Model-based hypothesis testing of key mechanisms in initial phase of insulin signaling

Continuous variable responses and signal gating form kinetic bases for pulsatile insulin signaling and emergence of resistance

Evolutionarily conserved insulin signaling is central to nutrient sensing, storage, and utilization across tissues. Dysfunctional insulin signaling is associated with metabolic disorders, cancer, and aging. Hence, the pathway components have emerged as key targets for pharmacological interventions in addition to insulin administration itself. Despite this, activation–inactivation dynamics of individual components, which exert regulatory control in a physiological context, is poorly understood. Now, with our systems-based approach, we reveal kinetic parameters, which define the flow of information through both metabolic and growth-factor arms and thus determine signaling architecture. We also provide a kinetic basis for 1) the advantage of pulsatile-fasted insulin signaling that enables fed-insulin response and 2) the detrimental impact of repeat fed-insulin inputs that causes resistance.

Understanding kinetic control of biological processes is as important as identifying components that constitute pathways. Insulin signaling is central for almost all metazoans, and its perturbations are associated with various developmental disorders, metabolic diseases, and aging. While temporal phosphorylation changes and kinetic constants have provided some insights, constant or variable parameters that establish and maintain signal topology are poorly understood. Here, we report kinetic parameters that encode insulin concentration and nutrient-dependent flow of information using iterative experimental and mathematical simulation-based approaches. Our results illustrate how dynamics of distinct phosphorylation events collectively contribute to selective kinetic gating of signals and maximum connectivity of the signaling cascade under normo-insulinemic but not hyper-insulinemic states. In addition to identifying parameters that provide predictive value for maintaining the balance between metabolic and growth-factor arms, we posit a kinetic basis for the emergence of insulin resistance. Given that pulsatile insulin secretion during a fasted state precedes a fed response, our findings reveal rewiring of insulin signaling akin to memory and anticipation, which was hitherto unknown. Striking disparate temporal behavior of key phosphorylation events that destroy the topology under hyper-insulinemic states underscores the importance of unraveling regulatory components that act as bandwidth filters. In conclusion, besides providing fundamental insights, our study will help in identifying therapeutic strategies that conserve coupling between metabolic and growth-factor arms, which is lost in diseases and conditions of hyper-insulinemia.

Signaling Heterogeneity is Defined by Pathway Architecture and Intercellular Variability in Protein Expression

Insulin's activation of PI3K/Akt signaling, stimulates glucose uptake by enhancing delivery of GLUT4 to the cell surface. Here we examined the origins of intercellular heterogeneity in insulin signaling. Akt activation alone accounted for ~25% of the variance in GLUT4, indicating that additional sources of variance exist. The Akt and GLUT4 responses were highly reproducible within the same cell, suggesting the variance is between cells (extrinsic) and not within cells (intrinsic). Generalized mechanistic models (supported by experimental observations) demonstrated that the correlation between the steady-state levels of two measured signaling processes decreases with increasing distance from each other and that intercellular variation in protein expression (as an example of extrinsic variance) is sufficient to account for the variance in and between Akt and GLUT4. Thus, the response of a population to insulin signaling is underpinned by considerable single-cell heterogeneity that is largely driven by variance in gene/protein expression between cells.

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Insulin signaling is heterogeneous between cells in the same population

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The temporal response of signaling components within a cell is highly reproducible

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Upstream responses (Akt) can only partially predict downstream response (GLUT4)

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Protein expression variance is a driver of intercellular signaling heterogeneity

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.

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.

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).

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.

Nodes with high centrality in protein interaction networks are responsible for driving signaling pathways in diabetic nephropathy

In spite of huge efforts, chronic diseases remain an unresolved problem in medicine. Systems biology could assist to develop more efficient therapies through providing quantitative holistic sights to these complex disorders. In this study, we have re-analyzed a microarray dataset to identify critical signaling pathways related to diabetic nephropathy. GSE1009 dataset was downloaded from Gene Expression Omnibus database and the gene expression profile of glomeruli from diabetic nephropathy patients and those from healthy individuals were compared. The protein-protein interaction network for differentially expressed genes was constructed and enriched. In addition, topology of the network was analyzed to identify the genes with high centrality parameters and then pathway enrichment analysis was performed. We found 49 genes to be variably expressed between the two groups. The network of these genes had few interactions so it was enriched and a network with 137 nodes was constructed. Based on different parameters, 34 nodes were considered to have high centrality in this network. Pathway enrichment analysis with these central genes identified 62 inter-connected signaling pathways related to diabetic nephropathy. Interestingly, the central nodes were more informative for pathway enrichment analysis compared to all network nodes and also 49 differentially expressed genes. In conclusion, we here show that central nodes in protein interaction networks tend to be present in pathways that co-occur in a biological state. Also, this study suggests a computational method for inferring underlying mechanisms of complex disorders from raw high-throughput data.

Simulation predicts IGFBP2-HIF1α interaction drives glioblastoma growth

Tremendous strides have been made in improving patients’ survival from cancer with one glaring exception: brain cancer. Glioblastoma is the most common, aggressive and highly malignant type of primary brain tumor. The average overall survival remains less than 1 year. Notably, cancer patients with obesity and diabetes have worse outcomes and accelerated progression of glioblastoma. The root cause of this accelerated progression has been hypothesized to involve the insulin signaling pathway. However, while the process of invasive glioblastoma progression has been extensively studied macroscopically, it has not yet been well characterized with regards to intracellular insulin signaling. In this study we connect for the first time microscale insulin signaling activity with macroscale glioblastoma growth through the use of computational modeling. Results of the model suggest a novel observation: feedback from IGFBP2 to HIF1α is integral to the sustained growth of glioblastoma. Our study suggests that downstream signaling from IGFI to HIF1α, which has been the target of many insulin signaling drugs in clinical trials, plays a smaller role in overall tumor growth. These predictions strongly suggest redirecting the focus of glioma drug candidates on controlling the feedback between IGFBP2 and HIF1α.

Current treatment for glioblastoma patients is limited to nonspecific methods: surgery followed by a combination of radio- and chemotherapy. With these methods, glioma patient survival is less than one year post-diagnosis. Targeting specific protein signaling pathways offers potentially more potent therapies. One promising potential target is the insulin signaling pathway, which is known to contribute to glioblastoma progression. However, drugs targeting this pathway have shown mixed results in clinical trials, and the detailed mechanisms of how the insulin signaling pathway promotes glioblastoma growth remain to be elucidated. Here, we developed a computational model of insulin signaling in glioblastoma in order to study this pathway’s role in tumor progression. Using the model, we systematically test contributions of different insulin signaling protein interactions on glioblastoma growth. Our model highlights a key driver for the growth of glioblastoma: IGFBP2-HIF1α feedback. This interaction provides a target that could open the door for new therapies in glioma and other solid tumors.

Dominant negative inhibition data should be analyzed using mathematical modeling--re-interpreting data from insulin signaling

As our ability to measure the complexity of intracellular networks has evolved, it has become increasingly clear that we need new methods for data analysis: methods involving mathematical modeling. Nevertheless, it is still uncontroversial to publish and interpret experimental results without a model-based proof that the reasoning is correct. In the present study, we argue that this attitude probably needs to change in the future. We illustrate this need for modeling by considering the common experimental technique of using dominant-negative constructs. More specifically, we consider published time-series and dose-response data which previously have been used to argue that the protein S6 kinase does not phosphorylate insulin receptor substrate-1 at a specific serine residue. Using a presented general approach to interpret such data, we now demonstrate that the given dominant-negative data are not conclusive (i.e. that in the absence of other proofs, S6 kinase still may be the kinase). Using simulations with uncertainty analysis and analytical solutions, we show that an alternative explanation is centered around depletion of substrate, which can be tested experimentally. This analysis thus illustrates both the necessity and the benefits of using mathematical modeling to fully understand the implications of biological data, even for a small system and relatively simple data.

Combining test statistics and models in bootstrapped model rejection: it is a balancing act

BACKGROUND

Model rejections lie at the heart of systems biology, since they provide conclusive statements: that the corresponding mechanistic assumptions do not serve as valid explanations for the experimental data. Rejections are usually done using e.g. the chi-square test (χ2) or the Durbin-Watson test (DW). Analytical formulas for the corresponding distributions rely on assumptions that typically are not fulfilled. This problem is partly alleviated by the usage of bootstrapping, a computationally heavy approach to calculate an empirical distribution. Bootstrapping also allows for a natural extension to estimation of joint distributions, but this feature has so far been little exploited.

RESULTS

We herein show that simplistic combinations of bootstrapped tests, like the max or min of the individual p-values, give inconsistent, i.e. overly conservative or liberal, results. A new two-dimensional (2D) approach based on parametric bootstrapping, on the other hand, is found both consistent and with a higher power than the individual tests, when tested on static and dynamic examples where the truth is known. In the same examples, the most superior test is a 2D χ2vsχ2, where the second χ2-value comes from an additional help model, and its ability to describe bootstraps from the tested model. This superiority is lost if the help model is too simple, or too flexible. If a useful help model is found, the most powerful approach is the bootstrapped log-likelihood ratio (LHR). We show that this is because the LHR is one-dimensional, because the second dimension comes at a cost, and because LHR has retained most of the crucial information in the 2D distribution. These approaches statistically resolve a previously published rejection example for the first time.

CONCLUSIONS

We have shown how to, and how not to, combine tests in a bootstrap setting, when the combination is advantageous, and when it is advantageous to include a second model. These results also provide a deeper insight into the original motivation for formulating the LHR, for the more general setting of nonlinear and non-nested models. These insights are valuable in cases when accuracy and power, rather than computational speed, are prioritized.

Optimal experiment design for model selection in biochemical networks

Background

Mathematical modeling is often used to formalize hypotheses on how a biochemical network operates by discriminating between competing models. Bayesian model selection offers a way to determine the amount of evidence that data provides to support one model over the other while favoring simple models. In practice, the amount of experimental data is often insufficient to make a clear distinction between competing models. Often one would like to perform a new experiment which would discriminate between competing hypotheses.

Results

We developed a novel method to perform Optimal Experiment Design to predict which experiments would most effectively allow model selection. A Bayesian approach is applied to infer model parameter distributions. These distributions are sampled and used to simulate from multivariate predictive densities. The method is based on a k-Nearest Neighbor estimate of the Jensen Shannon divergence between the multivariate predictive densities of competing models.

Conclusions

We show that the method successfully uses predictive differences to enable model selection by applying it to several test cases. Because the design criterion is based on predictive distributions, which can be computed for a wide range of model quantities, the approach is very flexible. The method reveals specific combinations of experiments which improve discriminability even in cases where data is scarce. The proposed approach can be used in conjunction with existing Bayesian methodologies where (approximate) posteriors have been determined, making use of relations that exist within the inferred posteriors.

Parameter trajectory analysis to identify treatment effects of pharmacological interventions

The field of medical systems biology aims to advance understanding of molecular mechanisms that drive disease progression and to translate this knowledge into therapies to effectively treat diseases. A challenging task is the investigation of long-term effects of a (pharmacological) treatment, to establish its applicability and to identify potential side effects. We present a new modeling approach, called Analysis of Dynamic Adaptations in Parameter Trajectories (ADAPT), to analyze the long-term effects of a pharmacological intervention. A concept of time-dependent evolution of model parameters is introduced to study the dynamics of molecular adaptations. The progression of these adaptations is predicted by identifying necessary dynamic changes in the model parameters to describe the transition between experimental data obtained during different stages of the treatment. The trajectories provide insight in the affected underlying biological systems and identify the molecular events that should be studied in more detail to unravel the mechanistic basis of treatment outcome. Modulating effects caused by interactions with the proteome and transcriptome levels, which are often less well understood, can be captured by the time-dependent descriptions of the parameters. ADAPT was employed to identify metabolic adaptations induced upon pharmacological activation of the liver X receptor (LXR), a potential drug target to treat or prevent atherosclerosis. The trajectories were investigated to study the cascade of adaptations. This provided a counter-intuitive insight concerning the function of scavenger receptor class B1 (SR-B1), a receptor that facilitates the hepatic uptake of cholesterol. Although activation of LXR promotes cholesterol efflux and -excretion, our computational analysis showed that the hepatic capacity to clear cholesterol was reduced upon prolonged treatment. This prediction was confirmed experimentally by immunoblotting measurements of SR-B1 in hepatic membranes. Next to the identification of potential unwanted side effects, we demonstrate how ADAPT can be used to design new target interventions to prevent these.

A driving ambition of medical systems biology is to advance our understanding of molecular processes that drive the progression of complex diseases such as Type 2 Diabetes and cardiovascular disease. This insight is essential to enable the development of therapies to effectively treat diseases. A challenging task is to investigate the long-term effects of a treatment, in order to establish its applicability and to identify potential side effects. As such, there is a growing need for novel approaches to support this research. Here, we present a new computational approach to identify treatment effects. We make use of a computational model of the biological system. The model is used to describe the experimental data obtained during different stages of the treatment. To incorporate the long-term/progressive adaptations in the system, induced by changes in gene and protein expression, the model is iteratively updated. The approach was employed to identify metabolic adaptations induced by a potential anti-atherosclerotic and anti-diabetic drug target. Our approach identifies the molecular events that should be studied in more detail to establish the mechanistic basis of treatment outcome. New biological insight was obtained concerning the metabolism of cholesterol, which was in turn experimentally validated.

Computational modelling of the regulation of Insulin signalling by oxidative stress

Background

Existing models of insulin signalling focus on short term dynamics, rather than the longer term dynamics necessary to understand many physiologically relevant behaviours. We have developed a model of insulin signalling in rodent adipocytes that includes both transcriptional feedback through the Forkhead box type O (FOXO) transcription factor, and interaction with oxidative stress, in addition to the core pathway. In the model Reactive Oxygen Species are both generated endogenously and can be applied externally. They regulate signalling though inhibition of phosphatases and induction of the activity of Stress Activated Protein Kinases, which themselves modulate feedbacks to insulin signalling and FOXO.

Results

Insulin and oxidative stress combined produce a lower degree of activation of insulin signalling than insulin alone. Fasting (nutrient withdrawal) and weak oxidative stress upregulate antioxidant defences while stronger oxidative stress leads to a short term activation of insulin signalling but if prolonged can have other effects including degradation of the insulin receptor substrate (IRS1) and FOXO. At high insulin the protective effect of moderate oxidative stress may disappear.

Conclusion

Our model is consistent with a wide range of experimental data, some of which is difficult to explain. Oxidative stress can have effects that are both up- and down-regulatory on insulin signalling. Our model therefore shows the complexity of the interaction between the two pathways and highlights the need for such integrated computational models to give insight into the dysregulation of insulin signalling along with more data at the individual level.

A complete SBML model file can be downloaded from BIOMODELS (https://www.ebi.ac.uk/biomodels-main) with unique identifier MODEL1212210000.

Other files and scripts are available as additional files with this journal article and can be downloaded from https://github.com/graham1034/Smith2012_insulin_signalling.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.

A dynamic network model of mTOR signaling reveals TSC-independent mTORC2 regulation

The kinase mammalian target of rapamycin (mTOR) exists in two multiprotein complexes (mTORC1 and mTORC2) and is a central regulator of growth and metabolism. Insulin activation of mTORC1, mediated by phosphoinositide 3-kinase (PI3K), Akt, and the inhibitory tuberous sclerosis complex 1/2 (TSC1-TSC2), initiates a negative feedback loop that ultimately inhibits PI3K. We present a data-driven dynamic insulin-mTOR network model that integrates the entire core network and used this model to investigate the less well understood mechanisms by which insulin regulates mTORC2. By analyzing the effects of perturbations targeting several levels within the network in silico and experimentally, we found that, in contrast to current hypotheses, the TSC1-TSC2 complex was not a direct or indirect (acting through the negative feedback loop) regulator of mTORC2. Although mTORC2 activation required active PI3K, this was not affected by the negative feedback loop. Therefore, we propose an mTORC2 activation pathway through a PI3K variant that is insensitive to the negative feedback loop that regulates mTORC1. This putative pathway predicts that mTORC2 would be refractory to Akt, which inhibits TSC1-TSC2, and, indeed, we found that mTORC2 was insensitive to constitutive Akt activation in several cell types. Our results suggest that a previously unknown network structure connects mTORC2 to its upstream cues and clarifies which molecular connectors contribute to mTORC2 activation.

Insulin signaling - mathematical modeling comes of age

Signaling pathways that only a few years ago appeared simple and understandable, albeit far from complete, have evolved into very complex multi-layered networks of cellular control mechanisms, which in turn are integrated in a similarly complex whole-body level of control mechanisms. This complexity sets limits for classical biochemical reasoning, such that a correct and complete analysis of experimental data while taking the full complexity into account is not possible. In this Opinion we propose that mathematical modeling can be used as a tool in insulin signaling research, and we demonstrate how recent developments in modeling - and the integration of modeling in the experimental process - provide new possibilities to approach and decipher complex biological systems more efficiently.

Molecular basis of signaling specificity of insulin and IGF receptors: neglected corners and recent advances

Insulin and insulin-like growth factor (IGF) receptors utilize common phosphoinositide 3-kinase/Akt and Ras/extracellular signal-regulated kinase signaling pathways to mediate a broad spectrum of "metabolic" and "mitogenic" responses. Specificity of insulin and IGF action in vivo must in part reflect expression of receptors and responsive pathways in different tissues but it is widely assumed that it is also determined by the ligand binding and signaling mechanisms of the receptors. This review focuses on receptor-proximal events in insulin/IGF signaling and examines their contribution to specificity of downstream responses. Insulin and IGF receptors may differ subtly in the efficiency with which they recruit their major substrates (IRS-1 and IRS-2 and Shc) and this could influence effectiveness of signaling to "metabolic" and "mitogenic" responses. Other substrates (Grb2-associated binder, downstream of kinases, SH2Bs, Crk), scaffolds (RACK1, β-arrestins, cytohesins), and pathways (non-receptor tyrosine kinases, phosphoinositide kinases, reactive oxygen species) have been less widely studied. Some of these components appear to be specifically involved in "metabolic" or "mitogenic" signaling but it has not been shown that this reflects receptor-preferential interaction. Very few receptor-specific interactions have been characterized, and their roles in signaling are unclear. Signaling specificity might also be imparted by differences in intracellular trafficking or feedback regulation of receptors, but few studies have directly addressed this possibility. Although published data are not wholly conclusive, no evidence has yet emerged for signaling mechanisms that are specifically engaged by insulin receptors but not IGF receptors or vice versa, and there is only limited evidence for differential activation of signaling mechanisms that are common to both receptors. Cellular context, rather than intrinsic receptor activity, therefore appears to be the major determinant of whether responses to insulin and IGFs are perceived as "metabolic" or "mitogenic."

Mechanistic explanations for counter-intuitive phosphorylation dynamics of the insulin receptor and insulin receptor substrate-1 in response to insulin in murine adipocytes

Insulin signaling through insulin receptor (IR) and insulin receptor substrate-1 (IRS1) is important for insulin control of target cells. We have previously demonstrated a rapid and simultaneous overshoot behavior in the phosphorylation dynamics of IR and IRS1 in human adipocytes. Herein, we demonstrate that in murine adipocytes a similar overshoot behavior is not simultaneous for IR and IRS1. The peak of IRS1 phosphorylation, which is a direct consequence of the phosphorylation and the activation of IR, occurs earlier than the peak of IR phosphorylation. We used a conclusive modeling framework to unravel the mechanisms behind this counter-intuitive order of phosphorylation. Through a number of rejections, we demonstrate that two fundamentally different mechanisms may create the reversed order of peaks: (i) two pools of phosphorylated IR, where a large pool of internalized IR peaks late, but phosphorylation of IRS1 is governed by a small plasma membrane-localized pool of IR with an early peak, or (ii) inhibition of the IR-catalyzed phosphorylation of IRS1 by negative feedback. Although (i) may explain the reversed order, this two-pool hypothesis alone requires extensive internalization of IR, which is not supported by experimental data. However, with the additional assumption of limiting concentrations of IRS1, (i) can explain all data. Also, (ii) can explain all available data. Our findings illustrate how modeling can potentiate reasoning, to help draw nontrivial conclusions regarding competing mechanisms in signaling networks. Our work also reveals new differences between human and murine insulin signaling.

Parameter adaptations during phenotype transitions in progressive diseases

Background

The study of phenotype transitions is important to understand progressive diseases, e.g., diabetes mellitus, metabolic syndrome, and cardiovascular diseases. A challenge remains to explain phenotype transitions in terms of adaptations in molecular components and interactions in underlying biological systems.

Results

Here, mathematical modeling is used to describe the different phenotypes by integrating experimental data on metabolic pools and fluxes. Subsequently, trajectories of parameter adaptations are identified that are essential for the phenotypical changes. These changes in parameters reflect progressive adaptations at the transcriptome and proteome level, which occur at larger timescales. The approach was employed to study the metabolic processes underlying liver X receptor induced hepatic steatosis. Model analysis predicts which molecular processes adapt in time after pharmacological activation of the liver X receptor. Our results show that hepatic triglyceride fluxes are increased and triglycerides are especially stored in cytosolic fractions, rather than in endoplasmic reticulum fractions. Furthermore, the model reveals several possible scenarios for adaptations in cholesterol metabolism. According to the analysis, the additional quantification of one cholesterol flux is sufficient to exclude many of these hypotheses.

Conclusions

We propose a generic computational approach to analyze biological systems evolving through various phenotypes and to predict which molecular processes are responsible for the transition. For the case of liver X receptor induced hepatic steatosis the novel approach yields information about the redistribution of fluxes and pools of triglycerides and cholesterols that was not directly apparent from the experimental data. Model analysis provides guidance which specific molecular processes to study in more detail to obtain further understanding of the underlying biological system.

A hierarchical whole-body modeling approach elucidates the link between in Vitro insulin signaling and in Vivo glucose homeostasis

Type 2 diabetes is a metabolic disease that profoundly affects energy homeostasis. The disease involves failure at several levels and subsystems and is characterized by insulin resistance in target cells and tissues (i.e. by impaired intracellular insulin signaling). We have previously used an iterative experimental-theoretical approach to unravel the early insulin signaling events in primary human adipocytes. That study, like most insulin signaling studies, is based on in vitro experimental examination of cells, and the in vivo relevance of such studies for human beings has not been systematically examined. Herein, we develop a hierarchical model of the adipose tissue, which links intracellular insulin control of glucose transport in human primary adipocytes with whole-body glucose homeostasis. An iterative approach between experiments and minimal modeling allowed us to conclude that it is not possible to scale up the experimentally determined glucose uptake by the isolated adipocytes to match the glucose uptake profile of the adipose tissue in vivo. However, a model that additionally includes insulin effects on blood flow in the adipose tissue and GLUT4 translocation due to cell handling can explain all data, but neither of these additions is sufficient independently. We also extend the minimal model to include hierarchical dynamic links to more detailed models (both to our own models and to those by others), which act as submodules that can be turned on or off. The resulting multilevel hierarchical model can merge detailed results on different subsystems into a coherent understanding of whole-body glucose homeostasis. This hierarchical modeling can potentially create bridges between other experimental model systems and the in vivo human situation and offers a framework for systematic evaluation of the physiological relevance of in vitro obtained molecular/cellular experimental data.

Workflow for generating competing hypothesis from models with parameter uncertainty

Mathematical models are increasingly used in life sciences. However, contrary to other disciplines, biological models are typically over-parametrized and loosely constrained by scarce experimental data and prior knowledge. Recent efforts on analysis of complex models have focused on isolated aspects without considering an integrated approach-ranging from model building to derivation of predictive experiments and refutation or validation of robust model behaviours. Here, we develop such an integrative workflow, a sequence of actions expanding upon current efforts with the purpose of setting the stage for a methodology facilitating an extraction of core behaviours and competing mechanistic hypothesis residing within underdetermined models. To this end, we make use of optimization search algorithms, statistical (machine-learning) classification techniques and cluster-based analysis of the state variables' dynamics and their corresponding parameter sets. We apply the workflow to a mathematical model of fat accumulation in the arterial wall (atherogenesis), a complex phenomena with limited quantitative understanding, thus leading to a model plagued with inherent uncertainty. We find that the mathematical atherogenesis model can still be understood in terms of a few key behaviours despite the large number of parameters. This result enabled us to derive distinct mechanistic predictions from the model despite the lack of confidence in the model parameters. We conclude that building integrative workflows enable investigators to embrace modelling of complex biological processes despite uncertainty in parameters.

Mass and information feedbacks through receptor endocytosis govern insulin signaling as revealed using a parameter-free modeling framework

Insulin and other hormones control target cells through a network of signal-mediating molecules. Such networks are extremely complex due to multiple feedback loops in combination with redundancy, shared signal mediators, and cross-talk between signal pathways. We present a novel framework that integrates experimental work and mathematical modeling to quantitatively characterize the role and relation between co-existing submechanisms in complex signaling networks. The approach is independent of knowing or uniquely estimating model parameters because it only relies on (i) rejections and (ii) core predictions (uniquely identified properties in unidentifiable models). The power of our approach is demonstrated through numerous iterations between experiments, model-based data analyses, and theoretical predictions to characterize the relative role of co-existing feedbacks governing insulin signaling. We examined phosphorylation of the insulin receptor and insulin receptor substrate-1 and endocytosis of the receptor in response to various different experimental perturbations in primary human adipocytes. The analysis revealed that receptor endocytosis is necessary for two identified feedback mechanisms involving mass and information transfer, respectively. Experimental findings indicate that interfering with the feedback may substantially increase overall signaling strength, suggesting novel therapeutic targets for insulin resistance and type 2 diabetes. Because the central observations are present in other signaling networks, our results may indicate a general mechanism in hormonal control.

Spatial insulin signalling in isolated skeletal muscle preparations

During in vitro incubation in the absence or presence of insulin, glycogen depletion occurs in the inner core of the muscle specimen, concomitant with increased staining of hypoxia-induced-factor-1-alpha and caspase-3, markers of hypoxia and apoptosis, respectively. The aim of this study was to determine whether insulin is able to diffuse across the entire muscle specimen in sufficient amounts to activate signalling cascades to promote glucose uptake and glycogenesis within isolated mouse skeletal muscle. Phosphoprotein multiplex assay on lysates from muscle preparation was performed to detect phosphorylation of insulin-receptor on Tyr(1146), Akt on Ser(473) and glycogen-synthases-kinase-3 on Ser(21)/Ser(9). To address the spatial resolution of insulin signalling, immunohistochemistry studies on cryosections were performed. Our results provide evidence to suggest that during the in vitro incubation, insulin sufficiently diffuses into the centre of tubular mouse muscles to promote phosphorylation of these signalling events. Interestingly, increased insulin signalling was observed in the core of the incubated muscle specimens, correlating with the location of oxidative fibres. In conclusion, insulin action was not restricted due to insufficient diffusion of the hormone during in vitro incubation in either extensor digitorum longus or soleus muscles from mouse under the specific experimental settings employed in this study. Hence, we suggest that the glycogen depleted core as earlier observed is not due to insufficient insulin action.

In silico generation of alternative hypotheses using causal mapping (CMAP)

Previously, we introduced causal mapping (CMAP) as an easy to use systems biology tool for studying the behavior of biological processes that occur at the cellular and molecular level. CMAP is a coarse-grained graphical modeling approach in which the system of interest is modeled as an interaction map between functional elements of the system, in a manner similar to portrayals of signaling pathways commonly used by molecular cell biologists. CMAP describes details of the interactions while maintaining the simplicity of other qualitative methods (e.g., Boolean networks).In this paper, we use the CMAP methodology as a tool for generating hypotheses about the mechanisms that regulate molecular and cellular systems. Furthermore, our approach allows competing hypotheses to be ranked according to a fitness index and suggests experimental tests to distinguish competing high fitness hypotheses. To motivate the CMAP as a hypotheses generating tool and demonstrate the methodology, we first apply this protocol to a simple test-case of a three-element signaling module. Our methods are next applied to the more complex phenomenon of cortical oscillations observed in spreading cells. This analysis produces two high fitness hypotheses for the mechanism that underlies this dynamic behavior and suggests experiments to distinguish the hypotheses. The method can be widely applied to other cellular systems to generate and compare alternative hypotheses based on experimentally observed data and using computer simulations.

Putting the pieces together in diabetes research: towards a hierarchical model of whole-body glucose homeostasis

Type 2 diabetes is one of the most widespread and rapidly spreading diseases world-wide and has been subject of extensive research efforts. However, understanding the molecular basis of the disease is increasing piecemeal and a consensus regarding the overall picture of normal metabolic regulation and malfunction in diabetes has not emerged. A systems biology approach, combining mathematical modelling with simultaneous high-throughput measurements, can be of considerable help. On the whole-body level, this has been done in pharmacokinetic and pharmacodynamic models, which recently have started to mature into more physiologically realistic organ-based models. At the other end of the spectrum, detailed models for crucial cellular processes are starting to mature into complete modules that potentially can be fitted into such whole-body organ-based models. The result of such a merge is a multi-level hierarchical model, which is a model type that has been common in technical systems. In this review, we report and exemplify some of the recent progress that has been made to achieve such a hierarchical model, and we argue why it is only through such a model that a complete picture of diabetes mellitus can be obtained.