David D. Friel

[Ca2+]i oscillations in sympathetic neurons: an experimental test of a theoretical model

[Ca2+]i oscillations have been described in a variety of cells. This study focuses on caffeine-induced [Ca2+]i oscillations in sympathetic neurons. Previous work has shown that these oscillations require Ca2+ entry from the extracellular medium and Ca(2+)-induced Ca2+ release from a caffeine- and ryanodine-sensitive store. The aim of the study was to understand the mechanism responsible for the oscillations. As a starting point, [Ca2+]i relaxations were examined after membrane depolarization and exposure to caffeine. For both stimuli, post-stimulus relaxations could be described by the sum of two decaying exponential functions, consistent with a one-pool system in which Ca2+ transport between compartments is regulated by linear Ca2+ pumps and leaks. After modifying the store to include a [Ca2+]i-sensitive leak, the model also exhibits oscillations such as those observed experimentally. The model was tested by comparing measured and predicted net Ca2+ fluxes during the oscillatory cycle. Three independent fluxes were measured, describing the rates of 1) Ca2+ entry across the plasma membrane, 2) Ca2+ release by the internal store, and 3) Ca2+ extrusion across the plasma membrane and uptake by the internal store. Starting with estimates of the model parameters deduced from post-stimulus relaxations and the rapid upstroke, a set of parameter values was found that provides a good description of [Ca2+]i throughout the oscillatory cycle. With the same parameter values, there was also good agreement between the measured and simulated net fluxes. Thus, a one-pool model with a single [Ca2+]i-sensitive Ca2+ permeability is adequate to account for many of the quantitative properties of steady-state [Ca2+]i oscillations in sympathetic neurons. Inactivation of the intracellular Ca2+ permeability, cooperative nonlinear Ca2+ uptake and extrusion mechanisms, and functional links between plasma membrane Ca2+ transport and the internal store are not required.

Calcium dynamics : analyzing the Ca2+ regulatory network in intact cells

Calcium signaling is critical for all cells. As a free ion (Ca(2+)), calcium links many physiological stimuli to their intracellular effectors by interacting with binding proteins whose occupancy determines the cellular effect of stimulation. Because binding site occupancy depends on the history of Ca(2+) concentration ([Ca(2+)]), Ca(2+) dynamics are critical. Calcium dynamics depend on the functional interplay between Ca(2+) transport and buffering systems whose activities depend nonlinearly on [Ca(2+)]. Thus, understanding Ca(2+) dynamics requires detailed information about these Ca(2+) handling systems and their regulation in intact cells. However, effective methods for measuring and characterizing intracellular Ca(2+) handling have not been available until recently. Using concepts relating voltage-gated ion-channel activity to membrane potential dynamics, we developed such methods to analyze Ca(2+) fluxes in intact cells. Here we describe this approach and applications to understanding depolarization-induced Ca(2+) responses in sympathetic neurons.

Differential Regulation of ER Ca2+ Uptake and Release Rates Accounts for Multiple Modes of Ca2+-induced Ca2+ Release

The ER is a central element in Ca2+ signaling, both as a modulator of cytoplasmic Ca2+ concentration ([Ca2+]i) and as a locus of Ca2+-regulated events. During surface membrane depolarization in excitable cells, the ER may either accumulate or release net Ca2+, but the conditions of stimulation that determine which form of net Ca2+ transport occurs are not well understood. The direction of net ER Ca2+ transport depends on the relative rates of Ca2+ uptake and release via distinct pathways that are differentially regulated by Ca2+, so we investigated these rates and their sensitivity to Ca2+ using sympathetic neurons as model cells. The rate of Ca2+ uptake by SERCAs (JSERCA), measured as the t-BuBHQ-sensitive component of the total cytoplasmic Ca2+ flux, increased monotonically with [Ca2+]i. Measurement of the rate of Ca2+ release (JRelease) during t-BuBHQ-induced [Ca2+]i transients made it possible to characterize the Ca2+ permeability of the ER (\documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}\overline{{\mathrm{P}}}_{{\mathrm{ER}}}\end{equation*}\end{document}), describing the activity of all Ca2+-permeable channels that contribute to passive ER Ca2+ release, including ryanodine-sensitive Ca2+ release channels (RyRs) that are responsible for CICR. Simulations based on experimentally determined descriptions of JSERCA, \documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}\overline{{\mathrm{P}}}_{{\mathrm{ER}}}\end{equation*}\end{document}, and of Ca2+ extrusion across the plasma membrane (Jpm) accounted for our previous finding that during weak depolarization, the ER accumulates Ca2+, but at a rate that is attenuated by activation of a CICR pathway operating in parallel with SERCAs to regulate net ER Ca2+ transport. Caffeine greatly increased the [Ca2+] sensitivity of \documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}\overline{{\mathrm{P}}}_{{\mathrm{ER}}}\end{equation*}\end{document}, accounting for the effects of caffeine on depolarization-evoked [Ca2+]i elevations and caffeine-induced [Ca2+]i oscillations. Extending the rate descriptions of JSERCA, \documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}\overline{{\mathrm{P}}}_{{\mathrm{ER}}}\end{equation*}\end{document}, and Jpm to higher [Ca2+]i levels shows how the interplay between Ca2+ transport systems with different Ca2+ sensitivities accounts for the different modes of CICR over different ranges of [Ca2+]i during stimulation.

TRP: Its Role in Phototransduction and Store-Operated Ca2+ Entry

Perhaps the best characterized SOC is the CRAC (Ca2+-release activated Ca2+) channel described in several cell types, including mast cells (Hoth and Penner 1992xHoth, M and Penner, R. Nature. 1992; 355: 353–356Crossref | PubMed | Scopus (1131)See all ReferencesHoth and Penner 1992) and T lymphocytes (Zweifach and Lewis 1993xZweifach, A and Lewis, R.S. Proc. Natl. Acad. Sci. USA. 1993; 90: 6295–6299Crossref | PubMedSee all ReferencesZweifach and Lewis 1993). It is highly selective for Ca2+ (PCa/PNa ∼ 1000), has a small unitary conductance (∼24 fS in 110 mM Ca2+) and exhibits gating kinetics that depend on Ca2+ (Lewis et al. 1996xSee all ReferencesLewis et al. 1996). Another SOC described in A431 cells is selective for Ba2+ over Ca2+ and exhibits a higher unitary conductance (2 pS in the presence of 200 mM Ca2+) (Clapham 1995xClapham, D.E. Cell. 1995; 80: 259–268Abstract | Full Text PDF | PubMed | Scopus (1958)See all ReferencesClapham 1995). What is the relationship between these channels and TRP? Although detailed biophysical information is not available for TRP due to the difficulty of measuring currents across the microvillar membrane, differences in Ca2+ selectivity alone would suggest that if trp encodes a channel, it is probably different from the CRAC channel. SOCs may be members of a broad family of ion channels with different permeation properties and sensitivity to stimulation; differences between TRP and TRPL illustrate the potential for functional diversity within this putative ion-channel family. If TRP and TRPL function as ion channels, it will be important to understand their subunit organization, in particular whether they form homomeric or heteromeric channels.With respect to the role of TRP in Drosophila photoreception, there are several possibilities. TRP could act as a SOC opened by a drop in intraluminal free Ca2+ concentration during phototransduction. This leads to at least two predictions: first, that light stimulation should release Ca2+ from internal stores, and second that depletion of stores should increase membrane conductance. Recent reports suggest that neither holds true: light-induced currents can be elicited in the absence of external Ca2+ without a rise in [Ca2+]i, and thapsigargin releases intracellular Ca2+ without stimulating a LIC (15xRanganathan, R, Malicki, D.M, and Zuker, C.S. Ann. Rev. Neurosci. 1995; 18: 283–317Crossref | PubMedSee all References, 6xHardie, R.C. J. Neurosci. 1996; 16: 2924–2933PubMedSee all References). Of course, this may reflect limited detection of localized [Ca2+]i elevations or an inability to rapidly discharge Ca2+ from the relevant pools (Hardie and Minke 1995xHardie, R.C and Minke, B. Cell Calcium. 1995; 18: 256–274Crossref | PubMed | Scopus (100)See all ReferencesHardie and Minke 1995). Another possibility is that TRP works as a SOC in the direct coupling mode through interactions with the InsP3 receptor (or some other component of the submicrovillar cisternae) to link PLC activation to channel opening. However, either model must address how light absorption in the distal microvillar membrane is communicated to the submicrovillar cisternae and back again over a distance of ∼0.5–1.0 μm with sufficient speed to account for the LIC latency (∼20 ms). Finally, it is possible that TRP is activated directly by one of the many potential signaling compounds generated by PLC.

The leaner P/Q-type calcium channel mutation renders cerebellar Purkinje neurons hyper-excitable and eliminates Ca2+-Na+ spike bursts

The leaner mouse mutation of the Cacna1a gene leads to a reduction in P‐type Ca2+ current, the dominant Ca2+ current in Purkinje cells (PCs). Here, we compare the electro‐responsiveness and structure of PCs from age‐matched leaner and wild‐type (WT) mice in pharmacological isolation from synaptic inputs in cerebellar slices. We report that compared with WT, leaner PCs exhibit lower current threshold for Na+ spike firing, larger subthreshold membrane depolarization, rapid adaptation followed by complete block of Na+ spikes upon strong depolarization, and fail to generate Ca2+‐Na+ spike bursts. The Na+ spike waveforms in leaner PCs have slower kinetics, reduced spike amplitude and afterhyperpolarization. We show that a deficit in the P‐type Ca2+ current caused by the leaner mutation accounts for most but not all of the changes in mutant PC electro‐responsiveness. The selective P‐type Ca2+ channel blocker, ω‐agatoxin‐IVA, eliminated differences in subthreshold membrane depolarization, adaptation of Na+ spikes upon strong current‐pulse stimuli, Na+ spike waveforms and Ca2+‐Na+ burst activity. In contrast, a lower current threshold for eliciting repetitive Na+ spikes in leaner PCs was still observed after blockade of the P‐type Ca2+ current, suggesting secondary effects of the mutation that render PCs hyper‐excitable. Higher input resistance, reduced whole‐cell capacitance and smaller dendritic size accompanied the enhanced excitability in leaner PCs, indicative of developmental retardation in these cells caused by P/Q‐type Ca2+ channel malfunction. Our data indicate that a deficit in P‐type Ca2+ current leads to complex functional and structural changes in PCs, impairing their intrinsic and integrative properties.

Depolarization-induced calcium responses in sympathetic neurons: relative contributions from Ca2+ entry, extrusion, ER/mitochondrial Ca2+ uptake and release, and Ca2+ buffering.

Many models have been developed to account for stimulus-evoked [Ca2+] responses, but few address how responses elicited in specific cell types are defined by the Ca2+ transport and buffering systems that operate in the same cells. In this study, we extend previous modeling studies by linking the time course of stimulus-evoked [Ca2+] responses to the underlying Ca2+ transport and buffering systems. Depolarization-evoked [Ca2+]i responses were studied in sympathetic neurons under voltage clamp, asking how response kinetics are defined by the Ca2+ handling systems expressed in these cells. We investigated five cases of increasing complexity, comparing observed and calculated responses deduced from measured Ca2+ handling properties. In Case 1, [Ca2+]i responses were elicited by small Ca2+ currents while Ca2+ transport by internal stores was inhibited, leaving plasma membrane Ca2+ extrusion intact. In Case 2, responses to the same stimuli were measured while mitochondrial Ca2+ uptake was active. In Case 3, responses were elicited as in Case 2 but with larger Ca2+ currents that produce larger and faster [Ca2+]i elevations. Case 4 included the mitochondrial Na/Ca exchanger. Finally, Case 5 included ER Ca2+ uptake and release pathways. We found that [Ca2+]i responses elicited by weak stimuli (Cases 1 and 2) could be quantitatively reconstructed using a spatially uniform model incorporating the measured properties of Ca2+ entry, removal, and buffering. Responses to strong depolarization (Case 3) could not be described by this model, but were consistent with a diffusion model incorporating the same Ca2+ transport and buffering descriptions, as long as endogenous buffers have low mobility, leading to steep radial [Ca2+]i gradients and spatially nonuniform Ca2+ loading by mitochondria. When extended to include mitochondrial Ca2+ release (Case 4) and ER Ca2+ transport (Case 5), the diffusion model could also account for previous measurements of stimulus-evoked changes in total mitochondrial and ER Ca concentration.

Impact of the leaner P/Q‐type Ca2+ channel mutation on excitatory synaptic transmission in cerebellar Purkinje cells

Loss‐of‐function mutations in the gene encoding P/Q‐type Ca2+ channels cause cerebellar ataxia in mice and humans, but the underlying mechanism(s) are unknown. These Ca2+ channels play important roles in regulating both synaptic transmission and intrinsic membrane properties, and defects in either could contribute to ataxia. Our previous work described changes in intrinsic properties and excitability of cerebellar Purkinje cells (PCs) resulting from the leaner mutation, which is known to reduce whole‐cell Ca2+ currents in PCs and cause severe ataxia. Here we describe the impact of this mutation on excitatory synaptic transmission from parallel and climbing fibres (PFs, CFs) to PCs in acute cerebellar slices. We found that in leaner PCs, PF‐evoked excitatory postsynaptic currents (PF‐EPSCs) are ∼50% smaller, and CF‐evoked EPSCs are ∼80% larger, than in wild‐type (WT) mice. To investigate whether reduced presynaptic Ca2+ entry plays a role in attenuating PF‐EPSCs in leaner mice, we examined paired‐pulse facilitation (PPF). We found that PPF is enhanced in leaner, suggesting that reduced presynaptic Ca2+ entry reduces neurotransmitter release at these synapses. Short‐term plasticity was unchanged at CF–PC synapses, suggesting that CF‐EPSCs are larger in leaner PCs because of increased synapse number or postsynaptic sensitivity, rather than enhanced presynaptic Ca2+ entry. To investigate the functional impact of the observed EPSC changes, we also compared excitatory postsynaptic potentials (EPSPs) elicited by PF and CF stimulation in WT and leaner PCs. Importantly, we found that despite pronounced changes in PF‐ and CF‐EPSCs, evoked EPSPs in leaner mice are very similar to those observed in WT animals. These results suggest that changes in synaptic currents and intrinsic properties of PCs produced by the leaner mutation together maintain PC responsiveness to excitatory synaptic inputs. They also implicate other consequences of the leaner mutation as causes of abnormal cerebellar motor control in mutant mice.

Enhanced Synaptic Inhibition Disrupts the Efferent Code of Cerebellar Purkinje Neurons in Leaner Cav2.1 Ca2+ Channel Mutant Mice

Cerebellar Purkinje cells (PCs) encode afferent information in the rate and temporal structure of their spike trains. Both spontaneous firing in these neurons and its modulation by synaptic inputs depend on Ca2+ current carried by Cav2.1 (P/Q) type channels. Previous studies have described how loss-of-function Cav2.1 mutations affect intrinsic excitability and excitatory transmission in PCs. This study examines the effects of the leaner mutation on fast GABAergic transmission and its modulation of spontaneous firing in PCs. The leaner mutation enhances spontaneous synaptic inhibition of PCs, leading to transitory reductions in PC firing rate and increased spike rate variability. Enhanced inhibition is paralleled by an increase in the frequency and amplitude of spontaneous inhibitory postsynaptic currents (sIPSCs) measured under voltage clamp. These differences are abolished by tetrodotoxin, implicating effects of the mutation on spike-induced GABA release. Elevated sIPSC frequency in leaner PCs is not accompanied by increased mean firing rate in molecular layer interneurons, but IPSCs evoked in PCs by direct stimulation of these neurons exhibit larger amplitude, slower decay rate, and a higher burst probability compared to wild-type PCs. Ca2+ release from internal stores appears to be required for enhanced inhibition since differences in sIPSC frequency and amplitude in leaner and wild-type PCs are abolished by thapsigargin, an ER Ca2+ pump inhibitor. These findings represent the first account of the functional consequences of a loss-of-function P/Q channel mutation on PC firing properties through altered GABAergic transmission. Gain in synaptic inhibition shown here would compromise the fidelity of information coding in these neurons and may contribute to impaired cerebellar function resulting from loss-of function mutations in the CaV2.1 channel gene.

Chronic impairment of ERK signaling in glutamatergic neurons of the forebrain does not affect spatial memory retention and LTP in the same manner as acute blockade of the ERK pathway

The ERK/MAPK signaling pathway has been extensively studied in the context of learning and memory. Defects in this pathway underlie genetic diseases associated with intellectual disability, including impaired learning and memory. Numerous studies have investigated the impact of acute ERK/MAPK inhibition on long‐term potentiation and spatial memory. However, genetic knockouts of the ERKs have not been utilized to determine whether developmental perturbations of ERK/MAPK signaling affect LTP and memory formation in postnatal life. In this study, two different ERK2 conditional knockout mice were generated that restrict loss of ERK2 to excitatory neurons in the forebrain, but at different time‐points (embryonically and post‐natally). We found that embryonic loss of ERK2 had minimal effect on spatial memory retention and novel object recognition, while loss of ERK2 post‐natally had more pronounced effects in these behaviors. Loss of ERK2 in both models showed intact LTP compared to control animals, while loss of both ERK1 and ERK2 impaired late phase LTP. These findings indicate that ERK2 is not necessary for LTP and spatial memory retention and provide new insights into the functional deficits associated with the chronic impairment of ERK signaling.

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.