Mathematical Models of the Effect of Glucagon on Glycemia in Individuals With Type 2 Diabetes Treated With Dapagliflozin.

Context: Sodium-glucose cotransporter 2 (SGLT2) inhibitors lower blood glucose levels by promoting urinary glucose excretion, but their overall effects on hormonal and metabolic status remain unclear. Objective: We here investigated the roles of insulin and glucagon in the regulation of glycemia in individuals treated with an SGLT2 inhibitor using mathematical model analysis. Methods: Hyperinsulinemic-euglycemic clamp and oral glucose tolerance tests were performed in 68 individuals with type 2 diabetes treated with the SGLT2 inhibitor dapagliflozin. Data previously obtained from such tests in 120 subjects with various levels of glucose tolerance and not treated with an SGLT2 inhibitor were examined as a control. Mathematical models of the feedback loops connecting glucose and insulin (GI model) or glucose, insulin, and glucagon (GIG model) were generated. Results: Analysis with the GI model revealed that the disposition index/clearance, which is defined as the product of insulin sensitivity and insulin secretion divided by the square of insulin clearance and represents the glucose-handling ability of insulin, was significantly correlated with glycemia in subjects not taking an SGLT2 inhibitor but not in those taking dapagliflozin. Analysis with the GIG model revealed that a metric defined as the product of glucagon sensitivity and glucagon secretion divided by glucagon clearance (designated production index/clearance) was significantly correlated with blood glucose level in subjects treated with dapagliflozin. Conclusion: Treatment with an SGLT2 inhibitor alters the relation between insulin effect and blood glucose concentration, and glucagon effect may account for variation in glycemia among individuals treated with such drugs.

DNA hypomethylation characterizes genes encoding tissue-dominant functional proteins in liver and skeletal muscle.

Each tissue has a dominant set of functional proteins required to mediate tissue-specific functions. Epigenetic modifications, transcription, and translational efficiency control tissue-dominant protein production. However, the coordination of these regulatory mechanisms to achieve such tissue-specific protein production remains unclear. Here, we analyzed the DNA methylome, transcriptome, and proteome in mouse liver and skeletal muscle. We found that DNA hypomethylation at promoter regions is globally associated with liver-dominant or skeletal muscle-dominant functional protein production within each tissue, as well as with genes encoding proteins involved in ubiquitous functions in both tissues. Thus, genes encoding liver-dominant proteins, such as those involved in glycolysis or gluconeogenesis, the urea cycle, complement and coagulation systems, enzymes of tryptophan metabolism, and cytochrome P450-related metabolism, were hypomethylated in the liver, whereas those encoding-skeletal muscle-dominant proteins, such as those involved in sarcomere organization, were hypomethylated in the skeletal muscle. Thus, DNA hypomethylation characterizes genes encoding tissue-dominant functional proteins.

DI/cle, a Measure Consisting of Insulin Sensitivity, Secretion, and Clearance, Captures Diabetic States.

CONTEXT: Insulin clearance is implicated in regulation of glucose homeostasis independently of insulin sensitivity and insulin secretion. OBJECTIVE: To understand the relation between blood glucose and insulin sensitivity, secretion, and clearance. METHODS: We performed a hyperglycemic clamp, a hyperinsulinemic-euglycemic clamp, and an oral glucose tolerance test (OGTT) in 47, 16, and 49 subjects with normal glucose tolerance (NGT), impaired glucose tolerance (IGT), and type 2 diabetes mellitus (T2DM), respectively. Mathematical analyses were retrospectively performed on this dataset. RESULTS: The disposition index (DI), defined as the product of insulin sensitivity and secretion, showed a weak correlation with blood glucose levels, especially in IGT (r = 0.04; 95% CI, -0.63 to 0.44). However, an equation relating DI, insulin clearance, and blood glucose levels was well conserved regardless of the extent of glucose intolerance. As a measure of the effect of insulin, we developed an index, designated disposition index/clearance, (DI/cle) that is based on this equation and corresponds to DI divided by the square of insulin clearance. DI/cle was not impaired in IGT compared with NGT, possibly as a result of a decrease in insulin clearance in response to a reduction in DI, whereas it was impaired in T2DM relative to IGT. Moreover, DI/cle estimated from a hyperinsulinemic-euglycemic clamp, OGTT, or a fasting blood test were significantly correlated with that estimated from 2 clamp tests (r = 0.52; 95% CI, 0.37 to 0.64, r = 0.43; 95% CI, 0.24 to 0.58, r = 0.54; 95% CI, 0.38 to 0.68, respectively). CONCLUSION: DI/cle can serve as a new indicator for the trajectory of changes in glucose tolerance.

Features extracted using tensor decomposition reflect the biological features of the temporal patterns of human blood multimodal metabolome.

High-throughput omics technologies have enabled the profiling of entire biological systems. For the biological interpretation of such omics data, two analyses, hypothesis- and data-driven analyses including tensor decomposition, have been used. Both analyses have their own advantages and disadvantages and are mutually complementary; however, a direct comparison of these two analyses for omics data is poorly examined.We applied tensor decomposition (TD) to a dataset representing changes in the concentrations of 562 blood molecules at 14 time points in 20 healthy human subjects after ingestion of 75 g oral glucose. We characterized each molecule by individual dependence (constant or variable) and time dependence (later peak or early peak). Three of the four features extracted by TD were characterized by our previous hypothesis-driven study, indicating that TD can extract some of the same features obtained by hypothesis-driven analysis in a non-biased manner. In contrast to the years taken for our previous hypothesis-driven analysis, the data-driven analysis in this study took days, indicating that TD can extract biological features in a non-biased manner without the time-consuming process of hypothesis generation.

In vivo transomic analyses of glucose-responsive metabolism in skeletal muscle reveal core differences between the healthy and obese states.

Metabolic regulation in skeletal muscle is essential for blood glucose homeostasis. Obesity causes insulin resistance in skeletal muscle, leading to hyperglycemia and type 2 diabetes. In this study, we performed multiomic analysis of the skeletal muscle of wild-type (WT) and leptin-deficient obese (ob/ob) mice, and constructed regulatory transomic networks for metabolism after oral glucose administration. Our network revealed that metabolic regulation by glucose-responsive metabolites had a major effect on WT mice, especially carbohydrate metabolic pathways. By contrast, in ob/ob mice, much of the metabolic regulation by glucose-responsive metabolites was lost and metabolic regulation by glucose-responsive genes was largely increased, especially in carbohydrate and lipid metabolic pathways. We present some characteristic metabolic regulatory pathways found in central carbon, branched amino acids, and ketone body metabolism. Our transomic analysis will provide insights into how skeletal muscle responds to changes in blood glucose and how it fails to respond in obesity.

Multi-omics-based label-free metabolic flux inference reveals obesity-associated dysregulatory mechanisms in liver glucose metabolism.

Glucose homeostasis is maintained by modulation of metabolic flux. Enzymes and metabolites regulate the involved metabolic pathways. Dysregulation of glucose homeostasis is a pathological event in obesity. Analyzing metabolic pathways and the mechanisms contributing to obesity-associated dysregulation in vivo is challenging. Here, we introduce OMELET: Omics-Based Metabolic Flux Estimation without Labeling for Extended Trans-omic Analysis. OMELET uses metabolomic, proteomic, and transcriptomic data to identify relative changes in metabolic flux, and to calculate contributions of metabolites, enzymes, and transcripts to the changes in metabolic flux. By evaluating the livers of fasting ob/ob mice, we found that increased metabolic flux through gluconeogenesis resulted primarily from increased transcripts, whereas that through the pyruvate cycle resulted from both increased transcripts and changes in substrates of metabolic enzymes. With OMELET, we identified mechanisms underlying the obesity-associated dysregulation of metabolic flux in the liver.

Four features of temporal patterns characterize similarity among individuals and molecules by glucose ingestion in humans.

Oral glucose ingestion induces systemic changes of many blood metabolites related not only to glucose, but also other metabolites such as amino acids and lipids through many blood hormones. However, the detailed temporal changes in the concentrations of comprehensive metabolites and hormones over a long time by oral glucose ingestion are uncharacterized. We measured 83 metabolites and 7 hormones in 20 healthy human subjects in response to glucose ingestion. We characterized temporal patterns of blood molecules by four features: (i) the decomposability into "amplitude" and "rate" components, (ii) the similarity of temporal patterns among individuals, (iii) the relation of molecules over time among individuals, and (iv) the similarity of temporal patterns among molecules. Glucose and glucose metabolism-related hormones indicated a rapid increase, and citrulline and lipids, which indicated a rapid decrease, returned to fasting levels faster than amino acids. Compared to glucose metabolism-related molecules and lipids, amino acids showed similar temporal patterns among individuals. The four features of temporal patterns of blood molecules by oral glucose ingestion characterize the differences among individuals and among molecules.

Trans-omic analysis reveals obesity-associated dysregulation of inter-organ metabolic cycles between the liver and skeletal muscle.

Systemic metabolic homeostasis is regulated by inter-organ metabolic cycles involving multiple organs. Obesity impairs inter-organ metabolic cycles, resulting in metabolic diseases. The systemic landscape of dysregulated inter-organ metabolic cycles in obesity has yet to be explored. Here, we measured the transcriptome, proteome, and metabolome in the liver and skeletal muscle and the metabolome in blood of fasted wild-type and leptin-deficient obese (ob/ob) mice, identifying components with differential abundance and differential regulation in ob/ob mice. By constructing and evaluating the trans-omic network controlling the differences in metabolic reactions between fasted wild-type and ob/ob mice, we provided potential mechanisms of the obesity-associated dysfunctions of metabolic cycles between liver and skeletal muscle involving glucose-alanine, glucose-lactate, and ketone bodies. Our study revealed obesity-associated systemic pathological mechanisms of dysfunction of inter-organ metabolic cycles.

Transomics analysis reveals allosteric and gene regulation axes for altered hepatic glucose-responsive metabolism in obesity.

Impaired glucose tolerance associated with obesity causes postprandial hyperglycemia and can lead to type 2 diabetes. To study the differences in liver metabolism in healthy and obese states, we constructed and analyzed transomics glucose-responsive metabolic networks with layers for metabolites, expression data for metabolic enzyme genes, transcription factors, and insulin signaling proteins from the livers of healthy and obese mice. We integrated multiomics time course data from wild-type and leptin-deficient obese (ob/ob) mice after orally administered glucose. In wild-type mice, metabolic reactions were rapidly regulated within 10 min of oral glucose administration by glucose-responsive metabolites, which functioned as allosteric regulators and substrates of metabolic enzymes, and by Akt-induced changes in the expression of glucose-responsive genes encoding metabolic enzymes. In ob/ob mice, the majority of rapid regulation by glucose-responsive metabolites was absent. Instead, glucose administration produced slow changes in the expression of carbohydrate, lipid, and amino acid metabolic enzyme-encoding genes to alter metabolic reactions on a time scale of hours. Few regulatory events occurred in both healthy and obese mice. Thus, our transomics network analysis revealed that regulation of glucose-responsive liver metabolism is mediated through different mechanisms in healthy and obese states. Rapid changes in allosteric regulators and substrates and in gene expression dominate the healthy state, whereas slow changes in gene expression dominate the obese state.

A developmental checkpoint directs metabolic remodelling as a strategy against starvation in Drosophila.

Steroid hormones are crucial regulators of life-stage transitions during development in animals. However, the molecular mechanisms by which developmental transition through these stages is coupled with optimal metabolic homeostasis remains poorly understood. Here, we demonstrate through mathematical modelling and experimental validation that ecdysteroid-induced metabolic remodelling from resource consumption to conservation can be a successful life-history strategy to maximize fitness in Drosophila larvae in a fluctuating environment. Specifically, the ecdysteroid-inducible protein ImpL2 protects against hydrolysis of circulating trehalose following pupal commitment in larvae. Stored glycogen and triglycerides in the fat body are also conserved, even under fasting conditions. Moreover, pupal commitment dictates reduced energy expenditure upon starvation to maintain available resources, thus negotiating trade-offs in resource allocation at the physiological and behavioural levels. The optimal stage-specific metabolic shift elucidated by our predictive and empirical approaches reveals that Drosophila has developed a highly controlled system for ensuring robust development that may be conserved among higher-order organisms in response to intrinsic and extrinsic cues.

Single-Cell Information Analysis Reveals That Skeletal Muscles Incorporate Cell-to-Cell Variability as Information Not Noise.

Cell-to-cell variability in signal transduction in biological systems is often considered noise. However, intercellular variation (i.e., cell-to-cell variability) has the potential to enable individual cells to encode different information. Here, we show that intercellular variation increases information transmission of skeletal muscle. We analyze the responses of multiple cultured myotubes or isolated skeletal muscle fibers as a multiple-cell channel composed of single-cell channels. We find that the multiple-cell channel, which incorporates intercellular variation as information, not noise, transmitted more information in the presence of intercellular variation than in the absence according to the "response diversity effect," increasing in the gradualness of dose response by summing the cell-to-cell variable dose responses. We quantify the information transmission of human facial muscle contraction during intraoperative neurophysiological monitoring and find that information transmission of muscle contraction is comparable to that of a multiple-cell channel. Thus, our data indicate that intercellular variation can increase the information capacity of tissues.

Quantitative Analysis of 3D Tissue Deformation Reveals Key Cellular Mechanism Associated with Initial Heart Looping.

Despite extensive study, the morphogenetic mechanisms of heart looping remain controversial because of a lack of information concerning precise tissue-level deformation and the quantitative relationship between tissue and cellular dynamics; this lack of information causes difficulties in evaluating previously proposed models. To overcome these limitations, we perform four-dimensional (4D) high-resolution imaging to reconstruct a tissue deformation map, which reveals that, at the tissue scale, initial heart looping is achieved by left-right (LR) asymmetry in the direction of deformation within the myocardial tube. We further identify F-actin-dependent directional cell rearrangement in the right myocardium as a major contributor to LR asymmetric tissue deformation. Our findings demonstrate that heart looping involves dynamic and intrinsic cellular behaviors within the tubular tissue and provide a significantly different viewpoint from current models that are based on LR asymmetry of growth and/or stress at the tube boundaries. Finally, we propose a minimally sufficient model for initial heart looping that is also supported by mechanical simulations.

Curved surface geometry-induced topological change of an excitable planar wavefront.

On the curved surfaces of living and nonliving materials, planar excitable wavefronts frequently exhibit a directional change and subsequently undergo a discontinuous (topological) change; i.e., a series of wavefront dynamics from collision, annihilation to splitting. Theoretical studies have shown that excitable planar stable waves change their topology significantly depending on the initial conditions on flat surfaces, whereas the directional change of the waves occurs based on the geometry of curved surfaces. However, it is not clear if the geometry of curved surfaces induces this topological change. In this study, we first demonstrated that the curved surface geometry induces bending, collision, and splitting of a planar stable wavefront by numerically solving an excitable reaction-diffusion equation on a bell-shaped surface. We determined two necessary conditions for inducing the topological change: the characteristic length of the curved surface (i.e., the height of the bell-shaped structure) should be greater than the width of the wave, and the ratio of the height to the width of the bell shape should be greater than a threshold. As for the geometrical mechanism of the latter, we found that a bifurcation of the geodesics on the curved surface provides the alternative minimal paths of the wavefront, which circumvent the surface region with a high local curvature, thereby resulting in the topological change. These conditions imply that the topological change of the wavefront can be predicted on the basis of the curved surfaces, whose structures are larger than the wave width.

Optimal Scaling of Critical Size for Metamorphosis in the Genus Drosophila.

Juveniles must reach a critical body size to become a mature adult. Molecular determinants of critical size have been studied, but the evolutionary importance of critical size is still unclear. Here, using nine fly species, we show that interspecific variation in organism size can be explained solely by species-specific critical size. The observed variation in critical size quantitatively agrees with the interspecific scaling relationship predicted by the life history model, which hypothesizes that critical size mediates an energy allocation switch between juvenile and adult tissues. The mechanism underlying critical size scaling is explained by an inverse relationship between growth duration and growth rate, which cancels out their contributions to the final size. Finally, we show that evolutionary changes in growth duration can be traced back to the scaling of ecdysteroid hormone dynamics. We conclude that critical size adaptively optimizes energy allocation, and has a central role in organism size determination.

Variant PRC1 competes with retinoic acid-related signals to repress Meis2 in the mouse distal forelimb bud.

Suppression of Meis genes in the distal limb bud is required for proximal-distal (PD) specification of the forelimb. Polycomb group (PcG) factors play a role in downregulation of retinoic acid (RA)-related signals in the distal forelimb bud, causing Meis repression. It is, however, not known whether downregulation of RA-related signals and PcG-mediated proximal gene repression are functionally linked. Here, we reveal that PcG factors and RA-related signals antagonize each other to polarize Meis2 expression along the PD axis in mouse. Supported by mathematical modeling and simulation, we propose that PcG factors are required to adjust the threshold for RA-related signaling to regulate Meis2 expression. Finally, we show that a variant Polycomb repressive complex 1 (PRC1), incorporating PCGF3 and PCGF5, represses Meis2 expression in the distal limb bud. Taken together, we reveal a previously unknown link between PcG proteins and downregulation of RA-related signals to mediate the phase transition of Meis2 transcriptional status during forelimb patterning.

Reconstructing 3D deformation dynamics for curved epithelial sheet morphogenesis from positional data of sparsely-labeled cells.

Quantifying global tissue deformation patterns is essential for understanding how organ-specific morphology is generated during development and regeneration. However, due to imaging difficulties and complex morphology, little is known about deformation dynamics for most vertebrate organs such as the brain and heart. To better understand these dynamics, we propose a method to precisely reconstruct global deformation patterns for three-dimensional morphogenesis of curved epithelial sheets using positional data from labeled cells representing only 1-10% of the entire tissue with limited resolution. By combining differential-geometrical and Bayesian frameworks, the method is applicable to any morphology described with arbitrary coordinates, and ensures the feasibility of analyzing many vertebrate organs. Application to data from chick forebrain morphogenesis demonstrates that our method provides not only a quantitative description of tissue deformation dynamics but also predictions of the mechanisms that determine organ-specific morphology, which could form the basis for the multi-scale understanding of organ morphogenesis.Quantifying deformation patterns of curved epithelial sheets is challenging owing to imaging difficulties. Here the authors develop a method to obtain a quantitative description of 3D tissue deformation dynamics from a small set of cell positional data and applied it to chick forebrain morphogenesis.

Adaptive significance of critical weight for metamorphosis in holometabolous insects.

Holometabolous insect larvae become committed to metamorphosis when they reach a critical weight. Although the physiological mechanisms involved in this process have been well-studied, the adaptive significance of the critical weight remains unclear. Here, we developed a life history model for holometabolous insects and evaluated it from the viewpoint of optimal energy allocation. We found that, without a priori assumptions about critical weight, the optimal growth schedule is always biphasic: larval tissues grow predominately until they reach a certain threshold, after which the imaginal tissues begin rapid growth, suggesting that the emergence of a critical weight as a phase-transition point is a natural consequence of optimal growth scheduling. Our model predicts the optimal timing of critical-weight attainment, in agreement with observations in phylogenetically-distinct species. Furthermore, it also predicts the scaling of growth scheduling against environmental change, i.e., the relative value and timing of the critical weight should be constant, thus providing a general interpretation of observed phenotypic plasticity. This scaling relationship allows the classification of adaptive responses in critical weight into five possible types that reflect the ecological features of focal insects. In this manner, our theory and its consistency with experimental observations demonstrate the adaptive significance of critical weight.

Cellular sensory mechanisms for detecting specific fold-changes in extracellular cues.

Cellular sensory systems often respond not to the absolute levels of inputs but to the fold-changes in inputs. Such a property is called fold-change detection (FCD) and is important for accurately sensing dynamic changes in environmental signals in the presence of fluctuations in their absolute levels. Previous studies defined FCD as input-scale invariance and proposed several biochemical models that achieve such a condition. Here, we prove that the previous FCD models can be approximated by a log-differentiator. Although the log-differentiator satisfies the input-scale invariance requirement, its response amplitude and response duration strongly depend on the input timescale. This creates limitations in the specificity and repeatability of detecting fold-changes in inputs. Nevertheless, FCD with specificity and repeatability by cells has been reported in the context of Drosophila wing development. Motivated by this fact and by extending previous FCD models, we here propose two possible mechanisms to achieve FCD with specificity and repeatability. One is the integrate-and-fire type: a system integrates the rate of temporal change in input and makes a response when the integrated value reaches a constant threshold, and this is followed by the reset of the integrated value. The other is the dynamic threshold type: a system response occurs when the input level reaches a threshold, whose value is multiplied by a certain constant after each response. These two mechanisms can be implemented biochemically by appropriately combining feed-forward and feedback loops. The main difference between the two models is their memory of input history; we discuss possible ways to distinguish between the two models experimentally.

Systems approach to developmental biology--designs for robust patterning.

Patterning is an important step in animal development that generates spatially non-uniform gene expression patterns or spatially heterogeneous cellular responses. Patterning is realised by the generation and reading of positional information provided by spatial gradients of morphogens, diffusive chemicals in the extracellular environment. To achieve normal development, accurate patterning that is robust against noise is necessary. Here the authors describe how morphogen gradient formation and gradient interpretation processes are designed to achieve highly reproducible patterning. Furthermore, recent advancements in measurement and imaging techniques have enabled researchers to obtain quantitative dynamic and multi-physical data, not only for chemical events, but also for the geometrical and mechanical properties of cells in vivo. The authors briefly review some recent studies on the effects of such non-chemical events on patterning.

Encoding and decoding of positional information in morphogen-dependent patterning.

Patterning during organogenesis is fundamentally realized through the interpretation of morphogen gradients by particular types of gene regulatory networks (GRNs). However, as quantitative studies have reported, spatial profiles of morphogen gradients include intra-embryo and inter-embryo variability, which could lead to errors in spatial recognition by cells and variations in patterning. By mathematically modeling the processes of generation and readout of spatial information - information encoding and decoding, by an analogy to computer communication - and maximizing the reproducibility of patterning against noise, the general designs of gradient profiles and their interpretation have been clarified. Furthermore, over the past few years, basic studies on patterning in more dynamic situations, that is, patterning in growing tissues with time-variant gradients, have been initiated. Here we provide an overview of patterning studies, pattern generating GRNs, concepts of information coding design for robust patterning, and patterning in growing tissues.