Insights to the minimal model of insulin secretion through a mean-field beta cell model

The present work introduces an extension of the original minimal model of second phase insulin secretion during the intravenous glucose tolerance test (IVGTT), which can provide both physiological and mathematical insights to the minimal model. The extension is named the mean-field beta cell model since it returns the average response of a large number of nonlinear secretory entities. Several secretion models have been proposed for the IVGTT, and we shall identify two fundamentally different theoretical features of these models. Both features can play a central role during the IVGTT, including the one presented in the mean-field beta cell model.     

A minimal model of non-hyperbolic enzyme and receptor kinetics

A simplified version of P.W. Kühl's Recovery Model [Biochem. J. 298 (1994) 171-180] has been developed in which the duration of the recovery phase of receptor or enzyme (macro)molecule was assumed to be a random value distributed exponentially like other model parameters. The model has been shown to retain all the properties of the original Recovery Model except for its ability to yield asymmetric dose-response curves (if plotted in semi-logarithmic scale). Due to its simplicity, the present model is applicable for routine fitting to experimental data. In enzyme kinetics, the model yields a diversity of non-hyperbolic dose-response curves both with higher and lower steepness than that of Henri-type ones. In receptor kinetics, the diversity of dose-response curves is further increased due to virtually no restraints being imposed on the efficacies of any state of the macromolecule.     

A 60 minute hyperglycemic clamp is sufficient to assess both phases of insulin secretion.

The hyperglycemic clamp is considered to be the gold standard for determining both first and second phase insulin secretion. In order to achieve a reasonable insulin plateau for the second phase, it has become common practice to clamp for 120 or even 180 minutes at 10 mM. It is unknown whether earlier insulin determinations would be sufficient to predict second phase insulin secretion. We therefore reviewed the hyperglycemic clamp data of 58 subjects with different degrees of glucose tolerance to assess whether one or more insulin concentrations determined at earlier time points of the clamp could predict second phase insulin secretion (insulin and C-peptide concentration at 120 minutes). The correlation coefficients between second-phase insulin secretion and plasma insulin or C-peptide at 60 min were 0.95 and 0.96, respectively (both p<0.00005). Averaging plasma insulin or C-peptide over 2 or more adjacent time points did not improve the correlation. In conclusion, a one-hour hyperglycemic clamp can provide the standard measurement of first phase insulin secretion plus a good approximation of second phase insulin secretion.     

A novel minimal model to describe NEFA kinetics following an intravenous glucose challenge

Dynamics of nonesterified fatty acid (NEFA) metabolism in humans requires quantification if we are to understand the etiology of such diseases as type 1 and 2 diabetes, as well as metabolic syndrome and obesity, or if we are to elucidate the mechanism of action of various interventions. We present a new compartmental model that employs the pattern of plasma glucose concentrations in healthy young adults to predict dynamic changes that occur in plasma NEFA concentrations during either a glucose-only intravenous glucose tolerance test, or an insulin-modified intravenous tolerance test, or a modified protocol during which variable-rate glucose infusions were administered to prevent plasma glucose from declining below 100 mg/dl. The model described all of the major features of NEFA response to an intravenous glucose tolerance test, including an initial latency phase, a phase during which plasma NEFA concentrations plummet to a nadir, and a rebound phase during which plasma NEFA concentrations may rise to a plateau concentration, which may be substantially higher than the initial basal NEFA concentration. This model is consistent with physiological processes and provides seven adjustable parameters that can be used to quantify NEFA production (lipolysis) and utilization (oxidation). When tested on data from the scientific literature, the range in estimated rate of lipolysis was 24-36 micromol.l(-1).min(-1) and for NEFA oxidation rate was 25-54 micromol.l(-1).min(-1). All model parameters were well identified and had coefficients of variation < 15% of their estimated values. It is concluded that this model is suitable to describe NEFA kinetics in human subjects.     

Oral glucose decreases hepatic extraction of insulin.

Peripheral venous (plasma) insulin and C-peptide concentrations were measured in eight normal subjects given oral or intravenous glucose sufficient to produce similar plasma glucose concentrations. The expected increased insulin response to oral as compared with intravenous glucose was not matched by a comparable increase in C-peptide concentration. The ratio of insulin to C-peptide concentrations doubled 30 minutes after oral glucose was given; no comparable rise was seen with intravenous glucose (p = 0.01). This finding is interpreted as evidence for decreased hepatic extraction of insulin after administration of oral glucose. Such a decrease could account for at least half of the well known difference in peripheral insulin concentrations after administration of oral as compared with intravenous glucose.     

Adaptations in pulsatile insulin secretion, hepatic insulin clearance, and beta-cell mass to age-related insulin resistance in rats

In health insulin is secreted in discrete insulin secretory bursts from pancreatic beta-cells, collectively referred to as beta-cell mass. We sought to establish the relationship between beta-cell mass, insulin secretory-burst mass, and hepatic insulin clearance over a range of age-related insulin sensitivity in adult rats. To address this, we used a novel rat model with chronically implanted portal vein catheters in which we recently established the parameters to permit deconvolution of portal vein insulin concentration profiles to measure insulin secretion and resolve its pulsatile components. In the present study, we examined total and pulsatile insulin secretion, insulin sensitivity, hepatic insulin clearance, and beta-cell mass in 35 rats aged 2-12 mo. With aging, insulin sensitivity declined, but euglycemia was sustained by an adaptive increase in fasting and glucose-stimulated insulin secretion through the mechanism of a selective augmentation of insulin pulse mass. The latter was attributable to a closely related increase in beta-cell mass (r=0.8, P<0.001). Hepatic insulin clearance increased with increasing portal vein insulin pulse amplitude, damping the delivery of insulin in the systemic circulation. In consequence, the curvilinear relationship previously reported between insulin secretion and insulin sensitivity was extended to both insulin pulse mass and beta-cell mass vs. insulin sensitivity. These data support a central role of adaptive changes in beta-cell mass to permit appropriate insulin secretion in the setting of decreasing insulin sensitivity in the aging animal. They emphasize the cooperative role of pancreatic beta-cells and the liver in regulating the secretion and delivery of insulin to the systemic circulation.     

Combinatorial insulin secretion dynamics of recombinant hepatic and enteroendocrine cells

One of the most promising cell-based therapies for combating insulin-dependent diabetes entails the use of genetically engineered non-β cells that secrete insulin in response to physiologic stimuli. A normal pancreatic β cell secretes insulin in a biphasic manner in response to glucose. The first phase is characterized by a transient stimulation of insulin to rapidly lower the blood glucose levels, which is followed by a second phase of insulin secretion to sustain the lowered blood glucose levels over a longer period of time. Previous studies have demonstrated hepatic and enteroendocrine cells to be appropriate hosts for recombinant insulin expression. Due to different insulin secretion kinetics from these cells, we hypothesized that a combination of the two cell types would mimic the biphasic insulin secretion of normal β cells with higher fidelity than either cell type alone. In this study, insulin secretion experiments were conducted with two hepatic cell lines (HepG2 and H4IIE) transduced with 1 of 3 adenoviruses expressing the insulin transgene and with a stably transfected recombinant intestinal cell line (GLUTag-INS). Insulin secretion was stimulated by exposing the cells to glucose only (hepatic cells), meat hydrolysate only (GLUTag-INS), or to a cocktail of the two secretagogues. It was found experimentally that the recombinant hepatic cells secreted insulin in a more sustained manner, whereas the recombinant intestinal cell line exhibited rapid insulin secretion kinetics upon stimulation. The insulin secretion profiles were computationally combined at different cell ratios to arrive at the combinatorial kinetics. Results indicate that combinations of these two cell types allow for tuning the first and second phase of insulin secretion better than either cell type alone. This work provides the basic framework in understanding the secretion kinetics of the combined system and advances it towards preclinical studies.     

A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes

Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta-cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta-cell mass (positive feedback). The model predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia).     

Glucose-stimulated insulin secretion suppresses hepatic triglyceride-rich lipoprotein and apoB production

The current study assessed in vivo the effect of insulin on triglyceride-rich lipoprotein (TRL) production by rat liver. Hepatic triglyceride and apolipoprotein B (apoB) production were measured in anesthetized, fasted rats injected intravenously with Triton WR-1339 (400 mg/kg). After intravascular catabolism was blocked by detergent treatment, glucose (500 mg/kg) was injected to elicit insulin secretion, and serum triglyceride and apoB accumulation were monitored over the next 3 h. In glucose-injected rats, triglyceride secretion averaged 22.5 +/- 2.1 microg.ml(-1).min(-1), which was significantly less by 30% than that observed in saline-injected rats, which averaged 32.1 +/- 1.4 microg.ml(-1).min(-1). ApoB secretion was also significantly reduced by 66% in glucose-injected rats. ApoB immunoblotting indicated that both B100 and B48 production were significantly reduced after glucose injection. Results support the conclusion that insulin acts in vivo to suppress hepatic very low density lipoprotein (VLDL) triglyceride and apoB secretion and strengthen the concept of a regulatory role for insulin in VLDL metabolism postprandially.     

A minimal model for hepatic fatty acid balance during fasting: Application to PPAR alpha-deficient mice

The purpose of this study is to identify the hierarchy of importance amongst pathways involved in fatty acid (FA) metabolism and their regulators in the control of hepatic FA composition. A modeling approach was applied to experimental data obtained during fasting in PPARα knockout (KO) mice and wild-type mice. A step-by-step procedure was used in which a very simple model was completed by additional pathways until the model fitted correctly the measured quantities of FA in the liver. The resulting model included FA uptake by the liver, FA oxidation, elongation and desaturation of FA, which were found active in both genotypes during fasting.From the model analysis we concluded that PPARα had a strong effect on FA oxidation. There were no indications that this effect changes during the fasting period, and it was thus considered to be constant.In PPARα KO mice, FA uptake was identified as the main pathway responsible for FA variation in the liver. The models showed that FA were oxidized at a constant and small rate, whereas desaturation of FA also occurred during fasting.The latter observation was rather unexpected, but was confirmed experimentally by the measurement of delta-6-desaturase mRNA using real-time quantitative PCR (QPCR). These results confirm that mathematical models can be a useful tool in identifying new biological hypotheses and nutritional routes in metabolism.     

A mathematical model for insulin kinetics. III. Sensitivity analysis of the model

A non-linear mathematical model involving four variables and several constants incorporating beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term had been applied in earlier papers to various forms of diabetes mellitus. In this paper, we examine the response of the system to variations in the parameters and to initial conditions using sensitivity analysis. It is found that such a method leads to results that are consistent with clinical findings. Further, it is suggested that such an analysis could help in making some predictions regarding future directions in the therapy of diabetes mellitus.     

A three-dimensional microfluidized liver system to assess hepatic drug metabolism and hepatotoxicity

In this study, we propose the design and fabrication of a liver system on a chip. We first chose the most suitable three-dimensional liver-like model between cell spheroids and microtissue precursors, both based on the use of hepatocellular carcinoma cells (HepG2) to provide proof-of-concept data. Spheroids displayed high cell density but low expression of the typical hepatic biomarkers, whereas microtissue precursors showed stable viability and function over the entire culture time. The two liver-like models were compared in terms of cell viability, function, metabolism, and the P-glycoprotein 1 (P-gp) transport-protein expression with the microtissue precursors showing the best performance. Thus, we cultured them into a microfluidic biochip featured with three parallel channels shaped to mimic the hepatic sinusoids. To assess the detoxification potential of the microtissue-loaded biochip we challenged it with a model molecule (ethanol) at different concentrations and time points. Ethanol cytotoxicity was detected by a noninvasive measurement of cell viability based on cell autofluorescence. As expected, a dose-dependent decrease of albumin and urea secretion was observed in the ethanol-treated samples. We believe that the described totally human-derived platform, suitable for integration into a multiorgan microfluidic system, can provide a consistent innovative platform for drug development and toxicity studies.     

Acute activation of central GLP-1 receptors enhances hepatic insulin action and insulin secretion in high-fat-fed, insulin resistant mice

Glucagon-like peptide-1 (GLP-1) receptor knockout (Glp1r(-/-)) mice exhibit impaired hepatic insulin action. High fat (HF)-fed Glp1r(-/-) mice exhibit improved, rather than the expected impaired, hepatic insulin action. This is due to decreased lipogenic gene expression and triglyceride accumulation. The present studies overcome these secondary adaptations by acutely modulating GLP-1R action in HF-fed wild-type mice. The central GLP-1R was targeted given its role as a regulator of hepatic insulin action. We hypothesized that acute inhibition of the central GLP-1R impairs hepatic insulin action beyond the effects of HF feeding. We further hypothesized that activation of the central GLP-1R improves hepatic insulin action in HF-fed mice. Insulin action was assessed in conscious, unrestrained mice using the hyperinsulinemic euglycemic clamp. Mice received intracerebroventricular (icv) infusions of artificial cerebrospinal fluid, GLP-1, or the GLP-1R antagonist exendin-9 (Ex-9) during the clamp. Intracerebroventricular Ex-9 impaired the suppression of hepatic glucose production by insulin, whereas icv GLP-1 improved it. Neither treatment affected tissue glucose uptake. Intracerebroventricular GLP-1 enhanced activation of hepatic Akt and suppressed hypothalamic AMP-activated protein kinase. Central GLP-1R activation resulted in lower hepatic triglyceride levels but did not affect muscle, white adipose tissue, or plasma triglyceride levels during hyperinsulinemia. In response to oral but not intravenous glucose challenges, activation of the central GLP-1R improved glucose tolerance. This was associated with higher insulin levels. Inhibition of the central GLP-1R had no effect on oral or intravenous glucose tolerance. These results show that inhibition of the central GLP-1R deteriorates hepatic insulin action in HF-fed mice but does not affect whole body glucose homeostasis. Contrasting this, activation of the central GLP-1R improves glucose homeostasis in HF-fed mice by increasing insulin levels and enhancing hepatic insulin action.     

A model approach to assess diaphragmatic volume displacement

Diaphragmatic volume displacement (Vdi) is calculated from two models using measurements obtained from anteroposterior fluoroscopic images of supine anesthetized dogs. In model 1, diaphragmatic descent was treated as if it were a "piston in a cylinder." In contrast, model 2 incorporated thoracic configuration as well as inspiratory changes in rib cage diameter and diaphragm shape. In one dog, a computerized tomography reconstruction of Vdi was compared with Vdi calculated using the models. Vdi calculated from model 2 lay within 11% of the computerized tomographic value, whereas Vdi based on model 1 was 30% larger. In seven animals, radiopaque markers were sewn to the right costal diaphragm. Digitized fluoroscopic images were used to measure intermarker distance, an index of muscle shortening. For four tidal breaths per dog, in model 2 Vdi averaged 49 +/- 18% of tidal volume and was weakly correlated with costal diaphragm muscle shortening (R = 0.74). It is concluded that Vdi can be estimated from linear dimensions in the coronal plane, provided that inspiratory changes in rib cage diameter and diaphragmatic shape change are taken into account.     

Beta-cell "rest" accompanies reduced first-pass hepatic insulin extraction in the insulin-resistant, fat-fed canine model

During insulin resistance, glucose homeostasis is maintained by an increase in plasma insulin via increased secretion and/or decreased first-pass hepatic insulin extraction. However, the relative importance of insulin secretion vs. clearance to compensate for insulin resistance in obesity has yet to be determined. This study utilizes the fat-fed dog model to examine longitudinal changes in insulin secretion and first-pass hepatic insulin extraction during development of obesity and insulin resistance. Six dogs were fed an isocaloric diet with an approximately 8% increase in fat calories for 12 wk and evaluated at weeks 0, 6, and 12 for changes in 1) insulin sensitivity by euglycemic-hyperinsulinemic clamp, 2) first-pass hepatic insulin extraction by direct assessment, and 3) glucose-stimulated insulin secretory response by hyperglycemic clamp. We found that 12 wk of a fat diet increased subcutaneous and visceral fat as assessed by MR imaging. Consistent with increased body fat, the dogs exhibited a approximately 30% decrease in insulin sensitivity and fasting hyperinsulinemia. Although insulin secretion was substantially increased at week 6, beta-cell sensitivity returned to prediet levels by week 12. However, peripheral hyperinsulinemia was maintained because of a significant decrease in first-pass hepatic insulin extraction, thus maintaining hyperinsulinemia, despite changes in insulin release. Our results indicate that when obesity and insulin resistance are induced by an isocaloric, increased-fat diet, an initial increase in insulin secretion by the beta-cells is followed by a decrease in first-pass hepatic insulin extraction. This may provide a secondary physiological mechanism to preserve pancreatic beta-cell function during insulin resistance.     

Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.     

A model of glucose kinetics and their control by insulin,compartmental and noncompartmental approaches

Compartmental and noncompartmental models are used to quantify, from multiple steady-state tracer experiments, glucose kinetics and the effect of insulin upon them. Some aspects of experiment design are discussed. A physiological three-compartment model of glucose kinetics is proposed which provides a new quantitative picture of insulin control of glucose metabolism. Noncompartmental modeling is shown to have structural errors which prevent physiological insight. Compartmental models make a better use of the informational content of kinetic data, even if more demanding both in terms of modeling and computational effort and in terms of physiological thinking.     

A mathematical model of indicator extraction by the pulmonary endothelium via saturation kinetics

When a bolus containing a nonpermeating indicator and an indicator which permeates the endothelial cell membrane by a saturable process is injected into the blood flowing into the lung, the instantaneous extraction ratio curves measured in the pulmonary venous outflow are asymmetric with respect to the nonpermeating indicator curve. If the bolus contains a sufficient quantity of the permeating indicator that the capillary concentration begins to saturate the transfort mechanism, the extraction ratio curves are concave upward as well. The purpose of this study was to determine whether a mathematical model which represents endothelial extraction by Michaelis-Menten kinetics could explain the time variation in the instantaneous extraction ratio curves. The venous concentration curves were assumed to be the result of the endothelial transfort and distributed capillary input and transit times. In addition, we evaluated a method for estimating the kinetic parameters (K_m and V_max) of the saturable transfort process in such an organ. The results of simulations indicate that the important features of the data can be reproduced by the model, and that useful estimates of the kinetic parameters will be obtained from linear multiple regression analysis of the venous concentration curves if the standard deviation of the capillary input time distribution is not less than that of the capillary transit time distribution.