Model for synchronization of pancreatic beta-cells by gap junction coupling

Functional coupling in bovine ciliary epithelial cells is modulated by carbachol

The functional coupling of the ciliary epithelium was studied in isolated pairs (couplets) of pigmented ciliary epithelial (PCE) and nonpigmented ciliary epithelial (NPCE) cells using the whole cell patch clamp and the fluorescent dye lucifer yellow. One cell of the pair (usually the NPCE cell of a NPCE-PCE cell couplet) was accessed with a 2-5 M omega electrode, containing 1-2 mM lucifer yellow, in the whole cell configuration of the patch clamp. After voltage-clamp experiments were completed, cells were viewed under a fluorescent microscope to confirm that the cells were coupled. The electrical coupling of the cells was also studied by calculating the capacitance (using the time-domain technique), assuming a "supercell" model for coupled cells. The mean capacitance of coupled pairs was 79.8 +/- 4.3 (SE) pF (n = 47) compared with single cell capacitances of 36.8 +/- 3.4 pF (n = 10) for PCE cells and 38.1 +/- 3.1 pF (n = 15) for NPCE cells. Octanol, carbachol (CCh), and raised extracellular Ca2+ concentration ([Ca2+]o) all caused uncoupling in pairs (couplets) of coupled NPCE and PCE cells. At room temperature (22-24 degrees C), the capacitance of the couplets decreased from 70.5 +/- 8.0 to 48.0 +/- 5.2 pF (n = 5) when exposed to octanol (1 mM), from 73.8 +/- 9.2 to 43.2 +/- 9.5 pF (n = 4) when exposed to CCh (100 microM), and from 80.5 +/- 6.7 to 49.9 +/- 7.8 pF (n = 4) when exposed to 10 mM [Ca2+]o. The response to CCh was dose dependent; at higher temperatures of 34-37 degrees C, 10 microM CCh caused a 38% reduction in capacitance, from 53.7 +/- 9.7 to 33.5 +/- 3.3 pF (n = 7) with a half-time of 249 s, and 100 microM CCh caused a 49% reduction in capacitance, from 51.3 +/- 5.6 to 26.0 +/- 2.4 pF (n = 7) with a half-time of 124 s. After pairs uncoupled and the uncoupling agent was washed out, the cell pairs often exhibited an increase in capacitance that we interpreted as "recoupling" or a reopening of the gap junctional communication pathway; the half-time for this process was 729 s after uncoupling with 100 microM CCh and 211 s after uncoupling with 10 microM CCh. This interpretation was confirmed optically by the spread of lucifer yellow into both cells of an uncoupled pair with a time course corresponding to the increase in electrical coupling. The controllable coupling of ciliary epithelial cells extends the idea of a functional syncytium involved in active transport. PCE cells take up solute and water from the blood, which then cross to NPCE cells via gap junctions and from there are secreted into the posterior chamber of the eye. Modulation of the coupling between NPCE and PCE cells may provide a mechanism to control secretion.

Modeling triggered cardiac activity: an analysis of the interactions between potassium blockade, rhythm pauses, and cellular coupling

It is known that under certain conditions, a combination of potassium channel blockade, sympathetic nervous activity, and pauses in sinus rhythm can increase the occurrence of cardiac arrhythmias. Although the arrhythmogenic interactions of these three factors are not completely understood, it is believed that the associated arrhythmias may be initiated by afterpotentials via a process that we refer to as propagated triggered activity. Using a two-cell computational model of ventricular action potential kinetics, we simulate nonuniform potassium blockade, sympathetic nervous activity, and pauses in sinus rhythm under conditions of hypokalemia. Under these conditions, the two-cell model suggests that (1) the arrhythmogenic interactions of potassium blockade and sympathetic nervous activity are highly dependent on heart rate; (2) triggered activity induced by potassium blockade would most likely occur during a pause in sinus rhythm; (3) during a sufficiently large pause in sinus rhythm, potassium blockade can induce triggered activity at normal levels of sympathetic activity; and (4) potassium blockade can increase the probability of triggered activity only if heart rate falls within a critical range. We also show that during pauses in sinus rhythm, two-cell triggering interactions between potassium blockade and sympathetic activity closely parallel the parametric displacement of the dynamic instability underlying the afterpotentials. Our results indicate that the behavior of the triggering mechanism studied here is consistent with that of pause-induced arrhythmias.

Single-microelectrode voltage clamp measurements of pancreatic beta-cell membrane ionic currents in situ

A conventional patch clamp amplifier was used to test the feasibility of measuring whole-cell ionic currents under voltage clamp conditions from beta-cells in intact mouse islets of Langerhans perifused with bicarbonate Krebs buffer at 37 degrees C. Cells impaled with a high resistance microelectrode (ca. 0.150 G omega) were identified as beta-cells by the characteristic burst pattern of electrical activity induced by 11 mM glucose. Voltage-dependent outward K+ currents were enhanced by glucose both in the presence and absence of physiological bicarbonate buffer and also by bicarbonate regardless of the presence or absence of glucose. For comparison with the usual patch clamp protocol, similar measurements were made from single rat beta-cells at room temperature; glucose did not enhance the outward currents in these cells. Voltage-dependent inward currents were recorded in the presence of tetraethylammonium (TEA), an effective blocker of the K+ channels known to be present in the beta-cell membrane. Inward currents exhibited a fast component with activation-inactivation kinetics and a delayed component with a rather slow inactivation; inward currents were dependent on Ca2+ in the extracellular solution. These results suggest the presence of either two types of voltage-gated Ca2+ channels or a single type with fast and slow inactivation. We conclude that it is feasible to use a single intracellular microelectrode to measure voltage-gated membrane currents in the beta-cell within the intact islet at 37 degrees C, under conditions that support normal glucose-induced insulin secretion and that glucose enhances an as yet unidentified voltage-dependent outward K+ current.

Estimating and eliminating junctional current in coupled cell populations by leak subtraction. A computational study

The quantitative characterization of ion channel properties in pancreatic beta-cells under typical patch clamp conditions can be questioned because of the unreconciled differences in experimental conditions and observed behavior between microelectrode recordings of membrane potential in intact islets of Langerhans and patch recordings of single cells. Complex bursting is reliably observed in islets but not in isolated cells under patch clamp conditions. E. Rojas et al. (J. Membrane Biol. 143:65-77, 1995) have attempted to circumvent these incompatibilities by measuring currents in beta-cells in intact islets by voltage-clamping with intracellular microelectrodes (150-250 M omega tip resistance). The major potential pitfall is that beta-cells within the islet are electrically coupled, and contaminating coupling currents must be subtracted from current measurements, just as linear leak currents are typically subtracted. To characterize the conditions under which such coupling current subtraction is valid, we have conducted a computational study of a model islet. Assuming that the impaled cell is well clamped, we calculate the native and coupling components of the observed current. Our simulations illustrate that coupling can be reliably subtracted when neighbor cells' potentials are constant or vary only slowly (e.g., during their silent phases) but not when they vary rapidly (e.g., during their active phases). We also show how to estimate coupling conductances in the intact islet from measurements of coupling currents.

Metabolic regulation of intracellular calcium concentration in mouse pancreatic islets of Langerhans

Intracellular Ca2+ concentration ([Ca2+]i) handling during K(+)-induced Ca2+ loads was studied in single islets of Langerhans. K(+)-induced depolarization caused a rapid and transient rise in [Ca2+]i. After K+ removal [Ca2+]i declined with a time course usually fitted by the sum of two exponential functions. Partial Na+ removal increased the resting [Ca2+]i level, indicating the existence of a Na+/Ca2+ exchange, but only slightly impaired the recovery from Ca2+ loads. Metabolic poisoning with CN- increased the resting Ca2+ level and slowed down the recovery from Ca2+ loads. Removal of external Na+ in islets poisoned with CN- strongly inhibited Ca2+ removal mechanisms. An increase in the glucose concentration from 0 to 16 mM (in the presence of diazoxide) resulted in a decrease in the resting [Ca2+]i and an acceleration of [Ca2+]i recovery from K+ loads. These results suggest that the main mechanism responsible for Ca2+ homeostasis is dependent on metabolic energy and that such energy can be provided by glucose metabolism.

Model Based on Extracellular Potassium for Spontaneous Synchronous Activity in Developing Retinas

Waves of action-potential bursts propagate across the ganglion-cell surface of isolated developing retinas. It has been suggested that the rise of extracellular potassium concentration following a burst of action potentials in a cell may underlie these waves by depolarizing neighbor cells. This suggestion is sensible for developing tissues, since their glial system is immature. We tested whether this extracellular-potassium suggestion is feasible. For this purpose, we built a realistic biophysical model of the ganglion-cell layer of the developing retina. Simulations with this model show that increases of extracellular potassium are sufficiently high (about fourfold) to mediate the waves consistently with experimental physiological and pharmacological data. Even if another mechanism mediates the waves, these simulations indicate that extracellular potassium should significantly modulate the waves' properties.

Anti-phase, asymmetric and aperiodic oscillations in excitable cells--I. Coupled bursters

I seek to explain phenomena observed in simulations of populations of gap junction-coupled bursting cells by studying the dynamics of identical pairs. I use a simplified model for pancreatic beta-cells and decompose the system into fast (spike-generating) and slow subsystems to show how bifurcations of the fast subsystem affect bursting behavior. When coupling is weak, the spikes are not in phase but rather are anti-phase, asymmetric or quasi-periodic. These solutions all support bursting with smaller amplitude spikes than the in-phase case, leading to increased burst period. A key geometrical feature underlying this is that the in-phase periodic solution branch terminates in a homoclinic orbit. The same mechanism also provides a model for bursting as an emergent property of populations; cells which are not intrinsic bursters can burst when coupled. This phenomenon is enhanced when symmetry is broken by making the cells differ in a parameter.

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.

Why pancreatic islets burst but single beta cells do not. The heterogeneity hypothesis

Previous mathematical modeling of beta cell electrical activity has involved single cells or, recently, clusters of identical cells. Here we model clusters of heterogeneous cells that differ in size, channel density, and other parameters. We use gap-junctional electrical coupling, with conductances determined by an experimental histogram. We find that, for reasonable parameter distributions, only a small proportion of isolated beta cells will burst when uncoupled, at any given value of a glucose-sensing parameter. However, a coupled, heterogeneous cluster of such cells, if sufficiently large (approximately 125 cells), will burst synchronously. Small clusters of such cells will burst only with low probability. In large clusters, the dynamics of intracellular calcium compare well with experiments. Also, these clusters possess a dose-response curve of increasing average electrical activity with respect to a glucose-sensing parameter that is sharp when the cluster is coupled, but shallow when the cluster is decoupled into individual cells. This is in agreement with comparative experiments on cells in suspension and islets.

Rhythmogenic effects of weak electrotonic coupling in neuronal models

Strong gap-junctional coupling can synchronize the electrical oscillations of cells, but we show, in a theoretical model, that weak coupling can phase lock two cells 180 degrees out-of-phase. Antiphase oscillations can exist in parameter regimens where in-phase oscillations break down. Some consequences are (i) coupling two excitable cells leads to pacemaking, (ii) coupling two pacemaker cells leads to bursting, and (iii) coupling two bursters increases burst period. The latter shows that details of the fast spikes can affect macroscopic properties of the slow bursts. These effects hold in other models for bursting and may play a role in the collective behavior of cellular ensembles.

Electrophysiological properties of rat calcitonin-secreting cells

The spontaneous electrical activity of calcitonin-secreting cells (C-cells) appears to play an important role in the coupling of fluctuations in the extracellular Ca2+ to changes in the intracellular Ca2+ concentration and thus for calcitonin secretion. Using the patch clamp technique, we have investigated the spontaneous electrical activity and the underlying ionic currents in C-cells of the rMTC 44-2 cell line. With 1.2 mM external Ca2+, the membrane potential was -46.1 +/- 1.7 mV (n = 58) and about 30% of the cells spontaneously fired action potentials. Rising the external Ca2+ to 1.8 mM caused the cells to depolarize to -42.1 +/- 2.1 mV (n = 56) and spontaneous electrical activity was seen in about 70% of cells. Under voltage clamp conditions, tetrodotoxin-sensitive voltage-dependent Na+ currents, outward-rectifying K+ currents and isradipine-, omega-conotoxin-sensitive as well as isradipine- and omega-conotoxin-insensitive Ca2+ currents were observed. These voltage-dependent currents appear to be the major ionic currents contributing to action potentials in C-cells and to participate in calcitonin secretion.