Fast-activating voltage- and calcium-dependent potassium (BK) conductance promotes bursting in pituitary cells: a dynamic clamp study

Long-term, Dynamic Remodelling of the Corticotroph Transcriptome and Excitability After a Period of Chronic Stress

Chronic stress results in long-term dynamic changes at multiple levels of the hypothalamic-pituitary-adrenal (HPA) axis resulting in stress axis dysregulation with long-term impacts on human and animal health. However, the underlying mechanisms and dynamics of altered of HPA axis function, in particular at the level of pituitary corticotrophs, during a period of chronic stress and in the weeks after its cessation (defined as "recovery") are very poorly understood. Here, we address the fundamental question of how a period of chronic stress results in altered anterior pituitary corticotroph function and whether this persists in recovery, as well as the transcriptomic changes underlying this. We demonstrate that, in mice, spontaneous and corticotrophin-releasing hormone-stimulated electrical excitability of corticotrophs, essential for ACTH secretion, is suppressed for weeks to months of recovery following a period of chronic stress. Surprisingly, there are only modest changes in the corticotroph transcriptome during the period of stress, but major alterations occur in recovery. Importantly, although transcriptional changes for a large proportion of mRNAs follow the time course suppression of corticotroph excitability, many other genes display highly dynamic transcriptional changes with distinct time courses throughout recovery. Taken together, this suggests that chronic stress results in complex dynamic transcriptional and functional changes in corticotroph physiology, which are highly dynamic for weeks following cessation of chronic stress. These insights provide a fundamental new framework to further understand underlying molecular mechanisms as well approaches to both diagnosis and treatment of stress-related dysfunction of the HPA axis.

Conversion of spikers to bursters in pituitary cell networks: Is it better to disperse for maximum exposure or circle the wagons?

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.

Sex differences in pituitary corticotroph excitability

Stress-related illness represents a major burden on health and society. Sex differences in stress-related disorders are well documented, with women having twice the lifetime rate of depression compared to men and most anxiety disorders. Anterior pituitary corticotrophs are central components of the hypothalamic-pituitary-adrenal (HPA) axis, receiving input from hypothalamic neuropeptides corticotrophin-releasing hormone (CRH) and arginine vasopressin (AVP), while regulating glucocorticoid output from the adrenal cortex. The dynamic control of electrical excitability by CRH/AVP and glucocorticoids is critical for corticotroph function; however, whether corticotrophs contribute to sexually differential responses of the HPA axis, which might underlie differences in stress-related disorders, is very poorly understood. Using perforated patch clamp electrophysiology in corticotrophs from mice expressing green fluorescent protein under the control of the Pomc promoter, we characterized basal and secretagogue-evoked excitability. Both male and female corticotrophs show predominantly single-spike action potentials under basal conditions; however, males predominantly display spikes with small-amplitude (<20 mV) afterhyperpolarizations (B-type), whereas females displayed a mixture of B-type spikes and spikes with a large-amplitude (>25 mV) afterhyperpolarization (A-type). In response to CRH, or CRH/AVP, male cells almost exclusively transition to a predominantly pseudo-plateau bursting, whereas only female B-type cells display bursting in response to CRH±AVP. Treatment of male or female corticotrophs with 1 nM estradiol (E2) for 24-72 h has no effect on the proportion of cells with A- or B-type spikes in either sex. However, E2 results in the cessation of CRH-induced bursting in both male and female corticotrophs, which can be partially reversed by adding a BK current using a dynamic clamp. RNA-seq analysis of purified corticotrophs reveals extensive differential gene expression at the transcriptional level, including more than 71 mRNAs encoding ion channel subunits. Interestingly, there is a two-fold lower level (p < 0.01) of BK channel pore-forming subunit (Kcnma1) expression in females compared to males, which may partially explain the decrease in CRH-induced bursting. This study identified sex differences at the level of the anterior pituitary corticotroph ion channel landscape and control of both spontaneous and CRH-evoked excitability. Determining the mechanisms of sex differences of corticotroph and HPA activity at the cellular level could be an important step for better understanding, diagnosing, and treating stress-related disorders.

Sodium-mediated plateau potentials in an identified decisional neuron contribute to feeding-related motor pattern genesis in Aplysia

Motivated behaviors such as feeding depend on the functional properties of decision neurons to provide the flexibility required for behavioral adaptation. Here, we analyzed the ionic basis of the endogenous membrane properties of an identified decision neuron (B63) that drive radula biting cycles underlying food-seeking behavior in Aplysia. Each spontaneous bite cycle arises from the irregular triggering of a plateau-like potential and resultant bursting by rhythmic subthreshold oscillations in B63's membrane potential. In isolated buccal ganglion preparations, and after synaptic isolation, the expression of B63's plateau potentials persisted after removal of extracellular calcium, but was completely suppressed in a tetrodotoxin (TTX)- containing bath solution, thereby indicating the contribution of a transmembrane Na⁺ influx. Potassium outward efflux through tetraethylammonium (TEA)- and calcium-sensitive channels was found to contribute to each plateau's active termination. This intrinsic plateauing capability, in contrast to B63's membrane potential oscillation, was blocked by the calcium-activated non-specific cationic current (I_CAN) blocker flufenamic acid (FFA). Conversely, the SERCA blocker cyclopianozic acid (CPA), which abolished the neuron's oscillation, did not prevent the expression of experimentally evoked plateau potentials. These results therefore indicate that the dynamic properties of the decision neuron B63 rely on two distinct mechanisms involving different sub-populations of ionic conductances.

Modeling pulsativity in the hypothalamic-pituitary-adrenal hormonal axis

A new mathematical model for biological rhythms in the hypothalamic–pituitary–adrenal (HPA) axis is proposed. This model takes the form of a system of impulsive time-delay differential equations which include pulsatile release of adrenocorticotropin (ACTH) by the pituitary gland and a time delay for the release of glucocorticoid hormones by the adrenal gland. Numerical simulations demonstrate that the model’s response to periodic and circadian inputs from the hypothalamus are consistent with those generated by recent models which do not include a pulsatile pituitary. In contrast the oscillatory phenomena generated by the impulsive delay equation mode occur even if the time delay is zero. The observation that the time delay merely introduces a small phase shift suggesting that the effects of the adrenal gland are “downstream” to the origin of pulsativity. In addition, the model accounts for the occurrence of ultradian oscillations in an isolated pituitary gland. These observations suggest that principles of pulse modulated control, familiar to control engineers, may have an increasing role to play in understanding the HPA axis.

Classification of bursting patterns: A tale of two ducks

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

Bursting is ubiquitous in cellular excitable rhythms and comes in a plethora of patterns, both experimentally recorded and reproduced through models. As these different patterns may reflect different coding or information properties, it is therefore crucial to develop modeling frameworks that can both capture them and understand their characteristics. In this review, we propose a comprehensive account of the main bursting classification systems that have been developed over the past 40 years, together with recent developments allowing us to extend these classifications. Based upon bifurcation theory and heavily reliant on timescale separation, these schemes take full advantage of the fast subsystem analysis, obtained when slow variables are frozen and considered as bifurcation parameters. We complement this classical view by showing that nontrivial slow subsystem may also encode key informations important to classify bursting rhythms, due to the presence of so-called folded-node singularities. We provide minimal idealized models as well as one generic conductance-based example displaying bursting oscillations that require our extended classification in order to be fully characterized. We also highlight examples of biological data that could be suitably revisited with the lenses of this extended classifications and could lead to new models of complex cellular activity.

Network Properties of Electrically Coupled Bursting Pituitary Cells

The endocrine cells of the anterior pituitary gland are electrically active when stimulated or, in some cases, when not inhibited. The activity pattern thought to be most effective in releasing hormones is bursting, which consists of depolarization with small spikes that are much longer than single spikes. Although a majority of the research on cellular activity patterns has been performed on dispersed cells, the environment in situ is characterized by networks of coupled cells of the same type, at least in the case of somatotrophs and lactotrophs. This produces some degree of synchronization of their activity, which can be greatly increased by hormones and changes in the physiological state. In this computational study, we examine how electrical coupling among model cells influences synchronization of bursting oscillations among the population. We focus primarily on weak electrical coupling, since strong coupling leads to complete synchronization that is not characteristic of pituitary cell networks. We first look at small networks to point out several unexpected behaviors of the coupled system, and then consider a larger random scale-free network to determine what features of the structural network formed through gap junctional coupling among cells produce a high degree of functional coupling, i.e., clusters of synchronized cells. We employ several network centrality measures, and find that cells that are closely related in terms of their closeness centrality are most likely to be synchronized. We also find that structural hubs (cells with extensive coupling to other cells) are typically not functional hubs (cells synchronized with many other cells). Overall, in the case of weak electrical coupling, it is hard to predict the functional network that arises from a structural network, or to use a functional network as a means for determining the structural network that gives rise to it.

Chronic stress facilitates bursting electrical activity in pituitary corticotrophs

Coordination of an appropriate stress response is dependent upon anterior pituitary corticotroph excitability in response to hypothalamic secretagogues and glucocorticoid negative feedback. A key determinant of corticotroph excitability is large conductance calcium- and voltage-activated (BK) potassium channels that are critical for promoting corticotrophin-releasing hormone (CRH)-induced bursting that enhances adrenocorticotrophic hormone secretion. Previous studies revealed hypothalamic-pituitary-adrenal axis hyperexcitability following chronic stress (CS) is partly a function of increased corticotroph output. Thus, we hypothesise that chronic stress promotes corticotroph excitability through a BK-dependent mechanism. Corticotrophs from CS mice displayed significant increase in spontaneous bursting, which was suppressed by the BK blocker paxilline. Mathematical modelling reveals that the time constant of BK channel activation, plus properties and proportion of BK channels functionally coupled to L-type Ca²⁺ channels determines bursting activity. Surprisingly, CS corticotrophs (but not unstressed) display CRH-induced bursting even when the majority of BK channels are inhibited by paxilline, which modelling suggests is a consequence of the stochastic behaviour of a small number of BK channels coupled to L-type Ca²⁺ channels. Our data reveal that changes in the stochastic behaviour of a small number of BK channels can finely tune corticotroph excitability through stress-induced changes in BK channel properties. Importantly, regulation of BK channel function is highly context dependent allowing dynamic control of corticotroph excitability over a large range of time domains and physiological challenges in health and disease. This is likely to occur in other BK-expressing endocrine cells, with important implications for the physiological processes they regulate and the potential for therapy. KEY POINTS: Chronic stress (CS) is predicted to modify the electrical excitability of anterior pituitary corticotrophs. Electrophysiological recordings from isolated corticotrophs from CS male mice display spontaneous electrical bursting behaviour compared to the tonic spiking behaviour of unstressed corticotrophs. The increased spontaneous bursting from CS corticotrophs is BK-dependent and mathematical modelling reveals that the time constant of activation, properties and proportion of BK channels functionally coupled to L-type calcium channels determines the promotion of bursting activity. CS (but not unstressed) corticotrophs display corticotrophin-releasing hormone-induced bursting even when the majority of BK channels are pharmacologically inhibited, which can be explained by the stochastic behaviour of a small number of BK channels with distinct properties. Corticotroph excitability can be finely tuned by the stochastic behaviour of a small number of BK channels dependent on their properties and functional co-localisation with L-type calcium channels to control corticotroph excitability over diverse time domains and physiological challenges.

Fast-slow analysis of a stochastic mechanism for electrical bursting

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.

Robust spike timing in an excitable cell with delayed feedback

The initiation and regeneration of pulsatile activity is a ubiquitous feature observed in excitable systems with delayed feedback. Here, we demonstrate this phenomenon in a real biological cell. We establish a critical role of the delay resulting from the finite propagation speed of electrical impulses in the emergence of persistent multiple-spike patterns. We predict the coexistence of a number of such patterns in a mathematical model and use a biological cell subject to dynamic clamp to confirm our predictions in a living mammalian system. Given the general nature of our mathematical model and experimental system, we believe that our results capture key hallmarks of physiological excitability that are fundamental to information processing.

Mathematical modeling approaches of cellular endocrinology within the hypothalamo-pituitary-gonadal axis

The reproductive neuroendocrine axis, or hypothalamo-pituitary-gonadal (HPG) axis, is a paragon of complex biological system involving numerous cell types, spread over several anatomical levels communicating through entangled endocrine feedback loops. The HPG axis exhibits remarkable dynamic behaviors on multiple time and space scales, which are an inexhaustible source of studies for mathematical and computational biology. In this review, we will describe a variety of modeling approaches of the HPG axis from a cellular endocrinology viewpoint. We will in particular investigate the questions raised by some of the most striking features of the HPG axis: (i) the pulsatile secretion of hypothalamic and pituitary hormones, and its counterpart, the cell signaling induced by frequency-encoded hormonal signals, and (ii) the dual, gametogenic and glandular function of the gonads, which relies on the tight control of the somatic cell populations ensuring the proper maturation and timely release of the germ cells.

The Mechanisms Underlying Autonomous Adrenocorticotropic Hormone Secretion in Cushing's Disease

Cushing’s disease caused due to adrenocorticotropic hormone (ACTH)-secreting pituitary adenomas (ACTHomas) leads to hypercortisolemia, resulting in increased morbidity and mortality. Autonomous ACTH secretion is attributed to the impaired glucocorticoid negative feedback (glucocorticoid resistance) response. Interestingly, other conditions, such as ectopic ACTH syndrome (EAS) and non-neoplastic hypercortisolemia (NNH, also known as pseudo-Cushing’s syndrome) also exhibit glucocorticoid resistance. Therefore, to differentiate between these conditions, several dynamic tests, including those with desmopressin (DDAVP), corticotrophin-releasing hormone (CRH), and Dex/CRH have been developed. In normal pituitary corticotrophs, ACTH synthesis and secretion are regulated mainly by CRH and glucocorticoids, which are the ACTH secretion-stimulating and -suppressing factors, respectively. These factors regulate ACTH synthesis and secretion through genomic and non-genomic mechanisms. Conversely, glucocorticoid negative feedback is impaired in ACTHomas, which could be due to the overexpression of 11β-HSD2, HSP90, or TR4, or loss of expression of CABLES1 or nuclear BRG1 proteins. Genetic analysis has indicated the involvement of several genes in the etiology of ACTHomas, including USP8, USP48, BRAF, and TP53. However, the association between glucocorticoid resistance and these genes remains unclear. Here, we review the clinical aspects and molecular mechanisms of ACTHomas and compare them to those of other related conditions.

Dynamic Clamp on a Windows PC

Dynamic clamp is a powerful tool for interfacing computational models and real cells. We describe here how to set up and carry out dynamic clamp experiments using a patch clamp amplifier, a National Instruments data acquisition card, and the freely available QuB software that operates on a PC running MS Windows.

Ion channel noise shapes the electrical activity of endocrine cells

Endocrine cells in the pituitary gland typically display either spiking or bursting electrical activity, which is related to the level of hormone secretion. Recent work, which combines mathematical modelling with dynamic clamp experiments, suggests the difference is due to the presence or absence of a few large-conductance potassium channels. Since endocrine cells only contain a handful of these channels, it is likely that stochastic effects play an important role in the pattern of electrical activity. Here, for the first time, we explicitly determine the effect of such noise by studying a mathematical model that includes the realistic noisy opening and closing of ion channels. This allows us to investigate how noise affects the electrical activity, examine the origin of spiking and bursting, and determine which channel types are responsible for the greatest noise. Further, for the first time, we address the role of cell size in endocrine cell electrical activity, finding that larger cells typically display more bursting, while the smallest cells almost always only exhibit spiking behaviour.

Case Report on: Very Early Afterdepolarizations in HiPSC-Cardiomyocytes-An Artifact by Big Conductance Calcium Activated Potassium Current (Ibk,Ca)

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) represent an unlimited source of human CMs that could be a standard tool in drug research. However, there is concern whether hiPSC-CMs express all cardiac ion channels at physiological level and whether they might express non-cardiac ion channels. In a control hiPSC line, we found large, “noisy” outward K⁺ currents, when we measured outward potassium currents in isolated hiPSC-CMs. Currents were sensitive to iberiotoxin, the selective blocker of big conductance Ca²⁺-activated K⁺ current (I_BK,Ca). Seven of 16 individual differentiation batches showed a strong initial repolarization in the action potentials (AP) recorded from engineered heart tissue (EHT) followed by very early afterdepolarizations, sometimes even with consecutive oscillations. Iberiotoxin stopped oscillations and normalized AP shape, but had no effect in other EHTs without oscillations or in human left ventricular tissue (LV). Expression levels of the alpha-subunit (K_Ca1.1) of the BK_Ca correlated with the presence of oscillations in hiPSC-CMs and was not detectable in LV. Taken together, individual batches of hiPSC-CMs can express sarcolemmal ion channels that are otherwise not found in the human heart, resulting in oscillating afterdepolarizations in the AP. HiPSC-CMs should be screened for expression of non-cardiac ion channels before being applied to drug research.

Activation of a nucleotide-dependent RCK domain requires binding of a cation cofactor to a conserved site

RCK domains regulate the activity of K⁺ channels and transporters in eukaryotic and prokaryotic organisms by responding to ions or nucleotides. The mechanisms of RCK activation by Ca²⁺ in the eukaryotic BK and bacterial MthK K⁺ channels are well understood. However, the molecular details of activation in nucleotide-dependent RCK domains are not clear. Through a functional and structural analysis of the mechanism of ATP activation in KtrA, a RCK domain from the B. subtilis KtrAB cation channel, we have found that activation by nucleotide requires binding of cations to an intra-dimer interface site in the RCK dimer. In particular, divalent cations are coordinated by the γ-phosphates of bound-ATP, tethering the two subunits and stabilizing the active state conformation. Strikingly, the binding site residues are highly conserved in many different nucleotide-dependent RCK domains, indicating that divalent cations are a general cofactor in the regulatory mechanism of many nucleotide-dependent RCK domains.

Temporally Tuned Corticosteroid Feedback Regulation of the Stress Axis

Activity of the hypothalamic-pituitary-adrenal (HPA) axis is tuned by corticosteroid feedback. Corticosteroids regulate cellular function via genomic and nongenomic mechanisms, which operate over diverse time scales. This review summarizes recent advances in our understanding of how corticosteroid feedback regulates hypothalamic stress neuron function and output through synaptic plasticity, changes in intrinsic excitability, and modulation of neuropeptide production. The temporal kinetics of corticosteroid actions in the brain versus the pituitary have important implications for how organisms respond to stress. Furthermore, we will discuss, some of the technical limitations and missing links in the field, and the potential implications these may have on our interpretations of corticosteroid negative feedback experiments.

Action potential propagation and synchronisation in myelinated axons

With the advent of advanced MRI techniques it has become possible to study axonal white matter non-invasively and in great detail. Measuring the various parameters of the long-range connections of the brain opens up the possibility to build and refine detailed models of large-scale neuronal activity. One particular challenge is to find a mathematical description of action potential propagation that is sufficiently simple, yet still biologically plausible to model signal transmission across entire axonal fibre bundles. We develop a mathematical framework in which we replace the Hodgkin-Huxley dynamics by a spike-diffuse-spike model with passive sub-threshold dynamics and explicit, threshold-activated ion channel currents. This allows us to study in detail the influence of the various model parameters on the action potential velocity and on the entrainment of action potentials between ephaptically coupled fibres without having to recur to numerical simulations. Specifically, we recover known results regarding the influence of axon diameter, node of Ranvier length and internode length on the velocity of action potentials. Additionally, we find that the velocity depends more strongly on the thickness of the myelin sheath than was suggested by previous theoretical studies. We further explain the slowing down and synchronisation of action potentials in ephaptically coupled fibres by their dynamic interaction. In summary, this study presents a solution to incorporate detailed axonal parameters into a whole-brain modelling framework.

With more and more data becoming available on white-matter tracts, the need arises to develop modelling frameworks that incorporate these data at the whole-brain level. This requires the development of efficient mathematical schemes to study parameter dependencies that can then be matched with data, in particular the speed of action potentials that cause delays between brain regions. Here, we develop a method that describes the formation of action potentials by threshold activated currents, often referred to as spike-diffuse-spike modelling. A particular focus of our study is the dependence of the speed of action potentials on structural parameters. We find that the diameter of axons and the thickness of the myelin sheath have a strong influence on the speed, whereas the length of myelinated segments and node of Ranvier length have a lesser effect. In addition to examining single axons, we demonstrate that action potentials between nearby axons can synchronise and slow down their propagation speed.

A computational model for gonadotropin releasing cells in the teleost fish medaka

Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca²⁺ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na⁺ currents (I_Na), high-voltage activated Ca²⁺ currents (I_Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I_Na is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by I_Ca. Unlike in rats, spontaneous I_Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by I_Na, and (3) the first pituitary cell model where the kinetics of the depolarizing currents, I_Na and I_Ca, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire I_Ca-based APs. We put a particular focus on how the big conductance K⁺ current (I_BK) modulates the AP shape. Interestingly, we find that I_BK can prolong AP duration in models that fire I_Ca-based APs, while it consistently shortens the duration of the predominantly I_Na-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire I_Na-mediated APs.

Excitable cells elicit electrical pulses called action potentials (APs), which are generated and shaped by a combination of ion channels in the cell membrane. Since one type of ion channels is permeable to Ca²⁺ ions, there is typically an influx of Ca²⁺ during an AP. Pituitary cells therefore use AP firing to regulate their cytosolic Ca²⁺ concentration, which in turn controls their hormone secretion rate. The amount of Ca²⁺ that enters during an AP depends strongly on how long it lasts, and it is therefore important to understand the mechanisms that control this. Pituitary APs are generally mediated by a combination of Ca²⁺ channels and Na⁺ channels, and the relative contributions of from the two vary between cell types, animal species and biological conditions. Previous computer models have predominantly been adapted to data from pituitary cells which tend to fire Ca²⁺-based APs. Here we develop a new model, adapted to data from pituitary cells in the fish medaka, which APs that are predominantly Na⁺-based, and compare its dynamical properties to the previous models that fire Ca²⁺-based APs.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Role of glucocorticoid negative feedback in the regulation of HPA axis pulsatility

The hypothalamic-pituitary-adrenal (HPA) axis is the major neuroendocrine axis regulating homeostasis in mammals. Glucocorticoid hormones are rapidly synthesized and secreted from the adrenal gland in response to stress. In addition, under basal conditions glucocorticoids are released rhythmically with both a circadian and an ultradian (pulsatile) pattern. These rhythms are important not only for normal function of glucocorticoid target organs, but also for the HPA axis responses to stress. Several studies have shown that disruption of glucocorticoid rhythms is associated with disease both in humans and in rodents. In this review, we will discuss our knowledge of the negative feedback mechanisms that regulate basal ultradian synthesis and secretion of glucocorticoids, including the role of glucocorticoid and mineralocorticoid receptors and their chaperone protein FKBP51. Moreover, in light of recent findings, we will also discuss the importance of intra-adrenal glucocorticoid receptor signaling in regulating glucocorticoid synthesis.

Common and diverse elements of ion channels and receptors underlying electrical activity in endocrine pituitary cells

The pituitary gland contains six types of endocrine cells defined by hormones they secrete: corticotrophs, melanotrophs, gonadotrophs, thyrotrophs, somatotrophs, and lactotrophs. All these cell types are electrically excitable, and voltage-gated calcium influx is the major trigger for their hormone secretion. Along with hormone intracellular content, G-protein-coupled receptor and ion channel expression can also be considered as defining cell type identity. While many aspects of the developmental and activity dependent regulation of hormone and G-protein-coupled receptor expression have been elucidated, much less is known about the regulation of the ion channels needed for excitation-secretion coupling in these cells. We compare the spontaneous and receptor-controlled patterns of electrical signaling among endocrine pituitary cell types, including insights gained from mathematical modeling. We argue that a common set of ionic currents unites these cells, while differential expression of another subset of ionic currents could underlie cell type-specific patterns. We demonstrate these ideas using a generic mathematical model, showing that it reproduces many observed features of pituitary electrical signaling. Mapping these observations to the developmental lineage suggests possible modes of regulation that may give rise to mature pituitary cell types.

Control of anterior pituitary cell excitability by calcium-activated potassium channels

In anterior pituitary endocrine cells, large (BK), small (SK) and intermediate (IK) conductance calcium activated potassium channels are key determinants in shaping cellular excitability in a cell type- and context-specific manner. Indeed, these channels are targeted by multiple signaling pathways that stimulate or inhibit cellular excitability. BK channels can, paradoxically, both promote electrical bursting as well as terminate bursting and spiking dependent upon intrinsic BK channel properties and proximity to voltage gated calcium channels in somatotrophs, lactotrophs and corticotrophs. In contrast, SK channels are predominantly activated by calcium released from intracellular IP3-sensitive calcium stores and mediate membrane hyperpolarization in cells including gonadotrophs and corticotrophs. IK channels are predominantly expressed in corticotrophs where they limit membrane excitability. A major challenge for the future is to determine the cell-type specific molecular composition of calcium-activated potassium channels and how they control anterior pituitary hormone secretion as well as other calcium-dependent processes.

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

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

Glucocorticoids Inhibit CRH/AVP-Evoked Bursting Activity of Male Murine Anterior Pituitary Corticotrophs

Corticotroph cells from the anterior pituitary are an integral component of the hypothalamic-pituitary-adrenal (HPA) axis, which governs the neuroendocrine response to stress. Corticotrophs are electrically excitable and fire spontaneous single-spike action potentials and also display secretagogue-induced bursting behavior. The HPA axis function is dependent on effective negative feedback in which elevated plasma glucocorticoids result in inhibition at the level of both the pituitary and the hypothalamus. In this study, we have used an electrophysiological approach coupled with mathematical modeling to investigate the regulation of spontaneous and CRH/arginine vasopressin-induced activity of corticotrophs by glucocorticoids. We reveal that pretreatment of corticotrophs with 100 nM corticosterone (CORT; 90 and 150 min) reduces spontaneous activity and prevents a transition from spiking to bursting after CRH/arginine vasopressin stimulation. In addition, previous studies have identified a role for large-conductance calcium- and voltage-activated potassium (BK) channels in the generation of secretagogue-induced bursting in corticotrophs. Using the dynamic clamp technique, we demonstrated that CRH-induced bursting can be switched to spiking by subtracting a fast BK current, whereas the addition of a fast BK current can induce bursting in CORT-treated cells. In addition, recordings from BK knockout mice (BK(-/-)) revealed that CORT can also inhibit excitability through BK-independent mechanisms to control spike frequency. Thus, we have established that glucocorticoids can modulate multiple properties of corticotroph electrical excitability through both BK-dependent and BK-independent mechanisms.

Spontaneous and CRH-Induced Excitability and Calcium Signaling in Mice Corticotrophs Involves Sodium, Calcium, and Cation-Conducting Channels

Transgenic mice expressing the tdimer2(12) form of Discosoma red fluorescent protein under control of the proopiomelanocortin gene's regulatory elements are a useful model for studying corticotrophs. Using these mice, we studied the ion channels and mechanisms controlling corticotroph excitability. Corticotrophs were either quiescent or electrically active, with a 22-mV difference in the resting membrane potential (RMP) between the 2 groups. In quiescent cells, CRH depolarized the membrane, leading to initial single spiking and sustained bursting; in active cells, CRH further facilitated or inhibited electrical activity and calcium spiking, depending on the initial activity pattern and CRH concentration. The stimulatory but not inhibitory action of CRH on electrical activity was mimicked by cAMP independently of the presence or absence of arachidonic acid. Removal of bath sodium silenced spiking and hyperpolarized the majority of cells; in contrast, the removal of bath calcium did not affect RMP but reduced CRH-induced depolarization, which abolished bursting electrical activity and decreased the spiking frequency but not the amplitude of single spikes. Corticotrophs with inhibited voltage-gated sodium channels fired calcium-dependent action potentials, whereas cells with inhibited L-type calcium channels fired sodium-dependent spikes; blockade of both channels abolished spiking without affecting the RMP. These results indicate that the background voltage-insensitive sodium conductance influences RMP, the CRH-depolarization current is driven by a cationic conductance, and the interplay between voltage-gated sodium and calcium channels plays a critical role in determining the status and pattern of electrical activity and calcium signaling.

From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability

Models of electrical activity in excitable cells involve nonlinear interactions between many ionic currents. Changing parameters in these models can produce a variety of activity patterns with sometimes unexpected effects. Further more, introducing new currents will have different effects depending on the initial parameter set. In this study we combined global sampling of parameter space and local analysis of representative parameter sets in a pituitary cell model to understand the effects of adding K (+) conductances, which mediate some effects of hormone action on these cells. Global sampling ensured that the effects of introducing K (+) conductances were captured across a wide variety of contexts of model parameters. For each type of K (+) conductance we determined the types of behavioral transition that it evoked. Some transitions were counterintuitive, and may have been missed without the use of global sampling. In general, the wide range of transitions that occurred when the same current was applied to the model cell at different locations in parameter space highlight the challenge of making accurate model predictions in light of cell-to-cell heterogeneity. Finally, we used bifurcation analysis and fast/slow analysis to investigate why specific transitions occur in representative individual models. This approach relies on the use of a graphics processing unit (GPU) to quickly map parameter space to model behavior and identify parameter sets for further analysis. Acceleration with modern low-cost GPUs is particularly well suited to exploring the moderate-sized (5-20) parameter spaces of excitable cell and signaling models.

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.

BK Channels and the Control of the Pituitary

The pituitary gland provides the important link between the nervous system and the endocrine system and regulates a diverse range of physiological functions. The pituitary is connected to the hypothalamus by the pituitary stalk and is comprised primarily of two lobes. The anterior lobe consists of five hormone-secreting cell types which are electrically excitable and display single-spike action potentials as well as complex bursting patterns. Bursting is of particular interest as it raises intracellular calcium to a greater extent than spiking and is believed to underlie secretagogue-induced hormone secretion. BK channels have been identified as a key regulator of bursting in anterior pituitary cells. Experimental data and mathematical modeling have demonstrated that BK activation during the upstroke of an action potential results in a prolonged depolarization and an increase in intracellular calcium. In contrast, the posterior lobe is primarily composed of axonal projections of magnocellular neurosecretory cells which extend from the supraoptic and paraventricular nuclei of the hypothalamus. In these neuroendocrine cells, BK channel activation results in a decrease in excitability and hormone secretion. The opposite effect of BK channels in the anterior and posterior pituitary highlights the diverse role of BK channels in regulating the activity of excitable cells. Further studies of pituitary cell excitability and the specific role of BK channels would lead to a greater understanding of how pituitary cell excitability is regulated by both hypothalamic secretagogues and negative feedback loops, and could ultimately lead to novel treatments to pituitary-related disorders.

Incorporating spike-rate adaptation into a rate code in mathematical and biological neurons

For a slowly varying stimulus, the simplest relationship between a neuron's input and output is a rate code, in which the spike rate is a unique function of the stimulus at that instant. In the case of spike-rate adaptation, there is no unique relationship between input and output, because the spike rate at any time depends both on the instantaneous stimulus and on prior spiking (the "history"). To improve the decoding of spike trains produced by neurons that show spike-rate adaptation, we developed a simple scheme that incorporates "history" into a rate code. We utilized this rate-history code successfully to decode spike trains produced by 1) mathematical models of a neuron in which the mechanism for adaptation (IAHP) is specified, and 2) the gastropyloric receptor (GPR2), a stretch-sensitive neuron in the stomatogastric nervous system of the crab Cancer borealis, that exhibits long-lasting adaptation of unknown origin. Moreover, when we modified the spike rate either mathematically in a model system or by applying neuromodulatory agents to the experimental system, we found that changes in the rate-history code could be related to the biophysical mechanisms responsible for altering the spiking.

Age-related changes in large-conductance calcium-activated potassium channels in mammalian circadian clock neurons

Aging impairs the function of the suprachiasmatic nucleus (SCN, the central mammalian clock), leading to a decline in the circadian rhythm of many physiological processes, including sleep-wake rhythms. Recent studies have found evidence of age-related changes in the circadian regulation of potassium currents; these changes presumably lead to a decrease in the SCN's electrical rhythm amplitude. Current through large-conductance Ca(2+)-activated K(+) (BK) channels promote rhythmicity in both SCN neuronal activity and behavior. In many neuron types, changes in BK activity are correlated with changes in intracellular Ca(2+) concentration ([Ca(2+)]i). We performed patch-clamp recordings of SCN neurons in aged mice and observed that the circadian modulation of BK channel activity was lost because of a reduction in BK currents during the night. This reduced current diminished the afterhyperpolarization, depolarized the resting membrane potential, widened the action potential, and increased [Ca(2+)]i. These data suggest that reduced BK current increases [Ca(2+)]i by altering the action potential waveform, possibly contributing to the observed age-related phenotype.

Large conductance Ca²⁺-activated K⁺ (BK) channels promote secretagogue-induced transition from spiking to bursting in murine anterior pituitary corticotrophs

Anterior pituitary corticotroph cells are a central component of the hypothalamic-pituitary-adrenal (HPA) axis essential for the neuroendocrine response to stress. Corticotrophs are excitable cells that receive input from two hypothalamic secretagogues, corticotrophin-releasing hormone (CRH) and arginine vasopressin (AVP) to control the release of adrenocorticotrophic hormone (ACTH). Although corticotrophs are spontaneously active and increase in excitability in response to CRH and AVP the patterns of electrical excitability and underlying ionic conductances are poorly understood. In this study, we have used electrophysiological, pharmacological and genetic approaches coupled with mathematical modelling to investigate whether CRH and AVP promote distinct patterns of electrical excitability and to interrogate the role of large conductance calcium- and voltage-activated potassium (BK) channels in spontaneous and secretagogue-induced activity. We reveal that BK channels do not play a significant role in the generation of spontaneous activity but are critical for the transition to bursting in response to CRH. In contrast, AVP promotes an increase in single spike frequency, a mechanism independent of BK channels but dependent on background non-selective conductances. Co-stimulation with CRH and AVP results in complex patterns of excitability including increases in both single spike frequency and bursting. The ability of corticotroph excitability to be differentially regulated by hypothalamic secretagogues provides a mechanism for differential control of corticotroph excitability in response to different stressors.

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other psychiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6Hz and 1.2Hz are obtained, but frequencies as high as 6Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.

Electrophysiological differences between fshb- and lhb-expressing gonadotropes in primary culture

Synthesis and release of FSH and LH are differentially regulated by GnRH, but the mechanisms by which this regulation is achieved are not well understood. Teleost fish are powerful models for studying this differential regulation because they have distinct pituitary cells producing either FSH or LH. By using pituitary cultures from Atlantic cod (Gadus morhua), we were able to investigate and compare the electrophysiological properties of fshb- and lhb-expressing cells, identified by single-cell quantitative PCR after recording. Both cell types fired action potentials spontaneously. The relative number of excitable cells was dependent on reproductive season but varied in opposing directions according to season in the 2 cell types. Excitable and quiescent gonadotropes displayed different ion channel repertoires. The dynamics of outward currents and GnRH-induced membrane responses differed between fshb- and lhb-expressing cells, whereas GnRH-induced cytosolic Ca²⁺ responses were similar. Expression of Ca²⁺-activated K⁺ channels also differed with cell type and showed seasonal variation when measured in whole pituitary. The differential presence of these channels corresponds to the differences observed in membrane response to GnRH. We speculate that differences in ion channel expression levels may be involved in seasonal regulation of hormone secretion as well as the differential response to GnRH in LH- and FSH-producing gonadotropes, through differences in excitability and Ca²⁺ influx.

Models of electrical activity: calibration and prediction testing on the same cell

Mathematical models are increasingly important in biology, and testability is becoming a critical issue. One limitation is that one model simulation tests a parameter set representing one instance of the biological counterpart, whereas biological systems are heterogeneous in their properties and behavior, and a model often is fitted to represent an ideal average. This is also true for models of a cell's electrical activity; even within a narrowly defined population there can be considerable variation in electrophysiological phenotype. Here, we describe a computational experimental approach for parameterizing a model of the electrical activity of a cell in real time. We combine the inexpensive parallel computational power of a programmable graphics processing unit with the flexibility of the dynamic clamp method. The approach involves 1), recording a cell's electrical activity, 2), parameterizing a model to the recording, 3), generating predictions, and 4), testing the predictions on the same cell used for the calibration. We demonstrate the experimental feasibility of our approach using a cell line (GH4C1). These cells are electrically active, and they display tonic spiking or bursting. We use our approach to predict parameter changes that can convert one pattern to the other.

Biophysical properties and computational modeling of calcium spikes in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nuclei, with their extensive innervation of nearly the whole brain have important modulatory effects on many cognitive and physiological processes. They play important roles in clinical depression and other psychiatric disorders. In order to quantify the effects of serotonergic transmission on target cells it is desirable to construct computational models and to this end these it is necessary to have details of the biophysical and spike properties of the serotonergic neurons. Here several basic properties are reviewed with data from several studies since the 1960s to the present. The quantities included are input resistance, resting membrane potential, membrane time constant, firing rate, spike duration, spike and afterhyperpolarization (AHP) amplitude, spike threshold, cell capacitance, soma and somadendritic areas. The action potentials of these cells are normally triggered by a combination of sodium and calcium currents which may result in autonomous pacemaker activity. We here analyse the mechanisms of high-threshold calcium spikes which have been demonstrated in these cells the presence of TTX (tetrodotoxin). The parameters for calcium dynamics required to give calcium spikes are quite different from those for regular spiking which suggests the involvement of restricted parts of the soma-dendritic surface as has been found, for example, in hippocampal neurons.

The relationship between two fast/slow analysis techniques for bursting oscillations

Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical manifold. In this article, we investigate the relationships between the key structures of the two analysis techniques. We find that the z-curve and Hopf bifurcation of the two-fast/one-slow decomposition are closely related to the voltage nullcline and folded node singularity of the one-fast/two-slow decomposition, respectively. They become identical in the double singular limit in which voltage is infinitely fast and calcium is infinitely slow.

Dependence of the excitability of pituitary cells on cyclic nucleotides

Cyclic 3',5'-adenosine monophosphate and cyclic 3',5'-guanosine monophosphate are intracellular (second) messengers that are produced from the nucleotide triphosphates by a family of enzymes consisting of adenylyl and guanylyl cyclases. These enzymes are involved in a broad array of signal transduction pathways mediated by the cyclic nucleotide monophosphates and their kinases, which control multiple aspects of cell function through the phosphorylation of protein substrates. We review the findings and working hypotheses on the role of the cyclic nucleotides and their kinases in the control of electrical activity of the endocrine pituitary cells and the plasma membrane channels involved in this process.