Model-Based Quantification of the Systemic Interplay between Glucose and Fatty Acids in the Postprandial State

Quantifying the contribution of triglycerides to metabolic resilience through the mixed meal model

Despite the pivotal role played by elevated circulating triglyceride levels in the pathophysiology of cardio-metabolic diseases many of the indices used to quantify metabolic health focus on deviations in glucose and insulin alone. We present the Mixed Meal Model, a computational model describing the systemic interplay between triglycerides, free fatty acids, glucose, and insulin. We show that the Mixed Meal Model can capture deviations in the post-meal excursions of plasma glucose, insulin, and triglyceride that are indicative of features of metabolic resilience; quantifying insulin resistance and liver fat; validated by comparison to gold-standard measures. We also demonstrate that the Mixed Meal Model is generalizable, applying it to meals with diverse macro-nutrient compositions. In this way, by coupling triglycerides to the glucose-insulin system the Mixed Meal Model provides a more holistic assessment of metabolic resilience from meal response data, quantifying pre-clinical metabolic deteriorations that drive disease development in overweight and obesity.

Digital twin predicting diet response before and after long-term fasting

Today, there is great interest in diets proposing new combinations of macronutrient compositions and fasting schedules. Unfortunately, there is little consensus regarding the impact of these different diets, since available studies measure different sets of variables in different populations, thus only providing partial, non-connected insights. We lack an approach for integrating all such partial insights into a useful and interconnected big picture. Herein, we present such an integrating tool. The tool uses a novel mathematical model that describes mechanisms regulating diet response and fasting metabolic fluxes, both for organ-organ crosstalk, and inside the liver. The tool can mechanistically explain and integrate data from several clinical studies, and correctly predict new independent data, including data from a new study. Using this model, we can predict non-measured variables, e.g. hepatic glycogen and gluconeogenesis, in response to fasting and different diets. Furthermore, we exemplify how such metabolic responses can be successfully adapted to a specific individual’s sex, weight, height, as well as to the individual’s historical data on metabolite dynamics. This tool enables an offline digital twin technology.

Fasting and diet are central components of prevention against cardiovascular disease. Unfortunately, there is little consensus regarding which diet schemes are optimal. This is partially because different clinical studies contribute with different non-connected pieces of knowledge, which have not been fully integrated into a useful and interconnected big picture. In principle, mathematical models describing meal responses could be used for such an integration. However, today’s models still lack critical mechanisms, such as protein metabolism and a dynamic glycogen regulation. Herein, we present a) a new expanded model structure including these mechanisms; b) a set of parameters which can simultaneously describe a wide array of complementary estimation data, in both healthy and diabetic populations; c) a personalisation-script, which allows these generic parameters to be tuned to an individual/sub-population, using demographics (age, weight, height, diabetes status) and historic metabolic data. We exemplify how this personalisation can be used to predict new independent data, including a new clinical study, where a qualitatively new prediction is validated: that an oral protein tolerance test gives a clear response in plasma glucose, after, but not before, a 48h fasting period. Our combined model, parameters, and fitting script lay the foundation for an offline digital twin.

A systems biology analysis of lipolysis and fatty acid release from adipocytes in vitro and from adipose tissue in vivo

Lipolysis and the release of fatty acids to supply energy fuel to other organs, such as between meals, during exercise, and starvation, are fundamental functions of the adipose tissue. The intracellular lipolytic pathway in adipocytes is activated by adrenaline and noradrenaline, and inhibited by insulin. Circulating fatty acids are elevated in type 2 diabetic individuals. The mechanisms behind this elevation are not fully known, and to increase the knowledge a link between the systemic circulation and intracellular lipolysis is key. However, data on lipolysis and knowledge from in vitro systems have not been linked to corresponding in vivo data and knowledge in vivo. Here, we use mathematical modelling to provide such a link. We examine mechanisms of insulin action by combining in vivo and in vitro data into an integrated mathematical model that can explain all data. Furthermore, the model can describe independent data not used for training the model. We show the usefulness of the model by simulating new and more challenging experimental setups in silico, e.g. the extracellular concentration of fatty acids during an insulin clamp, and the difference in such simulations between individuals with and without type 2 diabetes. Our work provides a new platform for model-based analysis of adipose tissue lipolysis, under both non-diabetic and type 2 diabetic conditions.

An Updated Organ-Based Multi-Level Model for Glucose Homeostasis: Organ Distributions, Timing, and Impact of Blood Flow

Glucose homeostasis is the tight control of glucose in the blood. This complex control is important, due to its malfunction in serious diseases like diabetes, and not yet sufficiently understood. Due to the involvement of numerous organs and sub-systems, each with their own intra-cellular control, we have developed a multi-level mathematical model, for glucose homeostasis, which integrates a variety of data. Over the last 10 years, this model has been used to insert new insights from the intra-cellular level into the larger whole-body perspective. However, the original cell-organ-body translation has during these years never been updated, despite several critical shortcomings, which also have not been resolved by other modeling efforts. For this reason, we here present an updated multi-level model. This model provides a more accurate sub-division of how much glucose is being taken up by the different organs. Unlike the original model, we now also account for the different dynamics seen in the different organs. The new model also incorporates the central impact of blood flow on insulin-stimulated glucose uptake. Each new improvement is clear upon visual inspection, and they are also supported by statistical tests. The final multi-level model describes >300 data points in >40 time-series and dose-response curves, resulting from a large variety of perturbations, describing both intra-cellular processes, organ fluxes, and whole-body meal responses. We hope that this model will serve as an improved basis for future data integration, useful for research and drug developments within diabetes.

A computational model of postprandial adipose tissue lipid metabolism derived using human arteriovenous stable isotope tracer data

Given the association of disturbances in non-esterified fatty acid (NEFA) metabolism with the development of Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, computational models of glucose-insulin dynamics have been extended to account for the interplay with NEFA. In this study, we use arteriovenous measurement across the subcutaneous adipose tissue during a mixed meal challenge test to evaluate the performance and underlying assumptions of three existing models of adipose tissue metabolism and construct a new, refined model of adipose tissue metabolism. Our model introduces new terms, explicitly accounting for the conversion of glucose to glyceraldehye-3-phosphate, the postprandial influx of glycerol into the adipose tissue, and several physiologically relevant delays in insulin signalling in order to better describe the measured adipose tissues fluxes. We then applied our refined model to human adipose tissue flux data collected before and after a diet intervention as part of the Yoyo study, to quantify the effects of caloric restriction on postprandial adipose tissue metabolism. Significant increases were observed in the model parameters describing the rate of uptake and release of both glycerol and NEFA. Additionally, decreases in the model's delay in insulin signalling parameters indicates there is an improvement in adipose tissue insulin sensitivity following caloric restriction.

Two nights of recovery sleep restores the dynamic lipemic response, but not the reduction of insulin sensitivity, induced by five nights of sleep restriction

Chronic inadequate sleep is associated with increased risk of cardiometabolic diseases. The mechanisms involved are poorly understood but involve changes in insulin sensitivity, including within adipose tissue. The aim of this study was to assess the effects of sleep restriction on nonesterified fatty acid (NEFA) suppression profiles in response to an intravenous glucose tolerance test (IVGTT) and to assess whether 2 nights of recovery sleep (a "weekend") is sufficient to restore metabolic health. We hypothesized that sleep restriction impairs both glucose and lipid metabolism, specifically adipocyte insulin sensitivity, and the dynamic lipemic response of adipocyte NEFA release during an IVGTT. Fifteen healthy men completed an inpatient study of 3 baseline nights (10 h of time in bed/night), followed by 5 nights of 5 h of time in bed/night and 2 recovery nights (10 h of time in bed/night). IVGTTs were performed on the final day of each condition. Reductions in insulin sensitivity without a compensatory change in acute insulin response to glucose were consistent with prior studies (insulin sensitivity P = 0.002; acute insulin response to glucose P = 0.23). The disposition index was suppressed by sleep restriction and did not recover after recovery sleep (P < 0.0001 and P = 0.01, respectively). Fasting NEFAs were not different from baseline in either the restriction or recovery conditions. NEFA rebound was significantly suppressed by sleep restriction (P = 0.01) but returned to baseline values after recovery sleep. Our study indicates that sleep restriction impacts NEFA metabolism and demonstrates that 2 nights of recovery sleep may not be adequate to restore glycemic health.

In vivo and in silico dynamics of the development of Metabolic Syndrome

The Metabolic Syndrome (MetS) is a complex, multifactorial disorder that develops slowly over time presenting itself with large differences among MetS patients. We applied a systems biology approach to describe and predict the onset and progressive development of MetS, in a study that combined in vivo and in silico models. A new data-driven, physiological model (MINGLeD: Model INtegrating Glucose and Lipid Dynamics) was developed, describing glucose, lipid and cholesterol metabolism. Since classic kinetic models cannot describe slowly progressing disorders, a simulation method (ADAPT) was used to describe longitudinal dynamics and to predict metabolic concentrations and fluxes. This approach yielded a novel model that can describe long-term MetS development and progression. This model was integrated with longitudinal in vivo data that was obtained from male APOE*3-Leiden.CETP mice fed a high-fat, high-cholesterol diet for three months and that developed MetS as reflected by classical symptoms including obesity and glucose intolerance. Two distinct subgroups were identified: those who developed dyslipidemia, and those who did not. The combination of MINGLeD with ADAPT could correctly predict both phenotypes, without making any prior assumptions about changes in kinetic rates or metabolic regulation. Modeling and flux trajectory analysis revealed that differences in liver fluxes and dietary cholesterol absorption could explain this occurrence of the two different phenotypes. In individual mice with dyslipidemia dietary cholesterol absorption and hepatic turnover of metabolites, including lipid fluxes, were higher compared to those without dyslipidemia. Predicted differences were also observed in gene expression data, and consistent with the emergence of insulin resistance and hepatic steatosis, two well-known MetS co-morbidities. Whereas MINGLeD specifically models the metabolic derangements underlying MetS, the simulation method ADAPT is generic and can be applied to other diseases where dynamic modeling and longitudinal data are available.

Overexpressing cell systems are a competitive option to primary adipocytes when predicting in vivo potency of dual GPR81/GPR109A agonists

Mathematical models predicting in vivo pharmacodynamic effects from in vitro data can accelerate drug discovery, and reduce costs and animal use. However, data integration and modeling is non-trivial when more than one drug-target receptor is involved in the biological response. We modeled the inhibition of non-esterified fatty acid release by dual G-protein-coupled receptor 81/109A (GPR81/GPR109A) agonists in vivo in the rat, to estimate the in vivo EC₅₀ values for 12 different compounds. We subsequently predicted those potency estimates using EC₅₀ values obtained from concentration-response data in isolated primary adipocytes and cell systems overexpressing GPR81 or GPR109A in vitro. A simple linear regression model based on data from primary adipocytes predicted the in vivo EC₅₀ better than simple linear regression models based on in vitro data from either of the cell systems. Three models combining the data from the overexpressing cell systems were also evaluated: two piecewise linear models defining logical OR- and AND-circuits, and a multivariate linear regression model. All three models performed better than the simple linear regression model based on data from primary adipocytes. The OR-model was favored since it is likely that activation of either GPR81 or GPR109A is sufficient to deactivate the cAMP pathway, and thereby inhibit non-esterified fatty acid release. The OR-model was also able to predict the in vivo selectivity between the two receptors. Finally, the OR-model was used to predict the in vivo potency of 1651 new compounds. This work suggests that data from the overexpressing cell systems are sufficient to predict in vivo potency of GPR81/GPR109A agonists, an approach contributing to faster and leaner drug discovery.

Mathematical modeling of white adipocyte exocytosis predicts adiponectin secretion and quantifies the rates of vesicle exo- and endocytosis

Adiponectin is a hormone secreted from white adipocytes and takes part in the regulation of several metabolic processes. Although the pathophysiological importance of adiponectin has been thoroughly investigated, the mechanisms controlling its release are only partly understood. We have recently shown that adiponectin is secreted via regulated exocytosis of adiponectin-containing vesicles, that adiponectin exocytosis is stimulated by cAMP-dependent mechanisms, and that Ca²⁺ and ATP augment the cAMP-triggered secretion. However, much remains to be discovered regarding the molecular and cellular regulation of adiponectin release. Here, we have used mathematical modeling to extract detailed information contained within our previously obtained high-resolution patch-clamp time-resolved capacitance recordings to produce the first model of adiponectin exocytosis/secretion that combines all mechanistic knowledge deduced from electrophysiological experimental series. This model demonstrates that our previous understanding of the role of intracellular ATP in the control of adiponectin exocytosis needs to be revised to include an additional ATP-dependent step. Validation of the model by introduction of data of secreted adiponectin yielded a very close resemblance between the simulations and experimental results. Moreover, we could show that Ca²⁺-dependent adiponectin endocytosis contributes to the measured capacitance signal, and we were able to predict the contribution of endocytosis to the measured exocytotic rate under different experimental conditions. In conclusion, using mathematical modeling of published and newly generated data, we have obtained estimates of adiponectin exo- and endocytosis rates, and we have predicted adiponectin secretion. We believe that our model should have multiple applications in the study of metabolic processes and hormonal control thereof.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.