The role of hyperpolarization-activated cationic current in spike-time precision and intrinsic resonance in cortical neurons in vitro

Theta patterns of stimulation induce synaptic and intrinsic potentiation in O-LM interneurons

Brain oscillations have long-lasting effects on synaptic and cellular properties. For instance, synaptic stimulation at theta (θ) frequency induces persistent depression of both excitatory synaptic transmission and intrinsic excitability in CA1 principal neurons. However, the incidence of θ activity on synaptic transmission and intrinsic excitability in hippocampal GABAergic interneurons is unclear. We report here the induction of both synaptic and intrinsic potentiation in oriens-lacunosum moleculare (O-LM) interneurons following stimulation of afferent glutamatergic inputs in the θ frequency range (∼5 Hz). Long-term synaptic potentiation (LTP) is induced by synaptic activation of calcium-permeable AMPA receptors (CP-AMPAR), whereas long-term potentiation of intrinsic excitability (LTP-IE) results from the mGluR1-dependent down-regulation of Kv7 voltage-dependent potassium channel and hyperpolarization activated and cyclic nucleotide-gated (HCN) channel through the depletion of phosphatidylinositol-4,5-biphosphate (PIP2). LTP and LTP-IE are reversible, demonstrating that both synaptic and intrinsic changes are bidirectional in O-LM cells. We conclude that synaptic activity at θ frequency induces both synaptic and intrinsic potentiation in O-LM interneurons, i.e., the opposite of what is typically seen in glutamatergic neurons.

Understanding primary blast injury: High frequency pressure acutely disrupts neuronal network dynamics in cerebral organoids

Blast exposure represents a common occupational risk capable of generating mild to severe traumatic brain injuries (TBI). During blast exposure, a pressure shockwave passes through the skull and exposes brain tissue to complex pressure waveforms. The primary neurophysiological response to blast-induced pressure waveforms remains poorly understood. Here, we use a computer-controlled table-top pressure chamber to expose human stem cell-derived cerebral organoids to varied frequency of pressure waves and characterize the neurophysiological response. Pressure waves that reach a maximum amplitude of 250kPa were used to model a less severe TBI and 350kPa for a more severe blast TBI event. With each amplitude, a frequency range of 500Hz, 3000Hz, and 5000Hz was tested. Following the 250 kPa overpressure a multielectrode array recorded organoid neural activity. We observed an acute suppression neuronal activity in single unit events, population events, and network oscillations that recovered within 24 hours. Additionally, we observed a network desynchronization after exposure higher frequency waveforms. Conversely, organoids exposed to higher amplitude pressure (350kPa) displayed drastic neurophysiological differences that failed to recover within 24 hours. Furthermore, lower amplitude 'blast' (250kPa) did not induce cellular damage whereas the higher amplitude 'blast' (350kPa) generated greater apoptosis throughout each organoid. Our data indicate that specific features of pressure waves found intracranially during blast TBI have varied effects on neurophysiological activity that can occur even without cellular damage.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Endocannabinoids Tune Intrinsic Excitability in O-LM Interneurons by Direct Modulation of Postsynaptic Kv7 Channels

KCNQ-Kv7 channels are found at the axon initial segment of pyramidal neurons, where they control cell firing and membrane potential. In oriens lacunosum moleculare (O-LM) interneurons, these channels are mainly expressed in the dendrites, suggesting a peculiar function of Kv7 channels in these neurons. Here, we show that Kv7 channel activity is upregulated following induction of presynaptic long-term synaptic depression (LTD) in O-LM interneurons from rats of both sex, thus resulting in a synergistic long-term depression of intrinsic excitability (LTD-IE). Both LTD and LTD-IE involve endocannabinoid (eCB) biosynthesis for induction. However, although LTD is dependent on cannabinoid type 1 receptors, LTD-IE is not. Molecular modeling shows a strong interaction of eCBs with Kv7.2/3 channel, suggesting a persistent action of these lipids on Kv7 channel activity. Our data thus unveil a major role for eCB synthesis in triggering both synaptic and intrinsic depression in O-LM interneurons.SIGNIFICANCE STATEMENT In principal cells, Kv7 channels are essentially located at the axon initial segment. In contrast, in O-LM interneurons, Kv7 channels are highly expressed in the dendrites, suggesting a singular role of these channels in O-LM cell function. Here, we show that LTD of excitatory inputs in O-LM interneurons is associated with an upregulation of Kv7 channels, thus resulting in a synergistic LTD of LTD-IE. Both forms of plasticity are mediated by the biosynthesis of eCBs. Stimulation of CB1 receptors induces LTD, whereas the direct interaction of eCBs with Kv7 channels induces LTD-IE. Our results thus provide a previously unexpected involvement of eCBs in long-lasting plasticity of intrinsic excitability in GABAergic interneurons.

Diversity amongst human cortical pyramidal neurons revealed via their sag currents and frequency preferences

In the human neocortex coherent interlaminar theta oscillations are driven by deep cortical layers, suggesting neurons in these layers exhibit distinct electrophysiological properties. To characterize this potential distinctiveness, we use in vitro whole-cell recordings from cortical layers 2 and 3 (L2&3), layer 3c (L3c) and layer 5 (L5) of the human cortex. Across all layers we observe notable heterogeneity, indicating human cortical pyramidal neurons are an electrophysiologically diverse population. L5 pyramidal cells are the most excitable of these neurons and exhibit the most prominent sag current (abolished by blockade of the hyperpolarization activated cation current, I_h). While subthreshold resonance is more common in L3c and L5, we rarely observe this resonance at frequencies greater than 2 Hz. However, the frequency dependent gain of L5 neurons reveals they are most adept at tracking both delta and theta frequency inputs, a unique feature that may indirectly be important for the generation of cortical theta oscillations.

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

Developmentally Regulated Rebound Depolarization Enhances Spike Timing Precision in Auditory Midbrain Neurons

The inferior colliculus (IC) is an auditory midbrain structure involved in processing biologically important temporal features of sounds. The responses of IC neurons to these temporal features reflect an interaction of synaptic inputs and neuronal biophysical properties. One striking biophysical property of IC neurons is the rebound depolarization produced following membrane hyperpolarization. To understand how the rebound depolarization is involved in spike timing, we made whole-cell patch clamp recordings from IC neurons in brain slices of P9-21 rats. We found that the percentage of rebound neurons was developmentally regulated. The precision of the timing of the first spike on the rebound increased when the neuron was repetitively injected with a depolarizing current following membrane hyperpolarization. The average jitter of the first spikes was only 0.5 ms. The selective T-type Ca²⁺ channel antagonist, mibefradil, significantly increased the jitter of the first spike of neurons in response to repetitive depolarization following membrane hyperpolarization. Furthermore, the rebound was potentiated by one to two preceding rebounds within a few hundred milliseconds. The first spike generated on the potentiated rebound was more precise than that on the non-potentiated rebound. With the addition of a calcium chelator, BAPTA, into the cell, the rebound potentiation no longer occurred, and the precision of the first spike on the rebound was not improved. These results suggest that the postinhibitory rebound mediated by T-type Ca²⁺ channel promotes spike timing precision in IC neurons. The rebound potentiation and precise spikes may be induced by increases in intracellular calcium levels.

Impaired Reliability and Precision of Spiking in Adults But Not Juveniles in a Mouse Model of Fragile X Syndrome

Fragile X syndrome (FXS) is the most common source of intellectual disability and autism. Extensive studies have been performed on the network and behavioral correlates of the syndrome, but our knowledge about intrinsic conductance changes is still limited. In this study, we show a differential effect of FMRP knockout in different subsections of hippocampus using whole-cell patch clamp in mouse hippocampal slices. We observed no significant change in spike numbers in the CA1 region of hippocampus, but a significant increase in CA3, in juvenile mice. However, in adult mice we see a reduction in spike number in the CA1 with no significant difference in CA3. In addition, we see increased variability in spike numbers in CA1 cells following a variety of steady and modulated current step protocols. This effect emerges in adult mice (8 weeks) but not juvenile mice (4 weeks). This increased spiking variability was correlated with reduced spike number and with elevated AHP. The increased AHP arose from elevated SK currents (small conductance calcium-activated potassium channels), but other currents involved in medium AHP, such as I_h and M, were not significantly different. We obtained a partial rescue of the cellular variability phenotype when we blocked SK current using the specific blocker apamin. Our observations provide a single-cell correlate of the network observations of response variability and loss of synchronization, and suggest that the elevation of SK currents in FXS may provide a partial mechanistic explanation for this difference.

The contribution of ion channels in input-output plasticity

Persistent changes that occur in brain circuits are classically thought to be mediated by long-term modifications in synaptic efficacy. Yet, many studies have shown that voltage-gated ion channels located at the input and output side of the neurons are also the subject to persistent modifications. These channels are thus responsible for intrinsic plasticity that is expressed in many different neuronal types including glutamatergic principal neurons and GABAergic interneurons. As for synaptic plasticity, activation of synaptic glutamate receptors initiate persistent modification in neuronal excitability. We review here how synaptic input can be efficiently altered by activity-dependent modulation of ion channels that control EPSP amplification, spike threshold or resting membrane potential. We discuss the nature of the learning rules shared by intrinsic and synaptic plasticity, the mechanisms of ion channel regulation and the impact of intrinsic plasticity on induction of synaptic modifications.

Frequency-dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp

Action potential generation in neurons depends on a membrane potential threshold and therefore on how subthreshold inputs influence this voltage. In oscillatory networks, for example, many neuron types have been shown to produce membrane potential ([Formula: see text]) resonance: a maximum subthreshold response to oscillatory inputs at a nonzero frequency. Resonance is usually measured by recording [Formula: see text] in response to a sinusoidal current ([Formula: see text]), applied at different frequencies (f), an experimental setting known as current clamp (I-clamp). Several recent studies, however, use the voltage clamp (V-clamp) method to control [Formula: see text] with a sinusoidal input at different frequencies [[Formula: see text]] and measure the total membrane current ([Formula: see text]). The two methods obey systems of differential equations of different dimensionality, and while I-clamp provides a measure of electrical impedance [[Formula: see text]], V-clamp measures admittance [[Formula: see text]]. We analyze the relationship between these two measurement techniques. We show that, despite different dimensionality, in linear systems the two measures are equivalent: [Formula: see text]. However, nonlinear model neurons produce different values for Z and [Formula: see text]. In particular, nonlinearities in the voltage equation produce a much larger difference between these two quantities than those in equations of recovery variables that describe activation and inactivation kinetics. Neurons are inherently nonlinear, and notably, with ionic currents that amplify resonance, the voltage clamp technique severely underestimates the current clamp response. We demonstrate this difference experimentally using the PD neurons in the crab stomatogastric ganglion. These findings are instructive for researchers who explore cellular mechanisms of neuronal oscillations.

Human cerebrospinal fluid promotes spontaneous gamma oscillations in the hippocampus in vitro

Gamma oscillations (30-80 Hz) are fast network activity patterns frequently linked to cognition. They are commonly studied in hippocampal brain slices in vitro, where they can be evoked via pharmacological activation of various receptor families. One limitation of this approach is that neuronal activity is studied in a highly artificial extracellular fluid environment, as provided by artificial cerebrospinal fluid (aCSF). Here, we examine the influence of human cerebrospinal fluid (hCSF) on kainate-evoked and spontaneous gamma oscillations in mouse hippocampus. We show that hCSF, as compared to aCSF of matched electrolyte and glucose composition, increases the power of kainate-evoked gamma oscillations and induces spontaneous gamma activity in areas CA3 and CA1 that is reversed by washout. Bath application of atropine entirely abolished hCSF-induced gamma oscillations, indicating critical contribution from muscarinic acetylcholine receptor-mediated signaling. In separate whole-cell patch clamp recordings from rat hippocampus, hCSF increased theta resonance frequency and strength in pyramidal cells along with enhancement of h-current (I_h ) amplitude. We found no evidence of intrinsic gamma frequency resonance at baseline (aCSF) among fast-spiking interneurons, and this was not altered by hCSF. However, hCSF increased the excitability of fast-spiking interneurons, which likely contributed to gamma rhythmogenesis. Our findings show that hCSF promotes network gamma oscillations in the hippocampus in vitro and suggest that neuromodulators distributed in CSF could have significant influence on neuronal network activity in vivo.

Active membrane conductances and morphology of a collision detection neuron broaden its impedance profile and improve discrimination of input synchrony

How neurons filter and integrate their complex patterns of synaptic inputs is central to their role in neural information processing. Synaptic filtering and integration are shaped by the frequency-dependent neuronal membrane impedance. Using single and dual dendritic recordings in vivo, pharmacology, and computational modeling, we characterized the membrane impedance of a collision detection neuron in the grasshopper Schistocerca americana. This neuron, the lobula giant movement detector (LGMD), exhibits consistent impedance properties across frequencies and membrane potentials. Two common active conductances g_H and g_M, mediated respectively by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and by muscarine-sensitive M-type K⁺ channels, promote broadband integration with high temporal precision over the LGMD's natural range of membrane potentials and synaptic input frequencies. Additionally, we found that a model based on the LGMD's branching morphology increased the gain and decreased the delay associated with the mapping of synaptic input currents to membrane potential. More generally, this was true for a wide range of model neuron morphologies, including those of neocortical pyramidal neurons and cerebellar Purkinje cells. These findings show the unexpected role played by two widespread active conductances and by dendritic morphology in shaping synaptic integration.NEW & NOTEWORTHY Neuronal filtering and integration of synaptic input patterns depend on the electrochemical properties of dendrites. We used an identified collision detection neuron in grasshoppers to examine how its morphology and two conductances affect its membrane impedance in relation to the computations it performs. The neuronal properties examined are ubiquitous and therefore promote a general understanding of neuronal computations, including those in the human brain.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

Dynamical Mechanism of Hyperpolarization-Activated Non-specific Cation Current Induced Resonance and Spike-Timing Precision in a Neuronal Model

Hyperpolarization-activated cyclic nucleotide-gated cation current (I_h) plays important roles in the achievement of many physiological/pathological functions in the nervous system by modulating the electrophysiological activities, such as the rebound (spike) to hyperpolarization stimulations, subthreshold membrane resonance to sinusoidal currents, and spike-timing precision to stochastic factors. In the present paper, with increasing g_h (conductance of I_h), the rebound (spike) and subthreshold resonance appear and become stronger, and the variability of the interspike intervals (ISIs) becomes lower, i.e., the enhancement of spike-timing precision, which are simulated in a conductance-based theoretical model and well explained by the nonlinear concept of bifurcation. With increasing g_h, the stable node to stable focus, to coexistence behavior, and to firing via the codimension-1 bifurcations (Hopf bifurcation, saddle-node bifurcation, saddle-node bifurcations on an invariant circle, and saddle homoclinic orbit) and codimension-2 bifurcations such as Bogdanov-Takens (BT) point related to the transition between saddle-node and Hopf bifurcations, are acquired with 1- and 2-parameter bifurcation analysis. The decrease of variability of ISIs with increasing g_h is induced by the fast decrease of the standard deviation of ISIs, which is related to the increase of the capacity of resisting noisy disturbance due to the firing becomes far away from the bifurcation point. The enhancement of the rebound (spike) with increasing g_h builds up a relationship to the decrease of the capacity of resisting disturbance like the hyperpolarization stimulus as the resting state approaches the bifurcation point. The “typical”-resonance and non-resonance appear in the parameter region of the stable focus and node far away from the bifurcation points, respectively. The complex or “strange” dynamics, such as the “weak”-resonance for the stable node near the transition point between the stable node and focus and the non-resonance for the stable focus close to the codimension-1 and −2 bifurcation points, are discussed.

Non-Decaying postsynaptics potentials and delayed spikes in hippocampal pyramidal neurons generated by a zero slope conductance created by the persistent Na+ current

The negative slope conductance created by the persistent sodium current (I_NaP) prolongs the decay phase of excitatory postsynaptic potentials (EPSPs). In a recent study, we demonstrated that this effect was due to an increase of the membrane time constant. When the negative slope conductance opposes completely the positive slope conductances of the other currents it creates a zero slope conductance region. In this region the membrane time constant is infinite and the decay phase of the EPSPs is virtually absent. Here we show that non-decaying EPSPs are present in CA1 hippocampal pyramidal cells in the zero slope conductance region, in the suprathreshold range of membrane potential. Na⁺ channel block with tetrodotoxin abolishes the non-decaying EPSPs. Interestingly, the non-decaying EPSPs are observed only in response to artificial excitatory postsynaptic currents (aEPSCs) of small amplitude, and not in response to aEPSCs of big amplitude. We also observed concomitantly delayed spikes with long latencies and high variability only in response to small amplitude aEPSCs. Our results showed that in CA1 pyramidal neurons I_NaP creates non-decaying EPSPs and delayed spikes in the subthreshold range of membrane potentials, which could potentiate synaptic integration of synaptic potentials coming from distal regions of the dendritic tree.

Plasticity of intrinsic excitability during LTD is mediated by bidirectional changes in h-channel activity

The polarity of excitability changes associated with induction of Long-Term synaptic Depression (LTD) in CA1 pyramidal neurons is a contentious issue. Postsynaptic neuronal excitability after LTD induction is found to be reduced in certain cases (i.e. synergistic changes) but enhanced in others (i.e. compensatory or homeostatic). We examined here whether these divergent findings could result from the activation of two separate mechanisms converging onto a single learning rule linking synergistic and homeostatic plasticity. We show that the magnitude of LTD induced with low frequency stimulation (LFS) of the Schaffer collaterals determines the polarity of intrinsic changes in CA1 pyramidal neurons. Apparent input resistance (R_in) is reduced following induction of moderate LTD (<20–30%). In contrast, R_in is increased after induction of large LTD (>40%) induced by repetitive episodes of LFS. The up-regulation of I_h observed after moderate LTD results from the activation of NMDA receptors whereas the down-regulation of I_h is due to activation of mGluR1 receptors. These changes in R_in were associated with changes in intrinsic excitability. In conclusion, our study indicates that changes in excitability after LTD induction follow a learning rule describing a continuum linking synergistic and compensatory changes in excitability.

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.

Resonance modulation, annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics

Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slave to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decreases with the input frequency. In contrast, for f ≪ 1 the dynamics are quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.

Dopamine Neurons Change the Type of Excitability in Response to Stimuli

The dynamics of neuronal excitability determine the neuron's response to stimuli, its synchronization and resonance properties and, ultimately, the computations it performs in the brain. We investigated the dynamical mechanisms underlying the excitability type of dopamine (DA) neurons, using a conductance-based biophysical model, and its regulation by intrinsic and synaptic currents. Calibrating the model to reproduce low frequency tonic firing results in N-methyl-D-aspartate (NMDA) excitation balanced by γ-Aminobutyric acid (GABA)-mediated inhibition and leads to type I excitable behavior characterized by a continuous decrease in firing frequency in response to hyperpolarizing currents. Furthermore, we analyzed how excitability type of the DA neuron model is influenced by changes in the intrinsic current composition. A subthreshold sodium current is necessary for a continuous frequency decrease during application of a negative current, and the low-frequency "balanced" state during simultaneous activation of NMDA and GABA receptors. Blocking this current switches the neuron to type II characterized by the abrupt onset of repetitive firing. Enhancing the anomalous rectifier Ih current also switches the excitability to type II. Key characteristics of synaptic conductances that may be observed in vivo also change the type of excitability: a depolarized γ-Aminobutyric acid receptor (GABAR) reversal potential or co-activation of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) leads to an abrupt frequency drop to zero, which is typical for type II excitability. Coactivation of N-methyl-D-aspartate receptors (NMDARs) together with AMPARs and GABARs shifts the type I/II boundary toward more hyperpolarized GABAR reversal potentials. To better understand how altering each of the aforementioned currents leads to changes in excitability profile of DA neuron, we provide a thorough dynamical analysis. Collectively, these results imply that type I excitability in dopamine neurons might be important for low firing rates and fine-tuning basal dopamine levels, while switching excitability to type II during NMDAR and AMPAR activation may facilitate a transient increase in dopamine concentration, as type II neurons are more amenable to synchronization by mutual excitation.

Membrane potential resonance frequency directly influences network frequency through electrical coupling

Oscillatory networks often include neurons with membrane potential resonance, exhibiting a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (f_res). Although f_res has been correlated to the network frequency (f_net) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift f_res, without changing other attributes of the impedance profile, also shift f_net in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsic oscillator (O) and resonator (R) neurons. We use a two-cell model of such a network to show that increasing f_res of R directly increases f_net and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of f_res on f_net is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in f_res, as long as this combination produces the same impedance vs. frequency relationship. We use the dynamic clamp technique to experimentally verify the model predictions by connecting a model resonator to the pacemaker pyloric dilator neurons of the crab Cancer borealis pyloric network using electrical synapses and show that the pyloric network frequency can be shifted by changing f_res in the resonator. Our results provide compelling evidence that f_res and resonance amplitude strongly influence f_net, and therefore, modulators may target these attributes to modify rhythmic activity.

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.

Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons

KEY POINTS

We determined the contribution of the hyperpolarization-activated cationic (h) current (Ih ) to the homeostatic regulation of CA1 pyramidal cells in vitro using chronic treatments (48 h) that either increase (picrotoxin) or decrease (kynurenate) neuronal activity. The h-conductance was found to be up- or down-regulated following chronic activity enhancement or activity deprivation, respectively. This bidirectional plasticity of Ih was found to subsequently alter both apparent input resistance and intrinsic neuronal excitability. Bidirectional homeostatic plasticity of Ih also determined EPSP waveform and EPSP summation tested at 5-30 Hz. Long-term synaptic modification induced by repetitive stimulation of the Schaffer collaterals was found to be constant across treatments in the presence of Ih but not when Ih was blocked pharmacologically. Thus, bidirectional homeostatic regulation of Ih stabilizes induction of long-term synaptic modification in CA1 pyramidal neurons that depends on EPSP summation.

ABSTRACT

The hyperpolarization-activated cationic (h) current is a voltage-shock absorber, highly expressed in the dendrites of CA1 pyramidal neurons. Up-regulation of Ih has been reported following episodes of intense network activity but the effect of activity deprivation on Ih and the functional consequence of homeostatic regulation of Ih remain unclear. We determined here the contribution of Ih to the homeostatic regulation of CA1 pyramidal cell excitability. Intrinsic neuronal excitability was decreased in neurons treated for 2-3 days with the GABAA channel blocker picrotoxin (PiTx) but increased in neurons treated (2-3 days) with the glutamate receptor antagonist kynurenate (Kyn). Membrane capacitance remained unchanged after treatment but the apparent input resistance was reduced for PiTx-treated neurons and enhanced for Kyn-treated neurons. Maximal Ih conductance was up-regulated after chronic hyperactivity but down-regulated following chronic hypoactivity. Up-regulation of Ih in PiTx-treated cultures was found to accelerate EPSP kinetics and reduce temporal summation of EPSPs whereas opposite effects were observed in Kyn-treated cultures, indicating that homeostatic regulation of Ih may control the induction of synaptic modification depending on EPSP summation. In fact, stimulation of the Schaffer collaterals at 3-10 Hz induced differential levels of plasticity in PiTx-treated and Kyn-treated neurons when Ih was blocked pharmacologically but not in control conditions. These data indicate that homeostatic regulation of Ih normalizes the threshold for long-term synaptic modification that depends on EPSP summation. In conclusion, bidirectional homeostatic regulation of Ih not only controls spiking activity but also stabilizes the threshold for long-term potentiation induced in CA1 pyramidal neurons by repetitive stimulation.

Activation of Ih and TTX-sensitive sodium current at subthreshold voltages during CA1 pyramidal neuron firing

We used dynamic clamp and action potential clamp techniques to explore how currents carried by tetrodotoxin-sensitive sodium channels and HCN channels (Ih) regulate the behavior of CA1 pyramidal neurons at resting and subthreshold voltages. Recording from rat CA1 pyramidal neurons in hippocampal slices, we found that the apparent input resistance and membrane time constant were strongly affected by both conductances, with Ih acting to decrease apparent input resistance and time constant and sodium current acting to increase both. We found that both Ih and sodium current were active during subthreshold summation of artificial excitatory postsynaptic potentials (EPSPs) generated by dynamic clamp, with Ih dominating at less depolarized voltages and sodium current at more depolarized voltages. Subthreshold sodium current-which amplifies EPSPs-was most effectively recruited by rapid voltage changes, while Ih-which blunts EPSPs-was maximal for slow voltage changes. The combined effect is to selectively amplify rapid EPSPs. We did similar experiments in mouse CA1 pyramidal neurons, doing voltage-clamp experiments using experimental records of action potential firing of CA1 neurons previously recorded in awake, behaving animals as command voltages to quantify flow of Ih and sodium current at subthreshold voltages. Subthreshold sodium current was larger and subthreshold Ih was smaller in mouse neurons than in rat neurons. Overall, the results show opposing effects of subthreshold sodium current and Ih in regulating subthreshold behavior of CA1 neurons, with subthreshold sodium current prominent in both rat and mouse CA1 pyramidal neurons and additional regulation by Ih in rat neurons.

Dorsoventral differences in Kv7/M-current and its impact on resonance, temporal summation and excitability in rat hippocampal pyramidal cells

In rodent hippocampi, the connections, gene expression and functions differ along the dorsoventral (D-V) axis. CA1 pyramidal cells show increasing excitability along the D-V axis, although the underlying mechanism is not known. In the present study, we investigated how the M-current (IM ), caused by Kv7/M (KCNQ) potassium channels, and known to often control neuronal excitability, contributes to D-V differences in intrinsic properties of CA1 pyramidal cells. Using whole-cell patch clamp recordings and the selective Kv7/M blocker 10,10-bis(4-pyridinylmethyl)-9(10H)-anthracenone dihydrochloride (XE991) in hippocampal slices from 3- to 4-week-old rats, we found that: (i) IM had a stronger impact on subthreshold electrical properties in dorsal than ventral CA1 pyramidal cells, including input resistance, temporal summation of artificial synaptic potentials, and M-resonance; (ii) IM activated at more negative potentials (left-shifted) and had larger peak amplitude in the dorsal than ventral CA1; and (iii) the initial spike threshold (during ramp depolarizations) was elevated, and the medium after-hyperpolarization and spike frequency adaptation were increased (i.e. excitability was lower) in the dorsal rather than ventral CA1. These differences were abolished or reduced by application of XE991, indicating that they were caused by IM . Thus, it appears that IM has stronger effects in dorsal than in ventral rat CA1 pyramidal cells because of a larger maximal M-conductance and left-shifted activation curve in the dorsal cells. These mechanisms may contribute to D-V differences in the rate and phase coding of position by CA1 place cells, and may also enhance epileptiform activity in ventral CA1.

Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents

We investigate the biophysical and dynamic mechanisms of generation of subthreshold amplitude and phase resonance in response to sinusoidal input currents in two-dimensional models of quadratic type. These models feature a parabolic voltage nullcline and a linear nullcline for the recovery gating variable, capturing the interplay of the so-called resonant currents (e.g., hyperpolarization-activated mixed-cation inward and slow potassium) and amplifying currents (e.g., persistent sodium) in biophysically realistic parameter regimes. These currents underlie the generation of resonance in medial entorhinal cortex layer II stellate cells and CA1 pyramidal cells. We show that quadratic models exhibit nonlinear amplifications of the voltage response to sinusoidal inputs in the resonant frequency band. These are expressed as an increase in the impedance profile as the input amplitude increases. They are stronger for values positive than negative to resting potential and are accompanied by a shift in the phase profile, a decrease in the resonant and phase-resonant frequencies, and an increase in the sharpness of the voltage response. These effects are more prominent for smaller values of ∊ (larger levels of the time scale separation between the voltage and the resonant gating variable) and for values of the resting potential closer to threshold for spike generation. All other parameter fixed, as ∊ increases the voltage response becomes "more linear"; i.e., the nonlinearities are present, but "ignored". In addition, the nonlinear effects are strongly modulated by the curvature of the parabolic voltage nullcline (partially reflecting the effects of the amplifying current) and the slope of the resonant current activation curve. Following the effects of changes in the biophysical conductances of realistic conductance-based models through the parameters of the quadratic model, we characterize the qualitatively different effects that resonant and amplifying currents have on the nonlinear properties of the voltage response. We identify different classes of resonant currents, represented by h- and slow potassium, according to whether they enhance (h-) or attenuate (slow potassium) the nonlinear effects. Finally, we use dynamical systems tools to investigate the dynamic mechanisms of generation of resonance and phase-resonance. We show that the nonlinear effects on the voltage response (e.g., amplification of the voltage response in the resonant frequency band and shifts in the resonant and phase-resonant frequencies) result from the ability of limit cycle trajectories to follow the unstable (right) branch of the voltage nullcline for a significant amount of time. This is a canard-related mechanism that has been shown to underlie the generation of intrinsic subthreshold oscillations in quadratic type models such as medial entorhinal cortex stellate cells. Overall, our results highlight the complexity of the voltage response to oscillatory inputs in nonlinear models and the roles that resonant and amplifying currents have in shaping these responses.

Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input

Neurons rely on action potentials, or spikes, to encode information. But spikes can encode different stimulus features in different neurons. We show here through simulations and experiments how neurons encode the integral or derivative of their input based on the distinct tuning properties conferred upon them by subthreshold currents. Slow-activating subthreshold inward (depolarizing) current mediates positive feedback control of subthreshold voltage, sustaining depolarization and allowing the neuron to spike on the basis of its integrated stimulus waveform. Slow-activating subthreshold outward (hyperpolarizing) current mediates negative feedback control of subthreshold voltage, truncating depolarization and forcing the neuron to spike on the basis of its differentiated stimulus waveform. Depending on its direction, slow-activating subthreshold current cooperates or competes with fast-activating inward current during spike initiation. This explanation predicts that sensitivity to the rate of change of stimulus intensity differs qualitatively between integrators and differentiators. This was confirmed experimentally in spinal sensory neurons that naturally behave as specialized integrators or differentiators. Predicted sensitivity to different stimulus features was confirmed by covariance analysis. Integration and differentiation, which are themselves inverse operations, are thus shown to be implemented by the slow feedback mediated by oppositely directed subthreshold currents expressed in different neurons.

The emerging functions of oligodendrocytes in regulating neuronal network behaviour

Myelin is required for efficient nerve conduction, but not all axons are myelinated to the same extent. Here we review recent studies that have revealed distinct myelination patterns of different axonal paths, suggesting that myelination is not an all or none phenomenon and that its presence is finely regulated in central nervous system networks. Whereas powerful reductionist biology has led to important knowledge of how oligodendrocytes function by themselves, little is known about their role in neuronal networks. We still do not understand how oligodendrocytes integrate information from neurons to adapt their function to the need of the system. An intricate cross talk between neurons and glia is likely to exist and to determine how neuronal circuits operate as a whole. Dissecting these mechanisms by using integrative systems biology approaches is one of the major challenges ahead.

Frequency Preference Response to Oscillatory Inputs in Two-dimensional Neural Models: A Geometric Approach to Subthreshold Amplitude and Phase Resonance

We investigate the dynamic mechanisms of generation of subthreshold and phase resonance in two-dimensional linear and linearized biophysical (conductance-based) models, and we extend our analysis to account for the effect of simple, but not necessarily weak, types of nonlinearities. Subthreshold resonance refers to the ability of neurons to exhibit a peak in their voltage amplitude response to oscillatory input currents at a preferred non-zero (resonant) frequency. Phase-resonance refers to the ability of neurons to exhibit a zero-phase (or zero-phase-shift) response to oscillatory input currents at a non-zero (phase-resonant) frequency. We adapt the classical phase-plane analysis approach to account for the dynamic effects of oscillatory inputs and develop a tool, the envelope-plane diagrams, that captures the role that conductances and time scales play in amplifying the voltage response at the resonant frequency band as compared to smaller and larger frequencies. We use envelope-plane diagrams in our analysis. We explain why the resonance phenomena do not necessarily arise from the presence of imaginary eigenvalues at rest, but rather they emerge from the interplay of the intrinsic and input time scales. We further explain why an increase in the time-scale separation causes an amplification of the voltage response in addition to shifting the resonant and phase-resonant frequencies. This is of fundamental importance for neural models since neurons typically exhibit a strong separation of time scales. We extend this approach to explain the effects of nonlinearities on both resonance and phase-resonance. We demonstrate that nonlinearities in the voltage equation cause amplifications of the voltage response and shifts in the resonant and phase-resonant frequencies that are not predicted by the corresponding linearized model. The differences between the nonlinear response and the linear prediction increase with increasing levels of the time scale separation between the voltage and the gating variable, and they almost disappear when both equations evolve at comparable rates. In contrast, voltage responses are almost insensitive to nonlinearities located in the gating variable equation. The method we develop provides a framework for the investigation of the preferred frequency responses in three-dimensional and nonlinear neuronal models as well as simple models of coupled neurons.

Inhibition-induced theta resonance in cortical circuits

Both circuit and single-cell properties contribute to network rhythms. In vitro, pyramidal cells exhibit theta-band membrane potential (subthreshold) resonance, but whether and how subthreshold resonance translates into spiking resonance in freely behaving animals is unknown. Here, we used optogenetic activation to trigger spiking in pyramidal cells or parvalbumin immunoreactive interneurons (PV) in the hippocampus and neocortex of freely behaving rodents. Individual directly activated pyramidal cells exhibited narrow-band spiking centered on a wide range of frequencies. In contrast, PV photoactivation indirectly induced theta-band-limited, excess postinhibitory spiking in pyramidal cells (resonance). PV-inhibited pyramidal cells and interneurons spiked at PV-inhibition troughs, similar to CA1 cells during spontaneous theta oscillations. Pharmacological blockade of hyperpolarization-activated (I(h)) currents abolished theta resonance. Inhibition-induced theta-band spiking was replicated in a pyramidal cell-interneuron model that included I(h). Thus, PV interneurons mediate pyramidal cell spiking resonance in intact cortical networks, favoring transmission at theta frequency.

Resonance properties of GABAergic interneurons in immature GAD67-GFP mouse neocortex

Subthreshold resonance is a characteristic membrane property of different neuronal classes, is critically involved in the generation of network oscillations, and tunes the integration of synaptic inputs to particular frequency ranges. In order to investigate whether neocortical GABAergic interneurons show resonant behavior already during early postnatal development, we performed whole-cell patch-clamp recordings from visually identified interneurons in supragranular layers of parietal regions in coronal neocortical slices from postnatal day (P) P6-P13 GAD67-GFP knock-in mice. Subthreshold resonance was analyzed by injection of sinusoidal current with varying frequency. About 50% of the investigated GABAergic interneurons showed subthreshold resonance with an average frequency of 2.0±0.2 Hz (n=38). Membrane hyperpolarization to -86 mV attenuated the frequency and strength of subthreshold resonance. In the presence of 1 mM Ni(2+) subthreshold resonance was virtually abolished, suggesting that T-type Ca(2+) currents are critically involved in the generation of resonance. In contrast, subthreshold resonance was not affected by ZD7288, a blocker of HCN channels. Application of TTX suppressed subthreshold resonance at depolarized, but not hyperpolarized membrane potential, suggesting that persistent Na(+) current contribute to the amplification of membrane resonance. In summary, these results demonstrate that GABAergic interneurons express subthreshold resonance at low frequencies, with T-type Ca(2+) and persistent Na(+) currents underlying the generation of membrane resonance. The membrane resonance of immature interneurons may contribute to the generation of slow oscillatory activity pattern in the immature neocortex and enhance the temporal precision of synaptic integration in developing cortical neurons.

Tonic GABAA conductance decreases membrane time constant and increases EPSP-spike precision in hippocampal pyramidal neurons

Because of a complex dendritic structure, pyramidal neurons have a large membrane surface relative to other cells and so a large electrical capacitance and a large membrane time constant (τ_m). This results in slow depolarizations in response to excitatory synaptic inputs, and consequently increased and variable action potential latencies, which may be computationally undesirable. Tonic activation of GABA_A receptors increases membrane conductance and thus regulates neuronal excitability by shunting inhibition. In addition, tonic increases in membrane conductance decrease the membrane time constant (τ_m), and improve the temporal fidelity of neuronal firing. Here we performed whole-cell current clamp recordings from hippocampal CA1 pyramidal neurons and found that bath application of 10μM GABA indeed decreases τ_m in these cells. GABA also decreased first spike latency and jitter (standard deviation of the latency) produced by current injection of 2 rheobases (500 ms). However, when larger current injections (3–6 rheobases) were used, GABA produced no significant effect on spike jitter, which was low. Using mathematical modeling we demonstrate that the tonic GABA_A conductance decreases rise time, decay time and half-width of EPSPs in pyramidal neurons. A similar effect was observed on EPSP/IPSP pairs produced by stimulation of Schaffer collaterals: the EPSP part of the response became shorter after application of GABA. Consistent with the current injection data, a significant decrease in spike latency and jitter was obtained in cell attached recordings only at near-threshold stimulation (50% success rate, S₅₀). When stimulation was increased to 2- or 3- times S₅₀, GABA significantly affected neither spike latency nor spike jitter. Our results suggest that a decrease in τ_m associated with elevations in ambient GABA can improve EPSP-spike precision at near-threshold synaptic inputs.

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.

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.

Regulation of epileptiform discharges in rat neocortex by HCN channels

Hyperpolarization-activated, cyclic nucleotide-gated, nonspecific cation (HCN) channels have a well-characterized role in regulation of cellular excitability and network activity. The role of these channels in control of epileptiform discharges is less thoroughly understood. This is especially pertinent given the altered HCN channel expression in epilepsy. We hypothesized that inhibition of HCN channels would enhance bicuculline-induced epileptiform discharges. Whole cell recordings were obtained from layer (L)2/3 and L5 pyramidal neurons and L1 and L5 GABAergic interneurons. In the presence of bicuculline (10 μM), HCN channel inhibition with ZD 7288 (20 μM) significantly increased the magnitude (defined as area) of evoked epileptiform events in both L2/3 and L5 neurons. We recorded activity associated with epileptiform discharges in L1 and L5 interneurons to test the hypothesis that HCN channels regulate excitatory synaptic inputs differently in interneurons versus pyramidal neurons. HCN channel inhibition increased the magnitude of epileptiform events in both L1 and L5 interneurons. The increased magnitude of epileptiform events in both pyramidal cells and interneurons was due to an increase in network activity, since holding cells at depolarized potentials under voltage-clamp conditions to minimize HCN channel opening did not prevent enhancement in the presence of ZD 7288. In neurons recorded with ZD 7288-containing pipettes, bath application of the noninactivating inward cationic current (Ih) antagonist still produced increases in epileptiform responses. These results show that epileptiform discharges in disinhibited rat neocortex are modulated by HCN channels.

Impact of neuronal properties on network coding: roles of spike initiation dynamics and robust synchrony transfer

Neural networks are more than the sum of their parts, but the properties of those parts are nonetheless important. For instance, neuronal properties affect the degree to which neurons receiving common input will spike synchronously, and whether that synchrony will propagate through the network. Stimulus-evoked synchrony can help or hinder network coding depending on the type of code. In this Perspective, we describe how spike initiation dynamics influence neuronal input-output properties, how those properties affect synchronization, and how synchronization affects network coding. We propose that synchronous and asynchronous spiking can be used to multiplex temporal (synchrony) and rate coding and discuss how pyramidal neurons would be well suited for that task.

Self-tuning of inhibition by endocannabinoids shapes spike-time precision in CA1 pyramidal neurons

In the hippocampus, activity-dependent changes of synaptic transmission and spike-timing coordination are thought to mediate information processing for the purpose of memory formation. Here, we investigated the self-tuning of intrinsic excitability and spiking reliability by CA1 hippocampal pyramidal cells via changes of their GABAergic inhibitory inputs and endocannabinoid (eCB) signaling. Firing patterns of CA1 place cells, when replayed in vitro, induced an eCB-dependent transient reduction of spontaneous GABAergic activity, sharing the main features of depolarization-induced suppression of inhibition (DSI), and conditioned a transient improvement of spike-time precision during consecutive burst discharges. When evaluating the consequences of DSI on excitatory postsynaptic potential (EPSP)-spike coupling, we found that transient reductions of uncorrelated (spontaneous) or correlated (feedforward) inhibition improved EPSP-spike coupling probability. The relationship between EPSP-spike-timing reliability and inhibition was, however, more complex: transient reduction of correlated (feedforward) inhibition disrupted or improved spike-timing reliability according to the initial spike-coupling probability. Thus eCB-mediated tuning of pyramidal cell spike-time precision is governed not only by the initial level of global inhibition, but also by the ratio between spontaneous and feedforward GABAergic activities. These results reveal that eCB-mediated self-tuning of spike timing by the discharge of pyramidal cells can constitute an important contribution to place-cell assemblies and memory formation in the hippocampus.

Resonance properties of different neuronal populations in the immature mouse neocortex

In vivo recordings in the immature neocortex revealed spontaneous and sensory-driven oscillatory activity from delta (0.5-4 Hz) to gamma (30-100 Hz) frequencies. In order to investigate whether the resonance properties of distinct neuronal populations in the immature neocortex contribute to these network oscillations, we performed whole-cell patch-clamp recordings from visually identified neurons in tangential and coronal neocortical slices from postnatal day (P)0-P7 C57Bl/6 mice. Subthreshold resonance was analysed by sinusoidal current injection of varying frequency. All Cajal-Retzius cells showed subthreshold resonance, with an average frequency of 2.6 ± 0.1 Hz (n = 60), which was massively reduced by ZD7288, a blocker of hyperpolarization-activated cation currents. Approximately 65.6% (n = 61) of the supragranular pyramidal neurons showed subthreshold resonance, with an average frequency of 1.4 ± 0.1 Hz (n = 40). Application of Ni(2+) suppressed subthreshold resonance, suggesting that low-threshold calcium currents contribute to resonance in these neurons. Approximately 63.6% (n = 77) of the layer V pyramidal neurons showed subthreshold resonance, with an average frequency of 1.4 ± 0.2 Hz (n = 49), which was abolished by ZD7288. Only 44.1% (n = 59) of the subplate neurons showed subthreshold resonance, with an average frequency of 1.3 ± 0.2 Hz (n = 26) and a small resonance strength. In summary, these results demonstrate that neurons in all investigated layers show resonance behavior, with either hyperpolarization-activated cation or low-threshold calcium currents contributing to the subthreshold resonance. The observed resonance frequencies are in the range of slow activity patterns observed in the immature neocortex, suggesting that subthreshold resonance may support the generation of this activity.

Distinct roles for I(T) and I(H) in controlling the frequency and timing of rebound spike responses

The ability for neurons to generate rebound bursts following inhibitory synaptic input relies on ion channels that respond in a unique fashion to hyperpolarization. Inward currents provided by T-type calcium channels (I(T)) and hyperpolarization-activated HCN channels (I(H)) increase in availability upon hyperpolarization, allowing for a rebound depolarization after a period of inhibition. Although rebound responses have long been recognized in deep cerebellar nuclear (DCN) neurons, the actual extent to which I(T) and I(H) contribute to rebound spike output following physiological levels of membrane hyperpolarization has not been clearly established. The current study used recordings and simulations of large diameter cells of the in vitro rat DCN slice preparation to define the roles for I(T) and I(H) in a rebound response. We find that physiological levels of hyperpolarization make only small proportions of the total I(T) and I(H) available, but that these are sufficient to make substantial contributions to a rebound response. At least 50% of the early phase of the rebound spike frequency increase is generated by an I(T)-mediated depolarization. An additional frequency increase is provided by I(H) in reducing the time constant and thus the extent of I(T) inactivation as the membrane returns from a hyperpolarized state to the resting level. An I(H)-mediated depolarization creates an inverse voltage-first spike latency relationship and produces a 35% increase in the precision of the first spike latency of a rebound. I(T) and I(H) can thus be activated by physiologically relevant stimuli and have distinct roles in the frequency, timing and precision of rebound responses.