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The growing complexity of biological data has spurred the development of innovative computational techniques to extract meaningful information and uncover hidden patterns within vast datasets. Biological networks, such as gene regulatory networks and protein-protein interaction networks, hold critical insights into biological features' connections and functions. Integrating and analyzing high-dimensional data, particularly in gene expression studies, stands prominent among the challenges in deciphering these networks. Clustering methods play a crucial role in addressing these challenges, with spectral clustering emerging as a potent unsupervised technique considering intrinsic geometric structures. However, spectral clustering's user-defined cluster number can lead to inconsistent and sometimes orthogonal clustering regimes. We propose the Multi-layer Bundling (MLB) method to address this limitation, combining multiple prominent clustering regimes to offer a comprehensive data view. We call the outcome clusters "bundles". This approach refines clustering outcomes, unravels hierarchical organization, and identifies bridge elements mediating communication between network components. By layering clustering results, MLB provides a global-to-local view of biological feature clusters enabling insights into intricate biological systems. Furthermore, the method enhances bundle network predictions by integrating the bundle co-cluster matrix with the affinity matrix. The versatility of MLB extends beyond biological networks, making it applicable to various domains where understanding complex relationships and patterns is needed. [ABSTRACT FROM AUTHOR]

The endocrine cells of the pituitary gland are electrically active, and in vivo they form small networks where the bidirectional cell-cell coupling is through gap junctions. Numerous studies of dispersed pituitary cells have shown that typical behaviors are tonic spiking and bursting, the latter being more effective at evoking secretion. In this article, we use mathematical modeling to examine the dynamics of small networks of spiking and bursting pituitary cells. We demonstrate that intrinsic bursting cells are capable of converting intrinsic spikers into bursters, and perform a fast/slow analysis to show why this occurs. We then demonstrate the sensitivity of network dynamics to the placement of bursting cells within the network, and demonstrate strategies that are most effective at maximizing secretion from the population of cells. This study provides insights into the in vivo behavior of cells such as the stress-hormone-secreting pituitary corticotrophs that are switched from spiking to bursting by hypothalamic neurohormones. While much is known about the electrical properties of these cells when isolated from the pituitary, how they behave when part of an electrically coupled network has been largely unstudied. [ABSTRACT FROM AUTHOR]

• Striking parallels between the developmental learning of human speech and birdsong suggest a deep conservation of brain function underlies the capacity for vocal imitation. • In juvenile zebra finches, an auditory memory of adult vocal sounds is encoded within the premotor architecture of the forebrain network that controls song. • Dual premotor pathways control the sensorimotor acquisition of song, one of which includes the basal ganglia, where auditory feedback and dopamine-driven 'actor-critic' functionality guides vocal output toward the auditory memory of adult vocal sounds. • Given the complexity of the overall network required for juveniles to learn song, a surprisingly small portion of the network is needed for adults to recite it. Understanding the sensorimotor control of the endless variety of human speech patterns stands as one of the apex problems in neuroscience. The capacity to learn – through imitation – to rapidly sequence vocal sounds in meaningful patterns is clearly one of the most derived of human behavioral traits. Selection pressure produced an analogous capacity in numerous species of vocal-learning birds, and due to an increasing appreciation for the cognitive and computational flexibility of avian cortex and basal ganglia, a general understanding of the forebrain network that supports the learning and production of birdsong is beginning to emerge. Here, we review recent advances in experimental studies of the zebra finch (Taeniopygia guttata), which offer new insights into the network dynamics that support this surprising analogue of human speech learning and production. [ABSTRACT FROM AUTHOR]

The pulsatile activity of gonadotropin-releasing hormone neurons (GnRH neurons) is a key factor in the regulation of reproductive hormones. This pulsatility is orchestrated by a network of neurons that release the neurotransmitters kisspeptin, neurokinin B, and dynorphin (KNDy neurons), and produce episodic bursts of activity driving the GnRH neurons. We show in this computational study that the features of coordinated KNDy neuron activity can be explained by a neural network in which connectivity among neurons is modular. That is, a network structure consisting of clusters of highly-connected neurons with sparse coupling among the clusters. This modular structure, with distinct parameters for intracluster and intercluster coupling, also yields predictions for the differential effects on synchronization of changes in the coupling strength within clusters versus between clusters. Author summary: Since the discovery of a small population of hypothalamic neurons that secrete kisspeptin, neurokinin B, and dynorphin (KNDy neurons), there has been interest in their role as a pacemaker for the pulsatile release of key reproductive hormones. A fundamental question is what mechanism coordinates KNDy neuron activity to generate population bursts. Optical imaging of the KNDy network at single-neuron resolution has revealed that individual KNDy neurons participate in many, but not all, population bursts. It has also shown that the order in which the neurons are recruited in each burst could be highly determined in some animals but not in others. We demonstrate here that these observations can be explained by a neural network with a modular structure, and that one benefit of the structure is the ability to differentially modulate the level of synchronization by changes in key coupling parameters. [ABSTRACT FROM AUTHOR]

Highlights • Oscillations are ubiquitous in insulin-secreting beta-cells of the pancreas. • These may be due to intrinsic glycolytic oscillations or calcium feedback onto glycolysis. • A pulsatile blood insulin level facilitates glucose clearance from the blood. • The oscillation mechanisms are analyzed here using fast-slow analysis. Abstract Insulin-secreting pancreatic β -cells are electrically excitable cells that are unusual because their electrical activity is influenced directly by metabolism via ATP-sensitive K + channels. At the same time, changes in the intracellular Ca 2 + concentration that result from the cell's electrical activity influence metabolism in several ways. Thus, there is bidirectional coupling between the electrical dynamics and the metabolic dynamics in β -cells. A mathematical model has been previously developed, called the Integrated. Oscillator Model (IOM), to highlight the bidirectional coupling involved in the oscillation mechanism. In this study, we show how this coupling can produce oscillations in β -cell activity. These oscillations have period similar to that of insulin secretion pulses observed in rats, mice, dogs, and humans, which has been shown to facilitate the action of the liver in maintaining glucose homeostasis. In a companion paper we show that the IOM can produce oscillations using two distinct mechanisms, depending on the values of electrical and metabolic parameters. In the present article, we use fast-slow analysis to understand the mechanisms underlying each of these oscillations. In particular, we show why a key variable in the glycolytic pathway generates a pulsatile time course in one type of oscillation, while it generates a sawtooth time course in the other type. The significance of these patterns is that the time course is a reflection of whether an intrinsic glycolytic oscillator is active, or whether the oscillations are a direct consequence of Ca 2 + feedback onto glycolysis. [ABSTRACT FROM AUTHOR]

Insulin secretion from pancreatic islet β-cells occurs in a pulsatile fashion, with a typical period of ∼5 min. The basis of this pulsatility in mouse islets has been investigated for more than four decades, and the various theories have been described as either qualitative or mathematical models. In many cases the models differ in their mechanisms for rhythmogenesis, as well as other less important details. In this Perspective, we describe two main classes of models: those in which oscillations in the intracellular Ca2+ concentration drive oscillations in metabolism, and those in which intrinsic metabolic oscillations drive oscillations in Ca2+ concentration and electrical activity. We then discuss nine canonical experimental findings that provide key insights into the mechanism of islet oscillations and list the models that can account for each finding. Finally, we describe a new model that integrates features from multiple earlier models and is thus called the Integrated Oscillator Model. In this model, intracellular Ca2+ acts on the glycolytic pathway in the generation of oscillations, and it is thus a hybrid of the two main classes of models. It alone among models proposed to date can explain all nine key experimental findings, and it serves as a good starting point for future studies of pulsatile insulin secretion from human islets. [ABSTRACT FROM AUTHOR]

Intrinsic physiology of inhibitory neurons changes over auditory development. J Neurophysiol 119: 290-304, 2018. First published October 18, 2017; doi:10.1152/jn.00447.2017.--During auditory development, changes in membrane properties promote the ability of excitatory neurons in the brain stem to code aspects of sound, including the level and timing of a stimulus. Some of these changes coincide with hearing onset, suggesting that sound-driven neural activity produces developmental plasticity of ion channel expression. While it is known that the coding properties of excitatory neurons are modulated by inhibition in the mature system, it is unknown whether there are also developmental changes in the membrane properties of brain stem inhibitory neurons. We investigated the primary source of inhibition in the avian auditory brain stem, the superior olivary nucleus (SON). The present studies test the hypothesis that, as in excitatory neurons, the membrane properties of these inhibitory neurons change after hearing onset. We examined SON neurons at different stages of auditory development: embryonic days 14-16 (E14-E16), a time at which cochlear ganglion neurons are just beginning to respond to sound; later embryonic stages (E18-E19); and after hatching (P0 -P2). We used in vitro whole cell patch electrophysiology to explore physiological changes in SON. Age-related changes were observed at the level of a single spike and in multispiking behavior. In particular, tonic behavior, measured as a neuron's ability to sustain tonic firing over a range of current steps, became more common later in development. Voltage-clamp recordings and biophysical models were employed to examine how agerelated increases in ion currents enhance excitability in SON. Our findings suggest that concurrent increases in sodium and potassium currents underlie the emergence of tonic behavior. NEW & NOTEWORTHY This article is the first to examine heterogeneity of neuronal physiology in the inhibitory nucleus of the avian auditory system and demonstrate that tonic firing here emerges over development. By pairing computer simulations with physiological data, we show that increases in both sodium and potassium channels over development are necessary for the emergence of tonic firing. [ABSTRACT FROM AUTHOR]

Neuronal polarization, a process wherein nascent neurons develop a single long axon and multiple short dendrites, can occur within in vitro cell cultures without environmental cues. This is an apparently random process in which one of several short processes, called neurites, grows to become long, while the others remain short. In this study, we propose a minimum model for neurite growth, which involves bistability and random excitations reflecting actin waves. Positive feedback is needed to produce the bistability, while negative feedback is required to ensure that no more than one neurite wins the winner-takes-all contest. By applying the negative feedback to different aspects of the neurite growth process, we demonstrate that targeting the negative feedback to the excitation amplitude results in the most persistent polarization. Also, we demonstrate that there are optimal ranges of values for the neurite count, and for the excitation rate and amplitude that best maintain the polarization. Finally, we show that a previously published model for neuronal polarization based on competition for limited resources shares key features with our best-performing minimal model: bistability and negative feedback targeted to the size of random excitations. • Bistability and random excitation amplitude reduction are minimum requirements for neuronal polarization. • There exists an optimal neurite count, excitation amplitude, and excitation rate that best maintain polarization. • Our findings are consistent with previously published, more detailed models which are catered to specific experimental observations. [ABSTRACT FROM AUTHOR]

Pancreatic islet $$\upbeta $$ -cells are electrically excitable cells that secrete insulin in an oscillatory fashion when the blood glucose concentration is at a stimulatory level. Insulin oscillations are the result of cytosolic $$\hbox {Ca}^{2+}$$ oscillations that accompany bursting electrical activity of $$\upbeta $$ -cells and are physiologically important. ATP-sensitive $$\hbox {K}^{+}$$ channels (K(ATP) channels) play the key role in setting the overall activity of the cell and in driving bursting, by coupling cell metabolism to the membrane potential. In humans, when there is a defect in K(ATP) channel function, $$\upbeta $$ -cells fail to respond appropriately to changes in the blood glucose level, and electrical and $$\hbox {Ca}^{2+}$$ oscillations are lost. However, mice compensate for K(ATP) channel defects in islet $$\upbeta $$ -cells by employing alternative mechanisms to maintain electrical and $$\hbox {Ca}^{2+}$$ oscillations. In a recent study, we showed that in mice islets in which K(ATP) channels are genetically knocked out another $$\hbox {K}^{+}$$ current, provided by inward-rectifying $$\hbox {K}^{+}$$ channels, is increased. With mathematical modeling, we demonstrated that a sufficient upregulation in these channels can account for the paradoxical electrical bursting and $$\hbox {Ca}^{2+}$$ oscillations observed in these $$\upbeta $$ -cells. However, the question of determining the correct level of upregulation that is necessary for this compensation remained unanswered, and this question motivates the current study. $$\hbox {Ca}^{2+}$$ is a well-known regulator of gene expression, and several examples have been shown of genes that are sensitive to the frequency of the $$\hbox {Ca}^{2+}$$ signal. In this mathematical modeling study, we demonstrate that a $$\hbox {Ca}^{2+}$$ oscillation frequency-sensitive gene transcription network can adjust the gene expression level of a compensating $$\hbox {K}^{+}$$ channel so as to rescue electrical bursting and $$\hbox {Ca}^{2+}$$ oscillations in a model $$\upbeta $$ -cell in which the key K(ATP) current is removed. This is done without the prescription of a target $$\hbox {Ca}^{2+}$$ level, but evolves naturally as a consequence of the feedback between the $$\hbox {Ca}^{2+}$$ -dependent enzymes and the cell's electrical activity. More generally, the study indicates how $$\hbox {Ca}^{2+}$$ can provide the link between gene expression and cellular electrical activity that promotes wild-type behavior in a cell following gene knockout. [ABSTRACT FROM AUTHOR]

Pseudo-plateau bursting is a type of oscillatory waveform associated with mixed mode dynamics in slow/fast systems and commonly found in neural bursting models. In a recent model for the electrical activity and calcium signaling in a pituitary lactotroph, two types of pseudo-plateau bursts were discovered: one in which the calcium drives the bursts and another in which the calcium simply follows them. Multiple methods from dynamical systems theory have been used to understand the bursting. The classic 2-timescale approach treats the calcium concentration as a slowly varying parameter and considers a parametrized family of fast subsystems. A more novel and successful 2-timescale approach divides the system so that there is only one fast variable and shows that the bursting arises from canard dynamics. Both methods can be effective analytic tools, but there has been little justification for one approach over the other. In this work, we use the lactotroph model to demonstrate that the two analysis techniques are different unfoldings of a 3-timescale system. We show that elementary applications of geometric singular perturbation theory in the 2-timescale and 3-timescale methods provide us with substantial predictive power. We use that predictive power to explain the transient and long-term dynamics of the pituitary lactotroph model. [ABSTRACT FROM AUTHOR]

Pulses of insulin from pancreatic beta-cells help maintain blood glucose in a narrow range, although the source of these pulses is unclear. It has been proposed that a positive feedback circuit exists within the glycolytic pathway, the autocatalytic activation of phosphofructokinase-1 (PFK1), which endows pancreatic beta-cells with the ability to generate oscillations in metabolism. Flux through PFK1 is controlled by the bifunctional enzyme PFK2/FBPase2 (6-phosphofructo-2-kinase/fructose- 2,6-bisphosphatase) in two ways: via (1) production/degradation of fructose-2,6-bisphosphate (Fru2,6-BP), a potent allosteric activator of PFK1, as well as (2) direct activation of glucokinase due to a protein-protein interaction. In this study, we used a combination of live-cell imaging and mathematical modeling to examine the effects of inducibly-expressed PFK2/ FBPase2 mutants on glucose-induced Ca2+ pulsatility in mouse islets. Irrespective of the ability to bind glucokinase, mutants of PFK2/FBPase2 that increased the kinase:phosphatase ratio reduced the period and amplitude of Ca2+ oscillations. Mutants which reduced the kinase:phosphatase ratio had the opposite effect. These results indicate that the main effect of the bifunctional enzyme on islet pulsatility is due to Fru2,6-BP alteration of the threshold for autocatalytic activation of PFK1 by Fru1,6-BP. Using computational models based on PFK1-generated islet oscillations, we then illustrated how moderate elevation of Fru-2,6-BP can increase the frequency of glycolytic oscillations while reducing their amplitude, with sufficiently high activation resulting in termination of slow oscillations. The concordance we observed between PFK2/FBPase2-induced modulation of islet oscillations and the models of PFK1-driven oscillations furthermore suggests that metabolic oscillations, like those found in yeast and skeletal muscle, are shaped early in glycolysis. [ABSTRACT FROM AUTHOR]

Abstract: The number of Ca2+ channels contributing to the exocytosis of a single neurotransmitter vesicle in a presynaptic terminal has been a question of significant interest and debate, and is important for a full understanding of localized Ca2+ signaling in general, and synaptic physiology in particular. This is usually estimated by measuring the sensitivity of the neurotransmitter release rate to changes in the synaptic Ca2+ current, which is varied using appropriate voltage-clamp protocols or via pharmacological Ca2+ channel block under the condition of constant single-channel Ca2+ current. The slope of the resulting log–log plot of transmitter release rate versus presynaptic Ca2+ current is termed Ca2+ current cooperativity of exocytosis, and provides indirect information about the underlying presynaptic morphology. In this review, we discuss the relationship between the Ca2+ current cooperativity and the average number of Ca2+ channels participating in the exocytosis of a single vesicle, termed the Ca2+ channel cooperativity. We relate these quantities to the morphology of the presynaptic active zone. We also review experimental studies of Ca2+ current cooperativity and its modulation during development in different classes of synapses. [Copyright &y& Elsevier]

Recently there has been significant interest and progress in the study of spatiotemporal dynamics of Ca2+that triggers exocytosis at a fast chemical synapse, which requires understanding the contribution of individual calcium channels to the release of a single vesicle. Experimental protocols provide insight into this question by probing the sensitivity of exocytosis to Ca2+ influx. While varying extracellular or intracellular Ca2+ concentration assesses the intrinsic biochemical Ca2+ cooperativity of neurotransmitter release, varying the number of open Ca2+ channels using pharmacological channel block or the tail current titration probes the cooperativity between individual Ca2+ channels in triggering exocytosis. Despite the wide use of these Ca2+ sensitivity measurements, their interpretation often relies on heuristic arguments. Here we provide a detailed analysis of the Ca2+ sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the Ca2+current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal Ca2+ current magnitude, and the underlying Ca2+ channel cooperativity, defined as the average number of channels involved in the release of a single vesicle. We find simple algebraic expressions that show that the two are different but linearly related. Further, we use three-dimensional computational modeling of buffered Ca2+ diffusion to analyze these distinct Ca2+cooperativity measures, and demonstrate the role of endogenous Ca2+buffers on such measures. We show that buffers can either increase or decrease the Ca2+current cooperativity of exocytosis, depending on their concentration and the single-channel Ca2+ current. [ABSTRACT FROM AUTHOR]

Enzyme isoforms are found in many cellular reactions, and can differ in the kind of reaction they catalyze, in their substrate affinity, or in their reaction rates. The evolutionary significance of enzyme isoforms is only partially understood. We used mathematical modeling to investigate the hypothesis that isoforms may be favored by selection because they can increase the phenotypic robustness of the system. We modify a model for circadian clock gene expression in Drosophila to incorporate the presence of isoforms in the phosphorylation pathway of the period gene. We consider the case in which different isoforms catalyze the same reaction but have different affinities for the substrate. Stability is increased if there is dynamic control of the expression of isoforms relative to each other. Thus, we show that controlling isoform proportion can be a powerful mechanism for reducing the effects of variations in the values of system parameters, increasing system robustness. [ABSTRACT FROM AUTHOR]

The timed secretion of the luteinizing hormone (LH) and follicle stimulating hormone (FSH) from pituitary gonadotrophs during the estrous cycle is crucial for normal reproductive functioning. The release of LH and FSH is stimulated by gonadotropin releasing hormone (GnRH) secreted by hypothalamic GnRH neurons. It is controlled by the frequency of the GnRH signal that varies during the estrous cycle. Curiously, the secretion of LH and FSH is differentially regulated by the frequency of GnRH pulses. LH secretion increases as the frequency increases within a physiological range, and FSH secretion shows a biphasic response, with a peak at a lower frequency. There is considerable experimental evidence that one key factor in these differential responses is the autocrine/paracrine actions of the pituitary polypeptides activin and follistatin. Based on these data, we develop a mathematical model that incorporates the dynamics of these polypeptides. We show that a model that incorporates the actions of activin and follistatin is sufficient to generate the differential responses of LH and FSH secretion to changes in the frequency of GnRH pulses. In addition, it shows that the actions of these polypeptides, along with the ovarian polypeptide inhibin and the estrogen-mediated variations in the frequency of GnRH pulses, are sufficient to account for the time courses of LH and FSH plasma levels during the rat estrous cycle. That is, a single peak of LH on the afternoon of proestrus and a double peak of FSH on proestrus and early estrus. We also use the model to identify which regulation pathways are indispensable for the differential regulation of LH and FSH and their time courses during the estrous cycle. We conclude that the actions of activin, inhibin, and follistatin are consistent with LH/FSH secretion patterns, and likely complement other factors in the production of the characteristic secretion patterns in female rats. [ABSTRACT FROM AUTHOR]

We describe a novel dynamic mechanism for episodic or compound bursting oscillations, in which bursts of electrical impulses are clustered together into episodes, separated by long silent phases. We demonstrate the mechanism for episodic bursting using a minimal mathematical model for "phantom bursting." Depending on the location in parameter space, this model can produce fast, medium, or slow bursting, or in the present case, fast, slow, and episodic bursting. The episodic bursting is modestly robust to noise and to parameter variation, and the effect that noise has on the episodic bursting pattern is quite different from that of an alternate episodic burst mechanism in which the slow envelope is produced by metabolic oscillations. This mechanism could account for episodic bursting produced in endocrine cells or neurons, such as pancreatic islets or gonadotropin releasing neurons of the hypothalamus. [ABSTRACT FROM AUTHOR]

Cytosolic Ca2+ dynamics are important in the regulation of insulin secretion from the pancreatic β-cells within islets of Langerhans. These dynamics are sculpted by the endoplasmic reticulum (ER), which takes up Ca2+ when cytosolic levels are high and releases it when cytosolic levels are low. Calcium uptake into the ER is through sarcoendoplasmic reticulum Ca2+-ATPases, or SERCA pumps. Two SERCA isoforms are expressed in the β-cell: the high Ca2+ affinity SERCA2b pump and the low affinity SERCA3 pump. Recent experiments with islets from SERCA3 knockout mice have shown that the cytosolic Ca2+ oscillations from the knockout islets are characteristically different from those of wild type islets.While the wild type islets often exhibit compound Ca2+ oscillations, composed of fast oscillations superimposed on much slower oscillations, the knockout islets rarely exhibit compound oscillations, but produce slow (single component) oscillations instead. Using mathematical modeling, we provide an explanation for this difference. We also investigate the effect that SERCA2b inhibition has on the model β-cell. Unlike SERCA3 inhibition, we demonstrate that SERCA2b inhibition has no long-term effect on cytosolic Ca2+ oscillations unless a store-operated current is activated. [ABSTRACT FROM AUTHOR]

Impairment of insulin secretion from the β-cells of the pancreatic islets of Langerhans is central to the development of type 2 diabetes mellitus and has therefore been the subject of much investigation. Great advances have been made in this area, but the mechanisms underlying the pulsatility of insulin secretion remain controversial. The period of these pulses is 4–6 min and reflects oscillations in islet membrane potential and intracellular free Ca2+ Pulsatile blood insulin levels appear to play an important physiological role in insulin action and are lost in patients with type 2 diabetes and their near relatives. We present evidence for a recently developed β-cell model, the ‘dual oscillator model,’ in which oscillations in activity are due to both electrical and metabolic mechanisms. This model is capable of explaining much of the available data on islet activity and offers possible resolutions of a number of longstanding issues. The model, however, still lacks direct confirmation and raises new issues. In this article, we highlight both the successes of the model and the challenges that it poses for the field. [ABSTRACT FROM AUTHOR]

Abstract: Most of the adenosine triphosphate (ATP) synthesized during glucose metabolism is produced in the mitochondria through oxidative phosphorylation. This is a complex reaction powered by the proton gradient across the mitochondrial inner membrane, which is generated by mitochondrial respiration. A detailed model of this reaction, which includes dynamic equations for the key mitochondrial variables, was developed earlier by Magnus and Keizer. However, this model is extraordinarily complicated. We develop a simpler model that captures the behavior of the original model but is easier to use and to understand. We then use it to investigate the mitochondrial responses to glycolytic and calcium input. We use the model to explain experimental observations of the opposite effects of raising cytosolic in low and high glucose, and to predict the effects of a mutation in the mitochondrial enzyme nicotinamide nucleotide transhydrogenase (Nnt) in pancreatic -cells. [Copyright &y& Elsevier]

Mating or vaginocervical stimulation [copulatory stimulus (CS)] induces two daily surges of the hormone prolactin (PRL) in rats. This unique secretory pattern of PRL surges is characteristic for the first half of pregnancy and is also present in ovariectomized (OVX) rats. Studies have shown that CS additionally provokes an acute release of the hormone oxytocin (OT). In this study, we tested whether a single injection of OT (iv) is sufficient to initiate the PRL secretion pattern of OVX/CS rats. Furthermore, we measured the 24-h profile of dopamine (DA) content in the anterior lobe of the pituitary gland, because DA is the major inhibitory factor of PRL secretion. The results indicated that a single injection of OT induces a PRL secretory rhythm and a DA release pattern similar to that initiated by CS. Immunocytochemical investigation showed that particular OTergic neurons in the hypothalamus express receptors for PRL, as well as for vasoactive intestinal polypeptide, which indicates an involvement in generating the PRL rhythm and entraining it to the ambient photoperiod. On the basis of this study, we suggest that the PRL-DA inhibitory feedback loop between lactotrophs and DAergic neurons plays a crucial role in generating the oscillatory PRL secretion pattern in CS rats. A timing signal, likely provided by the hypothalamic suprachiasmatic nucleus, entrains the autonomous PRL oscillation to a particular time of day. Mathematical modeling was used to illustrate the proposed network function. The experimental results further suggest an additional feedback mechanism in which certain hypothalamic OTergic neurons are influenced by PRL. [ABSTRACT FROM AUTHOR]

For the first 10 days of pregnancy and the first 12 days of pseudopregnancy, the secretion of prolactin (PRL) from pituitary lactotrophs is rhythmic, with two surges/day. This rhythm can also be triggered by bolus injection of oxytocin (OT). We describe a mathematical model for the initiation, maintenance, and termination of the OT-induced PRL rhythm. In our model, the mechanism for this circadian rhythm is mutual interaction between lactotrophs and neuroendocrine dopamine (DA) neurons. This rhythm is, under normal lighting conditions, entrained by the suprachiasmatic nucleus (SCN) but persists in the absence of input from the SCN. We postulate that OT injection triggers the rhythm by activating a population of bistable hypothalamic neurons that innervate and inhibit DA neurons. The bistable nature of these neurons allows them to act as a memory device, maintaining the rhythm long after OT has been cleared from the blood. The mechanism for this memory device and the arguments supporting it are detailed with computer simulations. Finally, we consider potential targets for a rhythm-terminating factor and make predictions that may be used to determine which mechanism is operational in terminating the OT- or mating-induced PRL rhythm. [ABSTRACT FROM AUTHOR]

Insulin-secreting β-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called ‘phantom bursters’ [Bertram et al. (2000) Biophys. J. 79, 2880–2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca2+ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by β-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca2+ stores. Although it is not presently a complete model of all β-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in β-cell modeling. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

The orientation data provided by solid-state NMR can provide a great deal of structural information about membrane proteins. The quality of the information provided is, however, somewhat degraded by sign degeneracies in measurements of the dipolar coupling tensor. This is reflected in the dipolar coupling penalty function used in atomic refinement, which is less capable of properly restraining atoms when dipolar sign degeneracies are present. In this report we generate simulated solid-state NMR data using a variety of procedures, including back-calculation from crystal structures of α-helical and β-sheet membrane proteins. We demonstrate that a large fraction of the dipolar sign degeneracies are resolved if anisotropic dipolar coupling measurements are correlated with anisotropic chemical shift measurements, and that all sign degeneracies can be resolved if three data types are correlated. The advantages of correlating data are demonstrated with atomic refinement of two test membrane proteins. When refinement is performed using correlated dipolar couplings and chemical shifts, perturbed structures converge to conformations with a larger fraction of correct dipolar signs than when data are uncorrelated. In addition, the final structures are closer to the original unperturbed structures when correlated data are used in the refinement. Thus, refinement with correlated data leads to improved atomic structures. The software used to correlate dipolar coupling and chemical shift data and to set up energy functions and their derivatives for refinement, CNS-SS02, is available at our web site. [Copyright &y& Elsevier]

We have previously reported the synthesis of vinylphosphonate-linked thymidine dimers and their incorporation into synthetic oligonucleotides to create vinylphosphonate internucleotide linkages in the DNA. Such linkages have a profound effect on DNA backbone rotational flexibility, and we have shown that the PcrA helicase, which requires such flexibility, is inhibited when it encounters these linkages on the translocating strand. In this study, we have investigated the effects of these linkages on the dsDNA specific exonuclease III and on the ssDNA specific mung bean nuclease to establish whether our modification confers resistance to nucleases making it suitable for antisense therapy applications. We also investigated the effect on DNA polymerase I to establish whether we could in the future use this enzyme to incorporate these linkages in the DNA. Our results show that a single modification does not affect the activity of DNA polymerase I, but four vinylphosphonate linkages in tandem inhibit its activity. Furthermore, such linkages do not confer significant nuclease resistance to either exonuclease III or mung bean nuclease, but unexpectedly, they alter the cleavage specificity of exonuclease III. [ABSTRACT FROM AUTHOR]

Examines the molecular mechanism of action of the DNA helicase. Interaction of helicases with DNA substrates; Hydrolysis of adenosine triphosphate; Inhibition of the helicase activity by vinylphosphonate internucleotide linkages.

The filtering of input signals carried out at synapses is key to the information processing performed by networks of neurons. Two forms of presynaptic depression, vesicle depletion and G-protein inhibition of Ca[sup 2+] channels, can play important roles in the presynaptic processing of information. Using computational models, we demonstrate that these two forms of depression filter information in very different ways. G-protein inhibition acts as a high-pass filter, preferentially transmitting high-frequency input signals to the postsynaptic cell, while vesicle depletion acts as a low-pass filter. We examine how these forms of depression separately and together affect the steady-state postsynaptic responses to trains of stimuli over a range of frequencies. Finally, we demonstrate how differential filtering permits the multiplexing of information within a single impulse train. [ABSTRACT FROM AUTHOR]

Describes a model of synaptic transmitter release and presynaptic facilitation that is based on activation of release bites by single calcium2+ microdomains. Deterministic equations derived for the mean release; Investigation of the effects of different input spike patterns on presynaptic facilitation; Model of dopamine-secreting neurons of the basal ganglia.

In this article, we report the numerical discovery of multi-mode attractors for reaction–diffusion systems in which the kinetics feature slow/fast dynamics. Multi-mode attractors (MMAs) are a class of attractors in which different regions of the spatial domain exhibit different modes of (temporal) oscillation. These modes include spiking modes, bursting modes of many different types with s small-amplitude oscillations at the end of each burst event, as well as alternating modes in which various sequences of spiking and bursting are exhibited in alternation. We present the numerical discovery of MMAs in the context of a spatially-extended pituitary cell model with diffusive coupling and a spatially inhomogeneous applied current. We demonstrate that the MMAs are robust, occurring on large open parameter sets and for a variety of biophysically-relevant spatially-inhomogeneous currents, including Gaussian and mollified step profiles. Also, we provide evidence that the MMAs exhibit new types of maximal spatio-temporal canards. These lie in the transition intervals between adjacent regions in which the MMA exhibits distinct modes of oscillation, and they are necessary for the smooth and gradual transitions between bursting and spiking, as well as between bursting modes with different numbers of small oscillations. Furthermore, we study how the structures of the MMAs change as the amplitude of the diffusivity decreases and the PDE model limits on a family of uncoupled ODEs, one for each point in the domain. Also, we show that the MMAs, which are spatially non-uniform, can coexist in the reaction–diffusion system with other types of attractors which are spatially-uniform. Finally, we report that the MMAs discovered here are also present in numerical simulations of other reaction–diffusion systems, especially those that arise in neural and cardiac models. • New Multi-Mode Attractors (MMAs) are discovered in reaction–diffusion systems. • MMAs consist of distinct oscillatory modes co-existing in different regions. • Modes include 1 0 spiking, 1 s bursting, some (1 s + 1) k (1 s ) l alternator modes. • Maximal spatio-temporal canards mediate transitions spatially between adjacent modes. • MMAs exist in pituitary cell line models, van der Pol PDE, cardiac electrical activity. [ABSTRACT FROM AUTHOR]

Early afterdepolarizations (EADs) are voltage oscillations that can occur during the plateau phase of a cardiac action potential. EADs at the cellular level have been linked to potentially deadly tissue-level arrhythmias, and the mechanisms for their arisal are not fully understood. There is ongoing debate as to which is the predominant biophysical mechanism of EAD production: imbalanced interactions between voltage-gated transmembrane currents or overactive Ca2+-dependent transmembrane currents brought about by pathological intracellularCa2+-release dynamics. In this article, we address this issue using a foundational 10-dimensional biophysical ventricular action potential model which contains both electrical and intracellularCa2+-components. Surprisingly, we find that the model can produce EADs through both biophysical mechanisms, which hints at a more fundamental dynamical mechanism for EAD production. Fast-slow analysis reveals EADs, in both cases, to be canard-induced mixed-mode oscillations. While the voltage-driven EADs arise from a fast-slow problem with two slow variables, the Ca2+--driven EADs arise from the addition of a third slow variable. Hence, we adapt existing computational methods in order to compute 2D slow manifolds and 1D canard orbits in the reduced 7D model from which voltage-driven EADs arise. Further, we extend these computational methods in order to compute, for the first time, 2D sets of maximal canards which partition the 3D slow manifolds of the 8D problem from which Ca2+--driven EADs arise. The canard viewpoint provides a unifying alternative to the voltage- or Ca2+--driven viewpoints while also providing explanatory and predictive insights that cannot be obtained through the use of the traditional fast-slow approach. [ABSTRACT FROM AUTHOR]

Electrical bursting oscillations in neurons and endocrine cells are activity patterns that facilitate the secretion of neurotransmitters and hormones and have been the focus of study for several decades. Mathematical modeling has been an extremely useful tool in this effort, and the use of fast-slow analysis has made it possible to understand bursting from a dynamic perspective and to make testable predictions about changes in system parameters or the cellular environment. It is typically the case that the electrical impulses that occur during the active phase of a burst are due to stable limit cycles in the fast subsystem of equations or, in the case of so-called "pseudo-plateau bursting," canards that are induced by a folded node singularity. In this article, we show an entirely different mechanism for bursting that relies on stochastic opening and closing of a key ion channel. We demonstrate, using fast-slow analysis, how the short-lived stochastic channel openings can yield a much longer response in which single action potentials are converted into bursts of action potentials. Without this stochastic element, the system is incapable of bursting. This mechanism can describe stochastic bursting in pituitary corticotrophs, which are small cells that exhibit a great deal of noise as well as other pituitary cells, such as lactotrophs and somatotrophs that exhibit noisy bursts of electrical activity. [ABSTRACT FROM AUTHOR]

Early afterdepolarizations (EADs) are pathological voltage oscillations in cardiomyocytes that have been observed in response to a number of pharmacological agents and disease conditions. Phase-2 EADs consist of small voltage fluctuations during the plateau of an action potential, typically under conditions in which the action potential is elongated. Although a single-cell behavior, EADs can lead to tissue-level arrhythmias. Much is currently known about the biophysical mechanisms (i.e., the roles of ion channels and intracellular Ca2+ stores) for the various forms of EADs, due partially to the development and analysis of mathematical models. This includes the application of slow-fast analysis, which takes advantage of timescale separation inherent in the system to simplify its analysis. We take this further, using a minimal three-dimensional model to demonstrate that phase-2 EADs are canards formed in the neighborhood of a folded node singularity. This allows us to predict the number of EADs that can be produced for a given parameter set, and provides guidance on parameter changes that facilitate or inhibit EAD production. With this approach, we demonstrate why periodic stimulation, as occurs in intact heart, preferentially facilitates EAD production when applied at low frequencies. We also explain the origin of complex alternan dynamics that can occur with intermediate-frequency stimulation, in which varying numbers of EADs are produced with each pulse. These revelations fall out naturally from an understanding of folded node singularities, but are difficult to glean from knowledge of the biophysical mechanism for EADs alone. Therefore, understanding the canard mechanism is a useful complement to understanding of the biophysical mechanism that has been developed over years of experimental and computational investigations. [ABSTRACT FROM AUTHOR]

The pumping of blood through the heart is due to a wave of muscle contractions that are in turn due to a wave of electrical activity initiated at the sinoatrial node. At the cellular level, this wave of electrical activity corresponds to the sequential excitation of electrically coupled cardiac cells. Under some conditions, the normally-long action potentials of cardiac cells are extended even further by small oscillations called early afterdepolarizations (EADs) that can occur either during the plateau phase or repolarizing phase of the action potential. Hence, cellular EADs have been implicated as a driver of potentially lethal cardiac arrhythmias. One of the major determinants of cellular EAD production and repolarization failure is the size of the overlap region between Ca2+ channel activation and inactivation, called the window region. In this article, we interpret the role of the window region in terms of the fast-slow structure of a low-dimensional model for ventricular action potential generation. We demonstrate that the effects of manipulation of the size of the window region can be understood from the point of view of canard theory. We use canard theory to explain why enlarging the size of the window region elicits EADs and why shrinking the window region can eliminate them. We also use the canard mechanism to explain why some manipulations in the size of the window region have a stronger influence on cellular electrical behavior than others. This dynamical viewpoint gives predictive power that is beyond that of the biophysical explanation alone while also uncovering a common mechanism for phenomena observed in experiments on both atrial and ventricular cardiac cells. Author summary: EADs are pathological voltage fluctuations that can occur during the plateau or repolarizing phase of cardiac action potentials. The EADs of single cells, when embedded in a network of cardiac tissue, can lead to deadly cardiac arrhythmia. Because of this, many experimental and theoretical investigations have been conducted to uncover the biophysical and dynamical origins of EAD genesis. A recurring finding is that suitable changes in the properties of the inward L-type calcium current are sufficient for EAD production. A particularly important property of the L-type calcium current, with respect to EAD production, is the size of its window region. In this work, we use a novel geometric approach to analyze the role of the window region in cellular electrical dynamics using a low-dimensional ventricular action potential model. We illustrate the mechanism underlying window region-induced EADs, and demonstrate how the number of EADs produced can be predicted, using dynamical systems techniques together with canard theory. These techniques allow us to explain precisely why the model reproduces myriad experimental observations while also allowing us to make the testable predictions that either advancing the activation rate or slowing the inactivation rate of the L-type calcium current—changes that would reasonably be expected to increase its active duration and the likelihood of EADs—should, instead, reduce its active duration and the likelihood of EADs. [ABSTRACT FROM AUTHOR]

Early afterdepolarizations (EADs) are pathological voltage fluctuations that can occur in cardiac cells and are a potent source of potentially fatal arrhythmias. Recent works examining the mechanisms underlying EADs in minimal computational cardiac models have revealed that voltage-driven EADs are canard-induced mixed-mode oscillations whose properties are mediated by the rate at which these cells are paced. In this work, we analyze the mechanisms for the pacing-induced generation of different EAD behaviors in a reduced four-dimensional Luo--Rudy I model using slow-fast analysis. While previous explanations for EADs in this model have required manipulation of the underlying multitimescale structure, our approach does not and we find that the canard mechanism persists in generating EADs in this context. We also find that the canard mechanism gives a more complete explanation for the onset and properties of the EADs induced (e.g., EAD amplitude and number). In addition, we also find that the canards play an essential role in producing a richer set of behaviors than were seen in other minimal models, some of which have also been observed in experiments. These behaviors include pacing-induced termination of EADs, the periodic alternation of cardiac action potentials with and without EADs, as well as bistability between standard and EAD-containing action potentials at a fixed pacing rate. Finally, we show that this bistability can lead to hysteretic transitions between standard and arrhythmogenic action potentials under sufficiently slow oscillations in the pacing rate. [ABSTRACT FROM AUTHOR]

Insulin pulsatility is important to hepatic response in regulating blood glucose. Growing evidence suggests that insulin-secreting pancreatic β-cells can adapt to chronic disruptions of pulsatility to rescue this physiologically important behavior. We determined the time scale for adaptation and examined potential ion channels underlying it. We induced the adaptation both by chronic application of the ATPsensitive K+ [K(ATP)] channel blocker tolbutamide and by application of the depolarizing agent potassium chloride (KCl). Acute application of tolbutamide without pretreatment results in elevated Ca2+ as measured by fura-2AM and the loss of endogenous pulsatility. We show that after chronic exposure to tolbutamide (12-24 h), Ca2+ oscillations occur with subsequent acute tolbutamide application. The same experiment was conducted with potassium chloride (KCl) to directly depolarize the β-cells. Once again, following chronic exposure to the cell stimulator, the islets produced Ca2+ oscillations when subsequently exposed to tolbutamide. These experiments suggest that it is the chronic stimulation, and not tolbutamide desensitization, that is responsible for the adaptation that rescues oscillatory β-cell activity. This compensatory response also causes islet glucose sensitivity to shift rightward following chronic tolbutamide treatment. Mathematical modeling shows that a small increase in the number of K(ATP) channels in the membrane is one adaptation mechanism that is compatible with the data. To examine other compensatory mechanisms, pharmacological studies provide support that Kir2.1 and TEAsensitive channels play some role. Overall, this investigation demonstrates β-cell adaptability to overstimulation, which is likely an important mechanism for maintaining glucose homeostasis in the face of chronic stimulation. [ABSTRACT FROM AUTHOR]

Adult female zebra finches (Taeniopygia guttata), which do not produce learned songs, have long been thought to possess only vestiges of the forebrain network that supports learned song in males. This view ostensibly explains why females do not sing—many of the neural populations and pathways that make up the male song control network appear rudimentary or even missing in females. For example, classic studies of vocal‐premotor cortex (HVC, acronym is name) in male zebra finches identified prominent efferent pathways from HVC to vocal‐motor cortex (RA, robust nucleus of the arcopallium) and from HVC to the avian basal ganglia (Area X). In females, by comparison, the efferent targets of HVC were thought to be only partially innervated by HVC axons (RA) or absent (Area X). Here, using a novel visually guided surgical approach to target tracer injections with precision, we mapped the extrinsic connectivity of the adult female HVC. We find that female HVC shows a mostly male‐typical pattern of afferent and efferent connectivity, including robust HVC innervation of RA and Area X. As noted by earlier investigators, we find large sex differences in the volume of many regions that control male singing (male > female). However, sex differences in volume were diminished in regions that convey ascending afferent input to HVC. Our findings do not support a vestigial interpretation of the song control network in females. Instead, our findings support the emerging view that the song control network may have an altogether different function in nonsinging females. Male zebra finches sing—females do not. Classic studies suggested that male song nuclei were diminished or entirely absent in females. A novel method to inject tracer into vocal premotor cortex (HVC, proper name) reveals largely male‐typical connectivity in females, with surprisingly little sex difference in regions afferent to HVC. [ABSTRACT FROM AUTHOR]

Pancreatic beta cells secrete insulin in response to plasma glucose. The ATP‐sensitive potassium channel (KATP) links glucose metabolism to islet electrical activity in these cells by responding to increased cytosolic [ATP]/[ADP]. It was recently proposed that pyruvate kinase (PK) in close proximity to beta cell KATP locally produces the ATP that inhibits KATP activity. This proposal was largely based on the observation that applying phosphoenolpyruvate (PEP) and ADP to the cytoplasmic side of excised inside‐out patches inhibited KATP. To test the relative contributions of local vs. mitochondrial ATP production, we recorded KATP activity using mouse beta cells and INS‐1 832/13 cells. In contrast to prior reports, we could not replicate inhibition of KATP activity by PEP + ADP. However, when the pH of the PEP solutions was not corrected for the addition of PEP, strong channel inhibition was observed as a result of the well‐known action of protons to inhibit KATP. In cell‐attached recordings, perifusing either a PK activator or an inhibitor had little or no effect on KATP channel closure by glucose, further suggesting that PK is not an important regulator of KATP. In contrast, addition of mitochondrial inhibitors robustly increased KATP activity. Finally, by measuring the [ATP]/[ADP] responses to imposed calcium oscillations in mouse beta cells, we found that oxidative phosphorylation could raise [ATP]/[ADP] even when ADP was at its nadir during the burst silent phase, in agreement with our mathematical model. These results indicate that ATP produced by mitochondrial oxidative phosphorylation is the primary controller of KATP in pancreatic beta cells. Key points: Phosphoenolpyruvate (PEP) plus adenosine diphosphate does not inhibit KATP activity in excised patches. PEP solutions only inhibit KATP activity if the pH is unbalanced.Modulating pyruvate kinase has minimal effects on KATP activity.Mitochondrial inhibition, in contrast, robustly potentiates KATP activity in cell‐attached patches.Although the ADP level falls during the silent phase of calcium oscillations, mitochondria can still produce enough ATP via oxidative phosphorylation to close KATP.Mitochondrial oxidative phosphorylation is therefore the main source of the ATP that inhibits the KATP activity of pancreatic beta cells. [ABSTRACT FROM AUTHOR]

In three-dimensional excitable systems, scroll waves are rotating vortex states that consist of smoothly stacked spirals. This stacking occurs along one-dimensional phase singularities called filaments. If the system has a positive filament tension, these curves either straighten or collapse over time. The collapse can be prevented if the filament pins to a nonreactive object or a group of objects, but even in this case, the filament length does not typically grow. Using numerical simulations, we provide examples of filament growth induced by pinning, such as a scroll ring pinning to an inert trefoil knot, and explain the mechanism of this growth. Surprisingly, the corresponding filament loop thus not only persists in time but also steadily extends far from the pinning object. [ABSTRACT FROM AUTHOR]

Neural activity within the cortical premotor nucleus HVC (acronym is name) encodes the learned songs of adult male zebra finches ( Taeniopygia guttata). HVC activity is driven and/or modulated by a group of five afferent nuclei (the Medial Magnocellular nucleus of the Anterior Nidopallium, MMAN; Nucleus Interface, NIf; nucleus Avalanche, Av; the Robust nucleus of the Arcopallium, RA; the Uvaeform nucleus, Uva). While earlier evidence suggested that HVC receives a uniformly distributed and nontopographic pattern of afferent input, recent evidence suggests this view is incorrect (Basista et al., ). Here, we used a double-labeling strategy (varying both the distance between and the axial orientation of dual tracer injections into HVC) to reveal a massively parallel and in some cases topographic pattern of afferent input. Afferent neurons target only one rostral or caudal location within medial or lateral HVC, and each HVC location receives convergent input from each afferent nucleus in parallel. Quantifying the distributions of single-labeled cells revealed an orthogonal topography in the organization of afferent input from MMAN and NIf, two cortical nuclei necessary for song learning. MMAN input is organized across the lateral-medial axis whereas NIf input is organized across the rostral-caudal axis. To the extent that HVC activity is influenced by afferent input during the learning, perception, or production of song, functional models of HVC activity may need revision to account for the parallel input architecture of HVC, along with the orthogonal input topography of MMAN and NIf. [ABSTRACT FROM AUTHOR]

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model. [ABSTRACT FROM AUTHOR]

G protein-coupled receptors are ubiquitous in neurons, as well as other cell types. Activation of receptors by hormones or neurotransmitters splits the G protein heterotrimer into Galpha and Gbetagamma subunits. It is now clear that Gbetagamma directly inhibits Ca2+ channels, putting them into a reluctant state. The effects of Gbetagamma depend on the specific beta and gamma subunits present, as well as the beta subunit isoform of the N-type Ca2+ channel. We describe a minimal mathematical model for the effects of G protein action on the dynamics of synaptic transmission. The model is calibrated by data obtained by transfecting G protein and Ca2+ channel subunits into tsA-201 cells. We demonstrate with numerical simulations that G protein action can provide a mechanism for either short-term synaptic facilitation or depression, depending on the manner in which G protein-coupled receptors are activated. The G protein action performs high-pass filtering of the presynaptic signal, with a filter cutoff that depends on the combination of G protein and Ca2+ channel subunits present. At stimulus frequencies above the cutoff, trains of single spikes are transmitted, while only doublets are transmitted at frequencies below the cutoff. Finally, we demonstrate that relief of G protein inhibition can contribute to paired-pulse facilitation. [ABSTRACT FROM AUTHOR]

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 Ca2+ influx. Typical electrical behaviors of pituitary cells include continuous spiking and so-called pseudo-plateau bursting. It has been shown that the amplitude of Ca2+ 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 Ca2+ channel activity, buffered Ca2+ diffusion, and Ca2+- 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 Ca2+ 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. [ABSTRACT FROM AUTHOR]

Neurons in the gustatory cortex (GC) represent taste through time-varying changes in their spiking activity. The predominant view is that the neural firing rate represents the sole unit of taste information. It is currently not known whether the phase of spikes relative to lick timing is used by GC neurons for taste encoding. To address this question, we recorded spiking activity from >500 single GC neurons in male and female mice permitted to freely lick to receive four liquid gustatory stimuli and water. We developed a set of data analysis tools to determine the ability of GC neurons to discriminate gustatory information and then to quantify the degree to which this information exists in the spike rate versus the spike timing or phase relative to licks. These tools include machine learning algorithms for classification of spike trains and methods from geometric shape and functional data analysis. Our results show that while GC neurons primarily encode taste information using a rate code, the timing of spikes is also an important factor in taste discrimination. A further finding is that taste discrimination using spike timing is improved when the timing of licks is considered in the analysis. That is, the interlick phase of spiking provides more information than the absolute spike timing itself. Overall, our analysis demonstrates that the ability of GC neurons to distinguish among tastes is best when spike rate and timing is interpreted relative to the timing of licks. [ABSTRACT FROM AUTHOR]

We used the patch clamp technique in situ to test the hypothesis that slow oscillations in metabolism mediate slow electrical oscillations in mouse pancreatic islets by causing oscillations in KATP channel activity. Total conductance was measured over the course of slow bursting oscillations in surface β-cells of islets exposed to 11.1 mM glucose by either switching from current clamp to voltage clamp at different phases of the bursting cycle or by clamping the cells to -60 mV and running two-second voltage ramps from -120 to -50 mV every 20 s. The membrane conductance, calculated from the slopes of the ramp current-voltage curves, oscillated and was larger during the silent phase than during the active phase of the burst. The ramp conductance was sensitive to diazoxide, and the oscillatory component was reduced by sulfonylureas or by lowering extracellular glucose to 2.8 mM, suggesting that the oscillatory total conductance is due to oscillatory KATP channel conductance. We demonstrate that these results are consistent with the Dual Oscillator model, in which glycolytic oscillations drive slow electrical bursting, but not with other models in which metabolic oscillations are secondary to calcium oscillations. The simulations also confirm that oscillations in membrane conductance can be well estimated from measurements of slope conductance and distinguished from gap junction conductance. Furthermore, the oscillatory conductance was blocked by tolbutamide in isolated β-cells. The data, combined with insights from mathematical models, support a mechanism of slow (~5 min) bursting driven by oscillations in metabolism, rather than by oscillations in the intracellular free calcium concentration. [ABSTRACT FROM AUTHOR]