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

A comprehensive compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects

We have expanded a former compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects. The former model was a detailed physiological model which considered the interactions of three substances, glucose, insulin and glucagon on regulating the blood sugar. The main drawback of the former model was its restriction on the route of glucose entrance to the body which was limited to the intravenous glucose injection. To handle the oral glucose intake, we have added a model of glucose absorption in the gastrointestinal tract to the former model to address the resultant variations of blood glucose concentrations following an oral glucose intake. Another model representing the incretins production in the gastrointestinal tract along with their hormonal effects on boosting pancreatic insulin production is also added to the former model. We have used two sets of clinical data obtained during oral glucose tolerance test and isoglycemic intravenous glucose infusion test from both type 2 diabetic and healthy subjects to estimate the model parameters and to validate the model results. The estimation of model parameters is accomplished through solving a nonlinear optimization problem. The results show acceptable precision of the estimated model parameters and demonstrate the capability of the model in accurate prediction of the body response during the clinical studies.

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.

Insulin resistance or hypersecretion? The βIG picture revisited

Mathematical models of glucose, insulin and pancreatic beta-cell mass dynamics are essential to our understanding of the physiological basis of the development of type 2 diabetes. The classical view of diabetes is that the disease develops due to insulin insufficiency. An alternate viewpoint that has recently staged a revival is that diabetogenesis is a hypersecretion disorder. A prominent model of diabetes progression is the βIG model due to Topp and coworkers. Here we study two new variants of the Topp model, which we name "Topp-IR" and "Topp-HS". Topp-IR is a model in which increasing insulin resistance is sufficient to drive a system away from health towards hyperglycemia. Topp-HS describes the hypersecretion model in mathematical terms. We thus show that the hypersecretion hypothesis is theoretically sound, and is therefore a potential route to diabetes. On the basis of insights derived from modeling, we clarify several subtleties of that argument, including postulating a central role for transient insulin peaks in driving insulin resistance.

Towards integrative systems pharmacology models in oncology drug development

Quantitative systems pharmacology (QSP) modeling represents an emerging area of value to further streamline knowledge integration and to better inform decision making processes in drug development. QSP models reside at the interface between systems biology models and pharmacological models, yet their concrete implementation still needs to be established further. This review outlines key modeling techniques in both of these areas and to subsequently discuss challenges and opportunities for further integration, in oncology drug development.

BioModels: Content, Features, Functionality, and Use

BioModels is a reference repository hosting mathematical models that describe the dynamic interactions of biological components at various scales. The resource provides access to over 1,200 models described in literature and over 140,000 models automatically generated from pathway resources. Most model components are cross-linked with external resources to facilitate interoperability. A large proportion of models are manually curated to ensure reproducibility of simulation results. This tutorial presents BioModels' content, features, functionality, and usage.

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.

BioModels: ten-year anniversary

BioModels (http://www.ebi.ac.uk/biomodels/) is a repository of mathematical models of biological processes. A large set of models is curated to verify both correspondence to the biological process that the model seeks to represent, and reproducibility of the simulation results as described in the corresponding peer-reviewed publication. Many models submitted to the database are annotated, cross-referencing its components to external resources such as database records, and terms from controlled vocabularies and ontologies. BioModels comprises two main branches: one is composed of models derived from literature, while the second is generated through automated processes. BioModels currently hosts over 1200 models derived directly from the literature, as well as in excess of 140 000 models automatically generated from pathway resources. This represents an approximate 60-fold growth for literature-based model numbers alone, since BioModels’ first release a decade ago. This article describes updates to the resource over this period, which include changes to the user interface, the annotation profiles of models in the curation pipeline, major infrastructure changes, ability to perform online simulations and the availability of model content in Linked Data form. We also outline planned improvements to cope with a diverse array of new challenges.

Virtual Systems Pharmacology (ViSP) software for simulation from mechanistic systems-level models

Multiple software programs are available for designing and running large scale system-level pharmacology models used in the drug development process. Depending on the problem, scientists may be forced to use several modeling tools that could increase model development time, IT costs and so on. Therefore, it is desirable to have a single platform that allows setting up and running large-scale simulations for the models that have been developed with different modeling tools. We developed a workflow and a software platform in which a model file is compiled into a self-contained executable that is no longer dependent on the software that was used to create the model. At the same time the full model specifics is preserved by presenting all model parameters as input parameters for the executable. This platform was implemented as a model agnostic, therapeutic area agnostic and web-based application with a database back-end that can be used to configure, manage and execute large-scale simulations for multiple models by multiple users. The user interface is designed to be easily configurable to reflect the specifics of the model and the user's particular needs and the back-end database has been implemented to store and manage all aspects of the systems, such as Models, Virtual Patients, User Interface Settings, and Results. The platform can be adapted and deployed on an existing cluster or cloud computing environment. Its use was demonstrated with a metabolic disease systems pharmacology model that simulates the effects of two antidiabetic drugs, metformin and fasiglifam, in type 2 diabetes mellitus patients.

Implementation of quantitative and systems pharmacology in large pharma

Quantitative and systems pharmacology concepts and tools are the foundation of the model-informed drug development paradigm at Merck for integrating knowledge, enabling decisions, and enhancing submissions. Rigorous prioritization of modeling and simulation activities has enabled key drug development decisions and led to a high return on investment through significant cost avoidance. Critical factors for the successful implementation, examples on impact on decision making with associated return of investment, and drivers for continued success are discussed.

Analysis of the efficacy of SGLT2 inhibitors using semi-mechanistic model

The Renal sodium-dependent glucose co-transporter 2 (SGLT2) is one of the most promising targets for the treatment of type 2 diabetes. Two SGLT2 inhibitors, dapagliflozin, and canagliflozin, have already been approved for use in USA and Europe; several additional compounds are also being developed for this purpose. Based on the in vitro IC₅₀ values and plasma concentration of dapagliflozin measured in clinical trials, the marketed dosage of the drug was expected to almost completely inhibit SGLT2 function and reduce glucose reabsorption by 90%. However, the administration of dapagliflozin resulted in only 30–50% inhibition of reabsorption. This study was aimed at investigating the mechanism underlying the discrepancy between the expected and observed levels of glucose reabsorption. To this end, systems pharmacology models were developed to analyze the time profile of dapagliflozin, canagliflozin, ipragliflozin, empagliflozin, and tofogliflozin in the plasma and urine; their filtration and active secretion from the blood to the renal proximal tubules; reverse reabsorption; urinary excretion; and their inhibitory effect on SGLT2. The model shows that concentration levels of tofogliflozin, ipragliflozin, and empagliflozin are higher than levels of other inhibitors following administration of marketed SGLT2 inhibitors at labeled doses and non-marketed SGLT2 inhibitors at maximal doses (approved for phase 2/3 studies). All the compounds exhibited almost 100% inhibition of SGLT2. Based on the results of our model, two explanations for the observed low efficacy of SGLT2 inhibitors were supported: (1) the site of action of SGLT2 inhibitors is not in the lumen of the kidney's proximal tubules, but elsewhere (e.g., the kidneys proximal tubule cells); and (2) there are other transporters that could facilitate glucose reabsorption under the conditions of SGLT2 inhibition (e.g., other transporters of SGLT family).

The mathematician's control toolbox for management of type 1 diabetes

Blood glucose levels are controlled by well-known physiological feedback loops: high glucose levels promote insulin release from the pancreas, which in turn stimulates cellular glucose uptake. Low blood glucose levels promote pancreatic glucagon release, stimulating glycogen breakdown to glucose in the liver. In healthy people, this control system is remarkably good at maintaining blood glucose in a tight range despite many perturbations to the system imposed by diet and fasting, exercise, medications and other stressors. Type 1 diabetes mellitus (T1DM) results from loss of the insulin-producing cells of the pancreas, the beta cells. These cells serve as both sensor (of glucose levels) and actuator (insulin/glucagon release) in a control physiological feedback loop. Although the idea of rebuilding this feedback loop seems intuitively easy, considerable control mathematics involving multiple types of control schema were necessary to develop an artificial pancreas that still does not function as well as evolved control mechanisms. Here, we highlight some tools from control engineering used to mimic normal glucose control in an artificial pancreas, and the constraints, trade-offs and clinical consequences inherent in various types of control schemes. T1DM can be viewed as a loss of normal physiologic controls, as can many other disease states. For this reason, we introduce basic concepts of control engineering applicable to understanding pathophysiology of disease and development of physiologically based control strategies for treatment.

Effects of IL-1β-Blocking Therapies in Type 2 Diabetes Mellitus: A Quantitative Systems Pharmacology Modeling Approach to Explore Underlying Mechanisms

Recent clinical studies suggest sustained treatment effects of interleukin-1β (IL-1β)–blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1β effects on β-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and β-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in β-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin–insulin ratio, and a small increase in β-cell mass. We propose that improved β-cell function, rather than mass, is likely to explain the main IL-1β–blocking effects seen in current clinical data, but that improved β-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

Autoimmune responses in T1DM: quantitative methods to understand onset, progression, and prevention of disease

Understanding the physiological processes that underlie autoimmune disorders and identifying biomarkers to predict their onset are two pressing issues that need to be thoroughly sorted out by careful thought when analyzing these diseases. Type 1 diabetes (T1D) is a typical example of such diseases. It is mediated by autoreactive cytotoxic CD4⁺ and CD8⁺ T-cells that infiltrate the pancreatic islets of Langerhans and destroy insulin-secreting β-cells, leading to abnormal levels of glucose in affected individuals. The disease is also associated with a series of islet-specific autoantibodies that appear in high-risk subjects (HRS) several years prior to the onset of diabetes-related symptoms. It has been suggested that T1D is relapsing-remitting in nature and that islet-specific autoantibodies released by lymphocytic B-cells are detectable at different stages of the disease, depending on their binding affinity (the higher, the earlier they appear). The multifaceted nature of this disease and its intrinsic complexity make this disease very difficult to analyze experimentally as a whole. The use of quantitative methods, in the form of mathematical models and computational tools, to examine the disease has been a very powerful tool in providing predictions and insights about the underlying mechanism(s) regulating its onset and development. Furthermore, the models developed may have prognostic implications by aiding in the enrollment of HRS into trials for T1D prevention. In this review, we summarize recent advances made in determining T- and B-cell involvement in T1D using these quantitative approaches and delineate areas where mathematical modeling can make further contributions in unraveling certain aspect of this disease.

Cardiovascular disease: the other face of diabetes

Despite glycemic control, evidence suggests that mortality and morbidity remain high in diabetes. Regulatory agencies deem, therefore, additional safety trials necessary for the approval of new antidiabetic drugs. Nevertheless, markers of cardiovascular risk, which can be used as response predictors, are not available. In contrast with current efforts on further understanding of glucose–insulin homeostasis, a model-based approach is required to assess the correlation between hyperglycemia and cardiometabolic phenotypes, enabling prediction of the underlying cardiovascular risk.