Electrical resonance in the θ frequency range in olfactory amygdala neurons

Astroglial gap junctions strengthen hippocampal network activity by sustaining afterhyperpolarization via KCNQ channels

Throughout the brain, astrocytes form networks mediated by gap junction channels that promote the activity of neuronal ensembles. Although their inputs on neuronal information processing are well established, how molecular gap junction channels shape neuronal network patterns remains unclear. Here, using astroglial connexin-deficient mice, in which astrocytes are disconnected and neuronal bursting patterns are abnormal, we show that astrocyte networks strengthen bursting activity via dynamic regulation of extracellular potassium levels, independently of glutamate homeostasis or metabolic support. Using a facilitation-depression model, we identify neuronal afterhyperpolarization as the key parameter underlying bursting pattern regulation by extracellular potassium in mice with disconnected astrocytes. We confirm this prediction experimentally and reveal that astroglial network control of extracellular potassium sustains neuronal afterhyperpolarization via KCNQ voltage-gated K+ channels. Altogether, these data delineate how astroglial gap junctions mechanistically strengthen neuronal population bursts and point to approaches for controlling aberrant activity in neurological diseases.

A role for circuitry of the cortical amygdala in excessive alcohol drinking, withdrawal, and alcohol use disorder

Alcohol use disorder (AUD) poses a significant public health challenge. Individuals with AUD engage in chronic and excessive alcohol consumption, leading to cycles of intoxication, withdrawal, and craving behaviors. This review explores the involvement of the cortical amygdala (CoA), a cortical brain region that has primarily been examined in relation to olfactory behavior, in the expression of alcohol dependence and excessive alcohol drinking. While extensive research has identified the involvement of numerous brain regions in AUD, the CoA has emerged as a relatively understudied yet promising candidate for future study. The CoA plays a vital role in rewarding and aversive signaling and olfactory-related behaviors and has recently been shown to be involved in alcohol-dependent drinking in mice. The CoA projects directly to brain regions that are critically important for AUD, such as the central amygdala, bed nucleus of the stria terminalis, and basolateral amygdala. These projections may convey key modulatory signaling that drives excessive alcohol drinking in alcohol-dependent subjects. This review summarizes existing knowledge on the structure and connectivity of the CoA and its potential involvement in AUD. Understanding the contribution of this region to excessive drinking behavior could offer novel insights into the etiology of AUD and potential therapeutic targets.

α2-Adrenergic modulation of Ih in adult-born granule cells in the olfactory bulb

In the olfactory bulb (OB), a large population of axon-less inhibitory interneurons, the granule cells (GCs), coordinate network activity and tune the output of principal neurons, the mitral and tufted cells (MCs), through dendrodendritic interactions. Furthermore, GCs undergo neurogenesis throughout life, providing a source of plasticity to the neural network of the OB. The function and integration of GCs in the OB are regulated by several afferent neuromodulatory signals, including noradrenaline (NA), a state-dependent neuromodulator that plays a crucial role in the regulation of cortical function and task-specific decision processes. However, the mechanisms by which NA regulates GC function are not fully understood. Here, we show that NA modulates hyperpolarization-activated currents (I_h) via the activation of α₂-adrenergic receptors (ARs) in adult-born GCs (abGCs), thus directly acting on channels that play essential roles in regulating neuronal excitability and network oscillations in the brain. This modulation affects the dendrodendritic output of GCs leading to an enhancement of lateral inhibition onto the MCs. Furthermore, we show that NA modulates subthreshold resonance in GCs, which could affect the temporal integration of abGCs. Together, these results provide a novel mechanism by which a state-dependent neuromodulator acting on I_h can regulate GC function in the OB.

Recurrence-Based Synchronization Analysis of Weakly Coupled Bursting Neurons Under External ELF Fields

We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.

Intracellular Properties of Deep-Layer Pyramidal Neurons in Frontal Eye Field of Macaque Monkeys

Although many details remain unknown, several positive statements can be made about the laminar distribution of primate frontal eye field (FEF) neurons with different physiological properties. Most certainly, pyramidal neurons in the deep layer of FEF that project to the brainstem carry movement and fixation signals but clear evidence also support that at least some deep-layer pyramidal neurons projecting to the superior colliculus carry visual responses. Thus, deep-layer neurons in FEF are functionally heterogeneous. Despite the useful functional distinctions between neuronal responses in vivo, the underlying existence of distinct cell types remain uncertain, mostly due to methodological limitations of extracellular recordings in awake behaving primates. To substantiate the functionally defined cell types encountered in the deep layer of FEF, we measured the biophysical properties of pyramidal neurons recorded intracellularly in brain slices issued from macaque monkey biopsies. Here, we found that biophysical properties recorded in vitro permit us to distinguish two main subtypes of regular-spiking neurons, with, respectively, low-resistance and low excitability vs. high-resistance and strong excitability. These results provide useful constraints for cognitive models of visual attention and saccade production by indicating that at least two distinct populations of deep-layer neurons exist.

Membrane Resonance in Pyramidal and GABAergic Neurons of the Mouse Perirhinal Cortex

The perirhinal cortex (PRC) is a polymodal associative region of the temporal lobe that works as a gateway between cortical areas and hippocampus. In recent years, an increasing interest arose in the role played by the PRC in learning and memory processes, such as object recognition memory, in contrast with certain forms of hippocampus-dependent spatial and episodic memory. The integrative properties of the PRC should provide all necessary resources to select and enhance the information to be propagated to and from the hippocampus. Among these properties, we explore in this paper the ability of the PRC neurons to amplify the output voltage to current input at selected frequencies, known as membrane resonance. Within cerebral circuits the resonance of a neuron operates as a filter toward inputs signals at certain frequencies to coordinate network activity in the brain by affecting the rate of neuronal firing and the precision of spike timing. Furthermore, the ability of the PRC neurons to resonate could have a fundamental role in generating subthreshold oscillations and in the selection of cortical inputs directed to the hippocampus. Here, performing whole-cell patch-clamp recordings from perirhinal pyramidal neurons and GABAergic interneurons of GAD67-GFP⁺ mice, we found, for the first time, that the majority of PRC neurons are resonant at their resting potential, with a resonance frequency of 0.5–1.5 Hz at 23°C and of 1.5–2.8 Hz at 36°C. In the presence of ZD7288 (blocker of HCN channels) resonance was abolished in both pyramidal neurons and interneurons, suggesting that I_h current is critically involved in resonance generation. Otherwise, application of TTx (voltage-dependent Na⁺ channel blocker) attenuates the resonance in pyramidal neurons but not in interneurons, suggesting that only in pyramidal neurons the persistent sodium current has an amplifying effect. These experimental results have also been confirmed by a computational model. From a functional point of view, the resonance in the PRC would affect the reverberating activity between neocortex and hippocampus, especially during slow wave sleep, and could be involved in the redistribution and strengthening of memory representation in cortical regions.

Differential contribution of the subthreshold operating currents IT, Ih, and IKir to the resonance of thalamocortical neurons

Membrane potential oscillations of thalamocortical (TC) neurons are believed to be involved in the generation and maintenance of brain rhythms that underlie global physiological and pathological brain states. These membrane potential oscillations depend on the synaptic interactions of TC neurons and their intrinsic electrical properties. These oscillations may be also shaped by increased output responses at a preferred frequency, known as intrinsic neuronal resonance. Here, we combine electrophysiological recordings in mouse brain slices, modern pharmacological tools, dynamic clamp, and computational modeling to study the ionic mechanisms that generate and modulate TC neuron resonance. We confirm findings of pioneering studies showing that most TC neurons display resonance that results from the interaction of the slow inactivation of the low-threshold calcium current I_T with the passive properties of the membrane. We also show that the hyperpolarization-activated cationic current I_h is not involved in the generation of resonance; instead it plays a minor role in the stabilization of TC neuron impedance magnitude due to its large contribution to the steady conductance. More importantly, we also demonstrate that TC neuron resonance is amplified by the inward rectifier potassium current I_Kir by a mechanism that hinges on its strong voltage-dependent inward rectification (i.e., a negative slope conductance region). Accumulating evidence indicate that the ion channels that control the oscillatory behavior of TC neurons participate in pathophysiological processes. Results presented here points to I_Kir as a new potential target for therapeutic intervention.NEW & NOTEWORTHY Our study expands the repertoire of ionic mechanisms known to be involved in the generation and control of resonance and provides the first experimental proof of previous theoretical predictions on resonance amplification mediated by regenerative hyperpolarizing currents. In thalamocortical neurons, we confirmed that the calcium current I_T generates resonance, determined that the large steady conductance of the cationic current I_h curtails resonance, and demonstrated that the inward rectifier potassium current I_Kir amplifies resonance.

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.

Post-stroke epileptogenesis is associated with altered intrinsic properties of hippocampal pyramidal neurons leading to increased theta resonance

Brain insults like stroke, trauma or infections often lead to blood-brain barrier-dysfunction (BBBd) frequently resulting into epileptogenesis. Affected patients suffer from seizures and cognitive comorbidities that are potentially linked to altered network oscillations. It has been shown that a hippocampal BBBd in rats leads to in vivo seizures and increased power at theta (3-8 Hz), an important type of network oscillations. However, the underlying cellular mechanisms remain poorly understood. At membrane potentials close to the threshold for action potentials (APs) a subpopulation of CA1 pyramidal cells (PCs) displays intrinsic resonant properties due to an interplay of the muscarine-sensitive K⁺-current (I_M) and the persistent Na⁺-current (I_NaP). Such resonant neurons are more excitable and generate more APs when stimulated at theta frequencies, being strong candidates for contributing to hippocampal theta oscillations during epileptogenesis. We tested this hypothesis by characterizing changes in intrinsic properties of hippocampal PCs one week after post-stroke epileptogenesis, a model associated with BBBd, using slice electrophysiology and computer modeling. We find a higher proportion of resonant neurons in BBBd compared to sham animals (47 vs. 29%), accompanied by an increase in their excitability. In contrast, BBBd non-resonant neurons showed a reduced excitability, presented with lower impedance and more positive AP threshold. We identify an increase in I_M combined with either a reduction in I_NaP or an increase in I_Leak as possible mechanisms underlying the observed changes. Our results support the hypothesis that a higher proportion of more excitable resonant neurons in the hippocampus contributes to increased theta oscillations and an increased likelihood of seizures in a model of post-stroke epileptogenesis.

Chemical modulation of Kv7 potassium channels

The rising interest in Kv7 modulators originates from their ability to evoke fundamental electrophysiological perturbations in a tissue-specific manner. A large number of therapeutic applications are, in part, based on the clinical experience with two broad-spectrum Kv7 agonists, flupirtine and retigabine. Since precise molecular structures of human Kv7 channel subtypes in closed and open states have only very recently started to emerge, computational studies have traditionally been used to analyze binding modes and direct the development of more potent and selective Kv7 modulators with improved safety profiles. Herein, the synthetic and medicinal chemistry of small molecule modulators and the representative biological properties are summarized. Furthermore, new therapeutic applications supported by in vitro and in vivo assay data are suggested.

Kv11 (ether-à-go-go-related gene) voltage-dependent K+ channels promote resonance and oscillation of subthreshold membrane potentials

Key points

Some ion channels are known to behave as inductors and make up the parallel resonant circuit in the plasma membrane of neurons, which enables neurons to respond to current inputs with a specific frequency (so‐called ‘resonant properties’).

Here, we report that heterologous expression of mouse Kv11 voltage‐dependent K⁺ channels generate resonance and oscillation at depolarized membrane potentials in HEK293 cells; expressions of individual Kv11 subtypes generate resonance and oscillation with different frequency properties.

Kv11.3‐expressing HEK293 cells exhibited transient conductance changes that opposed the current changes induced by voltage steps; this probably enables Kv11 channels to behave like an inductor.

The resonance and oscillation of inferior olivary neurons were impaired at the resting membrane potential in Kv11.3 knockout mice.

This study helps to elucidate basic ion channel properties that are crucial for the frequency responses of neurons.

Abstract

The plasma membranes of some neurons preferentially respond to current inputs with a specific frequency, and output as large voltage changes. This property is called resonance, and is thought to be mediated by ion channels that show inductor‐like behaviour. However, details of the candidate ion channels remain unclear. In this study, we mainly focused on the functional roles of Kv11 potassium (K⁺) channels, encoded by ether‐á‐go‐go‐related genes, in resonance in mouse inferior olivary (IO) neurons. We transfected HEK293 cells with long or short splice variants of Kv11.1 (Merg1a and Merg1b) or Kv11.3, and examined membrane properties using whole‐cell recording. Transfection with Kv11 channels reproduced resonance at membrane potentials depolarized from the resting state. Frequency ranges of Kv11.3‐, Kv11.1(Merg1b)‐ and Kv11.1(Merg1a)‐expressing cells were 2–6 Hz, 2–4 Hz, and 0.6–0.8 Hz, respectively. Responses of Kv11.3 currents to step voltage changes were essentially similar to those of inductor currents in the resistor–inductor–capacitor circuit. Furthermore, Kv11 transfections generated membrane potential oscillations. We also confirmed the contribution of HCN1 channels as a major mediator of resonance at more hyperpolarized potentials by transfection into HEK293 cells. The Kv11 current kinetics and properties of Kv11‐dependent resonance suggested that Kv11.3 mediated resonance in IO neurons. This finding was confirmed by the impairment of resonance and oscillation at –30 to –60 mV in Kcnh7 (Kv11.3) knockout mice. These results suggest that Kv11 channels have important roles in inducing frequency‐dependent responses in a subtype‐dependent manner from resting to depolarized membrane potentials.

Some ion channels are known to behave as inductors and make up the parallel resonant circuit in the plasma membrane of neurons, which enables neurons to respond to current inputs with a specific frequency (so‐called ‘resonant properties’).

Here, we report that heterologous expression of mouse Kv11 voltage‐dependent K⁺ channels generate resonance and oscillation at depolarized membrane potentials in HEK293 cells; expressions of individual Kv11 subtypes generate resonance and oscillation with different frequency properties.

Kv11.3‐expressing HEK293 cells exhibited transient conductance changes that opposed the current changes induced by voltage steps; this probably enables Kv11 channels to behave like an inductor.

The resonance and oscillation of inferior olivary neurons were impaired at the resting membrane potential in Kv11.3 knockout mice.

This study helps to elucidate basic ion channel properties that are crucial for the frequency responses of neurons.

Asymmetrical voltage response in resonant neurons shaped by nonlinearities

The conventional impedance profile of a neuron can identify the presence of resonance and other properties of the neuronal response to oscillatory inputs, such as nonlinear response amplifications, but it cannot distinguish other nonlinear properties such as asymmetries in the shape of the voltage response envelope. Experimental observations have shown that the response of neurons to oscillatory inputs preferentially enhances either the upper or lower part of the voltage envelope in different frequency bands. These asymmetric voltage responses arise in a neuron model when it is submitted to high enough amplitude oscillatory currents of variable frequencies. We show how the nonlinearities associated to different ionic currents or present in the model as captured by its voltage equation lead to asymmetrical response and how high amplitude oscillatory currents emphasize this response. We propose a geometrical explanation for the phenomenon where asymmetries result not only from nonlinearities in their activation curves but also from nonlinearites captured by the nullclines in the phase-plane diagram and from the system's time-scale separation. In addition, we identify an unexpected frequency-dependent pattern which develops in the gating variables of these currents and is a product of strong nonlinearities in the system as we show by controlling such behavior by manipulating the activation curve parameters. The results reported in this paper shed light on the ionic mechanisms by which brain embedded neurons process oscillatory information.

Mixed-mode oscillations in pyramidal neurons under antiepileptic drug conditions

Subthreshold oscillations in combination with large-amplitude oscillations generate mixed-mode oscillations (MMOs), which mediate various spatial and temporal cognition and memory processes and behavioral motor tasks. Although many studies have shown that canard theory is a reliable method to investigate the properties underlying the MMOs phenomena, the relationship between the results obtained by applying canard theory and conductance-based models of neurons and their electrophysiological mechanisms are still not well understood. The goal of this study was to apply canard theory to the conductance-based model of pyramidal neurons in layer V of the Entorhinal Cortex to investigate the properties of MMOs under antiepileptic drug conditions (i.e., when persistent sodium current is inhibited). We investigated not only the mathematical properties of MMOs in these neurons, but also the electrophysiological mechanisms that shape spike clustering. Our results show that pyramidal neurons can display two types of MMOs and the magnitude of the slow potassium current determines whether MMOs of type I or type II would emerge. Our results also indicate that slow potassium currents with large time constant have significant impact on generating the MMOs, as opposed to fast inward currents. Our results provide complete characterization of the subthreshold activities in MMOs in pyramidal neurons and provide explanation to experimental studies that showed MMOs of type I or type II in pyramidal neurons under antiepileptic drug conditions.

Competition between Persistent Na+ and Muscarine-Sensitive K+ Currents Shapes Perithreshold Resonance and Spike Tuning in CA1 Pyramidal Neurons

Neurons from many brain regions display intrinsic subthreshold theta-resonance, responding preferentially to theta-frequency oscillatory stimuli. Resonance may contribute to selective communication among neurons and to orchestrate brain rhythms. CA1 pyramidal neurons receive theta activity, generating place fields. In these neurons the expression of perithreshold frequency preference is controversial, particularly in the spiking regime, with evidence favoring either non-resonant (integrator-like) or resonant behavior. Perithreshold dynamics depends on the persistent Na⁺ current I_NaP developing above −70 mV and the muscarine-sensitive K⁺ current I_M activating above −60 mV. We conducted current and voltage clamp experiments in slices to investigate perithreshold excitability of CA1 neurons under oscillatory stimulation. Around 20% of neurons displayed perithreshold resonance that is expressed in spiking. The remaining neurons (~80%) acted as low-pass filters lacking frequency preference. Paired voltage clamp measurement of I_NaP and I_M showed that perithreshold activation of I_M is in general low while I_NaP is high enough to depolarize neurons toward threshold before resonance expression, explaining the most abundant non-resonant perithreshold behavior. Partial blockade of I_NaP by pharmacological tools or dynamic clamp changed non-resonant to resonant behavior. Furthermore, shifting I_M activation toward hyperpolarized potentials by dynamic clamp also transformed non-resonant neurons into resonant ones. We propose that the relative levels of I_NaP and I_M control perithreshold behavior of CA1 neurons constituting a gating mechanism for theta resonance in the spiking regime. Both currents are regulated by intracellular signaling and neuromodulators which may allow dynamic switching of perithreshold behavior between resonant and non-resonant.

Hyperpolarization-Activated Currents and Subthreshold Resonance in Granule Cells of the Olfactory Bulb

An important contribution to neural circuit oscillatory dynamics is the ongoing activation and inactivation of hyperpolarization-activated currents (Ih). Network synchrony dynamics play an important role in the initial processing of odor signals by the main olfactory bulb (MOB) and accessory olfactory bulb (AOB). In the mouse olfactory bulb, we show that Ih is present in granule cells (GCs), the most prominent inhibitory neuron in the olfactory bulb, and that Ih underlies subthreshold resonance in GCs. In accord with the properties of Ih, the currents exhibited sensitivity to changes in extracellular K+ concentration and ZD7288 (4-ethylphenylamino-1,2-dimethyl-6-methylaminopyrimidin chloride), a blocker of Ih. ZD7288 also caused GCs to hyperpolarize and increase their input resistance, suggesting that Ih is active at rest in GCs. The inclusion of cAMP in the intracellular solution shifted the activation of Ih to less negative potentials in the MOB, but not in the AOB, suggesting that channels with different subunit composition mediate Ih in these regions. Furthermore, we show that mature GCs exhibit Ih-dependent subthreshold resonance in the theta frequency range (4-12 Hz). Another inhibitory subtype in the MOB, the periglomerular cells, exhibited Ih-dependent subthreshold resonance in the delta range (1-4 Hz), while principal neurons, the mitral cells, do not exhibit Ih-dependent subthreshold resonance. Importantly, Ih size, as well as the strength and frequency of resonance in GCs, exhibited a postnatal developmental progression, suggesting that this development of Ih in GCs may differentially contribute to their integration of sensory input and contribution to oscillatory circuit dynamics.

The ionic mechanism of membrane potential oscillations and membrane resonance in striatal LTS interneurons

Striatal low-threshold spiking (LTS) interneurons spontaneously transition to a depolarized, oscillating state similar to that seen after sodium channels are blocked. In the depolarized state, whether spontaneous or induced by sodium channel blockade, the neurons express a 3- to 7-Hz oscillation and membrane impedance resonance in the same frequency range. The membrane potential oscillation and membrane resonance are expressed in the same voltage range (greater than -40 mV). We identified and recorded from LTS interneurons in striatal slices from a mouse that expressed green fluorescent protein under the control of the neuropeptide Y promoter. The membrane potential oscillation depended on voltage-gated calcium channels. Antagonism of L-type calcium currents (Ca_V1) reduced the amplitude of the oscillation, whereas blockade of N-type calcium currents (Ca_V2.2) reduced the frequency. Both calcium sources activate a calcium-activated chloride current (CaCC), the blockade of which abolished the oscillation. The blocking of any of these three channels abolished the membrane resonance. Immunohistochemical staining indicated anoctamin 2 (ANO2), and not ANO1, as the CaCC source. Biophysical modeling showed that Ca_V1, Ca_V2.2, and ANO2 are sufficient to generate a membrane potential oscillation and membrane resonance, similar to that in LTS interneurons. LTS interneurons exhibit a membrane potential oscillation and membrane resonance that are both generated by Ca_V1 and Ca_V2.2 activating ANO2. They can spontaneously enter a state in which the membrane potential oscillation dominates the physiological properties of the neuron.

Electrical resonance with voltage-gated ion channels: perspectives from biophysical mechanisms and neural electrophysiology

Electrical resonance, providing selective signal amplification at preferred frequencies, is a unique phenomenon of excitable membranes, which has been observed in the nervous system at the cellular, circuit and system levels. The mechanisms underlying electrical resonance have not been fully elucidated. Prevailing hypotheses attribute the resonance to voltage-gated ion channels on the membrane of single neurons. In this review, we follow this line of thinking to summarize and analyze the biophysical/molecular mechanisms, and also the physiological relevance of channel-mediated electrical resonance.

Mathematical modeling of subthreshold resonant properties in pyloric dilator neurons

Various types of neurons exhibit subthreshold resonance oscillation (preferred frequency response) to fluctuating sinusoidal input currents. This phenomenon is well known to influence the synaptic plasticity and frequency of neural network oscillation. This study evaluates the resonant properties of pacemaker pyloric dilator (PD) neurons in the central pattern generator network through mathematical modeling. From the pharmacological point of view, calcium currents cannot be blocked in PD neurons without removing the calcium-dependent potassium current. Thus, the effects of calcium (I_Ca) and calcium-dependent potassium (I_KCa) currents on resonant properties remain unclear. By taking advantage of Hodgkin-Huxley-type model of neuron and its equivalent RLC circuit, we examine the effects of changing resting membrane potential and those ionic currents on the resonance. Results show that changing the resting membrane potential influences the amplitude and frequency of resonance so that the strength of resonance (Q-value) increases by both depolarization and hyperpolarization of the resting membrane potential. Moreover, hyperpolarization-activated inward current (I_h) and I_Ca (in association with I_KCa) are dominant factors on resonant properties at hyperpolarized and depolarized potentials, respectively. Through mathematical analysis, results indicate that I_h and I_KCa affect the resonant properties of PD neurons. However, I_Ca only has an amplifying effect on the resonance amplitude of these neurons.