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

Glucose Transporters Are Key Components of the Human Glucostat

Mouse models are extensively used in metabolic studies. However, inherent differences between the species, notably their blood glucose levels, hampered data translation into clinical settings. In this study, we confirmed GLUT1 to be the predominantly expressed glucose transporter in both adult and fetal human β-cells. In comparison, GLUT2 is detected in a small yet significant subpopulation of adult β-cells and is expressed to a greater extent in fetal β-cells. Notably, GLUT1/2 expression in INS+ cells from human stem cell-derived islet-like clusters (SC-islets) exhibited a closer resemblance to that observed in fetal islets. Transplantation of primary human islets or SC-islets, but not murine islets, lowered murine blood glucose to the human glycemic range, emphasizing the critical role of β-cells in establishing species-specific glycemia. We further demonstrate the functional requirements of GLUT1 and GLUT2 in glucose uptake and insulin secretion through chemically inhibiting GLUT1 in primary islets and SC-islets and genetically disrupting GLUT2 in SC-islets. Finally, we developed a mathematical model to predict changes in glucose uptake and insulin secretion as a function of GLUT1/2 expression. Collectively, our findings illustrate the crucial roles of GLUTs in human β-cells, and identify them as key components in establishing species-specific glycemic set points.

ARTICLE HIGHLIGHTS

Achieving Occam's razor: Deep learning for optimal model reduction

All fields of science depend on mathematical models. Occam's razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can lead to incorrect estimates of model parameters from data, and thus inaccurate or ambiguous conclusions. Here, we show how deep learning can be powerfully leveraged to apply Occam's razor to model parameters. Our method, FixFit, uses a feedforward deep neural network with a bottleneck layer to characterize and predict the behavior of a given model from its input parameters. FixFit has three major benefits. First, it provides a metric to quantify the original model's degree of complexity. Second, it allows for the unique fitting of data. Third, it provides an unbiased way to discriminate between experimental hypotheses that add value versus those that do not. In three use cases, we demonstrate the broad applicability of this method across scientific domains. To validate the method using a known system, we apply FixFit to recover known composite parameters for the Kepler orbit model and a dynamic model of blood glucose regulation. In the latter, we demonstrate the ability to fit the latent parameters to real data. To illustrate how the method can be applied to less well-established fields, we use it to identify parameters for a multi-scale brain model and reduce the search space for viable candidate mechanisms.

A simplified longitudinal model for the development of Type 2 Diabetes Mellitus

Obesity and diabetes are a progressively more and more deleterious hallmark of modern, well fed societies. In order to study the potential impact of strategies designed to obviate the pathological consequences of detrimental lifestyles, a model for the development of Type 2 diabetes geared towards large population simulations would be useful. The present work introduces such a model, representing in simplified fashion the interplay between average glycemia, average insulinemia and functional beta-cell mass, and incorporating the effects of excess food intake or, conversely, of physical activity levels. Qualitative properties of the model are formally established and simulations are shown as examples of its use.

A mathematical model for ketosis-prone diabetes suggests the existence of multiple pancreatic β-cell inactivation mechanisms

Ketosis-prone diabetes mellitus (KPD) is a subtype of type 2 diabetes, which presents much like type 1 diabetes, with dramatic hyperglycemia and ketoacidosis. Although KPD patients are initially insulin-dependent, after a few months of insulin treatment, ~ 70% undergo near-normoglycemia remission and can maintain blood glucose without insulin, as in early type 2 diabetes or prediabetes. Here, we propose that these phenomena can be explained by the existence of a fast, reversible glucotoxicity process, which may exist in all people but be more pronounced in those susceptible to KPD. We develop a simple mathematical model of the pathogenesis of KPD, which incorporates this assumption, and show that it reproduces the phenomenology of KPD, including variations in the ability for patients to achieve and sustain remission. These results suggest that a variation of our model may be able to quantitatively describe variations in the course of remission among individuals with KPD.

Analysis and dynamical structure of glucose insulin glucagon system with Mittage-Leffler kernel for type I diabetes mellitus

In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.

Estimating insulin sensitivity and β-cell function from the oral glucose tolerance test: validation of a new insulin sensitivity and secretion (ISS) model

Efficient and accurate methods to estimate insulin sensitivity (SI) and β-cell function (BCF) are of great importance for studying the pathogenesis and treatment effectiveness of type 2 diabetes (T2D). Existing methods range in sensitivity, input data, and technical requirements. Oral glucose tolerance tests (OGTTs) are preferred because they are simpler and more physiological than intravenous methods. However, current analytical methods for OGTT-derived SI and BCF also range in complexity; the oral minimal models require mathematical expertise for deconvolution and fitting differential equations, and simple algebraic surrogate indices (e.g., Matsuda index, insulinogenic index) may produce unphysiological values. We developed a new insulin secretion and sensitivity (ISS) model for clinical research that provides precise and accurate estimates of SI and BCF from a standard OGTT, focusing on effectiveness, ease of implementation, and pragmatism. This model was developed by fitting a pair of differential equations to glucose and insulin without need of deconvolution or C-peptide data. This model is derived from a published model for longitudinal simulation of T2D progression that represents glucose-insulin homeostasis, including postchallenge suppression of hepatic glucose production and first- and second-phase insulin secretion. The ISS model was evaluated in three diverse cohorts across the lifespan. The new model had a strong correlation with gold-standard estimates from intravenous glucose tolerance tests and insulin clamps. The ISS model has broad applicability among diverse populations because it balances performance, fidelity, and complexity to provide a reliable phenotype of T2D risk.NEW & NOTEWORTHY The pathogenesis of type 2 diabetes (T2D) is determined by a balance between insulin sensitivity (SI) and β-cell function (BCF), which can be determined by gold standard direct measurements or estimated by fitting differential equation models to oral glucose tolerance tests (OGTTs). We propose and validate a new differential equation model that is simpler to use than current models and requires less data while maintaining good correlation and agreement with gold standards. Matlab and Python code is freely available.

Modelling remission from overweight type 2 diabetes reveals how altering advice may counter relapse

The development or remission of diet-induced overweight type 2 diabetes involves many biological changes which occur over very different timescales. Remission, defined by HbA1c<6.5%, or fasting plasma glucose concentration G<126 mg/dl, may be achieved rapidly by following weight loss guidelines. However, remission is often short-term, followed by relapse. Mathematical modelling provides a way of investigating a typical situation, in which patients are advised to lose weight and then maintain fat mass, a slow variable. Remission followed by relapse, in a modelling sense, is equivalent to changing from a remission trajectory with steady state G<126 mg/dl, to a relapse trajectory with steady state G≥126 mg/dl. Modelling predicts that a trajectory which maintains weight will be a relapse trajectory, if the fat mass chosen is too high, the threshold being dependent on the lipid to carbohydrate ratio of the diet. Modelling takes into account the effects of hepatic and pancreatic lipid on hepatic insulin sensitivity and β-cell function, respectively. This study leads to the suggestion that type 2 diabetes remission guidelines be given in terms of model parameters, not variables; that is, the patient should adhere to a given nutrition and exercise plan, rather than achieve a certain subset of variable values. The model predicts that calorie restriction, not weight loss, initiates remission from type 2 diabetes; and that advice of the form 'adhere to the diet and exercise plan' rather than 'achieve a certain weight loss' may help counter relapse.

Dynamical modeling the effect of glucagon-like peptide on glucose-insulin regulatory system based on mice experimental observation

As an emerging global epidemic, type 2 diabetes mellitus (T2DM) represents one of the leading causes of morbidity and mortality worldwide. Existing evidences demonstrated that glucagon-like peptide-1 (GLP-1) modulate the glucose regulatory system by enhancing the β-cell function. However, the detailed process of GLP-1 in glycaemic regulator for T2DM remains to be clarified. Thus, in this study, we propose an Institute of Cancer Research (ICR) mice high fat and cholesterol dietary experimental data-driven mathematical model to investigate the secretory effect of GLP-1 on the dynamics of glucose-insulin regulatory system. Specifically, we develop a mathematical model of GLP-1 dynamics as part of the interaction model of β-cell, insulin, and glucose dynamics. The parameter estimation and data fitting are in agreement with the data in mice experiments In addition, uncertainty quantification is performed to explore the possible factors that influence the pathways leading to the pathological state. Model analyses reveal that the high fat or high cholesterol diet stimulated GLP-1 plays an important role in the dynamics of glucose, insulin and β cells in short-term. These results show that enhanced GLP-1 may mitigate the dysregulation of glucose-insulin regulatory system via promoting the β cells function and stimulating secretion of insulin, which offers an in-depth insights into the mechanistic of hyperglycemia from dynamical approach and provide the theoretical basis for GLP-1 served as a potential clinical targeted drug for treatment of T2DM.

Steady solution and its stability of a mathematical model of diabetic atherosclerosis

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.

A data-driven computational model for obesity-driven diabetes onset and remission through weight loss

Obesity is a major risk factor for the development of type 2 diabetes (T2D), where a sustained weight loss may result in T2D remission in individuals with obesity. To design effective and feasible intervention strategies to prevent or reverse T2D, it is imperative to study the progression of T2D and remission together. Unfortunately, this is not possible through experimental and observational studies. To address this issue, we introduce a data-driven computational model and use human data to investigate the progression of T2D with obesity and remission through weight loss on the same timeline. We identify thresholds for the emergence of T2D and necessary conditions for remission. We explain why remission is only possible within a window of opportunity and the way that window depends on the progression history of T2D, individual's metabolic state, and calorie restrictions. These findings can help to optimize therapeutic intervention strategies for T2D prevention or treatment.

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.

A computational model of the effects of macronutrients absorption and physical exercise on hormonal regulation and metabolic homeostasis

Regular physical exercise and appropriate nutrition affect metabolic and hormonal responses and may reduce the risk of developing chronic non-communicable diseases such as high blood pressure, ischemic stroke, coronary heart disease, some types of cancer, and type 2 diabetes mellitus. Computational models describing the metabolic and hormonal changes due to the synergistic action of exercise and meal intake are, to date, scarce and mostly focussed on glucose absorption, ignoring the contribution of the other macronutrients. We here describe a model of nutrient intake, stomach emptying, and absorption of macronutrients in the gastrointestinal tract during and after the ingestion of a mixed meal, including the contribution of proteins and fats. We integrated this effort to our previous work in which we modeled the effects of a bout of physical exercise on metabolic homeostasis. We validated the computational model with reliable data from the literature. The simulations are overall physiologically consistent and helpful in describing the metabolic changes due to everyday life stimuli such as multiple mixed meals and variable periods of physical exercise over prolonged periods of time. This computational model may be used to design virtual cohorts of subjects differing in sex, age, height, weight, and fitness status, for specialized in silico challenge studies aimed at designing exercise and nutrition schemes to support health.

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so-called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs.

A simple modeling framework for prediction in the human glucose-insulin system

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

Estimating Insulin Sensitivity and Beta-Cell Function from the Oral Glucose Tolerance Test: Validation of a new Insulin Sensitivity and Secretion (ISS) Model

Efficient and accurate methods to estimate insulin sensitivity (SI) and beta-cell function (BCF) are of great importance for studying the pathogenesis and treatment effectiveness of type 2 diabetes. Many methods exist, ranging in input data and technical requirements. Oral glucose tolerance tests (OGTTs) are preferred because they are simpler and more physiological. However, current analytical methods for OGTT-derived SI and BCF also range in complexity; the oral minimal models require mathematical expertise for deconvolution and fitting differential equations, and simple algebraic models (e.g., Matsuda index, insulinogenic index) may produce unphysiological values. We developed a new ISS (Insulin Secretion and Sensitivity) model for clinical research that provides precise and accurate estimates of SI and BCF from a standard OGTT, focusing on effectiveness, ease of implementation, and pragmatism. The model was developed by fitting a pair of differential equations to glucose and insulin without need of deconvolution or C-peptide data. The model is derived from a published model for longitudinal simulation of T2D progression that represents glucose-insulin homeostasis, including post-challenge suppression of hepatic glucose production and first- and second-phase insulin secretion. The ISS model was evaluated in three diverse cohorts including individuals at high risk of prediabetes (adult women with a wide range of BMI and adolescents with obesity). The new model had strong correlation with gold-standard estimates from intravenous glucose tolerance tests and hyperinsulinemic-euglycemic clamp. The ISS model has broad clinical applicability among diverse populations because it balances performance, fidelity, and complexity to provide a reliable phenotype of T2D risk.

Benchmarking tools for a priori identifiability analysis

MOTIVATION

The theoretical possibility of determining the state and parameters of a dynamic model by measuring its outputs is given by its structural identifiability and its observability. These properties should be analysed before attempting to calibrate a model, but their a priori analysis can be challenging, requiring symbolic calculations that often have a high computational cost. In recent years, a number of software tools have been developed for this task, mostly in the systems biology community. These tools have vastly different features and capabilities, and a critical assessment of their performance is still lacking.

RESULTS

Here, we present a comprehensive study of the computational resources available for analysing structural identifiability. We consider 13 software tools developed in 7 programming languages and evaluate their performance using a set of 25 case studies created from 21 models. Our results reveal their strengths and weaknesses, provide guidelines for choosing the most appropriate tool for a given problem and highlight opportunities for future developments.

AVAILABILITY AND IMPLEMENTATION

https://github.com/Xabo-RB/Benchmarking_files.

Modeling the progression of Type 2 diabetes with underlying obesity

Environmentally induced or epigenetic-related beta-cell dysfunction and insulin resistance play a critical role in the progression to diabetes. We developed a mathematical modeling framework capable of studying the progression to diabetes incorporating various diabetogenic factors. Considering the heightened risk of beta-cell defects induced by obesity, we focused on the obesity-diabetes model to further investigate the influence of obesity on beta-cell function and glucose regulation. The model characterizes individualized glucose and insulin dynamics over the span of a lifetime. We then fit the model to the longitudinal data of the Pima Indian population, which captures both the fluctuations and long-term trends of glucose levels. As predicted, controlling or eradicating the obesity-related factor can alleviate, postpone, or even reverse diabetes. Furthermore, our results reveal that distinct abnormalities of beta-cell function and levels of insulin resistance among individuals contribute to different risks of diabetes. This study may encourage precise interventions to prevent diabetes and facilitate individualized patient treatment.

Epigenetic inheritance of gene silencing is maintained by a self-tuning mechanism based on resource competition

Biological systems can maintain memories over long timescales, with examples including memories in the brain and immune system. It is unknown how functional properties of memory systems, such as memory persistence, can be established by biological circuits. To address this question, we focus on transgenerational epigenetic inheritance in Caenorhabditis elegans. In response to a trigger, worms silence a target gene for multiple generations, resisting strong dilution due to growth and reproduction. Silencing may also be maintained indefinitely upon selection according to silencing levels. We show that these properties imply the fine-tuning of biochemical rates in which the silencing system is positioned near the transition to bistability. We demonstrate that this behavior is consistent with a generic mechanism based on competition for synthesis resources, which leads to self-organization around a critical state with broad silencing timescales. The theory makes distinct predictions and offers insights into the design principles of long-term memory systems.

The progression of secondary diabetes: A review of modeling studies

Mathematical modeling has provided quantitative information consistent with experimental data, greatly improving our understanding of the progression of type 1 and type 2 diabetes. However, diabetes is a complex metabolic disease and has been found to be involved in crosstalk interactions with diverse endocrine diseases. Mathematical models have also been developed to investigate the quantitative impact of various hormonal disorders on glucose imbalance, advancing the precision treatment for secondary diabetes. Here we review the models established for the study of dysglycemia induced by hormonal disorders, such as excessive glucocorticoids, epinephrine, and growth hormone. To investigate the influence of hyperthyroidism on the glucose regulatory system, we also propose a hyperthyroid-diabetes progression model. Model simulations indicate that timely thyroid treatment can halt the progression of hyperglycemia and prevent beta-cell failure. This highlights the diagnosis of hormonal disorders, together withblood sugar tests, as significant measures for the early diagnosis and treatment of diabetes. The work recapitulates updated biological research on the interactions between the glucose regulatory system and other endocrine axes. Further mathematical modeling of secondary diabetes is desired to promote the quantitative study of the disease and the development of individualized diabetic therapies.

Dynamics of a glucose-insulin model

Diabetes mellitus is a noncommunicable disease, which is a serious threat to human health around the world. In this paper, we propose a simple glucose-insulin model with Michaelis-Menten function as insulin degradation rate to mimic the pathogenic mechanism of diabetes. By theoretical analysis, a unique positive equilibrium of model exists and it is globally asymptotically stable. The four strategies are designed for diabetes patients based on the sensitivity of parameters, including insulin injection and medicine treatments. Numerical simulations are given to support the theoretical results.

Data assimilation on mechanistic models of glucose metabolism predicts glycemic states in adolescents following bariatric surgery

Type 2 diabetes mellitus is a complex and under-treated disorder closely intertwined with obesity. Adolescents with severe obesity and type 2 diabetes have a more aggressive disease compared to adults, with a rapid decline in pancreatic β cell function and increased incidence of comorbidities. Given the relative paucity of pharmacotherapies, bariatric surgery has become increasingly used as a therapeutic option. However, subsets of this population have sub-optimal outcomes with either inadequate weight loss or little improvement in disease. Predicting which patients will benefit from surgery is a difficult task and detailed physiological characteristics of patients who do not respond to treatment are generally unknown. Identifying physiological predictors of surgical response therefore has the potential to reveal both novel phenotypes of disease as well as therapeutic targets. We leverage data assimilation paired with mechanistic models of glucose metabolism to estimate pre-operative physiological states of bariatric surgery patients, thereby identifying latent phenotypes of impaired glucose metabolism. Specifically, maximal insulin secretion capacity, σ, and insulin sensitivity, SI, differentiate aberrations in glucose metabolism underlying an individual's disease. Using multivariable logistic regression, we combine clinical data with data assimilation to predict post-operative glycemic outcomes at 12 months. Models using data assimilation sans insulin had comparable performance to models using oral glucose tolerance test glucose and insulin. Our best performing models used data assimilation and had an area under the receiver operating characteristic curve of 0.77 (95% confidence interval 0.7665, 0.7734) and mean average precision of 0.6258 (0.6206, 0.6311). We show that data assimilation extracts knowledge from mechanistic models of glucose metabolism to infer future glycemic states from limited clinical data. This method can provide a pathway to predict long-term, post-surgical glycemic states by estimating the contributions of insulin resistance and limitations of insulin secretion to pre-operative glucose metabolism.

Integrated experimental-computational analysis of a HepaRG liver-islet microphysiological system for human-centric diabetes research

Microphysiological systems (MPS) are powerful tools for emulating human physiology and replicating disease progression in vitro. MPS could be better predictors of human outcome than current animal models, but mechanistic interpretation and in vivo extrapolation of the experimental results remain significant challenges. Here, we address these challenges using an integrated experimental-computational approach. This approach allows for in silico representation and predictions of glucose metabolism in a previously reported MPS with two organ compartments (liver and pancreas) connected in a closed loop with circulating medium. We developed a computational model describing glucose metabolism over 15 days of culture in the MPS. The model was calibrated on an experiment-specific basis using data from seven experiments, where HepaRG single-liver or liver-islet cultures were exposed to both normal and hyperglycemic conditions resembling high blood glucose levels in diabetes. The calibrated models reproduced the fast (i.e. hourly) variations in glucose and insulin observed in the MPS experiments, as well as the long-term (i.e. over weeks) decline in both glucose tolerance and insulin secretion. We also investigated the behaviour of the system under hypoglycemia by simulating this condition in silico, and the model could correctly predict the glucose and insulin responses measured in new MPS experiments. Last, we used the computational model to translate the experimental results to humans, showing good agreement with published data of the glucose response to a meal in healthy subjects. The integrated experimental-computational framework opens new avenues for future investigations toward disease mechanisms and the development of new therapies for metabolic disorders.

Microphysiological systems (MPS) are powerful tools to unravel biological knowledge underlying disease. MPS provide a physiologically relevant, human-based in vitro setting, which can potentially yield better translatability to humans than current animal models and traditional cell cultures. However, mechanistic interpretation and extrapolation of the experimental results to human outcome remain significant challenges. In this study, we confront these challenges using an integrated experimental-computational approach. We present a computational model describing glucose metabolism in a previously reported MPS integrating liver and pancreas. This MPS supports a homeostatic feedback loop between HepaRG/HHSteC spheroids and pancreatic islets, and allows for detailed investigations of mechanisms underlying type 2 diabetes in humans. We show that the computational model captures the complex dynamics of glucose-insulin regulation observed in the system, and can provide mechanistic insight into disease progression features, such as insulin resistance and β-cell dynamics. Furthermore, the computational model can explain key differences in temporal dynamics between MPS and human responses, and thus provides a tool for translating experimental insights into human outcome. The integrated experimental-computational framework opens new avenues for future investigations toward disease mechanisms and the development of new therapies for metabolic disorders.

Kinetic and data-driven modeling of pancreatic β-cell central carbon metabolism and insulin secretion

Pancreatic β-cells respond to increased extracellular glucose levels by initiating a metabolic shift. That change in metabolism is part of the process of glucose-stimulated insulin secretion and is of particular interest in the context of diabetes. However, we do not fully understand how the coordinated changes in metabolic pathways and metabolite products influence insulin secretion. In this work, we apply systems biology approaches to develop a detailed kinetic model of the intracellular central carbon metabolic pathways in pancreatic β-cells upon stimulation with high levels of glucose. The model is calibrated to published metabolomics datasets for the INS1 823/13 cell line, accurately capturing the measured metabolite fold-changes. We first employed the calibrated mechanistic model to estimate the stimulated cell's fluxome. We then used the predicted network fluxes in a data-driven approach to build a partial least squares regression model. By developing the combined kinetic and data-driven modeling framework, we gain insights into the link between β-cell metabolism and glucose-stimulated insulin secretion. The combined modeling framework was used to predict the effects of common anti-diabetic pharmacological interventions on metabolite levels, flux through the metabolic network, and insulin secretion. Our simulations reveal targets that can be modulated to enhance insulin secretion. The model is a promising tool to contextualize and extend the usefulness of metabolomics data and to predict dynamics and metabolite levels that are difficult to measure in vitro. In addition, the modeling framework can be applied to identify, explain, and assess novel and clinically-relevant interventions that may be particularly valuable in diabetes treatment.

The damage-independent evolution of ageing by selective destruction

Ageing is widely believed to reflect the accumulation of molecular damage due to energetic costs of maintenance, as proposed in disposable soma theory (DST). Here we use agent-based modelling to describe an alternative theory by which ageing could undergo positive selection independent of energetic costs. We suggest that the selective advantage of aberrant cells with fast growth might necessitate a mechanism of counterselection we name selective destruction that specifically removes the faster cells from tissues, preventing the morbidity and mortality risks they pose. The resulting survival advantage of slower mutants could switch the direction of selection, allowing them to outcompete both fast mutants and wildtype cells, causing them to spread and induce ageing in the form of a metabolic slowdown. Selective destruction could therefore provide a proximal cause of ageing that is both consistent with the gene expression hallmarks of ageing, and independent of accumulating damage. Furthermore, negligible senescence would acquire a new meaning of increased basal mortality.

Universal Minimal Model for Glucose-Insulin Relationship with the Influence of Food Dynamic

We propose a minimal model defining the relationship between glucose and insulin with the added influence of food intakes. The constructed model consists of a system of 3 nonlinear ordinary differential equations (ODEs). The solutions of our model for both normal and diabetic subjects are compared with a minimal model and a maximal model representing the same relationship. We found that the outputs of our model are similar to those from the minimal and maximal models for both normal and diabetic subjects; the R² are 0.9997 and 0.9922, respectively, when compared with the minimal model, and are 0.9995 and 0.9940, respectively, when compared with the maximal model. Moreover, the relative errors between solutions are at most 0.9035% and as low as 1.488 × 10⁻²% on average when compared with the minimal model for normal subjects and at most 1.331% and as low as 0.1159% on average for diabetic subjects. The discrepancy between our model and the maximal model are at most 1.590% and 5.453% for normal and diabetic subjects, respectively, with a relative error averaging 0.2138% and 0.9002% for normal and diabetic subjects, respectively.

A glucose-insulin-glucagon coupled model of the isoglycemic intravenous glucose infusion experiment

Type 2 diabetes (T2D) is a pathophysiology that is characterized by insulin resistance, beta- and alpha-cell dysfunction. Mathematical models of various glucose challenge experiments have been developed to quantify the contribution of insulin and beta-cell dysfunction to the pathophysiology of T2D. There is a need for effective extended models that also capture the impact of alpha-cell dysregulation on T2D. In this paper a delay differential equation-based model is developed to describe the coupled glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment. As the glucose profile in IIGI is tailored to match that of a corresponding oral glucose tolerance test (OGTT), it provides a perfect method for studying hormone responses that are in the normal physiological domain and without the confounding effect of incretins and other gut mediated factors. The model was fit to IIGI data from individuals with and without T2D. Parameters related to glucagon action, suppression, and secretion as well as measures of insulin sensitivity, and glucose stimulated response were determined simultaneously. Significant impairment in glucose dependent glucagon suppression was observed in patients with T2D (duration of T2D: 8 (6-36) months) relative to weight matched control subjects (CS) without diabetes (k1 (mM)-1: 0.16 ± 0.015 (T2D, n = 7); 0.26 ± 0.047 (CS, n = 7)). Insulin action was significantly lower in patients with T2D (a1 (10 pM min)-1: 0.000084 ± 0.0000075 (T2D); 0.00052 ± 0.00015 (CS)) and the Hill coefficient in the equation for glucose dependent insulin response was found to be significantly different in T2D patients relative to CS (h: 1.4 ± 0.15; 1.9 ± 0.14). Trends in parameters with respect to fasting plasma glucose, HbA1c and 2-h glucose values are also presented. Significantly, a negative linear relationship is observed between the glucagon suppression parameter, k1, and the three markers for diabetes and is thus indicative of the role of glucagon in exacerbating the pathophysiology of diabetes (Spearman Rank Correlation: (n = 12; (-0.79, 0.002), (-0.73,.007), (-0.86,.0003)) respectively).

Inferring Insulin Secretion Rate from Sparse Patient Glucose and Insulin Measures

The insulin secretion rate (ISR) contains information that can provide a personal, quantitative understanding of endocrine function. If the ISR can be reliably inferred from measurements, it could be used for understanding and clinically diagnosing problems with the glucose regulation system. Objective: This study aims to develop a model-based method for inferring a parametrization of the ISR and related physiological information among people with different glycemic conditions in a robust manner. The developed algorithm is applicable for both dense or sparsely sampled plasma glucose/insulin measurements, where sparseness is defined in terms of sampling time with respect to the fastest time scale of the dynamics. Methods: An algorithm for parametrizing and validating a functional form of the ISR for different compartmental models with unknown but estimable ISR function and absorption/decay rates describing the dynamics of insulin accumulation was developed. The method and modeling applies equally to c-peptide secretion rate (CSR) when c-peptide is measured. Accuracy of fit is reliant on reconstruction error of the measured trajectories, and when c-peptide is measured the relationship between CSR and ISR. The algorithm was applied to data from 17 subjects with normal glucose regulatory systems and 9 subjects with cystic fibrosis related diabetes (CFRD) in which glucose, insulin and c-peptide were measured in course of oral glucose tolerance tests (OGTT). Results: This model-based algorithm inferred parametrization of the ISR and CSR functional with relatively low reconstruction error for 12 of 17 control and 7 of 9 CFRD subjects. We demonstrate that when there are suspect measurements points, the validity of excluding them may be interrogated with this method. Significance: A new estimation method is available to infer the ISR and CSR functional profile along with plasma insulin and c-peptide absorption rates from sparse measurements of insulin, c-peptide, and plasma glucose concentrations. We propose a method to interrogate and exclude potentially erroneous OGTT measurement points based on reconstruction errors.

Dynamics of thyroid diseases and thyroid-axis gland masses

Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid-stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life-years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto's thyroiditis and Graves' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.

Reversal and Remission of T2DM - An Update for Practitioners

Over the past 50 years, many countries around the world have faced an unchecked pandemic of obesity and type 2 diabetes (T2DM). As best practice treatment of T2DM has done very little to check its growth, the pandemic of diabesity now threatens to make health-care systems economically more difficult for governments and individuals to manage within their budgets. The conventional view has been that T2DM is irreversible and progressive. However, in 2016, the World Health Organization (WHO) global report on diabetes added for the first time a section on diabetes reversal and acknowledged that it could be achieved through a number of therapeutic approaches. Many studies indicate that diabetes reversal, and possibly even long-term remission, is achievable, belying the conventional view. However, T2DM reversal is not yet a standardized area of practice and some questions remain about long-term outcomes. Diabetes reversal through diet is not articulated or discussed as a first-line target (or even goal) of treatment by any internationally recognized guidelines, which are mostly silent on the topic beyond encouraging lifestyle interventions in general. This review paper examines all the sustainable, practical, and scalable approaches to T2DM reversal, highlighting the evidence base, and serves as an interim update for practitioners looking to fill the practical knowledge gap on this topic in conventional diabetes guidelines.

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS WITH ADVANCED GLYCATION END-PRODUCTS

Atherosclerosis is a leading cause of death worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. The pathophysiology of diabetic vascular disease is generally understood. Dyslipidemia with increased levels of atherogenic LDL, hyperglycemia, oxidative stress and increased inflammation are factors that increase the risk and accelerate development of atherosclerosis. In a recent paper [53], we have developed mathematical model that includes the effect of hyperglycemia and insulin resistance on plaque growth. In this paper, we propose a more comprehensive mathematical model for diabetic atherosclerosis which include more variables; in particular it includes the variable for Advanced Glycation End-Products (AGEs)concentration. Hyperglycemia trigger vascular damage by forming AGEs, which are not easily metabolized and may accelerate the progression of vascular disease in diabetic patients. The model is given by a system of partial differential equations with a free boundary. We also establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

Beta-cell specific Insr deletion promotes insulin hypersecretion and improves glucose tolerance prior to global insulin resistance

Insulin receptor (Insr) protein is present at higher levels in pancreatic β-cells than in most other tissues, but the consequences of β-cell insulin resistance remain enigmatic. Here, we use an Ins1cre knock-in allele to delete Insr specifically in β-cells of both female and male mice. We compare experimental mice to Ins1cre-containing littermate controls at multiple ages and on multiple diets. RNA-seq of purified recombined β-cells reveals transcriptomic consequences of Insr loss, which differ between female and male mice. Action potential and calcium oscillation frequencies are increased in Insr knockout β-cells from female, but not male mice, whereas only male βInsrKO islets have reduced ATP-coupled oxygen consumption rate and reduced expression of genes involved in ATP synthesis. Female βInsrKO and βInsrHET mice exhibit elevated insulin release in ex vivo perifusion experiments, during hyperglycemic clamps, and following i.p. glucose challenge. Deletion of Insr does not alter β-cell area up to 9 months of age, nor does it impair hyperglycemia-induced proliferation. Based on our data, we adapt a mathematical model to include β-cell insulin resistance, which predicts that β-cell Insr knockout improves glucose tolerance depending on the degree of whole-body insulin resistance. Indeed, glucose tolerance is significantly improved in female βInsrKO and βInsrHET mice compared to controls at 9, 21 and 39 weeks, and also in insulin-sensitive 4-week old males. We observe no improved glucose tolerance in older male mice or in high fat diet-fed mice, corroborating the prediction that global insulin resistance obscures the effects of β-cell specific insulin resistance. The propensity for hyperinsulinemia is associated with mildly reduced fasting glucose and increased body weight. We further validate our main in vivo findings using an Ins1-CreERT transgenic line and find that male mice have improved glucose tolerance 4 weeks after tamoxifen-mediated Insr deletion. Collectively, our data show that β-cell insulin resistance in the form of reduced β-cell Insr contributes to hyperinsulinemia in the context of glucose stimulation, thereby improving glucose homeostasis in otherwise insulin sensitive sex, dietary and age contexts.

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS

Atherosclerosis is a leading cause of death in the United States and worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 21 million Americans have diabetes, a disease where patients' cells cannot efficiently take in dietary sugar, causing it to build up in the blood. In part because diabetes increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. Past work has shown that hyperglycemia and insulin resistance alter function of multiple cell types, including endothelium, smooth muscle cells and platelets, indicating the extent of vascular disarray in this disease. Although the pathophysiology of diabetic vascular disease is generally understood, there is no mathematical model to date that includes the effect of diabetes on plaque growth. In this paper, we propose a mathematical model for diabetic atherosclerosis; the model is given by a system of partial differential equations with a free boundary. We establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

Role of 14-3-3β protein on ovarian folliculogenesis, steroidogenesis and its correlation in the pathogenesis of PCOS in mice

This study was designed to assess for the first time the circulating and ovarian level of 14-3-3β protein in the PCOS mice and the possible correlation between 14-3-3β protein with PCOS related increase in testosterone (HA), insulin levels (HI) and reduced insulin sensitivity in the ovary. PCOS was induced in mice using treatment of letrozole (by oral gavage) for 21 days. Immunohistochemical study showed increased expression of 14-3-3β protein in PCOS ovary compared to the control ovary. The circulating testosterone and insulin levels, together with circulating and ovarian levels of 14-3-3β protein also showed significant increase in PCOS mice compared to the control mice. An increase in 14-3-3β protein was observed positively correlated with circulating testosterone and insulin levels but showed a negative correlation with ovarian expression of insulin receptor protein in PCOS mice. The treatment of 14-3-3β protein in vitro to the normal ovary showed a significant increase in testosterone synthesis but a significant decline in insulin receptor protein expression compared to the vehicle-treated ovary of adult mice. The present study showed the direct role of 14-3-3β protein in increasing testosterone synthesis along with decreasing insulin sensitivity. Thus, 14-3-3β protein may be playing possible role in PCOS pathogenesis.

Pharmacometrics Approaches and its Applications in Diabetes: An Overview

Type 2 diabetes mellitus is the most prevalent and progressive in nature. As the time progress, the multifaceted complications and comorbidities associated to diabetes worsen in the form of macrovascular or microvascular or both. Pharmacometrics modeling is a step forward in minimizing the risk or at least understanding the factors associated to its progression with the passage of time. These models investigate diabetes treatments effects and the progression factors with different viewpoints incorporating insulin-glucose dynamics, dose-response and pharmacokinetics, and pharmacodynamics relationships. Pharmacometrics modeling is an innovative approach in a sense that it is taking us away from the conventional analysis by providing all the opportunities in improving the decision-making in health sector. It has been suggested that we can achieve greater statistical power for determining drug effects through model-based evaluation than through traditional evaluations. The main aim of this review was to evaluate pharmacometrics approaches used in modeling diabetes progression through time and also the integrated models describing glucose-insulin dynamics.

When MINMOD Artifactually Interprets Strong Insulin Secretion as Weak Insulin Action

We address a problem with the Bergman-Cobelli Minimal Model, which has been used for 40 years to estimate S_I during an intravenous glucose tolerance test (IVGTT). During the IVGTT blood glucose and insulin concentrations are measured in response to an acute intravenous glucose load. Insulin secretion is often assessed by the area under the insulin curve during the first few minutes (Acute Insulin Response, AIR). The issue addressed here is that we have found in simulated IVGTTs, representing certain contexts, Minimal Model estimates of S_I are inversely related to AIR, resulting in artifactually lower S_I. This may apply to Minimal Model studies reporting lower S_I in Blacks than in Whites, a putative explanation for increased risk of T2D in Blacks. The hyperinsulinemic euglycemic clamp (HIEC), the reference method for assessing insulin sensitivity, by contrast generally does not show differences in insulin sensitivity between these groups. The reason for this difficulty is that glucose rises rapidly at the start of the IVGTT and reaches levels independent of S_I, whereas insulin during this time is determined by AIR. The minimal model in effect interprets this combination as low insulin sensitivity even when actual insulin sensitivity is unchanged. This happens in particular when high AIR results from increased number of readily releasable insulin granules, which may occur in Blacks. We conclude that caution should be taken when comparing estimates of S_I between Blacks and Whites.

Senescent cells and the incidence of age-related diseases

Age-related diseases such as cancer, cardiovascular disease, kidney failure, and osteoarthritis have universal features: Their incidence rises exponentially with age with a slope of 6-8% per year and decreases at very old ages. There is no conceptual model which explains these features in so many diverse diseases in terms of a single shared biological factor. Here, we develop such a model, and test it using a nationwide medical record dataset on the incidence of nearly 1000 diseases over 50 million life-years, which we provide as a resource. The model explains incidence using the accumulation of senescent cells, damaged cells that cause inflammation and reduce regeneration, whose level rise stochastically with age. The exponential rise and late drop in incidence are captured by two parameters for each disease: the susceptible fraction of the population and the threshold concentration of senescent cells that causes disease onset. We propose a physiological mechanism for the threshold concentration for several disease classes, including an etiology for diseases of unknown origin such as idiopathic pulmonary fibrosis and osteoarthritis. The model can be used to design optimal treatments that remove senescent cells, suggeting that treatment starting at old age can sharply reduce the incidence of all age-related diseases, and thus increase the healthspan.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Type 2 diabetes progression: A regulatory network approach

In order to elucidate central elements underlying type 2 diabetes, we constructed a regulatory network model involving 37 components (molecules, receptors, processes, etc.) associated to signaling pathways of pancreatic beta-cells. In a first approximation, the network topology was described by Boolean rules whose interacting dynamics predicted stationary patterns broadly classified as health, metabolic syndrome, and diabetes stages. A subsequent approximation based on a continuous logic analysis allowed us to characterize the progression of the disease as transitions between these states associated to alterations of cell homeostasis due to exhaustion or exacerbation of specific regulatory signals. The method allowed the identification of key transcription factors involved in metabolic stress as essential for the progression of the disease. Integration of the present analysis with existent mathematical models designed to yield accurate account of experimental data in human or animal essays leads to reliable predictions for beta-cell mass, insulinemia, glycemia, and glycosylated hemoglobin in diabetic fatty rats.

Type 2 diabetes: one disease, many pathways

Diabetes is a chronic, progressive disease that calls for longitudinal data and analysis. We introduce a longitudinal mathematical model that is capable of representing the metabolic state of an individual at any point in time during their progression from normal glucose tolerance to type 2 diabetes (T2D) over a period of years. As an application of the model, we account for the diversity of pathways typically followed, focusing on two extreme alternatives, one that goes through impaired fasting glucose (IFG) first and one that goes through impaired glucose tolerance (IGT) first. These two pathways are widely recognized to stem from distinct metabolic abnormalities in hepatic glucose production and peripheral glucose uptake, respectively. We confirm this but go beyond to show that IFG and IGT lie on a continuum ranging from high hepatic insulin resistance and low peripheral insulin resistance to low hepatic resistance and high peripheral resistance. We show that IFG generally incurs IGT and IGT generally incurs IFG on the way to T2D, highlighting the difference between innate and acquired defects and the need to assess patients early to determine their underlying primary impairment and appropriately target therapy. We also consider other mechanisms, showing that IFG can result from impaired insulin secretion, that non-insulin-dependent glucose uptake can also mediate or interact with these pathways, and that impaired incretin signaling can accelerate T2D progression. We consider whether hyperinsulinemia can cause insulin resistance in addition to being a response to it and suggest that this is a minor effect.

A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks

Stress activates a complex network of hormones known as the hypothalamic-pituitary-adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Prunus amygdalus extract exert antidiabetic effect via inhibition of DPP-IV: in-silico and in-vivo approaches

Prunus amygdalus (PA) is a popular invasive seed utilized in the management of diabetes in Jammu and Kashmir, India. The objective of the current study was to scrutinize the antidiabetic effect of Prunus amygdalus (PA) against Streptozotocin (STZ) induced diabetic rats and explore the possible mechanism of action at cellular and sub-cellular levels. Box Benkan Design (BBD) was performed to determine the effect of PA powder to methanol, extraction time and extraction temperature on DPPH and ABTS free radical scavenging activity of decoction. In-silico study was performed on GLUT1 (5EQG) and dipeptidyl peptidase IV (DPPIV) (2G63) protein. Type II diabetes mellitus was initiated by single intra-peritoneal injection of STZ. The Blood Glucose Level (BGL) and body weight were estimated at regular interval of time. The different biochemical parameters such as hepatic, antioxidant, and lipid parameters were estimated. At end of the study, pancreas was used for histopathological observation. The variation in DPPH antiradical scavenging activity 40.0-90.0% and ABTS antiradical scavenging activity 34-82%, were estimated respectively. STZ induced DM rats showed increased BGL at end of the experimental study. PA treatment significantly (p < 0.001) down-regulated the BGL level. PA significantly (p < 0.001) altered the biochemical, hepatic and antioxidant parameters in a dose-dependent manner. Histopathological examination demonstrated the constructive mass of β-cells in pancreas. Overall, the current study indicates that the PA treatment down-regulated the hyperglycemic, oxidative stress and hyperlipidaemia in diabetic rats, due to inhibition of enzymes or amelioration of oxidative stress. [Formula: see text] Communicated by Ramaswamy H. Sarma.

Mathematical model of diabetes and lipid metabolism linked to diet, leptin sensitivity, insulin sensitivity and VLDLTG clearance predicts paths to health and type II diabetes

An original model of diabetes linked to carbohydrate and lipid intake is presented and applied to predict the effects on biomarkers of various diets. The variables (biomarkers) are concentrations of fasting plasma glucose, insulin, leptin, glucagon, non-esterified fatty acids (NEFA) and very low density lipoprotein triglyceride (VLDLTG), as well as muscle lipids, hepatic lipids, pancreatic lipids, fat mass and mass of β-cells. The model predicts isocaloric high carbohydrate low fat (HCLF) diet and low carbohydrate high fat (LCHF) diet trajectories to health which vary in fat mass by at most a few kilograms at steady state. The LCHF trajectories to health are faster than isocaloric HCLF trajectories with respect to fat mass loss, although these trajectories may be slower initially if parameters are adjusting from HCLF values. On LC diets, leptin sensitivity and VLDLTG clearance are thought to increase. Increasing leptin sensitivity and VLDLTG clearance is predicted to lower lipids including fat mass and VLDLTG. The model predicts that changes in VLDLTG due to a change in diet happen rapidly, approaching steady state values after a few weeks, reflecting leptin sensitivity and VLDLTG clearance which are much harder to measure. The model predicts that if only insulin sensitivity increases on a LC diet, steady state fat mass would increase slightly. If leptin and insulin sensitivities increase concurrently, the combined effect could be a decrease in fat mass, consistent with the fact that increasing insulin sensitivity is often associated with fat mass loss in trials. The model predicts trajectories to fat type II diabetes with hypertriglyceridemia due to high carbohydrate moderate fat diets, on which insulin rises before falling, as ectopic fat deposits increase; made fatter and more diabetic by higher lipid consumption. It predicts trajectories to non-diabetic states with raised fat mass, VLDLTG and muscle, hepatic and pancreatic lipids due to moderate carbohydrate high fat diets. The model predicts paths to lean type II diabetes, on a diet of moderate energy but low β-cell replication rate or high death rate.