Modelling the onset of Type 1 diabetes: can impaired macrophage phagocytosis make the difference between health and disease?

Modelling the Impact of NETosis During the Initial Stage of Systemic Lupus Erythematosus

The development of autoimmune diseases often takes years before clinical symptoms become detectable. We propose a mathematical model for the immune response during the initial stage of Systemic Lupus Erythematosus which models the process of aberrant apoptosis and activation of macrophages and neutrophils. NETosis is a type of cell death characterised by the release of neutrophil extracellular traps, or NETs, containing material from the neutrophil's nucleus, in response to a pathogenic stimulus. This process is hypothesised to contribute to the development of autoimmunogenicity in SLE. The aim of this work is to study how NETosis contributes to the establishment of persistent autoantigen production by analysing the steady states and the asymptotic dynamics of the model by numerical experiment.

Macrophage: Key player in the pathogenesis of autoimmune diseases

The macrophage is an essential part of the innate immune system and also serves as the bridge between innate immunity and adaptive immune response. As the initiator and executor of the adaptive immune response, macrophage plays an important role in various physiological processes such as immune tolerance, fibrosis, inflammatory response, angiogenesis and phagocytosis of apoptotic cells. Consequently, macrophage dysfunction is a vital cause of the occurrence and development of autoimmune diseases. In this review, we mainly discuss the functions of macrophages in autoimmune diseases, especially in systemic lupus erythematosus (SLE), rheumatic arthritis (RA), systemic sclerosis (SSc) and type 1 diabetes (T1D), providing references for the treatment and prevention of autoimmune diseases.

Exploring Computational Data Amplification and Imputation for the Discovery of Type 1 Diabetes (T1D) Biomarkers from Limited Human Datasets

BACKGROUND

Type 1 diabetes (T1D) is a devastating disease with serious health complications. Early T1D biomarkers that could enable timely detection and prevention before the onset of clinical symptoms are paramount but currently unavailable. Despite their promise, omics approaches have so far failed to deliver such biomarkers, likely due to the fragmented nature of information obtained through the single omics approach. We recently demonstrated the utility of parallel multi-omics for the identification of T1D biomarker signatures. Our studies also identified challenges.

METHODS

Here, we evaluated a novel computational approach of data imputation and amplification as one way to overcome challenges associated with the relatively small number of subjects in these studies.

RESULTS

Using proprietary algorithms, we amplified our quadra-omics (proteomics, metabolomics, lipidomics, and transcriptomics) dataset from nine subjects a thousand-fold and analyzed the data using Ingenuity Pathway Analysis (IPA) software to assess the change in its analytical capabilities and biomarker prediction power in the amplified datasets compared to the original. These studies showed the ability to identify an increased number of T1D-relevant pathways and biomarkers in such computationally amplified datasets, especially, at imputation ratios close to the "golden ratio" of 38.2%:61.8%. Specifically, the Canonical Pathway and Diseases and Functions modules identified higher numbers of inflammatory pathways and functions relevant to autoimmune T1D, including novel ones not identified in the original data. The Biomarker Prediction module also predicted in the amplified data several unique biomarker candidates with direct links to T1D pathogenesis.

CONCLUSIONS

These preliminary findings indicate that such large-scale data imputation and amplification approaches are useful in facilitating the discovery of candidate integrated biomarker signatures of T1D or other diseases by increasing the predictive range of existing data mining tools, especially when the size of the input data is inherently limited.

CD47 and thrombospondin-1 regulation of mitochondria, metabolism, and diabetes

Thrombospondin-1 (TSP1) is the prototypical member of a family of secreted proteins that modulate cell behavior by engaging with molecules in the extracellular matrix and with receptors on the cell surface. CD47 is widely displayed on many, if not all, cell types and is a high-affinity TSP1 receptor. CD47 is a marker of self that limits innate immune cell activities, a feature recently exploited to enhance cancer immunotherapy. Another major role for CD47 in health and disease is to mediate TSP1 signaling. TSP1 acting through CD47 contributes to mitochondrial, metabolic, and endocrine dysfunction. Studies in animal models found that elevated TSP1 expression, acting in part through CD47, causes mitochondrial and metabolic dysfunction. Clinical studies established that abnormal TSP1 expression positively correlates with obesity, fatty liver disease, and diabetes. The unabated increase in these conditions worldwide and the availability of CD47 targeting drugs justify a closer look into how TSP1 and CD47 disrupt metabolic balance and the potential for therapeutic intervention.

A Mathematical Model for DC Vaccine Treatment of Type I Diabetes

Type I diabetes (T1D) is an autoimmune disease that can be managed, but for which there is currently no cure. Recent discoveries, particularly in mouse models, indicate that targeted modulation of the immune response has the potential to move an individual from a diabetic to a long-term, if not permanent, healthy state. In this paper we develop a single compartment mathematical model that captures the dynamics of dendritic cells (DC and tDC), T cells (effector and regulatory), and macrophages in the development of type I diabetes. The model supports the hypothesis that differences in macrophage clearance rates play a significant role in determining whether or not an individual is likely to become diabetic subsequent to a significant immune challenge. With this model we are able to explore the effects of strengthening the anti-inflammatory component of the immune system in a vulnerable individual. Simulations indicate that there are windows of opportunity in which treatment intervention is more likely to be beneficial in protecting an individual from entering a diabetic state. This model framework can be used as a foundation for modeling future T1D treatments as they are developed.

Agent-based modeling of the interaction between CD8+ T cells and Beta cells in type 1 diabetes

We propose an agent-based model for the simulation of the autoimmune response in T1D. The model incorporates cell behavior from various rules derived from the current literature and is implemented on a high-performance computing system, which enables the simulation of a significant portion of the islets in the mouse pancreas. Simulation results indicate that the model is able to capture the trends that emerge during the progression of the autoimmunity. The multi-scale nature of the model enables definition of rules or equations that govern cellular or sub-cellular level phenomena and observation of the outcomes at the tissue scale. It is expected that such a model would facilitate in vivo clinical studies through rapid testing of hypotheses and planning of future experiments by providing insight into disease progression at different scales, some of which may not be obtained easily in clinical studies. Furthermore, the modular structure of the model simplifies tasks such as the addition of new cell types, and the definition or modification of different behaviors of the environment and the cells with ease.

The dual role of autoimmune regulator in maintaining normal expression level of tissue-restricted autoantigen in the thymus: A modeling investigation

The expression level of tissue-restricted autoantigens (TSA) in the thymus is crucial for the negative selection of autoreactive T cells during central tolerance. The autoimmune regulator factor (AIRE) plays an important role in the positive regulation of these TSA in medullary thymic epithelial cells and, consequently, in the negative selection of high-avidity autoreactive T cells. Recent studies, however, revealed that thymic islet cell autoantigen (ICA69) expression level in non-obese diabetic (NOD) mice, prone to developing type 1 diabetes (T1D), is reduced due to an increase in the binding affinity of AIRE to the Ica1-promoter region, which regulates ICA69 protein synthesis. This seemed to suggest that AIRE acts as a transcriptional repressor of Ica1 gene in the thymus, causing down regulation in the expression level of ICA69. To investigate this hypothesis and the apparent dual role of AIRE in negative selection, we develop a series of mathematical models of increasing complexity describing the temporal dynamics of self-reactive T cells, AIRE-mRNA and AIRE-(in)dependent thymic TSA-associated genes. The goal is to understand how changing the binding affinity of AIRE to Ica1-promoter affects both T-cell tolerance and the dual role of the transcription factor. Using stability analysis and numerical computations, we show that the model possesses a bistable switch, consisting of healthy and autoimmune states, in the expression level of Ica1 gene with respect to AIRE binding affinity, and that it can capture the experimentally observed dual role of AIRE. We also show that the model must contain a positive feedback loop exerted by T cells on AIRE expression (e.g., via lymphotoxin released by T cells) to produce bistability. Our results suggest that the expression-level of AIRE-mRNA in the healthy state is lower than that of the autoimmune state, and that negative selection is very sensitive to parameter perturbations in T-cell avidity.

Spatiotemporal Dynamics of Insulitis in Human Type 1 Diabetes

Type 1 diabetes (T1D) is an auto-immune disease characterized by the selective destruction of the insulin secreting beta cells in the pancreas during an inflammatory phase known as insulitis. Patients with T1D are typically dependent on the administration of externally provided insulin in order to manage blood glucose levels. Whilst technological developments have significantly improved both the life expectancy and quality of life of these patients, an understanding of the mechanisms of the disease remains elusive. Animal models, such as the NOD mouse model, have been widely used to probe the process of insulitis, but there exist very few data from humans studied at disease onset. In this manuscript, we employ data from human pancreases collected close to the onset of T1D and propose a spatio-temporal computational model for the progression of insulitis in human T1D, with particular focus on the mechanisms underlying the development of insulitis in pancreatic islets. This framework allows us to investigate how the time-course of insulitis progression is affected by altering key parameters, such as the number of the CD20+ B cells present in the inflammatory infiltrate, which has recently been proposed to influence the aggressiveness of the disease. Through the analysis of repeated simulations of our stochastic model, which track the number of beta cells within an islet, we find that increased numbers of B cells in the peri-islet space lead to faster destruction of the beta cells. We also find that the balance between the degradation and repair of the basement membrane surrounding the islet is a critical component in governing the overall destruction rate of the beta cells and their remaining number. Our model provides a framework for continued and improved spatio-temporal modeling of human T1D.

Enforced Expression of Hoxa3 Inhibits Classical and Promotes Alternative Activation of Macrophages In Vitro and In Vivo

The regulated differentiation of macrophages (mφs) and their subsequent activation into proinflammatory or prohealing subtypes is critical for efficient wound healing. Chronic wounds such as diabetic (db) ulcers are associated with dysregulation of macrophage function. Whereas non-db mφs polarize to an M2-like, prohealing phenotype during the late stages of healing, db-derived mφs continue to display an M1-like, proinflammatory, or a mixed M1-like/M2-like phenotype. We have previously shown that sustained expression of Hoxa3 reduces the excessive number of leukocytes within the db wound; however, the effect of Hoxa3 on mφ polarization was unknown. In this study, we show that Hoxa3 protein transduction of mφs in vitro enhances macrophage maturation, inhibits M1 polarization, and promotes M2 polarization, in part via regulation of Pu.1/Spi1 and Stat6. Sustained expression of Hoxa3 in vivo in db wounds reduces the number of Nos2(+) (M1-like) mφs, increases the number of Arg1(+) and VEGF(+) (M2-like) mφs, and accelerates healing in a DNA-binding independent manner. Our findings suggest a role for Hox protein activity in promoting M1-to-M2-like phenotypic switching via interactions with myeloid transcription factors and provide insight into mechanisms regulating this process in db wound healing.

The macrophage and its role in inflammation and tissue repair: mathematical and systems biology approaches

Macrophages are central to the inflammatory response and its ability to resolve effectively. They are complex cells that adopt a range of subtypes depending on the tissue type and stimulus that they find themselves under. This flexibility allows them to play multiple, sometimes opposing, roles in inflammation and tissue repair. Their central role in the inflammatory process is reflected in macrophage dysfunction being implicated in chronic inflammation and poorly healing wounds. In this study, we discuss recent attempts to model mathematically and computationally the macrophage and how it partakes in the complex processes of inflammation and tissue repair. There are increasing data describing the variety of macrophage phenotypes and their underlying transcriptional programs. Dynamic mathematical and computational models are an ideal way to test biological hypotheses against experimental data and could aid in understanding this multi-functional cell and its potential role as an attractive therapeutic target for inflammatory conditions and tissue repair.

Continuum model of T-cell avidity: Understanding autoreactive and regulatory T-cell responses in type 1 diabetes

Type 1 diabetes (T1D) is an autoimmune disease that results from the destruction of insulin-secreting pancreatic β cells, leading to abolition of insulin secretion and onset of diabetes. Cytotoxic CD4(+) and CD8(+) T cells, activated by antigen presenting cells (APCs), are both implicated in disease onset and progression. Regulatory T cells (Tregs), on the other hand, play a leading role in regulating immunological tolerance and resistant homoeostasis in T1D by suppressing effector T cells (Teffs). Recent data indicates that after activation, conventional Teffs transiently produce interleukin IL-2, a cytokine that acts as a growth factor for both Teffs and Tregs. Tregs suppress Teffs through IL-2 deprivation, competition and Teff conversion into inducible Tregs (iTregs). To investigate the interactions of these components during T1D progression, a mathematical model of T-cell dynamics is developed as a predictor of β-cell loss, with the underlying hypothesis that avidity of Teffs and Tregs, i.e., the binding affinity of T-cell receptors to peptide-major histocompatibility complexes on host cells, is continuum. The model is used to infer a set of criteria that determines susceptibility to T1D in high risk subjects. Our findings show that diabetes onset is guided by the absence of Treg-to-Teff dominance at specific high avidities, rather than over the whole range of avidity, and that the lack of overall dominance of Teffs-to-Tregs over time is the underlying cause of the "honeymoon period", the remission phase observed in some T1D patients. The model also suggests that competition between Teffs and Tregs is more effective than Teff-induction into iTregs in suppressing Teffs, and that a prolonged full width at half maximum of IL-2 release is a necessary condition for curbing disease onset. Finally, the model provides a rationale for observing rapid and slow progressors of T1D based on modest heterogeneity in the kinetic parameters.

The benefits of diversity: heterogenous DC populations allow for both immunity and tolerance

The immune system must simultaneously mount a response against foreign antigens while tolerating self. How this happens is still unclear as many mechanisms of immune tolerance are antigen non-specific. Antigen specific immune cells called T-cells must first bind to Immunogenic Dendritic Cells (iDCs) before activating and proliferating. These iDCs present both self and foreign antigens during infection, so it is unclear how the immune response can be limited to primarily foreign reactive T-cells. Regulatory T-cells (Tregs) are known to play a key role in self-tolerance. Although they are antigen specific, they also act in an antigen non-specific manner by competing for space and growth factors as well as modifying DC behavior to help kill or deactivate other T-cells. In prior models, the lack of antigen specific control has made simultaneous foreign-immunity and self-tolerance extremely unlikely. We include a heterogeneous DC population, in which different DCs present antigens at different levels. In addition, we include Tolerogenic DC (tDCs) which can delete self-reactive T-cells under normal physiological conditions. We compare different mathematical models of immune tolerance with and without Tregs and heterogenous antigen presentation. For each model, we compute the final number of foreign-reactive and self-reactive T-cells, under a variety of different situations. We find that even if iDCs present more self-antigen than foreign antigen, the immune response will be primarily foreign-reactive as long as there is sufficient presentation of self-antigen on tDCs. Tregs are required primarily for rare or cryptic self-antigens that do not appear frequently on tDCs. We also find that Tregs can only be effective when we include heterogenous antigen presentation, as this allows Tregs and T-cells of the same antigen-specificity to colocalize to the same set of DCs. Tregs better aid immune tolerance when they can both compete for space and growth factors and directly eliminate other T-cells. Our results show the importance of the structure of the DC population in immune tolerance as well as the relative contribution of different cellular mechanisms.

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.

Human systems immunology: hypothesis-based modeling and unbiased data-driven approaches

Systems immunology is an emerging paradigm that aims at a more systematic and quantitative understanding of the immune system. Two major approaches have been utilized to date in this field: unbiased data-driven modeling to comprehensively identify molecular and cellular components of a system and their interactions; and hypothesis-based quantitative modeling to understand the operating principles of a system by extracting a minimal set of variables and rules underlying them. In this review, we describe applications of the two approaches to the study of viral infections and autoimmune diseases in humans, and discuss possible ways by which these two approaches can synergize when applied to human immunology.

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.

Integrated model of metabolism and autoimmune response in β-cell death and progression to type 1 diabetes

Progression to type 1 diabetes is characterized by complex interactions of environmental, metabolic and immune system factors, involving both degenerative pathways leading to loss of pancreatic β-cells as well as protective pathways. The interplay between the degenerative and protective pathways may hold the key to disease outcomes, but no models have so far captured the two together. Here we propose a mathematical framework, an ordinary differential equation (ODE) model, which integrates metabolism and the immune system in early stages of disease process. We hypothesize that depending on the degree of regulation, autoimmunity may also play a protective role in the initial response to stressors. We assume that β-cell destruction follows two paths of loss: degenerative and autoimmune-induced loss. The two paths are mutually competing, leading to termination of the degenerative loss and further to elimination of the stress signal and the autoimmune response, and ultimately stopping the β-cell loss. The model describes well our observations from clinical and non-clinical studies and allows exploration of how the rate of β-cell loss depends on the amplitude and duration of autoimmune response.

Reducing or increasing β-cell apoptosis without inflammation does not affect diabetes initiation in neonatal NOD mice

The presentation of islet antigens in the pancreatic LNs (PLNs) of mice is a developmentally regulated process. It has been hypothesized that, during physiological tissue remodeling, a wave of neonatal β-cell apoptosis may initiate diabetes in autoimmune-prone strains of mice. If true, increasing or decreasing physiological β-cell apoptosis in neonatal NOD mice should alter the time-course of antigen presentation in the PLNs. We used transgenic over-expression of either an anti-apoptotic protein (Bcl-2) or a toxic transgene (rat insulin promoter-Kb) in mouse β cells to reduce or increase neonatal β-cell apoptosis, respectively. Neither intervention affected the timing of antigen presentation in the PLNs or the initiation of islet infiltration. This suggests that under physiological conditions and in the absence of inflammation, neonatal β-cell apoptosis in NOD mice is not the trigger for antigen presentation in the draining LNs.

The in silico macrophage: toward a better understanding of inflammatory disease

Macrophages function as sentinel, cell-regulatory 'hubs' capable of initiating, perpetuating and contributing to the resolution of an inflammatory response, following their activation from a resting state. Highly complex and varied gene expression programs within the macrophage enable such functional diversity. To investigate how programs of gene expression relate to the phenotypic attributes of the macrophage, the development of in silico modeling methods is needed. Such models need to cover multiple scales, from molecular pathways in cell-autonomous immunity and intercellular communication pathways in tissue inflammation to whole organism response pathways in systemic disease. Here, we highlight the potential of in silico macrophage modeling as an amenable and important yet under-exploited tool in aiding in our understanding of the immune inflammatory response. We also discuss how in silico macrophage modeling can help in future therapeutic strategies for modulating both the acute protective effects of inflammation (such as host defense and tissue repair) and the harmful chronic effects (such as autoimmune diseases).

Modeling immune complex-mediated autoimmune inflammation

A number of autoimmune diseases are thought to feature a particular type of self-sustaining inflammation, caused by the deposition of immune complexes (IC) in the inflamed tissue and a consequent activation of local effector cells. The persistence of this inflammation is due to a positive feedback loop, where autoantigen particles released as part of the tissue damage caused by the inflammation stimulate autoreactive B cells, leading to the formation of further immune complexes and their subsequent deposition. We present a mathematical model for the exploration of IC-mediated autoimmune inflammation and its clinical implications. We characterize the possible differences between normal individuals and those susceptible to such inflammation, and show that both random perturbations and bifurcations can lead to disease onset. Our model explains how defects in the mechanisms responsible for cellular debris clearance contribute to the development of disease, in agreement with empirical evidence. Moreover, we show that parameters governing the dynamics of immune complexes, such as their clearance rate, have an even stronger effect in determining the behavior of the system. We demonstrate the existence of hysteresis, implying that once IC-mediated autoimmune inflammation is triggered, its long-term suppression may be difficult to achieve. Our results can serve to guide the development of novel therapies to autoimmune diseases involving this type of inflammation.

Mathematical modelling of immune regulation of type 1 diabetes

Type 1 diabetes is a disease characterized by progressive loss of β cell function due to an autoimmune reaction affecting the islets of Langerhans. Two types of T cells are involved in diabetes: turncoat auto-reactive T cells, or T cells gone bad, that kill the insulin-producing cells, and regulatory T cells that are unable to control the auto-reactive T cells. We formulate a mathematical model that incorporates the role of cytotoxic T cells and regulatory T cells in type 1 diabetes. This study shows that onset of type 1 diabetes is due to a collective, dynamical instability, rather than being caused by a single etiological factor. It is also a numbers game between regulatory T cells and auto-reactive T cells. The problem in the onset of this disease is that there are not enough of the regulatory cells that suppress the immune response against the body's insulin-producing pancreatic islet cells.

Smart sensors and virtual physiology human approach as a basis of personalized therapies in diabetes mellitus

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient's information to the models.A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies.

The role of low avidity T cells in the protection against type 1 diabetes: a modeling investigation

Cytotoxic T lymphocytes (CTLs) play a dominant role in the pathogenesis of autoimmune diabetes, commonly denoted Type 1 Diabetes (T1D). These CTLs (notably CD8(+) T cells) recognize and kill insulin-secreting pancreatic beta cells, reducing their number by approximately 90%. The resulting reduction of insulin secretion causes the defective regulation of glucose metabolism, leading to the characteristic symptoms of diabetes. Recognition of beta cells as targets by CTLs depends on the interactions between MHC-peptide complexes on the surface of beta cells and receptors (TCRs) on T cells. Those CTLs with high affinity TCRs (also called high avidity T cells) cause most of the harm, while those with low affinity TCRs (also called low avidity T cells) play a more mysterious role. Recent experimental evidence suggests that low avidity T cells accumulate as memory T cells during the disease and may be protective in NOD mice (a strain prone to developing T1D), delaying disease progression. It has been hypothesized that such low avidity T cells afford disease protection either by crowding the islets of Langerhans, where beta cells reside, or by killing antigen presenting cells (APCs). In this paper, we explore the hypothesized mechanisms for this protective effect in the context of a series of models for (1) the interactions of low and high avidity T cells, (2) the effect of APCs and (3) the feedback from beta cell killing to autoantigen-induced T cell proliferation. We analyze properties of these models, noting consistency of predictions with observed behaviour. We then use the models to examine the influence of various treatment strategies on the progression of the disease. The model reveals that progressive accumulation of memory low avidity autoreactive T cells during disease progression makes treatments aimed at expanding these protective T cell types more effective close to, or at the onset of clinical disease. It also provides evidence for the hypothesis that low avidity T cells kill APCs (rather than the alternate hypothesis that they crowd the islets).

A quantitative comparison of rates of phagocytosis and digestion of apoptotic cells by macrophages from normal (BALB/c) and diabetes-prone (NOD) mice

Macrophages play an important role in clearing apoptotic debris from tissue. Defective or reduced clearance, seen, for instance, in non-obese diabetic (NOD) mice, has been correlated with initiation of autoimmune (Type 1) diabetes (T1D) (O'Brien BA, Huang Y, Geng X, Dutz JP, Finegood DT. Diabetes 51: 2481-2488, 2002). To validate such a link, it is essential to quantify the reduced clearance (for example, by comparison to BALB/c control mice) and to determine which elements of that clearance are impaired. Recently, we fit data for the time course of in vitro macrophage feeding experiments to basic models of macrophage clearance dynamics, thus quantifying kinetics of uptake and digestion of apoptotic cells in both mouse strains (Marée AFM, Komba M, Dyck C, Łabeçki M, Finegood DT, Edelstein-Keshet L. J Theor Biol 233: 533-551, 2005). In the cycle of modeling and experimental investigation, we identified the importance of 1) measuring short-, intermediate-, and long-time data (to increase the accuracy of parameter fits), and 2) designing experiments with distinct observable regimes, including engulfment-only and digestion-only phases. Here, we report on new results from experiments so designed. In comparing macrophages from the two strains, we find that NOD macrophage engulfment of apoptotic cells is 5.5 times slower than BALB/c controls. Significantly, our new data demonstrate that digestion is at least two times slower in NOD, in contrast with previous conclusions. Moreover, new data enable us to detect an acceleration in engulfment (after the first engulfment) in both strains, but much smaller in NOD macrophages.

The Virtual NOD Mouse: Applying Predictive Biosimulation to Research in Type 1 Diabetes

Type 1 diabetes is a complex, multifactorial disease characterized by T cell-mediated autoimmune destruction of insulin-secreting pancreatic beta cells. To facilitate research in type 1 diabetes, a large-scale dynamic mathematical model of the female non-obese diabetic (NOD) mouse was developed. In this model, termed the Entelos Type 1 Diabetes PhysioLab platform, virtual NOD mice are constructed by mathematically representing components of the immune system and islet beta cell physiology important for the pathogenesis of type 1 diabetes. This report describes the scope of the platform and illustrates some of its capabilities. Specifically, using two virtual NOD mice with either average or early diabetes-onset times, we demonstrate the reproducibility of experimentally observed dynamics involved in diabetes progression, therapeutic responses to exogenous IL-10, and heterogeneity in disease onset. Additionally, we use the Type 1 Diabetes PhysioLab platform to investigate the impact of disease heterogeneity on the effectiveness of exogenous IL-10 therapy to prevent diabetes onset. Results indicate that the inability of a previously published IL-10 therapy protocol to protect NOD mice who exhibit early diabetes onset is due to high levels of pancreatic lymph node (PLN) inflammation, islet infiltration, and beta cell destruction at the time of treatment initiation. Further, simulation indicates that earlier administration of the treatment protocol can prevent NOD mice from developing diabetes by initiating treatment during the period when the disease is still sensitive to IL-10's protective function.

Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5-6 years, compared to only about one-third in the preceding 5-6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function-the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.

Contributions of inwardly rectifying K+ currents to repolarization assessed using mathematical models of human ventricular myocytes

Repolarization of the action potential (AP) in cardiac muscle is a major determinant of refractoriness and excitability, and can also strongly modulate excitation-contraction coupling. In clinical cardiac electrophysiology, the Q-T interval, and hence action potential duration, is both an essential marker of normal function and an indicator of risk for arrhythmic events. It is now well known that the termination of the plateau phase of the AP and the repolarization waveform involve a complex interaction of transmembrane ionic currents. These include a slowly inactivating Na+ current, inactivating Ca2+ current, the decline of an electrogenic current due to Na+/Ca2+ exchange and activation of three or four different K+ currents. At present, many of the quantitative aspects of this important physiological and pathophysiological process remain incompletely understood. Recently, three mathematical models of the membrane AP in human ventricle myocyte have been developed and made available on the Internet. In this study, we have implemented these models for the purpose of comparing the K+ currents, which are responsible for terminating the plateau phase of the AP and generating its repolarization. In this paper, our emphasis is on the two highly nonlinear inwardly rectifying potassium currents, (IK1) and (IK,r). A more general goal is to obtain improved understanding of the ionic mechanisms, which underlie all-or-none repolarization and the parameter denoted 'repolarization reserve' in the human ventricle. Further, insights into these fundamental variables can be expected to provide a more rational basis for clinical assessment of the Q-T and Q-TC intervals, and hence provide insights into some of the very substantial efforts in safety pharmacology, which are based on these parameters.

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.