Persistent network homology

Genome-wide association studies (GWAS) involving increasing sample sizes have identified hundreds of genetic variants associated with complex diseases, such as type 2 diabetes (T2D); however, it is unclear how GWAS hits form unique topological structures in protein-protein interaction (PPI) networks. Using persistent homology, this study explores the evolution and persistence of the topological features of T2D GWAS hits in the PPI network with increasing p -value thresholds. We define an n -dimensional persistent disease module as a higher-order generalization of the largest connected component (LCC)...

Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the dataset, that is, establishing the integrated taxonomic relation among points, lines, and simplices. Here, the simplicial network composed of all-order simplices in a simplicial complex is essential. Because the sequence of nested simplicial subnetworks can be regarded as a discrete Morse function from the simplicial network to real values, a method based on the concept of critical simplices can be developed by searching all-order spanning trees...

Parkinson's disease (PD) is a clinically heterogeneous disorder, which mainly affects patients' motor and non-motor function. Functional connectivity was preliminary explored and studied through resting state functional magnetic resonance imaging (rsfMRI). Through the topological analysis of 54 PD scans and 31 age-matched normal controls (NC) in the Neurocon dataset, leveraging on rsfMRI data, the brain functional connection and the Vietoris-Rips (VR) complex were constructed. The barcodes of the complex were calculated to reflect the changes of functional connectivity neural circuits (FCNC) in brain network...

Brain disease propagation is associated with characteristic alterations in the structural and functional connectivity networks of the brain. To identify disease-specific network representations, graph convolutional networks (GCNs) have been used because of their powerful graph embedding ability to characterize the non-Euclidean structure of brain networks. However, existing GCNs generally focus on learning the discriminative region of interest (ROI) features, often ignoring important topological information that enables the integration of connectome patterns of brain activity...

High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding ab initio calculations. When applying machine-learning potentials, the construction of descriptors to represent atomic configurations is crucial. These descriptors should be invariant to symmetry operations. Handcrafted representations using a smooth overlap of atomic positions and graph neural networks (GNN) are examples of methods used for constructing symmetry-invariant descriptors...

Pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure above 20 mmHg in the main pulmonary artery, is a cardiovascular disease impacting the pulmonary vasculature. PH is accompanied by chronic vascular remodeling, wherein vessels become stiffer, large vessels dilate, and smaller vessels constrict. Some types of PH, including hypoxia-induced PH (HPH), also lead to microvascular rarefaction. This study analyzes the change in pulmonary arterial morphometry in the presence of HPH using novel methods from topological data analysis (TDA)...

Proper activation of cytotoxic T cells via the T cell receptor and the costimulatory receptor CD28 is essential for adaptive immunity against viruses, many intracellular bacteria and cancers. Through biochemical analysis of RNA:protein interactions, we uncovered a non-coding RNA circuit regulating activation and differentiation of cytotoxic T cells composed of the long non-coding RNA Malat1 (Metastasis Associated Lung Adenocarcinoma Transcript 1) and the microRNA family miR-15/16. miR-15/16 is a widely and highly expressed tumor suppressor miRNA family important for cell proliferation and survival...

Root system architecture (RSA) is the primary predictor of nutrient intake and significantly influences potassium utilization efficiency (KUE). Uncertainty persists regarding the genetic factors governing root growth in rapeseed. The root transcriptome analysis reveals the genetic basis driving crop root growth. In this study, RNA-seq was used to profile the overall transcriptome in the root tissue of 20 Brassica napus accessions with high and low KUE. 71,437 genes in the roots displayed variable expression profiles between the two contrasting genotype groups...

There is increasing interest in investigating brain function based on functional connectivity networks (FCN) obtained from resting-state functional magnetic resonance imaging (fMRI). FCNs, typically obtained using measures of time series association such as Pearson's correlation, are sensitive to data acquisition parameters such as sampling period. This introduces non-neural variability in data pooled from different acquisition protocols and MRI scanners, negating the advantages of larger sample sizes in pooled data...

Infectious diseases are a significant health burden for developing countries, particularly with the rise of multidrug resistance. There is an urgent need to elucidate the factors underlying the persistence of pathogens such as Mycobacterium tuberculosis, Plasmodium falciparum and Trypanosoma brucei. In contrast to host cells, these pathogens traverse multiple and varied redox environments during their infectious cycles, including exposure to high levels of host-derived reactive oxygen species. Pathogen antioxidant defenses such as the peroxiredoxin and thioredoxin systems play critical roles in the redox stress tolerance of these cells...

The DNA double-strand breaks are particularly deleterious, especially when an error-free repair pathway is unavailable, enforcing the error-prone recombination pathways to repair the lesion. Cells can resume the cell cycle but at the expense of decreased viability due to genome rearrangements. One of the major players involved in recombinational repair of DNA damage is Rad51 recombinase, a protein responsible for presynaptic complex formation. We previously showed that an increased level of this protein promotes the usage of illegitimate recombination...

Recent attention has been given to topological data analysis (TDA), and more specifically persistent homology (PH), to identify the underlying shape of brain network connectivity beyond simple edge pairings by computing connective components across different connectivity thresholds (see Sizemore et al., 2019). In the present study, we applied PH to task-based functional connectivity, computing 0-dimension Betti (B0 ) curves and calculating the area under these curves (AUC); AUC indicates how quickly a single connected component is formed across correlation filtration thresholds, with lower values interpreted as potentially analogous to lower whole-brain system segregation (e...

The analysis of the resting-state functional connectome commonly relies on graph representations. However, the graph-based approach is restricted to pairwise interactions, not suitable to capture high-order interactions, that is, more than two regions. This work investigates the existence of cycles of synchronization emerging at the individual level in the resting-state fMRI dynamic. These cycles or loops correspond to more than three regions interacting in pairs surrounding a closed space in the resting dynamic...

Embryonic and early postnatal deletion of the gene phosphatase and tensin homolog (PTEN) results in neuronal hypertrophy, formation of aberrant neural networks and spontaneous seizures. Our previous studies document that deletion of PTEN in mature neurons also causes growth of cortical neuron cell bodies and dendrites, but it is unknown how this growth alters connectivity in mature circuits. Here, we explore consequences of deleting PTEN in a focal area of the dentate gyrus in adult male and female mice. PTEN deletion was accomplished by injecting AAV-Cre unilaterally into the dentate gyrus of double transgenic mice with lox-P sites flanking exon 5 of the PTEN gene and stop/flox tdTomato in the Rosa locus (PTENf/f /RosatdTomato )...

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology...

Epilepsy is a widespread neurological disorder, and its recurrence and suddenness are making automatic detection of seizure an urgent necessity. For this purpose, this paper performs topological data analysis (TDA) of electroencephalographic (EEG) signals by the medium of graphs to explore the potential brain activity information they contain. Through our innovative method, we first map the time series of epileptic EEGs into bi-directional weighted visibility graphs (BWVGs), which give more comprehensive reflections of the signals compared to previous existing structures...

Childhood maltreatment may adversely affect brain development and consequently behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter structure in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in global topology of the brain white-matter structural covariance network for child participants. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI)...

This work is dedicated to the topological analysis of complex transitional networks for dynamic state detection. Transitional networks are formed from time series data and they leverage graph theory tools to reveal information about the underlying dynamic system. However, traditional tools can fail to summarize the complex topology present in such graphs. In this work, we leverage persistent homology from topological data analysis to study the structure of these networks. We contrast dynamic state detection from time series using a coarse-grained state-space network (CGSSN) and topological data analysis (TDA) to two state of the art approaches: ordinal partition networks (OPNs) combined with TDA and the standard application of persistent homology to the time-delay embedding of the signal...

Brain-segregation attributes in resting-state functional networks have been widely investigated to understand cognition and cognitive aging using various approaches [e.g., average connectivity within/between networks and brain system segregation (BSS)]. While these approaches have assumed that resting-state functional networks operate in a modular structure, a complementary perspective assumes that a core-periphery or rich club structure accounts for brain functions where the hubs are tightly interconnected to each other to allow for integrated processing...

Spore-forming bacteria are prevalent in mammalian guts and have implications for host health and nutrition. The production of dormant spores is thought to play an important role in the colonization, persistence, and transmission of these bacteria. Spore formation also modifies interactions among microorganisms such as infection by phages. Recent studies suggest that phages may counter dormancy-mediated defense through the expression of phage-carried sporulation genes during infection, which can alter the transitions between active and inactive states...