Dynamic Hormone Control of Stress and Fertility

Neuroendocrine axes display a remarkable diversity of dynamic signaling processes relaying information between the brain, endocrine glands, and peripheral target tissues. These dynamic processes include oscillations, elastic responses to perturbations, and plastic long term changes observed from the cellular to the systems level. While small transient dynamic changes can be considered physiological, larger and longer disruptions are common in pathological scenarios involving more than one neuroendocrine axes, suggesting that a robust control of hormone dynamics would require the coordination of multiple neuroendocrine clocks. The idea of apparently different axes being in fact exquisitely intertwined through neuroendocrine signals can be investigated in the regulation of stress and fertility. The stress response and the reproductive cycle are controlled by the Hypothalamic-Pituitary-Adrenal (HPA) axis and the Hypothalamic-Pituitary-Gonadal (HPG) axis, respectively. Despite the evidence surrounding the effects of stress on fertility, as well as of the reproductive cycle on stress hormone dynamics, there is a limited understanding on how perturbations in one neuroendocrine axis propagate to the other. We hypothesize that the links between stress and fertility can be better understood by considering the HPA and HPG axes as coupled systems. In this manuscript, we investigate neuroendocrine rhythms associated to the stress response and reproduction by mathematically modeling the HPA and HPG axes as a network of interlocked oscillators. We postulate a network architecture based on physiological data and use the model to predict responses to stress perturbations under different hormonal contexts: normal physiological, gonadectomy, hormone replacement with estradiol or corticosterone (CORT), and high excess CORT (hiCORT) similar to hypercortisolism in humans. We validate our model predictions against experiments in rodents, and show how the dynamic responses of these endocrine axes are consistent with our postulated network architecture. Importantly, our model also predicts the conditions that ensure robustness of fertility to stress perturbations, and how chronodisruptions in glucocorticoid hormones can affect the reproductive axis' ability to withstand stress. This insight is key to understand how chronodisruption leads to disease, and to design interventions to restore normal rhythmicity and health.

Canard-induced complex oscillations in an excitatory network

In Neuroscience, mathematical modelling involving multiple spatial and temporal scales can unveil complex oscillatory activity such as excitable responses to an input current, subthreshold oscillations, spiking or bursting. While the number of slow and fast variables and the geometry of the system determine the type of the complex oscillations, canard structures define boundaries between them. In this study, we use geometric singular perturbation theory to identify and characterise boundaries between different dynamical regimes in multiple-timescale firing rate models of the developing spinal cord. These rate models are either three or four dimensional with state variables chosen within an overall group of two slow and two fast variables. The fast subsystem corresponds to a recurrent excitatory network with fast activity-dependent synaptic depression, and the slow variables represent the cell firing threshold and slow activity-dependent synaptic depression, respectively. We start by demonstrating canard-induced bursting and mixed-mode oscillations in two different three-dimensional rate models. Then, in the full four-dimensional model we show that a canard-mediated slow passage creates dynamics that combine these complex oscillations and give rise to mixed-mode bursting oscillations (MMBOs). We unveil complicated isolas along which MMBOs exist in parameter space. The profile of solutions along each isola undergoes canard-mediated transitions between the sub-threshold regime and the bursting regime; these explosive transitions change the number of oscillations in each regime. Finally, we relate the MMBO dynamics to experimental recordings and discuss their effects on the silent phases of bursting patterns as well as their potential role in creating subthreshold fluctuations that are often interpreted as noise. The mathematical framework used in this paper is relevant for modelling multiple timescale dynamics in excitable systems.

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.

A Compartmental Model to Investigate Local and Global Ca2+ Dynamics in Astrocytes

Intracellular Ca²⁺ dynamics in astrocytes can be triggered by neuronal activity and in turn regulate a variety of downstream processes that modulate neuronal function. In this fashion, astrocytic Ca²⁺ signaling is regarded as a processor of neural network activity by means of complex spatial and temporal Ca²⁺ dynamics. Accordingly, a key step is to understand how different patterns of neural activity translate into spatiotemporal dynamics of intracellular Ca²⁺ in astrocytes. Here, we introduce a minimal compartmental model for astrocytes that can qualitatively reproduce essential hierarchical features of spatiotemporal Ca²⁺ dynamics in astrocytes. We find that the rate of neuronal firing determines the rate of Ca²⁺ spikes in single individual processes as well as in the soma of the cell, while correlations of incoming neuronal activity are important in determining the rate of “global” Ca²⁺ spikes that can engulf soma and the majority of processes. Significantly, our model predicts that whether the endoplasmic reticulum is shared between soma and processes or not determines the relationship between the firing rate of somatic Ca²⁺ events and the rate of neural network activity. Together these results provide intuition about how neural activity in combination with inherent cellular properties shapes spatiotemporal astrocytic Ca²⁺ dynamics, and provide experimentally testable predictions.

The Effects of GABAergic Polarity Changes on Episodic Neural Network Activity in Developing Neural Systems

Early in development, neural systems have primarily excitatory coupling, where even GABAergic synapses are excitatory. Many of these systems exhibit spontaneous episodes of activity that have been characterized through both experimental and computational studies. As development progress the neural system goes through many changes, including synaptic remodeling, intrinsic plasticity in the ion channel expression, and a transformation of GABAergic synapses from excitatory to inhibitory. What effect each of these, and other, changes have on the network behavior is hard to know from experimental studies since they all happen in parallel. One advantage of a computational approach is that one has the ability to study developmental changes in isolation. Here, we examine the effects of GABAergic synapse polarity change on the spontaneous activity of both a mean field and a neural network model that has both glutamatergic and GABAergic coupling, representative of a developing neural network. We find some intuitive behavioral changes as the GABAergic neurons go from excitatory to inhibitory, shared by both models, such as a decrease in the duration of episodes. We also find some paradoxical changes in the activity that are only present in the neural network model. In particular, we find that during early development the inter-episode durations become longer on average, while later in development they become shorter. In addressing this unexpected finding, we uncover a priming effect that is particularly important for a small subset of neurons, called the “intermediate neurons.” We characterize these neurons and demonstrate why they are crucial to episode initiation, and why the paradoxical behavioral change result from priming of these neurons. The study illustrates how even arguably the simplest of developmental changes that occurs in neural systems can present non-intuitive behaviors. It also makes predictions about neural network behavioral changes that occur during development that may be observable even in actual neural systems where these changes are convoluted with changes in synaptic connectivity and intrinsic neural plasticity.

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.

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.

Direct stimulatory effects of oxytocin in female rat gonadotrophs and somatotrophs in vitro: comparison with lactotrophs

The peptide oxytocin (OT) is secreted by hypothalamic neurons and exerts numerous actions related to reproduction. OT stimulation of prolactin secretion in female rats is important during the estrous cycle, pregnancy, and lactation. Here we report that OT also stimulates transients of intracellular Ca(2+) concentration in somatotrophs and gonadotrophs as well as the release of GH and LH in a dose-dependent manner with EC50 values that closely correspond to the ligand affinity of the OT receptor (OTR). Remarkably, the hormone-releasing effect of OT in these two cell types is 2 orders of magnitude more sensitive than that in lactotrophs. The specific OTR agonist [Thr(4),Gly(7)]-oxytocin acutely stimulated the release of LH, GH, and prolactin from female rat pituitary cells in primary culture and increased intracellular Ca(2+) concentration in gonadotrophs, somatotrophs, and lactotrophs. In these three cell types, the effects on hormone release and intracellular Ca(2+) of both OT and [Thr(4),Gly(7)]oxytocin were abolished by the specific OT receptor antagonist desGly-NH2-d(CH2)5[D-Tyr(2),Thr(4)]OVT but not by the highly selective vasopressin V1a receptor antagonist, d(CH2)5[Tyr(Me)(2),Dab(5)]AVP. Furthermore, 10 nM arginine vasopressin stimulated LH and GH release comparably with a dose of OT that was at least 10 times lower. Finally, the presence of the OTR-like immunoreactivity could be observed in all three cell types. Taken together, these results show that OT directly stimulates gonadotrophs, somatotrophs, and lactotrophs through OT receptors and suggest that OT signaling may serve to coordinate the release of different pituitary hormones during specific physiological conditions.

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.

Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model

The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative feedback processes in the HH model that regulate rhythmic spiking. The first is an outward current with an activation variable n that has an opposite influence to the excitatory inward current and therefore provides subtractive negative feedback. The other is the inactivation of an inward current with an inactivation variable h that reduces the amount of positive feedback and therefore provides divisive feedback. Rhythmic spiking can be obtained with either negative feedback process, so we ask what is gained by having two feedback processes. We also ask how the different negative feedback processes contribute to spiking. We show that having two negative feedback processes makes the HH model more robust to changes in applied currents and conductance densities than models that possess only one negative feedback variable. We also show that the contributions made by the subtractive and divisive feedback variables are not static, but depend on time scales and conductance values. In particular, they contribute differently to the dynamics in Type I versus Type II neurons.

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.

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.

The dynamics underlying pseudo-plateau bursting in a pituitary cell model

Pituitary cells of the anterior pituitary gland secrete hormones in response to patterns of electrical activity. Several types of pituitary cells produce short bursts of electrical activity which are more effective than single spikes in evoking hormone release. These bursts, called pseudo-plateau bursts, are unlike bursts studied mathematically in neurons (plateau bursting) and the standard fast-slow analysis used for plateau bursting is of limited use. Using an alternative fast-slow analysis, with one fast and two slow variables, we show that pseudo-plateau bursting is a canard-induced mixed mode oscillation. Using this technique, it is possible to determine the region of parameter space where bursting occurs as well as salient properties of the burst such as the number of spikes in the burst. The information gained from this one-fast/two-slow decomposition complements the information obtained from a two-fast/one-slow decomposition.

Systemic oxytocin induces a prolactin secretory rhythm via the pelvic nerve in ovariectomized rats

We have shown previously that an intravenous injection of oxytocin (OT) in ovariectomized (OVX) rats initiates a circadian rhythm of prolactin (PRL) secretion similar to that observed after cervical stimulation (CS). In this study, we investigated the pathway through which OT triggers the PRL rhythm. We first tested whether an intracerebroventricular injection of OT could trigger the PRL secretory rhythm. As it did not, we injected OT intravenously while an OT receptor antagonist was infused intravenously. This antagonist completely abolished the PRL surges, suggesting that a peripheral target of OT is necessary for triggering the PRL rhythm. We hypothesized that OT may induce PRL release, which would be transported into the brain and trigger the rhythm. In agreement with this, OT injection increased circulating PRL by 5 min. To test whether this acute increase in PRL release would induce the PRL rhythm, we compared the effect of intravenously administered thyrotropin-releasing hormone (TRH) and OT. Although TRH injection also increased PRL to a comparable level after 5 min, only OT-injected animals expressed the PRL secretory rhythm. Motivated by prior findings that bilateral resection of the pelvic nerve blocks CS-induced pseudopregnancy and OT-induced facilitation of lordosis, we then hypothesized that the OT signal may be transmitted through the pelvic nerve. In fact, OT injection failed to induce a PRL secretory rhythm in pelvic-neurectomized animals, suggesting that the integrity of the pelvic nerve is necessary for the systemic OT induction of the PRL secretory rhythm in OVX rats.

Quantifying the relative contributions of divisive and subtractive feedback to rhythm generation

Biological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes: divisive (decreases the gain of the positive feedback loop) and subtractive (increases the input threshold) that both contribute to slowly move the system between the high- and low-activity states. Can we determine the relative contribution of each type of negative feedback process to the rhythmic activity? Does one dominate? Do they control the active and silent phase equally? To answer these questions we use a neural network model with excitatory coupling, regulated by synaptic depression (divisive) and cellular adaptation (subtractive feedback). We first attempt to apply standard experimental methodologies: either passive observation to correlate the variations of a variable of interest to system behavior, or deletion of a component to establish whether a component is critical for the system. We find that these two strategies can lead to contradictory conclusions, and at best their interpretive power is limited. We instead develop a computational measure of the contribution of a process, by evaluating the sensitivity of the active (high activity) and silent (low activity) phase durations to the time constant of the process. The measure shows that both processes control the active phase, in proportion to their speed and relative weight. However, only the subtractive process plays a major role in setting the duration of the silent phase. This computational method can be used to analyze the role of negative feedback processes in a wide range of biological rhythms.

As modern experimental techniques uncover new components in biological systems and describe their mutual interactions, the problem of determining the contribution of each component becomes critical. The many feedback loops created by these interactions can lead to oscillatory behavior. Examples of oscillations in biology include the cell cycle, circadian rhythms, the electrical activity of excitable cells, and predator-prey systems. While we understand how negative feedback loops can cause oscillations, when multiple feedback loops are present it becomes difficult to identify the dominant mechanism(s), if any. We address the problem of establishing the relative contribution of a feedback process using a biological oscillator model for which oscillations are controlled by two types of slow negative feedback. To determine which is the dominant process, we first use standard experimental methodologies: either passive observation to correlate a variable's behavior to system activity, or deletion of a component to establish whether that component is critical for the system. We find that these methods have limited applicability to the determination of the dominant process. We then develop a new quantitative measure of the contribution of each process to the oscillations. This computational method can be extended to a wide variety of oscillatory systems.

Modeling mechanisms of cell secretion

Secretion is a fundamental cellular process involving the regulated release of intracellular products from cells. Physiological functions such as neurotransmission, or the release of hormones and digestive enzymes, are all governed by cell secretion. Anomalies in the processes involved in secretion contribute to the development and progression of diseases such as diabetes and other hormonal disorders. To unravel the mechanisms that govern such diseases, it is essential to understand how hormones, growth factors and neurotransmitters are synthesized and processed, and how their signals are recognized, amplified and transmitted by intracellular signaling pathways in the target cells. Here, we discuss diverse aspects of the detailed mechanisms involved in secretion based on mathematical models. The models range from stochastic ones describing the trafficking of secretory vesicles to deterministic ones investigating the regulation of cellular processes that underlie hormonal secretion. In all cases, the models are closely related to experimental results and suggest theoretical predictions for the secretion mechanisms.

Investigating heterogeneity of intracellular calcium dynamics in anterior pituitary lactotrophs using a combined modelling/experimental approach

Cell responses are commonly heterogeneous, even within a subpopulation. In the present study, we investigate the source of heterogeneity in the Ca(2+) response of anterior pituitary lactotrophs to a Ca(2+) mobilisation agonist, thyrotrophin-releasing hormone. This response is characterised by a sharp increase of cytosolic Ca(2+) concentration as a result of mobilisation of Ca(2+) from intracellular stores, followed by a decrease to an elevated plateau level that results from Ca(2+) influx. We focus on heterogeneity of the evoked Ca(2+) spike under extracellular Ca(2+) free conditions. We introduce a method that uses the information provided by a mathematical model to characterise the source of heterogeneity. This method compares scatter plots of features of the Ca(2+) response obtained experimentally with those made from the mathematical model. The model scatter plots reflect random variation of parameters over different ranges, and matching the experimental and model scatter plots allows us to predict which parameters are most variable. We find that a large degree of variation in Ca(2+) efflux is a likely key contributor to the heterogeneity of Ca(2+) responses to thyrotrophin-releasing hormone in lactotrophs. This technique is applicable to any situation in which the heterogeneous biological response is described by a mathematical model.

Ion channels and signaling in the pituitary gland

Endocrine pituitary cells are neuronlike; they express numerous voltage-gated sodium, calcium, potassium, and chloride channels and fire action potentials spontaneously, accompanied by a rise in intracellular calcium. In some cells, spontaneous electrical activity is sufficient to drive the intracellular calcium concentration above the threshold for stimulus-secretion and stimulus-transcription coupling. In others, the function of these action potentials is to maintain the cells in a responsive state with cytosolic calcium near, but below, the threshold level. Some pituitary cells also express gap junction channels, which could be used for intercellular Ca(2+) signaling in these cells. Endocrine cells also express extracellular ligand-gated ion channels, and their activation by hypothalamic and intrapituitary hormones leads to amplification of the pacemaking activity and facilitation of calcium influx and hormone release. These cells also express numerous G protein-coupled receptors, which can stimulate or silence electrical activity and action potential-dependent calcium influx and hormone release. Other members of this receptor family can activate calcium channels in the endoplasmic reticulum, leading to a cell type-specific modulation of electrical activity. This review summarizes recent findings in this field and our current understanding of the complex relationship between voltage-gated ion channels, ligand-gated ion channels, gap junction channels, and G protein-coupled receptors in pituitary cells.

From plateau to pseudo-plateau bursting: making the transition

Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudo-plateau bursting, are often observed in neurons and endocrine cells, respectively. These two types of bursting have very different properties and likely serve different functions. This latter point is supported by the divergent expression of the bursting patterns into different cell types, and raises the question of whether it is even possible for a model for one type of cell to produce bursting of the type seen in the other type without large changes to the model. Using fast/slow analysis, we show here that this is possible, and we provide a procedure for achieving this transition. This suggests that the design principles for bursting in endocrine cells are just quantitative variations of those for bursting in neurons.

A tale of two rhythms: the emerging roles of oxytocin in rhythmic prolactin release

Hormone secretion often occurs in a pulsatile manner. In this review, we discuss two rhythms of in vivo prolactin release in female rats and the ongoing research that we and others have performed aiming to understand the mechanisms underlying them. The peptide hormone oxytocin appears to play an important role in both rhythms. One rhythm occurs during the first half of pregnancy, but can also be induced in ovariectomised rats. This is characterised by a circadian pattern with two prolactin surges per day. Two methods for triggering this rhythm are discussed, each utilising a unique physiological pathway that includes oxytocin action, presumably on pituitary lactotrophs. The second rhythm occurs during the oestrous cycle and is characterised by a surge of prolactin on the afternoon of pro-oestrus. We discuss recent findings that oxytocin is more effective at stimulating prolactin release from lactotrophs taken from animals on the afternoon of pro-oestrus than from those of animals on the morning of dioestrus 1, raising the possibility that this hormone plays a physiological role in the regulation of prolactin secretion during the oestrous cycle.

Variations in the response of pituitary lactotrophs to oxytocin during the rat estrous cycle

Although removal of dopamine inhibition is established as a major factor in prolactin (PRL) release, a large body of evidence suggests that hypothalamic oxytocin (OT) may serve as a PRL-releasing hormone in the rat. PRL release is modulated by estradiol (E2), which rises between diestrus and proestrus of the estrous cycle, causing a PRL surge in the afternoon of proestrus. Given that E2 strongly modulates OT actions in both central and peripheral tissues, OT action on lactotrophs might also be modulated by the stage of the estrous cycle. To test this hypothesis, we have monitored PRL release and intracellular calcium levels ([Ca(2+)](i)) induced by OT in pituitary lactotrophs obtained from female rats in either diestrus 1 or proestrus. We found that both secretory and [Ca(2+)](i) responses to OT are significantly increased in lactotrophs obtained on proestrus. Moreover, we show that these differences are due to an increase in both the number of OT-responding lactotrophs and the magnitude of their individual [Ca(2+)](i) responses. Both secretory and [Ca(2+)](i) responses were abolished by a specific OT antagonist. Finally, dose-dependent studies show that the increased PRL-releasing effect of OT on proestrus is significant over a wide range of concentrations, particularly those observed in hypophyseal portal plasma. These results suggest that the rising E2 titers that culminate on proestrus facilitate the stimulatory action of OT on lactotrophs and support the notion that OT is a PRL-releasing hormone with an important role in the production of the proestrous surge of PRL.

Mechanism for the universal pattern of activity in developing neuronal networks

Spontaneous episodic activity is a fundamental mode of operation of developing networks. Surprisingly, the duration of an episode of activity correlates with the length of the silent interval that precedes it, but not with the interval that follows. Here we use a modeling approach to explain this characteristic, but thus far unexplained, feature of developing networks. Because the correlation pattern is observed in networks with different structures and components, a satisfactory model needs to generate the right pattern of activity regardless of the details of network architecture or individual cell properties. We thus developed simple models incorporating excitatory coupling between heterogeneous neurons and activity-dependent synaptic depression. These models robustly generated episodic activity with the correct correlation pattern. The correlation pattern resulted from episodes being triggered at random levels of recovery from depression while they terminated around the same level of depression. To explain this fundamental difference between episode onset and termination, we used a mean field model, where only average activity and average level of recovery from synaptic depression are considered. In this model, episode onset is highly sensitive to inputs. Thus noise resulting from random coincidences in the spike times of individual neurons led to the high variability at episode onset and to the observed correlation pattern. This work further shows that networks with widely different architectures, different cell types, and different functions all operate according to the same general mechanism early in their development.

A-type K(+) current can act as a trigger for bursting in the absence of a slow variable

Models of bursting in single cells typically include two subsystems with different timescales. Variations in one or more slow variables switch the system between a silent and a spiking state. We have developed a model for bursting in the pituitary lactotroph that does not include any slow variable. The model incorporates fast, noninactivating calcium and potassium currents (the spike-generating mechanism), as well as the fast, inactivating A-type potassium current (I(A)). I(A) is active only briefly at the beginning of a burst, but this brief impulse of I(A) acts as a burst trigger, injecting the spike trajectory close to an unstable steady state. The spiraling of the trajectory away from the steady state produces a period of low-amplitude spiking typical of lactotrophs. Increasing the conductance of A-type potassium current brings the trajectory closer to the unstable steady state, increasing burst duration. However, this also increases interburst interval, and for larger conductance values, all activity stops. To our knowledge, this is the first example of a physiologically based, single-compartmental model of bursting with no slow subsystem.

Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents

Dopamine (DA) released from the hypothalamus tonically inhibits pituitary lactotrophs. DA (at micromolar concentration) opens potassium channels, hyperpolarizing the lactotrophs and thus preventing the calcium influx that triggers prolactin hormone release. Surprisingly, at concentrations approximately 1000 lower, DA can stimulate prolactin secretion. Here, we investigated whether an increase in a K+ current could mediate this stimulatory effect. We considered the fast K+ currents flowing through large-conductance BK channels and through A-type channels. We developed a minimal lactotroph model to investigate the effects of these two currents. Both IBK and IA could transform the electrical pattern of activity from spiking to bursting, but through distinct mechanisms. IBK always increased the intracellular Ca2+ concentration, while IA could either increase or decrease it. Thus, the stimulatory effects of DA could be mediated by a fast K+ conductance which converts tonically spiking cells to bursters. In addition, the study illustrates that

Differential control of active and silent phases in relaxation models of neuronal rhythms

Rhythmic bursting activity, found in many biological systems, serves a variety of important functions. Such activity is composed of episodes, or bursts (the active phase, AP) that are separated by quiescent periods (the silent phase, SP). Here, we use mean field, firing rate models of excitatory neural network activity to study how AP and SP durations depend on two critical network parameters that control network connectivity and cellular excitability. In these models, the AP and SP correspond to the network's underlying bistability on a fast time scale due to rapid recurrent excitatory connectivity. Activity switches between the AP and SP because of two types of slow negative feedback: synaptic depression-which has a divisive effect on the network input/output function, or cellular adaptation-a subtractive effect on the input/output function. We show that if a model incorporates the divisive process (regardless of the presence of the subtractive process), then increasing cellular excitability will speed up the activity, mostly by decreasing the silent phase. Reciprocally, if the subtractive process is present, increasing the excitatory connectivity will slow down the activity, mostly by lengthening the active phase. We also show that the model incorporating both slow processes is less sensitive to parameter variations than the models with only one process. Finally, we note that these network models are formally analogous to a type of cellular pacemaker and thus similar results apply to these cellular pacemakers.

Analysis of spontaneous bursting activity in random neural networks

Developing networks can generate bursting activity despite the absence of pacemaker cells and inhibitory synapses. Bursts are generated by positive feedback through excitatory connections and terminated by a slow depression of network excitability. Similar activity has been observed in cultures of spinal neurons containing inhibitory synapses. Is burst generation in these cultures operating according to the mechanism proposed for developing networks? To answer this question without perturbing the activity, we analyzed the burst pattern of individual neurons in active cultures. We observed a correlation between burst size and preceding interburst interval and a rapid rise and progressive decrease in firing rate during a burst. These findings are consistent with the mechanism of burst generation proposed for developing networks.

The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord

Spontaneous episodic activity occurs throughout the developing nervous system because immature circuits are hyperexcitable. It is not fully understood how the temporal pattern of this activity is regulated. Here, we study the role of activity-dependent depression of network excitability in the generation and regulation of spontaneous activity in the embryonic chick spinal cord. We demonstrate that the duration of an episode of activity depends on the network excitability at the beginning of the episode. We found a positive correlation between episode duration and the preceding inter-episode interval, but not with the following interval, suggesting that episode onset is stochastic whereas episode termination occurs deterministically, when network excitability falls to a fixed level. This is true over a wide range of developmental stages and under blockade of glutamatergic or GABAergic/glycinergic synapses. We also demonstrate that during glutamatergic blockade the remaining part of the network becomes more excitable, compensating for the loss of glutamatergic synapses and allowing spontaneous activity to recover. This compensatory increase in the excitability of the remaining network reflects the progressive increase in synaptic efficacy that occurs in the absence of activity. Therefore, the mechanism responsible for the episodic nature of the activity automatically renders this activity robust to network disruptions. The results are presented using the framework of our computational model of spontaneous activity in the developing cord. Specifically, we show how they follow logically from a bistable network with a slow activity-dependent depression switching periodically between the active and inactive states.

Parameter estimation methods for single neuron models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.

Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network

Spontaneous episodic activity is a general feature of developing neural networks. In the chick spinal cord, the activity comprises episodes of rhythmic discharge (duration 5-90 sec; cycle rate 0.1-2 Hz) that recur every 2-30 min. The activity does not depend on specialized connectivity or intrinsic bursting neurons and is generated by a network of functionally excitatory connections. Here, we develop an idealized, qualitative model of a homogeneous, excitatory recurrent network that could account for the multiple time-scale spontaneous activity in the embryonic chick spinal cord. We show that cycling can arise from the interplay between excitatory connectivity and fast synaptic depression. The slow episodic behavior is attributable to a slow activity-dependent network depression that is modeled either as a modulation of cellular excitability or as synaptic depression. Although the two descriptions share many features, the model with a slow synaptic depression accounts better for the experimental observations during blockade of excitatory synapses.

NMDA-induced dendritic oscillations during a soma voltage clamp of chick spinal neurons

An investigation of dendritic membrane properties was performed by whole-cell patch measurements of the biophysical properties of intact chick spinal neurons that are involved in rhythmogenesis. A whole-cell voltage clamp of the somatic membrane was used to block NMDA-induced voltage oscillations from the cell body, thus partially isolating the intrinsic oscillatory properties of dendritic membranes from those of the soma. An experimental approach was developed that takes into account the complexity of the dendritic tree in an environment as normal as possible, without the need for cell isolation or slice preparations. A computational study of the experimentally determined model showed that excitatory amino acid receptors on dendrites can dynamically control the electrotonic length of the dendrites through the activation of negative slope conductances. These experiments demonstrate the presence of NMDA receptors on the dendrites and that they induce intrinsic oscillations when the synaptic input from other cells is significantly reduced.

Spontaneous network activity transiently depresses synaptic transmission in the embryonic chick spinal cord

We examined the effects of spontaneous or evoked episodes of rhythmic activity on synaptic transmission in several spinal pathways of embryonic day 9-12 chick embryos. We compared the amplitude of synaptic potentials evoked by stimulation of the ventrolateral funiculus (VLF), the dorsal or ventral roots, before and after episodes of activity. With the exception of the short-latency responses evoked by dorsal root stimulation, the potentials were briefly potentiated and then reduced for several minutes after an episode of rhythmic activity. Their amplitude progressively recovered in the interval between successive episodes. The lack of post-episode depression in the short-latency component of the dorsal root evoked responses is probably attributable to the absence of firing in cut muscle afferents during an episode of activity. The post-episode depression of VLF-evoked potentials was mimicked by prolonged stimulation of the VLF, subthreshold for an episode of activity. By contrast, antidromically induced motoneuron firing and the accompanying calcium entry did not depress VLF-evoked potentials recorded from the stimulated ventral root. In addition, post-episode depression of VLF-evoked synaptic currents was observed in voltage-clamped spinal neurons. Collectively, these findings suggest that somatic postsynaptic activity and calcium entry are not required for the depression. We propose instead that the mechanism may involve a form of long-lasting activity-induced synaptic depression, possibly a combination of transmitter depletion and ligand-induced changes in the postsynaptic current accompanying transmitter release. This activity-dependent depression appears to be an important mechanism underlying the occurrence of spontaneous activity in developing spinal networks.

Mechanisms of spontaneous activity in the developing spinal cord and their relevance to locomotion

The isolated lumbosacral cord of the chick embryo generates spontaneous episodes of rhythmic activity. Muscle nerve recordings show that the discharge of sartorius (flexor) and femorotibialis (extensor) motoneurons alternates even though the motoneurons are depolarized simultaneously during each cycle. The alternation occurs because sartorius motoneuron firing is shunted or voltage-clamped by its synaptic drive at the time of peak femorotibialis discharge. Ablation experiments have identified a region dorsomedial to the lateral motor column that may be required for the alternation of sartorius and femorotibialis motoneurons. This region overlaps the location of interneurons activated by ventral root stimulation. Wholecell recordings from interneurons receiving short latency ventral root input indicate that they fire at an appropriate time to contribute to the cyclical pause in firing of sartorius motoneurons. Spontaneous activity was modeled by the interaction of three variables: network activity and two activity-dependent forms of network depression. A "slow" depression which regulates the occurrence of episodes and a "fast" depression that controls cycling during an episode. The model successfully predicts several aspects of spinal network behavior including spontaneous rhythmic activity and the recovery of network activity following blockade of excitatory synaptic transmission.

Simulation and parameter estimation study of a simple neuronal model of rhythm generation: role of NMDA and non-NMDA receptors

Simple neural network models of the Xenopus embryo swimming CPG, based on the one originally developed by Roberts and Tunstall (1990), were used to investigate the role of the voltage-dependent N-methyl-D-aspartate (NMDA) receptor channels, in conjunction with faster non-NMDA components of synaptic excitation, in rhythm generation. The voltage-dependent NMDA current "follows" the membrane potential, leading to a postinhibitory rebound that is more efficient than one without voltage dependency and allows neurons to fire more than one action potential per cycle. Furthermore, the model demonstrated limited rhythmic activity in the absence of synaptic inhibition, supporting the hypothesis that the NMDA channels provide a basic mechanism for rhythmicity. However, the rhythmic properties induced by the NMDA current were observed only when there was moderate activation of the non-NMDA synaptic channels, suggesting a modulatory role for this component. The simulations also show that the voltage dependency of the NMDA conductance, as well as the fast non-NMDA current, stabilizes the alternation pattern versus synchrony. To verify that these effects and their implications on the mechanism of swimming and transition to other types of activity take place in the real preparation, constraints on parameter values have to be specified. A method to estimate synaptic parameters was tested with generated data. It is shown that a global analysis, based on multiple iterations of the optimization process (Foster et al., 1993), gives a better understanding of the parameter subspace describing network activity than a standard fit with a sensitivity analysis for an individual solution.

Late phase bronchial obstruction following nonimmunologic mast cell degranulation

Immunologic degranulation of airway mast cells after antigen inhalation produces early and late airway obstructions in allergic sheep. In this study we determined whether nonimmunologic degranulation of airway mast cells by inhalation of compound 48/80 had similar effects. In five sheep, pulmonary flow resistance (RL), thoracic gas volume (Vtg), and arterial O2 tension (Pao2) were determined prior to and at predetermined times after inhalation of 48/80 aerosol. Immediately after challenge mean specific lung resistance (sRL = RL X Vtg) increased by 259% and mean Pao2 decreased by 29%. All values returned to normal by 3 h. By 5-h postchallenge sRL again increased significantly; this second increase in sRL (92% above base line) was maximal at 7 h and was accompanied by a 17% drop in Pao2. In these same sheep inhalation of Ascaris suum antigen produced comparable early changes in sRL, but the onset of the late response was somewhat delayed and more pronounced. In a second group of sheep (n = 5), pretreatment with the mast cell stabilizer cromolyn sodium prevented both early and late responses by compound 48/80. Pretreatment with the histamine H1-antagonist chlorpheniramine had no significant effect on either response, whereas pretreatment with FPL 55712, an antagonist of slow-reacting substance of anaphylaxis (SRS-A), slightly but not significantly attenuated the early response and completely prevented the late response. We conclude that, like immunologic stimuli, nonimmunologic mast cell degranulation produces early and late bronchial obstructions in allergic sheep; that these responses are mediator dependent; and that while histamine and SRS-A contribute to the early response, it is the early appearance of SRS-A which is an important prerequisite for the late response.

Survival of patients with cancer in a medical critical care unit

The records of 40 patients with cancer and 684 patients without cancer admitted to a medical critical care unit were reviewed for the purpose of comparing survival. Patients with cancer had a higher mortality (55%, 22/40) than the patients without cancer (17%, 118/864). Patients with cancer and respiratory failure had a higher mortality (75%, 18/24) than patients without cancer but with respiratory failure (25%, 66/273) and a higher mortality than patients with cancer but without respiratory failure (25%, 4/16). In patients with cancer, the manifestation of respiratory failure as the adult respiratory distress syndrome (ARDS) was associated with a high mortality (86%, 12/14), which was not statistically higher than in patients with cancer with non-ARDS respiratory failure (60%, 6/10) or in patients without cancer with ARDS (65%, 28/43). Patients with cancer but without respiratory failure had a mortality of 25% (4/16). All eight patients with cancer admitted to the hospital because of life-threatening metabolic disturbances survived. In deciding whether to apply critical care techniques to a patient with cancer, the physician should consider the specific nature of the life-threatening illness.