A unified framework for prediction of liver steatosis dynamics in response to different diet and drug interventions.

BACKGROUND & AIMS: Non-alcoholic fatty liver disease (NAFLD) is a common metabolic disorder, characterized by the accumulation of excess fat in the liver, and is a driving factor for various severe liver diseases. These multi-factorial and multi-timescale changes are observed in different clinical studies, but these studies have not been integrated into a unified framework. In this study, we aim to present such a unified framework in the form of a dynamic mathematical model. METHODS: For model training and validation, we collected data for dietary or drug-induced interventions aimed at reducing or increasing liver fat. The model was formulated using ordinary differential equations (ODEs) and the mathematical analysis, model simulation, model formulation and the model parameter estimation were all performed in MATLAB. RESULTS: Our mathematical model describes accumulation of fat in the liver and predicts changes in lipid fluxes induced by both dietary and drug interventions. The model is validated using data from a wide range of drug and dietary intervention studies and can predict both short-term (days) and long-term (weeks) changes in liver fat. Importantly, the model computes the contribution of each individual lipid flux to the total liver fat dynamics. Furthermore, the model can be combined with an established bodyweight model, to simulate even longer scenarios (years), also including the effects of insulin resistance and body weight. To help prepare for corresponding eHealth applications, we also present a way to visualize the simulated changes, using dynamically changing lipid droplets, seen in images of liver biopsies. CONCLUSION: In conclusion, we believe that the minimal model presented herein might be a useful tool for future applications, and to further integrate and understand data regarding changes in dietary and drug induced changes in ectopic TAG in the liver. With further development and validation, the minimal model could be used as a disease progression model for steatosis.

A multi-scale digital twin for adiposity-driven insulin resistance in humans: diet and drug effects.

BACKGROUND: The increased prevalence of insulin resistance is one of the major health risks in society today. Insulin resistance involves both short-term dynamics, such as altered meal responses, and long-term dynamics, such as the development of type 2 diabetes. Insulin resistance also occurs on different physiological levels, ranging from disease phenotypes to organ-organ communication and intracellular signaling. To better understand the progression of insulin resistance, an analysis method is needed that can combine different timescales and physiological levels. One such method is digital twins, consisting of combined mechanistic mathematical models. We have previously developed a model for short-term glucose homeostasis and intracellular insulin signaling, and there exist long-term weight regulation models. Herein, we combine these models into a first interconnected digital twin for the progression of insulin resistance in humans. METHODS: The model is based on ordinary differential equations representing biochemical and physiological processes, in which unknown parameters were fitted to data using a MATLAB toolbox. RESULTS: The interconnected twin correctly predicts independent data from a weight increase study, both for weight-changes, fasting plasma insulin and glucose levels, and intracellular insulin signaling. Similarly, the model can predict independent weight-change data in a weight loss study with the weight loss drug topiramate. The model can also predict non-measured variables. CONCLUSIONS: The model presented herein constitutes the basis for a new digital twin technology, which in the future could be used to aid medical pedagogy and increase motivation and compliance and thus aid in the prevention and treatment of insulin resistance.

Mathematical models disentangle the role of IL-10 feedbacks in human monocytes upon proinflammatory activation.

Inflammation is one of the vital mechanisms through which the immune system responds to harmful stimuli. During inflammation, proinflammatory and anti-inflammatory cytokines interplay to orchestrate fine-tuned and dynamic immune responses. The cytokine interplay governs switches in the inflammatory response and dictates the propagation and development of the inflammatory response. Molecular pathways underlying the interplay are complex, and time-resolved monitoring of mediators and cytokines is necessary as a basis to study them in detail. Our understanding can be advanced by mathematical models that enable to analyze the system of interactions and their dynamical interplay in detail. We, therefore, used a mathematical modeling approach to study the interplay between prominent proinflammatory and anti-inflammatory cytokines with a focus on tumor necrosis factor and interleukin 10 (IL-10) in lipopolysaccharide-primed primary human monocytes. Relevant time-resolved data were generated by experimentally adding or blocking IL-10 at different time points. The model was successfully trained and could predict independent validation data and was further used to perform simulations to disentangle the role of IL-10 feedbacks during an acute inflammatory event. We used the insight to obtain a reduced predictive model including only the necessary IL-10-mediated feedbacks. Finally, the validated reduced model was used to predict early IL-10-tumor necrosis factor switches in the inflammatory response. Overall, we gained detailed insights into fine-tuning of inflammatory responses in human monocytes and present a model for further use in studying the complex and dynamic process of cytokine-regulated acute inflammation.

A comprehensive mechanistic model of adipocyte signaling with layers of confidence.

Adipocyte signaling, normally and in type 2 diabetes, is far from fully understood. We have earlier developed detailed dynamic mathematical models for several well-studied, partially overlapping, signaling pathways in adipocytes. Still, these models only cover a fraction of the total cellular response. For a broader coverage of the response, large-scale phosphoproteomic data and systems level knowledge on protein interactions are key. However, methods to combine detailed dynamic models with large-scale data, using information about the confidence of included interactions, are lacking. We have developed a method to first establish a core model by connecting existing models of adipocyte cellular signaling for: (1) lipolysis and fatty acid release, (2) glucose uptake, and (3) the release of adiponectin. Next, we use publicly available phosphoproteome data for the insulin response in adipocytes together with prior knowledge on protein interactions, to identify phosphosites downstream of the core model. In a parallel pairwise approach with low computation time, we test whether identified phosphosites can be added to the model. We iteratively collect accepted additions into layers and continue the search for phosphosites downstream of these added layers. For the first 30 layers with the highest confidence (311 added phosphosites), the model predicts independent data well (70-90% correct), and the predictive capability gradually decreases when we add layers of decreasing confidence. In total, 57 layers (3059 phosphosites) can be added to the model with predictive ability kept. Finally, our large-scale, layered model enables dynamic simulations of systems-wide alterations in adipocytes in type 2 diabetes.

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.

A systems biology analysis of adrenergically stimulated adiponectin exocytosis in white adipocytes.

Circulating levels of the adipocyte hormone adiponectin are typically reduced in obesity, and this deficiency has been linked to metabolic diseases. It is thus important to understand the mechanisms controlling adiponectin exocytosis. This understanding is hindered by the high complexity of both the available data and the underlying signaling network. To deal with this complexity, we have previously investigated how different intracellular concentrations of Ca2+, cAMP, and ATP affect adiponectin exocytosis, using both patch-clamp recordings and systems biology mathematical modeling. Recent work has shown that adiponectin exocytosis is physiologically triggered via signaling pathways involving adrenergic ß3 receptors (ß3ARs). Therefore, we developed a mathematical model that also includes adiponectin exocytosis stimulated by extracellular epinephrine or the ß3AR agonist CL 316243. Our new model is consistent with all previous patch-clamp data as well as new data (collected from stimulations with a combination of the intracellular mediators and extracellular adrenergic stimuli) and can predict independent validation data. We used this model to perform new in silico experiments where corresponding wet lab experiments would be difficult to perform. We simulated adiponectin exocytosis in single cells in response to the reduction of ß3ARs that is observed in adipocytes from animals with obesity-induced diabetes. Finally, we used our model to investigate intracellular dynamics and to predict both cAMP levels and adiponectin release by scaling the model from single-cell to a population of cells-predictions corroborated by experimental data. Our work brings us one step closer to understanding the intricate regulation of adiponectin exocytosis.

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.

Mechanisms of a Sustained Anti-inflammatory Drug Response in Alveolar Macrophages Unraveled with Mathematical Modeling.

Both initiation and suppression of inflammation are hallmarks of the immune response. If not balanced, the inflammation may cause extensive tissue damage, which is associated with common diseases, e.g., asthma and atherosclerosis. Anti-inflammatory drugs come with side effects that may be aggravated by high and fluctuating drug concentrations. To remedy this, an anti-inflammatory drug should have an appropriate pharmacokinetic half-life or better still, a sustained anti-inflammatory drug response. However, we still lack a quantitative mechanistic understanding of such sustained effects. Here, we study the anti-inflammatory response to a common glucocorticoid drug, dexamethasone. We find a sustained response 22 hours after drug removal. With hypothesis testing using mathematical modeling, we unravel the underlying mechanism-a slow release of dexamethasone from the receptor-drug complex. The developed model is in agreement with time-resolved training and testing data and is used to simulate hypothetical treatment schemes. This work opens up for a more knowledge-driven drug development to find sustained anti-inflammatory responses and fewer side effects.

Perturbation biology links temporal protein changes to drug responses in a melanoma cell line.

Cancer cells have genetic alterations that often directly affect intracellular protein signaling processes allowing them to bypass control mechanisms for cell death, growth and division. Cancer drugs targeting these alterations often work initially, but resistance is common. Combinations of targeted drugs may overcome or prevent resistance, but their selection requires context-specific knowledge of signaling pathways including complex interactions such as feedback loops and crosstalk. To infer quantitative pathway models, we collected a rich dataset on a melanoma cell line: Following perturbation with 54 drug combinations, we measured 124 (phospho-)protein levels and phenotypic response (cell growth, apoptosis) in a time series from 10 minutes to 67 hours. From these data, we trained time-resolved mathematical models that capture molecular interactions and the coupling of molecular levels to cellular phenotype, which in turn reveal the main direct or indirect molecular responses to each drug. Systematic model simulations identified novel combinations of drugs predicted to reduce the survival of melanoma cells, with partial experimental verification. This particular application of perturbation biology demonstrates the potential impact of combining time-resolved data with modeling for the discovery of new combinations of cancer drugs.

Trigger factors in takotsubo syndrome - A systematic review of case reports.

INTRODUCTION: Takotsubo syndrome is an acute heart failure syndrome often preceded by a trigger factor of physical or emotional origin, although the proportion is unclear. The aim of the present study was to determine how common different trigger factors are in takotsubo syndrome divided by sex and age in women. MATERIAL AND METHODS: The study consisted of a systematic review of all available case reports in PubMed and Web of Science up to March 2018. Trigger factors were categorized into physical and emotional trigger factors. RESULTS: Males had to a higher degree experienced a trigger factor (92.6%) compared to females (81.9%, p < .001). Physical trigger factors were most common (67.3%). Males had to a higher degree experienced a physical trigger factor (85.7%) compared to females (63.5%, p < .001). Females ≤50 years of age had to a higher degree experienced a trigger factor (90.8%) compared to females >50 years of age (79.2%, p < .001). Additionally, females ≤50 years of age had to a higher degree experienced a physical trigger factor (75.6%) compared to females >50 years of age (59.3%, p < .01). CONCLUSION: A physical trigger factor is more common than an emotional trigger factor in takotsubo syndrome. Physical triggers includes drugs, surgery and central nervous system conditions. Furthermore, females ≤50 years of age and males more often have an evident trigger factor and it is more often physical, compared to the most common patient, a female >50 years of age.

Inhibition of FOXO1 transcription factor in primary human adipocytes mimics the insulin-resistant state of type 2 diabetes.

Type 2 diabetes is characterized by insulin resistance in the expanding adipose tissue of obesity. The insulin resistance manifests in human adipocytes as system-wide impairment of insulin signalling. An exception is the regulation of transcription factor FOXO1 (forkhead box protein O1), which is phosphorylated downstream of mTORC2 (mammalian/mechanistic target of rapamycin in complex with raptor) and is therefore not exhibiting impaired response to insulin. However, the abundance, and activity, of FOXO1 is reduced by half in adipocytes from patients with diabetes. To elucidate the effect of reduced FOXO1 activity, we here transduced human adipocytes with a dominant-negative construct of FOXO1 (DN-FOXO1). Inhibition of FOXO1 reduced the abundance of insulin receptor, glucose transporter-4, ribosomal protein S6, mTOR and raptor. Functionally, inhibition of FOXO1 induced an insulin-resistant state network-wide, a state that qualitatively and quantitatively mimicked adipocytes from patients with type 2 diabetes. In contrast, and in accordance with these effects of DN-FOXO1, overexpression of wild-type FOXO1 appeared to augment insulin signalling. We combined experimental data with mathematical modelling to show that the impaired insulin signalling in FOXO1-inhibited cells to a large extent can be explained by reduced mTORC1 activity - a mechanism that defines much of the diabetic state in human adipocytes. Our findings demonstrate that FOXO1 is critical for maintaining normal insulin signalling of human adipocytes.

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.

Systems biology reveals uncoupling beyond UCP1 in human white fat-derived beige adipocytes.

Pharmaceutical induction of metabolically active beige adipocytes in the normally energy storing white adipose tissue has potential to reduce obesity. Mitochondrial uncoupling in beige adipocytes, as in brown adipocytes, has been reported to occur via the uncoupling protein 1 (UCP1). However, several previous in vitro characterizations of human beige adipocytes have only measured UCP1 mRNA fold increase, and assumed a direct correlation with metabolic activity. Here, we provide an example of pharmaceutical induction of beige adipocytes, where increased mRNA levels of UCP1 are not translated into increased protein levels, and perform a thorough analysis of this example. We incorporate mRNA and protein levels of UCP1, time-resolved mitochondrial characterizations, and numerous perturbations, and analyze all data with a new fit-for-purpose mathematical model. The systematic analysis challenges the seemingly obvious experimental conclusion, i.e., that UCP1 is not active in the induced cells, and shows that hypothesis testing with iterative modeling and experimental work is needed to sort out the role of UCP1. The analyses demonstrate, for the first time, that the uncoupling capability of human beige adipocytes can be obtained without UCP1 activity. This finding thus opens the door to a new direction in drug discovery that targets obesity and its associated comorbidities. Furthermore, the analysis advances our understanding of how to evaluate UCP1-independent thermogenesis in human beige adipocytes.

LASSIM-A network inference toolbox for genome-wide mechanistic modeling.

Recent technological advancements have made time-resolved, quantitative, multi-omics data available for many model systems, which could be integrated for systems pharmacokinetic use. Here, we present large-scale simulation modeling (LASSIM), which is a novel mathematical tool for performing large-scale inference using mechanistically defined ordinary differential equations (ODE) for gene regulatory networks (GRNs). LASSIM integrates structural knowledge about regulatory interactions and non-linear equations with multiple steady state and dynamic response expression datasets. The rationale behind LASSIM is that biological GRNs can be simplified using a limited subset of core genes that are assumed to regulate all other gene transcription events in the network. The LASSIM method is implemented as a general-purpose toolbox using the PyGMO Python package to make the most of multicore computers and high performance clusters, and is available at https://gitlab.com/Gustafsson-lab/lassim. As a method, LASSIM works in two steps, where it first infers a non-linear ODE system of the pre-specified core gene expression. Second, LASSIM in parallel optimizes the parameters that model the regulation of peripheral genes by core system genes. We showed the usefulness of this method by applying LASSIM to infer a large-scale non-linear model of naïve Th2 cell differentiation, made possible by integrating Th2 specific bindings, time-series together with six public and six novel siRNA-mediated knock-down experiments. ChIP-seq showed significant overlap for all tested transcription factors. Next, we performed novel time-series measurements of total T-cells during differentiation towards Th2 and verified that our LASSIM model could monitor those data significantly better than comparable models that used the same Th2 bindings. In summary, the LASSIM toolbox opens the door to a new type of model-based data analysis that combines the strengths of reliable mechanistic models with truly systems-level data. We demonstrate the power of this approach by inferring a mechanistically motivated, genome-wide model of the Th2 transcription regulatory system, which plays an important role in several immune related diseases.

A systems biology analysis connects insulin receptor signaling with glucose transporter translocation in rat adipocytes.

Type 2 diabetes is characterized by insulin resistance, which arises from malfunctions in the intracellular insulin signaling network. Knowledge of the insulin signaling network is fragmented, and because of the complexity of this network, little consensus has emerged for the structure and importance of the different branches of the network. To help overcome this complexity, systems biology mathematical models have been generated for predicting both the activation of the insulin receptor (IR) and the redistribution of glucose transporter 4 (GLUT4) to the plasma membrane. Although the insulin signal transduction between IR and GLUT4 has been thoroughly studied with modeling and time-resolved data in human cells, comparable analyses in cells from commonly used model organisms such as rats and mice are lacking. Here, we combined existing data and models for rat adipocytes with new data collected for the signaling network between IR and GLUT4 to create a model also for their interconnections. To describe all data (>140 data points), the model needed three distinct pathways from IR to GLUT4: (i) via protein kinase B (PKB) and Akt substrate of 160 kDa (AS160), (ii) via an AS160-independent pathway from PKB, and (iii) via an additional pathway from IR, e.g. affecting the membrane constitution. The developed combined model could describe data not used for training the model and was used to generate predictions of the relative contributions of the pathways from IR to translocation of GLUT4. The combined model provides a systems-level understanding of insulin signaling in rat adipocytes, which, when combined with corresponding models for human adipocytes, may contribute to model-based drug development for diabetes.

Cross-talks via mTORC2 can explain enhanced activation in response to insulin in diabetic patients.

The molecular mechanisms of insulin resistance in Type 2 diabetes have been extensively studied in primary human adipocytes, and mathematical modelling has clarified the central role of attenuation of mammalian target of rapamycin (mTOR) complex 1 (mTORC1) activity in the diabetic state. Attenuation of mTORC1 in diabetes quells insulin-signalling network-wide, except for the mTOR in complex 2 (mTORC2)-catalysed phosphorylation of protein kinase B (PKB) at Ser473 (PKB-S473P), which is increased. This unique increase could potentially be explained by feedback and interbranch cross-talk signals. To examine if such mechanisms operate in adipocytes, we herein analysed data from an unbiased phosphoproteomic screen in 3T3-L1 adipocytes. Using a mathematical modelling approach, we showed that a negative signal from mTORC1-p70 S6 kinase (S6K) to rictor-mTORC2 in combination with a positive signal from PKB to SIN1-mTORC2 are compatible with the experimental data. This combined cross-branch signalling predicted an increased PKB-S473P in response to attenuation of mTORC1 - a distinguishing feature of the insulin resistant state in human adipocytes. This aspect of insulin signalling was then verified for our comprehensive model of insulin signalling in human adipocytes. Introduction of the cross-branch signals was compatible with all data for insulin signalling in human adipocytes, and the resulting model can explain all data network-wide, including the increased PKB-S473P in the diabetic state. Our approach was to first identify potential mechanisms in data from a phosphoproteomic screen in a cell line, and then verify such mechanisms in primary human cells, which demonstrates how an unbiased approach can support a direct knowledge-based study.

Systems-wide Experimental and Modeling Analysis of Insulin Signaling through Forkhead Box Protein O1 (FOXO1) in Human Adipocytes, Normally and in Type 2 Diabetes.

Insulin resistance is a major aspect of type 2 diabetes (T2D), which results from impaired insulin signaling in target cells. Signaling to regulate forkhead box protein O1 (FOXO1) may be the most important mechanism for insulin to control transcription. Despite this, little is known about how insulin regulates FOXO1 and how FOXO1 may contribute to insulin resistance in adipocytes, which are the most critical cell type in the development of insulin resistance. We report a detailed mechanistic analysis of insulin control of FOXO1 in human adipocytes obtained from non-diabetic subjects and from patients with T2D. We show that FOXO1 is mainly phosphorylated through mTORC2-mediated phosphorylation of protein kinase B at Ser(473) and that this mechanism is unperturbed in T2D. We also demonstrate a cross-talk from the MAPK branch of insulin signaling to stimulate phosphorylation of FOXO1. The cellular abundance and consequently activity of FOXO1 are halved in T2D. Interestingly, inhibition of mTORC1 with rapamycin reduces the abundance of FOXO1 to the levels in T2D. This suggests that the reduction of the concentration of FOXO1 is a consequence of attenuation of mTORC1, which defines much of the diabetic state in human adipocytes. We integrate insulin control of FOXO1 in a network-wide mathematical model of insulin signaling dynamics based on compatible data from human adipocytes. The diabetic state is network-wide explained by attenuation of an mTORC1-to-insulin receptor substrate-1 (IRS1) feedback and reduced abundances of insulin receptor, GLUT4, AS160, ribosomal protein S6, and FOXO1. The model demonstrates that attenuation of the mTORC1-to-IRS1 feedback is a major mechanism of insulin resistance in the diabetic state.

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.

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

In metabolic diseases such as Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, the systemic regulation of postprandial metabolite concentrations is disturbed. To understand this dysregulation, a quantitative and temporal understanding of systemic postprandial metabolite handling is needed. Of particular interest is the intertwined regulation of glucose and non-esterified fatty acids (NEFA), due to the association between disturbed NEFA metabolism and insulin resistance. However, postprandial glucose metabolism is characterized by a dynamic interplay of simultaneously responding regulatory mechanisms, which have proven difficult to measure directly. Therefore, we propose a mathematical modelling approach to untangle the systemic interplay between glucose and NEFA in the postprandial period. The developed model integrates data of both the perturbation of glucose metabolism by NEFA as measured under clamp conditions, and postprandial time-series of glucose, insulin, and NEFA. The model can describe independent data not used for fitting, and perturbations of NEFA metabolism result in an increased insulin, but not glucose, response, demonstrating that glucose homeostasis is maintained. Finally, the model is used to show that NEFA may mediate up to 30-45% of the postprandial increase in insulin-dependent glucose uptake at two hours after a glucose meal. In conclusion, the presented model can quantify the systemic interactions of glucose and NEFA in the postprandial state, and may therefore provide a new method to evaluate the disturbance of this interplay in metabolic disease.

Mathematical modeling improves EC50 estimations from classical dose-response curves.

UNLABELLED: The ß-adrenergic response is impaired in failing hearts. When studying ß-adrenergic function in vitro, the half-maximal effective concentration (EC50 ) is an important measure of ligand response. We previously measured the in vitro contraction force response of chicken heart tissue to increasing concentrations of adrenaline, and observed a decreasing response at high concentrations. The classical interpretation of such data is to assume a maximal response before the decrease, and to fit a sigmoid curve to the remaining data to determine EC50 . Instead, we have applied a mathematical modeling approach to interpret the full dose-response curve in a new way. The developed model predicts a non-steady-state caused by a short resting time between increased concentrations of agonist, which affect the dose-response characterization. Therefore, an improved estimate of EC50 may be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined using additional time-resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180-525 nm) is higher than the classically interpreted EC50 (46-191 nm). Mathematical modeling thus makes it possible to re-interpret previously obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible. DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database, and may be accessed at http://jjj.bio.vu.nl/database/nyman.