A Statistical Model for In Vivo Neuronal Dynamics

Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input current to the membrane potential of the neuron. Those types of models have been extensively fitted to in vitro data where the input current is controlled. Those models are however of little use when it comes to characterize intracellular in vivo recordings since the input to the neuron is not known. Here we propose a novel single neuron model that characterizes the statistical properties of in vivo recordings. More specifically, we propose a stochastic process where the subthreshold membrane potential follows a Gaussian process and the spike emission intensity depends nonlinearly on the membrane potential as well as the spiking history. We first show that the model has a rich dynamical repertoire since it can capture arbitrary subthreshold autocovariance functions, firing-rate adaptations as well as arbitrary shapes of the action potential. We then show that this model can be efficiently fitted to data without overfitting. We finally show that this model can be used to characterize and therefore precisely compare various intracellular in vivo recordings from different animals and experimental conditions.     

Glutamate Mediated Astrocytic Filtering of Neuronal Activity

Neuron-astrocyte communication is an important regulatory mechanism in various brain functions but its complexity and role are yet to be fully understood. In particular, the temporal pattern of astrocyte response to neuronal firing has not been fully characterized. Here, we used neuron-astrocyte cultures on multi-electrode arrays coupled to Ca²⁺ imaging and explored the range of neuronal stimulation frequencies while keeping constant the amount of stimulation. Our results reveal that astrocytes specifically respond to the frequency of neuronal stimulation by intracellular Ca²⁺ transients, with a clear onset of astrocytic activation at neuron firing rates around 3-5 Hz. The cell-to-cell heterogeneity of the astrocyte Ca²⁺ response was however large and increasing with stimulation frequency. Astrocytic activation by neurons was abolished with antagonists of type I metabotropic glutamate receptor, validating the glutamate-dependence of this neuron-to-astrocyte pathway. Using a realistic biophysical model of glutamate-based intracellular calcium signaling in astrocytes, we suggest that the stepwise response is due to the supralinear dynamics of intracellular IP₃ and that the heterogeneity of the responses may be due to the heterogeneity of the astrocyte-to-astrocyte couplings via gap junction channels. Therefore our results present astrocyte intracellular Ca²⁺ activity as a nonlinear integrator of glutamate-dependent neuronal activity.     

Mathematical Models for Sleep-Wake Dynamics: Comparison of the Two-Process Model and a Mutual Inhibition Neuronal Model

Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alternative, more recent, model considers the mutual inhibition of sleep promoting neurons and the ascending arousal system regulated by homeostatic and circadian processes. Here we show there are fundamental similarities between these two models. The implications are illustrated with two important sleep-wake phenomena. Firstly, we show that in the two-process model, transitions between different numbers of daily sleep episodes can be classified as grazing bifurcations. This provides the theoretical underpinning for numerical results showing that the sleep patterns of many mammals can be explained by the mutual inhibition model. Secondly, we show that when sleep deprivation disrupts the sleep-wake cycle, ostensibly different measures of sleepiness in the two models are closely related. The demonstration of the mathematical similarities of the two models is valuable because not only does it allow some features of the two-process model to be interpreted physiologically but it also means that knowledge gained from study of the two-process model can be used to inform understanding of the behaviour of the mutual inhibition model. This is important because the mutual inhibition model and its extensions are increasingly being used as a tool to understand a diverse range of sleep-wake phenomena such as the design of optimal shift-patterns, yet the values it uses for parameters associated with the circadian and homeostatic processes are very different from those that have been experimentally measured in the context of the two-process model.     

A Predictive In Vitro Model of the Impact of Drugs with Anticholinergic Properties on Human Neuronal and Astrocytic Systems

The link between off-target anticholinergic effects of medications and acute cognitive impairment in older adults requires urgent investigation. We aimed to determine whether a relevant in vitro model may aid the identification of anticholinergic responses to drugs and the prediction of anticholinergic risk during polypharmacy. In this preliminary study we employed a co-culture of human-derived neurons and astrocytes (NT2.N/A) derived from the NT2 cell line. NT2.N/A cells possess much of the functionality of mature neurons and astrocytes, key cholinergic phenotypic markers and muscarinic acetylcholine receptors (mAChRs). The cholinergic response of NT2 astrocytes to the mAChR agonist oxotremorine was examined using the fluorescent dye fluo-4 to quantitate increases in intracellular calcium [Ca²⁺]i. Inhibition of this response by drugs classified as severe (dicycloverine, amitriptyline), moderate (cyclobenzaprine) and possible (cimetidine) on the Anticholinergic Cognitive Burden (ACB) scale, was examined after exposure to individual and pairs of compounds. Individually, dicycloverine had the most significant effect regarding inhibition of the astrocytic cholinergic response to oxotremorine, followed by amitriptyline then cyclobenzaprine and cimetidine, in agreement with the ACB scale. In combination, dicycloverine with cyclobenzaprine had the most significant effect, followed by dicycloverine with amitriptyline. The order of potency of the drugs in combination frequently disagreed with predicted ACB scores derived from summation of the individual drug scores, suggesting current scales may underestimate the effect of polypharmacy. Overall, this NT2.N/A model may be appropriate for further investigation of adverse anticholinergic effects of multiple medications, in order to inform clinical choices of suitable drug use in the elderly.     

Inducing Plasticity of Astrocytic Receptors by Manipulation of Neuronal Firing Rates

Close to two decades of research has established that astrocytes in situ and in vivo express numerous G protein-coupled receptors (GPCRs) that can be stimulated by neuronally-released transmitter. However, the ability of astrocytic receptors to exhibit plasticity in response to changes in neuronal activity has received little attention. Here we describe a model system that can be used to globally scale up or down astrocytic group I metabotropic glutamate receptors (mGluRs) in acute brain slices. Included are methods on how to prepare parasagittal hippocampal slices, construct chambers suitable for long-term slice incubation, bidirectionally manipulate neuronal action potential frequency, load astrocytes and astrocyte processes with fluorescent Ca²⁺ indicator, and measure changes in astrocytic Gq GPCR activity by recording spontaneous and evoked astrocyte Ca²⁺ events using confocal microscopy. In essence, a “calcium roadmap” is provided for how to measure plasticity of astrocytic Gq GPCRs. Applications of the technique for study of astrocytes are discussed. Having an understanding of how astrocytic receptor signaling is affected by changes in neuronal activity has important implications for both normal synaptic function as well as processes underlying neurological disorders and neurodegenerative disease.     

Monitoring Astrocytic Proteome Dynamics by Cell Type-Specific Protein Labeling

The ability of the nervous system to undergo long-term plasticity is based on changes in cellular and synaptic proteomes. While many studies have explored dynamic alterations in neuronal proteomes during plasticity, there has been less attention paid to the astrocytic counterpart. Indeed, progress in identifying cell type-specific proteomes is limited owing to technical difficulties. Here, we present a cell type-specific metabolic tagging technique for a mammalian coculture model based on the bioorthogonal amino acid azidonorleucine and the mutated Mus musculus methionyl-tRNA synthetase^L274G enabling azidonorleucine introduction into de novo synthesized proteins. Azidonorleucine incorporation resulted in cell type-specific protein labeling and retained neuronal or astrocytic cell viability. Furthermore, we were able to label astrocytic de novo synthesized proteins and identified both Connexin-43 and 60S ribosomal protein L10a upregulated upon treatment with Brain-derived neurotrophic factor in astrocytes of a neuron-glia coculture. Taken together, we demonstrate the successful dissociation of astrocytic from neuronal proteomes by cell type-specific metabolic labeling offering new possibilities for the analyses of cell type-specific proteome dynamics.     

The Role of Astrocytic Glycogen in Supporting the Energetics of Neuronal Activity

Energy homeostasis in the brain is maintained by oxidative metabolism of glucose, primarily to fulfil the energy demand associated with ionic movements in neurons and astrocytes. In this contribution we review the experimental evidence that grounds a specific role of glycogen metabolism in supporting the functional energetic needs of astrocytes during the removal of extracellular potassium. Based on theoretical considerations, we further discuss the hypothesis that the mobilization of glycogen in astrocytes serves the purpose to enhance the availability of glucose for neuronal glycolytic and oxidative metabolism at the onset of stimulation. Finally, we provide an evolutionary perspective for explaining the selection of glycogen as carbohydrate reserve in the energy-sensing machinery of cell metabolism.     

Neurotrophin-Induced Migration and Neuronal Differentiation of Multipotent Astrocytic Stem Cells In Vitro

Hypoxic ischemic encephalopathy (HIE) affects 2–3 per 1000 full-term neonates. Up to 75% of newborns with severe HIE die or have severe neurological handicaps. Stem cell therapy offers the potential to replace HIE-damaged cells and enhances the autoregeneration process. Our laboratory implanted Multipotent Astrocytic Stem Cells (MASCs) into a neonatal rat model of hypoxia-ischemia (HI) and demonstrated that MASCs move to areas of injury in the cortex and hippocampus. However, only a small proportion of the implanted MASCs differentiated into neurons. MASCs injected into control pups did not move into the cortex or differentiate into neurons. We do not know the mechanism by which the MASCs moved from the site of injection to the injured cortex. We found neurotrophins present after the hypoxic-ischemic milieu and hypothesized that neurotrophins could enhance the migration and differentiation of MASCs. Using a Boyden chamber device, we demonstrated that neurotrophins potentiate the in vitro migration of stem cells. NGF, GDNF, BDNF and NT-3 increased stem cell migration when compared to a chemokinesis control. Also, MASCs had increased differentiation toward neuronal phenotypes when these neurotrophins were added to MASC culture tissue. Due to this finding, we believed neurotrophins could guide migration and differentiation of stem cell transplants after brain injury.     

Conformational Dynamics in the Selectivity Filter of KcsA in Response to Potassium Ion Concentration

Conformational change in the selectivity filter of KcsA as a function of ambient potassium concentration is studied with solid-state NMR. This highly conserved region of the protein is known to chelate potassium ions selectively. We report solid-state NMR chemical shift fingerprints of two distinct conformations of the selectivity filter; significant changes are observed in the chemical shifts of key residues in the filter as the potassium ion concentration is changed from 50 mM to 1 μM. Potassium ion titration studies reveal that the site-specific K_d for K⁺ binding at the key pore residue Val76 is on the order of ∼ 7 μM and that a relatively high sample hydration is necessary to observe the low-K⁺ conformer. Simultaneous detection of both conformers at low ambient potassium concentration suggests that the high-K⁺ and low-K⁺ states are in slow exchange on the NMR timescale (k_ex < 500 s^− 1). The slow rate and tight binding for evacuating both inner sites simultaneously differ from prior observations in detergent in solution, but agree well with measurements by electrophysiology and appear to result from our use of a hydrated bilayer environment. These observations strongly support a common assumption that the low-K⁺ state is not involved in ion transmission, and that during transmission one of the two inner sites is always occupied. On the other hand, these kinetic and thermodynamic characteristics of the evacuation of the inner sites certainly could be compatible with participation in a control mechanism at low ion concentration such as C-type inactivation, a process that is coupled to activation and involves closing of the outer mouth of the channel.     

Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

We describe and analyze a model for a stochastic pulse-coupled neuronal network with many sources of randomness: random external input, potential synaptic failure, and random connectivity topologies. We show that different classes of network topologies give rise to qualitatively different types of synchrony: uniform (Erdős–Rényi) and “small-world” networks give rise to synchronization phenomena similar to that in “all-to-all” networks (in which there is a sharp onset of synchrony as coupling is increased); in contrast, in “scale-free” networks the dependence of synchrony on coupling strength is smoother. Moreover, we show that in the uniform and small-world cases, the fine details of the network are not important in determining the synchronization properties; this depends only on the mean connectivity. In contrast, for scale-free networks, the dynamics are significantly affected by the fine details of the network; in particular, they are significantly affected by the local neighborhoods of the “hubs” in the network.     

Cross-Correlation Functions for a Neuronal Model

Cross-correlation functions, R_XY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, R_XY(t,τ) = f_U [θ-h(τ), t + τ] {h′(τ) + E_U [u′(t + τ)]} for positive values of this quantity, where f_U(u,t) is the probability density function of U(t) and E_U [u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in R_XY(t,τ) for a neuron subjected only to excitation. (3) For large τ, R_XY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) R_XY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time.     

Activation,Permeability, and Inhibition of Astrocytic and Neuronal Large Pore (Hemi)channels

Astrocytes and neurons express several large pore (hemi)channels that may open in response to various stimuli, allowing fluorescent dyes, ions, and cytoplasmic molecules such as ATP and glutamate to permeate. Several of these large pore (hemi)channels have similar characteristics with regard to activation, permeability, and inhibitor sensitivity. Consequently, their behaviors and roles in astrocytic and neuronal (patho)physiology remain undefined. We took advantage of the Xenopus laevis expression system to determine the individual characteristics of several large pore channels in isolation. Expression of connexins Cx26, Cx30, Cx36, or Cx43, the pannexins Px1 or Px2, or the purinergic receptor P2X₇ yielded functional (hemi)channels with isoform-specific characteristics. Connexin hemichannels had distinct sensitivity to alterations of extracellular Ca²⁺ and their permeability to dyes and small atomic ions (conductance) were not proportional. Px1 and Px2 exhibited conductance at positive membrane potentials, but only Px1 displayed detectable fluorescent dye uptake. P2X₇, in the absence of Px1, was permeable to fluorescent dyes in an agonist-dependent manner. The large pore channels displayed overlapping sensitivity to the inhibitors Brilliant Blue, gadolinium, and carbenoxolone. These results demonstrated isoform-specific characteristics among the large pore membrane channels; an open (hemi)channel is not a nonselective channel. With these isoform-specific properties in mind, we characterized the divalent cation-sensitive permeation pathway in primary cultured astrocytes. We observed no activation of membrane conductance or Cx43-mediated dye uptake in astrocytes nor in Cx43-expressing C6 cells. Our data underscore that although Cx43-mediated transport is observed in overexpressing cell systems, such transport may not be detectable in native cells under comparable experimental conditions.     

Mitochondrial Dynamics Impairment in Dexamethasone-Treated Neuronal Cells

Neurochemical Research - Dexamethasone is an approved steroid for clinical use to activate or suppress cytokines, chemokines, inflammatory enzymes and adhesion molecules. It enters the brain,...     

Bidirectional Scaling of Astrocytic Metabotropic Glutamate Receptor Signaling following Long-Term Changes in Neuronal Firing Rates

Very little is known about the ability of astrocytic receptors to exhibit plasticity as a result of changes in neuronal activity. Here we provide evidence for bidirectional scaling of astrocytic group I metabotropic glutamate receptor signaling in acute mouse hippocampal slices following long-term changes in neuronal firing rates. Plasticity of astrocytic mGluRs was measured by recording spontaneous and evoked Ca²⁺ elevations in both astrocytic somata and processes. An exogenous astrocytic Gq G protein-coupled receptor was resistant to scaling, suggesting that the alterations in astrocyte Ca²⁺ signaling result from changes in activity of the surface mGluRs rather than a change in intracellular G protein signaling molecules. These findings suggest that astrocytes actively detect shifts in neuronal firing rates and adjust their receptor signaling accordingly. This type of long-term plasticity in astrocytes resembles neuronal homeostatic plasticity and might be important to ensure an optimal or expected level of input from neurons.     

Astrocytic Ca2+ Waves Guide CNS Growth Cones to Remote Regions of Neuronal Activity

Activity plays a critical role in network formation during developmental, experience-dependent, and injury related remodeling. Here we report a mechanism by which axon trajectory can be altered in response to remote neuronal activity. Using photoconductive stimulation to trigger high frequency action potentials in rat hippocampal neurons in vitro, we find that activity functions as an attractive cue for growth cones in the local environment. The underlying guidance mechanism involves astrocyte Ca²⁺ waves, as the connexin-43 antagonist carbenoxolone abolishes the attraction when activity is initiated at a distance greater than 120 µm. The asymmetric growth cone filopodia extension that precedes turning can be blocked with CNQX (10 µM), but not with the ATP and adenosine receptor antagonists suramin (100 µM) and alloxazine (4 µM), suggesting non-NMDA glutamate receptors on the growth cone mediate the interaction with astrocytes. These results define a potential long-range signalling pathway for activity-dependent axon guidance in which growth cones turn towards directional, temporally coordinated astrocyte Ca²⁺ waves that are triggered by neuronal activity. To assess the viability of the guidance effect in an injury paradigm, we performed the assay in the presence of conditioned media from lipopolysaccharide (LPS) activated purified microglial cultures, as well as directly activating the glia present in our co-cultures. Growth cone attraction was not inhibited under these conditions, suggesting this mechanism could be used to guide regeneration following axonal injury.     

Acidosis,Acid-Sensing Ion Channels,and Neuronal Cell Death

Acidosis is a common feature of many neuronal diseases and often accompanied with adverse consequences such as pain and neuronal injury. Before the discovery of acid-sensing ion channels (ASICs), protons were usually considered as a modulator of other ion channels, such as voltage-gated calcium channels, N-methyl-d-aspartate, and γ-amino butyric acid(A) receptor channels. Accordingly, the functional effects of acidosis were considered as consequences of modulations of these channels. Since the first cloning of ASICs in 1997, the conventional view on acidosis-mediated pain and cell injury has been dramatically changed. To date, ASICs, which are directly activated by extracellular protons, are shown to mediate most of the acidosis-associated physiological and pathological functions. For example, ASIC1a channels are reported to mediate acidosis-induced ischemic neuronal death. In this article, we will review the possible mechanisms that underlie ASIC1a channel-mediated neuronal death and discuss ASIC1a channel modulators involved in this process.     

Dynamics from Seconds to Hours in Hodgkin-Huxley Model with Time-Dependent Ion Concentrations and Buffer Reservoirs

The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.