Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency

Dynamics of interaction between IH and IKLT currents to mediate double resonances of medial superior olive neurons related to sound localization

Neurons in the medial superior olive (MSO) exhibit high frequency responses such as subthreshold resonance, which is helpful to sensitively detect a small difference in the arrival time of sounds between two ears for precise sound localization. Recently, except for the high frequency depolarization resonance mediated by a low threshold potassium (IKLT) current, a low frequency hyperpolarization resonance mediated by a hyperpolarization-activated cation (IH) current is observed in experiments on the MSO neurons, forming double resonances. The complex dynamics underlying double resonances are studied in an MSO neuron model in the present paper. Firstly, double resonances similar to the experimental observations are simulated as the resting membrane potential is between half-activation voltages of IH and IKLT currents, and stimulation current (IZAP) with large amplitude and exponentially increasing frequency is applied. Secondly, multiple effective factors to modulate double resonances are obtained. Especially, the decrease of time constant of IKLT current and increase of conductance of IH and IKLT currents can enhance the depolarization resonance frequency for precise sound localization. Last, different frequency responses of slow IH and fast IKLT currents in formation of the resonances are acquired. A middle phase difference between IZAP and IKLT currents appears at a high frequency, and the interaction between the positive part of IZAP and the negative IKLT current forms the depolarization resonance. Interaction between the negative part of IZAP and positive IH current with a middle phase difference results in hyperpolarization resonance at a low frequency. Furthermore, the phase difference between IZAP and resonance current can well explain the increase of depolarization resonance frequency modulated by the increase of conductance of IH or IKLT currents. The results present the dynamical and biophysical mechanisms for the double resonances mediated by two currents in the MSO neurons, which is helpful to enhance the depolarization resonance frequency for precise sound localization.

The effects of different acetylcholinesterase inhibitors on EEG patterns in patients with Alzheimer's disease: A systematic review

OBJECTIVE

Alzheimer's disease (AD) is a progressive neurodegenerative disorder and the most common type of dementia. The early diagnosis of AD is an important factor for the control of AD progression. Electroencephalography (EEG) can be used for early diagnosis of AD. Acetylcholinesterase inhibitors (AChEIs) are also used for the amelioration of AD symptoms. In this systematic review, we reviewed the effect of different AChEIs including donepezil, rivastigmine, tacrine, physostigmine, and galantamine on EEG patterns in patients with AD.

METHODS

PubMed electronic database was searched and 122 articles were found. After removal of unrelated articles, 24 articles were selected for the present study.

RESULTS

AChEIs can decrease beta, theta, and delta frequency bands in patients with AD. However, conflicting results were found for alpha band. Some studies have shown increased alpha frequency, while others have shown decreased alpha frequency following treatment with AChEIs. The only difference was the type of drug.

CONCLUSIONS

We found that studies reporting the decreased alpha frequency used donepezil and galantamine, while studies reporting the increased alpha frequency used rivastigmine and tacrine. It was suggested that future studies should focus on the effect of different AChEIs on EEG bands, especially alpha frequency in patients with AD, to compare their effects and find the reason for their different influence on EEG patterns. Also, differences between the effects of AChEIs on oligodendrocyte differentiation and myelination may be another important factor. This is the first article investigating the effect of different AChEIs on EEG patterns in patients with AD.

Human NMDAR autoantibodies disrupt excitatory-inhibitory balance, leading to hippocampal network hypersynchrony

Anti-NMDA receptor autoantibodies (NMDAR-Abs) in patients with NMDAR encephalitis cause severe disease symptoms resembling psychosis and cause cognitive dysfunction. After passive transfer of patients' cerebrospinal fluid or human monoclonal anti-GluN1-autoantibodies in mice, we find a disrupted excitatory-inhibitory balance resulting from CA1 neuronal hypoexcitability, reduced AMPA receptor (AMPAR) signaling, and faster synaptic inhibition in acute hippocampal slices. Functional alterations are also reflected in widespread remodeling of the hippocampal proteome, including changes in glutamatergic and GABAergic neurotransmission. NMDAR-Abs amplify network γ oscillations and disrupt θ-γ coupling. A data-informed network model reveals that lower AMPAR strength and faster GABAA receptor current kinetics chiefly account for these abnormal oscillations. As predicted in silico and evidenced ex vivo, positive allosteric modulation of AMPARs alleviates aberrant γ activity, reinforcing the causative effects of the excitatory-inhibitory imbalance. Collectively, NMDAR-Ab-induced aberrant synaptic, cellular, and network dynamics provide conceptual insights into NMDAR-Ab-mediated pathomechanisms and reveal promising therapeutic targets that merit future in vivo validation.

Simulations predict differing phase responses to excitation vs. inhibition in theta-resonant pyramidal neurons

Rhythmic activity is ubiquitous in neural systems, with theta-resonant pyramidal neurons integrating rhythmic inputs in many cortical structures. Impedance analysis has been widely used to examine frequency-dependent responses of neuronal membranes to rhythmic inputs, but it assumes that the neuronal membrane is a linear system, requiring the use of small signals to stay in a near-linear regime. However, postsynaptic potentials are often large and trigger nonlinear mechanisms (voltage-gated ion channels). The goals of this work were to 1) develop an analysis method to evaluate membrane responses in this nonlinear domain and 2) explore phase relationships between rhythmic stimuli and subthreshold and spiking membrane potential (Vmemb) responses in models of theta-resonant pyramidal neurons. Responses in these output regimes were asymmetrical, with different phase shifts during hyperpolarizing and depolarizing half-cycles. Suprathreshold theta-rhythmic stimuli produced nonstationary Vmemb responses. Sinusoidal inputs produced "phase retreat": action potentials occurred progressively later in cycles of the input stimulus, resulting from adaptation. Sinusoidal current with increasing amplitude over cycles produced "phase advance": action potentials occurred progressively earlier. Phase retreat, phase advance, and subthreshold phase shifts were modulated by multiple ion channel conductances. Our results suggest differential responses of cortical neurons depending on the frequency of oscillatory input, which will play a role in neuronal responses to shifts in network state. We hypothesize that intrinsic cellular properties complement network properties and contribute to in vivo phase-shift phenomena such as phase precession, seen in place and grid cells, and phase roll, also observed in hippocampal CA1 neurons.NEW & NOTEWORTHY We augmented electrical impedance analysis to characterize phase shifts between large-amplitude current stimuli and nonlinear, asymmetric membrane potential responses. We predict different frequency-dependent phase shifts in response excitation vs. inhibition, as well as shifts in spike timing over multiple input cycles, in theta-resonant pyramidal neurons. We hypothesize that these effects contribute to navigation-related phenomena such as phase precession and phase roll. Our neuron-level hypothesis complements, rather than falsifies, prior network-level explanations of these phenomena.

Temporal dynamics of Na/K pump mediated memory traces: insights from conductance-based models of Drosophila neurons

Sodium potassium ATPases (Na/K pumps) mediate long-lasting, dynamic cellular memories that can last tens of seconds. The mechanisms controlling the dynamics of this type of cellular memory are not well understood and can be counterintuitive. Here, we use computational modeling to examine how Na/K pumps and the ion concentration dynamics they influence shape cellular excitability. In a Drosophila larval motor neuron model, we incorporate a Na/K pump, a dynamic intracellular Na⁺ concentration, and a dynamic Na⁺ reversal potential. We probe neuronal excitability with a variety of stimuli, including step currents, ramp currents, and zap currents, then monitor the sub- and suprathreshold voltage responses on a range of time scales. We find that the interactions of a Na⁺-dependent pump current with a dynamic Na⁺ concentration and reversal potential endow the neuron with rich response properties that are absent when the role of the pump is reduced to the maintenance of constant ion concentration gradients. In particular, these dynamic pump-Na⁺ interactions contribute to spike rate adaptation and result in long-lasting excitability changes after spiking and even after sub-threshold voltage fluctuations on multiple time scales. We further show that modulation of pump properties can profoundly alter a neuron's spontaneous activity and response to stimuli by providing a mechanism for bursting oscillations. Our work has implications for experimental studies and computational modeling of the role of Na/K pumps in neuronal activity, information processing in neural circuits, and the neural control of animal behavior.

Distinct Mechanisms Underlie Electrical Coupling Resonance and Its Interaction with Membrane Potential Resonance

Neurons in oscillatory networks often exhibit membrane potential resonance, a peak impedance at a non-zero input frequency. In electrically coupled oscillatory networks, the coupling coefficient (the ratio of post- and prejunctional voltage responses) could also show resonance. Such coupling resonance may emerge from the interaction between the coupling current and resonance properties of the coupled neurons, but this relationship has not been clearly described. Additionally, it is unknown if the gap-junction mediated electrical coupling conductance may have frequency dependence. We examined these questions by recording a pair of electrically coupled neurons in the oscillatory pyloric network of the crab Cancer borealis. We performed dual current- and voltage-clamp recordings and quantified the frequency preference of the coupled neurons, the coupling coefficient, the electrical conductance, and the postjunctional neuronal response. We found that all components exhibit frequency selectivity, but with distinct preferred frequencies. Mathematical and computational analysis showed that membrane potential resonance of the postjunctional neuron was sufficient to give rise to resonance properties of the coupling coefficient, but not the coupling conductance. A distinct coupling conductance resonance frequency therefore emerges either from other circuit components or from the gating properties of the gap junctions. Finally, to explore the functional effect of the resonance of the coupling conductance, we examined its role in synchronizing neuronal the activities of electrically coupled bursting model neurons. Together, our findings elucidate factors that produce electrical coupling resonance and the function of this resonance in oscillatory networks.

Multiple intrinsic membrane properties are modulated in a switch from single- to dual-network activity

Neural network flexibility includes changes in neuronal participation between networks, such as the switching of neurons between single- and dual-network activity. We previously identified a neuron that is recruited to burst in time with an additional network via modulation of its intrinsic membrane properties, instead of being recruited synaptically into the second network. However, the modulated intrinsic properties were not determined. Here, we use small networks in the Jonah crab (Cancer borealis) stomatogastric nervous system (STNS) to examine modulation of intrinsic properties underlying neuropeptide (Gly1-SIFamide)-elicited neuronal switching. The lateral posterior gastric neuron (LPG) switches from exclusive participation in the fast pyloric (∼1 Hz) network, due to electrical coupling, to dual-network activity that includes periodic escapes from the fast rhythm via intrinsically generated oscillations at the slower gastric mill network frequency (∼0.1 Hz). We isolated LPG from both networks by pharmacology and hyperpolarizing current injection. Gly1-SIFamide increased LPG intrinsic excitability and rebound from inhibition and decreased spike frequency adaptation, which can all contribute to intrinsic bursting. Using ion substitution and channel blockers, we found that a hyperpolarization-activated current, a persistent sodium current, and calcium or calcium-related current(s) appear to be primary contributors to Gly1-SIFamide-elicited LPG intrinsic bursting. However, this intrinsic bursting was more sensitive to blocking currents when LPG received rhythmic electrical coupling input from the fast network than in the isolated condition. Overall, a switch from single- to dual-network activity can involve modulation of multiple intrinsic properties, while synaptic input from a second network can shape the contributions of these properties.NEW & NOTEWORTHY Neuropeptide-elicited intrinsic bursting was recently determined to switch a neuron from single- to dual-network participation. Here we identified multiple intrinsic properties modulated in the dual-network state and candidate ion channels underlying the intrinsic bursting. Bursting at the second network frequency was more sensitive to blocking currents in the dual-network state than when neurons were synaptically isolated from their home network. Thus, synaptic input can shape the contributions of modulated intrinsic properties underlying dual-network activity.

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.

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.

Multimodal Functional Analysis Platform: 4. Optogenetics-Induced Oscillatory Activation to Explore Neural Circuits

To elucidate neural mechanisms underlying oscillatory phenomena in brain function, we have developed optogenetic tools and statistical methods. Specifically, opto-current-clamp induced oscillation reveals intrinsic frequency preferences in the neural circuits by oscillatory resonance. Furthermore, resonance or entrainment to intrinsic frequency is state-dependent. When resonance phenomena go beyond a certain range, it could even induce epileptic seizure in highly reproducible manner. We are able to study how seizures start, develop, and stop in neural circuits. Therefore, the optogenetics-induced oscillatory activation is a powerful tool in neuroscience research.

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.

Generating Brain Waves, the Power of Astrocytes

Synchronization of neuronal activity in the brain underlies the emergence of neuronal oscillations termed “brain waves”, which serve various physiological functions and correlate with different behavioral states. It has been postulated that at least ten distinct mechanisms are involved in the formulation of these brain waves, including variations in the concentration of extracellular neurotransmitters and ions, as well as changes in cellular excitability. In this mini review we highlight the contribution of astrocytes, a subtype of glia, in the formation and modulation of brain waves mainly due to their close association with synapses that allows their bidirectional interaction with neurons, and their syncytium-like activity via gap junctions that facilitate communication to distal brain regions through Ca²⁺ waves. These capabilities allow astrocytes to regulate neuronal excitability via glutamate uptake, gliotransmission and tight control of the extracellular K⁺ levels via a process termed K⁺ clearance. Spatio-temporal synchrony of activity across neuronal and astrocytic networks, both locally and distributed across cortical regions, underpins brain states and thereby behavioral states, and it is becoming apparent that astrocytes play an important role in the development and maintenance of neural activity underlying these complex behavioral states.

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.

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.

Short-term synaptic dynamics control the activity phase of neurons in an oscillatory network

In oscillatory systems, neuronal activity phase is often independent of network frequency. Such phase maintenance requires adjustment of synaptic input with network frequency, a relationship that we explored using the crab, Cancer borealis, pyloric network. The burst phase of pyloric neurons is relatively constant despite a > two fold variation in network frequency. We used noise input to characterize how input shape influences burst delay of a pyloric neuron, and then used dynamic clamp to examine how burst phase depends on the period, amplitude, duration, and shape of rhythmic synaptic input. Phase constancy across a range of periods required a proportional increase of synaptic duration with period. However, phase maintenance was also promoted by an increase of amplitude and peak phase of synaptic input with period. Mathematical analysis shows how short-term synaptic plasticity can coordinately change amplitude and peak phase to maximize the range of periods over which phase constancy is achieved.

Dynamic interplay between H-current and M-current controls motoneuron hyperexcitability in amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a type of motor neuron disease (MND) in which humans lose motor functions due to progressive loss of motoneurons in the cortex, brainstem, and spinal cord. In patients and in animal models of MND it has been observed that there is a change in the properties of motoneurons, termed neuronal hyperexcitability, which is an exaggerated response of the neurons to a stimulus. Previous studies suggested neuronal excitability is one of the leading causes for neuronal loss, however the factors that instigate excitability in neurons over the course of disease onset and progression are not well understood, as these studies have looked mainly at embryonic or early postnatal stages (pre-symptomatic). As hyperexcitability is not a static phenomenon, the aim of this study was to assess the overall excitability of upper motoneurons during disease progression, specifically focusing on their oscillatory behavior and capabilities to fire repetitively. Our results suggest that increases in the intrinsic excitability of motoneurons are a global phenomenon of aging, however the cellular mechanisms that underlie this hyperexcitability are distinct in SOD1G93A ALS mice compared with wild-type controls. The ionic mechanism driving increased excitability involves alterations of the expression levels of HCN and KCNQ channel genes leading to a complex dynamic of H-current and M-current activation. Moreover, we show a negative correlation between the disease onset and disease progression, which correlates with a decrease in the expression level of HCN and KCNQ channels. These findings provide a potential explanation for the increased vulnerability of motoneurons to ALS with aging.

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).

Distinct Co-Modulation Rules of Synapses and Voltage-Gated Currents Coordinate Interactions of Multiple Neuromodulators

Multiple neuromodulators act in concert to shape the properties of neural circuits. Different neuromodulators usually activate distinct receptors but can have overlapping targets. Therefore, circuit output depends on neuromodulator interactions at shared targets, a poorly understood process. We explored quantitative rules of co-modulation of two principal targets of neuromodulation: synapses and voltage-gated ionic currents. In the stomatogastric ganglion of the male crab Cancer borealis, the neuropeptides proctolin (Proc) and the crustacean cardioactive peptide (CCAP) modulate synapses of the pyloric circuit and activate a voltage-gated current (I _MI) in multiple neurons. We examined the validity of a simple dose-dependent quantitative rule, that co-modulation by Proc and CCAP is predicted by the linear sum of the individual effects of each modulator up to saturation. We found that this rule is valid for co-modulation of synapses, but not for the activation of I _MI, in which co-modulation was sublinear. The predictions for the co-modulation of I _MI activation were greatly improved if we assumed that the intracellular pathways activated by two peptide receptors inhibit one another. These findings suggest that the pathways activated by two neuromodulators could have distinct interactions, leading to distinct co-modulation rules for different targets even in the same neuron. Given the evolutionary conservation of neuromodulator receptors and signaling pathways, such distinct rules for co-modulation of different targets are likely to be common across neuronal circuits.SIGNIFICANCE STATEMENT We examine the quantitative rules of co-modulation at multiple shared targets, the first such characterization to our knowledge. Our results show that dose-dependent co-modulation of distinct targets in the same cells by the same two neuromodulators follows different rules: co-modulation of synaptic currents is linearly additive up to saturation, whereas co-modulation of the voltage-gated ionic current targeted in a single neuron is nonlinear, a mechanism that is likely generalizable. Given that all neural systems are multiply modulated and neuromodulators often act on shared targets, these findings and the methodology could guide studies to examine dynamic actions of neuromodulators at the biophysical and systems level in sensory and motor functions, sleep/wake regulation, and cognition.

Astrocytic modulation of cortical oscillations

Brain waves are rhythmic voltage oscillations emerging from the synchronization of individual neurons into a neuronal network. These oscillations range from slow to fast fluctuations, and are classified by power and frequency band, with different frequency bands being associated with specific behaviours. It has been postulated that at least ten distinct mechanisms are required to cover the frequency range of neural oscillations, however the mechanisms that gear the transition between distinct oscillatory frequencies are unknown. In this study, we have used electrophysiological recordings to explore the involvement of astrocytic K⁺ clearance processes in modulating neural oscillations at both network and cellular levels. Our results indicate that impairment of astrocytic K⁺ clearance capabilities, either through blockade of K⁺ uptake or astrocytic connectivity, enhance network excitability and form high power network oscillations over a wide range of frequencies. At the cellular level, local increases in extracellular K⁺ results in modulation of the oscillatory behaviour of individual neurons, which underlies the network behaviour. Since astrocytes are central for maintaining K⁺ homeostasis, our study suggests that modulation of their inherent capabilities to clear K⁺ from the extracellular milieu is a potential mechanism to optimise neural resonance behaviour and thus tune neural oscillations.

Network oscillation rules imposed by species-specific electrical coupling

Electrical junctions are widespread within the mammalian CNS. Yet, their role in organizing neuronal ensemble activity remains incompletely understood. Here, in a functionally well-characterized system – neuroendocrine tuberoinfundibular dopamine (TIDA) neurons - we demonstrate a striking species difference in network behavior: rat TIDA cells discharge in highly stereotyped, robust, synchronized slow oscillations, whereas mouse oscillations are faster, flexible and show substantial cell-to-cell variability. We show that these distinct operational modes are explained by the presence of strong TIDA-TIDA gap junction coupling in the rat, and its complete absence in the mouse. Both species, however, encompass a similar heterogeneous range of intrinsic resonance frequencies, suggesting similar network building blocks. We demonstrate that gap junctions select and impose the slow network rhythm. These data identify a role for electrical junctions in determining oscillation frequency and show how related species can rely on distinct network strategies to accomplish adaptive control of hormone release.

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.

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.

Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents

Neuronal membrane potential resonance (MPR) is associated with subthreshold and network oscillations. A number of voltage-gated ionic currents can contribute to the generation or amplification of MPR, but how the interaction of these currents with linear currents contributes to MPR is not well understood. We explored this in the pacemaker PD neurons of the crab pyloric network. The PD neuron MPR is sensitive to blockers of H- (I_H) and calcium-currents (I_Ca). We used the impedance profile of the biological PD neuron, measured in voltage clamp, to constrain parameter values of a conductance-based model using a genetic algorithm and obtained many optimal parameter combinations. Unlike most cases of MPR, in these optimal models, the values of resonant- (f_res) and phasonant- (f_{ϕ = 0}) frequencies were almost identical. Taking advantage of this fact, we linked the peak phase of ionic currents to their amplitude, in order to provide a mechanistic explanation the dependence of MPR on the I_Ca gating variable time constants. Additionally, we found that distinct pairwise correlations between I_Ca parameters contributed to the maintenance of f_res and resonance power (Q_Z). Measurements of the PD neuron MPR at more hyperpolarized voltages resulted in a reduction of f_res but no change in Q_Z. Constraining the optimal models using these data unmasked a positive correlation between the maximal conductances of I_H and I_Ca. Thus, although I_H is not necessary for MPR in this neuron type, it contributes indirectly by constraining the parameters of I_Ca.

Many neuron types exhibit membrane potential resonance (MPR) in which the neuron produces the largest response to oscillatory input at some preferred (resonant) frequency and, in many systems, the network frequency is correlated with neuronal MPR. MPR is captured by a peak in the impedance vs. frequency curve (Z-profile), which is shaped by the dynamics of voltage-gated ionic currents. Although neuron types can express variable levels of ionic currents, they may have a stable resonant frequency. We used the PD neuron of the crab pyloric network to understand how MPR emerges from the interplay of the biophysical properties of multiple ionic currents, each capable of generating resonance. We show the contribution of an inactivating current at the resonant frequency in terms of interacting time constants. We measured the Z-profile of the PD neuron and explored possible combinations of model parameters that fit this experimentally measured profile. We found that the Z-profile constrains and defines correlations among parameters associated with ionic currents. Furthermore, the resonant frequency and amplitude are sensitive to different parameter sets and can be preserved by co-varying pairs of parameters along their correlation lines. Furthermore, although a resonant current may be present in a neuron, it may not directly contribute to MPR, but constrain the properties of other currents that generate MPR. Finally, constraining model parameters further to those that modify their MPR properties to changes in voltage range produces maximal conductance correlations.

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.

BIOPHYSICAL PROPERTIES OF SUBTHRESHOLD RESONANCE OSCILLATIONS AND SUBTHRESHOLD MEMBRANE OSCILLATIONS IN NEURONS

Subthreshold-level activities in neurons play a crucial role in neuronal oscillations. These small-amplitude oscillations have been suggested to be involved in synaptic plasticity and in determining the frequency of network oscillations. Subthreshold membrane oscillations (STOs) and subthreshold resonance oscillations (SROs) are the main constituents of subthreshold-level activities in neurons. In this study, a general theoretical framework for analyzing the mechanisms underlying STOs and SROs in neurons is presented. Results showed that the resting membrane potential and the hyperpolarization-activated potassium channel (h-channel) affect the subthreshold-level activities in stellate cells. The contribution of h-channel on resonance is attributed to its large time constant, which produces the time lag between I_h and the membrane potential. Conversely, the persistent sodium channels (Nap-channels) only play an amplifying role in these neurons.

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.

Differential dopaminergic regulation of inwardly rectifying potassium channel mediated subthreshold dynamics in striatal medium spiny neurons

The dorsal striatum plays a key role in motor control and cognitive processes. Proper functioning of the striatum relies on the fine dynamic balance between the direct pathway projection medium spiny neurons (MSNs) that express D1 dopamine receptor (D1 MSNs) and indirect pathway projection MSNs that express D2 dopamine receptor (D2 MSNs). The inwardly rectifying K(+) channels (Kir), which express on both D1 and D2 MSNs, participate in the subthreshold dynamics including the membrane resonance and dendritic integration. However, it remains unclear whether dopamine differentially regulates Kir mediated subthreshold dynamics in two subtypes MSNs. Using transgenic mice that express either tdTomato in D1 MSNs or eGFP in D2 MSNs, we explored the Kir mediated subthreshold dynamics in D1 or D2 MSNs with whole cell patch clamp recording in acute brain slices. We found that D1 receptor agonist increased the Kir current while D2 receptor activation decreased the Kir conductance. The dopamine regulation of the Kir enhanced the resonant frequency and reduced the resonant impedance of D1 MSNs. The converse is ture for D2 MSNs. It also caused an opposing effect on dendritic integration between D1 and D2 MSNs, which can promote stability of the two pathways. The D1 receptor activation modulated Kir through cAMP-PKA signaling, whereas the D2 receptor modulated Kir through PLC-PKC signaling. Our findings demonstrated the differential dopaminergic regulation role of Kir, which mediates distinct subthreshold dynamics, and thus, contributes to the role of dopamine in fine tuning the balance of the striatal direct and indirect pathway activities.

Measurement of the entrainment window of islets of Langerhans by microfluidic delivery of a chirped glucose waveform

Within single islets of Langerhans, the endocrine portion of the pancreas, intracellular metabolites, as well as insulin secretion, oscillate with a period of ∼5 min. In vivo, pulsatile insulin oscillations are also observed with periods ranging from 5-15 minutes. In order for oscillations of insulin to be observed in vivo, the majority of islets in the pancreas must synchronize their output. It is known that populations of islets can be synchronized via entrainment of the individual islets to low amplitude glucose oscillations that have periods close to islets' natural period. However, the range of glucose periods and amplitudes that can entrain islets has not been rigorously examined. To find the range of glucose periods that can entrain islets, a microfluidic system was utilized to produce and deliver a chirped glucose waveform to populations of islets while their individual intracellular [Ca(2+)] ([Ca(2+)]i) oscillations were imaged. Waveforms with amplitudes of 0.5, 1, and 1.5 mM above a median value of 11 mM were applied while the period was swept from 20-2 min. Oscillations of [Ca(2+)]i resonated the strongest when the period of the glucose wave was within 2 min of the natural period of the islets, typically close to 5 min. Some examples of 1 : 2 and 2 : 1 entrainment were observed during exposure to long and short glucose periods, respectively. These results shed light on the dynamic nature of islet behavior and may help to understand dynamics observed in vivo.

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

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

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.

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.

The frequency preference of neurons and synapses in a recurrent oscillatory network

A variety of neurons and synapses shows a maximal response at a preferred frequency, generally considered to be important in shaping network activity. We are interested in whether all neurons and synapses in a recurrent oscillatory network can have preferred frequencies and, if so, whether these frequencies are the same or correlated, and whether they influence the network activity. We address this question using identified neurons in the pyloric network of the crab Cancer borealis. Previous work has shown that the pyloric pacemaker neurons exhibit membrane potential resonance whose resonance frequency is correlated with the network frequency. The follower lateral pyloric (LP) neuron makes reciprocally inhibitory synapses with the pacemakers. We find that LP shows resonance at a higher frequency than the pacemakers and the network frequency falls between the two. We also find that the reciprocal synapses between the pacemakers and LP have preferred frequencies but at significantly lower values. The preferred frequency of the LP to pacemaker synapse is correlated with the presynaptic preferred frequency, which is most pronounced when the peak voltage of the LP waveform is within the dynamic range of the synaptic activation curve and a shift in the activation curve by the modulatory neuropeptide proctolin shifts the frequency preference. Proctolin also changes the power of the LP neuron resonance without significantly changing the resonance frequency. These results indicate that different neuron types and synapses in a network may have distinct preferred frequencies, which are subject to neuromodulation and may interact to shape network oscillations.

Riluzole suppresses postinhibitory rebound in an excitatory motor neuron of the medicinal leech

Postinhibitory rebound (PIR) is an intrinsic property often exhibited by neurons involved in generating rhythmic motor behaviors. Cell DE-3, a dorsal excitatory motor neuron in the medicinal leech exhibits PIR responses that persist for several seconds following the offset of hyperpolarizing stimuli and are suppressed in reduced Na(+) solutions or by Ca(2+) channel blockers. The long duration and Na(+) dependence of PIR suggest a possible role for persistent Na(+) current (I NaP). In vertebrate neurons, the neuroprotective agent riluzole can produce a selective block of I NaP. This study demonstrates that riluzole inhibits cell DE-3 PIR in a concentration- and Ca(2+)-dependent manner. In 1.8 mM Ca(2+) solution, 50-100 µM riluzole selectively blocked the late phase of PIR, an effect similar to that of the neuromodulator serotonin. However, 200 µM riluzole blocked both the early and late phases of PIR. Increasing extracellular Ca(2+) to 10 mM strengthened PIR, but high riluzole concentrations continued to suppress both phases of PIR. These results indicate that riluzole may suppress PIR via a nonspecific inhibition of Ca(2+) conductances and suggest that a Ca(2+)-activated nonspecific current (I(CAN)), rather than I NaP, may underlie the Na(+)-dependent component of PIR.

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.

The spectro-contextual encoding and retrieval theory of episodic memory

The spectral fingerprint hypothesis, which posits that different frequencies of oscillations underlie different cognitive operations, provides one account for how interactions between brain regions support perceptual and attentive processes (Siegel etal., 2012). Here, we explore and extend this idea to the domain of human episodic memory encoding and retrieval. Incorporating findings from the synaptic to cognitive levels of organization, we argue that spectrally precise cross-frequency coupling and phase-synchronization promote the formation of hippocampal-neocortical cell assemblies that form the basis for episodic memory. We suggest that both cell assembly firing patterns as well as the global pattern of brain oscillatory activity within hippocampal-neocortical networks represents the contents of a particular memory. Drawing upon the ideas of context reinstatement and multiple trace theory, we argue that memory retrieval is driven by internal and/or external factors which recreate these frequency-specific oscillatory patterns which occur during episodic encoding. These ideas are synthesized into a novel model of episodic memory (the spectro-contextual encoding and retrieval theory, or "SCERT") that provides several testable predictions for future research.

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents

Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g(L) - g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.

Optogenetic manipulation of neural and non-neural functions

Optogenetic manipulation of the neuronal activity enables one to analyze the neuronal network both in vivo and in vitro with precise spatio-temporal resolution. Channelrhodopsins (ChRs) are light-sensitive cation channels that depolarize the cell membrane, whereas halorhodopsins and archaerhodopsins are light-sensitive Cl(-) and H(+) transporters, respectively, that hyperpolarize it when exogenously expressed. The cause-effect relationship between a neuron and its function in the brain is thus bi-directionally investigated with evidence of necessity and sufficiency. In this review we discuss the potential of optogenetics with a focus on three major requirements for its application: (i) selection of the light-sensitive proteins optimal for optogenetic investigation, (ii) targeted expression of these selected proteins in a specific group of neurons, and (iii) targeted irradiation with high spatiotemporal resolution. We also discuss recent progress in the application of optogenetics to studies of non-neural cells such as glial cells, cardiac and skeletal myocytes. In combination with stem cell technology, optogenetics may be key to successful research using embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs) derived from human patients through optical regulation of differentiation-maturation, through optical manipulation of tissue transplants and, furthermore, through facilitating survival and integration of transplants.

Resonance in neocortical neurons and networks

Neocortical networks produce oscillations that often correspond to characteristic physiological or pathological patterns. However, the mechanisms underlying the generation of and the transitions between such oscillatory states remain poorly understood. In this study, we examined resonance in mouse layer V neocortical pyramidal neurons. To accomplish this, we employed standard electrophysiology to describe cellular resonance parameters. Bode plot analysis revealed a range of resonance magnitude values in layer V neurons and demonstrated that both magnitude and phase response characteristics of layer V neocortical pyramidal neurons are modulated by changes in the extracellular environment. Specifically, increased resonant frequencies and total inductive areas were observed at higher extracellular potassium concentrations and more hyperpolarised membrane potentials. Experiments using pharmacological agents suggested that current through hyperpolarization-activated cyclic nucleotide-gated channels (I(h) ) acts as the primary driver of resonance in these neurons, with other potassium currents, such as A-type potassium current and delayed-rectifier potassium current (Kv1.4 and Kv1.1, respectively), contributing auxiliary roles. The persistent sodium current was also shown to play a role in amplifying the magnitude of resonance without contributing significantly to the phase response. Although resonance effects in individual neurons are small, their properties embedded in large networks may significantly affect network behavior and may have potential implications for pathological processes.

The role of voltage dependence of the NMDA receptor in cellular and network oscillation

Unraveling the mechanisms underlying oscillatory behavior is critical for understanding normal and pathological brain processes. Here we used electrophysiology in mouse neocortical slices and principles of nonlinear dynamics to demonstrate how an increase in the N-methyl-d-aspartic acid receptor (NMDAR) conductance can create a nonlinear whole-cell current-voltage (I-V) relationship which leads to changes in cellular stability. We discovered two behaviorally and morphologically distinct pyramidal cell populations. Under control conditions, both cell types responded to depolarizing current injection with regular spiking patterns. However, upon NMDAR activation, an intrinsic oscillatory (IO) cell type (n = 44) showed a nonlinear whole-cell I-V relationship, intrinsic voltage-dependent oscillations plus amplification of alternating input current, and these properties persisted after disabling action potential generation with tetrodotoxin (TTX). The other non-oscillatory (NO) neuronal population (n = 24) demonstrated none of these behaviors. Simultaneous intra- and extracellular recordings demonstrated the NMDAR's capacity to promote low-frequency seizure-like network oscillations via its effects on intrinsic neuronal properties. The two pyramidal cell types demonstrated different relationships with network oscillation--the IO cells were leaders that were activated early in the population activity cycle while the activation of the NO cell type was distributed across network bursts. The properties of IO neurons disappeared in a low-magnesium environment where the voltage dependence of the receptor is abolished; concurrently, the cellular contribution to network oscillation switched to synchronous firing. Thus, depending upon the efficacy of NMDAR in altering the linearity of the whole-cell I-V relationship, the two cell populations played different roles in sustaining network oscillation.

Postnatal development of electrophysiological properties of principal neurons in the rat basolateral amygdala

The basolateral amygdala (BLA) is critically involved in the pathophysiology of psychiatric disorders, which often emerge during brain development. Several studies have characterized postnatal changes to the morphology and biochemistry of BLA neurons, and many more have identified sensitive periods of emotional maturation. However, it is impossible to determine how BLA development contributes to emotional development or the aetiology of psychiatric disorders because no study has characterized the physiological maturation of BLA neurons. We addressed this critical knowledge gap for the first time using whole-cell patch clamp recording in rat BLA principal neurons to measure electrophysiological properties at postnatal day (P)7, P10, P14, P21, P28 and after P35. We show that intrinsic properties of these neurons undergo significant transitions before P21 and reach maturity around P28. Specifically, we observed significant reductions in input resistance and membrane time constant of nearly 10-and 4-fold, respectively, from P7 to P28. The frequency selectivity of these neurons to input also changed significantly, with peak resonance frequency increasing from 1.0 Hz at P7 to 5.7 Hz at P28. In the same period, maximal firing frequency significantly increased and doublets and triplets of action potentials emerged. Concomitantly, individual action potentials became significantly faster, firing threshold hyperpolarized 6.7 mV, the medium AHP became faster and shallower, and a fast AHP emerged. These results demonstrate neurons of the BLA undergo vast change throughout postnatal development, and studies of emotional development and treatments for juvenile psychiatric disorders should consider the dynamic physiology of the immature BLA.

The stomatogastric nervous system as a model for studying sensorimotor interactions in real-time closed-loop conditions

The perception of proprioceptive signals that report the internal state of the body is one of the essential tasks of the nervous system and helps to continuously adapt body movements to changing circumstances. Despite the impact of proprioceptive feedback on motor activity it has rarely been studied in conditions in which motor output and sensory activity interact as they do in behaving animals, i.e., in closed-loop conditions. The interaction of motor and sensory activities, however, can create emergent properties that may govern the functional characteristics of the system. We here demonstrate a method to use a well-characterized model system for central pattern generation, the stomatogastric nervous system, for studying these properties in vitro. We created a real-time computer model of a single-cell muscle tendon organ in the gastric mill of the crab foregut that uses intracellular current injections to control the activity of the biological proprioceptor. The resulting motor output of a gastric mill motor neuron is then recorded intracellularly and fed into a simple muscle model consisting of a series of low-pass filters. The muscle output is used to activate a one-dimensional Hodgkin-Huxley type model of the muscle tendon organ in real-time, allowing closed-loop conditions. Model properties were either hand tuned to achieve the best match with data from semi-intact muscle preparations, or an exhaustive search was performed to determine the best set of parameters. We report the real-time capabilities of our models, its performance and its interaction with the biological motor system.

Cellular mechanisms underlying spatiotemporal features of cholinergic retinal waves

Before vision, a transient network of recurrently connected cholinergic interneurons, called starburst amacrine cells (SACs), generates spontaneous retinal waves. Despite an absence of robust inhibition, cholinergic retinal waves initiate infrequently and propagate within finite boundaries. Here, we combine a variety of electrophysiological and imaging techniques and computational modeling to elucidate the mechanisms underlying these spatial and temporal properties of waves in developing mouse retina. Waves initiate via rare spontaneous depolarizations of SACs. Waves propagate through recurrent cholinergic connections between SACs and volume release of ACh as demonstrated using paired recordings and a cell-based ACh optical sensor. Perforated-patch recordings and two-photon calcium imaging reveal that individual SACs have slow afterhyperpolarizations that induce SACs to have variable depolarizations during sequential waves. Using a computational model in which the properties of SACs are based on these physiological measurements, we reproduce the slow frequency, speed, and finite size of recorded waves. This study represents a detailed description of the circuit that mediates cholinergic retinal waves and indicates that variability of the interneurons that generate this network activity may be critical for the robustness of waves across different species and stages of development.

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

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

Peptide neuromodulation of synaptic dynamics in an oscillatory network

Although neuromodulation of synapses is extensively documented, its consequences in the context of network oscillations are not well known. We examine the modulation of synaptic strength and short-term dynamics in the crab pyloric network by the neuropeptide proctolin. Pyloric oscillations are driven by a pacemaker group which receives feedback through the inhibitory synapse from the lateral pyloric (LP) to pyloric dilator (PD) neurons. We show that proctolin modulates the spike-mediated and graded components of the LP to PD synapse. Proctolin enhances the graded component and unmasks a surprising heterogeneity in its dynamics where there is depression or facilitation depending on the amplitude of the voltage waveform of the presynaptic LP neuron. The spike-mediated component is influenced by the baseline membrane potential and is also enhanced by proctolin at all baseline potentials. In addition to direct modulation of this synapse, proctolin also changes the shape and amplitude of the presynaptic voltage waveform which additionally enhances synaptic output during ongoing activity. During ongoing oscillations, proctolin reduces the variability of cycle period but only when the LP to PD synapse is functionally intact. Using the dynamic clamp technique we find that the reduction in variability is a direct consequence of modulation of the LP to PD synapse. These results demonstrate that neuromodulation of synapses involves complex and interacting influences that target different synaptic components and dynamics as well as the presynaptic voltage waveform. At the network level, modulation of feedback inhibition can result in reduction of variability and enhancement of stable oscillatory output.

Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms

Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. This complex is comprised of the Anterior Burster (AB) neuron and two Pyloric Dilator (PD) neurons that are all electrically coupled. Artificial excitatory synaptic conductance pulses of different strengths and durations were injected into one of the AB or PD somata using the Dynamic Clamp. Previously, we characterized the inhibitory PRCs by assuming a single slow process that enabled synaptic inputs to trigger switches between an up state in which spiking occurs and a down state in which it does not. Excitation produced five different PRC shapes, which could not be explained with such a simple model. A separate dendritic compartment was required to separate the mechanism that generates the up and down phases of the bursting envelope (1) from synaptic inputs applied at the soma, (2) from axonal spike generation and (3) from a slow process with a slower time scale than burst generation. This study reveals that due to the nonlinear properties and compartmentalization of ionic channels, the response to excitation is more complex than inhibition.

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

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