Insulin secretory granules enter a highly calcium-sensitive state following palmitate-induced dissociation from calcium channels: a theoretical study

Statistical Frailty Modeling for Quantitative Analysis of Exocytotic Events Recorded by Live Cell Imaging: Rapid Release of Insulin-Containing Granules Is Impaired in Human Diabetic β-cells

Hormones and neurotransmitters are released when secretory granules or synaptic vesicles fuse with the cell membrane, a process denoted exocytosis. Modern imaging techniques, in particular total internal reflection fluorescence (TIRF) microscopy, allow the investigator to monitor secretory granules at the plasma membrane before and when they undergo exocytosis. However, rigorous statistical approaches for temporal analysis of such exocytosis data are still lacking. We propose here that statistical methods from time-to-event (also known as survival) analysis are well suited for the problem. These methods are typically used in clinical settings when individuals are followed over time to the occurrence of an event such as death, remission or conception. We model the rate of exocytosis in response to pulses of stimuli in insulin-secreting pancreatic β-cell from healthy and diabetic human donors using piecewise-constant hazard modeling. To study heterogeneity in the granule population we exploit frailty modeling, which describe unobserved differences in the propensity to exocytosis. In particular, we insert a discrete frailty in our statistical model to account for the higher rate of exocytosis in an immediately releasable pool (IRP) of insulin-containing granules. Estimates of parameters are obtained from maximum-likelihood methods. Since granules within the same cell are correlated, i.e., the data are clustered, a modified likelihood function is used for log-likelihood ratio tests in order to perform valid inference. Our approach allows us for example to estimate the size of the IRP in the cells, and we find that the IRP is deficient in diabetic cells. This novel application of time-to-event analysis and frailty modeling should be useful also for the study of other well-defined temporal events at the cellular level.

Mathematical models for insulin secretion in pancreatic β-cells

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

Coupling of metabolic, second messenger pathways and insulin granule dynamics in pancreatic beta-cells: a computational analysis

Insulin secretory responses to nutrient stimuli and hormonal modulators in pancreatic beta-cells are controlled by a variety of secondary messengers. We have analyzed numerous mechanisms responsible for regulated exocytosis in these cells and present an integrated mathematical model of cytosolic Ca²⁺, cAMP and granule dynamics. The insulin-containing granules in the beta-cell were divided into four classes: a large "reserve" granule pool, a smaller pool of the morphologically docked granules that is chemically 'primed' for release or the "readily releasable pool", and a pool of "restless newcomer granules" that undergoes preferential exocytosis. The model incorporates glucose and other aspects of metabolism, the cAMP amplifying pathway, insulin granule dynamics and the exocyst concept for granule binding. The values of most of the model parameters were inferred from available experimental data. The model can generate both the fast first phase and slow biphasic insulin secretion found experimentally in response to a step increase of membrane potential or of glucose. The numerical simulations have also reproduced a variety of experimental conditions, such as periodic stimulation by high K⁺ and the potentiation induced in islets by pre-incubation with cAMP pathway activators. The explicit incorporation of Ca²⁺ channels, Ca²⁺ and cAMP dynamics allows the model to be further connected to current models for calcium and metabolic dynamics and provides an interpretation of the roles of the triggering and amplifying pathways of glucose-stimulated insulin secretion. The model may be important in the identification of pharmacological targets for improving insulin secretion in type 2 diabetes.

Mathematical modeling and statistical analysis of calcium-regulated insulin granule exocytosis in β-cells from mice and humans

Insulin is released from pancreatic β-cells as a result of Ca²⁺-evoked exocytosis of dense-core granules. Secretion is biphasic, which has been suggested to correspond to the release of different granule pools. Here we review and carefully reanalyze previously published patch-clamp data on depolarization-evoked Ca²⁺-currents and corresponding capacitance measurements. Using a statistical mixed-effects model, we show that the data indicate that pool depletion is negligible in response to short depolarizations in mouse β-cells. We then review mathematical models of granule dynamics and exocytosis in rodent β-cells and present a mathematical description of Ca²⁺-evoked exocytosis in human β-cells, which show clear differences to their rodent counterparts. The model suggests that L- and P/Q-type Ca²⁺-channels are involved to a similar degree in exocytosis during electrical activity in human β-cells.