Local and global effects of I(h) distribution in dendrites of mammalian 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.

Missing Puzzle Pieces in Dementia Research: HCN Channels and Theta Oscillations

Increasing evidence indicates a role of hyperpolarization activated cation (HCN) channels in controlling the resting membrane potential, pacemaker activity, memory formation, sleep, and arousal. Their disfunction may be associated with the development of epilepsy and age-related memory decline. Neuronal hyperexcitability involved in epileptogenesis and EEG desynchronization occur in the course of dementia in human Alzheimer's Disease (AD) and animal models, nevertheless the underlying ionic and cellular mechanisms of these effects are not well understood. Some suggest that theta rhythms involved in memory formation could be used as a marker of memory disturbances in the course of neurogenerative diseases, including AD. This review focusses on the interplay between hyperpolarization HCN channels, theta oscillations, memory formation and their role(s) in dementias, including AD. While individually, each of these factors have been linked to each other with strong supportive evidence, we hope here to expand this linkage to a more inclusive picture. Thus, HCN channels could provide a molecular target for developing new therapeutic agents for preventing and/or treating dementia.

The enigmatic HCN channels: A cellular neurophysiology perspective

What physiological role does a slow hyperpolarization-activated ion channel with mixed cation selectivity play in the fast world of neuronal action potentials that are driven by depolarization? That puzzling question has piqued the curiosity of physiology enthusiasts about the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are widely expressed across the body and especially in neurons. In this review, we emphasize the need to assess HCN channels from the perspective of how they respond to time-varying signals, while also accounting for their interactions with other co-expressing channels and receptors. First, we illustrate how the unique structural and functional characteristics of HCN channels allow them to mediate a slow negative feedback loop in the neurons that they express in. We present the several physiological implications of this negative feedback loop to neuronal response characteristics including neuronal gain, voltage sag and rebound, temporal summation, membrane potential resonance, inductive phase lead, spike triggered average, and coincidence detection. Next, we argue that the overall impact of HCN channels on neuronal physiology critically relies on their interactions with other co-expressing channels and receptors. Interactions with other channels allow HCN channels to mediate intrinsic oscillations, earning them the "pacemaker channel" moniker, and to regulate spike frequency adaptation, plateau potentials, neurotransmitter release from presynaptic terminals, and spike initiation at the axonal initial segment. We also explore the impact of spatially non-homogeneous subcellular distributions of HCN channels in different neuronal subtypes and their interactions with other channels and receptors. Finally, we discuss how plasticity in HCN channels is widely prevalent and can mediate different encoding, homeostatic, and neuroprotective functions in a neuron. In summary, we argue that HCN channels form an important class of channels that mediate a diversity of neuronal functions owing to their unique gating kinetics that made them a puzzle in the first place.

Developmental timing-dependent organization of synaptic connections between mossy fibers and granule cells in the cerebellum

The long-standing hypothesis that synapses between mossy fibers (MFs) and cerebellar granule cells (GCs) are organized according to the origins of MFs and locations of GC axons, parallel fibers (PFs), is supported by recent findings. However, the mechanisms of such organized synaptic connections remain unknown. Here, using our technique that enabled PF location-dependent labeling of GCs in mice, we confirmed that synaptic connections of GCs with specific MFs originating from the pontine nucleus (PN-MFs) and dorsal column nuclei (DCoN-MFs) were gently but differentially organized according to their PF locations. We then found that overall MF-GC synaptic connectivity was biased in a way that dendrites of GCs having nearby PFs tended to connect with the same MF terminals, implying that the MF origin- and PF location-dependent organization is associated with the overall biased MF-GC synaptic connectivity. Furthermore, the development of PN-MFs preceded that of DCoN-MFs, which matches the developmental sequence of GCs that preferentially connect with each type of these MFs. Thus, our results revealed that overall MF-GC synaptic connectivity is biased in terms of PF locations, and suggested that such connectivity is likely the result of synaptic formation between developmental timing-matched partners.

A synaptic learning rule for exploiting nonlinear dendritic computation

Information processing in the brain depends on the integration of synaptic input distributed throughout neuronal dendrites. Dendritic integration is a hierarchical process, proposed to be equivalent to integration by a multilayer network, potentially endowing single neurons with substantial computational power. However, whether neurons can learn to harness dendritic properties to realize this potential is unknown. Here, we develop a learning rule from dendritic cable theory and use it to investigate the processing capacity of a detailed pyramidal neuron model. We show that computations using spatial or temporal features of synaptic input patterns can be learned, and even synergistically combined, to solve a canonical nonlinear feature-binding problem. The voltage dependence of the learning rule drives coactive synapses to engage dendritic nonlinearities, whereas spike-timing dependence shapes the time course of subthreshold potentials. Dendritic input-output relationships can therefore be flexibly tuned through synaptic plasticity, allowing optimal implementation of nonlinear functions by single neurons.

Ih from synapses to networks: HCN channel functions and modulation in neurons

Hyperpolarization-activated cyclic nucleotide gated (HCN) channels and the current they carry, I_h, are widely and diversely distributed in the central nervous system (CNS). The distribution of the four subunits of HCN channels is variable within the CNS, within brain regions, and often within subcellular compartments. The precise function of I_h can depend heavily on what other channels are co-expressed. In this review, we give an overview of HCN channel structure, distribution, and modulation by cyclic adenosine monophosphate (cAMP). We then discuss HCN channel and I_h functions, where we have parsed the roles into two main effects: a steady effect on maintaining the resting membrane potential at relatively depolarized values, and slow channel dynamics. Within this framework, we discuss I_h involvement in resonance, synaptic integration, transmitter release, plasticity, and point out a special case, where the effects of I_h on the membrane potential and its slow channel dynamics have dual roles in thalamic neurons.

Computational and theoretical insights into the homeostatic response to the decreased cell size of midbrain dopamine neurons

Midbrain dopamine neurons communicate signals of reward anticipation and attribution of salience. This capacity is distorted in heroin or cocaine abuse or in conditions such as human mania. A shared characteristic among rodent models of these behavioral disorders is that dopamine neurons in these animals acquired a small size and manifest an augmented spontaneous and burst activity. The biophysical mechanism underlying this increased excitation is currently unknown, but is believed to primarily follow from a substantial drop in K+ conductance secondary to morphology reduction. This work uses a dopamine neuron mathematical model to show, surprisingly, that under size diminution a reduction in K+ conductance is an adaptation that attempts to decrease cell excitability. The homeostatic response that preserves the intrinsic activity is the conservation of the ion channel density for each conductance; a result that is analytically demonstrated and challenges the experimentalist tendency to reduce intrinsic excitation to K+ conductance expression level. Another unexpected mechanism that buffers the raise in intrinsic activity is the presence of the ether-a-go-go-related gen K+ channel since its activation is illustrated to increase with size reduction. Computational experiments finally demonstrate that size attenuation results in the paradoxical enhancement of afferent-driven bursting as a reduced temporal summation indexed correlates with improved depolarization. This work illustrates, on the whole, that experimentation in the absence of mathematical models may lead to the erroneous interpretation of the counterintuitive aspects of empirical data.

Integration of Within-Cell Experimental Data With Multi-Compartmental Modeling Predicts H-Channel Densities and Distributions in Hippocampal OLM Cells

Determining biophysical details of spatially extended neurons is a challenge that needs to be overcome if we are to understand the dynamics of brain function from cellular perspectives. Moreover, we now know that we should not average across recordings from many cells of a given cell type to obtain quantitative measures such as conductance since measures can vary multiple-fold for a given cell type. In this work we examine whether a tight combination of experimental and computational work can address this challenge. The oriens-lacunosum/moleculare (OLM) interneuron operates as a “gate” that controls incoming sensory and ongoing contextual information in the CA1 of the hippocampus, making it essential to understand how its biophysical properties contribute to memory function. OLM cells fire phase-locked to the prominent hippocampal theta rhythms, and we previously used computational models to show that OLM cells exhibit high or low theta spiking resonance frequencies that depend respectively on whether their dendrites have hyperpolarization-activated cation channels (h-channels) or not. However, whether OLM cells actually possess dendritic h-channels is unknown at present. We performed a set of whole-cell recordings of OLM cells from mouse hippocampus and constructed three multi-compartment models using morphological and electrophysiological parameters extracted from the same OLM cell, including per-cell pharmacologically isolated h-channel currents. We found that the models best matched experiments when h-channels were present in the dendrites of each of the three model cells created. This strongly suggests that h-channels must be present in OLM cell dendrites and are not localized to their somata. Importantly, this work shows that a tight integration of model and experiment can help tackle the challenge of characterizing biophysical details and distributions in spatially extended neurons. Full spiking models were built for two of the OLM cells, matching their current clamp cell-specific electrophysiological recordings. Overall, our work presents a technical advancement in modeling OLM cells. Our models are available to the community to use to gain insight into cellular dynamics underlying hippocampal function.

Extracellular GABA waves regulate coincidence detection in excitatory circuits

KEY POINTS

Rapid changes in neuronal network activity trigger widespread waves of extracellular GABA in hippocampal neuropil. Elevations of extracellular GABA narrow the coincidence detection window for excitatory inputs to CA1 pyramidal cells. GABA transporters control the effect of extracellular GABA on coincidence detection. Small changes in the kinetics of dendritic excitatory currents amplify when reaching the soma.

ABSTRACT

Coincidence detection of excitatory inputs by principal neurons underpins the rules of signal integration and Hebbian plasticity in the brain. In the hippocampal circuitry, detection fidelity is thought to depend on the GABAergic synaptic input through a feedforward inhibitory circuit also involving the hyperpolarisation-activated Ih current. However, afferent connections often bypass feedforward circuitry, suggesting that a different GABAergic mechanism might control coincidence detection in such cases. To test whether fluctuations in the extracellular GABA concentration [GABA] could play a regulatory role here, we use a GABA 'sniffer' patch in acute hippocampal slices of the rat and document strong dependence of [GABA] on network activity. We find that blocking GABAergic signalling strongly widens the coincidence detection window of direct excitatory inputs to pyramidal cells whereas increasing [GABA] through GABA uptake blockade shortens it. The underlying mechanism involves membrane-shunting tonic GABAA receptor current; it does not have to rely on Ih but depends strongly on the neuronal GABA transporter GAT-1. We use dendrite-soma dual patch-clamp recordings to show that the strong effect of membrane shunting on coincidence detection relies on nonlinear amplification of changes in the decay of dendritic synaptic currents when they reach the soma. Our results suggest that, by dynamically regulating extracellular GABA, brain network activity can optimise signal integration rules in local excitatory circuits.

An axon-specific expression of HCN channels catalyzes fast action potential signaling in GABAergic interneurons

During high-frequency network activities, fast-spiking, parvalbumin-expressing basket cells (PV⁺-BCs) generate barrages of fast synaptic inhibition to control the probability and precise timing of action potential (AP) initiation in principal neurons. Here we describe a subcellular specialization that contributes to the high speed of synaptic inhibition mediated by PV⁺-BCs. Mapping of hyperpolarization-activated cyclic nucleotide-gated (HCN) channel distribution in rat hippocampal PV⁺-BCs with subcellular patch-clamp methods revealed that functional HCN channels are exclusively expressed in axons and completely absent from somata and dendrites. HCN channels not only enhance AP initiation during sustained high-frequency firing but also speed up the propagation of AP trains in PV⁺-BC axons by dynamically opposing the hyperpolarization produced by Na⁺-K⁺ ATPases. Since axonal AP signaling determines the timing of synaptic communication, the axon-specific expression of HCN channels represents a specialization for PV⁺-BCs to operate at high speed.

The precise subcellular location of ion channels is a key determinant of their functions. Here, subcellular patch-clamp recordings demonstrate that an axon-specific expression of HCN channels facilitates the initiation and propagation of action potentials in parvalbumin-expressing basket cells.

Intra- and Extracellular Pillars of a Unifying Framework for Homeostatic Plasticity: A Crosstalk Between Metabotropic Receptors and Extracellular Matrix

In the face of chronic changes in incoming sensory inputs, neuronal networks are capable of maintaining stable conditions of electrical activity over prolonged periods of time by adjusting synaptic strength, to amplify or dampen incoming inputs [homeostatic synaptic plasticity (HSP)], or by altering the intrinsic excitability of individual neurons [homeostatic intrinsic plasticity (HIP)]. Emerging evidence suggests a synergistic interplay between extracellular matrix (ECM) and metabotropic receptors in both forms of homeostatic plasticity. Activation of dopaminergic, serotonergic, or glutamate metabotropic receptors stimulates intracellular signaling through calmodulin-dependent protein kinase II, protein kinase A, protein kinase C, and inositol trisphosphate receptors, and induces changes in expression of ECM molecules and proteolysis of both ECM molecules (lecticans) and ECM receptors (NPR, CD44). The resulting remodeling of perisynaptic and synaptic ECM provides permissive conditions for HSP and plays an instructive role by recruiting additional signaling cascades, such as those through metabotropic glutamate receptors and integrins. The superimposition of all these signaling events determines intracellular and diffusional trafficking of ionotropic glutamate receptors, resulting in HSP and modulation of conditions for inducing Hebbian synaptic plasticity (i.e., metaplasticity). It also controls cell-surface delivery and activity of voltage- and Ca2+-gated ion channels, resulting in HIP. These mechanisms may modify epileptogenesis and become a target for therapeutic interventions.

Endogenous HCN Channels Modulate the Firing Activity of Globus Pallidus Neurons in Parkinsonian Animals

The globus pallidus occupies a critical position in the indirect pathway of the basal ganglia motor control system. Hyperpolarization-activated cyclic-nucleotide gated (HCN) channels play an important role in the modulation of neuronal excitability. In vivo extracellular single unit recording, behavioral test and immunohistochemistry were performed to explore the possible modulation of endogenous HCN channels in the globus pallidus under parkinsonian states. In MPTP parkinsonian mice, micro-pressure application of the selective HCN channel antagonist, ZD7288, decreased the firing rate in 10 out of the 28 pallidal neurons, while increased the firing rate in another 15 out of the 28 neurons. In 6-OHDA parkinsonian rats, ZD7288 also bidirectionally regulated the spontaneous firing activity of the globus pallidus neurons. The proportion of pallidal neurons with ZD7288-induced slowing of firing rate tended to reduce in both parkinsonian animals. Morphological studies revealed a weaker staining of HCN channels in the globus pallidus under parkinsonian state. Finally, behavioral study demonstrated that intrapallidal microinjection of ZD7288 alleviated locomotor deficits in MPTP parkinsonian mice. These results suggest that endogenous HCN channels modulate the activities of pallidal neurons under parkinsonian states.

h-Channels Contribute to Divergent Intrinsic Membrane Properties of Supragranular Pyramidal Neurons in Human versus Mouse Cerebral Cortex

Gene expression studies suggest that differential ion channel expression contributes to differences in rodent versus human neuronal physiology. We tested whether h-channels more prominently contribute to the physiological properties of human compared to mouse supragranular pyramidal neurons. Single-cell/nucleus RNA sequencing revealed ubiquitous HCN1-subunit expression in excitatory neurons in human, but not mouse, supragranular layers. Using patch-clamp recordings, we found stronger h-channel-related membrane properties in supragranular pyramidal neurons in human temporal cortex, compared to mouse supragranular pyramidal neurons in temporal association area. The magnitude of these differences depended upon cortical depth and was largest in pyramidal neurons in deep L3. Additionally, pharmacologically blocking h-channels produced a larger change in membrane properties in human compared to mouse neurons. Finally, using biophysical modeling, we provide evidence that h-channels promote the transfer of theta frequencies from dendrite-to-soma in human L3 pyramidal neurons. Thus, h-channels contribute to between-species differences in a fundamental neuronal property.

h-Type Membrane Current Shapes the Local Field Potential from Populations of Pyramidal Neurons

In cortex, the local field potential (LFP) is thought to mainly stem from correlated synaptic input to populations of geometrically aligned neurons. Computer models of single cortical pyramidal neurons showed that subthreshold voltage-dependent membrane conductances can also shape the LFP signal, in particular the hyperpolarization-activated cation current (I_h; h-type). This ion channel is prominent in various types of pyramidal neurons, typically showing an increasing density gradient along the apical dendrites. Here, we investigate how I_h affects the LFP generated by a model of a population of cortical pyramidal neurons. We find that the LFP from populations of neurons that receive uncorrelated synaptic input can be well predicted by the LFP from single neurons. In this case, when input impinges on the distal dendrites, where most h-type channels are located, a strong resonance in the LFP was measured near the soma, whereas the opposite configuration does not reveal an I_h contribution to the LFP. Introducing correlations in the synaptic inputs to the pyramidal cells strongly amplifies the LFP, while maintaining the differential effects of I_h for distal dendritic versus perisomatic input. Previous theoretical work showed that input correlations do not amplify LFP power when neurons receive synaptic input uniformly across the cell. We find that this crucially depends on the membrane conductance distribution: the asymmetric distribution of I_h results in a strong amplification of the LFP when synaptic inputs to the cell population are correlated. In conclusion, we find that the h-type current is particularly suited to shape the LFP signal in cortical populations.SIGNIFICANCE STATEMENT The local field potential (LFP), the low-frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. While the cortical LFP is thought to mainly reflect synaptic inputs onto pyramidal neurons, little is known about the role of subthreshold active conductances in shaping the LFP. By means of biophysical modeling we obtain a comprehensive, qualitative understanding of how LFPs generated by populations of cortical pyramidal neurons depend on active subthreshold currents, and identify the key importance of the h-type channel. Our results show that LFPs can give information about the active properties of neurons and that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

HCN Channel Modulation of Synaptic Integration in GABAergic Interneurons in Malformed Rat Neocortex

Cortical malformations are often associated with pharmaco-resistant epilepsy. Alterations in hyperpolarization-activated, cyclic nucleotide-gated, non-specific cation (HCN) channels have been shown to contribute to malformation associated hyperexcitability. We have recently demonstrated that expression of HCN channels and I_h current amplitudes are reduced in layer (L) 5 pyramidal neurons of rats with freeze lesion induced malformations. These changes were associated with an increased EPSP temporal summation. Here, we examine the effects of HCN channel inhibition on synaptic responses in fast spiking, presumptive basket cells and accommodating, presumptive Martinotti, GABAergic interneurons in slices from freeze lesioned animals. In control animals, fast spiking cells showed small sag responses which were reduced by the HCN channel antagonist ZD7288. Fast spiking cells in lesioned animals showed absent or reduced sag responses. The amplitude of single evoked EPSPs in fast spiking cells in the control group was not affected by HCN channel inhibition with ZD7288. EPSP ratios during short stimulus trains at 25 Hz were not significantly different between control and lesion groups. ZD7288 produced an increase in EPSP ratios in the control but not lesion groups. Under voltage clamp conditions, ZD7288 did not affect EPSC ratios. In the control group, accommodating interneurons showed robust sag responses which were significantly reduced by ZD7288. HCN channel inhibition increased EPSP ratios and area in controls but not the lesioned group. The results indicate that HCN channels differentially modulate EPSPs in different classes of GABAergic interneurons and that this control is reduced in malformed rat neocortex.

A novel mechanism of cone photoreceptor adaptation

An animal’s ability to survive depends on its sensory systems being able to adapt to a wide range of environmental conditions, by maximizing the information extracted and reducing the noise transmitted. The visual system does this by adapting to luminance and contrast. While luminance adaptation can begin at the retinal photoreceptors, contrast adaptation has been shown to start at later stages in the retina. Photoreceptors adapt to changes in luminance over multiple time scales ranging from tens of milliseconds to minutes, with the adaptive changes arising from processes within the phototransduction cascade. Here we show a new form of adaptation in cones that is independent of the phototransduction process. Rather, it is mediated by voltage-gated ion channels in the cone membrane and acts by changing the frequency response of cones such that their responses speed up as the membrane potential modulation depth increases and slow down as the membrane potential modulation depth decreases. This mechanism is effectively activated by high-contrast stimuli dominated by low frequencies such as natural stimuli. However, the more generally used Gaussian white noise stimuli were not effective since they did not modulate the cone membrane potential to the same extent. This new adaptive process had a time constant of less than a second. A critical component of the underlying mechanism is the hyperpolarization-activated current, I_h, as pharmacologically blocking it prevented the long- and mid- wavelength sensitive cone photoreceptors (L- and M-cones) from adapting. Consistent with this, short- wavelength sensitive cone photoreceptors (S-cones) did not show the adaptive response, and we found they also lacked a prominent I_h. The adaptive filtering mechanism identified here improves the information flow by removing higher-frequency noise during lower signal-to-noise ratio conditions, as occurs when contrast levels are low. Although this new adaptive mechanism can be driven by contrast, it is not a contrast adaptation mechanism in its strictest sense, as will be argued in the Discussion.

An animal’s ability to survive depends on its ability to adapt to a wide range of light conditions, by maximizing the information flow through the retina. Here, we show a new form of adaptation in cone photoreceptors that helps them optimize the information they transmit by adjusting their response kinetics to better match the visual conditions. The adaptive mechanism we describe is independent of the cone phototransduction process and is instead mediated by membrane processes in which the hyperpolarization-activated current, I_h, plays a critical role. Consistent with the critical role of this current, we also found that cones sensitive to short wavelengths lacked a prominent I_h current and did not show this new form of adaptation. As voltage-dependent processes underlie the adaptational mechanism, it is only apparent when the stimuli are able to sufficiently modulate the membrane potential of cones. This happens with natural stimuli, which are able to deliver high levels of “effective” contrast. However, even though this new adaptive mechanism can be driven by contrast, we argue in the Discussion that in its strictest sense it is not a contrast adaptation mechanism per se.

Computational models of O-LM cells are recruited by low or high theta frequency inputs depending on h-channel distributions

Although biophysical details of inhibitory neurons are becoming known, it is challenging to map these details onto function. Oriens-lacunosum/moleculare (O-LM) cells are inhibitory cells in the hippocampus that gate information flow, firing while phase-locked to theta rhythms. We build on our existing computational model database of O-LM cells to link model with function. We place our models in high-conductance states and modulate inhibitory inputs at a wide range of frequencies. We find preferred spiking recruitment of models at high (4-9 Hz) or low (2-5 Hz) theta depending on, respectively, the presence or absence of h-channels on their dendrites. This also depends on slow delayed-rectifier potassium channels, and preferred theta ranges shift when h-channels are potentiated by cyclic AMP. Our results suggest that O-LM cells can be differentially recruited by frequency-modulated inputs depending on specific channel types and distributions. This work exposes a strategy for understanding how biophysical characteristics contribute to function.

Cocaine sensitization increases subthreshold activity in dopamine neurons from the ventral tegmental area

The progressive escalation of psychomotor responses that results from repeated cocaine administration is termed sensitization. This phenomenon alters the intrinsic properties of dopamine (DA) neurons from the ventral tegmental area (VTA), leading to enhanced dopaminergic transmission in the mesocorticolimbic network. The mechanisms underlying this augmented excitation are nonetheless poorly understood. DA neurons display the hyperpolarization-activated, nonselective cation current, dubbed I_h We recently demonstrated that I_h and membrane capacitance are substantially reduced in VTA DA cells from cocaine-sensitized rats. The present study shows that 7 days of cocaine withdrawal did not normalize I_h and capacitance. In cells from cocaine-sensitized animals, the amplitude of excitatory synaptic potentials, at -70 mV, was ∼39% larger in contrast to controls. Raise and decay phases of the synaptic signal were faster under cocaine, a result associated with a reduced membrane time constant. Synaptic summation was paradoxically elevated by cocaine exposure, as it consisted of a significantly reduced summation indexed but a considerably increased depolarization. These effects are at least a consequence of the reduced capacitance. I_h attenuation is unlikely to explain such observations, since at -70 mV, no statistical differences exist in I_h or input resistance. The neuronal shrinkage associated with a diminished capacitance may help to understand two fundamental elements of drug addiction: incentive sensitization and negative emotional states. A reduced cell size may lead to substantial enhancement of cue-triggered bursting, which underlies drug craving and reward anticipation, whereas it could also result in DA depletion, as smaller neurons might express low levels of tyrosine hydroxylase.

NEW & NOTEWORTHY

This work uses a new approach that directly extracts important biophysical parameters from alpha function-evoked synaptic potentials. Two of these parameters are the cell membrane capacitance (C_m) and rate at any time point of the synaptic waveform. The use of such methodology shows that cocaine sensitization reduces C_m and increases the speed of synaptic signaling. Paradoxically, although synaptic potentials show a faster decay under cocaine their temporal summation is substantially elevated.

Subcellular Patch-clamp Recordings from the Somatodendritic Domain of Nigral Dopamine Neurons

Dendrites of dopaminergic neurons receive and convey synaptic input, support action potential back-propagation and neurotransmitter release. Understanding these fundamental functions will shed light on the information transfer in these neurons. Dendritic patch-clamp recordings provide the possibility to directly examine the electrical properties of dendrites and underlying voltage-gated ion channels. However, these fine structures are not easily accessible to patch pipettes because of their small diameter. This report describes a step-by-step procedure to collect stable and reliable recordings from the dendrites of dopaminergic neurons in acute slices. Electrophysiological measurements are combined with post hoc recovery of cell morphology. Successful experiments rely on improved preparation of slices, solutions and pipettes, adequate adjustment of the optics and stability of the pipette in contact with the recorded structure. Standard principles of somatic patch-clamp recording are applied to dendrites but with a gentler approach of the pipette. These versatile techniques can be implemented to address various questions concerning the excitable properties of dendrites.

Purkinje cell intrinsic excitability increases after synaptic long term depression

Coding in cerebellar Purkinje cells not only depends on synaptic plasticity but also on their intrinsic membrane excitability. We performed whole cell patch-clamp recordings of Purkinje cells in sagittal cerebellar slices in mice. We found that inducing long-term depression (LTD) in the parallel fiber to Purkinje cell synapses results in an increase in the gain of the firing rate response. This increase in excitability is accompanied by an increase in the input resistance and a decrease in the amplitude of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel-mediated voltage sag. Application of a HCN channel blocker prevents the increase in input resistance and excitability without blocking the expression of synaptic LTD. We conclude that the induction of parallel fiber-Purkinje cell LTD is accompanied by an increase in excitability of Purkinje cells through downregulation of the HCN-mediated h current. We suggest that HCN downregulation is linked to the biochemical pathway that sustains synaptic LTD. Given the diversity of information carried by the parallel fiber system, we suggest that changes in intrinsic excitability enhance the coding capacity of the Purkinje cell to specific input sources.

Electrophysiological and Immunohistochemical Evidence for an Increase in GABAergic Inputs and HCN Channels in Purkinje Cells that Survive Developmental Ethanol Exposure

Ethanol exposures during the early postnatal period of the rat result in significant death of Purkinje cells (PCs). The magnitude, time-course, and lobular specificity of PC death have been well characterized in several studies. Additionally, significant reduction of climbing fiber inputs to the surviving PCs has been characterized. This study investigates whether further alterations to the cerebellar cortical circuits might occur as a result of developmental ethanol exposures. We first examined the firing pattern of PCs in acute slice preparations on postnatal days 13-15. While the basic firing frequency was not significantly altered, PCs from rat pups treated with ethanol on postnatal days 4-6 showed a significantly increased number of inhibitory postsynaptic potentials (IPSCs) and a larger Ih current. We conducted immunofluorescent studies to identify the probable cause of the increased IPSCs. We found a significant 21 % increase in the number of basket cells per PC and a near doubling of the volume of co-localized basket cell axonal membrane with PC. In addition, we identified a significant (~147 %) increase in HCN1 channel volume co-localized to PC volume. Therefore, the cerebellar cortex that survives targeted postnatal ethanol exposure is dramatically altered in development subsequent to PC death. The cerebellar cortical circuit that results is one that operates under a significant degree of increased resting inhibition. The alterations in the development of cerebellar circuitry following ethanol exposure, and the significant loss of PCs, could result in modifications of the structure and function of other brain regions that receive cerebellar inputs.

Dendritic integration: 60 years of progress

Understanding how individual neurons integrate the thousands of synaptic inputs they receive is critical to understanding how the brain works. Modeling studies in silico and experimental work in vitro, dating back more than half a century, have revealed that neurons can perform a variety of different passive and active forms of synaptic integration on their inputs. But how are synaptic inputs integrated in the intact brain? With the development of new techniques, this question has recently received substantial attention, with new findings suggesting that many of the forms of synaptic integration observed in vitro also occur in vivo, including in awake animals. Here we review six decades of progress, which collectively highlights the complex ways that single neurons integrate their inputs, emphasizing the critical role of dendrites in information processing in the brain.

Non-linear leak currents affect mammalian neuron physiology

In their seminal works on squid giant axons, Hodgkin, and Huxley approximated the membrane leak current as Ohmic, i.e., linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted) varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents) and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells.

High dendritic expression of Ih in the proximity of the axon origin controls the integrative properties of nigral dopamine neurons

KEY POINTS

The hyperpolarization-activated cation current Ih is expressed in dopamine neurons of the substantia nigra, but the subcellular distribution of the current and its role in synaptic integration remain unknown. We used cell-attached patch recordings to determine the localization profile of Ih along the somatodendritic axis of nigral dopamine neurons in slices from young rats. Ih density is higher in axon-bearing dendrites, in a membrane area close to the axon origin, than in the soma and axon-lacking dendrites. Dual current-clamp recordings revealed a similar contribution of Ih to the waveform of single excitatory postsynaptic potentials throughout the somatodendritic domain. The Ih blocker ZD 7288 increased the temporal summation in all dendrites with a comparable effect in axon- and non-axon dendrites. The strategic position of Ih in the proximity of the axon may influence importantly transitions between pacemaker and bursting activities and consequently the downstream release of dopamine.

ABSTRACT

Dendrites of most neurons express voltage-gated ion channels in their membrane. In combination with passive properties, active currents confer to dendrites a high computational potential. The hyperpolarization-activated cation current Ih present in the dendrites of some pyramidal neurons affects their membrane and integration properties, synaptic plasticity and higher functions such as memory. A gradient of increasing h-channel density towards distal dendrites has been found to be responsible for the location independence of excitatory postsynaptic potential (EPSP) waveform and temporal summation in cortical and hippocampal pyramidal cells. However, reports on other cell types revealed that smoother gradients or even linear distributions of Ih can achieve homogeneous temporal summation. Although the existence of a robust, slowly activating Ih current has been repeatedly demonstrated in nigral dopamine neurons, its subcellular distribution and precise role in synaptic integration are unknown. Using cell-attached patch-clamp recordings, we find a higher Ih current density in the axon-bearing dendrite than in the soma or in dendrites without axon in nigral dopamine neurons. Ih is mainly concentrated in the dendritic membrane area surrounding the axon origin and decreases with increasing distances from this site. Single EPSPs and temporal summation are similarly affected by blockade of Ih in axon- and non-axon-bearing dendrites. The presence of Ih close to the axon is pivotal to control the integrative functions and the output signal of dopamine neurons and may consequently influence the downstream coding of movement.

Differential effects of conductances on the phase resetting curve of a bursting neuronal oscillator

The intrinsically oscillating neurons in the crustacean pyloric circuit have membrane conductances that influence their spontaneous activity patterns and responses to synaptic activity. The relationship between the magnitudes of these membrane conductances and the response of the oscillating neurons to synaptic input has not yet been fully or systematically explored. We examined this relationship using the phase resetting curve (PRC), which summarizes the change in the cycle period of a neuronal oscillator as a function of the input's timing within the oscillation. We first utilized a large database of single-compartment model neurons to determine the effect of individual membrane conductances on PRC shape; we found that the effects vary across conductance space, but on average, the hyperpolarization-activated and leak conductances advance the PRC. We next investigated how membrane conductances affect PRCs of the isolated pacemaker kernel in the pyloric circuit of Cancer borealis by: (1) tabulating PRCs while using dynamic clamp to artificially add varying levels of specific conductances, and (2) tabulating PRCs before and after blocking the endogenous hyperpolarization-activated current. We additionally used a previously described four-compartment model to determine how the location of the hyperpolarization-activated conductance influences that current's effect on the PRC. We report that while dynamic-clamp-injected leak current has much smaller effects on the PRC than suggested by the single-compartment model, an increase in the hyperpolarization-activated conductance both advances and reduces the noisiness of the PRC in the pacemaker kernel of the pyloric circuit in both modeling and experimental studies.

Extracellular pH regulates excitability of vomeronasal sensory neurons

The mouse vomeronasal organ (VNO) plays a critical role in semiochemical detection and social communication. Vomeronasal stimuli are typically secreted in various body fluids. Following direct contact with urine deposits or other secretions, a peristaltic vascular pump mediates fluid entry into the recipient's VNO. Therefore, while vomeronasal sensory neurons (VSNs) sample various stimulatory semiochemicals dissolved in the intraluminal mucus, they might also be affected by the general physicochemical properties of the "solvent." Here, we report cycle stage-correlated variations in urinary pH among female mice. Estrus-specific pH decline is observed exclusively in urine samples from sexually experienced females. Moreover, patch-clamp recordings in acute VNO slices reveal that mouse VSNs reliably detect extracellular acidosis. Acid-evoked responses share the biophysical and pharmacological hallmarks of the hyperpolarization-activated current Ih. Mechanistically, VSN acid sensitivity depends on a pH-induced shift in the voltage-dependence of Ih activation that causes the opening of HCN channels at rest, thereby increasing VSN excitability. Together, our results identify extracellular acidification as a potent activator of vomeronasal Ih and suggest HCN channel-dependent vomeronasal gain control of social chemosignaling. Our data thus reveal a potential mechanistic basis for stimulus pH detection in rodent chemosensory communication.

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels regulate firing of globus pallidus neurons in vivo

The globus pallidus plays a significant role in motor control under both health and pathological states. Recent studies have revealed that hyperpolarization-activated cyclic nucleotide-gated (HCN) channels occupy a critical position in globus pallidus pacemaking activity. Morphological studies have shown the expression of HCN channels in the globus pallidus. To investigate the in vivo effects of HCN channels in the globus pallidus, extracellular recordings and behavioral tests were performed in the present study. In normal rats, micro-pressure ejection of 0.05mM ZD7288, the selective HCN channel blocker, decreased the frequency of spontaneous firing in 21 out of the 40 pallidal neurons. The average decrease was 50.4±5.4%. Interestingly, in another 18 out of the 40 pallidal neurons, ZD7288 increased the firing rate by 137.1±27.6%. Similar bidirectional modulation on the firing rate was observed by a higher concentration of ZD7288 (0.5mM) as well as another HCN channel blocker, CsCl. Furthermore, activation of HCN channels by 8-Br-cAMP increased the firing rate by 63.0±9.3% in 15 out of the 25 pallidal neurons and decreased the firing rate by 46.9±9.4% in another 8 out of the 25 pallidal neurons. Further experiments revealed that modulation of glutamatergic but not GABAergic transmission may be involved in ZD7288-induced increase in firing rate. Consistent with electrophysiological results, further studies revealed that modulation of HCN channels also had bidirectional effects on behavior. Taken together, the present studies suggest that HCN channels may modulate the activity of pallidal neurons by different pathways in vivo.

Distribution and function of HCN channels in the apical dendritic tuft of neocortical pyramidal neurons

The apical tuft is the most remote area of the dendritic tree of neocortical pyramidal neurons. Despite its distal location, the apical dendritic tuft of layer 5 pyramidal neurons receives substantial excitatory synaptic drive and actively processes corticocortical input during behavior. The properties of the voltage-activated ion channels that regulate synaptic integration in tuft dendrites have, however, not been thoroughly investigated. Here, we use electrophysiological and optical approaches to examine the subcellular distribution and function of hyperpolarization-activated cyclic nucleotide-gated nonselective cation (HCN) channels in rat layer 5B pyramidal neurons. Outside-out patch recordings demonstrated that the amplitude and properties of ensemble HCN channel activity were uniform in patches excised from distal apical dendritic trunk and tuft sites. Simultaneous apical dendritic tuft and trunk whole-cell current-clamp recordings revealed that the pharmacological blockade of HCN channels decreased voltage compartmentalization and enhanced the generation and spread of apical dendritic tuft and trunk regenerative activity. Furthermore, multisite two-photon glutamate uncaging demonstrated that HCN channels control the amplitude and duration of synaptically evoked regenerative activity in the distal apical dendritic tuft. In contrast, at proximal apical dendritic trunk and somatic recording sites, the blockade of HCN channels decreased excitability. Dynamic-clamp experiments revealed that these compartment-specific actions of HCN channels were heavily influenced by the local and distributed impact of the high density of HCN channels in the distal apical dendritic arbor. The properties and subcellular distribution pattern of HCN channels are therefore tuned to regulate the interaction between integration compartments in layer 5B pyramidal neurons.

Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization

The Purkinje cell (PC) is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN). In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1), we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS) and Ranvier nodes (RNs), proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.

Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal oriens-lacunosum/moleculare (O-LM) cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron's output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron's biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (Ih). Although dendritic Ih could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of Ih on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic Ih. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic Ih. These findings inform future experiments that differentiate between somatic and dendritic Ih, thereby continuing a cycle between model and experiment.

Active dendrites regulate spectral selectivity in location-dependent spike initiation dynamics of hippocampal model neurons

How does the presence of plastic active dendrites in a pyramidal neuron alter its spike initiation dynamics? To answer this question, we measured the spike-triggered average (STA) from experimentally constrained, conductance-based hippocampal neuronal models of various morphological complexities. We transformed the STA computed from these models to the spectral and the spectrotemporal domains and found that the spike initiation dynamics exhibited temporally localized selectivity to a characteristic frequency. In the presence of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, the STA characteristic frequency strongly correlated with the subthreshold resonance frequency in the theta frequency range. Increases in HCN channel density or in input variance increased the STA characteristic frequency and its selectivity strength. In the absence of HCN channels, the STA exhibited weak delta frequency selectivity and the characteristic frequency was related to the repolarization dynamics of the action potentials and the recovery kinetics of sodium channels from inactivation. Comparison of STA obtained with inputs at various dendritic locations revealed that nonspiking and spiking dendrites increased and reduced the spectrotemporal integration window of the STA with increasing distance from the soma as direct consequences of passive filtering and dendritic spike initiation, respectively. Finally, the presence of HCN channels set the STA characteristic frequency in the theta range across the somatodendritic arbor and specific STA measurements were strongly related to equivalent transfer-impedance-related measurements. Our results identify explicit roles for plastic active dendrites in neural coding and strongly recommend a dynamically reconfigurable multi-STA model to characterize location-dependent input feature selectivity in pyramidal neurons.

The Green's function formalism as a bridge between single- and multi-compartmental modeling

Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of brain networks use point-neurons-neurons without a morphological component-as computational units to keep the conceptual complexity and computational costs low. Inevitably, these applications thus omit a fundamental property of neuronal computation. In this work, we present an approach to model an artificial synapse that mimics dendritic processing without the need to explicitly simulate dendritic dynamics. The model synapse employs an analytic solution for the cable equation to compute the neuron's membrane potential following dendritic inputs. Green's function formalism is used to derive the closed version of the cable equation. We show that by using this synapse model, point-neurons can achieve results that were previously limited to the realms of multi-compartmental models. Moreover, a computational advantage is achieved when only a small number of simulated synapses impinge on a morphologically elaborate neuron. Opportunities and limitations are discussed.

Signal processing by T-type calcium channel interactions in the cerebellum

T-type calcium channels of the Cav3 family are unique among voltage-gated calcium channels due to their low activation voltage, rapid inactivation, and small single channel conductance. These special properties allow Cav3 calcium channels to regulate neuronal processing in the subthreshold voltage range. Here, we review two different subthreshold ion channel interactions involving Cav3 channels and explore the ability of these interactions to expand the functional roles of Cav3 channels. In cerebellar Purkinje cells, Cav3 and intermediate conductance calcium-activated potassium (IKCa) channels form a novel complex which creates a low voltage-activated, transient outward current capable of suppressing temporal summation of excitatory postsynaptic potentials (EPSPs). In large diameter neurons of the deep cerebellar nuclei, Cav3-mediated calcium current (I T) and hyperpolarization-activated cation current (I H) are activated during trains of inhibitory postsynaptic potentials. These currents have distinct, and yet synergistic, roles in the subthreshold domain with I T generating a rebound burst and I H controlling first spike latency and rebound spike precision. However, by shortening the membrane time constant the membrane returns towards resting value at a faster rate, allowing I H to increase the efficacy of I T and increase the range of burst frequencies that can be generated. The net effect of Cav3 channels thus depends on the channels with which they are paired. When expressed in a complex with a KCa channel, Cav3 channels reduce excitability when processing excitatory inputs. If functionally coupled with an HCN channel, the depolarizing effect of Cav3 channels is accentuated, allowing for efficient inversion of inhibitory inputs to generate a rebound burst output. Therefore, signal processing relies not only on the activity of individual subtypes of channels but also on complex interactions between ion channels whether based on a physical complex or by indirect effects on membrane properties.

HCN1 channels in cerebellar Purkinje cells promote late stages of learning and constrain synaptic inhibition

Neural computations rely on ion channels that modify neuronal responses to synaptic inputs. While single cell recordings suggest diverse and neurone type-specific computational functions for HCN1 channels, their behavioural roles in any single neurone type are not clear. Using a battery of behavioural assays, including analysis of motor learning in vestibulo-ocular reflex and rotarod tests, we find that deletion of HCN1 channels from cerebellar Purkinje cells selectively impairs late stages of motor learning. Because deletion of HCN1 modifies only a subset of behaviours involving Purkinje cells, we asked whether the channel also has functional specificity at a cellular level. We find that HCN1 channels in cerebellar Purkinje cells reduce the duration of inhibitory synaptic responses but, in the absence of membrane hyperpolarization, do not affect responses to excitatory inputs. Our results indicate that manipulation of subthreshold computation in a single neurone type causes specific modifications to behaviour.

Somatic versus dendritic resonance: differential filtering of inputs through non-uniform distributions of active conductances

Synaptic inputs to neurons are processed in a frequency-dependent manner, with either low-pass or resonant response characteristics. These types of filtering play a key role in the frequency-specific information flow in neuronal networks. While the generation of resonance by specific ionic conductances is well investigated, less attention has been paid to the spatial distribution of the resonance-generating conductances across a neuron. In pyramidal neurons – one of the major excitatory cell-types in the mammalian brain – a steep gradient of resonance-generating h-conductances with a 60-fold increase towards distal dendrites has been demonstrated experimentally. Because the dendritic trees of these cells are large, spatial compartmentalization of resonant properties can be expected. Here, we use mathematical descriptions of spatially extended neurons to investigate the consequences of such a distal, dendritic localization of h-conductances for signal processing. While neurons with short dendrites do not exhibit a pronounced compartmentalization of resonance, i.e. the filter properties of dendrites and soma are similar, we find that neurons with longer dendrites ( space constant) can show distinct filtering of dendritic and somatic inputs due to electrotonic segregation. Moreover, we show that for such neurons, experimental classification as resonant versus nonresonant can be misleading when based on somatic recordings, because for these morphologies a dendritic resonance could easily be undetectable when using somatic input. Nevertheless, noise-driven membrane-potential oscillations caused by dendritic resonance can propagate to the soma where they can be recorded, hence contrasting with the low-pass filtering at the soma. We conclude that non-uniform distributions of active conductances can underlie differential filtering of synaptic input in neurons with spatially extended dendrites, like pyramidal neurons, bearing relevance for the localization-dependent targeting of synaptic input pathways to these cells.

Temporal synchrony and gamma-to-theta power conversion in the dendrites of CA1 pyramidal neurons

Timing is a crucial aspect of synaptic integration. For pyramidal neurons that integrate thousands of synaptic inputs spread across hundreds of microns, it is thus a challenge to maintain the timing of incoming inputs at the axo-somatic integration site. Here we show that pyramidal neurons in the rodent hippocampus use a gradient of inductance in the form of HCN channels as an active mechanism to counteract location-dependent temporal differences of dendritic inputs at the soma. Using simultaneous multi-site whole cell recordings complemented by computational modeling, we find that this intrinsic biophysical mechanism produces temporal synchrony of rhythmic inputs in the theta and gamma frequency ranges across wide regions of the dendritic tree. While gamma and theta oscillations are known to synchronize activity across space in neuronal networks, our results identify a novel mechanism by which this synchrony extends to activity within single pyramidal neurons with complex dendritic arbors.

The Role of Extracellular Conductivity Profiles in Compartmental Models for Neurons: Particulars for Layer 5 Pyramidal Cells

With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the neuronal reactivity to an electrical stimulation using external microelectrodes.

An integrator circuit in cerebellar cortex

The brain builds dynamic models of the body and the outside world to predict the consequences of actions and stimuli. A well-known example is the oculomotor integrator, which anticipates the position-dependent elasticity forces acting on the eye ball by mathematically integrating over time oculomotor velocity commands. Many models of neural integration have been proposed, based on feedback excitation, lateral inhibition or intrinsic neuronal nonlinearities. We report here that a computational model of the cerebellar cortex, a structure thought to implement dynamic models, reveals a hitherto unrecognized integrator circuit. In this model, comprising Purkinje cells, molecular layer interneurons and parallel fibres, Purkinje cells were able to generate responses lasting more than 10 s, to which both neuronal and network mechanisms contributed. Activation of the somatic fast sodium current by subthreshold voltage fluctuations was able to maintain pulse-evoked graded persistent activity, whereas lateral inhibition among Purkinje cells via recurrent axon collaterals further prolonged the responses to step and sine wave stimulation. The responses of Purkinje cells decayed with a time-constant whose value depended on their baseline spike rate, with integration vanishing at low (< 1 per s) and high rates (> 30 per s). The model predicts that the apparently fast circuit of the cerebellar cortex may control the timing of slow processes without having to rely on sensory feedback. Thus, the cerebellar cortex may contain an adaptive temporal integrator, with the sensitivity of integration to the baseline spike rate offering a potential mechanism of plasticity of the response time-constant.

Differential expression of HCN subunits alters voltage-dependent gating of h-channels in CA1 pyramidal neurons from dorsal and ventral hippocampus

The rodent hippocampus can be divided into dorsal (DHC) and ventral (VHC) domains on the basis of behavioral, anatomical, and biochemical differences. Recently, we reported that CA1 pyramidal neurons from the VHC were intrinsically more excitable than DHC neurons, but the specific ionic conductances contributing to this difference were not determined. Here we investigated the hyperpolarization-activated current (I(h)) and the expression of HCN1 and HCN2 channel subunits in CA1 pyramidal neurons from the DHC and VHC. Measurement of Ih with cell-attached patches revealed a significant depolarizing shift in the V(1/2) of activation for dendritic h-channels in VHC neurons (but not DHC neurons), and ultrastructural immunolocalization of HCN1 and HCN2 channels revealed a significantly larger HCN1-to-HCN2 ratio for VHC neurons (but not DHC neurons). These observations suggest that a shift in the expression of HCN1 and HCN2 channels drives functional changes in I(h) for VHC neurons (but not DHC neurons) and could thereby significantly alter the capacity for dendritic integration of these neurons.

Functional maps within a single neuron

The presence and plasticity of dendritic ion channels are well established. However, the literature is divided on what specific roles these dendritic ion channels play in neuronal information processing, and there is no consensus on why neuronal dendrites should express diverse ion channels with different expression profiles. In this review, we present a case for viewing dendritic information processing through the lens of the sensory map literature, where functional gradients within neurons are considered as maps on the neuronal topograph. Under such a framework, drawing analogies from the sensory map literature, we postulate that the formation of intraneuronal functional maps is driven by the twin objectives of efficiently encoding inputs that impinge along different dendritic locations and of retaining homeostasis in the face of changes that are required in the coding process. In arriving at this postulate, we relate intraneuronal map physiology to the vast literature on sensory maps and argue that such a metaphorical association provides a fresh conceptual framework for analyzing and understanding single-neuron information encoding. We also describe instances where the metaphor presents specific directions for research on intraneuronal maps, derived from analogous pursuits in the sensory map literature. We suggest that this perspective offers a thesis for why neurons should express and alter ion channels in their dendrites and provides a framework under which active dendrites could be related to neural coding, learning theory, and homeostasis.

A calibration-free electrode compensation method

In a single-electrode current-clamp recording, the measured potential includes both the response of the membrane and that of the measuring electrode. The electrode response is traditionally removed using bridge balance, where the response of an ideal resistor representing the electrode is subtracted from the measurement. Because the electrode is not an ideal resistor, this procedure produces capacitive transients in response to fast or discontinuous currents. More sophisticated methods exist, but they all require a preliminary calibration phase, to estimate the properties of the electrode. If these properties change after calibration, the measurements are corrupted. We propose a compensation method that does not require preliminary calibration. Measurements are compensated offline by fitting a model of the neuron and electrode to the trace and subtracting the predicted electrode response. The error criterion is designed to avoid the distortion of compensated traces by spikes. The technique allows electrode properties to be tracked over time and can be extended to arbitrary models of electrode and neuron. We demonstrate the method using biophysical models and whole cell recordings in cortical and brain-stem neurons.

The effect of dendritic voltage-gated conductances on the neuronal impedance: a quantitative model

Neuronal impedance characterizes the magnitude and timing of the subthreshold response of a neuron to oscillatory input at a given frequency. It is known to be influenced by both the morphology of the neuron and the presence of voltage-gated conductances in the cell membrane. Most existing theoretical accounts of neuronal impedance considered the effects of voltage-gated conductances but neglected the spatial extent of the cell, while others examined spatially extended dendrites with a passive or spatially uniform quasi-active membrane. We derived an explicit mathematical expression for the somatic input impedance of a model neuron consisting of a somatic compartment coupled to an infinite dendritic cable which contained voltage-gated conductances, in the more general case of non-uniform dendritic membrane potential. The validity and generality of this model was verified through computer simulations of various model neurons. The analytical model was then applied to the analysis of experimental data from real CA1 pyramidal neurons. The model confirmed that the biophysical properties and predominantly dendritic localization of the hyperpolarization-activated cation current I (h) were important determinants of the impedance profile, but also predicted a significant contribution from a depolarization-activated fast inward current. Our calculations also implicated the interaction of I (h) with amplifying currents as the main factor governing the shape of the impedance-frequency profile in two types of hippocampal interneuron. Our results provide not only a theoretical advance in our understanding of the frequency-dependent behavior of nerve cells, but also a practical tool for the identification of candidate mechanisms that determine neuronal response properties.

Neural circuits of the cerebellum: hypothesis for function

The rapid growth of cerebellar research is going to clarify several aspects of cellular and circuit physiology. However, the concepts about cerebellar mechanisms of function are still largely related to clinical observations and to models elaborated before the last discoveries appeared. In this paper, the major issues are revisited, suggesting that previous concepts can now be refined and modified. The cerebellum is fundamentally involved in timing and in controlling the ordered and precise execution of motor sequences. The fast reaction of the cerebellum to the inputs is sustained by specific cellular mechanisms ensuring precision on the millisecond scale. These include burst-burst reconversion in the granular layer and instantaneous frequency modulation on the 100-Hz band in Purkinje and deep cerebellar nuclei cells. Precisely timed signals can be used for perceptron operations in Purkinje cells and to establish appropriate correlations with climbing fiber signals inducing learning at parallel fiber synapses. In the granular layer, plasticity turns out to be instrumental to timing, providing a conceptual solution to the discrepancy between cerebellar learning and timing. The granular layer sub-circuit can be tuned by long-term synaptic plasticity and synaptic inhibition to delay the incoming signals over a 100-ms range. For longer sequences, large circuit sections can be entrained into coherent activity in 100-ms cycles. These dynamic aspects, which have not been accounted for by original theories, could in fact represent the essence of cerebellar functioning. It is suggested that the cerebellum can, in this way, operate the realignment of temporally incongruent signals, allowing their binding and pattern recognition in Purkinje cells. The demonstration of these principles, their behavioral relevance and their relationship with internal model theories represent a challenge for future cerebellar research.

Intermediate conductance calcium-activated potassium channels modulate summation of parallel fiber input in cerebellar Purkinje cells

Encoding sensory input requires the expression of postsynaptic ion channels to transform key features of afferent input to an appropriate pattern of spike output. Although Ca(2+)-activated K(+) channels are known to control spike frequency in central neurons, Ca(2+)-activated K(+) channels of intermediate conductance (KCa3.1) are believed to be restricted to peripheral neurons. We now report that cerebellar Purkinje cells express KCa3.1 channels, as evidenced through single-cell RT-PCR, immunocytochemistry, pharmacology, and single-channel recordings. Furthermore, KCa3.1 channels coimmunoprecipitate and interact with low voltage-activated Cav3.2 Ca(2+) channels at the nanodomain level to support a previously undescribed transient voltage- and Ca(2+)-dependent current. As a result, subthreshold parallel fiber excitatory postsynaptic potentials (EPSPs) activate Cav3 Ca(2+) influx to trigger a KCa3.1-mediated regulation of the EPSP and subsequent after-hyperpolarization. The Cav3-KCa3.1 complex provides powerful control over temporal summation of EPSPs, effectively suppressing low frequencies of parallel fiber input. KCa3.1 channels thus contribute to a high-pass filter that allows Purkinje cells to respond preferentially to high-frequency parallel fiber bursts characteristic of sensory input.

Tonic nanomolar dopamine enables an activity-dependent phase recovery mechanism that persistently alters the maximal conductance of the hyperpolarization-activated current in a rhythmically active neuron

The phases at which network neurons fire in rhythmic motor outputs are critically important for the proper generation of motor behaviors. The pyloric network in the crustacean stomatogastric ganglion generates a rhythmic motor output wherein neuronal phase relationships are remarkably invariant across individuals and throughout lifetimes. The mechanisms for maintaining these robust phase relationships over the long-term are not well described. Here we show that tonic nanomolar dopamine (DA) acts at type 1 DA receptors (D1Rs) to enable an activity-dependent mechanism that can contribute to phase maintenance in the lateral pyloric (LP) neuron. The LP displays continuous rhythmic bursting. The activity-dependent mechanism was triggered by a prolonged decrease in LP burst duration, and it generated a persistent increase in the maximal conductance (G(max)) of the LP hyperpolarization-activated current (I(h)), but only in the presence of steady-state DA. Interestingly, micromolar DA produces an LP phase advance accompanied by a decrease in LP burst duration that abolishes normal LP network function. During a 1 h application of micromolar DA, LP phase recovered over tens of minutes because, the activity-dependent mechanism enabled by steady-state DA was triggered by the micromolar DA-induced decrease in LP burst duration. Presumably, this mechanism restored normal LP network function. These data suggest steady-state DA may enable homeostatic mechanisms that maintain motor network output during protracted neuromodulation. This DA-enabled, activity-dependent mechanism to preserve phase may be broadly relevant, as diminished dopaminergic tone has recently been shown to reduce I(h) in rhythmically active neurons in the mammalian brain.

Properties and functional implications of I (h) in hippocampal area CA3 interneurons

The present study examines the biophysical properties and functional implications of I (h) in hippocampal area CA3 interneurons with somata in strata radiatum and lacunosum-moleculare. Characterization studies showed a small maximum h-conductance (2.6 ± 0.3 nS, n = 11), shallow voltage dependence with a hyperpolarized half-maximal activation (V (1/2) = -91 mV), and kinetics characterized by double-exponential functions. The functional consequences of I (h) were examined with regard to temporal summation and impedance measurements. For temporal summation experiments, 5-pulse mossy fiber input trains were activated. Blocking I (h) with 50 μM ZD7288 resulted in an increase in temporal summation, suggesting that I (h) supports sensitivity of response amplitude to relative input timing. Impedance was assessed by applying sinusoidal current commands. From impedance measurements, we found that I (h) did not confer theta-band resonance, but flattened the impedance-frequency relations instead. Double immunolabeling for hyperpolarization-activated cyclic nucleotide-gated proteins and glutamate decarboxylase 67 suggests that all four subunits are present in GABAergic interneurons from the strata considered for electrophysiological studies. Finally, a model of I (h) was employed in computational analyses to confirm and elaborate upon the contributions of I (h) to impedance and temporal summation.

The fast and slow ups and downs of HCN channel regulation

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels (h channels) form the molecular basis for the hyperpolarization-activated current, I(h), and modulation of h channels contributes to changes in cellular properties critical for normal functions in the mammalian brain and heart. Numerous mechanisms underlie h channel modulation during both physiological and pathological conditions, leading to distinct changes in gating, kinetics, surface expression, channel conductance or subunit composition of h channels. Here we provide a focused review examining mechanisms of h channel regulation, with an emphasis on recent findings regarding interacting proteins such as TRIP8b. This review is intended to serve as a comprehensive resource for physiologists to provide potential molecular mechanisms underlying functionally important changes in I(h) in different biological models, as well as for molecular biologists to delineate the predicted h channel changes associated with complex regulatory mechanisms in both normal function and in disease states.