Modeling Cyclic Waves of Circulating T Cells in Autoimmune Diabetes

Mahaffy, Joseph M.; Edelstein‐Keshet, Leah

doi:10.1137/060661144

Cited by 35 publications

(23 citation statements)

References 25 publications

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“…However, for simplicity and tractability, we will assume that all progeny are produced instantaneously upon contact with a pAPC. This approach is similar to that taken by Mahaffy and Edelstein-Keshet (2007) in modelling Type 1 diabetes. Another approach, taken by León et al (2000) and Burroughs et al (2006), assumes that T cells (both conventional and regulatory) are capable of proliferation throughout their lifetimes.…”

Section: Production Of Active T Cells (λ E a And (π 1 E + β)A)mentioning

confidence: 89%

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Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Alexander

Wahl

2010

Bull. Math. Biol.

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The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R(0) for each system. When R(0)<1, only the trivial equilibrium exists and is stable; when R(0)>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach).

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Section: Production Of Active T Cells (λ E a And (π 1 E + β)A)mentioning

confidence: 89%

“…The death rate of pAPCs is less certain (Kim et al 2007); we assume that the lifetime of a mature pAPC is of a similar order and take μ A = 0.25 day −1 as well. Peptide dynamics occur on the order of hours (Mahaffy and Edelstein-Keshet 2007); we estimate μ G = 5 day −1 . (Kim et al 2007).…”

Section: Parameter Estimationmentioning

confidence: 99%

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Alexander

Wahl

2010

Bull. Math. Biol.

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“…17). The same modeling framework also accounts for large cyclic fluctuations in effector cells that can occur in certain cases (10,16,22).…”

Section: Mathematical Modelsmentioning

confidence: 99%

On How Monospecific Memory-Like Autoregulatory CD8+ T Cells Can Blunt Diabetogenic Autoimmunity: A Computational Approach

Khadra

Tsai

Santamaría

et al. 2010

The Journal of Immunology

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We have recently shown that during progression to autoimmune diabetes in NOD mice, memory autoreactive regulatory CD8+ T cells arising from low-avidity precursors can be expanded to therapeutic levels using nanoparticles coated with disease-relevant peptide-major histocompatibility complexes (pMHCs). Here we examine the dynamics of memory autoregulatory CD8+ T cells specific for islet-specific glucose-6-phosphatase catalytic subunit-related protein206–214, a prevalent β cell autoantigen; their high-avidity counterparts (dominant effectors); and all other autoreactive non-islet-specific glucose-6-phosphatase catalytic subunit-related protein206–214-specific CD8+ T cell specificities (subdominant effectors) in response to pMHC-coated nanoparticle (pMHC-nanoparticle) therapy. We combine experimental data with mathematical modeling to investigate the clonal competition dynamics of these T cell pools. To mimic the response diversity observed in NOD mice, we simulated many individual mice, using a wide range of parameters, and averaged the results as done experimentally. We find that under certain circumstances, pMHC-nanoparticle–induced expansion of autoregulatory CD8+ T cells can effectively suppress the expansion of dominant and subdominant effectors simultaneously but, in some few cases, can lead to the substitution (or switching) of one effector population by another. The model supports the idea that disease suppression is based on the elimination of autoantigen-loaded APCs by the expanded autoregulatory CD8+ T cells. The model also predicts that treatment strategies that operate by selectively inhibiting autoantigen-loaded APCs, such as the pMHC-nanoparticle approach, have the highest promise to blunt polyclonal, multiantigen-specific autoimmune responses in vivo without impairing systemic immunity.

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“…These dynamics have been described as “waves” and have been explained mathematically by transitions through Hopf and homoclinic bifurcations in Mahaffy and Edelstein-Keshet (2007) and by transient bistability of the autoimmune state in Jaberi-Douraki et al (2014b). Interestingly, in the latter of these two theoretical studies, inclusion of multiple clones of T cells with different avidities can give rise to multiple waves in the T cell dynamics, which can significantly impact the rate of overall beta cell destruction.…”

Section: Discussionmentioning

confidence: 99%

“…Through model construction and analysis, candidate mechanisms giving rise to T1D can be interrogated in a systematic way. To this end, a number of authors have developed models describing: beta cell function (Bertram and Sherman, 2004), defective macrophage clearing (Marée et al, 2006), immune cell populations (Mahaffy and Edelstein-Keshet, 2007), multi-clonal populations of immune cells (Khadra et al, 2009, 2011; Jaberi-Douraki et al, 2015), immune cell cycles (Jaberi-Douraki et al, 2014b), and apoptotic stress generated by the loss of beta cell mass (Jaberi-Douraki et al, 2014c). …”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of Insulitis in Human Type 1 Diabetes

et al. 2016

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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.

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Modeling Cyclic Waves of Circulating T Cells in Autoimmune Diabetes

Cited by 35 publications

References 25 publications

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

On How Monospecific Memory-Like Autoregulatory CD8+ T Cells Can Blunt Diabetogenic Autoimmunity: A Computational Approach

Spatiotemporal Dynamics of Insulitis in Human Type 1 Diabetes

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