Insulin signaling - mathematical modeling comes of age

Insulin Signaling Pathway Model in Adipocyte Cells

BACKGROUND

Worldwide, type 2 diabetes mellitus (T2DM) is one of the most pervasive and fastgrowing disorders, bringing long-term adverse effects. T2DM arises from pancreatic β-cells deficiency to produce enough insulin or when the body cannot effectively use the insulin produced by such cells. Accordingly, early diagnosis will decrease the long-term effects and high-healthcare costs of diabetes.

OBJECTIVE

The objective is developing an integrated mathematical model of the insulin signaling network based on Brännmark's model, which can simulate the signaling events more comprehensively with the added key components.

METHODS

In this study, a thorough mathematical model of the insulin signaling network was developed by expanding the previously validated model and incorporating the glycogen synthesis module. Parameters (69 parameters) of the integrated model were evaluated by a genetic algorithm by fitting the model predictions to eighty percent of experimental data from the literature. Twenty percent of the experimental data were used to evaluate the final optimized model.

RESULTS

The time-response curves indicate that the GS phosphorylation reaches its maximum in response to 10^-7 M insulin after 4 min, while the maximum phosphorylated GSK3 is attained within ~50 min. The doseresponse curves for the GSP and GSK3 of the insulin signaling intermediaries in response to the increased concentration of insulin, after 10 min, in the input from 0-100 nM exhibits a decreasing trend, whereas an increasing trend was observed for the GS and GSK3P. The GSK and GS phosphorylation sensitivity was enhanced by increasing the initial insulin concentration level from 0.001 to 100 nM. However, the sensitivity of GSK3 to insulin concentration changes (from 0.001 to 100 nM) was 3-fold higher than GS sensitivity.

CONCLUSION

Considerably, the trends of all signaling components simulated by the expanded model shows high compatibility with experimental data (R2 ≥ 0.9), which approves the accuracy of the proposed model. The proposed mathematical model can be used in many biological systems and combined with the whole-body model of the blood glucose regulation system for a better understanding of the causes and potential treatment of type 2 diabetes. Although, this model is not a complete description of insulin signaling, yet it can make profound contributions to improvements regarding other important components and signaling branches such as epidermal growth factor (EGF) signaling, as well as signaling in other cell types in the model structure of future works.

GLUT4 On the move

Insulin rapidly stimulates GLUT4 translocation and glucose transport in fat and muscle cells. Signals from the occupied insulin receptor are translated into downstream signalling changes in serine/threonine kinases within timescales of seconds, and this is followed by delivery and accumulation of the glucose transporter GLUT4 at the plasma membrane. Kinetic studies have led to realisation that there are distinct phases of this stimulation by insulin. There is a rapid initial burst of GLUT4 delivered to the cell surface from a subcellular reservoir compartment and this is followed by a steady-state level of continuing stimulation in which GLUT4 recycles through a large itinerary of subcellular locations. Here, we provide an overview of the phases of insulin stimulation of GLUT4 translocation and the molecules that are currently considered to activate these trafficking steps. Furthermore, we suggest how use of new experimental approaches together with phospho-proteomic data may help to further identify mechanisms for activation of these trafficking processes.

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.

Dynamic modelling of the PI3K/MTOR signalling network uncovers biphasic dependence of mTORC1 activity on the mTORC2 subunit SIN1

The PI3K/MTOR signalling network regulates a broad array of critical cellular processes, including cell growth, metabolism and autophagy. The mechanistic target of rapamycin (MTOR) kinase functions as a core catalytic subunit in two physically and functionally distinct complexes mTORC1 and mTORC2, which also share other common components including MLST8 (also known as GβL) and DEPTOR. Despite intensive research, how mTORC1 and 2 assembly and activity are coordinated, and how they are functionally linked remain to be fully characterized. This is due in part to the complex network wiring, featuring multiple feedback loops and intricate post-translational modifications. Here, we integrate predictive network modelling, in vitro experiments and -omics data analysis to elucidate the emergent dynamic behaviour of the PI3K/MTOR network. We construct new mechanistic models that encapsulate critical mechanistic details, including mTORC1/2 coordination by MLST8 (de)ubiquitination and the Akt-to-mTORC2 positive feedback loop. Model simulations validated by experimental studies revealed a previously unknown biphasic, threshold-gated dependence of mTORC1 activity on the key mTORC2 subunit SIN1, which is robust against cell-to-cell variation in protein expression. In addition, our integrative analysis demonstrates that ubiquitination of MLST8, which is reversed by OTUD7B, is regulated by IRS1/2. Our results further support the essential role of MLST8 in enabling both mTORC1 and 2’s activity and suggest MLST8 as a viable therapeutic target in breast cancer. Overall, our study reports a new mechanistic model of PI3K/MTOR signalling incorporating MLST8-mediated mTORC1/2 formation and unveils a novel regulatory linkage between mTORC1 and mTORC2.

Signalling networks are the key information-processing machineries that underpin the ability of living cells to respond proportionately to extra- (and intra-) cellular cues. The PI3K/MTOR signalling network is one of the most important signalling networks in human cells that regulates cellular response to critical hormones such as insulin; yet our understanding of the network behaviour remains far from complete. Here, we employed a highly integrative approach that combines predictive mathematical modelling, biological experimentation, and data analysis to gain novel systems-level insights into PI3K/MTOR signalling. We constructed new mathematical models of this complex network incorporating important regulatory mechanisms. In contrary to commonly-held views that mTORC2 lies upstream and is a positive regulator of mTORC1, we found that their relationship is highly non-linear and dose dependent. This finding has major implications for anti-mTORC2 therapy as depending on the cellular contexts, inhibiting mTORC2 may either reduce or enhance mTORC1 activation, the latter could inadvertently dampen the effect of mTORC2 blockade. Furthermore, our results demonstrate that MLST8 is required for the assembly and activity of both MTOR complexes and suggest MLST8 is a viable therapeutic target in breast cancer.

Akt phosphorylates insulin receptor substrate to limit PI3K-mediated PIP3 synthesis

The phosphoinositide 3-kinase (PI3K)-Akt network is tightly controlled by feedback mechanisms that regulate signal flow and ensure signal fidelity. A rapid overshoot in insulin-stimulated recruitment of Akt to the plasma membrane has previously been reported, which is indicative of negative feedback operating on acute timescales. Here, we show that Akt itself engages this negative feedback by phosphorylating insulin receptor substrate (IRS) 1 and 2 on a number of residues. Phosphorylation results in the depletion of plasma membrane-localised IRS1/2, reducing the pool available for interaction with the insulin receptor. Together these events limit plasma membrane-associated PI3K and phosphatidylinositol (3,4,5)-trisphosphate (PIP3) synthesis. We identified two Akt-dependent phosphorylation sites in IRS2 at S306 (S303 in mouse) and S577 (S573 in mouse) that are key drivers of this negative feedback. These findings establish a novel mechanism by which the kinase Akt acutely controls PIP3 abundance, through post-translational modification of the IRS scaffold.

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.

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.

Cardiometabolic profile of non-functioning and autonomous cortisol-secreting adrenal incidentalomas. Is the cardiometabolic risk similar or are there differences?

OBJECTIVE

To study the differences in the cardiometabolic profile between patients with non-functioning adrenal incidentalomas (NFAI) and incidentalomas with autonomous cortisol secretion (ACS).

METHODS

A total of 149 patients with adrenal incidentalomas were retrospectively evaluated and followed-up for a mean time of 34.6 months at Departments of Endocrinology and Metabolic Diseases Units of four tertiary Spanish hospitals. Patients were grouped as NFAI or ACS adenomas based on two cutoffs in the dexamethasone suppression test (DST): 3.0 µg/dl (NFAI_DST3 or ACS_DST3) and 1.8 µg/dl (ACS_DST1.8 and NFAI_DST1.8).

RESULTS

The mean age of both groups was 62.0 (10.31) and was similar in ACS and NFAI. The prevalence of diabetes, high blood pressure, cardiovascular, and cerebrovascular disease was higher in ACS than in NFAI, but differences only reached statistical significance for cerebrovascular disease using the 3.0 µg/dl cutoff (15.8% vs 2.3%, p = 0.01) and for diabetes using the 1.8 µg/dl cutoff (38.0% vs 22.0%, p = 0.04). No differences were found in the prevalence of dyslipidemia. The prevalence of obesity was lower in patients with ACS than in NFAI 26.3% vs 39.2%, p = 0.18 (NFAI_DST3 vs ACS_DST3) and 32.1% vs 40.6%, p = 0.56 (ACS_DST1.8 vs NFAI_DST1.8), but the differences did not reach statistical significance. Maximum adenoma diameter (R-squared = 0.15, p < 0.001) and cerebrovascular disease (OR = 1.59, p = 0.04) were the only parameters that could be predicted by the DST. The DST was an inadequate predictor of clinical (systolic and diastolic blood pressure, body mass index), hormonal (DHEAS, ACTH, UFC, and basal serum cortisol), biochemical (glucose, cholesterol, LDL, HDL, and triglycerides), and other radiological (laterality, lipid content) parameters. Throughout the follow-up, patients did not develop overt Cushing's Syndrome; three NFAI_DST3 developed ACS_DST3, eight NFAI_DST1.8 developed ACS_DST1.8, and one NFAI_DST1.8 progressed to ACS_DST3. In both groups (NFAI and ACS) the metabolic profile remained stable.

CONCLUSIONS

Our data suggest higher prevalence of diabetes and cerebrovascular disease in ACS patients compared with NFAI. However, probably because of the small sample size, the differences only reached statistical significance using the cutoffs of 1.8 µg/dl for diabetes and 3.0 µg/dl for cerebrovascular disease. Patients with ACS and NFAI rarely progress to more aggressive forms of hypercortisolism, and the metabolic profile usually remains stable during the follow-up.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Insulin resistance and adrenal incidentalomas: A bidirectional relationship

An adrenal incidentaloma (AI) is an adrenal mass incidentally found via a radiological modality, independent of an endocrinological investigation. In this review, we aimed to investigate the possible reasons behind the increased frequency in AI detection, especially in ageing populations. The pathophysiological effects of insulin resistance (IR), hyperinsulinemia and various anabolic pathways are analyzed. In addition, we review data from studies indicating an increased incidence of adrenal adenomas and carcinomas in patients with type 2 diabetes mellitus (T2DM). The establishment of obesity as a global epidemic, with a higher prevalence in the female than in the male population, coincide with data regarding AIs and the conditions may share a pathophysiological basis. Furthermore, we discuss the bidirectional association of AIs with obesity, insulin resistance and T2DM, especially in patients with autonomous cortisol secretion. Lastly, as per the definition of an AI, we touch upon the evolution of radiological imaging as another possible cause of the rise in prevalence of AIs, especially concerning the greater use and precision of computed tomography (CT).

The role of insulin-like growth factor system in the adrenocortical tumors

INTRODUCTION

The different presentation of adrenocortical tumors in benign adenoma (ACA) or adrenocortical carcinoma (ACC) is related to the variability at the molecular level. The insulin-like growth factor (IGF) system is one of the most frequently altered pathways in ACC. In this review we will critically analyze the evidence regarding the pathogenic role of the IGF system in adrenal tumorigenesis, focusing on ACC. We will also examine the preclinical and clinical studies which investigated the targeting of the IGF system as a therapeutic approach in ACC.

EVIDENCE ACQUISITION

The IGF system plays a crucial role in the embryogenesis of adrenal glands. No significant alterations of the IGF system were observed in ACA. In ACC, the IGF2 overexpression is one of the most frequent molecular change presented in more than 85% of cases. However, IGF2 seems to be only a tumor progression factor which requires additional hits to trigger adrenal tumorigenesis. Also, the IGF1 receptor (IGF1R) appears to be higher expressed in ACC. Many IGF1R target-drugs have been developed to inhibit the activation of the IGF system.

EVIDENCE SYNTHESIS

Preclinical studies using antibody or tyrosine kinase which target the IGF1R, or the dual-targeting of IGF1R and insulin receptor (IR) reduced ACC cells proliferation both in vitro and in vivo in mouse xenograft model. However, these promising results were not confirmed in clinical trials.

CONCLUSIONS

Nowadays, predictive markers for the response of target-IGF therapy are missing and further studies which investigate new molecular markers and evaluate the entire IGF receptors, including the IR, are urgently needed.

iNKT cells prevent obesity-induced hepatic steatosis in mice in a C-C chemokine receptor 7-dependent manner

Non-alcoholic fatty liver disease and non-alcoholic steatohepatitis are characterized by an increase in hepatic triglyceride content with infiltration of immune cells, which can cause steatohepatitis and hepatic insulin resistance. C-C chemokine receptor 7 (CCR7) is primarily expressed in immune cells, and CCR7 deficiency leads to the development of multi-organ autoimmunity, chronic renal disease and autoimmune diabetes. Here, we investigated the effect of CCR7 on hepatic steatosis in a mouse model and its underlying mechanism. Our results demonstrated that body and liver weights were higher in the CCR7^−/− mice than in the wild-type (WT) mice when they were fed a high-fat diet. Further, glucose tolerance and insulin sensitivity were markedly diminished in CCR7^−/− mice. The number of invariant natural killer T (iNKT) cells was reduced in the livers of the CCR7^−/− mice. Moreover, liver inflammation was detected in obese CCR7^−/− mice, which was ameliorated by the adoptive transfer of hepatic mononuclear cells from WT mice, but not through the transfer of hepatic mononuclear cells from CD1d^−/− or interleukin-10-deficient (IL-10^−/−) mice. Overall, these results suggest that CCR7⁺ mononuclear cells in the liver could regulate obesity-induced hepatic steatosis via induction of IL-10-expressing iNKT cells.

Understanding the mTOR signaling pathway via mathematical modeling

The mechanistic target of rapamycin (mTOR) is a central regulatory pathway that integrates a variety of environmental cues to control cellular growth and homeostasis by intricate molecular feedbacks. In spite of extensive knowledge about its components, the molecular understanding of how these function together in space and time remains poor and there is a need for Systems Biology approaches to perform systematic analyses. In this work, we review the recent progress how the combined efforts of mathematical models and quantitative experiments shed new light on our understanding of the mTOR signaling pathway. In particular, we discuss the modeling concepts applied in mTOR signaling, the role of multiple feedbacks and the crosstalk mechanisms of mTOR with other signaling pathways. We also discuss the contribution of principles from information and network theory that have been successfully applied in dissecting design principles of the mTOR signaling network. We finally propose to classify the mTOR models in terms of the time scale and network complexity, and outline the importance of the classification toward the development of highly comprehensive and predictive models. WIREs Syst Biol Med 2017, 9:e1379. doi: 10.1002/wsbm.1379 For further resources related to this article, please visit the WIREs website.

Modelling the molecular mechanisms of aging

The aging process is driven at the cellular level by random molecular damage that slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the aging process. The complexity of the aging process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards and discusses many specific examples of models that have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field.

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.

A rule-based model of insulin signalling pathway

BACKGROUND

The insulin signalling pathway (ISP) is an important biochemical pathway, which regulates some fundamental biological functions such as glucose and lipid metabolism, protein synthesis, cell proliferation, cell differentiation and apoptosis. In the last years, different mathematical models based on ordinary differential equations have been proposed in the literature to describe specific features of the ISP, thus providing a description of the behaviour of the system and its emerging properties. However, protein-protein interactions potentially generate a multiplicity of distinct chemical species, an issue referred to as "combinatorial complexity", which results in defining a high number of state variables equal to the number of possible protein modifications. This often leads to complex, error prone and difficult to handle model definitions.

RESULTS

In this work, we present a comprehensive model of the ISP, which integrates three models previously available in the literature by using the rule-based modelling (RBM) approach. RBM allows for a simple description of a number of signalling pathway characteristics, such as the phosphorylation of signalling proteins at multiple sites with different effects, the simultaneous interaction of many molecules of the signalling pathways with several binding partners, and the information about subcellular localization where reactions take place. Thanks to its modularity, it also allows an easy integration of different pathways. After RBM specification, we simulated the dynamic behaviour of the ISP model and validated it using experimental data. We the examined the predicted profiles of all the active species and clustered them in four clusters according to their dynamic behaviour. Finally, we used parametric sensitivity analysis to show the role of negative feedback loops in controlling the robustness of the system.

CONCLUSIONS

The presented ISP model is a powerful tool for data simulation and can be used in combination with experimental approaches to guide the experimental design. The model is available at http://sysbiobig.dei.unipd.it/ was submitted to Biomodels Database ( https://www.ebi.ac.uk/biomodels-main/ # MODEL 1604100005).

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.

Adrenocortical tumors and insulin resistance: What is the first step?

The pathogenetic mechanisms underlying the onset of adrenocortical tumors (ACTs) are still largely unknown. Recently, more attention has been paid to the role of insulin and insulin-like growth factor (IGF) system on general tumor development and progression. Increased levels of insulin, IGF-1 and IGF-2 are associated with tumor cell growth and increased risk of cancer promotion and progression in patients with type 2 diabetes. Insulin resistance and compensatory hyperinsulinemia may play a role in adrenal tumor growth through the activation of insulin and IGF-1 receptors. Interestingly, apparently non-functioning ACTs are often associated with a high prevalence of insulin resistance and metabolic syndrome. However, it is unclear if ACT develops from a primary insulin resistance and compensatory hyperinsulinemia or if insulin resistance is only secondary to the slight cortisol hypersecretion by ACT. The aim of this review is to summarize the current evidence regarding the relationship between hyperinsulinemia and adrenocortical tumors.

Quasi-Steady-State Analysis based on Structural Modules and Timed Petri Net Predict System's Dynamics: The Life Cycle of the Insulin Receptor

The insulin-dependent activation and recycling of the insulin receptor play an essential role in the regulation of the energy metabolism, leading to a special interest for pharmaceutical applications. Thus, the recycling of the insulin receptor has been intensively investigated, experimentally as well as theoretically. We developed a time-resolved, discrete model to describe stochastic dynamics and study the approximation of non-linear dynamics in the context of timed Petri nets. Additionally, using a graph-theoretical approach, we analyzed the structure of the regulatory system and demonstrated the close interrelation of structural network properties with the kinetic behavior. The transition invariants decomposed the model into overlapping subnetworks of various sizes, which represent basic functional modules. Moreover, we computed the quasi-steady states of these subnetworks and demonstrated that they are fundamental to understand the dynamic behavior of the system. The Petri net approach confirms the experimental results of insulin-stimulated degradation of the insulin receptor, which represents a common feature of insulin-resistant, hyperinsulinaemic states.

Causal drift, robust signaling, and complex disease

The phenotype of many regulatory circuits in which mutations can cause complex, polygenic diseases is to some extent robust to DNA mutations that affect circuit components. Here I demonstrate how such mutational robustness can prevent the discovery of genetic disease determinants. To make my case, I use a mathematical model of the insulin signaling pathway implicated in type 2 diabetes, whose signaling output is governed by 15 genetically determined parameters. Using multiple complementary measures of a parameter's importance for this phenotype, I show that any one disease determinant that is crucial in one genetic background will be virtually irrelevant in other backgrounds. In an evolving population that drifts through the parameter space of this or other robust circuits through DNA mutations, the genetic changes that can cause disease will vary randomly over time. I call this phenomenon causal drift. It means that mutations causing disease in one (human or non-human) population may have no effect in another population, and vice versa. Causal drift casts doubt on our ability to infer the molecular mechanisms of complex diseases from non-human model organisms.

Development, growth and maintenance of β-cell mass: models are also part of the story

Pancreatic β-cells in the islets of Langerhans play a crucial role in regulating glucose homeostasis in the circulation. Loss of β-cell mass or function due to environmental, genetic and immunological factors leads to the manifestation of diabetes mellitus. The mechanisms regulating the dynamics of pancreatic β-cell mass during normal development and diabetes progression are complex. To fully unravel such complexity, experimental and clinical approaches need to be combined with mathematical and computational models. In the natural sciences, mathematical and computational models have aided the identification of key mechanisms underlying the behavior of systems comprising multiple interacting components. A number of mathematical and computational models have been proposed to explain the development, growth and death of pancreatic β-cells. In this review, we discuss some of these models and how their predictions provide novel insight into the mechanisms controlling β-cell mass during normal development and diabetes progression. Lastly, we discuss a handful of the major open questions in the field.

A single mechanism can explain network-wide insulin resistance in adipocytes from obese patients with type 2 diabetes

The response to insulin is impaired in type 2 diabetes. Much information is available about insulin signaling, but understanding of the cellular mechanisms causing impaired signaling and insulin resistance is hampered by fragmented data, mainly obtained from different cell lines and animals. We have collected quantitative and systems-wide dynamic data on insulin signaling in primary adipocytes and compared cells isolated from healthy and diabetic individuals. Mathematical modeling and experimental verification identified mechanisms of insulin control of the MAPKs ERK1/2. We found that in human adipocytes, insulin stimulates phosphorylation of the ribosomal protein S6 and hence protein synthesis about equally via ERK1/2 and mTORC1. Using mathematical modeling, we examined the signaling network as a whole and show that a single mechanism can explain the insulin resistance of type 2 diabetes throughout the network, involving signaling both through IRS1, PKB, and mTOR and via ERK1/2 to the nuclear transcription factor Elk1. The most important part of the insulin resistance mechanism is an attenuated feedback from the protein kinase mTORC1 to IRS1, which spreads signal attenuation to all parts of the insulin signaling network. Experimental inhibition of mTORC1 using rapamycin in adipocytes from non-diabetic individuals induced and thus confirmed the predicted network-wide insulin resistance.

Regulatory interactions maintaining self-renewal of human embryonic stem cells as revealed through a systems analysis of PI3K/AKT pathway

MOTIVATION

Maintenance of the self-renewal state in human embryonic stem cells (hESCs) is the foremost critical step for regenerative therapy applications. The insulin-mediated PI3K/AKT pathway is well appreciated as being the central pathway supporting hESC self-renewal; however, the regulatory interactions in the pathway that maintain cell state are not yet known. Identification of these regulatory pathway components will be critical for designing targeted interventions to facilitate a completely defined platform for hESC propagation and differentiation. Here, we have developed a systems analysis approach to identify regulatory components that control PI3K/AKT pathway in self-renewing hESCs.

RESULTS

A detailed mathematical model was adopted to explain the complex regulatory interactions in the PI3K/AKT pathway. We evaluated globally sensitive processes of the pathway in a computationally efficient manner by replacing the detailed model by a surrogate meta-model. Our mathematical analysis, supported by experimental validation, reveals that negative regulators of the molecules IRS1 and PIP3 primarily govern the steady state of the pathway in hESCs. Among the regulators, negative feedback via IRS1 reduces the sensitivity of various reactions associated with direct trunk of the pathway and also constraints the propagation of parameter uncertainty to the levels of post receptor signaling molecules. Furthermore, our results suggest that inhibition of negative feedback can significantly increase p-AKT levels and thereby, better support hESC self-renewal. Our integrated mathematical modeling and experimental workflow demonstrates the significant advantage of computationally efficient meta-model approaches to detect sensitive targets from signaling pathways.

AVAILABILITY AND IMPLEMENTATION

FORTRAN codes for the PI3K/AKT pathway and the RS-HDMR implementation are available from the authors upon request.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

Insulin signaling in type 2 diabetes: experimental and modeling analyses reveal mechanisms of insulin resistance in human adipocytes

Type 2 diabetes originates in an expanding adipose tissue that for unknown reasons becomes insulin resistant. Insulin resistance reflects impairments in insulin signaling, but mechanisms involved are unclear because current research is fragmented. We report a systems level mechanistic understanding of insulin resistance, using systems wide and internally consistent data from human adipocytes. Based on quantitative steady-state and dynamic time course data on signaling intermediaries, normally and in diabetes, we developed a dynamic mathematical model of insulin signaling. The model structure and parameters are identical in the normal and diabetic states of the model, except for three parameters that change in diabetes: (i) reduced concentration of insulin receptor, (ii) reduced concentration of insulin-regulated glucose transporter GLUT4, and (iii) changed feedback from mammalian target of rapamycin in complex with raptor (mTORC1). Modeling reveals that at the core of insulin resistance in human adipocytes is attenuation of a positive feedback from mTORC1 to the insulin receptor substrate-1, which explains reduced sensitivity and signal strength throughout the signaling network. Model simulations with inhibition of mTORC1 are comparable with experimental data on inhibition of mTORC1 using rapamycin in human adipocytes. We demonstrate the potential of the model for identification of drug targets, e.g. increasing the feedback restores insulin signaling, both at the cellular level and, using a multilevel model, at the whole body level. Our findings suggest that insulin resistance in an expanded adipose tissue results from cell growth restriction to prevent cell necrosis.

From steady-state to synchronized yeast glycolytic oscillations II: model validation

In an accompanying paper [du Preez et al., (2012) FEBS J279, 2810-2822], we adapt an existing kinetic model for steady-state yeast glycolysis to simulate limit-cycle oscillations. Here we validate the model by testing its capacity to simulate a wide range of experiments on dynamics of yeast glycolysis. In addition to its description of the oscillations of glycolytic intermediates in intact cells and the rapid synchronization observed when mixing out-of-phase oscillatory cell populations (see accompanying paper), the model was able to predict the Hopf bifurcation diagram with glucose as the bifurcation parameter (and one of the bifurcation points with cyanide as the bifurcation parameter), the glucose- and acetaldehyde-driven forced oscillations, glucose and acetaldehyde quenching, and cell-free extract oscillations (including complex oscillations and mixed-mode oscillations). Thus, the model was compliant, at least qualitatively, with the majority of available experimental data for glycolytic oscillations in yeast. To our knowledge, this is the first time that a model for yeast glycolysis has been tested against such a wide variety of independent data sets.

DATABASE

The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.