Supralinear Ca2+ signaling by cooperative and mobile Ca2+ buffering in Purkinje neurons

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells

Calcium (Ca²⁺) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP₃)-induced Ca²⁺ release. These Ca²⁺ transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca²⁺, requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca²⁺ transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca²⁺ transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca²⁺ transients in different dynamical situations. We test two different models of the IP₃ receptor (IP₃R). The model with nonlinear concentration response of binding of activating Ca²⁺ reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca²⁺-dependent inhibition of the IP₃R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca²⁺ and IP₃ production sensitizing IP₃R for Ca²⁺-induced Ca²⁺ release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca²⁺ transients. Finally, we propose possible ways of recovering Ca²⁺ transients under ataxia.

Useful Caged Compounds for Cell Physiology

Light has been instrumental in the study of living cells since its use helped in their discovery in the late 17th century. Further, combining chemical technology with light microscopy was an essential part of the Nobel Prize for Physiology in 1906. Such landmark scientific findings involved passive observation of cells. However, over the past 50 years, a "second use" of light has emerged in cell physiology, namely one of rational control. The seminal method for this emerged in late 1970s with the invention of caged compounds. This was the point when "caged compounds" were defined as optical probes in which the active functionality of a physiological signaling molecule was blocked with a photochemical protecting group. Caged compounds are analogous to prodrugs; in both, the activity of the effector is latent. However, caged compounds, unlike prodrugs, use a trigger that confers the power of full temporal and spatial manipulation of the effects of release of its latent biological cargo. Light is distinct because it is bio-orthogonal, passes through living tissue (even into the cell interior), and initiates rapid release of the "caged" biomolecule. Further, because light can be directed to broad areas or focused to small points, caged compounds offer an array of timing scenarios for physiologists to dissect virtually any type of cellular process.The collaborative interaction between chemists and physiologists plays a fundamental role in the development of caged compounds. First, the physiologists must define the problem to be addressed; then, with the help of chemists, decide if a caged compound would be useful. For this, structure-activity relationships of the potential optical probe and receptor must be determined. If rational targets seem feasible, synthetic organic chemistry is used to make the caged compound. The crucial property of prephotolysis bio-inertness relies on physiological or biochemical assays. Second, detailed optical characterization of the caged compound requires the skill of photochemists because the rate and efficiency of uncaging are also crucial properties for a useful caged compound. Often, these studies reveal limitations in the caged compound which has been developed; thus, chemists and physiologists use their abilities for iterative development of even more powerful optical probes. A similar dynamic will be familiar to scientists in the pharmaceutical industry. Therefore, caged compound development provides an excellent training framework for (young) chemists both intellectually and professionally. In this Account, I draw on my long experience in the field of making useful caged compounds for cell physiology by showing how each probe I have developed has been defined by an important physiological problem. Fundamental to this process has been my initial training by the pioneers in aromatic photochemistry, Derek Bryce-Smith and Andrew Gilbert. I discuss making a range of "caged calcium" probes, ones which went on to be the most widely used of all caged compounds. Then, I describe the development of caged neurotransmitters for two-photon uncaging microscopy. Finally, I survey recent work on making new photochemical protecting groups for wavelength orthogonal, two-color, and ultraefficient two-photon uncaging.

Is Purkinje Neuron Hyperpolarisation Important for Cerebellar Synaptic Plasticity? A Retrospective and Prospective Analysis

Two recent studies have demonstrated that the dendritic Ca²⁺ signal associated with a climbing fibre (CF) input to the cerebellar Purkinje neuron (PN) depends on the membrane potential (V_m). Specifically, when the cell is hyperpolarised, this signal is mediated by T-type voltage-gated Ca²⁺ channels; in contrast, when the cell is firing, the CF-PN signal is mediated by P/Q-type voltage-gated Ca²⁺ channels. When the CF input is paired with parallel fibre (PF) activity, the signal is locally amplified at the sites of PF-activated synapses according to the V_m at the time of the CF input, suggesting that the standing V_m is a critical parameter for the induction of PF synaptic plasticity. In this review, I analyse how the V_m can potentially play a role in cerebellar learning focussing, in particular, on the hyperpolarised state that appears to occur episodically, since PNs are mostly firing under physiological conditions. By revisiting the recent literature reporting in vivo recordings and synaptic plasticity studies, I speculate on how a putative role of the PN V_m can provide an interpretation for the results of these studies.

The Origin of Physiological Local mGluR1 Supralinear Ca2+ Signals in Cerebellar Purkinje Neurons

In mouse cerebellar Purkinje neurons (PNs), the climbing fiber (CF) input provides a signal to parallel fiber (PF) synapses, triggering PF synaptic plasticity. This signal is given by supralinear Ca²⁺ transients, associated with the CF synaptic potential and colocalized with the PF Ca²⁺ influx, occurring only when PF activity precedes the CF input. Here, we unravel the biophysical determinants of supralinear Ca²⁺ signals associated with paired PF-CF synaptic activity. We used membrane potential (V _m) and Ca²⁺ imaging to investigate the local CF-associated Ca²⁺ influx following a train of PF synaptic potentials in two cases: (1) when the dendritic V _m is hyperpolarized below the resting V _m, and (2) when the dendritic V _m is at rest. We found that supralinear Ca²⁺ signals are mediated by type-1 metabotropic glutamate receptors (mGluR1s) when the CF input is delayed by 100-150 ms from the first PF input in both cases. When the dendrite is hyperpolarized only, however, mGluR1s boost neighboring T-type channels, providing a mechanism for local coincident detection of PF-CF activity. The resulting Ca²⁺ elevation is locally amplified by saturation of endogenous Ca²⁺ buffers produced by the PF-associated Ca²⁺ influx via the mGluR1-mediated nonselective cation conductance. In contrast, when the dendritic V _m is at rest, mGluR1s increase dendritic excitability by inactivating A-type K⁺ channels, but this phenomenon is not restricted to the activated PF synapses. Thus, V _m is likely a crucial parameter in determining PF synaptic plasticity, and the occurrence of hyperpolarization episodes is expected to play an important role in motor learning.SIGNIFICANCE STATEMENT In Purkinje neurons, parallel fiber synaptic plasticity, determined by coincident activation of the climbing fiber input, underlies cerebellar learning. We unravel the biophysical mechanisms allowing the CF input to produce a local Ca²⁺ signal exclusively at the sites of activated parallel fibers. We show that when the membrane potential is hyperpolarized with respect to the resting membrane potential, type-1 metabotropic glutamate receptors locally enhance Ca²⁺ influx mediated by T-type Ca²⁺ channels, and that this signal is amplified by saturation of endogenous buffer also mediated by the same receptors. The combination of these two mechanisms is therefore capable of producing a Ca²⁺ signal at the activated parallel fiber sites, suggesting a role of Purkinje neuron membrane potential in cerebellar learning.

Cytosolic Ca2+ Buffers Are Inherently Ca2+ Signal Modulators

For precisely regulating intracellular Ca²⁺ signals in a time- and space-dependent manner, cells make use of various components of the "Ca²⁺ signaling toolkit," including Ca²⁺ entry and Ca²⁺ extrusion systems. A class of cytosolic Ca²⁺-binding proteins termed Ca²⁺ buffers serves as modulators of such, mostly short-lived Ca²⁺ signals. Prototypical Ca²⁺ buffers include parvalbumins (α and β isoforms), calbindin-D9k, calbindin-D28k, and calretinin. Although initially considered to function as pure Ca²⁺ buffers, that is, as intracellular Ca²⁺ signal modulators controlling the shape (amplitude, decay, spread) of Ca²⁺ signals, evidence has accumulated that calbindin-D28k and calretinin have additional Ca²⁺ sensor functions. These other functions are brought about by direct interactions with target proteins, thereby modulating their targets' function/activity. Dysregulation of Ca²⁺ buffer expression is associated with several neurologic/neurodevelopmental disorders including autism spectrum disorder (ASD) and schizophrenia. In some cases, the presence of these proteins is presumed to confer a neuroprotective effect, as evidenced in animal models of Parkinson's or Alzheimer's disease.

Gold-substituted Silver-intensified Peroxidase Immunolabeling for FIB-SEM Imaging

Modern electron microscopy offers a wide variety of tools to investigate the ultrastructural organization of cells and tissues and to accurately pinpoint intracellular localizations of macromolecules of interest. New volumetric electron microscopy techniques and new instrumentation provide unique opportunities for high-throughput analysis of comparatively large volumes of tissue and their complete reconstitution in three-dimensional (3D) electron microscopy. However, due to a variety of technical issues such as the limited penetration of label into the tissue, low antigen preservation, substantial electron density of secondary detection reagents, and many others, the adaptation of immuno-detection techniques for use with such 3D imaging methods as focused ion beam-scanning electron microscopy (FIB-SEM) has been challenging. Here, we describe a sample preparation method for 3D FIB-SEM, which results in an optimal preservation and staining of ultrastructural details at a resolution necessary for tracing immunolabeled neuronal structures and detailed reconstruction of synapses. This technique is applicable to neuronal and non-neuronal cells, tissues, and a wide variety of antigens.

Calbindin-D28k in the Brain Influences the Expression of Cellular Prion Protein

The phenotypes of calbindin-D9k- (CaBP-9k-) knockout (KO), calbindin-D28k- (CaBP-28k-) KO, and CaBP-9k/28k-KO mice are similar to those of wild-type (WT) mice due to the compensatory action of other calcium transport proteins. In this study, we investigated the expression of cellular prion protein (PrP^C) in the brains of CaBP-9k-, CaBP-28k-, and CaBP-9k/28k-KO mice. PrP^C expression was significantly upregulated in the brain of all three strains. Levels of phospho-Akt (Ser473) and phospho-Bad (Ser136) were significantly elevated, but those of phospho-ERK and phospho-Bad (Ser155 and 112) were significantly reduced in the brains of CaBP-9k-, CaBP-28k-, and CaBP-9k/28k-KO mice. The expressions of the Bcl-2, p53, Bax, Cu/Zn-SOD, and Mn-SOD proteins were decreased in the brains of all KO mice. Expression of the endoplasmic reticulum marker protein BiP/GRP78 was decreased, and that of the CHOP protein was increased in the brains of those KO mice. To identify the roles of CaBP-28k, we transfected PC12 cells with siRNA for CaBP-28k and found increased expression of the PrP^C protein compared to the levels in control cells. These results suggest that CaBP-28k expression may regulate PrP^C protein expression and these mice may be vulnerable to the influence of prion disease.

Mechanisms of Spontaneous Climbing Fiber Discharge-Evoked Pauses and Output Modulation of Cerebellar Purkinje Cell in Mice

Climbing fiber (CF) afferents modulate the frequency and patterns of cerebellar Purkinje cell (PC) simple spike (SS) activity, but its mechanism is unclear. In the present study, we investigated the mechanisms of spontaneous CF discharge-evoked pauses and the output modulation of cerebellar PCs in urethane-anesthetized mice using in vivo whole-cell recording techniques and pharmacological methods. Under voltage-clamp recording conditions, spontaneous CF discharge evoked strong inward currents followed by small conductance calcium-activated potassium (SK) channels that mediated outward currents. The application of a GABA_A receptor antagonist did not significantly alter the spontaneous SS firing rate, although an AMPA receptor blocker abolished complex spike (CS) activity and induced significantly increased SS firing rates and a decreased coefficient of variation (CV) SS value. Either removal of extracellular calcium or chelated intracellular calcium induced a decrease in amplitude of CS-evoked after-hyperpolarization (AHP) potential accompanied by an increase in SS firing rate. In addition, blocking SK channels activity with a selective antagonist, dequalinium decreased the amplitude of AHP and increased SS firing rate. Moreover, we found repeated CF stimulation at 1 Hz induced a significant decrease in the spontaneous firing rate of SS, and accompanied with an increase in CV of SS in cerebellar slices, which was also abolished by dequalinium. These results indicated that the spontaneous CF discharge contributed to decreasing SS firing rate via activation of SK channels in the cerebellar PCs in vivo in mice.

Reassessment of long-term depression in cerebellar Purkinje cells in mice carrying mutated GluA2 C terminus

Long-term depression (LTD) of synaptic transmission from parallel fibers (PFs) to a Purkinje cell (PC) in the cerebellum has been considered to be a core mechanism of motor learning. Recently, however, discrepancies between LTD and motor learning have been reported in mice with a mutation that targeted the expression of PF-PC LTD by blocking AMPA-subtype glutamate receptor internalization regulated via the phosphorylation of AMPA receptors. In these mice, motor learning behavior was normal, but no PF-PC LTD was observed. We reexamined slices obtained from these GluA2 K882A and GluA2 Δ7 knockin mutants at 3-6 mo of age. The conventional protocols of stimulation did not induce LTD in these mutant mice, as previously reported, but surprisingly, LTD was induced using certain modified protocols. Such modifications involved increases in the number of PF stimulation (from one to two or five), replacement of climbing fiber stimulation with somatic depolarization (50 ms), filling a patch pipette with a Cs(+)-based solution, or extension of the duration of conjunction. We also found that intracellular infusion of a selective PKCα inhibitor (Gö6976) blocked LTD induction in the mutants, as in WT, suggesting that functional compensation occurred downstream of PKCα. The possibility that LTD in the mutants was caused by changes in membrane resistance, access resistance, or presynaptic property was excluded. The present results demonstrate that LTD is inducible by intensified conjunctive stimulations even in K882A and Δ7 mutants, indicating no contradiction against the LTD hypothesis of motor learning.

N-methyl-D-Aspartate Receptors Contribute to Complex Spike Signaling in Cerebellar Purkinje Cells: An In vivo Study in Mice

N-methyl-D-aspartate receptors (NMDARs) are post-synaptically expressed at climbing fiber-Purkinje cell (CF-PC) synapses in cerebellar cortex in adult mice and contributed to CF-PC synaptic transmission under in vitro conditions. In this study, we investigated the role of NMDARs at CF-PC synapses during the spontaneous complex spike (CS) activity in cerebellar cortex in urethane-anesthetized mice, by in vivo whole-cell recording technique and pharmacological methods. Under current-clamp conditions, cerebellar surface application of NMDA (50 μM) induced an increase in the CS-evoked pause of simple spike (SS) firing accompanied with a decrease in the SS firing rate. Under voltage-clamp conditions, application of NMDA enhanced the waveform of CS-evoked inward currents, which expressed increases in the area under curve (AUC) and spikelet number of spontaneous CS. NMDA increased the AUC of spontaneous CS in a concentration-dependent manner. The EC₅₀ of NMDA for increasing AUC of spontaneous CS was 33.4 μM. Moreover, NMDA significantly increased the amplitude, half-width and decay time of CS-evoked after-hyperpolarization (AHP) currents. Blockade of NMDARs with D-(-)-2-amino-5-phosphonopentanoic acid (D-APV, 250 μM) decreased the AUC, spikelet number, and amplitude of AHP currents. In addition, the NMDA-induced enhancement of CS activity could not be observed after α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors were blocked. The results indicated that NMDARs of CF-PC synapses contributed to the spontaneous CS activity by enhancing CS-evoked inward currents and AHP currents.

Ryanodine receptor gating controls generation of diastolic calcium waves in cardiac myocytes

Calcium waves can form and propagate at low frequencies of spontaneous calcium sparks if the calcium dependence of spark frequency is sufficiently steep, or the number of open RyRs is sufficiently large.

The role of cardiac ryanodine receptor (RyR) gating in the initiation and propagation of calcium waves was investigated using a mathematical model comprising a stochastic description of RyR gating and a deterministic description of calcium diffusion and sequestration. We used a one-dimensional array of equidistantly spaced RyR clusters, representing the confocal scanning line, to simulate the formation of calcium sparks. Our model provided an excellent description of the calcium dependence of the frequency of diastolic calcium sparks and of the increased tendency for the production of calcium waves after a decrease in cytosolic calcium buffering. We developed a hypothesis relating changes in the propensity to form calcium waves to changes of RyR gating and tested it by simulation. With a realistic RyR gating model, increased ability of RyR to be activated by Ca²⁺ strongly increased the propensity for generation of calcium waves at low (0.05–0.1-µM) calcium concentrations but only slightly at high (0.2–0.4-µM) calcium concentrations. Changes in RyR gating altered calcium wave formation by changing the calcium sensitivity of spontaneous calcium spark activation and/or the average number of open RyRs in spontaneous calcium sparks. Gating changes that did not affect RyR activation by Ca²⁺ had only a weak effect on the propensity to form calcium waves, even if they strongly increased calcium spark frequency. Calcium waves induced by modulating the properties of the RyR activation site could be suppressed by inhibiting the spontaneous opening of the RyR. These data can explain the increased tendency for production of calcium waves under conditions when RyR gating is altered in cardiac diseases.

Bursting reverberation as a multiscale neuronal network process driven by synaptic depression-facilitation

Neuronal networks can generate complex patterns of activity that depend on membrane properties of individual neurons as well as on functional synapses. To decipher the impact of synaptic properties and connectivity on neuronal network behavior, we investigate the responses of neuronal ensembles from small (5-30 cells in a restricted sphere) and large (acute hippocampal slice) networks to single electrical stimulation: in both cases, a single stimulus generated a synchronous long-lasting bursting activity. While an initial spike triggered a reverberating network activity that lasted 2-5 seconds for small networks, we found here that it lasted only up to 300 milliseconds in slices. To explain this phenomena present at different scales, we generalize the depression-facilitation model and extracted the network time constants. The model predicts that the reverberation time has a bell shaped relation with the synaptic density, revealing that the bursting time cannot exceed a maximum value. Furthermore, before reaching its maximum, the reverberation time increases sub-linearly with the synaptic density of the network. We conclude that synaptic dynamics and connectivity shape the mean burst duration, a property present at various scales of the networks. Thus bursting reverberation is a property of sufficiently connected neural networks, and can be generated by collective depression and facilitation of underlying functional synapses.

Reduced endogenous Ca2+ buffering speeds active zone Ca2+ signaling

Calcium influx during action potentials triggers neurotransmitter release at presynaptic active zones. Calcium buffers limit the spread of calcium and restrict neurotransmitter release to the vicinity of calcium channels. To sustain synchronous release during repetitive activity, rapid removal of calcium from the active zone is essential, but the underlying mechanisms are unclear. Therefore, we focused on cerebellar mossy fiber synapses, which are among the fastest synapses in the mammalian brain and found very weak presynaptic calcium buffering. One might assume that strong calcium buffering has the potential to efficiently remove calcium from active zones. In contrast, our results show that weak calcium buffering speeds active zone calcium clearance. Thus, the strength of presynaptic buffering limits the rate of synaptic transmission.

Fast synchronous neurotransmitter release at the presynaptic active zone is triggered by local Ca²⁺ signals, which are confined in their spatiotemporal extent by endogenous Ca²⁺ buffers. However, it remains elusive how rapid and reliable Ca²⁺ signaling can be sustained during repetitive release. Here, we established quantitative two-photon Ca²⁺ imaging in cerebellar mossy fiber boutons, which fire at exceptionally high rates. We show that endogenous fixed buffers have a surprisingly low Ca²⁺-binding ratio (∼15) and low affinity, whereas mobile buffers have high affinity. Experimentally constrained modeling revealed that the low endogenous buffering promotes fast clearance of Ca²⁺ from the active zone during repetitive firing. Measuring Ca²⁺ signals at different distances from active zones with ultra-high-resolution confirmed our model predictions. Our results lead to the concept that reduced Ca²⁺ buffering enables fast active zone Ca²⁺ signaling, suggesting that the strength of endogenous Ca²⁺ buffering limits the rate of synchronous synaptic transmission.

Buffer mobility and the regulation of neuronal calcium domains

The diffusion of calcium inside neurons is determined in part by the intracellular calcium binding species that rapidly bind to free calcium ions upon entry. It has long been known that some portion of a neuron's intracellular calcium binding capacity must be fixed or poorly mobile, as calcium diffusion is strongly slowed in the intracellular environment relative to diffusion in cytosolic extract. The working assumption was that these immobile calcium binding sites are provided by structural proteins bound to the cytoskeleton or intracellular membranes and may thereby be relatively similar in composition and capacity across different cell types. However, recent evidence suggests that the immobile buffering capacity can vary greatly between cell types and that some mobile calcium binding proteins may alter their mobility upon binding calcium, thus blurring the line between mobile and immobile. The ways in which immobile buffering capacity might be relevant to different calcium domains within neurons has been explored primarily through modeling. In certain regimes, the presence of immobile buffers and the interaction between mobile and immobile buffers have been shown to result in complex spatiotemporal patterns of free calcium. In total, these experimental and modeling findings call for a more nuanced consideration of the local intracellular calcium microenvironment. In this review we focus on the different amounts, affinities, and mobilities of immobile calcium binding species; propose a new conceptual category of physically diffusible but functionally immobile buffers; and discuss how these buffers might interact with mobile calcium binding partners to generate characteristic calcium domains.

EF-hand protein Ca2+ buffers regulate Ca2+ influx and exocytosis in sensory hair cells

EF-hand Ca(2+)-binding proteins are thought to shape the spatiotemporal properties of cellular Ca(2+) signaling and are prominently expressed in sensory hair cells in the ear. Here, we combined genetic disruption of parvalbumin-α, calbindin-D28k, and calretinin in mice with patch-clamp recording, in vivo physiology, and mathematical modeling to study their role in Ca(2+) signaling, exocytosis, and sound encoding at the synapses of inner hair cells (IHCs). IHCs lacking all three proteins showed excessive exocytosis during prolonged depolarizations, despite enhanced Ca(2+)-dependent inactivation of their Ca(2+) current. Exocytosis of readily releasable vesicles remained unchanged, in accordance with the estimated tight spatial coupling of Ca(2+) channels and release sites (effective "coupling distance" of 17 nm). Substitution experiments with synthetic Ca(2+) chelators indicated the presence of endogenous Ca(2+) buffers equivalent to 1 mM synthetic Ca(2+)-binding sites, approximately half of them with kinetics as fast as 1,2-Bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA). Synaptic sound encoding was largely unaltered, suggesting that excess exocytosis occurs extrasynaptically. We conclude that EF-hand Ca(2+) buffers regulate presynaptic IHC function for metabolically efficient sound coding.

Subcellular structural plasticity caused by the absence of the fast Ca(2+) buffer calbindin D-28k in recurrent collaterals of cerebellar Purkinje neurons

Purkinje cells (PC) control spike timing of neighboring PC by their recurrent axon collaterals. These synapses underlie fast cerebellar oscillations and are characterized by a strong facilitation within a time window of <20 ms during paired-pulse protocols. PC express high levels of the fast Ca(2+) buffer protein calbindin D-28k (CB). As expected from the absence of a fast Ca(2+) buffer, presynaptic action potential-evoked [Ca(2+)]i transients were previously shown to be bigger in PC boutons of young (second postnatal week) CB-/- mice, yet IPSC mean amplitudes remained unaltered in connected CB-/- PC. Since PC spine morphology is altered in adult CB-/- mice (longer necks, larger spine head volume), we summoned that morphological compensation/adaptation mechanisms might also be induced in CB-/- PC axon collaterals including boutons. In these mice, biocytin-filled PC reconstructions revealed that the number of axonal varicosities per PC axon collateral was augmented, mostly confined to the granule cell layer. Additionally, the volume of individual boutons was increased, evidenced from z-stacks of confocal images. EM analysis of PC-PC synapses revealed an enhancement in active zone (AZ) length by approximately 23%, paralleled by a higher number of docked vesicles per AZ in CB-/- boutons. Moreover, synaptic cleft width was larger in CB-/- (23.8 ± 0.43 nm) compared to wild type (21.17 ± 0.39 nm) synapses. We propose that the morphological changes, i.e., the larger bouton volume, the enhanced AZ length and the higher number of docked vesicles, in combination with the increase in synaptic cleft width likely modifies the GABA release properties at this synapse in CB-/- mice. We view these changes as adaptation/homeostatic mechanisms to likely maintain characteristics of synaptic transmission in the absence of the fast Ca(2+) buffer CB. Our study provides further evidence on the functioning of the Ca(2+) homeostasome.

Intracellular calcium dynamics permit a Purkinje neuron model to perform toggle and gain computations upon its inputs

Without synaptic input, Purkinje neurons can spontaneously fire in a repeating trimodal pattern that consists of tonic spiking, bursting and quiescence. Climbing fiber input (CF) switches Purkinje neurons out of the trimodal firing pattern and toggles them between a tonic firing and a quiescent state, while setting the gain of their response to Parallel Fiber (PF) input. The basis to this transition is unclear. We investigate it using a biophysical Purkinje cell model under conditions of CF and PF input. The model can replicate these toggle and gain functions, dependent upon a novel account of intracellular calcium dynamics that we hypothesize to be applicable in real Purkinje cells.

Augmenting Plasticity Induction in Human Motor Cortex by Disinhibition Stimulation

Cellular studies showed that disinhibition, evoked pharmacologically or by a suitably timed priming stimulus, can augment long-term plasticity (LTP) induction. We demonstrated previously that transcranial magnetic stimulation evokes a period of presumably GABA(B)ergic late cortical disinhibition (LCD) in human primary motor cortex (M1). Here, we hypothesized that, in keeping with cellular studies, LCD can augment LTP-like plasticity in humans. In Experiment 1, patterned repetitive TMS was applied to left M1, consisting of 6 trains (intertrain interval, 8 s) of 4 doublets (interpulse interval equal to individual peak I-wave facilitation, 1.3-1.5 ms) spaced by the individual peak LCD (interdoublet interval (IDI), 200-250 ms). This intervention (total of 48 pulses applied over ∼45 s) increased motor-evoked potential amplitude, a marker of corticospinal excitability, in a right hand muscle by 147% ± 4%. Control experiments showed that IDIs shorter or longer than LCD did not result in LTP-like plasticity. Experiment 2 indicated topographic specificity to the M1 hand region stimulated by TMS and duration of the LTP-like plasticity of 60 min. In conclusion, GABA(B)ergic LCD offers a powerful new approach for augmenting LTP-like plasticity induction in human cortex. We refer to this protocol as disinhibition stimulation (DIS).

"Permethrin chronic exposure alters motor coordination in rats: effect of calcium supplementation and amlodipine"

Recently was observed that pyrethroids decrease motor coordination and that calcium channels can be important targets for this effect. To contribute with this observation, this work studied the motor coordination and exploration (using hole-board apparatus), and locomotion (using open-field apparatus) of rats exposed to following treatments: permethrin (PM), PM plus calcium gluconate (CG) and PM plus amlodipine (AML). The results obtained show that CG or AML alone not changed the motor coordination while PM decreases it. CG kept the effect of permethrin; AML, however, decreased the values of permethrin to the control. Locomotor activity and exploration, which could confound results of motor coordination, were not modified by treatments. The concentration of PM in brain tissue was increased by the CG and AML. The neurosomatic index (weight brain/body weight) was increased by the PM and PM+CG. In conclusion, the combined results here obtained indicates that the calcium ion and the channels in which it is involved can be important targets for the toxic effect of pyrethroid insecticide permethrin on motor nerve activity of rats.

The control of brain mitochondrial energization by cytosolic calcium: the mitochondrial gas pedal

This review focuses on problems of the intracellular regulation of mitochondrial function in the brain via the (i) supply of mitochondria with ADP by means of ADP shuttles and channels and (ii) the Ca(2+) control of mitochondrial substrate supply. The permeability of the mitochondrial outer membrane for adenine nucleotides is low. Therefore rate dependent concentration gradients exist between the mitochondrial intermembrane space and the cytosol. The existence of dynamic ADP gradients is an important precondition for the functioning of ADP shuttles, for example CrP-shuttle. Cr at mM concentrations instead of ADP diffuses from the cytosol through the porin pores into the intermembrane space. The CrP-shuttle isoenzymes work in different directions which requires different metabolite concentrations mainly caused by dynamic ADP compartmentation. The ADP shuttle mechanisms alone cannot explain the load dependent changes in mitochondrial energization, and a complete model of mitochondrial regulation have to account the Ca(2+) -dependent substrate supply too. According to the old paradigmatic view, Ca(2+) (cyt) taken up by the mitochondrial Ca(2+) uniporter activates dehydrogenases within the matrix. However, recently it was found that Ca(2+) (cyt) at low nM concentrations exclusively activates the state 3 respiration via aralar, the mitochondrial glutamate/aspartate carrier. At higher Ca(2+) (cyt) (> 500 nM), brain mitochondria take up Ca(2+) for activation of substrate oxidation rates. Since brain mitochondrial pyruvate oxidation is only slightly influenced by Ca(2+) (cyt) , it was proposed that the cytosolic formation of pyruvate from its precursors is tightly controlled by the Ca(2+) dependent malate/aspartate shuttle. At low (50-100 nM) Ca(2+) (cyt) the pyruvate formation is suppressed, providing a substrate limitation control in neurons. This so called "gas pedal" mechanism explains why the energy metabolism of neurons in the nucleus suprachiasmaticus could be down-regulated at night but activated at day as a basis for the circadian changes in Ca(2+) (cyt) . It also could explain the energetic disadvantages caused by altered Ca(2+) (cyt) at mitochondrial diseases and neurodegeneration.

Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cells

Intracellular Ca(2+) concentrations play a crucial role in the physiological interaction between Ca(2+) channels and Ca(2+)-activated K(+) channels. The commonly used model, a Ca(2+) pool with a short relaxation time, fails to simulate interactions occurring at multiple time scales. On the other hand, detailed computational models including various Ca(2+) buffers and pumps can result in large computational cost due to radial diffusion in large compartments, which may be undesirable when simulating morphologically detailed Purkinje cell models. We present a method using a compensating mechanism to replace radial diffusion and compared the dynamics of different Ca(2+) buffering models during generation of a dendritic Ca(2+) spike in a single compartment model of a PC dendritic segment with Ca(2+) channels of P- and T-type and Ca(2+)-activated K(+) channels of BK- and SK-type. The Ca(2+) dynamics models used are (1) a single Ca(2+) pool; (2) two Ca(2+) pools, respectively, for the fast and slow transients; (3) detailed Ca(2+) dynamics with buffers, pump, and diffusion; and (4) detailed Ca(2+) dynamics with buffers, pump, and diffusion compensation. Our results show that detailed Ca(2+) dynamics models have significantly better control over Ca(2+)-activated K(+) channels and lead to physiologically more realistic simulations of Ca(2+) spikes and bursting. Furthermore, the compensating mechanism largely eliminates the effect of removing diffusion from the model on Ca(2+) dynamics over multiple time scales.

Diffusion and extrusion shape standing calcium gradients during ongoing parallel fiber activity in dendrites of Purkinje neurons

Synaptically induced calcium transients in dendrites of Purkinje neurons (PNs) play a key role in the induction of plasticity in the cerebellar cortex (Ito, Physiol Rev 81:1143-1195, 2001). Long-term depression at parallel fiber-PN synapses can be induced by stimulation paradigms that are associated with long-lasting (>1 min) calcium signals. These signals remain strictly localized (Eilers et al., Learn Mem 3:159-168, 1997), an observation that was rather unexpected, given the high concentration of the mobile endogenous calcium-binding proteins parvalbumin and calbindin in PNs (Fierro and Llano, J Physiol (Lond) 496:617-625, 1996; Kosaka et al., Exp Brain Res 93:483-491, 1993). By combining two-photon calcium imaging experiments in acute slices with numerical computer simulations, we found that significant calcium diffusion out of active branches indeed takes places. It is outweighed, however, by rapid and powerful calcium extrusion along the dendritic shaft. The close interplay of diffusion and extrusion defines the spread of calcium between active and inactive dendritic branches, forming a steep gradient in calcium with drop ranges of ~13 μm (interquartile range, 10-18 μm).

Effects of calretinin on Ca2+ signals in cerebellar granule cells: implications of cooperative Ca2+ binding

Calretinin is thought to be the main endogenous calcium buffer in cerebellar granule cells (GrCs). However, little is known about the impact of cooperative Ca(2+) binding to calretinin on highly localized and more global (regional) Ca(2+) signals in these cells. Using numerical simulations, we show that an essential property of calretinin is a delayed equilibration with Ca(2+). Therefore, the amount of Ca(2+), which calretinin can accumulate with respect to equilibrium levels, depends on stimulus conditions. Based on our simulations of buffered Ca(2+) diffusion near a single Ca(2+) channel or a large cluster of Ca(2+) channels and previous experimental findings that 150 μM 1,2-bis(o-aminophenoxy) ethane-N, N, N', N'-tetraacetic acid (BAPTA) and endogenous calretinin have similar effects on GrC excitability, we estimated the concentration of mobile calretinin in GrCs in the range of 0.7-1.2 mM. Our results suggest that this estimate can provide a starting point for further analysis. We find that calretinin prominently reduces the action potential associated increase in cytosolic free Ca(2+) concentration ([Ca(2+)]( i )) even at a distance of 30 nm from a single Ca(2+) channel. In spite of a buildup of residual Ca(2+), it maintains almost constant maximal [Ca(2+)]( i ) levels during repetitive channel openings with a frequency less than 80 Hz. This occurs because of accelerated Ca(2+) binding as calretinin binds more Ca(2+). Unlike the buffering of high Ca(2+) levels within Ca(2+) nano/microdomains sensed by large conductance Ca(2+)-activated K(+) channels, the buffering of regional Ca(2+) signals by calretinin can never be mimicked by certain concentration of BAPTA under all different experimental conditions.

Dendritic calcium signaling in cerebellar Purkinje cell

The Purkinje cells in the cerebellum are unique neurons that generate local and global Ca(2+) signals in response to two types of excitatory inputs, parallel fiber and climbing fiber, respectively. The spatiotemporal distribution and interaction of these synaptic inputs produce complex patterns of Ca(2+) dynamics in the Purkinje cell dendrites. The Ca(2+) signals originate from Ca(2+) influx through voltage-gated Ca(2+) channels and Ca(2+) release from intracellular stores that are mediated by the metabotropic glutamate receptor signaling pathway. These Ca(2+) signals are essential for the induction of various forms of synaptic plasticity and for controlling the input-output relationship of Purkinje cells. In this article we review Ca(2+) signaling in Purkinje cell dendrites.

Three functional facets of calbindin D-28k

Many neurons of the vertebrate central nervous system (CNS) express the Ca²⁺ binding protein calbindin D-28k (CB), including important projection neurons like cerebellar Purkinje cells but also neocortical interneurons. CB has moderate cytoplasmic mobility and comprises at least four EF-hands that function in Ca²⁺ binding with rapid to intermediate kinetics and affinity. Classically it was viewed as a pure Ca²⁺ buffer important for neuronal survival. This view was extended by showing that CB is a critical determinant in the control of synaptic Ca²⁺ dynamics, presumably with strong impact on plasticity and information processing. Already 30 years ago, in vitro studies suggested that CB could have an additional Ca²⁺ sensor function, like its prominent acquaintance calmodulin (CaM). More recent work substantiated this hypothesis, revealing direct CB interactions with several target proteins. Different from a classical sensor, however, CB appears to interact with its targets both, in its Ca²⁺-loaded and Ca²⁺-free forms. Finally, CB has been shown to be involved in buffered transport of Ca²⁺, in neurons but also in kidney. Thus, CB serves a threefold function as buffer, transporter and likely as a non-canonical sensor.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Dendritic calcium signaling triggered by spontaneous and sensory-evoked climbing fiber input to cerebellar Purkinje cells in vivo

Cerebellar Purkinje cells have one of the most elaborate dendritic trees in the mammalian CNS, receiving excitatory synaptic input from a single climbing fiber (CF) and from ∼200,000 parallel fibers. The dendritic Ca(2+) signals triggered by activation of these inputs are crucial for the induction of synaptic plasticity at both of these synaptic connections. We have investigated Ca(2+) signaling in Purkinje cell dendrites in vivo by combining targeted somatic or dendritic patch-clamp recording with simultaneous two-photon microscopy. Both spontaneous and sensory-evoked CF inputs triggered widespread Ca(2+) signals throughout the dendritic tree that were detectable even in individual spines of the most distal spiny branchlets receiving parallel fiber input. The amplitude of these Ca(2+) signals depended on dendritic location and could be modulated by membrane potential, reflecting modulation of dendritic spikes triggered by the CF input. Furthermore, the variability of CF-triggered Ca(2+) signals was regulated by GABAergic synaptic input. These results indicate that dendritic Ca(2+) signals triggered by sensory-evoked CF input can act as associative signals for synaptic plasticity in Purkinje cells in vivo and may differentially modulate plasticity at parallel fiber synapses depending on the location of synapses, firing state of the Purkinje cell, and ongoing GABAergic synaptic input.

Quantitative comparison of genetically encoded Ca indicators in cortical pyramidal cells and cerebellar Purkinje cells

Genetically encoded Ca²⁺ indicators (GECIs) are promising tools for cell type-specific and chronic recording of neuronal activity. In the mammalian central nervous system, however, GECIs have been tested almost exclusively in cortical and hippocampal pyramidal cells, and the usefulness of recently developed GECIs has not been systematically examined in other cell types. Here we expressed the latest series of GECIs, yellow cameleon (YC) 2.60, YC3.60, YC-Nano15, and GCaMP3, in mouse cortical pyramidal cells as well as cerebellar Purkinje cells using in utero injection of recombinant adenoviral vectors. We characterized the performance of the GECIs by simultaneous two-photon imaging and whole-cell patch-clamp recording in acute brain slices at 33 ± 2°C. The fluorescent responses of GECIs to action potentials (APs) evoked by somatic current injection or to synaptic stimulation were examined using rapid dendritic imaging. In cortical pyramidal cells, YC2.60 showed the largest responses to single APs, but its decay kinetics were slower than YC3.60 and GCaMP3, while GCaMP3 showed the largest responses to 20 APs evoked at 20 Hz. In cerebellar Purkinje cells, only YC2.60 and YC-Nano15 could reliably report single complex spikes (CSs), and neither showed signal saturation over the entire stimulus range tested (1–10 CSs at 10 Hz). The expression and response of YC2.60 in Purkinje cells remained detectable and comparable for at least over 100 days. These results provide useful information for selecting an optimal GECI depending on the experimental requirements: in cortical pyramidal cells, YC2.60 is suitable for detecting sparse firing of APs, whereas GCaMP3 is suitable for detecting burst firing of APs; in cerebellar Purkinje cells, YC2.60 as well as YC-Nano15 is suitable for detecting CSs.

Cytosolic Ca2+ buffers

"Ca(2+) buffers," a class of cytosolic Ca(2+)-binding proteins, act as modulators of short-lived intracellular Ca(2+) signals; they affect both the temporal and spatial aspects of these transient increases in [Ca(2+)](i). Examples of Ca(2+) buffers include parvalbumins (α and β isoforms), calbindin-D9k, calbindin-D28k, and calretinin. Besides their proven Ca(2+) buffer function, some might additionally have Ca(2+) sensor functions. Ca(2+) buffers have to be viewed as one of the components implicated in the precise regulation of Ca(2+) signaling and Ca(2+) homeostasis. Each cell is equipped with proteins, including Ca(2+) channels, transporters, and pumps that, together with the Ca(2+) buffers, shape the intracellular Ca(2+) signals. All of these molecules are not only functionally coupled, but their expression is likely to be regulated in a Ca(2+)-dependent manner to maintain normal Ca(2+) signaling, even in the absence or malfunctioning of one of the components.

Stabilization of Ca current in Purkinje neurons during high-frequency firing by a balance of Ca-dependent facilitation and inactivation

Purkinje neurons fire spontaneous action potentials at ∼50 spikes/sec and generate more than 100 spikes/sec during cerebellum-mediated behaviors. Many voltage-gated channels, including Ca channels, can inactivate and/or facilitate with repeated stimulation, raising the question of how these channels respond to regular, rapid trains of depolarizations. To test whether Ca currents are modulated during firing, we recorded voltage-clamped Ca currents, predominantly carried by P-type Ca channels, from acutely dissociated mouse Purkinje neurons at 30-33°C (1 mM Ca). With 0.5 mM intracellular EGTA, 1-second trains of either spontaneous action potential waveforms or brief depolarizing steps at 50 Hz evoked Ca tail currents that were stable, remaining within 5% of the first tail current throughout the train. Higher frequency trains (100 and 200 Hz) elicited a maximal inactivation of <10%. To test whether this stability of Ca currents resulted from a lack of modulation or from an equilibrium between facilitation and inactivation, we manipulated the permeant ion (Ca vs. Ba) and Ca buffering (0.5 vs. 10 mM EGTA). With low buffering, Ba accelerated the initial inactivation evoked by 1-second trains, but reduced its extent at 200 Hz, consistent with an early calcium-dependent facilitation (CDF) and late calcium-dependent inactivation (CDI) at high frequencies. Increasing the Ca buffer favored CDF. These data suggest that stable Ca current amplitudes result from a balance of CDF, CDI, and voltage-dependent inactivation. This modest net Ca-dependent modulation may contribute to the ability of Purkinje neurons to sustain long periods of regular firing and synaptic transmission.

Spine neck geometry determines spino-dendritic cross-talk in the presence of mobile endogenous calcium binding proteins

Dendritic spines are thought to compartmentalize second messengers like Ca2+. The notion of isolated spine signaling, however, was challenged by the recent finding that under certain conditions mobile endogenous Ca(2+)-binding proteins may break the spine limit and lead to activation of Ca(2+)-dependent dendritic signaling cascades. Since the size of spines is variable, the spine neck may be an important regulator of this spino-dendritic crosstalk. We tested this hypothesis by using an experimentally defined, kinetic computer model in which spines of Purkinje neurons were coupled to their parent dendrite by necks of variable geometry. We show that Ca2+ signaling and calmodulin activation in spines with long necks is essentially isolated from the dendrite, while stubby spines show a strong coupling with their dendrite, mediated particularly by calbindin D28k. We conclude that the spine neck geometry, in close interplay with mobile Ca(2+)-binding proteins, regulates the spino-dendritic crosstalk.

Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP

The architecture of parallel fiber axons contacting cerebellar Purkinje neurons retains spatial information over long distances. Parallel fiber synapses can trigger local dendritic calcium spikes, but whether and how this calcium signal leads to plastic changes that decode the parallel fiber input organization is unknown. By combining voltage and calcium imaging, we show that calcium signals, elicited by parallel fiber stimulation and mediated by voltage-gated calcium channels, increase non-linearly during high-frequency bursts of electrically constant calcium spikes, because they locally and transiently saturate the endogenous buffer. We demonstrate that these non-linear calcium signals, independently of NMDA or metabotropic glutamate receptor activation, can induce parallel fiber long-term potentiation. Two-photon imaging in coronal slices revealed that calcium signals inducing long-term potentiation can be observed by stimulating either the parallel fiber or the ascending fiber pathway. We propose that local dendritic calcium spikes, evoked by synaptic potentials, provide a unique mechanism to spatially decode parallel fiber signals into cerebellar circuitry changes.

Computational study of non-homogeneous distribution of Ca(2+) handling systems in cerebellar granule cells

The spatiotemporal distribution of cytosolic free calcium concentration ([Ca(2+)](i)) in cerebellar granule cells (GrCs) is thought to be critical in defining the occurrence and direction of long-term changes in synaptic strength at cerebellar mossy fiber-GrC synapses. Despite this, the mechanisms responsible for shaping Ca(2+) transients in GrCs are not well understood. To investigate the interplay between Ca(2+) entry, extrusion, buffering and dendritic morphology in shaping Ca(2+) elevations in GrCs, we developed a model of Ca(2+) regulation in these cells and examined the requirements for reproducing fluorescence responses to depolarization and synaptic stimulation previously described in the literature. Two conclusions can be drawn from our simulation results. First, a significant progressive decrease in the amplitudes of depolarization-evoked fluorescence transients from the dendritic endings (digits) toward the soma of GrCs, can be reproduced in the model only if the density of Ca(2+) channels is considerably higher or the concentration of endogenous buffers is much lower in the digits than in the parent dendrites. In contrast, heterogeneities in the distribution of Ca(2+) pumps or in cytosolic fractional volume cannot account for the formation of [Ca(2+)](i) gradients in GrCs. Second, much lower amplitudes of fluorescence transients induced by depolarization and synaptic stimulation than expected from typical measurements of Ca(2+) and NMDA receptor-mediated currents can be reconciled with a pronounced slowing of the decay of fluorescence responses in the digits of GrCs after introducing a high-affinity Ca(2+) indicator if a high-capacity immobile Ca(2+) buffer (presumably plasma membrane-associated) is suggested to be present in the soma and apical part of digits. Mitochondria also are likely to modulate synaptically evoked Ca(2+) responses in GrCs. The alternative hypotheses are thoroughly discussed and research avenues for their testing in future experiments are proposed.

A limited contribution of Ca2+ current facilitation to paired-pulse facilitation of transmitter release at the rat calyx of Held

Recent studies have suggested that transmitter release facilitation at synapses is largely mediated by presynaptic Ca(2+) current facilitation, but the exact contribution of Ca(2+) current facilitation has not been determined quantitatively. Here, we determine the contribution of Ca(2+) current facilitation, and of an increase in the residual free Ca(2+) concentration ([Ca(2+)](i)) in the nerve terminal, to paired-pulse facilitation of transmitter release at the calyx of Held. Under conditions of low release probability imposed by brief presynaptic voltage-clamp steps, transmitter release facilitation at short interstimulus intervals (4 ms) was 227 +/- 31% of control, Ca(2+) current facilitation was 113 +/- 4% of control, and the peak residual [Ca(2+)](i) was 252 +/- 18 nm over baseline. By inferring the 'local' [Ca(2+)](i) transients that drive transmitter release during these voltage-clamp stimuli with the help of a kinetic release model, we estimate that Ca(2+) current facilitation contributes to approximately 40% to paired-pulse facilitation of transmitter release. The remaining component of facilitation strongly depends on the build-up, and on the decay of the residual free [Ca(2+)](i), but cannot be explained by linear summation of the residual free [Ca(2+)](i), and the back-calculated 'local' [Ca(2+)](i) signal, which only accounts for approximately 10% of the total release facilitation. Further voltage-clamp experiments designed to compensate for Ca(2+) current facilitation demonstrated that about half of the observed transmitter release facilitation remains in the absence of Ca(2+) current facilitation. Our results indicate that paired-pulse facilitation of transmitter release at the calyx of Held is driven by at least two distinct mechanisms: Ca(2+) current facilitation, and a mechanism independent of Ca(2+) current facilitation that closely tracks the time course of residual free [Ca(2+)](i).

Order-dependent coincidence detection in cerebellar Purkinje neurons at the inositol trisphosphate receptor

Associative long-term depression (LTD) at cerebellar parallel fiber-Purkinje cell synapses is sensitive to the temporal order in which the parallel fiber is coactivated with the climbing fiber input, but how order sensitivity is achieved is unknown. Here we show that the cerebellar inositol-1,4,5-trisphosphate (IP3) receptor, whose activation is required for LTD induction, is sensitive in situ to the order of presentation of its coagonists, IP3 and cytoplasmic calcium. By focally photolyzing a novel caged IP3 compound in dendritic spines, we find that pairing IP3 with climbing fiber-mediated calcium entry leads to a large calcium release transient if the climbing fiber is activated up to 100 ms before or up to 500 ms after IP3 uncaging. This asymmetric timing window for coactivation follows the kinetics of calcium removal and IP3 unbinding from the receptor and is not limited by IP3 metabolism. IP3 receptor binding thus acts as an eligibility trace that can drive temporal order-dependent calcium release and LTD induction in Purkinje cells and event order-dependent sensory plasticity in the whole animal.

Recurrent axon collaterals underlie facilitating synapses between cerebellar Purkinje cells

Morphological studies have provided ample evidence for synaptic connections between cerebellar Purkinje cells (PCs), but the functional properties of these synapses remain elusive. We report on direct recordings of synaptically connected PCs in mice cerebellar slices. In PCs filled with a fluorescent dye to aid axon visualization and postsynaptic target identification, presynaptic action potentials elicited unitary inhibitory postsynaptic currents in neighboring PCs in 10% of potential connections tested. In 11 pairs, postsynaptic currents had a delay onset of 1.62 +/- 0.16 ms with respect to the presynaptic spike, a 10-90% rise time of 2.20 +/- 0.33 ms, and a monoexponential decay with a time constant of 13.3 +/- 1.7 ms. Average values for peak current and variance-to-mean ratio were 55 +/- 14 and 30 +/- 3 pA, respectively. In contrast to the depressing nature of the synapse between PCs and deep cerebellar nuclei neurons, PC-PC synapses exhibited strong facilitation operating within a time window of a few milliseconds; paired-pulse ratios for 3- and 20-ms intervals were 1.79 +/- 0.18 and 1.01 +/- 0.14, respectively (n = 6). The facilitation is of presynaptic nature because it is accompanied by a decrease in failure rate. Trains of action potentials evoked in presynaptic varicosities volume-averaged calcium transients whose peak increased 1.7-fold as the frequency increased from 50 to 166 Hz. We suggest that PC-PC synapses are tuned for high fidelity of transmission during bursts of PC activity and that their operation in the cerebellar circuit modulates synchronized PC firing.

Optical and electrophysiological recordings of corticospinal synaptic activity and its developmental change in in vitro rat slice co-cultures

Electrophysiological recordings and optical imaging with a fast voltage-sensitive dye (di-4-ANNEPS) were used to directly examine the spatiotemporal properties of in vitro corticospinal synapses formed in co-cultures of cerebral cortex and spinal cord slices. Whole cell recordings from spinal cord cells showed both monosynaptic and polysynaptic excitatory postsynaptic currents (EPSCs) in response to stimulation of corticospinal axons. Monosynaptic EPSCs and excitatory postsynaptic potentials (EPSPs) were isolated in artificial cerebrospinal fluid containing high concentrations of divalent cations. Optical imaging and extracellular recordings were done simultaneously. Both EPSPs and optically recorded excitatory postsynaptic potentials (optEPSPs) lasted 300-500 ms and were almost always positive. The major component of these long-lasting potentials was blocked by ifenprodil, a specific antagonist of the NR2B subunit-containing N-methyl-d-aspartate receptor (NMDAR). The spatial distribution of corticospinal optEPSPs paralleled that of the corticospinal field excitatory postsynaptic potentials (fEPSPs), suggesting that positive fEPSP amplitude is a reliable indicator of the distribution of corticospinal synapses. Corticospinal optEPSPs spread into the ventrolateral region by 6-7 days in vitro (DIV), but were restricted to the dorsomedial area by 11-13 DIV, suggesting synapses were eliminated from the ventrolateral side of the spinal cord. After the recordings were complete, corticospinal fibers were often anterogradely labeled with biocytin to assess the relation between presynaptic fiber distribution and the optical signals (optically-recorded presynaptic fiber volley (opt-prevolley) and optEPSP). The distributions of the opt-prevolleys and optEPSPs correlated well with the distribution of presynaptic fibers, suggesting the opt-prevolley reflects corticospinal fiber activity and that the fibers made synapses relatively evenly along their axons. The NR2B-mediated component of the corticospinal synaptic response declined during the interval between 6 and 7 DIV and 11-13 DIV, suggesting that a shift in the NMDAR subtype from NR2B to something else (perhaps NR2A) may be involved in regulating developmental plasticity in the rat spinal cord and the process of corticospinal synapse elimination.

Ca2+ requirements for cerebellar long-term synaptic depression: role for a postsynaptic leaky integrator

Photolysis of a caged Ca(2+) compound was used to characterize the dependence of cerebellar long-term synaptic depression (LTD) on postsynaptic Ca(2+) concentration ([Ca(2+)](i)). Elevating [Ca(2+)](i) was sufficient to induce LTD without requiring any of the other signals produced by synaptic activity. A sigmoidal relationship between [Ca(2+)](i) and LTD indicated a highly cooperative triggering of LTD by Ca(2+). The duration of the rise in [Ca(2+)](i) influenced the apparent Ca(2+) affinity of LTD, and this time-dependent behavior could be described by a leaky integrator process with a time constant of 0.6 s. A computational model, based on a positive-feedback cycle that includes protein kinase C and MAP kinase, was capable of simulating these properties of Ca(2+)-triggered LTD. Disrupting this cycle experimentally also produced the predicted changes in the Ca(2+) dependence of LTD. We conclude that LTD arises from a mechanism that integrates postsynaptic Ca(2+) signals and that this integration may be produced by the positive-feedback cycle.

Synapse specificity of calcium release probed by chemical two-photon uncaging of inositol 1,4,5-trisphosphate

Biological messengers can be "caged" by adding a single photosensitive group that can be photolyzed by a light flash to achieve spatially and temporally precise biochemical control. Here we report that photolysis of a double-caged form of the second messenger inositol 1,4,5-trisphosphate (IP3) triggers focal calcium release in Purkinje cell somata, dendrites, and spines as measured by two-photon microscopy. In calbindin knock-out Purkinje cells, peak calcium increased with flash energy with higher cooperativity for double-caged IP3 than for conventional single-caged IP3, consistent with a chemical two-photon effect. Spine photolysis of double-caged IP3 led to local calcium release. Uncaging of glycerophosphoryl-myo-inositol 4,5-bisphosphate (gPIP2), a poorly metabolizable IP3 analog, led to less well localized release. Thus, IP3 breakdown is necessary for spine-specificity. IP3- and gPIP2-evoked signals declined from peak with similar, slow time courses, indicating that release lasts hundreds of milliseconds and is terminated not by IP3 degradation but by intrinsic receptor dynamics. Based on measurements of spine-dendrite coupling, IP3-evoked calcium signals are expected to be at least 2.4-fold larger in their spine of origin than in nearby spines, allowing IP3 to act as a synapse-specific second messenger. Unexpectedly, single-caged IP3 led to less release in somata and was ineffective in dendrites and spines. Calcium release using caged gPIP2 was inhibited by the addition of single-caged IP3, suggesting that single-caged IP3 is an antagonist of calcium release. Caging at multiple sites may be an effective general approach to reducing residual receptor interaction.

Anomalous diffusion in Purkinje cell dendrites caused by spines

We combined local photolysis of caged compounds with fluorescence imaging to visualize molecular diffusion within dendrites of cerebellar Purkinje cells. Diffusion of a volume marker, fluorescein dextran, within spiny dendrites was remarkably slow in comparison to its diffusion in smooth dendrites. Computer simulations indicate that this retardation is due to a transient trapping of molecules within dendritic spines, yielding anomalous diffusion. We considered the influence of spine trapping on the diffusion of calcium ions (Ca(2+)) and inositol-1,4,5-triphospate (IP(3)), two synaptic second messengers. Diffusion of IP(3) was strongly influenced by the presence of dendritic spines, while Ca(2+) was removed so rapidly that it could not diffuse far enough to be trapped. We conclude that an important function of dendritic spines may be to trap chemical signals and thereby create slowed anomalous diffusion within dendrites.

Persistent activation of protein kinase Calpha is not necessary for expression of cerebellar long-term depression

Protein kinase Calpha (PKCalpha) plays a major role in the induction of long-term depression (LTD) in a cerebellar Purkinje cell (PC). The sequential activation model for classical PKC states that PKCalpha translocates to the plasma membrane by binding Ca(++) and then becomes fully activated by binding diacylglycerol (DAG), which enables estimation of the activity by monitoring its localization. Here, we performed simultaneous electrophysiological recording and fluorescence imaging in a cultured PC expressing GFP-tagged PKCalpha. When a PC was depolarized, PKCalpha transiently translocated to the plasma membrane in a Ca(++)-dependent manner. Application of membrane permeable DAG or the blocker of DAG lipase prolonged the translocation. These results suggest that the sequential activation model is applicable to PCs. Conjunctive applications of glutamate and depolarization pulse induced LTD, but did not prolong the translocation. Thus, our results imply that persistent activation of PKCalpha is not necessary for the expression of LTD.

Nanodomains of single Ca2+ channels contribute to action potential repolarization in cortical neurons

The precise shape of action potentials in cortical neurons is a key determinant of action potential-dependent Ca2+ influx, as well as of neuronal signaling, on a millisecond scale. In cortical neurons, Ca2+-sensitive K+ channels, or BK channels (BKChs), are crucial for action potential termination, but the precise functional interplay between Ca2+ channels and BKChs has remained unclear. In this study, we investigate the mechanisms allowing for rapid and reliable activation of BKChs by single action potentials in hippocampal granule cells and the impact of endogenous Ca2+ buffers. We find that BKChs are operated by nanodomains of single Ca2+ channels. Using a novel approach based on a linear approximation of buffered Ca2+ diffusion in microdomains, we quantitatively analyze the prolongation of action potentials by the Ca2+ chelator BAPTA. This analysis allowed us to estimate that the mean diffusional distance for Ca2+ ions from a Ca2+ channel to a BKCh is approximately 13 nm. This surprisingly short diffusional distance cannot be explained by a random distribution of Ca2+ channels and renders the activation of BKChs insensitive to the relatively high concentrations of endogenous Ca2+ buffers in hippocampal neurons. These data suggest that tight colocalization of the two types of channels permits hippocampal neurons to regulate global Ca2+ signals by a high cytoplasmic Ca2+ buffer capacity without affecting the fast and brief activation of BKChs required for proper repolarization of action potentials.

Climbing fiber discharge regulates cerebellar functions by controlling the intrinsic characteristics of purkinje cell output

The contribution of Purkinje cells to cerebellar motor coordination and learning is determined in part by the chronic and acute effects of climbing fiber (CF) afferents. Whereas the chronic effects of CF discharge, such as the depression of conjunctive parallel fiber (PF) inputs, are well established, the acute cellular functions of CF discharge remain incompletely understood. In rat cerebellar slices, we show that CF discharge presented at physiological frequencies substantially modifies the frequency and pattern of Purkinje cell spike output in vitro. Repetitive CF discharge converts a spontaneous trimodal pattern of output characteristic of Purkinje cells in vitro to a more naturalistic nonbursting pattern consisting of spike trains interrupted by short CF-evoked pauses or longer pauses associated with state transitions. All effects of CF discharge could be reproduced in the presence of synaptic blockers by using current injections to simulate complex spike depolarizations, revealing that CF-evoked changes in Purkinje cell output can occur independently of network activation. Rather postsynaptic changes are sufficient to account for the CF-evoked block of trimodal activity and include at least the activation of Ca(2+)-dependent K(+) channels. Furthermore by controlling the frequency of Purkinje cell spike output over three discrete firing levels, CF discharge modulates the gain of Purkinje cell responsiveness to PF inputs in vitro through postsynaptic mechanisms triggered by the complex spike depolarization. The ability for CF discharge to acutely modulate diverse aspects of Purkinje cell output provides important insights into the probable cellular factors contributing to motor disturbances following CF denervation.

Residual Bound Ca2+ Can Account for the Effects of Ca2+ Buffers on Synaptic Facilitation

Facilitation is a transient stimulation-induced increase in synaptic response, a ubiquitous form of short-term synaptic plasticity that can regulate synaptic transmission on fast time scales. In their pioneering work, Katz and Miledi and Rahamimoff demonstrated the dependence of facilitation on presynaptic Ca2+ influx and proposed that facilitation results from the accumulation of residual Ca2+ bound to vesicle release triggers. However, this bound Ca2+ hypothesis appears to contradict the evidence that facilitation is reduced by exogenous Ca2+ buffers. This conclusion led to a widely held view that facilitation must depend solely on the accumulation of Ca2+ in free form. Here we consider a more realistic implementation of the bound Ca2+ mechanism, taking into account spatial diffusion of Ca2+, and show that a model with slow Ca2+ unbinding steps can retain sensitivity to free residual Ca2+. We demonstrate that this model agrees with the facilitation accumulation time course and its biphasic decay exhibited by the crayfish inhibitor neuromuscular junction (NMJ) and relies on fewer assumptions than the most recent variants of the free residual Ca2+ hypothesis. Further, we show that the bound Ca2+ accumulation is consistent with Kamiya and Zucker's experimental results, which revealed that photolytic liberation of a fast Ca2+ buffer decreases the synaptic response within milliseconds. We conclude that Ca2+ binding processes with slow unbinding times (tens to hundreds of milliseconds) constitute a viable mechanism of synaptic facilitation at some synapses and discuss the experimental evidence for such a mechanism.

Nitric oxide regulates input specificity of long-term depression and context dependence of cerebellar learning

Recent studies have shown that multiple internal models are acquired in the cerebellum and that these can be switched under a given context of behavior. It has been proposed that long-term depression (LTD) of parallel fiber (PF)–Purkinje cell (PC) synapses forms the cellular basis of cerebellar learning, and that the presynaptically synthesized messenger nitric oxide (NO) is a crucial “gatekeeper” for LTD. Because NO diffuses freely to neighboring synapses, this volume learning is not input-specific and brings into question the biological significance of LTD as the basic mechanism for efficient supervised learning. To better characterize the role of NO in cerebellar learning, we simulated the sequence of electrophysiological and biochemical events in PF–PC LTD by combining established simulation models of the electrophysiology, calcium dynamics, and signaling pathways of the PC. The results demonstrate that the local NO concentration is critical for induction of LTD and for its input specificity. Pre- and postsynaptic coincident firing is not sufficient for a PF–PC synapse to undergo LTD, and LTD is induced only when a sufficient amount of NO is provided by activation of the surrounding PFs. On the other hand, above-adequate levels of activity in nearby PFs cause accumulation of NO, which also allows LTD in neighboring synapses that were not directly stimulated, ruining input specificity. These findings lead us to propose the hypothesis that NO represents the relevance of a given context and enables context-dependent selection of internal models to be updated. We also predict sparse PF activity in vivo because, otherwise, input specificity would be lost.

The cerebellum is essential for coordinated movements. The skills for executing such movements are acquired in modules of the cerebellum, and the appropriate modules in which to store the skill for a certain movement are selected according to the environment, or the context, where the movement is made. We are interested in the molecular mechanisms that enable context-dependent cerebellar learning. In search of the key molecules, we combined established simulation models of Purkinje cells, the only output neurons in the cerebellar cortex, and constructed a new model. Using computer simulation, we found that nitric oxide is likely to have a pivotal role in context-dependent learning. Our simulation also provides insights into how sparse sensory information is coded in the cerebellar cortex. These findings have led us to propose the experimentally testable hypothesis that the relevance of a given context to learning modules is represented by the concentration of nitric oxide.

Analytical solutions for nonlinear cable equations with calcium dynamics. I: Derivations

The interaction between membrane potential and internal calcium concentration plays many important roles in regulating synaptic integration and neuronal firing. In order to gain a better theoretical understanding between the voltage-calcium interaction, a nonlinear cable equation with calcium dynamics is solved analytically. This general reaction-diffusion system represents a model of a cylindrical dendritic segment in which calcium diffuses internally in the presence of buffers, pumps and exchangers, and where ion channels are sparsely distributed over the membrane,in the form of hotspots, acting as point current sources along the dendritic membrane. In order to proceed, the reaction-diffusion system is recast into a system of coupled nonlinear integral equations, with which a perturbative expansion in dimensionless voltage and calcium concentration are used to find analytical solutions to this general system. The resulting solutions can be used to investigate, the interaction between the membrane potential and underlying calcium dynamics in a natural (non-discretized) setting.

Deficiency in parvalbumin, but not in calbindin D-28k upregulates mitochondrial volume and decreases smooth endoplasmic reticulum surface selectively in a peripheral, subplasmalemmal region in the soma of Purkinje cells

The Ca(2+)-binding proteins parvalbumin (PV) and calbindin D-28k (CB) are key players in the intracellular Ca(2+)-buffering in specific cells including neurons and have profound effects on spatiotemporal aspects of Ca(2+) transients. The previously observed increase in mitochondrial volume density in fast-twitch muscle of PV-/- mice is viewed as a specific compensation mechanism to maintain Ca(2+) homeostasis. Since cerebellar Purkinje cells (PC) are characterized by high expression levels of the Ca(2+) buffers PV and CB, the question was raised, whether homeostatic mechanisms are induced in PC lacking these buffers. Mitochondrial volume density, i.e. relative mitochondrial mass was increased by 40% in the soma of PV-/- PC. Upregulation of mitochondrial volume density was not homogenous throughout the soma, but was selectively restricted to a peripheral region of 1.5 microm width underneath the plasma membrane. Accompanied was a decreased surface of subplasmalemmal smooth endoplasmic reticulum (sPL-sER) in a shell of 0.5 microm thickness underneath the plasma membrane. These alterations were specific for the absence of the "slow-onset" buffer PV, since in CB-/- mice neither changes in peripheral mitochondria nor in sPL-sER were observed. This implicates that the morphological alterations are aimed to specifically substitute the function of the slow buffer PV. We propose a novel concept that homeostatic mechanisms of components involved in Ca(2+) homeostasis do not always occur at the level of similar or closely related molecules. Rather the cell attempts to restore spatiotemporal aspects of Ca(2+) signals prevailing in the undisturbed (wildtype) situation by subtly fine tuning existing components involved in the regulation of Ca(2+) fluxes.

Malleability of spike-timing-dependent plasticity at the CA3-CA1 synapse

The magnitude and direction of synaptic plasticity can be determined by the precise timing of presynaptic and postsynaptic action potentials on a millisecond timescale. In vivo, however, neural activity has structure on longer timescales. Here we show that plasticity at the CA3-CA1 synapse depends strongly on parameters other than millisecond spike timing. As a result, the notion that a single spike-timing-dependent plasticity (STDP) rule alone can fully describe the mapping between neural activity and synapse strength is invalid. We have begun to explore the influence of additional behaviorally relevant activity parameters on STDP and found conditions under which underlying spike-timing-dependent rules for potentiation and depression can be separated from one another. Potentiation requires postsynaptic burst firing at 5 Hz or higher, a firing pattern that occurs during the theta rhythm. Potentiation is measurable after only tens of presynaptic-before-postsynaptic pairings. Depression requires hundreds of pairings but has less stringent long timescale requirements and broad timing dependence. By varying these parameters, we obtain STDP curves that are long-term potentiation only, bidirectional, or long-term depression only. This expanded description of the CA3-CA1 learning rule reconciles apparent contradictions between spike-timing-dependent plasticity and previous work at CA3-CA1 synapses.