Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly "apparent disorder," rather than true "frustration."combinatorial optimization | social network theory O nline social networks are examples of large-scale communities of interacting individuals in which local ties between users (friend, fan, colleague, but also friend/foe, trust/distrust, etc.) give rise to a complex, multidimensional web of aggregated social behavior (1-4). For such complex networks, the emergence of global properties from local interactions is an intriguing subject, so far investigated mostly at structural and topological level (2,(5)(6)(7)(8). In social network theory (9-11), however, the content of the relationships is often even more important than their topology, and this calls for the development of appropriate analytical and computational tools, able to extrapolate content-related features out of the set of interactions of a social community. Obtaining efficient tools is particularly challenging when, as in social networks retrieved from online media, the size of the community is very big, of the order of 10 5 individuals or higher.A global property that has recently attracted some attention (1,(12)(13)(14) is determining the structural balance of a signed social network. Structural (or social) balance theory was first formulated by Heider (15) in order to understand the structure and origin of tensions and conflicts in a network of individuals whose mutual relationships are characterizable in terms of friendship and hostility. It was modeled in terms of signed graphs by Cartwright and Harary (16); see refs. 10 and 11 for an overview of the theory. The nodes of the graph represent users and the positive/ negative edges their friendly/hostile relationships. It has been known for some time how to interpret structural balance on such networks (16): The potential source of tensions are the cycles of the graph (i.e., the closed paths beginning and ending on the same node), notably those of negative sign (i.e., having an odd number of negative edges). It follows that the concept of balance is not related to the actual number of negative edges on the cycles but only to their parity; see Fig. 1 for an illustration on basic graphs. In particular, a signed graph is exactly balanced (i.e., tensions are completely absent) if and only if all its cycles are positive (16). As such, structural balance ...

Background Single-cell RNA sequencing (scRNA-seq) plays a pivotal role in our understanding of cellular heterogeneity. Current analytical workflows are driven by categorizing principles that consider cells as individual entities and classify them into complex taxonomies. Results We devise a conceptually different computational framework based on a holistic view, where single-cell datasets are used to infer global, large-scale regulatory networks. We develop correlation metrics that are specifically tailored to single-cell data, and then generate, validate, and interpret single-cell-derived regulatory networks from organs and perturbed systems, such as diabetes and Alzheimer’s disease. Using tools from graph theory, we compute an unbiased quantification of a gene’s biological relevance and accurately pinpoint key players in organ function and drivers of diseases. Conclusions Our approach detects multiple latent regulatory changes that are invisible to single-cell workflows based on clustering or differential expression analysis, significantly broadening the biological insights that can be obtained with this leading technology. Electronic supplementary material The online version of this article (10.1186/s13059-019-1713-4) contains supplementary material, which is available to authorized users.

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Homeostatic plasticity, a form of synaptic plasticity, maintains the fine balance between overall excitation and inhibition in developing and mature neuronal networks. Although the synaptic mechanisms of homeostatic plasticity are well characterized, the associated transcriptional program remains poorly understood. We show that the Kleefstra-syndrome-associated protein EHMT1 plays a critical and cell-autonomous role in synaptic scaling by responding to attenuated neuronal firing or sensory drive. Chronic activity deprivation increased the amount of neuronal dimethylated H3 at lysine 9 (H3K9me2), the catalytic product of EHMT1 and an epigenetic marker for gene repression. Genetic knockdown and pharmacological blockade of EHMT1 or EHMT2 prevented the increase of H3K9me2 and synaptic scaling up. Furthermore, BDNF repression was preceded by EHMT1/2-mediated H3K9me2 deposition at the Bdnf promoter during synaptic scaling up, both in vitro and in vivo. Our findings suggest that H3K9me2-mediated changes in chromatin structure govern a repressive program that controls synaptic scaling.

To examine the role of sex steroid hormones in the development of autoimmune diseases, we studied five patients with Klinefelter's syndrome associated with autoimmune disease, three of whom had Sjögren's syndrome (SS) and two of whom had systemic lupus erythematosus (SLE). Serum testosterone (T) and LH levels, antinuclear antibodies (ANA) and rheumatoid factor (RF) titers, erythrocyte sedimentation rate (ESR), hemolytic complement (CH50) levels, and peripheral T lymphocyte subsets (OKT3+, OKT4+, and OKT8+) were measured before treatment, after 60 days of placebo treatment, and after 60 days of oral T undecanoate (TU) treatment. Before treatment and after placebo, with respect to normal men, the patients had lower serum T and higher LH levels, lower percentages and absolute values of OKT3+ (total T lymphocytes) and OKT8+ (suppressor/cytotoxic T lymphocytes) cells, and, consequently, an increased OKT4/OKT8 ratio. Hemolytic complement (CH50) in serum was below normal in the two patients with SLE, while it was normal in the patients with SS. The ESR was above normal in all patients, and all had high titers of ANA and RF. After TU therapy, serum T levels increased and LH levels decreased, but not to normal. OKT3+ and OKT8+ cells and the OKT4/OKT8 ratio became normal, and RF and ANA titers decreased. The CH50 level did not change in the SS patients, while it increased to normal in the two patients with SLE. The ESR decreased in all patients during therapy. Furthermore, after TU therapy, both the SS and SLE patients had a clinical remission of their autoimmune disease. Our results indicate a therapeutic effect of T on autoimmune diseases in patients with hypogonadism and Klinefelter's syndrome.

Synapse development and neuronal activity represent fundamental processes for the establishment of cognitive function. Structural organization as well as signalling pathways from receptor stimulation to gene expression regulation are mediated by synaptic activity and misregulated in neurodevelopmental disorders such as autism spectrum disorder (ASD) and intellectual disability (ID). Deleterious mutations in the PTCHD1 (Patched domain containing 1) gene have been described in male patients with X-linked ID and/or ASD. The structure of PTCHD1 protein is similar to the Patched (PTCH1) receptor; however, the cellular mechanisms and pathways associated with PTCHD1 in the developing brain are poorly determined. Here we show that PTCHD1 displays a C-terminal PDZ-binding motif that binds to the postsynaptic proteins PSD95 and SAP102. We also report that PTCHD1 is unable to rescue the canonical sonic hedgehog (SHH) pathway in cells depleted of PTCH1, suggesting that both proteins are involved in distinct cellular signalling pathways. We find that Ptchd1 deficiency in male mice (Ptchd1−/y) induces global changes in synaptic gene expression, affects the expression of the immediate-early expression genes Egr1 and Npas4 and finally impairs excitatory synaptic structure and neuronal excitatory activity in the hippocampus, leading to cognitive dysfunction, motor disabilities and hyperactivity. Thus our results support that PTCHD1 deficiency induces a neurodevelopmental disorder causing excitatory synaptic dysfunction.

Haploinsufficiency of transcriptional regulators causes human congenital heart disease (CHD). However, underlying CHD gene regulatory network (GRN) imbalances are unknown.Here, we define transcriptional consequences of reduced dosage of the CHD-linked transcription factor, TBX5, in individual cells during cardiomyocyte differentiation from human induced pluripotent stem cells (iPSCs). We discovered highly sensitive dysregulation of TBX5dependent pathways-including lineage decisions and genes associated with cardiomyocyte function and CHD genetics-in discrete subpopulations of cardiomyocytes. GRN analysis identified vulnerable nodes enriched for CHD genes, indicating that cardiac network stability is sensitive to TBX5 dosage. A GRN-predicted genetic interaction between Tbx5 and Mef2c was validated in mouse, manifesting as ventricular septation defects. These results demonstrate exquisite sensitivity to TBX5 dosage by diverse transcriptional responses in heterogeneous subsets of iPSC-derived cardiomyocytes. This predicts candidate GRNs for human CHDs, with implications for quantitative transcriptional regulation in disease.

Single-cell RNA sequencing (scRNA-seq) has significantly deepened our insights into complex tissues, with the latest techniques capable of processing tens of thousands of cells simultaneously. Analyzing increasing numbers of cells, however, generates extremely large data sets, extending processing time and challenging computing resources. Current scRNA-seq analysis tools are not designed to interrogate large data sets and often lack sensitivity to identify marker genes. With bigSCale, we provide a scalable analytical framework to analyze millions of cells, which addresses the challenges associated with large data sets. To handle the noise and sparsity of scRNA-seq data, bigSCale uses large sample sizes to estimate an accurate numerical model of noise. The framework further includes modules for differential expression analysis, cell clustering, and marker identification. A directed convolution strategy allows processing of extremely large data sets, while preserving transcript information from individual cells. We evaluated the performance of bigSCale using both a biological model of aberrant gene expression in patient-derived neuronal progenitor cells and simulated data sets, which underlines the speed and accuracy in differential expression analysis. To test its applicability for large data sets, we applied bigSCale to assess 1.3 million cells from the mouse developing forebrain. Its directed down-sampling strategy accumulates information from single cells into index cell transcriptomes, thereby defining cellular clusters with improved resolution. Accordingly, index cell clusters identified rare populations, such as reelin (Reln)-positive Cajal-Retzius neurons, for which we report previously unrecognized heterogeneity associated with distinct differentiation stages, spatial organization, and cellular function. Together, bigSCale presents a solution to address future challenges of large single-cell data sets.[Supplemental material is available for this article.]Single-cell RNA sequencing (scRNA-seq) is at the forefront of techniques to chart molecular properties of individual cells. Recent microfluidic-based methods are scalable to tens of thousands of cells, enabling an unbiased sampling and in-depth characterization without prior knowledge Macosko et al. 2015;Zheng et al. 2017). Consequently, studies are less confined by the number of cells and aim to produce comprehensive cellular atlases of entire tissues, organs, and organisms (Regev et al. 2017). Increasing cell numbers, however, generate extremely large data sets, which extend processing time and challenge computing resources. Current scRNA-seq analysis tools are not designed to analyze data sets larger than thousands of cells and often lack sensitivity and specificity to identify marker genes for cell populations or experimental conditions.To address the challenges of large scRNA-seq data sets, we developed bigSCale, an analytical framework for the sensitive detection of population markers and differentially expressed genes, being scalable to analyze mil...