Modelling and analysis of cAMP-induced mixed-mode oscillations in cortical neurons: Critical roles of HCN and M-type potassium channels.

Cyclic AMP controls neuronal ion channel activity. For example hyperpolarization-activated cyclic nucleotide-gated (HCN) and M-type K+ channels are activated by cAMP. These effects have been suggested to be involved in astrocyte control of neuronal activity, for example, by controlling the action potential firing frequency. In cortical neurons, cAMP can induce mixed-mode oscillations (MMOs) consisting of small-amplitude, subthreshold oscillations separating complete action potentials, which lowers the firing frequency greatly. We extend a model of neuronal activity by including HCN and M channels, and show that it can reproduce a series of experimental results under various conditions involving and inferring with cAMP-induced activation of HCN and M channels. In particular, we find that the model can exhibit MMOs as found experimentally, and argue that both HCN and M channels are crucial for reproducing these patterns. To understand how M and HCN channels contribute to produce MMOs, we exploit the fact that the model is a three-time scale dynamical system with one fast, two slow, and two super-slow variables. We show that the MMO mechanism does not rely on the super-slow dynamics of HCN and M channel gating variables, since the model is able to produce MMOs even when HCN and M channel activity is kept constant. In other words, the cAMP-induced increase in the average activity of HCN and M channels allows MMOs to be produced by the slow-fast subsystem alone. We show that the slow-fast subsystem MMOs are due to a folded node singularity, a geometrical structure well known to be involved in the generation of MMOs in slow-fast systems. Besides raising new mathematical questions for multiple-timescale systems, our work is a starting point for future research on how cAMP signalling, for example resulting from interactions between neurons and glial cells, affects neuronal activity via HCN and M channels.

Amplitude-modulated spiking as a novel route to bursting: Coupling-induced mixed-mode oscillations by symmetry breaking.

Mixed-mode oscillations consisting of alternating small- and large-amplitude oscillations are increasingly well understood and are often caused by folded singularities, canard orbits, or singular Hopf bifurcations. We show that coupling between identical nonlinear oscillators can cause mixed-mode oscillations because of symmetry breaking. This behavior is illustrated for diffusively coupled FitzHugh-Nagumo oscillators with negative coupling constant, and we show that it is caused by a singular Hopf bifurcation related to a folded saddle-node (FSN) singularity. Inspired by earlier work on models of pancreatic beta-cells [Sherman, Bull. Math. Biol. 56, 811 (1994)], we then identify a new type of bursting dynamics due to diffusive coupling of cells firing action potentials when isolated. In the presence of coupling, small-amplitude oscillations in the action potential height precede transitions to square-wave bursting. Confirming the hypothesis from the earlier work that this behavior is related to a pitchfork-of-limit-cycles bifurcation in the fast subsystem, we find that it is caused by symmetry breaking. Moreover, we show that it is organized by a FSN in the averaged system, which causes a singular Hopf bifurcation. Such behavior is related to the recently studied dynamics caused by the so-called torus canards.

Calcium signaling and secretory granule pool dynamics underlie biphasic insulin secretion and its amplification by glucose: experiments and modeling.

Glucose-stimulated insulin secretion from pancreatic ß-cells is controlled by a triggering pathway that culminates in calcium influx and regulated exocytosis of secretory granules, and by a less understood amplifying pathway that augments calcium-induced exocytosis. In response to an abrupt increase in glucose concentration, insulin secretion exhibits a first peak followed by a lower sustained second phase. This biphasic secretion pattern is disturbed in diabetes. It has been attributed to depletion and subsequent refilling of a readily releasable pool of granules or to the phasic cytosolic calcium dynamics induced by glucose. Here, we apply mathematical modeling to experimental data from mouse islets to investigate how calcium and granule pool dynamics interact to control dynamic insulin secretion. Experimental calcium traces are used as inputs in three increasingly complex models of pool dynamics, which are fitted to insulin secretory patterns obtained using a set of protocols of glucose and tolbutamide stimulation. New calcium and secretion data for so-called staircase protocols, in which the glucose concentration is progressively increased, are presented. These data can be reproduced without assuming any heterogeneity in the model, in contrast to previous modeling, because of nontrivial calcium dynamics. We find that amplification by glucose can be explained by increased mobilization and priming of granules. Overall, our results indicate that calcium dynamics contribute substantially to shaping insulin secretion kinetics, which implies that better insight into the events creating phasic calcium changes in human ß-cells is needed to understand the cellular mechanisms that disturb biphasic insulin secretion in diabetes.

Gap-junction coupling can prolong beta-cell burst period by an order of magnitude via phantom bursting.

Pancreatic ß-cells show multiple intrinsic modes of oscillation with bursting electrical activity playing a crucial role. Bursting is seen both in experimentally isolated ß-cells as well as in electrically coupled cells in the pancreatic islets, but the burst period is typically an order of magnitude greater in coupled cells. This difference has previously been attributed to noisier dynamics, or perturbed electrophysiological properties, in isolated ß-cells. Here, we show that diffusive coupling alone can extend the period more than ten-fold in bursting oscillators modeled with a so-called phantom burster model and analyze this result with slow-fast bifurcation analysis of an electrically coupled pair of cells. Our results should be applicable to other scenarios where coupling of bursting units, e.g., neurons, may increase the oscillation period drastically.

Spatiotemporal Modeling of Triggering and Amplifying Pathways in GLP-1 Secreting Intestinal L Cells.

Glucagon-like peptide 1 (GLP-1) is secreted by intestinal L-cells, and augments glucose-induced insulin secretion, thus playing an important role in glucose control. The stimulus-secretion pathway in L-cells is still incompletely understood and a topic of debate. It is known that GLP-1 secreting cells can sense glucose to promote electrical activity either by the electrogenic sodium-glucose cotransporter SGLT1, or by closure of ATP-sensitive potassium channels after glucose metabolism. Glucose also has an effect on GLP-1 secretion downstream of electrical activity. An important aspect to take into account is the spatial organization of the cell. Indeed, the glucose transporter GLUT2 is located at the basolateral, vascular side, while SGLT1 is exposed to luminal glucose at the apical side of the cell, suggesting that the two types of transporters play different roles in glucose sensing. Here, we extend our recent model of electrical activity in primary L-cells to include spatiotemporal glucose and Ca2+ dynamics, and GLP-1 secretion. The model confirmed that glucose transportation into the cell through SGLT1 cotransporters can induce Ca2+ influx and release of GLP-1 as a result of electrical activity, while glucose metabolism alone is insufficient to depolarize the cell and evoke GLP-1 secretion in the model, suggesting a crucial role for SGLT1 in triggering GLP-1 release in agreement with experimental studies. We suggest a secondary, but participating, role of GLUT2 and glucose metabolism for GLP-1 secretion via an amplifying pathway that increases the secretion rate at a given Ca2+ level.

Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry.

Large-conductance Ca2+-dependent K+ (BKCa) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca2+ (CaV) channels. Recent stochastic simulations of the BKCa-CaV complex with 1:1 stoichiometry have given important insight into the local control of BKCa channels by fluctuating nanodomains of Ca2+. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BKCa-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BKCa-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BKCa currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BKCa description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BKCa-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BKCa current that respects local interactions in BKCa-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

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.

Mathematical Modeling of Interacting Glucose-Sensing Mechanisms and Electrical Activity Underlying Glucagon-Like Peptide 1 Secretion.

Intestinal L-cells sense glucose and other nutrients, and in response release glucagon-like peptide 1 (GLP-1), peptide YY and other hormones with anti-diabetic and weight-reducing effects. The stimulus-secretion pathway in L-cells is still poorly understood, although it is known that GLP-1 secreting cells use sodium-glucose co-transporters (SGLT) and ATP-sensitive K+-channels (K(ATP)-channels) to sense intestinal glucose levels. Electrical activity then transduces glucose sensing to Ca2+-stimulated exocytosis. This particular glucose-sensing arrangement with glucose triggering both a depolarizing SGLT current as well as leading to closure of the hyperpolarizing K(ATP) current is of more general interest for our understanding of glucose-sensing cells. To dissect the interactions of these two glucose-sensing mechanisms, we build a mathematical model of electrical activity underlying GLP-1 secretion. Two sets of model parameters are presented: one set represents primary mouse colonic L-cells; the other set is based on data from the GLP-1 secreting GLUTag cell line. The model is then used to obtain insight into the differences in glucose-sensing between primary L-cells and GLUTag cells. Our results illuminate how the two glucose-sensing mechanisms interact, and suggest that the depolarizing effect of SGLT currents is modulated by K(ATP)-channel activity. Based on our simulations, we propose that primary L-cells encode the glucose signal as changes in action potential amplitude, whereas GLUTag cells rely mainly on frequency modulation. The model should be useful for further basic, pharmacological and theoretical investigations of the cellular signals underlying endogenous GLP-1 and peptide YY release.

Heterogeneity and nearest-neighbor coupling can explain small-worldness and wave properties in pancreatic islets.

Many multicellular systems consist of coupled cells that work as a syncytium. The pancreatic islet of Langerhans is a well-studied example of such a microorgan. The islets are responsible for secretion of glucose-regulating hormones, mainly glucagon and insulin, which are released in distinct pulses. In order to observe pulsatile insulin secretion from the ß-cells within the islets, the cellular responses must be synchronized. It is now well established that gap junctions provide the electrical nearest-neighbor coupling that allows excitation waves to spread across islets to synchronize the ß-cell population. Surprisingly, functional coupling analysis of calcium responses in ß-cells shows small-world properties, i.e., a high degree of local coupling with a few long-range "short-cut" connections that reduce the average path-length greatly. Here, we investigate how such long-range functional coupling can appear as a result of heterogeneity, nearest-neighbor coupling, and wave propagation. Heterogeneity is also able to explain a set of experimentally observed synchronization and wave properties without introducing all-or-none cell coupling and percolation theory. Our theoretical results highlight how local biological coupling can give rise to functional small-world properties via heterogeneity and wave propagation.

Mathematical modelling of local calcium and regulated exocytosis during inhibition and stimulation of glucagon secretion from pancreatic alpha-cells.

Glucagon secretion from pancreatic alpha-cells is dysregulated in diabetes. Despite decades of investigations of the control of glucagon release by glucose and hormones, the underlying mechanisms are still debated. Recently, mathematical models have been applied to investigate the modification of electrical activity in alpha-cells as a result of glucose application. However, recent studies have shown that paracrine effects such as inhibition of glucagon secretion by glucagon-like peptide 1 (GLP-1) or stimulation of release by adrenaline involve cAMP-mediated effects downstream of electrical activity. In particular, depending of the intracellular cAMP concentration, specific types of Ca(2+) channels are inhibited or activated, which interacts with mobilization of secretory granules. To investigate these aspects of alpha-cell function theoretically, we carefully developed a mathematical model of Ca(2+) levels near open or closed Ca(2+) channels of various types, which was linked to a description of Ca(2+) below the plasma membrane, in the bulk cytosol and in the endoplasmic reticulum. We investigated how the various subcellular Ca(2+) compartments contribute to control of glucagon-exocytosis in response to glucose, GLP-1 or adrenaline. Our studies refine previous modelling studies of alpha-cell function, and provide deeper insight into the control of glucagon secretion.

Inwardly rectifying Kir2.1 currents in human ß-cells control electrical activity: characterisation and mathematical modelling.

Pancreatic ß-cells fire action potentials as do cardiac cells and neurons, and electrical activity plays a central role in glucose-stimulated insulin secretion, which is disturbed in diabetes. The inwardly rectifying Kir2.1 potassium channels (KCNJ2 gene) control cardiac electrical activity by stabilising the interspike interval. Loss-of-function abnormalities in cardiac Kir2.1 currents can lead to the long QT syndrome and alterations of cardiac excitability, and patients with some forms of long QT syndrome suffer from over-secretion of insulin, hyperinsulinemia and symptomatic hypoglycemia. The KCNJ2 gene is also expressed in human pancreatic islets, and we show that functional Kir2.1 currents are present in human ß-cells. We characterised the human Kir2.1 ß-cell current, and included it in a recent mathematical model of electrical activity in human ß-cells. Based on our simulations we propose that Kir2.1 currents control the interspike interval, and predict that blocking Kir2.1 channels increases the action potential frequency, which should augment the rate of insulin secretion. Vice versa, the model suggests that hyperactive Kir2.1 channels may lead to reduced insulin secretion. Our findings provide a putative link between increased insulin secretion and the long QT syndrome, and give novel insight into normal and disturbed ß-cell function.

Mathematical modeling of gap junction coupling and electrical activity in human ß-cells.

Coordinated insulin secretion is controlled by electrical coupling of pancreatic ß-cells due to connexin-36 gap junctions. Gap junction coupling not only synchronizes the heterogeneous ß-cell population, but can also modify the electrical behavior of the cells. These phenomena have been widely studied with mathematical models based on data from mouse ß-cells. However, it is now known that human ß-cell electrophysiology shows important differences to its rodent counterpart, and although human pancreatic islets express connexin-36 and show evidence of ß-cell coupling, these aspects have been little investigated in human ß-cells. Here we investigate theoretically, the gap junction coupling strength required for synchronizing electrical activity in a small cluster of cells simulated with a recent mathematical model of human ß-cell electrophysiology. We find a lower limit for the coupling strength of approximately 20 pS (i.e., normalized to cell size, ∼2 pS pF(-1)) below which spiking electrical activity is asynchronous. To confront this theoretical lower bound with data, we use our model to estimate from an experimental patch clamp recording that the coupling strength is approximately 100-200 pS (10-20 pS pF(-1)), similar to previous estimates in mouse ß-cells. We then investigate the role of gap junction coupling in synchronizing and modifying other forms of electrical activity in human ß-cell clusters. We find that electrical coupling can prolong the period of rapid bursting electrical activity, and synchronize metabolically driven slow bursting, in particular when the metabolic oscillators are in phase. Our results show that realistic coupling conductances are sufficient to promote synchrony in small clusters of human ß-cells as observed experimentally, and provide motivation for further detailed studies of electrical coupling in human pancreatic islets.

Mathematical modeling of heterogeneous electrophysiological responses in human ß-cells.

Electrical activity plays a pivotal role in glucose-stimulated insulin secretion from pancreatic ß-cells. Recent findings have shown that the electrophysiological characteristics of human ß-cells differ from their rodent counterparts. We show that the electrophysiological responses in human ß-cells to a range of ion channels antagonists are heterogeneous. In some cells, inhibition of small-conductance potassium currents has no effect on action potential firing, while it increases the firing frequency dramatically in other cells. Sodium channel block can sometimes reduce action potential amplitude, sometimes abolish electrical activity, and in some cells even change spiking electrical activity to rapid bursting. We show that, in contrast to L-type Ca2+-channels, P/Q-type Ca2+-currents are not necessary for action potential generation, and, surprisingly, a P/Q-type Ca2+-channel antagonist even accelerates action potential firing. By including SK-channels and Ca2+ dynamics in a previous mathematical model of electrical activity in human ß-cells, we investigate the heterogeneous and nonintuitive electrophysiological responses to ion channel antagonists, and use our findings to obtain insight in previously published insulin secretion measurements. Using our model we also study paracrine signals, and simulate slow oscillations by adding a glycolytic oscillatory component to the electrophysiological model. The heterogenous electrophysiological responses in human ß-cells must be taken into account for a deeper understanding of the mechanisms underlying insulin secretion in health and disease, and as shown here, the interdisciplinary combination of experiments and modeling increases our understanding of human ß-cell physiology.

Minimal modeling of insulin secretion in the perfused rat pancreas: a drug effect case study.

The experimental protocol of the perfused rat pancreas is commonly used to evaluate ß-cell function. In this context, mathematical models become useful tools through the determination of indexes that allow the assessment of ß-cell function in different experimental groups and the quantification of the effects of antidiabetic drugs, secretagogues, or treatments. However, a minimal model applicable to the isolated perfused rat pancreas has so far been unavailable. In this work, we adapt the C-peptide minimal model applied previously to the intravenous glucose tolerance test to obtain a specific model for the experimental settings of the perfused pancreas. Using the model, it is possible to estimate indexes describing ß-cell responsivity for first (ΦD) and second phase (ΦS, T) of insulin secretion. The model was initially applied to untreated pancreata and afterward used for the assessment of pharmacologically relevant agents (the gut hormone GLP-1, the potent GLP-1 receptor agonist lixisenatide, and a GPR40/FFAR1 agonist, SAR1) to quantify and differentiate their effect on insulin secretion. Model fit was satisfactory, and parameters were estimated with good precision for both untreated and treated pancreata. Model application showed that lixisenatide reaches improvement of ß-cell function similarly to GLP-1 (11.7- vs. 13.1-fold increase in ΦD and 2.3- vs. 2.8-fold increase in ΦS) and demonstrated that SAR1 leads to an additional improvement of ß-cell function in the presence of postprandial GLP-1 levels.

Modeling Doxorubicin Pharmacokinetics in Multiple Myeloma Suggests Mechanism of Drug Resistance.

OBJECTIVE: Multiple myeloma (MM) is a plasma cell malignancy often treated with chemotherapy drugs. Among these, doxorubicin (DOXO) is commonly employed, sometimes in combined-drug therapies, but it has to be optimally administered in order to maximize its efficacy and reduce possible side effects. To support DOXO studies and treatment optimization, here we propose an experimental/modeling approach to establish a model describing DOXO pharmacokinetics (PK) in MM cells. METHODS: A series of in vitro experiments were performed in MM1R and MOLP-2 cells. DOXO was administered at two dosages (200 nM, 450 nM) at [Formula: see text] = 0 and removed at [Formula: see text] = 3 hrs. Intracellular DOXO concentration was measured via fluorescence microscopy during both drug uptake ([Formula: see text] = 0-3 hrs) and release phases ([Formula: see text] = 3-8 hrs). Four PK candidate models were identified, and were compared and selected based on their ability to describe DOXO data and numerical parameter identification. RESULTS: The most parsimonious model consists of three compartments describing DOXO distribution between the extracellular space, the cell cytoplasm and the nucleus, and defines the intracellular DOXO efflux rate through a Hill function, simulating a threshold/saturation drug resistance mechanism. This model predicted DOXO data well in all the experiments and provided precise parameter estimates (mean ± standard deviation coefficient of variation: 15.8 ± 12.2%). CONCLUSIONS: A reliable PK model describing DOXO uptake and release in MM cells has been successfully developed. SIGNIFICANCE: The proposed PK model, once integrated with DOXO pharmacodynamics, has the potential of allowing the study and the optimization of DOXO treatment strategies in MM.

Complex patterns of metabolic and Ca²âº entrainment in pancreatic islets by oscillatory glucose.

Glucose-stimulated insulin secretion is pulsatile and driven by intrinsic oscillations in metabolism, electrical activity, and Ca(2+) in pancreatic islets. Periodic variations in glucose can entrain islet Ca(2+) and insulin secretion, possibly promoting interislet synchronization. Here, we used fluorescence microscopy to demonstrate that glucose oscillations can induce distinct 1:1 and 1:2 entrainment of oscillations (one and two oscillations for each period of exogenous stimulus, respectively) in islet Ca(2+), NAD(P)H, and mitochondrial membrane potential. To our knowledge, this is the first demonstration of metabolic entrainment in islets, and we found that entrainment of metabolic oscillations requires voltage-gated Ca(2+) influx. We identified diverse patterns of 1:2 entrainment and showed that islet synchronization during entrainment involves adjustments of both oscillatory phase and period. All experimental findings could be recapitulated by our recently developed mathematical model, and simulations suggested that interislet variability in 1:2 entrainment patterns reflects differences in their glucose sensitivity. Finally, our simulations and recordings showed that a heterogeneous group of islets synchronized during 1:2 entrainment, resulting in a clear oscillatory response from the collective. In summary, we demonstrate that oscillatory glucose can induce complex modes of entrainment of metabolically driven oscillations in islets, and provide additional support for the notion that entrainment promotes interislet synchrony in the pancreas.

Newcomer insulin secretory granules as a highly calcium-sensitive pool.

Insulin secretion is biphasic in response to a step in glucose stimulation. Recent experiments suggest that 2 different mechanisms operate during the 2 phases, with transient first-phase secretion due to exocytosis of docked granules but the second sustained phase due largely to newcomer granules. Another line of research has shown that there exist 2 pools of releasable granules with different Ca(2+) sensitivities. An immediately releasable pool (IRP) is located in the vicinity of Ca(2+) channels, whereas a highly Ca(2+)-sensitive pool (HCSP) resides mainly away from Ca(2+) channels. We extend a previous model of exocytosis and insulin release by adding an HCSP and show that the inclusion of this pool naturally leads to insulin secretion mainly from newcomer granules during the second phase of secretion. We show that the model is compatible with data from single cells on the HCSP and from stimulation of islets by glucose, including L- and R-type Ca(2+) channel knockouts, as well as from Syntaxin-1A-deficient cells. We also use the model to investigate the relative contribution of calcium signaling and pool depletion in controlling biphasic secretion.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells.

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

Calcium Signaling in the Photodamaged Skin: In Vivo Experiments and Mathematical Modeling.

The epidermis forms an essential barrier against a variety of insults. The overall goal of this study was to shed light not only on the effects of accidental epidermal injury, but also on the mechanisms that support laser skin resurfacing with intra-epidermal focal laser-induced photodamage, a widespread medical practice used to treat a range of skin conditions. To this end, we selectively photodamaged a single keratinocyte with intense, focused and pulsed laser radiation, triggering Ca2+ waves in the epidermis of live anesthetized mice with ubiquitous expression of a genetically encoded Ca2+ indicator. Waves expanded radially and rapidly, reaching up to eight orders of bystander cells that remained activated for tens of minutes, without displaying oscillations of the cytosolic free Ca2+ concentration ([Formula: see text]). By combining in vivo pharmacological dissection with mathematical modeling, we demonstrate that Ca2+ wave propagation depended primarily on the release of ATP, a prime damage-associated molecular patterns (DAMPs), from the hit cell. Increments of the [Formula: see text] in bystander cells were chiefly due to Ca2+ release from the endoplasmic reticulum (ER), downstream of ATP binding to P2Y purinoceptors. ATP-dependent ATP release though connexin hemichannels (HCs) affected wave propagation at larger distances, where the extracellular ATP concentration was reduced by the combined effect of passive diffusion and hydrolysis due to the action of ectonucleotidases, whereas pannexin channels had no role. Bifurcation analysis suggests basal keratinocytes have too few P2Y receptors (P2YRs) and/or phospholipase C (PLC) to transduce elevated extracellular ATP levels into inositol trisphosphate (IP3) production rates sufficiently large to sustain [Formula: see text] oscillations.

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

Secretion from many endocrine cells is a result of calcium-regulated exocytosis due to Ca²âº influx. Using the patch-clamp technique, voltage pulses can be applied to the cells to open Ca²âº channels, resulting in a measurable Ca²âº current, and evoke exocytosis, which can be seen as an increase in membrane capacitance. A common tool for evaluating the relation between Ca²âº influx and exocytosis is to plot the increase in capacitance (ΔC(m)) as a function of the integral of the measured Ca²âºcurrent (Q). When depolarizations of different lengths are imposed, the rate of exocytosis is typically higher for shorter than for longer pulses, which has been suggested to result from depletion of a granule pool or from Ca²âº current inactivation. It is here demonstrated that ΔC(m) as a function of Q can reveal whether Ca²âº current inactivation masquerades as pool depletion. Moreover, it is shown that a convex, cooperativity-like, relation between ΔC(m) and Q surprisingly cannot occur as a result of cooperative effects, but can result from delays in the exocytotic process or in Ca²âºdynamics. An overview of expected ΔC(m)-versus-Q relations for a range of explicit situations is given, which should help in the interpretation of data of depolarization-evoked exocytosis in endocrine cells.