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Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic β -cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in a biological or mathematical sense, has relied on the search for a treatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomena, are proposed under the prey–predator scheme. T1DM fits in this scheme due to the complicated relationship between pancreatic β -cell population growth and leukocyte population growth via the immune response. In this scenario, β -cells represent the prey, and leukocytes the predator. This paper studies the global dynamics of T1DM reported by Magombedze et al. in 2010. This model describes the interaction of resting macrophages, activated macrophages, antigen cells, autolytic T-cells, and β -cells. Therefore, the localization of compact invariant sets is applied to provide a bounded positive invariant domain in which one can ensure that once the dynamics of the T1DM enter into this domain, they will remain bounded with a maximum and minimum value. Furthermore, we analyzed this model in a closed-loop scenario based on nonlinear control theory, and proposed bases for possible control inputs, complementing the model with them. These entries are based on the existing relationship between cell–cell interaction and the role that they play in the unchaining of a diabetic condition. The closed-loop analysis aims to give a deeper understanding of the impact of autolytic T-cells and the nature of the β -cell population interaction with the innate immune system response. This analysis strengthens the proposal, providing a system free of this illness—that is, a condition wherein the pancreatic β -cell population holds and there are no antigen cells labeled by the activated macrophages.

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An important role for the mineralocorticoid receptor (MR) in vascular inflammation has been proposed. Polymorphonuclear (PMN) leukocytes are critical players following an inflammatory response. We studied the role of aldosterone (ALDO) on ex vivo PMN function by isolation of cells from circulating human blood following density gradient sedimentation with polymorphprep from otherwise healthy subjects. These cells express MR as confirmed by western blot, qRT-PCR and 3H-aldosterone binding analyses. Incubation of ex vivo PMN cells with ALDO (1-10 nM) showed a rise in superoxide production (P<0.01, n=9), an event that was blunted by pre-incubation with 500 nM canrenoic acid (CA), a MR antagonist (P<0.03, n=6). Consistent with these results, we observed that 10 nM ALDO led to rapid increases in cytosolic Ca2+ levels using FURA-2AM fluorescence and was associated with decreases in cellular Mg2+ levels using MagFURA-2AM following 1.5 hr of ALDO. These events were associated with increases in VEGF secretion from PMN as determined by ELISA of supernatants (260.64±44.6 vs. 134.03±1.99 pg/ml, P<0.01 when compared to vehicle, n=8) that was likewise sensitive to CA (P<0.04, n=8); thus suggesting that ALDO-activated PMN cells increase factors involved in migration and endothelial cell activation. Indeed, we showed that 10 nM ALDO increased PMN cell migration in a time-dependent manner by CyQuant fluorescence that lasted up to 60 min and could be blocked by CA (P<0.01, n=3). We then studied the effect of 10 nM ALDO-stimulated PMN cells followed by co-incubation of these cells with human endothelial cells for 4 hr. We observed that incubation of ALDO-stimulated PMNs vs vehicle treated cells led to a 2.1 fold increase in ICAM-1 expression levels using qRT-PCR but not VCAM-1 (P<0.01, n=3) in endothelial cells. We observed similar findings in DMSO-differentiated HL-60 cells, a neutrophil-like human cell line. We detected the presence of MR by western blot and qRT-PCR in these cells. Incubation with 10 nM ALDO led to increases in cellular calcium, superoxide production (P<0.01, n=3) and HL-60 migration (P<0.03, n=4) when compared to vehicle. Thus our results suggest that activation of MR leads to PMN cell activation that may contribute to vascular inflammatory responses in vivo.