Investigating How Calcium Diffusion Affects Metabolic Oscillations and Synchronization of Pancreatic Beta Cells

Diabetes is a disease characterized by improper concentrations of blood glucose due to irregular insulin production or sensitivity. Coupled in islets of Langerhans within the pancreas, β-cells are responsible for the production and regulation of insulin based on changes in glucose levels. Using the Dual Oscillator Model (DOM), we will examine how calcium handling between individual pancreatic β-cells affects the synchronization of metabolic oscillations within electrically coupled islets. Calcium permeability was implemented into the DOM, and numerical solutions of the system were obtained via MATLAB using a modified ordinary differential equation solver for stiff systems and the Automatic Differentiation for MATLAB software. We developed a synchronization index to quantitatively describe the synchronization of variables between nearest neighboring cells and throughout the islet as a whole. We considered how calcium permeability between heterogeneous cells affects the behavior of metabolic oscillations and their synchronization. In particular, we examined fructose-1, 6-bisphosphate. In our study metabolic oscillations were always maintained. We also showed that, for low to moderate levels of electrical coupling, calcium permeability increased the synchronization index, but increasing calcium permeability had little effect on synchronization when cells were already strongly synchronized with strong electrical coupling. Heterogeneity due to glucose influx or initial state of the cells had similar synchronization results

The Interaction of Calcium and Metabolic Oscillations in Pancreatic β-cells

Diabetes is a disease characterized by an excessive level of glucose in the bloodstream, which may be a result of improper insulin secretion. Insulin is secreted in a bursting behavior of pancreatic $\beta$-cells in islets, which is affected by oscillations of cytosolic calcium concentration. We used the Dual Oscillator Model to explore the role of calcium in calcium oscillation independent and calcium oscillation dependent modes and the synchronization of metabolic oscillations in electrically coupled $\beta$-cells. We implemented a synchronization index in order to better measure the synchronization of the $\beta$-cells within an islet and we studied heterogeneous modes of coupled $\beta$-cells. We saw that increasing calcium coupling or voltage coupling in heterogeneous cases increases synchronization; however, in certain cases increasing both voltage and calcium coupling causes desynchronization. To better represent an islet, we altered previous code to allow for a greater number of cells to be simulated

Spontaneous Calcium Release in Cardiac Myocytes: Store Overload and Electrical Dynamics

Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca2+) mishandling in cardiac muscle cells. We adapt Izu\u27s et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes implemented by Gobbert, and analyzed in Coulibaly et al. to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca2+ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with known biological models and principles, giving us a thorough understanding of several factors that influence Ca2+ dynamics in cardiac myocytes. Specifically, dynamic calcium store will cap previous calcium blow-up seen in the model. Calcium channels located in spatial opposition of calcium release units produce more predictable intracellular calcium propagation. And we used multi-parametric calcium dynamics tables, which act as a multidimensional bifurcation diagram, to visualize parameter boundaries between different biophysical dynamics

Vitamin D Binding Protein and Monocyte Response to 25-Hydroxyvitamin D and 1,25-Dihydroxyvitamin D: Analysis by Mathematical Modeling

Vitamin D binding protein (DBP) plays a key role in the bioavailability of active 1,25-dihydroxyvitamin D (1,25(OH)2D) and its precursor 25-hydroxyvitamin D (25OHD), but accurate analysis of DBP-bound and free 25OHD and 1,25(OH)2D is difficult. To address this, two new mathematical models were developed to estimate: 1) serum levels of free 25OHD/1,25(OH)2D based on DBP concentration and genotype; 2) the impact of DBP on the biological activity of 25OHD/1,25(OH)2D in vivo. The initial extracellular steady state (eSS) model predicted that 50 nM 25OHD and 100 pM 1,25(OH)2D), <0.1% 25OHD and <1.5% 1,25(OH)2D are ‘free’ in vivo. However, for any given concentration of total 25OHD, levels of free 25OHD are higher for low affinity versus high affinity forms of DBP. The eSS model was then combined with an intracellular (iSS) model that incorporated conversion of 25OHD to 1,25(OH)2D via the enzyme CYP27B1, as well as binding of 1,25(OH)2D to the vitamin D receptor (VDR). The iSS model was optimized to 25OHD/1,25(OH)2D-mediated in vitro dose-responsive induction of the vitamin D target gene cathelicidin (CAMP) in human monocytes. The iSS model was then used to predict vitamin D activity in vivo (100% serum). The predicted induction of CAMP in vivo was minimal at basal settings but increased with enhanced expression of VDR (5-fold) and CYP27B1 (10-fold). Consistent with the eSS model, the iSS model predicted stronger responses to 25OHD for low affinity forms of DBP. Finally, the iSS model was used to compare the efficiency of endogenously synthesized versus exogenously added 1,25(OH)2D. Data strongly support the endogenous model as the most viable mode for CAMP induction by vitamin D in vivo. These novel mathematical models underline the importance of DBP as a determinant of vitamin D ‘status’ in vivo, with future implications for clinical studies of vitamin D status and supplementation

Synchronizing beta cells in the pancreas

The secretion of insulin from the pancreas relies on both gap junctions and subpopulations of beta cells with specific intrinsic properties

Vitamin D binding protein and monocyte response to 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D: analysis by mathematical modeling.

Vitamin D binding protein (DBP) plays a key role in the bioavailability of active 1,25-dihydroxyvitamin D (1,25(OH)(2)D) and its precursor 25-hydroxyvitamin D (25OHD), but accurate analysis of DBP-bound and free 25OHD and 1,25(OH)(2)D is difficult. To address this, two new mathematical models were developed to estimate: 1) serum levels of free 25OHD/1,25(OH)(2)D based on DBP concentration and genotype; 2) the impact of DBP on the biological activity of 25OHD/1,25(OH)(2)D in vivo. The initial extracellular steady state (eSS) model predicted that 50 nM 25OHD and 100 pM 1,25(OH)(2)D), &lt;0.1% 25OHD and &lt;1.5% 1,25(OH)(2)D are 'free' in vivo. However, for any given concentration of total 25OHD, levels of free 25OHD are higher for low affinity versus high affinity forms of DBP. The eSS model was then combined with an intracellular (iSS) model that incorporated conversion of 25OHD to 1,25(OH)(2)D via the enzyme CYP27B1, as well as binding of 1,25(OH)(2)D to the vitamin D receptor (VDR). The iSS model was optimized to 25OHD/1,25(OH)(2)D-mediated in vitro dose-responsive induction of the vitamin D target gene cathelicidin (CAMP) in human monocytes. The iSS model was then used to predict vitamin D activity in vivo (100% serum). The predicted induction of CAMP in vivo was minimal at basal settings but increased with enhanced expression of VDR (5-fold) and CYP27B1 (10-fold). Consistent with the eSS model, the iSS model predicted stronger responses to 25OHD for low affinity forms of DBP. Finally, the iSS model was used to compare the efficiency of endogenously synthesized versus exogenously added 1,25(OH)(2)D. Data strongly support the endogenous model as the most viable mode for CAMP induction by vitamin D in vivo. These novel mathematical models underline the importance of DBP as a determinant of vitamin D 'status' in vivo, with future implications for clinical studies of vitamin D status and supplementation