On depolarization-evoked exocytosis as a function of calcium entry: possibilities and pitfalls

Explicit Theoretical Analysis of How the Rate of Exocytosis Depends on Local Control by Ca2+ Channels

Hormones and neurotransmitters are released from cells by calcium-regulated exocytosis, and local coupling between Ca²⁺ channels (CaVs) and secretory granules is a key factor determining the exocytosis rate. Here, we devise a methodology based on Markov chain models that allows us to obtain analytic results for the expected rate. First, we analyze the property of the secretory complex obtained by coupling a single granule with one CaV. Then, we extend our results to a more general case where the granule is coupled with n CaVs. We investigate how the exocytosis rate is affected by varying the location of granules and CaVs. Moreover, we assume that the single granule can form complexes with inactivating or non-inactivating CaVs. We find that increasing the number of CaVs coupled with the granule determines a much higher rise of the exocytosis rate that, in case of inactivating CaVs, is more pronounced when the granule is close to CaVs, while, surprisingly, in case of non-inactivating CaVs, the highest relative increase in rate is obtained when the granule is far from the CaVs. Finally, we exploit the devised model to investigate the relation between exocytosis and calcium influx. We find that the quantities are typically linearly related, as observed experimentally. For the case of inactivating CaVs, our simulations show a change of the linear relation due to near-complete inactivation of CaVs.

Ca2+ channel clustering with insulin-containing granules is disturbed in type 2 diabetes

Loss of first-phase insulin secretion is an early sign of developing type 2 diabetes (T2D). Ca²⁺ entry through voltage-gated L-type Ca²⁺ channels triggers exocytosis of insulin-containing granules in pancreatic β cells and is required for the postprandial spike in insulin secretion. Using high-resolution microscopy, we have identified a subset of docked insulin granules in human β cells and rat-derived clonal insulin 1 (INS1) cells for which localized Ca²⁺ influx triggers exocytosis with high probability and minimal latency. This immediately releasable pool (IRP) of granules, identified both structurally and functionally, was absent in β cells from human T2D donors and in INS1 cells cultured in fatty acids that mimic the diabetic state. Upon arrival at the plasma membrane, IRP granules slowly associated with 15 to 20 L-type channels. We determined that recruitment depended on a direct interaction with the synaptic protein Munc13, because expression of the II–III loop of the channel, the C2 domain of Munc13-1, or of Munc13-1 with a mutated C2 domain all disrupted L-type channel clustering at granules and ablated fast exocytosis. Thus, rapid insulin secretion requires Munc13-mediated recruitment of L-type Ca²⁺ channels in close proximity to insulin granules. Loss of this organization underlies disturbed insulin secretion kinetics in T2D.

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.

Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells

Most endocrine cells secrete hormones as a result of Ca²⁺-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca²⁺ channels, and the resulting Ca²⁺ influx elevate the intracellular Ca²⁺ concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca²⁺ dynamics, which depends on the particular pattern of electrical activity as well as Ca²⁺ channel kinetics, exocytosis is dependent on the spatial arrangement of Ca²⁺ channels and secretory granules. For example, the creation of local Ca²⁺ microdomains, where the Ca²⁺ concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca²⁺ diffusion have provided important insight into the interplay between electrical activity, Ca²⁺ channel kinetics, and the location of granules and Ca²⁺ channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca²⁺ regulated exocytosis of hormone-containing granules.

Is bursting more effective than spiking in evoking pituitary hormone secretion? A spatiotemporal simulation study of calcium and granule dynamics

Endocrine cells of the pituitary gland secrete a number of hormones, and the amount of hormone released by a cell is controlled in large part by the cell's electrical activity and subsequent Ca(2+) influx. Typical electrical behaviors of pituitary cells include continuous spiking and so-called pseudo-plateau bursting. It has been shown that the amplitude of Ca(2+) fluctuations is greater in bursting cells, leading to the hypothesis that bursting cells release more hormone than spiking cells. In this work, we apply computer simulations to test this hypothesis. We use experimental recordings of electrical activity as input to mathematical models of Ca(2+) channel activity, buffered Ca(2+) diffusion, and Ca(2+)-driven exocytosis. To compare the efficacy of spiking and bursting on the same cell, we pharmacologically block the large-conductance potassium (BK) current from a bursting cell or add a BK current to a spiking cell via dynamic clamp. We find that bursting is generally at least as effective as spiking at evoking hormone release and is often considerably more effective, even when normalizing to Ca(2+) influx. Our hybrid experimental/modeling approach confirms that adding a BK-type K(+) current, which is typically associated with decreased cell activity and reduced secretion, can actually produce an increase in hormone secretion, as suggested earlier.

Calcium current inactivation rather than pool depletion explains reduced exocytotic rate with prolonged stimulation in insulin-secreting INS-1 832/13 cells

Impairment in beta-cell exocytosis is associated with reduced insulin secretion and diabetes. Here we aimed to investigate the dynamics of Ca2+-dependent insulin exocytosis with respect to pool depletion and Ca2+-current inactivation. We studied exocytosis, measured as increase in membrane capacitance (ΔCm), as a function of calcium entry (Q) in insulin secreting INS-1 832/13 cells using patch clamp and mixed-effects statistical analysis. The observed linear relationship between ΔCm and Q suggests that Ca2+-channel inactivation rather than granule pool restrictions is responsible for the decline in exocytosis observed at longer depolarizations. INS-1 832/13 cells possess an immediately releasable pool (IRP) of ∼10 granules and most exocytosis of granules occurs from a large pool. The latter is attenuated by the calcium-buffer EGTA, while IRP is unaffected. These findings suggest that most insulin release occurs away from Ca2+-channels, and that pool depletion plays a minor role in the decline of exocytosis upon prolonged stimulation.

Ca(2+)-dependent desensitization of insulin secretion by strong potassium depolarization

Depolarization by a high K(+) concentration is a widely used experimental tool to stimulate insulin secretion. The effects occurring after the initial rise in secretion were investigated here. After the initial peak a fast decline occurred, which was followed by a slowly progressive decrease in secretion when a strong K(+) depolarization was used. At 40 mM KCl, but not at lower concentrations, the decrease continued when the glucose concentration was raised from 5 to 10 mM, suggesting an inhibitory effect of the K(+) depolarization. When tolbutamide was added instead of the glucose concentration being raised, a complete inhibition down to prestimulatory values was observed. Equimolar reduction of the NaCl concentration to preserve isoosmolarity enabled an increase in secretion in response to glucose. Unexpectedly, the same was true when the Na(+)-reduced media were made hyperosmolar by choline chloride or mannitol. The insulinotropic effect of tolbutamide was not rescued by the compensatory reduction of NaCl, suggesting a requirement for activated energy metabolism. These inhibitory effects could not be explained by a lack of depolarizing strength or by a diminished free cytosolic Ca(2+) concentration ([Ca(2+)](i)). Rather, the complexation of extracellular Ca(2+) concomitant with the K(+) depolarization markedly diminished [Ca(2+)](i) and attenuated the inhibitory action of 40 mM KCl. This suggests that a strong but not a moderate depolarization by K(+) induces a [Ca(2+)](i)-dependent, slowly progressive desensitization of the secretory machinery. In contrast, the decline immediately following the initial peak of secretion may result from the inactivation of voltage-dependent Ca(2+) channels.

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.