How noise and coupling induce bursting action potentials in pancreatic {beta}-cells

Unlike isolated beta-cells, which usually produce continuous spikes or fast and irregular bursts, electrically coupled beta-cells are apt to exhibit robust bursting action potentials. We consider the noise induced by thermal fluctuations as well as that by channel-gating stochasticity and examine its effects on the action potential behavior of the beta-cell model. It is observed numerically that such noise in general helps single cells to produce a variety of electrical activities. In addition, we also probe coupling via gap junctions between neighboring cells, with heterogeneity induced by noise, to find that it enhances regular bursts.     

Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing.

Pancreatic beta-cells in an intact Islet of Langerhans exhibit bursting electrical behavior. The Chay-Keizer model describes this using a calcium-activated potassium (K-Ca) channel, but cannot account for the irregular spiking of isolated beta-cells. Atwater I., L. Rosario, and E. Rojas, Cell Calcium. 4:451-461, proposed that the K-Ca channels, which are rarely open, are shared by several cells. This suggests that the chaotic behavior of isolated cells is stochastic. We have revised the Chay-Keizer model to incorporate voltage clamp data of Rorsman and Trube and extended it to include stochastic K-Ca channels. This model can describe the behavior of single cells, as well as that of clusters of cells tightly coupled by gap junctions. As the size of the clusters is increased, the electrical activity shows a transition from chaotic spiking to regular bursting. Although the model of coupling is over-simplified, the simulations lend support to the hypothesis that bursting is the result of channel sharing.     

Bifurcations of emergent bursting in a neuronal network

Complex neuronal networks are an important tool to help explain paradoxical phenomena observed in biological recordings. Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms. Using a previously developed network model of the milk-ejection reflex in oxytocin cells, we show how we can reduce a complex model with many variables and complex network topologies to a tractable model with two variables, while retaining all key qualitative features of the original model. The approach enables us to uncover how emergent synchronous bursting can arise from a neuronal network which embodies known biological features. Surprisingly, the bursting mechanisms are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multiple time scale oscillations at the membrane potential level and the firing rate level.     

Role of single-channel stochastic noise on bursting clusters of pancreatic beta-cells.

To study why pancreatic beta-cells prefer to burst as a multi-cellular complex, we have formulated a stochastic model for bursting clusters of excitable cells. Our model incorporated a delayed rectifier K+ channel, a fast voltage-gated Ca2+ channel, and a slow Cai-blockable Ca2+ channel. The fraction of ATP-sensitive K+ channels that may still be active in the bursting regime was included in the model as a leak current. We then developed an efficient method for simulating an ionic current component of an excitable cell that contains several thousands of channels opening simultaneously under unclamped voltage. Single channel open-close stochastic events were incorporated into the model by use of binomially distributed random numbers. Our simulations revealed that in an isolated beta-cell [Ca2+]i oscillates with a small amplitude about a low [Ca2+]i. However, in a large cluster of tightly coupled cells, stable bursts develop, and [Ca2+]i oscillates with a larger amplitude about a higher [Ca2+]i. This may explain why single beta-cells do not burst and also do not release insulin.     

Three roads to islet bursting: emergent oscillations in coupled phantom bursters

Glucose-induced membrane potential and Ca(2+) oscillations in isolated pancreatic beta-cells occur over a wide range of frequencies, from >6/min (fast) to <1/min (slow). However, cells within intact islets generally oscillate with periods of 10-60 s (medium). The phantom bursting concept addresses how beta-cells can generate such a wide range of frequencies. Here, we explore an updated phantom bursting model to determine how heterogeneity in a single parameter can explain both the broad frequency range observed in single cells and the rarity of medium oscillations. We then incorporate the single-cell model into an islet model with parameter heterogeneity. We show that strongly coupled islets must be composed of predominantly medium oscillating single cells or a mixture of fast and slow cells to robustly produce medium oscillations. Surprisingly, we find that this constraint does not hold for moderate coupling, and that robustly medium oscillating islets can arise from populations of single cells that are essentially all slow or all fast. Thus, with coupled phantom bursters, medium oscillating islets can be constructed out of cells that are either all fast, all slow, or a combination of the two.     

ATP-sensitive potassium channel and bursting in the pancreatic beta cell. A theoretical study.

Based on the existence of ATP-sensitive potassium channels in the plasma membrane of pancreatic beta cells, we develop a quantitative explanation of the electrical activity observed in pancreatic islets. The proposed mechanism involves the voltage-dependent inward calcium and outward potassium currents described by Rorsman and Trube (1986), which are voltage-activated when an increase in the cytoplasmic ATP/ADP ratio decreases the conductance of the ATP-sensitive potassium channels. It is proposed that modulation of the ATP/ADP ratio occurs through calcium inhibition of oxidative phosphorylation. In this picture the mitochondria serve as a transducer of metabolic activity whose sensitivity is modulated by cytosolic calcium. Solution of the differential equations that describe this mechanism gives rise to both bursting and continuous spiking electrical activity similar to that observed experimentally. While the mechanism for bursting in this model involves the ATP/ADP ratio, the feedback is still provided by calcium, as originally proposed by Chay and Keizer (1983) using a Ca2+-activated potassium conductance. A mixed-model, which includes both ATP-sensitive and Ca2+-activated potassium conductances, also reproduces the experimentally observed electrical activity and may correspond more closely to the actual situation in vivo.     

Complex bursting in pancreatic islets: a potential glycolytic mechanism

The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis.     

Afferent bursting activity of ruff lateral line induced by background noise stimulation

Summary Single unit resting activities were recorded from fibres innervating a neuromast of the supra-orbital canal of the lateral line system of the ruff (Acerina cernua). The interval histogram of 1 of the 4 types of resting activity had a bimodal distribution (bursting activity). The resting activity of these fibres was compared with the measured vibration of the experimental table. The conclusion that the bursting activity is not spontaneous but is caused by small background vibrations of the table was supported by recording of extracellular hair cell responses.Abbreviation ISI Interspike interval     

Large dense-core vesicle exocytosis in pancreatic β-cells monitored by capacitance measurements

This article discusses the currently used methodologies for monitoring exocytosis as changes in cell capacitance. Details are given on composition of solutions, experimental protocols, and how the observed responses can be interpreted physiologically. The concepts are illustrated by examples from our own work on insulin-releasing pancreatic β-cells. Finally, we consider the feasibility of applying capacitance measurements to endocrine cells in intact pancreatic islets, where the cells are electrically coupled to each other.     

Modulation of the bursting properties of single mouse pancreatic beta-cells by artificial conductances

Glucose triggers bursting activity in pancreatic islets, which mediates the Ca2+ uptake that triggers insulin secretion. Aside from the channel mechanism responsible for bursting, which remains unsettled, it is not clear whether bursting is an endogenous property of individual beta-cells or requires an electrically coupled islet. While many workers report stochastic firing or quasibursting in single cells, a few reports describe single-cell bursts much longer (minutes) than those of islets (15-60 s). We studied the behavior of single cells systematically to help resolve this issue. Perforated patch recordings were made from single mouse beta-cells or hamster insulinoma tumor cells in current clamp at 30-35 degrees C, using standard K+-rich pipette solution and external solutions containing 11.1 mM glucose. Dynamic clamp was used to apply artificial KATP and Ca2+ channel conductances to cells in current clamp to assess the role of Ca2+ and KATP channels in single cell firing. The electrical activity we observed in mouse beta-cells was heterogeneous, with three basic patterns encountered: 1) repetitive fast spiking; 2) fast spikes superimposed on brief (<5 s) plateaus; or 3) periodic plateaus of longer duration (10-20 s) with small spikes. Pattern 2 was most similar to islet bursting but was significantly faster. Burst plateaus lasting on the order of minutes were only observed when recordings were made from cell clusters. Adding gCa to cells increased the depolarizing drive of bursting and lengthened the plateaus, whereas adding gKATP hyperpolarized the cells and lengthened the silent phases. Adding gCa and gKATP together did not cancel out their individual effects but could induce robust bursts that resembled those of islets, and with increased period. These added currents had no slow components, indicating that the mechanisms of physiological bursting are likely to be endogenous to single beta-cells. It is unlikely that the fast bursting (class 2) was due to oscillations in gKATP because it persisted in 100 microM tolbutamide. The ability of small exogenous currents to modify beta-cell firing patterns supports the hypothesis that single cells contain the necessary mechanisms for bursting but often fail to exhibit this behavior because of heterogeneity of cell parameters.     

Phantom bursting is highly sensitive to noise and unlikely to account for slow bursting in beta-cells: considerations in favor of metabolically driven oscillations

Pancreatic beta-cells show bursting electrical activity with a wide range of burst periods ranging from a few seconds, often seen in isolated cells, over tens of seconds (medium bursting), usually observed in intact islets, to several minutes. The phantom burster model [Bertram, R., Previte, J., Sherman, A., Kinard, T.A., Satin, L.S., 2000. The phantom burster model for pancreatic beta-cells. Biophys. J. 79, 2880-2892] provided a framework, which covered this span, and gave an explanation of how to obtain medium bursting combining two processes operating on different time scales. However, single cells are subjected to stochastic fluctuations in plasma membrane currents, which are likely to disturb the bursting mechanism and transform medium bursters into spikers or very fast bursters. We present a polynomial, minimal, phantom burster model and show that noise modifies the plateau fraction and lowers the burst period dramatically in phantom bursters. It is therefore unlikely that slow bursting in single cells is driven by the slow phantom bursting mechanism, but could instead be driven by oscillations in glycolysis, which we show are stable to random ion channel fluctuations. Moreover, so-called compound bursting can be converted to apparent slow bursting by noise, which could explain why compound bursting and mixed Ca(2+) oscillations are seen mainly in intact islets.     

Variability of bursting patterns in a neuron model in the presence of noise

Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent, and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped windows.