Quantitative aspects of L-type Ca2+ currents

A model of zinc dynamics evoked by intense stimulation at the cleft of hippocampal mossy fiber synapses

Zinc is a transition metal that is particularly abundant in the mossy fibers of the hippocampal CA3 area. Despite the large number of studies about the zinc role in mossy fibers, the action of zinc in synaptic mechanisms is only partly known. The use of computational models can be a useful tool for this study. In a previous work, a model was developed to evaluate zinc dynamics at the mossy fiber synaptic cleft, following weak stimulation, insufficient to evoke zinc entry into postsynaptic neurons. For intense stimulation, cleft zinc effluxes must be considered. Therefore, the initial model was extended to include postsynaptic zinc effluxes based on the Goldman-Hodgkin-Katz current equation combined with Hodgkin and Huxley conductance changes. These effluxes occur through different postsynaptic escape routes, namely L- and N-types voltage-dependent calcium channels and NMDA receptors. For that purpose, various stimulations were assumed to induce high concentrations of cleft free zinc, named as intense (10 μM), very intense (100 μM) and extreme (500 μM). It was observed that the main postsynaptic escape routes of cleft zinc are the L-type calcium channels, followed by the NMDA receptor channels and by N-type calcium channels. However, their relative contribution for cleft zinc clearance was relatively small and decreased for higher amounts of zinc, most likely due to the blockade action of zinc in postsynaptic receptors and channels. Therefore, it can be concluded that the larger the zinc release, the more predominant the zinc uptake process will be in the cleft zinc clearance.

Synaptic Plasticity Is Predicted by Spatiotemporal Firing Rate Patterns and Robust to In Vivo-like Variability

Synaptic plasticity, the experience-induced change in connections between neurons, underlies learning and memory in the brain. Most of our understanding of synaptic plasticity derives from in vitro experiments with precisely repeated stimulus patterns; however, neurons exhibit significant variability in vivo during repeated experiences. Further, the spatial pattern of synaptic inputs to the dendritic tree influences synaptic plasticity, yet is not considered in most synaptic plasticity rules. Here, we investigate how spatiotemporal synaptic input patterns produce plasticity with in vivo-like conditions using a data-driven computational model with a plasticity rule based on calcium dynamics. Using in vivo spike train recordings as inputs to different size clusters of spines, we show that plasticity is strongly robust to trial-to-trial variability of spike timing. In addition, we derive general synaptic plasticity rules describing how spatiotemporal patterns of synaptic inputs control the magnitude and direction of plasticity. Synapses that strongly potentiated have greater firing rates and calcium concentration later in the trial, whereas strongly depressing synapses have hiring firing rates early in the trial. The neighboring synaptic activity influences the direction and magnitude of synaptic plasticity, with small clusters of spines producing the greatest increase in synaptic strength. Together, our results reveal that calcium dynamics can unify diverse plasticity rules and reveal how spatiotemporal firing rate patterns control synaptic plasticity.

Dopamine Oppositely Modulates State Transitions in Striosome and Matrix Direct Pathway Striatal Spiny Neurons

Corticostriatal synaptic integration is partitioned among striosome (patch) and matrix compartments of the dorsal striatum, allowing compartmentalized control of discrete aspects of behavior. Despite the significance of such organization, it's unclear how compartment-specific striatal output is dynamically achieved, particularly considering new evidence that overlap of afferents is substantial. We show that dopamine oppositely shapes responses to convergent excitatory inputs in mouse striosome and matrix striatal spiny projection neurons (SPNs). Activation of postsynaptic D1 dopamine receptors promoted the generation of long-lasting synaptically evoked "up-states" in matrix SPNs but opposed it in striosomes, which were more excitable under basal conditions. Differences in dopaminergic modulation were mediated, in part, by dendritic voltage-gated calcium channels (VGCCs): pharmacological manipulation of L-type VGCCs reversed compartment-specific responses to D1 receptor activation. These results support a novel mechanism for the selection of striatal circuit components, where fluctuating levels of dopamine shift the balance of compartment-specific striatal output.

Electrophysiological models of the human pancreatic δ-cell: From single channels to the firing of action potentials

Minimal mathematical models were developed to describe the electrophysiological properties of human δ-cells. Markov models of single channels were first developed based on the analysis of electrophysiological data. Monte Carlo simulations of voltage-clamp experiments were performed in an iteratively optimization procedure to estimate the number of channels required to reproduce the main characteristics of the macroscopic currents recorded experimentally. A membrane model of the firing of action potentials was then developed based on the kinetic schemes of single channels and the number of channels estimated. We showed that macroscopic currents of human δ-cells can be reproduced by minimal models of single channels when the appropriate number of channels is considered. In addition, our simulations suggest that human δ-cells are capable of generating action potentials through the interaction of the ionic currents involved. Finally, we determined the relative contribution of the currents underlying the firing of action potentials in human pancreatic δ-cells, which allowed us to propose a qualitative model of an action potential in terms of the underlying ionic currents.

Location Specificity of Transcranial Electrical Stimulation on Neuronal Electrodynamics: A Mathematical Model of Ion Channel Gating Dynamics and Ionic Flux Due to Neurostimulation

Transcranial Electrical Stimulation (TES) continues to demonstrate success as a medical intervention for individuals with neurodegenerative diseases. Despite promising results from these neuromodulation modalities, the cellular level mechanisms by which this neurotherapy operates are not fully comprehended. In particular, the effects of TES on ion channel gating and ion transport are not known. Using the Poisson-Nernst-Planck model of electrodiffusion, coupled with a Hodgkin-Huxley based model of cellular ion transport, we present a model of TES that, for the first time, integrates electric potential energy, individualized ion species, voltage-gated ion channels, and transmembrane ionic flux during TES administration. Computational simulations are executed on a biologically-inspired domain with medically-based TES treatment parameters and quantify neuron-level electrical processes resulting from this form of neurostimulation. Results confirm prior findings that show that TES polarizes the cell membrane, however, these are extended as simulations in this paper show that polarization occurs in a location specific manner, where the type and degree of polarization depends on the position on the membrane within a node of Ranvier. In addition, results demonstrate that TES causes ion channel gating variables to change in a location specific fashion and, as a result, transmembrane current from distinct ion species depends on both time and membrane location. Another simulation finding is that intracellular calcium concentrations increase significantly due to a TES-induced calcium influx. As cytosolic calcium is critical in intracellular signaling pathways that govern proper neurotransmitter secretion as well as support cell viability, this alteration in calcium homeostasis suggests a possible mechanism by which TES operates at the neuronal level to achieve neurotherapeutic success.

Inhibition enhances spatially-specific calcium encoding of synaptic input patterns in a biologically constrained model

Synaptic plasticity, which underlies learning and memory, depends on calcium elevation in neurons, but the precise relationship between calcium and spatiotemporal patterns of synaptic inputs is unclear. Here, we develop a biologically realistic computational model of striatal spiny projection neurons with sophisticated calcium dynamics, based on data from rodents of both sexes, to investigate how spatiotemporally clustered and distributed excitatory and inhibitory inputs affect spine calcium. We demonstrate that coordinated excitatory synaptic inputs evoke enhanced calcium elevation specific to stimulated spines, with lower but physiologically relevant calcium elevation in nearby non-stimulated spines. Results further show a novel and important function of inhibition-to enhance the difference in calcium between stimulated and non-stimulated spines. These findings suggest that spine calcium dynamics encode synaptic input patterns and may serve as a signal for both stimulus-specific potentiation and heterosynaptic depression, maintaining balanced activity in a dendritic branch while inducing pattern-specific plasticity.

Neuritin promotes neurite and spine growth in rat cerebellar granule cells via L-type calcium channel-mediated calcium influx

Neuritin is a neurotrophic factor that is activated by neural activity and neurotrophins. Its major function is to promote neurite growth and branching; however, the underlying mechanisms are not fully understood. To address this issue, this study investigated the effects of neuritin on neurite and spine growth and intracellular Ca²⁺ concentration in rat cerebellar granule neurons (CGNs). Incubation of CGNs for 24 h with neuritin increased neurite length and spine density; this effect was mimicked by insulin and abolished by inhibiting insulin receptor (IR) or mitogen‐activated protein kinase kinase/extracellular signal‐regulated kinase (ERK) activity. Calcium imaging and western blot analysis revealed that neuritin enhanced the increase in intracellular Ca²⁺ level induced by high K⁺, and stimulated the cell surface expression of Ca_V1.2 and Ca_V1.3 α subunits of the L‐type calcium channel, which was suppressed by inhibition of IR or mitogen‐activated protein kinase kinase/ERK. Treatment with inhibitors of L‐type calcium channels, calmodulin, and calcineurin (CaN) abrogated the effects of neuritin on neurite length and spine density. A similar result was obtained by silencing nuclear factor of activated T cells c4, which is known to be activated by neuritin in CGNs. These results indicate that IR and ERK signaling as well as the Ca²⁺/CaN/nuclear factor of activated T cells c4 axis mediate the effects of neuritin on neurite and spine growth in CGNs.

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Cover Image for this issue: doi: 10.1111/jnc.14195.

Biophysical attributes that affect CaMKII activation deduced with a novel spatial stochastic simulation approach

Calcium/calmodulin-dependent protein kinase II (CaMKII) holoenzymes play a critical role in decoding Ca2+ signals in neurons. Understanding how this occurs has been the focus of numerous studies including many that use models. However, CaMKII is notoriously difficult to simulate in detail because of its multi-subunit nature, which causes a combinatorial explosion in the number of species that must be modeled. To study the Ca2+-calmodulin-CaMKII reaction network with detailed kinetics while including the effect of diffusion, we have customized an existing stochastic particle-based simulator, Smoldyn, to manage the problem of combinatorial explosion. With this new method, spatial and temporal aspects of the signaling network can be studied without compromising biochemical details. We used this new method to examine how calmodulin molecules, both partially loaded and fully loaded with Ca2+, choose pathways to interact with and activate CaMKII under various Ca2+ input conditions. We found that the dependence of CaMKII phosphorylation on Ca2+ signal frequency is intrinsic to the network kinetics and the activation pattern can be modulated by the relative amount of Ca2+ to calmodulin and by the rate of Ca2+ diffusion. Depending on whether Ca2+ influx is saturating or not, calmodulin molecules could choose different routes within the network to activate CaMKII subunits, resulting in different frequency dependence patterns. In addition, the size of the holoenzyme produces a subtle effect on CaMKII activation. The more extended the subunits are organized, the easier for calmodulin molecules to access and activate the subunits. The findings suggest that particular intracellular environmental factors such as crowding and calmodulin availability can play an important role in decoding Ca2+ signals and can give rise to distinct CaMKII activation patterns in dendritic spines, Ca2+ channel nanodomains and cytoplasm.

Enhanced Sensitivity to Hyperpolarizing Inhibition in Mesoaccumbal Relative to Nigrostriatal Dopamine Neuron Subpopulations

Midbrain dopamine neurons recorded in vivo pause their firing in response to reward omission and aversive stimuli. While the initiation of pauses typically involves synaptic or modulatory input, intrinsic membrane properties may also enhance or limit hyperpolarization, raising the question of how intrinsic conductances shape pauses in dopamine neurons. Using retrograde labeling and electrophysiological techniques combined with computational modeling, we examined the intrinsic conductances that shape pauses evoked by current injections and synaptic stimulation in subpopulations of dopamine neurons grouped according to their axonal projections to the nucleus accumbens or dorsal striatum in mice. Testing across a range of conditions and pulse durations, we found that mesoaccumbal and nigrostriatal neurons differ substantially in rebound properties with mesoaccumbal neurons displaying significantly longer delays to spiking following hyperpolarization. The underlying mechanism involves an inactivating potassium (I_A) current with decay time constants of up to 225 ms, and small-amplitude hyperpolarization-activated currents (I_H), characteristics that were most often observed in mesoaccumbal neurons. Pharmacological block of I_A completely abolished rebound delays and, importantly, shortened synaptically evoked inhibitory pauses, thereby demonstrating the involvement of A-type potassium channels in prolonging pauses evoked by GABAergic inhibition. Therefore, these results show that mesoaccumbal and nigrostriatal neurons display differential responses to hyperpolarizing inhibitory stimuli that favors a higher sensitivity to inhibition in mesoaccumbal neurons. These findings may explain, in part, observations from in vivo experiments that ventral tegmental area neurons tend to exhibit longer aversive pauses relative to SNc neurons.SIGNIFICANCE STATEMENT Our study examines rebound, postburst, and synaptically evoked inhibitory pauses in subpopulations of midbrain dopamine neurons. We show that pauses in dopamine neuron firing, evoked by either stimulation of GABAergic inputs or hyperpolarizing current injections, are enhanced by a subclass of potassium conductances that are recruited at voltages below spike threshold. Importantly, A-type potassium currents recorded in mesoaccumbal neurons displayed substantially slower inactivation kinetics, which, combined with weaker expression of hyperpolarization-activated currents, lengthened hyperpolarization-induced delays in spiking relative to nigrostriatal neurons. These results suggest that input integration differs among dopamine neurons favoring higher sensitivity to inhibition in mesoaccumbal neurons and may partially explain in vivo observations that ventral tegmental area neurons exhibit longer aversive pauses relative to SNc neurons.

Models of utricular bouton afferents: role of afferent-hair cell connectivity in determining spike train regularity

Vestibular bouton afferent terminals in turtle utricle can be categorized into four types depending on their location and terminal arbor structure: lateral extrastriolar (LES), striolar, juxtastriolar, and medial extrastriolar (MES). The terminal arbors of these afferents differ in surface area, total length, collecting area, number of boutons, number of bouton contacts per hair cell, and axon diameter (Huwe JA, Logan CJ, Williams B, Rowe MH, Peterson EH. J Neurophysiol 113: 2420-2433, 2015). To understand how differences in terminal morphology and the resulting hair cell inputs might affect afferent response properties, we modeled representative afferents from each region, using reconstructed bouton afferents. Collecting area and hair cell density were used to estimate hair cell-to-afferent convergence. Nonmorphological features were held constant to isolate effects of afferent structure and connectivity. The models suggest that all four bouton afferent types are electrotonically compact and that excitatory postsynaptic potentials are two to four times larger in MES afferents than in other afferents, making MES afferents more responsive to low input levels. The models also predict that MES and LES terminal structures permit higher spontaneous firing rates than those in striola and juxtastriola. We found that differences in spike train regularity are not a consequence of differences in peripheral terminal structure, per se, but that a higher proportion of multiple contacts between afferents and individual hair cells increases afferent firing irregularity. The prediction that afferents having primarily one bouton contact per hair cell will fire more regularly than afferents making multiple bouton contacts per hair cell has implications for spike train regularity in dimorphic and calyx afferents.NEW & NOTEWORTHY Bouton afferents in different regions of turtle utricle have very different morphologies and afferent-hair cell connectivities. Highly detailed computational modeling provides insights into how morphology impacts excitability and also reveals a new explanation for spike train irregularity based on relative numbers of multiple bouton contacts per hair cell. This mechanism is independent of other proposed mechanisms for spike train irregularity based on ionic conductances and can explain irregularity in dimorphic units and calyx endings.

Calcium dynamics predict direction of synaptic plasticity in striatal spiny projection neurons

The striatum is a major site of learning and memory formation for sensorimotor and cognitive association. One of the mechanisms used by the brain for memory storage is synaptic plasticity - the long-lasting, activity-dependent change in synaptic strength. All forms of synaptic plasticity require an elevation in intracellular calcium, and a common hypothesis is that the amplitude and duration of calcium transients can determine the direction of synaptic plasticity. The utility of this hypothesis in the striatum is unclear in part because dopamine is required for striatal plasticity and in part because of the diversity in stimulation protocols. To test whether calcium can predict plasticity direction, we developed a calcium-based plasticity rule using a spiny projection neuron model with sophisticated calcium dynamics including calcium diffusion, buffering and pump extrusion. We utilized three spike timing-dependent plasticity (STDP) induction protocols, in which postsynaptic potentials are paired with precisely timed action potentials and the timing of such pairing determines whether potentiation or depression will occur. Results show that despite the variation in calcium dynamics, a single, calcium-based plasticity rule, which explicitly considers duration of calcium elevations, can explain the direction of synaptic weight change for all three STDP protocols. Additional simulations show that the plasticity rule correctly predicts the NMDA receptor dependence of long-term potentiation and the L-type channel dependence of long-term depression. By utilizing realistic calcium dynamics, the model reveals mechanisms controlling synaptic plasticity direction, and shows that the dynamics of calcium, not just calcium amplitude, are crucial for synaptic plasticity.

GDF-15 enhances intracellular Ca2+ by increasing Cav1.3 expression in rat cerebellar granule neurons

GDF-15 (growth/differentiation factor 15) is a novel member of the TGF (transforming growth factor)-β superfamily that has critical roles in the central and peripheral nervous systems. We reported previously that GDF-15 increased delayed rectifier outward K⁺ currents and K_v2.1 α subunit expression through TβRII (TGF-β receptor II) to activate Src kinase and Akt/mTOR (mammalian target of rapamycin) signalling in rat CGNs (cerebellar granule neurons). In the present study, we found that treatment of CGNs with GDF-15 for 24 h increased the intracellular Ca²⁺ concentration ([Ca²⁺]_i) in response to membrane depolarization, as determined by Ca²⁺ imaging. Whole-cell current recordings indicated that GDF-15 increased the inward Ca²⁺ current (I_Ca) without altering steady-state activation of Ca²⁺ channels. Treatment with nifedipine, an inhibitor of L-type Ca²⁺ channels, abrogated GDF-15-induced increases in [Ca²⁺]_i and I_Ca. The GDF-15-induced increase in I_Ca was mediated via up-regulation of the Ca_v1.3 α subunit, which was attenuated by inhibiting Akt/mTOR and ERK (extracellular-signal-regulated kinase) pathways and by pharmacological inhibition of Src-mediated TβRII phosphorylation. Given that Ca_v1.3 is not only a channel for Ca²⁺ influx, but also a transcriptional regulator, our data confirm that GDF-15 induces protein expression via TβRII and activation of a non-Smad pathway, and provide novel insight into the mechanism of GDF-15 function in neurons.

Inferring Neuronal Dynamics from Calcium Imaging Data Using Biophysical Models and Bayesian Inference

Calcium imaging has been used as a promising technique to monitor the dynamic activity of neuronal populations. However, the calcium trace is temporally smeared which restricts the extraction of quantities of interest such as spike trains of individual neurons. To address this issue, spike reconstruction algorithms have been introduced. One limitation of such reconstructions is that the underlying models are not informed about the biophysics of spike and burst generations. Such existing prior knowledge might be useful for constraining the possible solutions of spikes. Here we describe, in a novel Bayesian approach, how principled knowledge about neuronal dynamics can be employed to infer biophysical variables and parameters from fluorescence traces. By using both synthetic and in vitro recorded fluorescence traces, we demonstrate that the new approach is able to reconstruct different repetitive spiking and/or bursting patterns with accurate single spike resolution. Furthermore, we show that the high inference precision of the new approach is preserved even if the fluorescence trace is rather noisy or if the fluorescence transients show slow rise kinetics lasting several hundred milliseconds, and inhomogeneous rise and decay times. In addition, we discuss the use of the new approach for inferring parameter changes, e.g. due to a pharmacological intervention, as well as for inferring complex characteristics of immature neuronal circuits.

Calcium imaging of single neurons enables the indirect observation of neuronal dynamics, for example action potential firing. In contrast to the precise timing of spike trains, the calcium trace is temporally rather smeared and measured as a fluorescence trace. Consequently, several methods have been proposed to reconstruct spikes from calcium imaging data. However, a common feature of these methods is that they are not based on the biophysics of how neurons fire spikes and bursts. We propose to introduce well-established biophysical models to create a direct link between neuronal dynamics, e.g. the membrane potential, and fluorescence traces. Using both synthetic and experimental data, we show that this approach not only provides a robust and accurate spike reconstruction but also a reliable inference about the biophysically relevant parameters and variables. This enables novel ways of analyzing calcium imaging experiments in terms of the underlying biophysical quantities.

A novel explanation for observed CaMKII dynamics in dendritic spines with added EGTA or BAPTA

We present a simplified reaction network in a single well-mixed volume that captures the general features of CaMKII dynamics observed during both synaptic input and spine depolarization. Our model can also account for the greater-than-control CaMKII activation observed with added EGTA during depolarization. Calcium input currents are modeled after experimental observations, and existing models of calmodulin and CaMKII autophosphorylation are used. After calibration against CaMKII activation data in the absence of chelators, CaMKII activation dynamics due to synaptic input via n-methyl-d-aspartate receptors are qualitatively accounted for in the presence of the chelators EGTA and BAPTA without additional adjustments to the model. To account for CaMKII activation dynamics during spine depolarization with added EGTA or BAPTA, the model invokes the modulation of CaV2.3 (R-type) voltage-dependent calcium channel (VDCC) currents observed in the presence of EGTA or BAPTA. To our knowledge, this is a novel explanation for the increased CaMKII activation seen in dendritic spines with added EGTA, and suggests that differential modulation of VDCCs by EGTA and BAPTA offers an alternative or complementary explanation for other experimental results in which addition of EGTA or BAPTA produces different effects. Our results also show that a simplified reaction network in a single, well-mixed compartment is sufficient to account for the general features of observed CaMKII dynamics.

Stimulation-induced Ca(2+) influx at nodes of Ranvier in mouse peripheral motor axons

KEY POINTS

In peripheral myelinated axons of mammalian spinal motor neurons, Ca(2+) influx was thought to occur only in pathological conditions such as ischaemia. Using Ca(2+) imaging in mouse large motor axons, we find that physiological stimulation with trains of action potentials transiently elevates axoplasmic [C(2+)] around nodes of Ranvier. These stimulation-induced [Ca(2+)] elevations require Ca(2+) influx, and are partially reduced by blocking T-type Ca(2+) channels (e.g. mibefradil) and by blocking the Na(+)/Ca(2+) exchanger (NCX), suggesting an important contribution of Ca(2+) influx via reverse-mode NCX activity. Acute disruption of paranodal myelin dramatically increases stimulation-induced [Ca(2+)] elevations around nodes by allowing activation of sub-myelin L-type (nimodipine-sensitive) Ca(2+) channels. The Ca(2+) that enters myelinated motor axons during normal activity is likely to contribute to several signalling pathways; the larger Ca(2+) influx that occurs following demyelination may contribute to the axonal degeneration that occurs in peripheral demyelinating diseases. Activity-dependent Ca(2+) signalling is well established for somata and terminals of mammalian spinal motor neurons, but not for their axons. Imaging of an intra-axonally injected fluorescent [Ca(2+)] indicator revealed that during repetitive action potential stimulation, [Ca(2+)] elevations localized to nodal regions occurred in mouse motor axons from ventral roots, phrenic nerve and intramuscular branches. These [Ca(2+)] elevations (∼ 0.1 μm with stimulation at 50 Hz, 10 s) were blocked by removal of Ca(2+) from the extracellular solution. Effects of pharmacological blockers indicated contributions from both T-type Ca(2+) channels and reverse mode Na(+)/Ca(2+) exchange (NCX). Acute disruption of paranodal myelin (by stretch or lysophosphatidylcholine) increased the stimulation-induced [Ca(2+)] elevations, which now included a prominent contribution from L-type Ca(2+) channels. These results suggest that the peri-nodal axolemma of motor axons includes multiple pathways for stimulation-induced Ca(2+) influx, some active in normally-myelinated axons (T-type channels, NCX), others active only when exposed by myelin disruption (L-type channels). The modest axoplasmic peri-nodal [Ca(2+)] elevations measured in intact motor axons might mediate local responses to axonal activation. The larger [Ca(2+) ] elevations measured after myelin disruption might, over time, contribute to the axonal degeneration observed in peripheral demyelinating neuropathies.

Modeling Ca(2+) currents and buffered diffusion of Ca(2+) in human β-cells during voltage clamp experiments

Macroscopic Ca(2+) currents of the human β-cells were characterized using the Hodgkin-Huxley formalism. Expressions describing the Ca(2+)-dependent inactivation process of the L-type Ca(2+) channels in terms of the concentration of Ca(2+) were obtained. By coupling the modeled Ca(2+) currents to a three-dimensional model of buffered diffusion of Ca(2+), we simulated the Ca(2+) transients formed in the immediate vicinity of the cell membrane during voltage clamp experiments performed in high buffering conditions. Our modeling approach allowed us to consider the distribution of the Ca(2+) sources over the cell membrane. The effect of exogenous (EGTA) and endogenous Ca(2+) buffers on the temporal course of the Ca(2+) transients was evaluated. We show that despite the high Ca(2+) buffering capacity, nanodomains are formed in the submembrane space, where a peak Ca(2+) concentration between ∼76 and 143 µM was estimated from our simulations. In addition, the contribution of each Ca(2+) current to the formation of the Ca(2+) nanodomains was also addressed. Here we provide a general framework to incorporate the spatial aspects to the models of the pancreatic β-cell, such as a more detailed and realistic description of Ca(2+) dynamics in response to electrical activity in physiological conditions can be provided by future models.

In Vitro Early Safety Pharmacology Screening: Perspectives Related to Cardiovascular Safety

In vitro screening for cardiovascular safety liabilities of novel drug candidates presents a challenge for the pharmaceutical industry. Such approaches rely on detecting pharmacologic effects on key components of complex integrated system early in drug discovery to define potential safety liabilities. Key to such studies are the concepts of hazard identification vs. risk assessment, drug specificity vs. selectivity, and an appreciation of the challenges faced when attempting to translate in vitro findings to preclinical in vivo as well as clinical effects. This chapter defines some key aspects of early safety pharmacology screening for cardiovascular liabilities, citing studies of two key depolarizing cardiac currents (fast sodium current and L-type calcium current) as examples linked to effects on cardiac conduction and repolarization.

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other psychiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6Hz and 1.2Hz are obtained, but frequencies as high as 6Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.

Psychostimulants, antidepressants and neurokinin-1 receptor antagonists ('motor disinhibitors') have overlapping, but distinct, effects on monoamine transmission: the involvement of L-type Ca2+ channels and implications for the treatment of ADHD

Both psychostimulants and antidepressants target monoamine transporters and, as a consequence, augment monoamine transmission. These two groups of drugs also increase motor activity in preclinical behavioural screens for antidepressants. Substance P-preferring receptor (NK1R) antagonists similarly increase both motor activity in these tests and monoamine transmission in the brain. In this article, the neurochemical and behavioural responses to these three groups of drugs are compared. It becomes evident that NK1R antagonists represent a distinct class of compounds ('motor disinhibitors') that differ substantially from both psychostimulants and antidepressants, especially during states of heightened arousal or stress. Also, all three groups of drugs influence the activation of voltage-gated Ca(v)1.2 and Ca(v)1.3 L-type channels (LTCCs) in the brain, albeit in different ways. This article discusses evidence that points to disruption of these functional interactions between NK1R and LTCCs as a contributing factor in the cognitive and behavioural abnormalities that are prominent features of Attention Deficit Hyperactivity Disorder (ADHD). Arising from this is the interesting possibility that the hyperactivity and impulsivity (as in ADHD) and psychomotor retardation (as in depression) reflect opposite poles of a behavioural continuum. A better understanding of this pharmacological network could help explain why psychostimulants augment motor behaviour during stress (e.g., in preclinical screens for antidepressants) and yet reduce locomotor activity and impulsivity in ADHD. This article is part of the Special Issue entitled 'CNS Stimulants'.

Insulinotropic effect of high potassium concentration beyond plasma membrane depolarization

The question whether K⁺ depolarization is an appropriate experimental substitute for the physiological nutrient-induced depolarization of the β-cell plasma membrane was investigated using primary mouse β-cells and islets. At basal glucose 40 mM K⁺ induced a massive monophasic response, whereas 15 mM K⁺ had only a minimal insulinotropic effect, even though the increase in the cytosolic Ca²⁺ concentration ([Ca²⁺]i) was not inferior to that by 20 mM glucose. In voltage-clamp experiments, Ca²⁺ influx appeared as nifedipine-inhibitable inward action currents in the presence of sulfonylurea plus TEA to block compensatory outward K⁺ currents. Under these conditions, 15 mM K⁺ induced prolonged action currents and 40 mM K⁺ transformed the action current pattern into a continuous inward current. Correspondingly, 15 mM K⁺ led to an oscillatory increase and 40 mM K⁺ to a plateau of [Ca²⁺]i superimposed on the [Ca²⁺]i elevated by sulfonylurea plus TEA. Raising K⁺ to 15 or 40 mM in the presence of sulfonylurea (±TEA) led to a fast further increase of insulin secretion. This was reduced to basal levels by nifedipine or CoCl₂. The effects of 15 mM K⁺ on depolarization, action currents, and insulin secretion were mimicked by adding 35 mM Cs⁺ and those of 40 mM K⁺ by adding 35 mM Rb⁺, in parallel with their ability to substitute for K⁺ as permeant cation. In conclusion, the alkali metals K⁺, Rb⁺, or Cs⁺ concentration-dependently transform the pattern of Ca²⁺ influx into the β-cell and may thus generate stimuli of supraphysiological strength for insulin secretion.

Dendritic spines: the locus of structural and functional plasticity

The introduction of high-resolution time lapse imaging and molecular biological tools has changed dramatically the rate of progress towards the understanding of the complex structure-function relations in synapses of central spiny neurons. Standing issues, including the sequence of molecular and structural processes leading to formation, morphological change, and longevity of dendritic spines, as well as the functions of dendritic spines in neurological/psychiatric diseases are being addressed in a growing number of recent studies. There are still unsettled issues with respect to spine formation and plasticity: Are spines formed first, followed by synapse formation, or are synapses formed first, followed by emergence of a spine? What are the immediate and long-lasting changes in spine properties following exposure to plasticity-producing stimulation? Is spine volume/shape indicative of its function? These and other issues are addressed in this review, which highlights the complexity of molecular pathways involved in regulation of spine structure and function, and which contributes to the understanding of central synaptic interactions in health and disease.

Approaches and tools for modeling signaling pathways and calcium dynamics in neurons

Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.

A novel analysis of excitatory currents during an action potential from suprachiasmatic nucleus neurons

A new application of the action potential (AP) voltage-clamp technique is described based on computational analysis. An experimentally recorded AP is digitized. The resulting Vi vs. ti data set is applied to mathematical models of the ionic conductances underlying excitability for the cell from which the AP was recorded to test model validity. The method is illustrated for APs from suprachiasmatic nucleus (SCN) neurons and the underlying tetrodotoxin-sensitive Na(+) current, INa, and the Ca(2+) current, ICa. Voltage-step recordings have been made for both components from SCN neurons (Jackson et al. 2004). The combination of voltage-step and AP clamp results provides richer constraints for mathematical models of voltage-gated ionic conductances than either set of results alone, in particular the voltage-step results. For SCN neurons the long-term goal of this work is a realistic mathematical model of the SCN AP in which the equations for I(Na) and I(Ca) obtained from this analysis will be a part. Moreover, the method described in this report is general. It can be applied to any excitable cell.

Dynamic modulation of spike timing-dependent calcium influx during corticostriatal upstates

The striatum of the basal ganglia demonstrates distinctive upstate and downstate membrane potential oscillations during slow-wave sleep and under anesthetic. The upstates generate calcium transients in the dendrites, and the amplitude of these calcium transients depends strongly on the timing of the action potential (AP) within the upstate. Calcium is essential for synaptic plasticity in the striatum, and these large calcium transients during the upstates may control which synapses undergo plastic changes. To investigate the mechanisms that underlie the relationship between calcium and AP timing, we have developed a realistic biophysical model of a medium spiny neuron (MSN). We have implemented sophisticated calcium dynamics including calcium diffusion, buffering, and pump extrusion, which accurately replicate published data. Using this model, we found that either the slow inactivation of dendritic sodium channels (NaSI) or the calcium inactivation of voltage-gated calcium channels (CDI) can cause high calcium corresponding to early APs and lower calcium corresponding to later APs. We found that only CDI can account for the experimental observation that sensitivity to AP timing is dependent on NMDA receptors. Additional simulations demonstrated a mechanism by which MSNs can dynamically modulate their sensitivity to AP timing and show that sensitivity to specifically timed pre- and postsynaptic pairings (as in spike timing-dependent plasticity protocols) is altered by the timing of the pairing within the upstate. These findings have implications for synaptic plasticity in vivo during sleep when the upstate-downstate pattern is prominent in the striatum.

Microtubule organization and L-type voltage-activated calcium current in olfactory neuronal cells obtained from patients with schizophrenia and bipolar disorder

Olfactory neuroepithelial cells in culture have been proposed as a model to study the physiopathology of psychiatric disorders and biomarker characterization for diagnosis. In patients with schizophrenia (SZ) and bipolar disorder (BD) diminished microtubule-associated proteins expression occurs, which might lead to aberrant microtubular organization and which in turn may affect Ca(2+) voltage-activated currents. The aim of this work was to characterize of microtubule organization as well as of the L-type Ca(2+) current in neuronal precursors obtained from nasal exfoliates of patients with SZ and BD. Microtubule organization was studied by immunofluorescence with a specific anti-III β-tubulin antibody and by quantification of globular and assembled tubulin by Western blot. L-type current recording was performed by whole-cell patch-clamp technique and nifedipine superfusion. The results showed differential altered microtubular organization in neuronal precursors of SZ and BD. Short microtubules were observed in BD neurons, while extensive, unstained subcellular areas and disorganized microtubules were evident in SZ neuronal precursors. Patients with BD showed a decrease in amounts of tubulin in total homogenates and 40% decrease in the globular fraction. However, L-type current in BD was similar to that in healthy subjects (HS). In contrast, this current in SZ was 50% lower. These reduction in L-type current in SZ together with differential microtubule alterations are potential biomarkers that may differentiates SZ and BD.

Cav1.3 and Cav1.2 channels of adrenal chromaffin cells: emerging views on cAMP/cGMP-mediated phosphorylation and role in pacemaking

Voltage-gated Ca²⁺ channels (VGCCs) are voltage sensors that convert membrane depolarizations into Ca²⁺ signals. In the chromaffin cells of the adrenal medulla, the Ca²⁺ signals driven by VGCCs regulate catecholamine secretion, vesicle retrievals, action potential shape and firing frequency. Among the VGCC-types expressed in these cells (N-, L-, P/Q-, R- and T-types), the two L-type isoforms, Ca(v)1.2 and Ca(v)1.3, control key activities due to their particular activation-inactivation gating and high-density of expression in rodents and humans. The two isoforms are also effectively modulated by G protein-coupled receptor pathways delimited in membrane micro-domains and by the cAMP/PKA and NO/cGMP/PKG phosphorylation pathways which induce prominent Ca²⁺ current changes if opposingly regulated. The two L-type isoforms shape the action potential and directly participate to vesicle exocytosis and endocytosis. The low-threshold of activation and slow rate of inactivation of Ca(v)1.3 confer to this channel the unique property of carrying sufficient inward current at subthreshold potentials able to activate BK and SK channels which set the resting potential, the action potential shape, the cell firing mode and the degree of spike frequency adaptation during spontaneous firing or sustained depolarizations. These properties help chromaffin cells to optimally adapt when switching from normal to stress-mimicking conditions. Here, we will review past and recent findings on cAMP- and cGMP-mediated modulations of Ca(v)1.2 and Ca(v)1.3 and the role that these channels play in the control of chromaffin cell firing. This article is part of a Special Issue entitled: Calcium channels.

Ca²⁺-dependent ion channels underlying spontaneous activity in insect circadian pacemaker neurons

Electrical activity in the gamma frequency range is instrumental for temporal encoding on the millisecond scale in attentive vertebrate brains. Surprisingly, also circadian pacemaker neurons in the cockroach Rhyparobia maderae (Leucophaea maderae) employ fast spontaneous rhythmic activity in the gamma band frequency range (20-70  Hz) together with slow rhythmic activity. The ionic conductances controlling this fast spontaneous activity are still unknown. Here, Ca(2+) imaging combined with pharmacology was employed to analyse ion channels underlying spontaneous activity in dispersed circadian pacemakers of the adult accessory medulla, which controls circadian locomotor activity rhythms. Fast spontaneous Ca(2+) transients in circadian pacemakers accompany tetrodotoxin (TTX)-blockable spontaneous action potentials. In contrast to vertebrate pacemakers, the spontaneous depolarisations from rest appear to be rarely initiated via TTX-sensitive sustained Na(+) channels. Instead, they are predominantly driven by mibefradil-sensitive, low-voltage-activated Ca(2+) channels and DK-AH269-sensitive hyperpolarisation-activated, cyclic nucleotide-gated cation channels. Rhythmic depolarisations activate voltage-gated Na(+) channels and nifedipine-sensitive high-voltage-activated Ca(2+) channels. Together with Ca(2+) rises, the depolarisations open repolarising small-conductance but not large-conductance Ca(2+) -dependent K(+) channels. In contrast, we hypothesise that P/Q-type Ca(2+) channels coupled to large-conductance Ca(2+) -dependent K(+) channels are involved in input-dependent activity.

Interaction of NMDA receptors and L-type calcium channels during early odor preference learning in rats

Early odor preference learning in rats provides a simple model for studying learning and memory. Learning results in an enhanced output from mitral cells, which carry odor information from the olfactory bulb to the olfactory cortex. Mitral cell NMDA receptors (NMDARs) are critically involved in plasticity at the olfactory nerve to mitral cell synapse during odor learning. Here we provide evidence that L-type calcium channels (LTCCs) provide an additional and necessary source of calcium for learning induction. LTCCs are thought to act downstream of NMDARs to bridge synaptic activation and the transcription of the plasticity-related proteins necessary for 24-h learning and memory. Using immunohistochemistry, we have demonstrated that LTCCs are present in the mitral cell and are primarily located on mitral cell proximal dendrites in neonate rats. Behavioral experiments demonstrate that inhibiting the function of LTCCs via intrabulbar infusion of nimidopine successfully blocks learning induced by pairing isoproterenol infusion with odor, while activation of LTCCs via an intrabulbar infusion of BayK-8644 rescues isoproterenol-induced learning from a D-APV block. Interestingly, the infusion of BayK-8644 paired with odor is by itself not sufficient to induce learning. Synaptoneurosome Western blot and immunohistochemistry measurement of synapsin I phosphorylation following BayK-8644 infusion suggest LTCCs are involved in synaptic release. Finally, odor preference can be induced by gabazine disinhibition of mitral cells, and NMDAR opening is sufficient for the gabazine-induced learning. These results provide the first evidence that NMDARs and LTCCs interact to permit calcium-dependent mitral cell plasticity during early odor preference learning.

Calcium signals induced by FGF-2 in parasympathetic neurons: role of second messenger pathways

Basic Fibroblast Growth Factor, or FGF-2, has been shown to promote neuronal survival and neurite outgrowth in dissociated neurons from the embryonic chick ciliary ganglion; in these effects the three main signal transduction pathways downstream the activated FGFR receptor, i.e. the MAPK, the PI3-K and the PLCγ ones, are differentially involved. While it has been shown that FGF-2 can elicit long lasting elevations in intracellular calcium concentration, [Ca(2+)](i), the role of the three pathways in this process has not been elucidated. Here we show, by means of pharmacological inhibitors, that all three are involved, at a different extent, in the generation of the [Ca(2+)](i) increase induced by FGF-2; in particular, inhibition of the PLCγ pathway, in addition to reducing the number of responsive cells, induces, in a significant population of cells, basal calcium oscillations in the absence of the growth factor and interferes with calcium signals elicited by depolarization. We propose that this complex behaviour can be due to a perturbation in PIP(2) levels at the plasmamembrane.

Properties of I(A) in a neuron of the dorsal raphe nucleus

Voltage clamp data were analyzed in order to characterize the properties of the fast potassium transient current I(A) for a presumed serotonergic neuron of the rat dorsal raphe nucleus (DRN). We obtain maximal conductance, time constants of activation and inactivation, and the steady state activation and inactivation functions m(∞) and h(∞), as Boltzmann curves, defined by half-activation potentials and slope factors. I(A) is estimated as g¯(V-V(rev))m(4)h, with g¯=20.5nS. For activation, the half-activation potential is V(a)=-52.5mV with slope factor k(a)=16.5mV, whereas for inactivation the corresponding quantities are -91.5mV and -9.3mV. We discuss the results in terms of the corresponding properties of I(A) in other cell types and their possible relevance to pacemaking activity in cells of the DRN. Methods of identification of serotonergic DRN neurons and the nature of the K(v) channels underlying the A-type current are also discussed.