Annealing approach to root-finding.

The Newton-Raphson method stands as the {\it ur}-root-finding technique. In this study, we propose a parameterized variant of the Newton-Raphson method, inspired by principles from physics. Through analytical and empirical validation, we demonstrate that this novel approach offers increased robustness and faster convergence during root-finding iterations. Furthermore, we establish connections to the Adomian series method and provide a natural interpretation within a series framework. Remarkably, the introduced parameter, akin to a temperature variable, enables an annealing approach. This advancement sets the stage for a fresh exploration of numerical iterative root-finding methodologies.

Dory: Computation of persistence diagrams up to dimension two for Vietoris-Rips filtrations of large data sets.

Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various applications, computational requirements have limited applications to small data sets of a few thousand points. We present Dory, an efficient and scalable algorithm that can compute the persistent homology of sparse Vietoris-Rips complexes on larger data sets, up to and including dimension two and over the field Z2. As an application, we compute the PH of the human genome at high resolution as revealed by a genome-wide Hi-C data set containing approximately three million points. Extant algorithms were unable to process it, whereas Dory processed it within five minutes, using less than five GB of memory. Results show that the topology of the human genome changes significantly upon treatment with auxin, a molecule that degrades cohesin, corroborating the hypothesis that cohesin plays a crucial role in loop formation in DNA.

Geometric and topological characterization of the cytoarchitecture of islets of Langerhans.

The islets of Langerhans are critical endocrine micro-organs that secrete hormones regulating energy metabolism in animals. Insulin and glucagon, secreted by beta and alpha cells, respectively, are responsible for metabolic switching between fat and glucose utilization. Dysfunction in their secretion and/or counter-regulatory influence leads to diabetes. Debate in the field centers on the cytoarchitecture of islets, as the signaling that governs hormonal secretion depends on structural and functional factors, including electrical connectivity, innervation, vascularization, and physical proximity. Much effort has therefore been devoted to elucidating which architectural features are significant for function and how derangements in these features are correlated or causative for dysfunction, especially using quantitative network science or graph theory characterizations. Here, we ask if there are non-local features in islet cytoarchitecture, going beyond standard network statistics, that are relevant to islet function. An example is ring structures, or cycles, of α and δ cells surrounding ß cell clusters or the opposite, ß cells surrounding α and δ cells. These could appear in two-dimensional islet section images if a sphere consisting of one cell type surrounds a cluster of another cell type. To address these issues, we developed two independent computational approaches, geometric and topological, for such characterizations. For the latter, we introduce an application of topological data analysis to determine locations of topological features that are biologically significant. We show that both approaches, applied to a large collection of islet sections, are in complete agreement in the context both of developmental and diabetes-related changes in islet characteristics. The topological approach can be applied to three-dimensional imaging data for islets as well.

Tight basis cycle representatives for persistent homology of large biological data sets.

Persistent homology (PH) is a popular tool for topological data analysis that has found applications across diverse areas of research. It provides a rigorous method to compute robust topological features in discrete experimental observations that often contain various sources of uncertainties. Although powerful in theory, PH suffers from high computation cost that precludes its application to large data sets. Additionally, most analyses using PH are limited to computing the existence of nontrivial features. Precise localization of these features is not generally attempted because, by definition, localized representations are not unique and because of even higher computation cost. Such a precise location is a sine qua non for determining functional significance, especially in biological applications. Here, we provide a strategy and algorithms to compute tight representative boundaries around nontrivial robust features in large data sets. To showcase the efficiency of our algorithms and the precision of computed boundaries, we analyze the human genome and protein crystal structures. In the human genome, we found a surprising effect of the impairment of chromatin loop formation on loops through chromosome 13 and the sex chromosomes. We also found loops with long-range interactions between functionally related genes. In protein homologs with significantly different topology, we found voids attributable to ligand-interaction, mutation, and differences between species.

Longitudinal multi-omics analyses of the gut-liver axis reveals metabolic dysregulation in hepatitis C infection and cirrhosis.

The gut and liver are connected via the portal vein, and this relationship, which includes the gut microbiome, is described as the gut-liver axis. Hepatitis C virus (HCV) can infect the liver and cause fibrosis with chronic infection. HCV has been associated with an altered gut microbiome; however, how these changes impact metabolism across the gut-liver axis and how this varies with disease severity and time is unclear. Here we used multi-omics analysis of portal and peripheral blood, faeces and liver tissue to characterize the gut-liver axis of patients with HCV across a fibrosis severity gradient before (n = 29) and 6 months after (n = 23) sustained virologic response, that is, no detection of the virus. Fatty acids were the major metabolites perturbed across the liver, portal vein and gut microbiome in HCV, especially in patients with cirrhosis. Decreased fatty acid degradation by hepatic peroxisomes and mitochondria was coupled with increased free fatty acid (FFA) influx to the liver via the portal vein. Metatranscriptomics indicated that Anaerostipes hadrus-mediated fatty acid synthesis influences portal FFAs. Both microbial fatty acid synthesis and portal FFAs were associated with enhanced hepatic fibrosis. Bacteroides vulgatus-mediated intestinal glycan breakdown was linked to portal glycan products, which in turn correlated with enhanced portal inflammation in HCV. Paired comparison of patient samples at both timepoints showed that hepatic metabolism, especially in peroxisomes, is persistently dysregulated in cirrhosis independently of the virus. Sustained virologic response was associated with a potential beneficial role for Methanobrevibacter smithii, which correlated with liver disease severity markers. These results develop our understanding of the gut-liver axis in HCV and non-HCV liver disease aetiologies and provide a foundation for future therapies.

Rosiglitazone treatment enhances intracellular actin dynamics and glucose transport in hypertrophic adipocytes.

AIMS: To accommodate surplus energy, adipose tissue expands by increasing both adipose cell size (hypertrophy) and cell number (hyperplasia). Enlarged, hypertrophic adipocytes are known to have reduced insulin response and impaired glucose transport, which negatively influence whole-body glucose homeostasis. Rosiglitazone is a peroxisome proliferator-activated receptor gamma (PPARγ) agonist, known to stimulate hyperplasia and to efficiently improve insulin sensitivity. Still, a limited amount of research has investigated the effects of rosiglitazone in mature, hypertrophic adipocytes. Therefore, the objective of this study was to examine rosiglitazone's effect on insulin-stimulated glucose uptake in hypertrophic adipocytes. MAIN METHODS: C57BL/6J male mice were subjected to 2 weeks of high-fat diet (HFD) followed by 1 week of HFD combined with daily administration of rosiglitazone (10 mg/kg). Adipose cell-size distribution and gene expression were analysed in intact adipose tissue, and glucose uptake, insulin response, and protein expression were examined using primary adipocytes isolated from epididymal and inguinal adipose tissue. KEY FINDINGS: HFD-feeding induced an accumulation of hypertrophic adipocytes, which was not affected by rosiglitazone-treatment. Still, rosiglitazone efficiently improved insulin-stimulated glucose transport without restoring insulin signaling or GLUT4 expression in similar-sized adipocytes. This improvement occurred concurrently with extracellular matrix remodelling and restored intracellular levels of targets involved in actin turnover. SIGNIFICANCE: These results demonstrate that rosiglitazone improves glucose transport in hypertrophic adipocytes, and highlights the importance of the cytoskeleton and extracellular matrix as potential therapeutic targets.

Effects of colchicine on lipolysis and adipose tissue inflammation in adults with obesity and metabolic syndrome.

OBJECTIVE: The aim of this study was to examine whether colchicine's anti-inflammatory effects would improve measures of lipolysis and distribution of leukocyte populations in subcutaneous adipose tissue (SAT). METHODS: A secondary analysis was conducted for a double-blind, randomized, placebo-controlled pilot study in which 40 adults with obesity and metabolic syndrome (MetS) were randomized to colchicine 0.6 mg or placebo twice daily for 3 months. Non-insulin-suppressible (l0 ), insulin-suppressible (l2 ), and maximal (l0 +l2 ) lipolysis rates were calculated by minimal model analysis. Body composition was determined by dual-energy x-ray absorptiometry. SAT leukocyte populations were characterized by flow cytometry analysis from biopsied samples obtained before and after the intervention. RESULTS: Colchicine treatment significantly decreased l2 and l0 +l2 versus placebo (p < 0.05). These changes were associated with a significant reduction in markers of systemic inflammation, including high-sensitivity C-reactive protein, resistin, and circulating monocytes and neutrophils (p < 0.01). Colchicine did not significantly alter SAT leukocyte population distributions (p > 0.05). CONCLUSIONS: In adults with obesity and MetS, colchicine appears to improve insulin regulation of lipolysis and reduce markers of systemic inflammation independent of an effect on local leukocyte distributions in SAT. Further studies are needed to better understand the mechanisms by which colchicine affects adipose tissue metabolic pathways in adults with obesity and MetS.

Mechanistic gene networks inferred from single-cell data with an outlier-insensitive method.

With advances in single-cell techniques, measuring gene dynamics at cellular resolution has become practicable. In contrast, the increased complexity of data has made it more challenging computationally to unravel underlying biological mechanisms. Thus, it is critical to develop novel computational methods capable of dealing with such complexity and of providing predictive deductions from such data. Many methods have been developed to address such challenges, each with its own advantages and limitations. We present an iterative regression algorithm for inferring a mechanistic gene network from single-cell data, especially suited to overcoming problems posed by measurement outliers. Using this regression, we infer a developmental model for the gene dynamics in Drosophila melanogaster blastoderm embryo. Our results show that the predictive power of the inferred model is higher than that of other models inferred with least squares and ridge regressions. As a baseline for how well a mechanistic model should be expected to perform, we find that model predictions of the gene dynamics are more accurate than predictions made with neural networks of varying architectures and complexity. This holds true even in the limit of small sample sizes. We compare predictions for various gene knockouts with published experimental results, finding substantial qualitative agreement. We also make predictions for gene dynamics under various gene network perturbations, impossible in non-mechanistic models.

Inference of stochastic time series with missing data.

Inferring dynamics from time series is an important objective in data analysis. In particular, it is challenging to infer stochastic dynamics given incomplete data. We propose an expectation maximization (EM) algorithm that iterates between alternating two steps: E-step restores missing data points, while M-step infers an underlying network model from the restored data. Using synthetic data of a kinetic Ising model, we confirm that the algorithm works for restoring missing data points as well as inferring the underlying model. At the initial iteration of the EM algorithm, the model inference shows better model-data consistency with observed data points than with missing data points. As we keep iterating, however, missing data points show better model-data consistency. We find that demanding equal consistency of observed and missing data points provides an effective stopping criterion for the iteration to prevent going beyond the most accurate model inference. Using the EM algorithm and the stopping criterion together, we infer missing data points from a time-series data of real neuronal activities. Our method reproduces collective properties of neuronal activities such as correlations and firing statistics even when 70% of data points are masked as missing points.

Genome-wide covariation in SARS-CoV-2.

The SARS-CoV-2 virus causing the global pandemic is a coronavirus with a genome of about 30Kbase length. The design of vaccines and choice of therapies depends on the structure and mutational stability of encoded proteins in the open reading frames (ORFs) of this genome. In this study, we computed, using Expectation Reflection, the genome-wide covariation of the SARS-CoV-2 genome based on an alignment of ≈130000 SARS-CoV-2 complete genome sequences obtained from GISAID. We used this covariation to compute the Direct Information between pairs of positions across the whole genome, investigating potentially important relationships within the genome, both within each encoded protein and between encoded proteins. We then computed the covariation within each clade of the virus. The covariation detected recapitulates all clade determinants and each clade exhibits distinct covarying pairs.

Associations of GlycA and high-sensitivity C-reactive protein with measures of lipolysis in adults with obesity.

BACKGROUND: Obesity-associated inflammation promotes metabolic dysfunction. However, it is unclear how different inflammatory biomarkers predict dysregulation in specific tissues/organs, particularly adipose tissue. OBJECTIVE: The aim of our study was to examine whether GlycA, a nuclear magnetic resonance-measured biomarker of inflammation, is a better predictor of insulin-suppressible lipolysis and other measures of metabolic dysfunction compared with high-sensitivity C-reactive protein (hsCRP) in human obesity. METHODS: This was a cross-sectional study of 58 nondiabetic adults with obesity (body mass index: 39.8 ± 7.0 kg/m2, age 46.5 ± 12.2 years, 67.2% female) who underwent a frequently sampled intravenous glucose tolerance test in the fasted state. Noninsulin-suppressible (l0), insulin-suppressible (l2), and maximal (l0+l2) lipolysis rates, as well as insulin sensitivity and acute insulin response to glucose, were calculated by minimal model analysis. Nuclear magnetic resonance was used to measure GlycA. Body composition was determined by dual-energy X-ray absorptiometry. RESULTS: GlycA was strongly correlated with hsCRP (r = +0.46; P < .001). GlycA and hsCRP were positively associated with l2, l0+l2, and fat mass (Ps < .01). In linear regression models accounting for age, race, sex, and fat mass, GlycA remained significantly associated with l2 and l0+l2 (Ps < .05), whereas hsCRP did not (Ps ≥ .20). Neither GlycA nor hsCRP was associated with l0, insulin sensitivity, or acute insulin response to glucose. CONCLUSIONS: GlycA was associated with elevated lipolysis, independent of adiposity, in adults with obesity. Our findings suggest that GlycA and hsCRP have distinct inflammation-mediated metabolic effects, with GlycA having a greater association with adipose tissue dysfunction. Further studies are warranted to investigate the mechanisms underlying these associations.

Cryptic genetic variation enhances primate L1 retrotransposon survival by enlarging the functional coiled coil sequence space of ORF1p.

Accounting for continual evolution of deleterious L1 retrotransposon families, which can contain hundreds to thousands of members remains a major issue in mammalian biology. L1 activity generated upwards of 40% of some mammalian genomes, including humans where they remain active, causing genetic defects and rearrangements. L1 encodes a coiled coil-containing protein that is essential for retrotransposition, and the emergence of novel primate L1 families has been correlated with episodes of extensive amino acid substitutions in the coiled coil. These results were interpreted as an adaptive response to maintain L1 activity, however its mechanism remained unknown. Although an adventitious mutation can inactivate coiled coil function, its effect could be buffered by epistatic interactions within the coiled coil, made more likely if the family contains a diverse set of coiled coil sequences-collectively referred to as the coiled coil sequence space. Amino acid substitutions that do not affect coiled coil function (i.e., its phenotype) could be "hidden" from (not subject to) purifying selection. The accumulation of such substitutions, often referred to as cryptic genetic variation, has been documented in various proteins. Here we report that this phenomenon was in effect during the latest episode of primate coiled coil evolution, which occurred 30-10 MYA during the emergence of primate L1Pa7-L1Pa3 families. First, we experimentally demonstrated that while coiled coil function (measured by retrotransposition) can be eliminated by single epistatic mutations, it nonetheless can also withstand extensive amino acid substitutions. Second, principal component and cluster analysis showed that the coiled coil sequence space of each of the L1Pa7-3 families was notably increased by the presence of distinct, coexisting coiled coil sequences. Thus, sampling related networks of functional sequences rather than traversing discrete adaptive states characterized the persistence L1 activity during this evolutionary event.

Erasure machine: Inverse Ising inference from reweighting of observation frequencies.

Maximum likelihood estimation (MLE) is fundamental to system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of partition functions summing over all configurations, both observed and unobserved. We present a conceptually transparent data-driven inference computation based on a reweighting of observed configuration frequencies that allows us to recast the inference problem as a simpler calculation. Modeling our approach on the high-temperature limit of statistical physics, we reweight the frequencies of observed configurations by multiplying with reciprocals of Boltzmann weights and update the Boltzmann weights iteratively to make these products close to the high-temperature limit of the Boltzmann weights. This converts the required partition function computation in the reweighted MLE to a tractable leading-order high-temperature term. We show that this is a convex optimization at each step. Then, for systems with a large number of degrees of freedom where other approaches are intractable, we demonstrate that this data-driven algorithm gives accurate inference with both synthetic data and two real-world examples.

A mathematical model of calcium dynamics: Obesity and mitochondria-associated ER membranes.

Multiple cellular organelles tightly orchestrate intracellular calcium (Ca2+) dynamics to regulate cellular activities and maintain homeostasis. The interplay between the endoplasmic reticulum (ER), a major store of intracellular Ca2+, and mitochondria, an important source of adenosine triphosphate (ATP), has been the subject of much research, as their dysfunction has been linked with metabolic diseases. Interestingly, throughout the cell's cytosolic domain, these two organelles share common microdomains called mitochondria-associated ER membranes (MAMs), where their membranes are in close apposition. The role of MAMs is critical for intracellular Ca2+ dynamics as they provide hubs for direct Ca2+ exchange between the organelles. A recent experimental study reported correlation between obesity and MAM formation in mouse liver cells, and obesity-related cellular changes that are closely associated with the regulation of Ca2+ dynamics. We constructed a mathematical model to study the effects of MAM Ca2+ dynamics on global Ca2+ activities. Through a series of model simulations, we investigated cellular mechanisms underlying the altered Ca2+ dynamics in the cells under obesity. We predict that, as the dosage of stimulus gradually increases, liver cells from obese mice will reach the state of saturated cytosolic Ca2+ concentration at a lower stimulus concentration, compared to cells from healthy mice.

Data-driven inference of hidden nodes in networks.

The explosion of activity in finding interactions in complex systems is driven by availability of copious observations of complex natural systems. However, such systems, e.g., the human brain, are rarely completely observable. Interaction network inference must then contend with hidden variables affecting the behavior of the observed parts of the system. We present an effective approach for model inference with hidden variables. From configurations of observed variables, we identify the observed-to-observed, hidden-to-observed, observed-to-hidden, and hidden-to-hidden interactions, the configurations of hidden variables, and the number of hidden variables. We demonstrate the performance of our method by simulating a kinetic Ising model, and show that our method outperforms existing methods. Turning to real data, we infer the hidden nodes in a neuronal network in the salamander retina and a stock market network. We show that predictive modeling with hidden variables is significantly more accurate than that without hidden variables. Finally, an important hidden variable problem is to find the number of clusters in a dataset. We apply our method to classify MNIST handwritten digits. We find that there are about 60 clusters which are roughly equally distributed among the digits.

Network inference in stochastic systems from neurons to currencies: Improved performance at small sample size.

The fundamental problem in modeling complex phenomena such as human perception using probabilistic methods is that of deducing a stochastic model of interactions between the constituents of a system from observed configurations. Even in this era of big data, the complexity of the systems being modeled implies that inference methods must be effective in the difficult regimes of small sample sizes and large coupling variability. Thus, model inference by means of minimization of a cost function requires additional assumptions such as sparsity of interactions to avoid overfitting. In this paper, we completely divorce iterative model updates from the value of a cost function quantifying goodness of fit. This separation enables the use of goodness of fit as a natural rationale for terminating model updates, thereby avoiding overfitting. We do this within the mathematical formalism of statistical physics by defining a formal free energy of observations from a partition function with an energy function chosen precisely to enable an iterative model update. Minimizing this free energy, we demonstrate coupling strength inference in nonequilibrium kinetic Ising models, and show that our method outperforms other existing methods in the regimes of interest. Our method has no tunable learning rate, scales to large system sizes, and has a systematic expansion to obtain higher-order interactions. As applications, we infer a functional connectivity network in the salamander retina and a currency exchange rate network from time-series data of neuronal spiking and currency exchange rates, respectively. Accurate small sample size inference is critical for devising a profitable currency hedging strategy.

Intact glucose uptake despite deteriorating signaling in adipocytes with high-fat feeding.

To capture immediate cellular changes during diet-induced expansion of adipocyte cell volume and number, we characterized mature adipocytes during a short-term high-fat diet (HFD) intervention. Male C57BL6/J mice were fed chow diet, and then switched to HFD for 2, 4, 6 or 14 days. Systemic glucose clearance was assessed by glucose tolerance test. Adipose tissue was dissected for RNA-seq and cell size distribution analysis using coulter counting. Insulin response in isolated adipocytes was monitored by glucose uptake assay and Western blotting, and confocal microscopy was used to assess autophagic activity. Switching to HFD was accompanied by an immediate adipocyte size expansion and onset of systemic insulin resistance already after two days, followed by recruitment of new adipocytes. Despite an initially increased non-stimulated and preserved insulin-stimulated glucose uptake, we observed a decreased phosphorylation of insulin receptor substrate-1 (IRS-1) and protein kinase B (PKB). After 14 days of HFD, both the insulin-stimulated phosphorylation of Akt substrate of 160 kDa (AS160) and glucose uptake was blunted. RNA-seq analysis of adipose tissue revealed transient changes in gene expression at day four, including highly significant upregulation of Trp53inp, previously demonstrated to be involved in autophagy. We confirmed increased autophagy, measured as an increased density of LC3-positive puncta and decreased p62 expression after 14 days of HFD. In conclusion, HFD rapidly induced systemic insulin resistance, whereas insulin-stimulated glucose uptake remained intact throughout 6 days of HFD feeding. We also identified autophagy as an early cellular process that potentially influences adipocyte function upon switching to HFD.

Block network mapping approach to quantitative trait locus analysis.

BACKGROUND: Advances in experimental biology have enabled the collection of enormous troves of data on genomic variation in living organisms. The interpretation of this data to extract actionable information is one of the keys to developing novel therapeutic strategies to treat complex diseases. Network organization of biological data overcomes measurement noise in several biological contexts. Does a network approach, combining information about the linear organization of genomic markers with correlative information on these markers in a Bayesian formulation, lead to an analytic method with higher power for detecting quantitative trait loci? RESULTS: Block Network Mapping, combining Similarity Network Fusion (Wang et al., NM 11:333-337, 2014) with a Bayesian locus likelihood evaluation, leads to large improvements in area under the receiver operating characteristic and power over interval mapping with expectation maximization. The method has a monotonically decreasing false discovery rate as a function of effect size, unlike interval mapping. CONCLUSIONS: Block Network Mapping provides an alternative data-driven approach to mapping quantitative trait loci that leverages correlations in the sampled genotypes. The evaluation methodology can be combined with existing approaches such as Interval Mapping. Python scripts are available at http://lbm.niddk.nih.gov/vipulp/ . Genotype data is available at http://churchill-lab.jax.org/website/GattiDOQTL .

Adipose cell hypertrophy precedes the appearance of small adipocytes by 3 days in C57BL/6 mouse upon changing to a high fat diet.

Adipose tissue is the energy buffer in mammals. The cellularity of adipose tissue has a major role in determining the response of adipose tissue to insulin action. A reduction in the ability of adipose tissue to store ingested caloric excess can lead to dyslipidemia and lipotoxicity, impacting insulin action systemically. The dynamic response of adipose tissue to changes in diet is therefore a crucial aspect of metabolism, and has attracted attention in the context of the ongoing worldwide increase in overweight and obesity and resulting metabolic syndrome dysfunctions. We investigated in a mouse model if there is a specific delay between an increase in caloric intake and the recruitment of new adipocytes, and if there are other changes in adipose tissue dynamics concomitant with such a diet change. By developing a dynamic mathematical model, we found that there is a delay of 3 days between the start of a high fat diet and the recruitment of new adipocytes, and that the rate of fat mass increase modulates lipid turnover and adipose cell hypertrophy.

Adaptation of pancreatic islet cyto-architecture during development.

Plasma glucose in mammals is regulated by hormones secreted by the islets of Langerhans embedded in the exocrine pancreas. Islets consist of endocrine cells, primarily α, ß, and δ cells, which secrete glucagon, insulin, and somatostatin, respectively. ß cells form irregular locally connected clusters within islets that act in concert to secrete insulin upon glucose stimulation. Varying demands and available nutrients during development produce changes in the local connectivity of ß cells in an islet. We showed in earlier work that graph theory provides a framework for the quantification of the seemingly stochastic cyto-architecture of ß cells in an islet. To quantify the dynamics of endocrine connectivity during development requires a framework for characterizing changes in the probability distribution on the space of possible graphs, essentially a Fokker-Planck formalism on graphs. With large-scale imaging data for hundreds of thousands of islets containing millions of cells from human specimens, we show that this dynamics can be determined quantitatively. Requiring that rearrangement and cell addition processes match the observed dynamic developmental changes in quantitative topological graph characteristics strongly constrained possible processes. Our results suggest that there is a transient shift in preferred connectivity for ß cells between 1-35 weeks and 12-24 months.