently from network dynamics but shall be jointly studied, which is key for the interpretability of the analyses. The model-based perspective here proposed serves to integrate into a common context both the classical graph analysis and the more recent network metrics defined in the literature which were, directly or indirectly, inspired by propagation phenomena on networks.

Recent advances in electrochemical cell-based biosensors for food analysis: Strategies for sensor construction

Owing to their advantages such as great specificity, sensitivity, rapidity, and possibility of noninvasive and real-time monitoring, electrochemical cell-based biosensors (ECBBs) have been a powerful tool for food analysis encompassing the areas of nutrition, flavor, and safety. Notably, the distinctive biological relevance of ECBBs enables them to mimic physiological environments and reflect cellular behaviors, leading to valuable insights into the biological function of target components in food. Compared with previous reviews, this review fills the current gap in the narrative of ECBB construction strategies. The review commences by providing an overview of the materials and configuration of ECBBs, including cell types, cell immobilization strategies, electrode modification materials, and electrochemical sensing types. Subsequently, a detailed discussion is presented on the fabrication strategies of ECBBs in food analysis applications, which are categorized based on distinct signal sources. Lastly, we summarize the merits, drawbacks, and application scope of these diverse strategies, and discuss the current challenges and future perspectives of ECBBs. Consequently, this review provides guidance for the design of ECBBs with specific functions and promotes the application of ECBBs in food analysis.

Gene expression networks regulated by human personality

Genome-wide association studies of human personality have been carried out, but transcription of the whole genome has not been studied in relation to personality in humans. We collected genome-wide expression profiles of adults to characterize the regulation of expression and function in genes related to human personality. We devised an innovative multi-omic approach to network analysis to identify the key control elements and interactions in multi-modular networks. We identified sets of transcribed genes that were co-expressed in specific brain regions with genes known to be associated with personality. Then we identified the minimum networks for the co-localized genes using bioinformatic resources. Subjects were 459 adults from the Young Finns Study who completed the Temperament and Character Inventory and provided peripheral blood for genomic and transcriptomic analysis. We identified an extrinsic network of 45 regulatory genes from seed genes in brain regions involved in self-regulation of emotional reactivity to extracellular stimuli (e.g., self-regulation of anxiety) and an intrinsic network of 43 regulatory genes from seed genes in brain regions involved in self-regulation of interpretations of meaning (e.g., production of concepts and language). We discovered that interactions between the two networks were coordinated by a control hub of 3 miRNAs and 3 protein-coding genes shared by both. Interactions of the control hub with proteins and ncRNAs identified more than 100 genes that overlap directly with known personality-related genes and more than another 4000 genes that interact indirectly. We conclude that the six-gene hub is the crux of an integrative network that orchestrates information-transfer throughout a multi-modular system of over 4000 genes enriched in liquid-liquid-phase-separation (LLPS)-related RNAs, diverse transcription factors, and hominid-specific miRNAs and lncRNAs. Gene expression networks associated with human personality regulate neuronal plasticity, epigenesis, and adaptive functioning by the interactions of salience and meaning in self-awareness.

Fractal and first-passage properties of a class of self-similar networks

A class of self-similar networks, obtained by recursively replacing each edge of the current network with a well-designed structure (generator) and known as edge-iteration networks, has garnered considerable attention owing to its role in presenting rich network models to mimic real objects with self-similar structures. The generator dominates the structural and dynamic properties of edge-iteration networks. However, the general relationships between these networks' structural and dynamic properties and their generators remain unclear. We study the fractal and first-passage properties, such as the fractal dimension, walk dimension, resistance exponent, spectral dimension, and global mean first-passage time, which is the mean time for a walker, starting from a randomly selected node and reaching the fixed target node for the first time. We disclose the properties of the generators that dominate the fractal and first-passage properties of general edge-iteration networks. A clear relationship between the fractal and first-passage properties of the edge-iteration networks and the related properties of the generators are presented. The upper and lower bounds of these quantities are also discussed. Thus, networks can be customized to meet the requirements of fractal and dynamic properties by selecting an appropriate generator and tuning their structural parameters. The results obtained here shed light on the design and optimization of network structures.

Resource allocation in mammalian systems

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

Complex regulatory networks influence pluripotent cell state transitions in human iPSCs

Stem cells exist in vitro in a spectrum of interconvertible pluripotent states. Analyzing hundreds of hiPSCs derived from different individuals, we show the proportions of these pluripotent states vary considerably across lines. We discover 13 gene network modules (GNMs) and 13 regulatory network modules (RNMs), which are highly correlated with each other suggesting that the coordinated co-accessibility of regulatory elements in the RNMs likely underlie the coordinated expression of genes in the GNMs. Epigenetic analyses reveal that regulatory networks underlying self-renewal and pluripotency are more complex than previously realized. Genetic analyses identify thousands of regulatory variants that overlapped predicted transcription factor binding sites and are associated with chromatin accessibility in the hiPSCs. We show that the master regulator of pluripotency, the NANOG-OCT4 Complex, and its associated network are significantly enriched for regulatory variants with large effects, suggesting that they play a role in the varying cellular proportions of pluripotency states between hiPSCs. Our work bins tens of thousands of regulatory elements in hiPSCs into discrete regulatory networks, shows that pluripotency and self-renewal processes have a surprising level of regulatory complexity, and suggests that genetic factors may contribute to cell state transitions in human iPSC lines.

Heterogeneous Popularity of Metabolic Reactions from Evolution

The composition of cellular metabolism is different across species. Empirical data reveal that bacterial species contain similar numbers of metabolic reactions but that the cross-species popularity of reactions is so heterogenous that some reactions are found in all the species while others are in just few species, characterized by a power-law distribution with the exponent one. Introducing an evolutionary model concretizing the stochastic recruitment of chemical reactions into the metabolism of different species at different times and their inheritance to descendants, we demonstrate that the exponential growth of the number of species containing a reaction and the saturated recruitment rate of brand-new reactions lead to the empirically identified power-law popularity distribution. Furthermore, the structural characteristics of metabolic networks and the species' phylogeny in our simulations agree well with empirical observations.

Rethinking cancer initiation: The role of large-scale mutational events

Cancer initiation is revisited in light of recent discoveries in cancer pathogenesis. Of note is the detection of mutated cancer genes in benign conditions. More significantly, somatic clones, which harbor mutations in cancer genes, arise in normal tissues from early development through adulthood, but seldom do they transform into cancer. Further, clustered mutational events-kataegis, chromothripsis and chromoplexy-are widespread in cancer, generating point mutations and chromosomal rearrangements in a single cellular catastrophe. These observations are contrary to the prevailing somatic mutation theory, which states that a cancer is caused by the gradual accumulation of mutations over time. A different perspective is proposed within the framework of Waddington's epigenetic landscape wherein tumorigenesis is viewed primarily as a disruption of cell development. Cell types are defined by their specific gene-expression profiles, determined by the gene regulatory network, and can be regarded as attractor states of the network dynamics: they represent specific, self-stabilizing patterns of gene activities across the genome. However, large-scale mutational events reshape the landscape topology, creating abnormal "unphysiological" attractors. This is the crux of the process of initiation. Initiation primes the cell for conversion into a tumor phenotype by oncogenes and tumor suppressor genes, which drive cell proliferation and clonal diversification. This view of tumorigenesis calls for a different approach to therapy.

Reverse Engineering in Biotechnology: The Role of Genetic Engineering in Synthetic Biology

Synthetic biology is built on genetic engineering and principles of design engineering, which provides control over the biological functions of interest. This chapter explores the uses, processes, and applications of genetic engineering in synthetic biology. The chapter provides a brief history and course of development of the field of synthetic biology and genetic engineering and their unbreakable association. Next, the chapter delves into materials and methods and the applications of synthetic biology. This includes discussing the generally used components of genetic engineering to design new functions into organisms and even the general steps that are part of any synthetic biology experiment. Lastly, the chapter also explains the use of the materials and methodology discussed in solving a specific problem related to a model mentioned in the paper titled "Development of Integrase-mediated differentiation circuits to improve evolutionary stability in E. coli." It explains how by using genetic engineering a synthetic biology-related problem was solved efficiently.

Greedy routing optimisation in hyperbolic networks

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods take advantage of the exponentially growing volume of the hyperbolic space as a function of the radius from the origin, allowing a (roughly) uniform spatial distribution of the nodes even for scale-free small-world networks, where the connection probability between pairs decays with hyperbolic distance. One of the motivations behind hyperbolic embedding is that optimal placement of the nodes in a hyperbolic space is widely thought to enable efficient navigation on top of the network. According to that, one of the measures that can be used to quantify the quality of different embeddings is given by the fraction of successful greedy paths following a simple navigation protocol based on the hyperbolic coordinates. In the present work, we develop an optimisation scheme for this score in the native disk representation of the hyperbolic space. This optimisation algorithm can be either used as an embedding method alone, or it can be applied to improve this score for embeddings obtained from other methods. According to our tests on synthetic and real networks, the proposed optimisation can considerably enhance the success rate of greedy paths in several cases, improving the given embedding from the point of view of navigability.

GeneMAP: A discovery platform for metabolic gene function

Organisms maintain metabolic homeostasis through the combined functions of small molecule transporters and enzymes. While many of the metabolic components have been well-established, a substantial number remains without identified physiological substrates. To bridge this gap, we have leveraged large-scale plasma metabolome genome-wide association studies (GWAS) to develop a multiomic Gene-Metabolite Associations Prediction (GeneMAP) discovery platform. GeneMAP can generate accurate predictions, even pinpointing genes that are distant from the variants implicated by GWAS. In particular, our work identified SLC25A48 as a genetic determinant of plasma choline levels. Mechanistically, SLC25A48 loss strongly impairs mitochondrial choline import and synthesis of its downstream metabolite, betaine. Rare variant testing and polygenic risk score analyses have elucidated choline-relevant phenomic consequences of SLC25A48 dysfunction. Altogether, our study proposes SLC25A48 as a mitochondrial choline transporter and provides a discovery platform for metabolic gene function.

A cellular platform for production of C4 monomers

Living organisms carry out a wide range of remarkable functions, including the synthesis of thousands of simple and complex chemical structures for cellular growth and maintenance. The manipulation of this reaction network has allowed for the genetic engineering of cells for targeted chemical synthesis, but it remains challenging to alter the program underlying their fundamental chemical behavior. By taking advantage of the unique ability of living systems to use evolution to find solutions to complex problems, we have achieved yields of up to ∼95% for three C4 commodity chemicals, n-butanol, 1,3-butanediol, and 4-hydroxy-2-butanone. Genomic sequencing of the evolved strains identified pcnB and rpoBC as two gene loci that are able to alter carbon flow by remodeling the transcriptional landscape of the cell, highlighting the potential of synthetic pathways as a tool to identify metabolic control points.

The modular biochemical reaction network structure of cellular translation

Translation is an essential attribute of all living cells. At the heart of cellular operation, it is a chemical information decoding process that begins with an input string of nucleotides and ends with the synthesis of a specific output string of peptides. The translation process is interconnected with gene expression, physiological regulation, transcription, and responses to signaling molecules, among other cellular functions. Foundational efforts have uncovered a wealth of knowledge about the mechanistic functions of the components of translation and their many interactions between them, but the broader biochemical connections between translation, metabolism and polymer biosynthesis that enable translation to occur have not been comprehensively mapped. Here we present a multilayer graph of biochemical reactions describing the translation, polymer biosynthesis and metabolism networks of an Escherichia coli cell. Intriguingly, the compounds that compose these three layers are distinctly aggregated into three modes regardless of their layer categorization. Multimodal mass distributions are well-known in ecosystems, but this is the first such distribution reported at the biochemical level. The degree distributions of the translation and metabolic networks are each likely to be heavy-tailed, but the polymer biosynthesis network is not. A multimodal mass-degree distribution indicates that the translation and metabolism networks are each distinct, adaptive biochemical modules, and that the gaps between the modes reflect evolved responses to the functional use of metabolite, polypeptide and polynucleotide compounds. The chemical reaction network of cellular translation opens new avenues for exploring complex adaptive phenomena such as percolation and phase changes in biochemical contexts.

A glimpse into the fungal metabolomic abyss: Novel network analysis reveals relationships between exogenous compounds and their outputs

Fungal specialized metabolites are a major source of beneficial compounds that are routinely isolated, characterized, and manufactured as pharmaceuticals, agrochemical agents, and industrial chemicals. The production of these metabolites is encoded by biosynthetic gene clusters that are often silent under standard growth conditions. There are limited resources for characterizing the direct link between abiotic stimuli and metabolite production. Herein, we introduce a network analysis-based, data-driven algorithm comprising two routes to characterize the production of specialized fungal metabolites triggered by different exogenous compounds: the direct route and the auxiliary route. Both routes elucidate the influence of treatments on the production of specialized metabolites from experimental data. The direct route determines known and putative metabolites induced by treatments and provides additional insight over traditional comparison methods. The auxiliary route is specific for discovering unknown analytes, and further identification can be curated through online bioinformatic resources. We validated our algorithm by applying chitooligosaccharides and lipids at two different temperatures to the fungal pathogen Aspergillus fumigatus. After liquid chromatography-mass spectrometry quantification of significantly produced analytes, we used network centrality measures to rank the treatments' ability to elucidate these analytes and confirmed their identity through fragmentation patterns or in silico spiking with commercially available standards. Later, we examined the transcriptional regulation of these metabolites through real-time quantitative polymerase chain reaction. Our data-driven techniques can complement existing metabolomic network analysis by providing an approach to track the influence of any exogenous stimuli on metabolite production. Our experimental-based algorithm can overcome the bottlenecks in elucidating novel fungal compounds used in drug discovery.

Analysis of regulatory network modules in hundreds of human stem cell lines reveals complex epigenetic and genetic factors contribute to pluripotency state differences between subpopulations

Stem cells exist in vitro in a spectrum of interconvertible pluripotent states. Analyzing hundreds of hiPSCs derived from different individuals, we show the proportions of these pluripotent states vary considerably across lines. We discovered 13 gene network modules (GNMs) and 13 regulatory network modules (RNMs), which were highly correlated with each other suggesting that the coordinated co-accessibility of regulatory elements in the RNMs likely underlied the coordinated expression of genes in the GNMs. Epigenetic analyses revealed that regulatory networks underlying self-renewal and pluripotency have a surprising level of complexity. Genetic analyses identified thousands of regulatory variants that overlapped predicted transcription factor binding sites and were associated with chromatin accessibility in the hiPSCs. We show that the master regulator of pluripotency, the NANOG-OCT4 Complex, and its associated network were significantly enriched for regulatory variants with large effects, suggesting that they may play a role in the varying cellular proportions of pluripotency states between hiPSCs. Our work captures the coordinated activity of tens of thousands of regulatory elements in hiPSCs and bins these elements into discrete functionally characterized regulatory networks, shows that regulatory elements in pluripotency networks harbor variants with large effects, and provides a rich resource for future pluripotent stem cell research.

Local flux coordination and global gene expression regulation in metabolic modeling

Genome-scale metabolic networks (GSMs) are fundamental systems biology representations of a cell's entire set of stoichiometrically balanced reactions. However, such static GSMs do not incorporate the functional organization of metabolic genes and their dynamic regulation (e.g., operons and regulons). Specifically, there are numerous topologically coupled local reactions through which fluxes are coordinated; the global growth state often dynamically regulates many gene expression of metabolic reactions via global transcription factor regulators. Here, we develop a GSM reconstruction method, Decrem, by integrating locally coupled reactions and global transcriptional regulation of metabolism by cell state. Decrem produces predictions of flux and growth rates, which are highly correlated with those experimentally measured in both wild-type and mutants of three model microorganisms Escherichia coli, Saccharomyces cerevisiae, and Bacillus subtilis under various conditions. More importantly, Decrem can also explain the observed growth rates by capturing the experimentally measured flux changes between wild-types and mutants. Overall, by identifying and incorporating locally organized and regulated functional modules into GSMs, Decrem achieves accurate predictions of phenotypes and has broad applications in bioengineering, synthetic biology, and microbial pathology.

Multifractality of Complex Networks Is Also Due to Geometry: A Geometric Sandbox Algorithm

Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity, which often manifests itself in a fractal or even multifractal structure. As a generalization of fractal analysis, the multifractal analysis of complex networks is a useful tool for identifying and quantitatively describing the spatial hierarchy of both theoretical and numerical fractal patterns. Nowadays, there are many methods of multifractal analysis. However, all these methods take into account only the fact of connection between nodes (and eventually the weight of edges) and do not take into account the real positions (coordinates) of nodes in space. However, intuition suggests that the geometry of network nodes' position should have a significant impact on the true fractal structure. Many networks identified in nature (e.g., air connection networks, energy networks, social networks, mountain ridge networks, networks of neurones in the brain, and street networks) have their own often unique and characteristic geometry, which is not taken into account in the identification process of multifractality in commonly used methods. In this paper, we propose a multifractal network analysis method that takes into account both connections between nodes and the location coordinates of nodes (network geometry). We show the results for different geometrical variants of the same network and reveal that this method, contrary to the commonly used method, is sensitive to changes in network geometry. We also carry out tests for synthetic as well as real-world networks.

Tracing the birth of structural domains from loops during protein evolution

The structures and functions of proteins are embedded into the loop scaffolds of structural domains. Their origin and evolution remain mysterious. Here, we use a novel graph-theoretical approach to describe how modular and non-modular loop prototypes combine to form folded structures in protein domain evolution. Phylogenomic data-driven chronologies reoriented a bipartite network of loops and domains (and its projections) into 'waterfalls' depicting an evolving 'elementary functionome' (EF). Two primordial waves of functional innovation involving founder 'p-loop' and 'winged-helix' domains were accompanied by an ongoing emergence and reuse of structural and functional novelty. Metabolic pathways expanded before translation functionalities. A dual hourglass recruitment pattern transferred scale-free properties from loop to domain components of the EF network in generative cycles of hierarchical modularity. Modeling the evolutionary emergence of the oldest P-loop and winged-helix domains with AlphFold2 uncovered rapid convergence towards folded structure, suggesting that a folding vocabulary exists in loops for protein fold repurposing and design.

Efficient, Formal, Material, and Final Causes in Biology and Technology

This paper considers how a classification of causal effects as comprising efficient, formal, material, and final causation can provide a useful understanding of how emergence takes place in biology and technology, with formal, material, and final causation all including cases of downward causation; they each occur in both synchronic and diachronic forms. Taken together, they underlie why all emergent levels in the hierarchy of emergence have causal powers (which is Noble's principle of biological relativity) and so why causal closure only occurs when the upwards and downwards interactions between all emergent levels are taken into account, contra to claims that some underlying physics level is by itself causality complete. A key feature is that stochasticity at the molecular level plays an important role in enabling agency to emerge, underlying the possibility of final causation occurring in these contexts.

Inferring gene regulatory network from single-cell transcriptomes with graph autoencoder model

The gene regulatory structure of cells involves not only the regulatory relationship between two genes, but also the cooperative associations of multiple genes. However, most gene regulatory network inference methods for single cell only focus on and infer the regulatory relationships of pairs of genes, ignoring the global regulatory structure which is crucial to identify the regulations in the complex biological systems. Here, we proposed a graph-based Deep learning model for Regulatory networks Inference among Genes (DeepRIG) from single-cell RNA-seq data. To learn the global regulatory structure, DeepRIG builds a prior regulatory graph by transforming the gene expression of data into the co-expression mode. Then it utilizes a graph autoencoder model to embed the global regulatory information contained in the graph into gene latent embeddings and to reconstruct the gene regulatory network. Extensive benchmarking results demonstrate that DeepRIG can accurately reconstruct the gene regulatory networks and outperform existing methods on multiple simulated networks and real-cell regulatory networks. Additionally, we applied DeepRIG to the samples of human peripheral blood mononuclear cells and triple-negative breast cancer, and presented that DeepRIG can provide accurate cell-type-specific gene regulatory networks inference and identify novel regulators of progression and inhibition.

Defining the Scale to Build Complex Networks with a 40-Year Norwegian Intraplate Seismicity Dataset

We present a new complex network-based study focused on intraplate earthquakes recorded in southern Norway during the period 1980-2020. One of the most recognized limitations of spatial complex network procedures and analyses concerns the definition of adequate cell size, which is the focus of this approach. In the present study, we analyze the influence of observational errors of hypocentral and epicentral locations of seismic events in the construction of a complex network, looking for the best cell size to build it and to develop a basis for interpreting the results in terms of the structure of the complex network in this seismic region. We focus the analysis on the degree distribution of the complex networks. We observed a strong result of the cell size for the slope of the degree distribution of the nodes, called the critical exponent γ. Based on the Abe-Suzuki method, the slope (γ) showed a negligible variation between the construction of 3- and 2-dimensional complex networks. The results were also very similar for a complex network built with subsets of seismic events. These results suggest a weak influence of observational errors measured for the coordinates latitude, longitude, and depth in the outcomes obtained with this particular methodology and for this high-quality dataset. These results imply stable behavior of the complex network, which shows a structure of hubs for small values of the cell size and a more homogeneous degree distribution when the cell size increases. In all the analyses, the γ parameter showed smaller values of the error bars for greater values of the cell size. To keep the structure of hubs and small error bars, a better range of the side sizes was determined to be between 8 to 16 km. From now on, these values can be used as the most stable cell sizes to perform any kind of study concerning complex network studies in southern Norway.

A Structure-Guided Molecular Network Strategy for Global Untargeted Metabolomics Data Annotation

Large-scale metabolite annotation is a bottleneck in untargeted metabolomics. Here, we present a structure-guided molecular network strategy (SGMNS) for deep annotation of untargeted ultra-performance liquid chromatography-high resolution mass spectrometry (MS) metabolomics data. Different from the current network-based metabolite annotation method, SGMNS is based on a global connectivity molecular network (GCMN), which was constructed by molecular fingerprint similarity of chemical structures in metabolome databases. Neighbor metabolites with similar structures in GCMN are expected to produce similar spectra. Network annotation propagation of SGMNS is performed using known metabolites as seeds. The experimental MS/MS spectra of seeds are assigned to corresponding neighbor metabolites in GCMN as their "pseudo" spectra; the propagation is done by searching predicted retention times, MS1, and "pseudo" spectra against metabolite features in untargeted metabolomics data. Then, the annotated metabolite features were used as new seeds for annotation propagation again. Performance evaluation of SGMNS showed its unique advantages for metabolome annotation. The developed method was applied to annotate six typical biological samples; a total of 701, 1557, 1147, 1095, 1237, and 2041 metabolites were annotated from the cell, feces, plasma (NIST SRM 1950), tissue, urine, and their pooled sample, respectively, and the annotation accuracy was >83% with RSD <2%. The results show that SGMNS fully exploits the chemical space of the existing metabolomes for metabolite deep annotation and overcomes the shortcoming of insufficient reference MS/MS spectra.

Identifying Influential Nodes in Social Networks: Exploiting Self-Voting Mechanism

The influence maximization (IM) problem is defined as identifying a group of influential nodes in a network such that these nodes can affect as many nodes as possible. Due to its great significance in viral marketing, disease control, social recommendation, and so on, considerable efforts have been devoted to the development of methods to solve the IM problem. In the literature, VoteRank and its improved algorithms have been proposed to select influential nodes based on voting approaches. However, in the voting process of these algorithms, a node cannot vote for itself. We argue that this voting schema runs counter to many real scenarios. To address this issue, we designed the VoteRank* algorithm, in which we first introduce the self-voting mechanism into the voting process. In addition, we also take into consideration the diversities of nodes. More explicitly, we measure the voting ability of nodes and the amount of a node voting for its neighbors based on the H-index of nodes. The effectiveness of the proposed algorithm is experimentally verified on 12 benchmark networks. The results demonstrate that VoteRank* is superior to the baseline methods in most cases.

Topological properties and organizing principles of semantic networks

Interpreting natural language is an increasingly important task in computer algorithms due to the growing availability of unstructured textual data. Natural Language Processing (NLP) applications rely on semantic networks for structured knowledge representation. The fundamental properties of semantic networks must be taken into account when designing NLP algorithms, yet they remain to be structurally investigated. We study the properties of semantic networks from ConceptNet, defined by 7 semantic relations from 11 different languages. We find that semantic networks have universal basic properties: they are sparse, highly clustered, and many exhibit power-law degree distributions. Our findings show that the majority of the considered networks are scale-free. Some networks exhibit language-specific properties determined by grammatical rules, for example networks from highly inflected languages, such as e.g. Latin, German, French and Spanish, show peaks in the degree distribution that deviate from a power law. We find that depending on the semantic relation type and the language, the link formation in semantic networks is guided by different principles. In some networks the connections are similarity-based, while in others the connections are more complementarity-based. Finally, we demonstrate how knowledge of similarity and complementarity in semantic networks can improve NLP algorithms in missing link inference.

Functional decomposition of metabolism allows a system-level quantification of fluxes and protein allocation towards specific metabolic functions

Quantifying the contribution of individual molecular components to complex cellular processes is a grand challenge in systems biology. Here we establish a general theoretical framework (Functional Decomposition of Metabolism, FDM) to quantify the contribution of every metabolic reaction to metabolic functions, e.g. the synthesis of biomass building blocks. FDM allowed for a detailed quantification of the energy and biosynthesis budget for growing Escherichia coli cells. Surprisingly, the ATP generated during the biosynthesis of building blocks from glucose almost balances the demand from protein synthesis, the largest energy expenditure known for growing cells. This leaves the bulk of the energy generated by fermentation and respiration unaccounted for, thus challenging the common notion that energy is a key growth-limiting resource. Moreover, FDM together with proteomics enables the quantification of enzymes contributing towards each metabolic function, allowing for a first-principle formulation of a coarse-grained model of global protein allocation based on the structure of the metabolic network.

Agency in evolution of biomolecular communication

Biomolecular communication demands that interactions between parts of a molecular system act as scaffolds for message transmission. It also requires an organized system of signs-a communicative agency-for creating and transmitting meaning. The emergence of agency, the capacity to act in a given context and generate end-directed behaviors, has baffled evolutionary biologists for centuries. Here, I explore its emergence with knowledge grounded in over two decades of evolutionary genomic and bioinformatic exploration. Biphasic processes of growth and diversification exist that generate hierarchy and modularity in biological systems at widely ranging time scales. Similarly, a biphasic process exists in communication that constructs a message before it can be transmitted for interpretation. Transmission dissipates matter-energy and information and involves computation. Agency emerges when molecular machinery generates hierarchical layers of vocabularies in an entangled communication network clustered around the universal Turing machine of the ribosome. Computations canalize biological systems to perform biological functions in a dissipative quest to structure long-lived occurrents. This occurs within the confines of a "triangle of persistence" that maximizes invariance with trade-offs between economy, flexibility, and robustness. Thus, learning from previous historical and circumstantial experiences unifies modules in a hierarchy that expands the agency of systems.

Network medicine: an approach to complex kidney disease phenotypes

Scientific reductionism has been the basis of disease classification and understanding for more than a century. However, the reductionist approach of characterizing diseases from a limited set of clinical observations and laboratory evaluations has proven insufficient in the face of an exponential growth in data generated from transcriptomics, proteomics, metabolomics and deep phenotyping. A new systematic method is necessary to organize these datasets and build new definitions of what constitutes a disease that incorporates both biological and environmental factors to more precisely describe the ever-growing complexity of phenotypes and their underlying molecular determinants. Network medicine provides such a conceptual framework to bridge these vast quantities of data while providing an individualized understanding of disease. The modern application of network medicine principles is yielding new insights into the pathobiology of chronic kidney diseases and renovascular disorders by expanding the understanding of pathogenic mediators, novel biomarkers and new options for renal therapeutics. These efforts affirm network medicine as a robust paradigm for elucidating new advances in the diagnosis and treatment of kidney disorders.

Overlapping communities detection through weighted graph community games

We propose a new model to detect the overlapping communities of a network that is based on cooperative games and mathematical programming. More specifically, communities are defined as stable coalitions of a weighted graph community game and they are revealed as the optimal solution of a mixed-integer linear programming problem. Exact optimal solutions are obtained for small and medium sized instances and it is shown that they provide useful information about the network structure, improving on previous contributions. Next, a heuristic algorithm is developed to solve the largest instances and used to compare two variations of the objective function.

Biotransformation of bisphenol A in vivo and in vitro by laccase-producing Trametes hirsuta La-7: Kinetics, products, and mechanisms

Bisphenol A (BPA) is a ubiquitous endocrine disruptor that poses adverse human health risks. Herein, biotransformation kinetics, products, and mechanisms of BPA undergoing a laccase-producing Trametes hirsuta La-7 metabolism were for the first time reported. Strain La-7 could completely biotransform ≤0.5 mmol·L^-1 BPA within 6 d in vivo. Notably, its extracellular crude laccase solution (ECLS) and intracellular homogenized mycelium (HM) only required 6 h to convert 85.71% and 84.24% of 0.5 mmol·L^-1 BPA in vitro, respectively. The removal of BPA was noticeably hampered by adding a cytochrome P-450 inhibitor (piperonyl butoxide) in HM, disclosing that cytochrome P-450 monooxygenase participated in BPA oxidation and metabolism. BPA intermediates were elaborately identified by high-resolution mass spectrometry (HRMS) combined with ¹³C stable isotope ratios (BPA: ¹³C₁₂-BPA = 0.25: 0.25, molar concentration). Based on the accurate molecular mass, isotope labeling difference, and relative intensity ratio of product peaks, 6 versatile metabolic mechanisms of BPA, including polymerization, hydroxylation, dehydration, bond cleavage, dehydrogenation, and carboxylation in vivo and in vitro, were confirmed. Germination index values revealed that inoculating strain La-7 in a BPA-contaminated medium presented no phytotoxicity to the germinated radish (Raphanus sativus L.) seeds. In vivo, Mg²⁺, Fe²⁺, Fe³⁺, and Mn²⁺ were conducive to BPA removal, but Cd²⁺ and Hg²⁺ significantly obstructed BPA elimination. Additionally, strain La-7 also exhibited high-efficiency metabolic ability toward estrone (E1), 17β-estradiol (E2), and 17α-ethinylestradiol (EE2), with more than 96.13%, 96.65%, and 100% of E1, E2, and EE2 having been converted, respectively. Our findings provide an environmentally powerful laccase-producing fungus to decontaminate endocrine disruptor-contaminated water matrices by radical polymerization and oxidative decomposition.

Variational kinetic clustering of complex networks

Efficiently identifying the most important communities and key transition nodes in weighted and unweighted networks is a prevalent problem in a wide range of disciplines. Here, we focus on the optimal clustering using variational kinetic parameters, linked to Markov processes defined on the underlying networks, namely, the slowest relaxation time and the Kemeny constant. We derive novel relations in terms of mean first passage times for optimizing clustering via the Kemeny constant and show that the optimal clustering boundaries have equal round-trip times to the clusters they separate. We also propose an efficient method that first projects the network nodes onto a 1D reaction coordinate and subsequently performs a variational boundary search using a parallel tempering algorithm, where the variational kinetic parameters act as an energy function to be extremized. We find that maximization of the Kemeny constant is effective in detecting communities, while the slowest relaxation time allows for detection of transition nodes. We demonstrate the validity of our method on several test systems, including synthetic networks generated from the stochastic block model and real world networks (Santa Fe Institute collaboration network, a network of co-purchased political books, and a street network of multiple cities in Luxembourg). Our approach is compared with existing clustering algorithms based on modularity and the robust Perron cluster analysis, and the identified transition nodes are compared with different notions of node centrality.

Transport collapse in dynamically evolving networks

Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to random failures, attacks or maintenance optimization in the network remain unknown. In this article, the effects of both the distance between the source and drain nodes and the degree of the source node on the time of transport collapse are studied in scale-free and lattice-based transport networks. These effects are numerically evaluated for two strategies, which employ either transport-based or random link removal. Scale-free networks with small distances are found to result in larger times of collapse. In lattice-based networks, both the dimension and boundary conditions are shown to have a major effect on the time of collapse. We also show that adding a direct link between the source and the drain increases the robustness of scale-free networks when subject to random link removals. Interestingly, the distribution of the times of collapse is then similar to the one of lattice-based networks.

Bow-tie architectures in biological and artificial neural networks: Implications for network evolution and assay design

Modern artificial neural networks (ANNs) have long been designed on foundations of mathematics as opposed to their original foundations of biomimicry. However, the structure and function of these modern ANNs are often analogous to real-life biological networks. We propose that the ubiquitous information-theoretic principles underlying the development of ANNs are similar to the principles guiding the macro-evolution of biological networks and that insights gained from one field can be applied to the other. We generate hypotheses on the bow-tie network structure of the Janus kinase - signal transducers and activators of transcription (JAK-STAT) pathway, additionally informed by the evolutionary considerations, and carry out ANN simulation experiments to demonstrate that an increase in the network's input and output complexity does not necessarily require a more complex intermediate layer. This observation should guide novel biomarker discovery-namely, to prioritize sections of the biological networks in which information is most compressed as opposed to biomarkers representing the periphery of the network.

Exploring the expressiveness of abstract metabolic networks

Metabolism is characterised by chemical reactions linked to each other, creating a complex network structure. The whole metabolic network is divided into pathways of chemical reactions, such that every pathway is a metabolic function. A simplified representation of metabolism, which we call an abstract metabolic network, is a graph in which metabolic pathways are nodes and there is an edge between two nodes if their corresponding pathways share one or more compounds. The abstract metabolic network of a given organism results in a small network that requires low computational power to be analysed and makes it a suitable model to perform a large-scale comparison of organisms' metabolism. To explore the potentials and limits of such a basic representation, we considered a comprehensive set of KEGG organisms, represented through their abstract metabolic network. We performed pairwise comparisons using graph kernel methods and analyse the results through exploratory data analysis and machine learning techniques. The results show that abstract metabolic networks discriminate macro evolutionary events, indicating that they are expressive enough to capture key steps in metabolism evolution.

Evolving scattering networks for engineering disorder

Network science provides a powerful tool for unraveling the complexities of social, technological and biological systems. Constructing networks using wave phenomena is also of great interest in devising advanced hardware for machine learning, as shown in optical neural networks. Although most wave-based networks have employed static network models, the impact of evolving models in network science provides strong motivation to apply dynamical network modeling to wave physics. Here the concept of evolving scattering networks for scattering phenomena is developed. The network is defined by links, node degrees and their evolution processes modeling multi-particle interferences, which directly determine scattering from disordered materials. I demonstrate the concept by examining network-based material classification, microstructure screening and preferential attachment in evolutions, which are applied to stealthy hyperuniformity. The results enable independent control of scattering from different length scales, revealing superdense material phases in short-range order. The proposed concept provides a bridge between wave physics and network science to resolve multiscale material complexities and open-system material design.

Metabolic Pathway Analysis: Advantages and Pitfalls for the Functional Interpretation of Metabolomics and Lipidomics Data

Over the past decades, pathway analysis has become one of the most commonly used approaches for the functional interpretation of metabolomics data. Although the approach is widely used, it is not well standardized and the impact of different methodologies on the functional outcome is not well understood. Using four publicly available datasets, we investigated two main aspects of topological pathway analysis, namely the consideration of non-human native enzymatic reactions (e.g., from microbiota) and the interconnectivity of individual pathways. The exclusion of non-human native reactions led to detached and poorly represented reaction networks and to loss of information. The consideration of connectivity between pathways led to better emphasis of certain central metabolites in the network; however, it occasionally overemphasized the hub compounds. We proposed and examined a penalization scheme to diminish the effect of such compounds in the pathway evaluation. In order to compare and assess the results between different methodologies, we also performed over-representation analysis of the same datasets. We believe that our findings will raise awareness on both the capabilities and shortcomings of the currently used pathway analysis practices in metabolomics. Additionally, it will provide insights on various methodologies and strategies that should be considered for the analysis and interpretation of metabolomics data.

Application of Graphs in a One Health Framework

The One Health framework, which advocates the crucial interconnection between environmental, animal, and human health and well-being, is becoming of increasing importance and acceptance in health sciences over the last years. The hottest public health topics of the latest years, like zoonotic diseases (e.g., the recent pandemic) or the increasing antibiotic resistance, characterized by many as "pandemic of the future," make the more holistic and combinatorial approach of One Health a necessity to combat such complex problems. Multiple graphs and graph theory have found applications in health sciences for many years, and they can now extend to usage across all levels of a One Health approach to health, ranging from genome, one disease level, to epidemiology and ecosystem graphs. For that last ecosystem layer, a proposed approach is the utilization of process graphs from the chemical engineering field, in order to understand a whole system and what constitute the most crucial aspects of a One Health issue in ecosystem level. Here P-graphs are focused alongside their combinatorial algorithms, implemented in R, and their application researched in an effort to extract information and plan interventions.

Chemical reaction networks and opportunities for machine learning

Chemical reaction networks (CRNs), defined by sets of species and possible reactions between them, are widely used to interrogate chemical systems. To capture increasingly complex phenomena, CRNs can be leveraged alongside data-driven methods and machine learning (ML). In this Perspective, we assess the diverse strategies available for CRN construction and analysis in pursuit of a wide range of scientific goals, discuss ML techniques currently being applied to CRNs and outline future CRN-ML approaches, presenting scientific and technical challenges to overcome.

Robustness of Interdependent Networks with Weak Dependency Based on Bond Percolation

Real-world systems interact with one another via dependency connectivities. Dependency connectivities make systems less robust because failures may spread iteratively among systems via dependency links. Most previous studies have assumed that two nodes connected by a dependency link are strongly dependent on each other; that is, if one node fails, its dependent partner would also immediately fail. However, in many real scenarios, nodes from different networks may be weakly dependent, and links may fail instead of nodes. How interdependent networks with weak dependency react to link failures remains unknown. In this paper, we build a model of fully interdependent networks with weak dependency and define a parameter α in order to describe the node-coupling strength. If a node fails, its dependent partner has a probability of failing of 1−α. Then, we develop an analytical tool for analyzing the robustness of interdependent networks with weak dependency under link failures, with which we can accurately predict the system robustness when 1−p fractions of links are randomly removed. We find that as the node coupling strength increases, interdependent networks show a discontinuous phase transition when α<αc and a continuous phase transition when α>αc. Compared to site percolation with nodes being attacked, the crossover points αc are larger in the bond percolation with links being attacked. This finding can give us some suggestions for designing and protecting systems in which link failures can happen.

Sharpest possible clustering bounds using robust random graph analysis

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a robust assessment of complex networks that does not depend on the entire degree distribution, but only on its mean, range, and dispersion: summary statistics that are easy to obtain for most real-world networks. By solving several semi-infinite linear programs, we obtain tight (the sharpest possible) bounds for correlation and clustering measures, for all networks with degree distributions that share the same summary statistics. We identify various extremal random graphs that attain these tight bounds as the graphs with specific three-point degree distributions. We leverage the tight bounds to obtain robust laws that explain how degree-degree correlations and local clustering evolve as a function of node degrees and network size. These robust laws indicate that power-law networks with diverging variance are among the most extreme networks in terms of correlation and clustering, building a further theoretical foundation for the widely reported scale-free network phenomena such as correlation and clustering decay.

Degree distributions under general node removal: Power-law or Poisson?

Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resulting disturbance in network properties is quintessential to understand real networks in action. The removal of nodes is a representative disturbance, but previous studies are seemingly contrasting about its effect on arguably the most fundamental network statistic, the degree distribution. The key question is about the functional form of the degree distributions that can be altered during node removal or sampling. The functional form is decisive in the remaining subnetwork's static and dynamical properties. In this work, we clarify the situation by utilizing the relative entropies with respect to the reference distributions in the Poisson and power-law form, to quantify the distance between the subnetwork's degree distribution and either of the reference distributions. Introducing general sequential node removal processes with continuously different levels of hub protection to encompass a series of scenarios including uniform random removal and preferred or protective (i.e., biased random) removal of the hub, we classify the altered degree distributions starting from various power-law forms by comparing two relative entropy values. From the extensive investigation in various scenarios based on direct node-removal simulations and by solving the rate equation of degree distributions, we discover in the parameter space two distinct regimes, one where the degree distribution is closer to the power-law reference distribution and the other closer to the Poisson distribution.

Stabilizing Large-Scale Probabilistic Boolean Networks by Pinning Control

This article aims to stabilize probabilistic Boolean networks (PBNs) via a novel pinning control strategy. In a PBN, the state evolution of each gene switches among a collection of candidate Boolean functions with preassigned probability distributions, which govern the activation frequency of each Boolean function. Due to the existence of stochasticity, the mode-independent pinning controller might be disabled. Thus, both mode-independent and mode-dependent pinning controller are required here. Moreover, a criterion is derived to determine whether mode-independent controllers are applicable while the pinned nodes are given. It is worth pointing out that this pinning control is based on the n×n network structure rather than 2ⁿ ×2ⁿ state transition matrix. Therefore, compared with the existing results, this pinning control strategy is more practicable and has the ability to handle large-scale networks, especially sparsely connected networks. To demonstrate the effectiveness of the designed control scheme, a PBN that describes the mammalian cell-cycle encountering a mutated phenotype is discussed as a simulation.

Who's driving? The default mode network in healthy elderly individuals at risk of cognitive decline

Introduction

Age is the main risk factor for the development of neurocognitive disorders, with Alzheimer's disease being the most common. Its physiopathological features may develop decades before the onset of clinical symptoms. Quantitative electroencephalography (qEEG) is a promising and cost-effective tool for the prediction of cognitive decline in healthy older individuals that exhibit an excess of theta activity. The aim of the present study was to evaluate the feasibility of brain connectivity variable resolution electromagnetic tomography (BC-VARETA), a novel source localization algorithm, as a potential tool to assess brain connectivity with 19-channel recordings, which are common in clinical practice.

Methods

We explored differences in terms of functional connectivity among the nodes of the default mode network between two groups of healthy older participants, one of which exhibited an EEG marker of risk for cognitive decline.

Results

The risk group exhibited increased levels of delta, theta, and beta functional connectivity among nodes of the default mode network, as well as reversed directionality patterns of connectivity among nodes in every frequency band when compared to the control group.

Discussion

We propose that an ongoing pathological process may be underway in healthy elderly individuals with excess theta activity in their EEGs, which is further evidenced by changes in their connectivity patterns. BC-VARETA implemented on 19-channels EEG recordings appears to be a promising tool to detect dysfunctions at the connectivity level in clinical settings.

Intersection of network medicine and machine learning towards investigating the key biomarkers and pathways underlying amyotrophic lateral sclerosis: a systematic review

BACKGROUND

Network medicine is an emerging area of research that focuses on delving into the molecular complexity of the disease, leading to the discovery of network biomarkers and therapeutic target discovery. Amyotrophic lateral sclerosis (ALS) is a complicated rare disease with unknown pathogenesis and no available treatment. In ALS, network properties appear to be potential biomarkers that can be beneficial in disease-related applications when explored independently or in tandem with machine learning (ML) techniques.

OBJECTIVE

This systematic literature review explores recent trends in network medicine and implementations of network-based ML algorithms in ALS. We aim to provide an overview of the identified primary studies and gather details on identifying the potential biomarkers and delineated pathways.

METHODS

The current study consists of searching for and investigating primary studies from PubMed and Dimensions.ai, published between 2018 and 2022 that reported network medicine perspectives and the coupling of ML techniques. Each abstract and full-text study was individually evaluated, and the relevant studies were finally included in the review for discussion once they met the inclusion and exclusion criteria.

RESULTS

We identified 109 eligible publications from primary studies representing this systematic review. The data coalesced into two themes: application of network science to identify disease modules and promising biomarkers in ALS, along with network-based ML approaches. Conclusion This systematic review gives an overview of the network medicine approaches and implementations of network-based ML algorithms in ALS to determine new disease genes, and identify critical pathways and therapeutic target discovery for personalized treatment.