A Statistical View on Calcium Oscillations.

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

N10 -carbonyl-substituted phenothiazines inhibiting lipid peroxidation and associated nitric oxide consumption powerfully protect brain tissue against oxidative stress.

During some investigations into the mechanism of nitric oxide consumption by brain preparations, several potent inhibitors of this process were identified. Subsequent tests revealed the compounds act by inhibiting lipid peroxidation, a trigger for a form of regulated cell death known as ferroptosis. A quantitative structure-activity study together with XED (eXtended Electron Distributions) field analysis allowed a qualitative understanding of the structure-activity relationships. A representative compound N-(3,5-dimethyl-4H-1,2,4-triazol-4-yl)-10H-phenothiazine-10-carboxamide (DT-PTZ-C) was able to inhibit completely oxidative damage brought about by two different procedures in organotypic hippocampal slice cultures, displaying a 30- to 100-fold higher potency than the standard vitamin E analogue, Trolox or edaravone. The compounds are novel, small, drug-like molecules of potential therapeutic use in neurodegenerative disorders and other conditions associated with oxidative stress.

Correction: Distribution of vesicle pools in cerebellar parallel fibre terminals after depression of ectopic transmission.

[This corrects the article DOI: 10.1371/journal.pone.0200937.].

Distribution of vesicle pools in cerebellar parallel fibre terminals after depression of ectopic transmission.

At parallel fibre terminals in the cerebellar cortex, glutamate released outside of the active zone can activate AMPA receptors on juxtaposed Bergmann glial cell processes. This process is termed "ectopic" release, and allows for directed transmission to astroglial cells that is functionally independent of synaptic transmission to postsynaptic Purkinje neurons. The location of ectopic sites in presynaptic terminals is uncertain. Functional evidence suggests that stimulation of parallel fibres at 1 Hz exhausts ectopic transmission due to a failure to rapidly recycle vesicles to the ectopic pool, and so would predict a loss of vesicles in the near vicinity of extrasynaptic glial processes. In this study we used this stimulation protocol to investigate whether the distribution of vesicles within the presynaptic terminal is altered after suppression of ectopic release. Stimulation at 1 Hz had only a minor impact on the distribution of vesicles in presynaptic terminals when analysed with electron microscopy. Vesicle number and terminal size were unaffected by 1 Hz stimulation, but the relative abundance of vesicles in close proximity to the active zone was marginally reduced. In contrast, the fraction of vesicles facing glial membranes was unchanged after suppression of ectopic transmission. 1 Hz stimulation also resulted in a small but statistically-significant increase in the distance between glial membrane and presynaptic terminal, suggesting withdrawal of glial membranes from synapses is detectable in ultrastructural anatomy within minutes. These results raise doubts about the location of ectopic release sites, but indicate that neuron-glial association varies on a dynamic time scale.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations.

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimulus time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environment.

Probabilistic encoding of stimulus strength in astrocyte global calcium signals.

Astrocyte calcium signals can range in size from subcellular microdomains to waves that spread through the whole cell (and into connected cells). The differential roles of such local or global calcium signaling are under intense investigation, but the mechanisms by which local signals evolve into global signals in astrocytes are not well understood, nor are the computational rules by which physiological stimuli are transduced into a global signal. To investigate these questions, we transiently applied receptor agonists linked to calcium signaling to primary cultures of cerebellar astrocytes. Astrocytes repetitively tested with the same stimulus responded with global signals intermittently, indicating that each stimulus had a defined probability for triggering a response. The response probability varied between agonists, increased with agonist concentration, and could be positively and negatively modulated by crosstalk with other signaling pathways. To better understand the processes determining the evolution of a global signal, we recorded subcellular calcium "puffs" throughout the whole cell during stimulation. The key requirement for puffs to trigger a global calcium wave following receptor activation appeared to be the synchronous release of calcium from three or more sites, rather than an increasing calcium load accumulating in the cytosol due to increased puff size, amplitude, or frequency. These results suggest that the concentration of transient stimuli will be encoded into a probability of generating a global calcium response, determined by the likelihood of synchronous release from multiple subcellular sites.

Plasticity of Neuron-Glial Transmission: Equipping Glia for Long-Term Integration of Network Activity.

The capacity of synaptic networks to express activity-dependent changes in strength and connectivity is essential for learning and memory processes. In recent years, glial cells (most notably astrocytes) have been recognized as active participants in the modulation of synaptic transmission and synaptic plasticity, implicating these electrically nonexcitable cells in information processing in the brain. While the concept of bidirectional communication between neurons and glia and the mechanisms by which gliotransmission can modulate neuronal function are well established, less attention has been focussed on the computational potential of neuron-glial transmission itself. In particular, whether neuron-glial transmission is itself subject to activity-dependent plasticity and what the computational properties of such plasticity might be has not been explored in detail. In this review, we summarize current examples of plasticity in neuron-glial transmission, in many brain regions and neurotransmitter pathways. We argue that induction of glial plasticity typically requires repetitive neuronal firing over long time periods (minutes-hours) rather than the short-lived, stereotyped trigger typical of canonical long-term potentiation. We speculate that this equips glia with a mechanism for monitoring average firing rates in the synaptic network, which is suited to the longer term roles proposed for astrocytes in neurophysiology.

Localization of Presynaptic Plasticity Mechanisms Enables Functional Independence of Synaptic and Ectopic Transmission in the Cerebellum.

In the cerebellar molecular layer parallel fibre terminals release glutamate from both the active zone and from extrasynaptic "ectopic" sites. Ectopic release mediates transmission to the Bergmann glia that ensheathe the synapse, activating Ca(2+)-permeable AMPA receptors and glutamate transporters. Parallel fibre terminals exhibit several forms of presynaptic plasticity, including cAMP-dependent long-term potentiation and endocannabinoid-dependent long-term depression, but it is not known whether these presynaptic forms of long-term plasticity also influence ectopic transmission to Bergmann glia. Stimulation of parallel fibre inputs at 16 Hz evoked LTP of synaptic transmission, but LTD of ectopic transmission. Pharmacological activation of adenylyl cyclase by forskolin caused LTP at Purkinje neurons, but only transient potentiation at Bergmann glia, reinforcing the concept that ectopic sites lack the capacity to express sustained cAMP-dependent potentiation. Activation of mGluR1 caused depression of synaptic transmission via retrograde endocannabinoid signalling but had no significant effect at ectopic sites. In contrast, activation of NMDA receptors suppressed both synaptic and ectopic transmission. The results suggest that the signalling mechanisms for presynaptic LTP and retrograde depression by endocannabinoids are restricted to the active zone at parallel fibre synapses, allowing independent modulation of synaptic transmission to Purkinje neurons and ectopic transmission to Bergmann glia.

Caffeine Modulates Vesicle Release and Recovery at Cerebellar Parallel Fibre Terminals, Independently of Calcium and Cyclic AMP Signalling.

BACKGROUND: Cerebellar parallel fibres release glutamate at both the synaptic active zone and at extrasynaptic sites-a process known as ectopic release. These sites exhibit different short-term and long-term plasticity, the basis of which is incompletely understood but depends on the efficiency of vesicle release and recycling. To investigate whether release of calcium from internal stores contributes to these differences in plasticity, we tested the effects of the ryanodine receptor agonist caffeine on both synaptic and ectopic transmission. METHODS: Whole cell patch clamp recordings from Purkinje neurons and Bergmann glia were carried out in transverse cerebellar slices from juvenile (P16-20) Wistar rats. KEY RESULTS: Caffeine caused complex changes in transmission at both synaptic and ectopic sites. The amplitude of postsynaptic currents in Purkinje neurons and extrasynaptic currents in Bergmann glia were increased 2-fold and 4-fold respectively, but paired pulse ratio was substantially reduced, reversing the short-term facilitation observed under control conditions. Caffeine treatment also caused synaptic sites to depress during 1 Hz stimulation, consistent with inhibition of the usual mechanisms for replenishing vesicles at the active zone. Unexpectedly, pharmacological intervention at known targets for caffeine--intracellular calcium release, and cAMP signalling--had no impact on these effects. CONCLUSIONS: We conclude that caffeine increases release probability and inhibits vesicle recovery at parallel fibre synapses, independently of known pharmacological targets. This complex effect would lead to potentiation of transmission at fibres firing at low frequencies, but depression of transmission at high frequency connections.

Stimulus discrimination in cerebellar Purkinje neurons.

Cerebellar Purkinje neurons fire spontaneously in the absence of synaptic input. Overlaid on this intrinsic activity, excitatory input from parallel fibres can add simple spikes to the output train, whereas inhibitory input from interneurons can introduce pauses. These and other influences lead to an irregular spike train output in Purkinje neurons in vitro and in vivo, supplying a variable inhibitory drive to deep cerebellar nuclear neurons. From a computational perspective, this variability raises some questions, as individual spikes induced by excitatory inputs are indistinguishable from intrinsic firing activity. Although bursts of high-frequency excitatory input could be discriminated unambiguously from background activity, granule neurons are known to fire in vivo over a wide range of frequencies. This would mean that much of the sensory information relayed through the cerebellar cortex would be lost within the random variation in background activity. We speculated that alternative mechanisms for signal discrimination may exist, and sought to identify characteristic motifs within the sequence of spikes that followed stimulation events. We found that under certain conditions, parallel fibre stimulation could reliably add a "couplet" of spikes with an unusually short interspike interval to the output train. Therefore, despite representing a small fraction of the total number of spikes, these signals can be reliably discriminated from background firing on a moment-to-moment basis, and could result in a differential downstream response.

Ectopic release of glutamate contributes to spillover at parallel fibre synapses in the cerebellum.

In the rat cerebellar molecular layer, spillover of glutamate between parallel fibre synapses can lead to activation of perisynaptic receptors that mediate short- and long-term plasticity. This effect is greatest when clusters of fibres are stimulated at high frequencies, suggesting that glutamate clearance mechanisms must be overwhelmed before spillover can occur. However, parallel fibres can also release transmitter directly into the extracellular space, from 'ectopic' release sites. Ectopic transmission activates AMPA receptors on the Bergmann glial cell processes that envelop parallel fibre synapses, but the possible contribution of this extrasynaptic release to intersynaptic communication has not been explored. We exploited long-term depression of ectopic transmission, and selective pharmacology, to investigate the impact of these release sites on the time course of Purkinje neuron excitatory postsynaptic currents (EPSCs). Depletion of ectopic release pools by activity-dependent long-term depression decreased EPSC decay time, revealing a 'late' current that is present when fibres are stimulated at low frequencies. This effect was enhanced when glutamate transporters were inhibited, and reduced when extracellular diffusion was impeded. Blockade of N-type Ca(2+) channels inhibited ectopic transmission to Bergmann glia and decreased EPSC decay time. Similarly, perfusion of the Ca(2+) chelator EGTA-AM into the slice progressively eliminated ectopic transmission to glia and decreased EPSC decay time with closely similar time courses. Collectively, this evidence suggests that ectopically released glutamate contributes to spillover transmission, and that ectopic release therefore degrades the spatial precision of synapses that fire infrequently, and may make them more prone to exhibit plasticity.

High-throughput analysis of calcium signalling kinetics in astrocytes stimulated with different neurotransmitters.

Astrocytes express a wide range of receptors for neurotransmitters and hormones that are coupled to increases in intracellular Ca(2+) concentration, enabling them to detect activity in both neuronal and vascular networks. There is increasing evidence that astrocytes are able to discriminate between different Ca(2+)-linked stimuli, as the efficiency of some Ca(2+) dependent processes--notably release of gliotransmitters--depends on the stimulus that initiates the Ca(2+) signal. The spatiotemporal complexity of Ca(2+) signals is substantial, and we here tested the hypothesis that variation in the kinetics of Ca(2+) responses could offer a means of selectively engaging downstream targets, if agonists exhibited a "signature shape" in evoked Ca(2+) response. To test this, astrocytes were exposed to three different receptor agonists (ATP, glutamate and histamine) and the resultant Ca(2+) signals were analysed for systematic differences in kinetics that depended on the initiating stimulus. We found substantial heterogeneity between cells in the time course of Ca(2+) responses, but the variation did not correlate with the type or concentration of the stimulus. Using a simple metric to quantify the extent of difference between populations, it was found that the variation between agonists was insufficient to allow signal discrimination. We conclude that the time course of global intracellular Ca(2+) signals does not offer the cells a means for distinguishing between different neurotransmitters.

Ectopic release sites lack fast vesicle recycling mechanisms, causing long-term depression of neuron-glial transmission in rat cerebellum.

Classical synaptic transmission occurs at active zones within the synaptic cleft, but increasing evidence suggests that vesicle fusion can also occur outside of these zones, releasing transmitter directly into the extrasynaptic space. The role of such "ectopic" release is unclear, but in the cerebellar molecular layer it is thought to guide the processes of Bergmann glia toward synaptic terminals through activation of glial α-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate (AMPA) receptors. Once surrounding the terminal, the glial process is presumed to limit spillover of neurotransmitter between synapses by rapid uptake of glutamate. We have previously reported that this route for neuron-glial transmission exhibits long-term depression following repetitive stimulation at frequencies in the 0.1-1 Hz range, in ex vivo slices from rat cerebellum. Here, we present evidence that LTD arises because ectopic sites lack the fast recycling mechanisms that operate at the active zone. Consequently, ectopic vesicles constitute an exhaustible pool that is depleted at normal synaptic firing rates and only recovers slowly. This effect is cumulative, meaning that the strength of ectopic transmission provides a read-out of the average frequency of presynaptic firing over several minutes. Glial processes are therefore likely to interact most closely with terminals that fire infrequently; conditions that may promote elimination of, rather than support for, the connection.

Control of cerebellar long-term potentiation by P-Rex-family guanine-nucleotide exchange factors and phosphoinositide 3-kinase.

BACKGROUND: Long-term potentiation (LTP) at the parallel fibre-Purkinje cell synapse in the cerebellum is a recently described and poorly characterized form of synaptic plasticity. The induction mechanism for LTP at this synapse is considered reciprocal to "classical" LTP at hippocampal CA1 pyramidal neurons: kinases promote increased trafficking of AMPA receptors into the postsynaptic density in the hippocampus, whereas phosphatases decrease internalization of AMPA receptors in the cerebellum. In the hippocampus, LTP occurs in overlapping phases, with the transition from early to late phases requiring the consolidation of initial induction processes by structural re-arrangements at the synapse. Many signalling pathways have been implicated in this process, including PI3 kinases and Rho GTPases. PRINCIPAL FINDINGS: We hypothesized that analogous phases are present in cerebellar LTP, and took as the starting point for investigation our recent discovery that P-Rex--a Rac guanine nucleotide exchange factor which is activated by PtdIns(3,4,5)P(3)--is highly expressed in mouse cerebellar Purkinje neurons and plays a role in motor coordination. We found that LTP evoked at parallel fibre synapses by 1 Hz stimulation or by NO donors was not sustained beyond 30 min when P-Rex was eliminated or Rac inhibited, suggesting that cerebellar LTP exhibits a late phase analogous to hippocampal LTP. In contrast, inhibition of PI3 kinase activity eliminated LTP at the induction stage. CONCLUSIONS: Our data suggest that a PI3K/P-Rex/Rac pathway is required for late phase LTP in the mouse cerebellum, and that other PI3K targets, which remain to be discovered, control LTP induction.

A real-time fluorescent assay of the purified nitric oxide receptor, guanylyl cyclase.

Nitric oxide (NO) mediates intercellular signaling through activation of its receptor, soluble guanylyl cyclase (sGC), leading to elevation of intracellular guanosine 3',5'-cyclic monophosphate (cGMP) levels. Through this signal transduction pathway, NO regulates a diverse range of physiological effects, from vasodilatation and platelet disaggregation to synaptic plasticity. Measurement of sGC activity has traditionally been carried out using end-point assays of cGMP accumulation or by transfection of cells with "detector" proteins such as fluorescent proteins coupled to cGMP binding domains or cyclic nucleotide gated channels. Here we report a simpler approach: the use of a fluorescently labeled substrate analog, mant-GTP (2'-O-(N-methylanthraniloyl) guanosine 5'-triphosphate), which gives an increase in emission intensity after enzymatic cyclization to mant-cGMP. Activation of purified recombinant sGC by NO led to a rapid rise in fluorescence intensity within seconds, reaching a maximal 1.6- to 1.8-fold increase above basal levels. The sGC inhibitor, ODQ (1H-[1,2,4]oxadiazolo[4,3-a]quinoxalin-1-one), eliminated the fluorescence increase due to NO, and the synergistic activator of sGC, BAY 41-2272 (3-(4-amino-5-cyclopropylpyrimidin-2-yl)-1-(2-fluorobenzyl)-1H-pyrazolo[3,4-b]pyridine), increased the rate at which the maximal fluorescence increase was attained. High-performance liquid chromatography (HPLC) confirmed the formation of mant-cGMP product. This real-time assay allows the progress of purified sGC activation to be quantified precisely and, with refinement, could be optimized for use in a cellular environment.

Depression of parallel and climbing fiber transmission to Bergmann glia is input specific and correlates with increased precision of synaptic transmission.

In the cerebellar cortex, Bergmann glia enclose the synapses of both parallel and climbing fiber inputs to the Purkinje neuron. The glia express Ca(2+)-permeable AMPA receptors, and the GLAST and GLT-1 classes of glutamate transporter, which are activated by glutamate released during synaptic transmission. We have previously reported that parallel fiber to Bergmann glial transmission in rat cerebellar slices exhibits a form of frequency-dependent plasticity, namely long-term depression, following repetitive stimulation at 0.1-1 Hz. Here, we report that this form of plasticity is also present at the climbing fiber input, that climbing and parallel fibers can be depressed independently, that discrete parallel fiber inputs can also be depressed independently, and that depression is maintained when a distributed array of parallel fibers are stimulated (in contrast to several forms of synaptic plasticity at the Purkinje neuron). Depression of glutamate transporter currents does not correlate with a decrease in the stringency with which Purkinje neuron synapses are isolated. Rather, postsynaptic currents in Purkinje neurons decay more rapidly and perisynaptic metabotropic glutamate receptors are activated less effectively after stimulation at 0.2 and 1 Hz, suggesting that depression arises from a decrease in extrasynaptic glutamate concentration and not from impairment of glutamate clearance in and around the synapse. These results indicate that neuron-glial plasticity is activity dependent, input specific and does not require spillover between adjacent synapses to manifest. They also argue against a withdrawal of the glial sheath from synaptic regions as the putative mechanism of plasticity.

Calcium oscillations.

Changes in cellular Ca2+ concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Ca2+ can also trigger cell death through both apoptosis and necrosis, and so the regulation of cellular Ca2+ concentration must be tightly controlled through the concerted action of pumps, channels and buffers that transport Ca2+ into and out of the cell cytoplasm. A hallmark of cellular Ca2+ signalling is its spatiotemporal complexity: stimulation of cells by a hormone or neurotransmitter leads to oscillations in cytoplasmic Ca2+ concentration that can vary markedly in time course, amplitude, frequency, and spatial range. In this chapter we review some of the biological roles of Ca2+, the experimental characterisation of complex dynamic changes in Ca2+ concentration, and attempts to explain this complexity using computational models. We consider the 'toolkit' of cellular proteins which influence Ca2+ concentrarion, describe mechanistic models of key elements of the toolkit, and fit these into the framework of whole cell models of Ca2+ oscillations and waves. Finally, we will touch on recent efforts to use stochastic modelling to elucidate elementary Ca2+ signal events, and how these may evolve into global signals.

Presynaptic modulation of parallel fibre signalling to Bergmann glia.

Transmission at the parallel fibre-Purkinje neurone synapse of the cerebellum can be depressed by a number of presynaptic receptors: endocannabinoid (CB1), metabotropic glutamate (mGluR4), adenosine (A1) and GABA (GABA(B)), which have been implicated in both short- and long-term synaptic plasticity. Stimulation of parallel fibres also activates glutamate receptors and transporters on the Bergmann glial cell that forms a sheath around the synapse. The resulting glial extrasynaptic currents (ESC) exhibit short- and long-term plasticity, which differs from the plasticity of adjacent synapses. This functional independence could arise from differential modulation of presynaptic release sites targeted to synapses or glia, but the sensitivity of glial ESC to these inhibitory pathways is unknown. Here I show that all four presynaptic receptors depress parallel fibre-Bergmann glial cell signalling with similar potency to synaptic transmission. Depression of glial ESC is accompanied by a decrease in paired pulse ratio. However, application of receptor antagonists had no effect on ESC amplitude, indicating that tonic activation of these pathways does not occur, and antagonists failed to block the activity-dependent depression of glial ESC observed during tetanic or low frequency stimulation. These data suggest that modulation of presynaptic glutamate release does not underlie glial plasticity.

Interactions between Purkinje neurones and Bergmann glia.

Throughout the development of the cerebellar cortex, Purkinje neurones interact closely with Bergmann glial cells, a specialized form of astrocyte. This review summarizes the intimate developmental, anatomical and functional relationships between these two cell types, with particular emphasis on recent discoveries regarding glutamate release from climbing and parallel fibres as a pathway for signalling synaptic activity to Bergmann glia.