No Evidence of Progressive Proinflammatory Cytokine Storm in Brain-dead Organ Donors-A Time-course Analysis Using Clinical Samples.

BACKGROUND: Solid organ transplantation is a cost-effective treatment for end-stage organ failure. Organ donation after brain death is an important source of transplanted organs. Data are limited on the effects of brain injury or donor management on grafts. The consensus view has been that brain death creates a progressively proinflammatory environment. We aimed to investigate time-course changes across a range of cytokines in a donation after brain death cohort of donors who died of intracranial hemorrhage without any other systemic source of inflammation. METHODS: A donor cohort was defined using the UK Quality in Organ Donation biobank. Serum levels of proteins involved in proinflammatory and brain injury pathways (tumor necrosis factor-alpha, interleukin-6, complement C5a, neuron-specific enolase, and glial fibrillary acidic protein) were measured from admission to organ recovery. Moving median analysis was used to combine donor trajectories and delineate a time-course. RESULTS: A cohort of 27 donors with brain death duration between 10 and 30 h was created, with 24 donors contributing to the time-course analysis. We observed no increase in tumor necrosis factor-alpha or interleukin-6 throughout the donor management period. Neuronal injury marker and complement C5a remain high from admission to organ recovery, whereas glial fibrillary acidic protein rises around the confirmation of brain death. CONCLUSIONS: We found no evidence of a progressive rise of proinflammatory mediators with prolonged duration of brain death, questioning the hypothesis of a progressively proinflammatory environment. Furthermore, the proposed approach allows us to study chronological changes and identify biomarkers or target pathways when logistical or ethical considerations limit sample availability.

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.

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.

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.

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.

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.

Large conductance Ca²âº-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.

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+ channels (BK) 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 adrenocorticotrophin 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 modeling to investigate whether CRH and AVP promote distinct patterns of electrical excitability and to interrogate the role of large conductance calcium- and voltage-activated (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. This article is protected by copyright. All rights reserved.

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.

Interpreting frequency responses to dose-conserved pulsatile input signals in simple cell signaling motifs.

Many hormones are released in pulsatile patterns. This pattern can be modified, for instance by changing pulse frequency, to encode relevant physiological information. Often other properties of the pulse pattern will also change with frequency. How do signaling pathways of cells targeted by these hormones respond to different input patterns? In this study, we examine how a given dose of hormone can induce different outputs from the target system, depending on how this dose is distributed in time. We use simple mathematical models of feedforward signaling motifs to understand how the properties of the target system give rise to preferences in input pulse pattern. We frame these problems in terms of frequency responses to pulsatile inputs, where the amplitude or duration of the pulses is varied along with frequency to conserve input dose. We find that the form of the nonlinearity in the steady state input-output function of the system predicts the optimal input pattern. It does so by selecting an optimal input signal amplitude. Our results predict the behavior of common signaling motifs such as receptor binding with dimerization, and protein phosphorylation. The findings have implications for experiments aimed at studying the frequency response to pulsatile inputs, as well as for understanding how pulsatile patterns drive biological responses via feedforward signaling pathways.

A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells.

The electrical activity of endocrine pituitary cells is mediated by a plethora of ionic currents and establishing the role of a single channel type is difficult. Experimental observations have shown however that fast-activating voltage- and calcium-dependent potassium (BK) current tends to promote bursting in pituitary cells. This burst promoting effect requires fast activation of the BK current, otherwise it is inhibitory to bursting. In this work, we analyze a pituitary cell model in order to answer the question of why the BK activation must be fast to promote bursting. We also examine how the interplay between the activation rate and conductance of the BK current shapes the bursting activity. We use the multiple timescale structure of the model to our advantage and employ geometric singular perturbation theory to demonstrate the origin of the bursting behaviour. In particular, we show that the bursting can arise from either canard dynamics or slow passage through a dynamic Hopf bifurcation. We then compare our theoretical predictions with experimental data using the dynamic clamp technique and find that the data is consistent with a burst mechanism due to a slow passage through a Hopf.

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.

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

The electrical activity pattern of endocrine pituitary cells regulates their basal secretion level. Rat somatotrophs and lactotrophs exhibit spontaneous bursting and have high basal levels of hormone secretion, while gonadotrophs exhibit spontaneous spiking and have low basal hormone secretion. It has been proposed that the difference in electrical activity between bursting somatotrophs and spiking gonadotrophs is due to the presence of large conductance potassium (BK) channels on somatotrophs but not on gonadotrophs. This is one example where the role of an ion channel type may be clearly established. We demonstrate here that BK channels indeed promote bursting activity in pituitary cells. Blocking BK channels in bursting lacto-somatotroph GH4C1 cells changes their firing activity to spiking, while further adding an artificial BK conductance via dynamic clamp restores bursting. Importantly, this burst-promoting effect requires a relatively fast BK activation/deactivation, as predicted by computational models. We also show that adding a fast-activating BK conductance to spiking gonadotrophs converts the activity of these cells to bursting. Together, our results suggest that differences in BK channel expression may underlie the differences in electrical activity and basal hormone secretion levels among pituitary cell types and that the rapid rate of BK channel activation is key to its role in burst promotion.