Adipose tissue grows by two mechanisms: hyperplasia (cell number increase) and hypertrophy (cell size increase). Genetics and diet affect the relative contributions of these two mechanisms to the growth of adipose tissue in obesity. In this study, the size distributions of epididymal adipose cells from two mouse strains, obesity-resistant FVB/N and obesity-prone C57BL/6, were measured after 2, 4, and 12 weeks under regular and high-fat feeding conditions. The total cell number in the epididymal fat pad was estimated from the fat pad mass and the normalized cell-size distribution. The cell number and volume-weighted mean cell size increase as a function of fat pad mass. To address adipose tissue growth precisely, we developed a mathematical model describing the evolution of the adipose cell-size distributions as a function of the increasing fat pad mass, instead of the increasing chronological time. Our model describes the recruitment of new adipose cells and their subsequent development in different strains, and with different diet regimens, with common mechanisms, but with diet- and genetics-dependent model parameters. Compared to the FVB/N strain, the C57BL/6 strain has greater recruitment of small adipose cells. Hyperplasia is enhanced by high-fat diet in a strain-dependent way, suggesting a synergistic interaction between genetics and diet. Moreover, high-fat feeding increases the rate of adipose cell size growth, independent of strain, reflecting the increase in calories requiring storage. Additionally, high-fat diet leads to a dramatic spreading of the size distribution of adipose cells in both strains; this implies an increase in size fluctuations of adipose cells through lipid turnover.
Success in modeling complex phenomena such as human perception hinges critically on the availability of data and computational power. Significant progress has been made in modeling such phenomena using probabilistic methods, particularly in image analysis and speech recognition. Maximum Likelihood Estimation (MLE) combined with Bayesian model selection is the basis of much of this progress, as MLE converges to the true model with copious data. In the sciences, large enough datasets are rarae aves, so alternatives to MLE must be developed for small sample size. We introduce a data-driven statistical physics approach to model inference based on minimizing a free energy of data and show superior model recovery for small sample sizes. We demonstrate coupling strength inference in non-equilibrium kinetic Ising models, including in the difficult large coupling variability regime, and show scaling to systems of arbitrary size. 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.
The islets of Langerhans, ranging in size from clusters of a few cells to several thousand cells, are scattered near large blood vessels. While the β-cell mass in mammals is proportional to body weight, the size ranges of islets are similar between species with different body sizes, possibly reflecting an optimal functional size. The large range of islet sizes suggests a stochastic developmental process. It is not fully understood how islets develop to reach such size distributions, and how their sizes change under certain physiological and pathological conditions such as development, pregnancy, aging, obesity, and diabetes. The lack of a high-resolution in vivo imaging technique for pancreatic islets implies that the only data available to elucidate the dynamics of islet development are cross-sectional quantifications of islet size distributions. In this review, we infer biological processes affecting islet morphology in the large by examining changes of islet size distributions. Neonatal islet formation and growth is shown as a particular example of developing a mathematical model of islet size distribution. Application of this modeling to elucidate islet changes under other conditions is also discussed.
Finite sample size corrections to the reparametrization-invariant solution of the inverse problem of probability are computed, and shown to converge uniformly to the correct distribution.
Abstract Sequence covariation in multiple sequence alignments of homologous proteins has been used extensively to obtain insights into protein structure. However, global statistical inference is required in order to ascertain direct relationships between amino acid positions in these sequences that are not simply secondary correlations induced by interactions with a third residue. Methods for statistical inference of such covariation have been developed to exploit the growing availability of sequence data. These hints about the folded protein structure provide critical a priori information for more detailed 3D predictions by neural networks. We present a novel method for protein structure inference using an iterative parameter-free model estimator which uses the formalism of statistical physics. With no tunable learning rate, our method scales to large system sizes while providing improved performance in the regime of small sample sizes. We apply this method to 40974 PDB structures and compare its performance to that of other methods. Our method outperforms existing methods for 76% of analysed proteins.
Machine learning using deep neural networks (DNNs) has become ubiquitous in data-driven predictive learning. However, their complex architecture often obscures what they have learned from the data. This information is crucial to validate these models when their predictions can affect human life, for example, biological and clinical predictions. We design SensX, a model agnostic explainable AI (XAI) framework to explain what a trained DNN has learned. We introduce the notion of justifiable perturbations to systematically conduct global sensitivity analysis. Benchmarks using synthetic data sets show that SensX outperformed current state-of-the-art XAI in accuracy (up to 50% higher) and computation time (up to 158 times faster), with higher consistency in all cases. Moreover, only SensX scaled to explain vision transformer (ViT) models defined for input images with more than 150,000 features. SensX validated the ViT models by showing that the features they learn as important for different facial attributes are intuitively accurate. Further, SensX revealed that there may be biases inherent to the model architecture, an observation that is possible only when the model is explained at the full resolution of the input image. Finally, we use SensX to explain a DNN trained to annotate biological cell types using single-cell RNA-seq data sets with more than a million cells and more than 56,000 genes measured per cell. SensX determines the different sets of genes that the DNNs have learned to be important to different cell types.
In obesity, increases in free fatty acid (FFA) flux can predict development of insulin resistance. Adult women release more FFA relative to resting energy expenditure (REE) and have greater FFA clearance rates than men. In adolescents, it is unknown whether sex differences in FFA flux occur. Our objective was to determine the associations of sex, REE, and body composition with FFA kinetics in obese adolescents. Participants were from a convenience sample of 112 non-Hispanic white and black adolescents (31% male; age range, 12–18 years; body mass index SD score range, 1.6–3.1) studied before initiating obesity treatment. Glucose, insulin, and FFA were measured during insulin-modified frequently sampled iv glucose tolerance tests. Minimal models for glucose and FFA calculated insulin sensitivity index (SI) and FFA kinetics, including maximum (l0 + l2) and insulin-suppressed (l2) lipolysis rates, clearance rate constant (cf), and insulin concentration for 50% lipolysis suppression (ED50). Relationships of FFA measures to sex, REE, fat mass (FM), lean body mass (LBM) and visceral adipose tissue (VAT) were examined. In models accounting for age, race, pubertal status, height, FM, and LBM, we found sex, pubertal status, age, and REE independently contributed to the prediction of l2 and l0 + l2 (P < .05). Sex and REE independently predicted ED50 (P < .05). Sex, FM/VAT, and LBM were independent predictors of cf. Girls had greater l2, l0 + l2 and ED50 (P < .05, adjusted for REE) and greater cf (P < .05, adjusted for FM or VAT) than boys. Independent of the effects of REE and FM, FFA kinetics differ significantly in obese adolescent girls and boys, suggesting greater FFA flux among girls.
Models of random surfaces defined by integrals over self-dual unitary quaternion matrices are solved exactly in a double-scaling limit. There are contributions to the specific heat from surfaces with odd Euler characteristic, indicating that these are theories of unoriented strings. For the k=1 model, these contributions are determined from the quantum mechanics of a particle moving in a potential given by the specific heat of the k=1 unitary model, up to a linear term. A by-product of this analysis is a new solution of unitary-matrix models, formulated in terms of matrix differential operators.
