Apamin-sensitive small conductance calcium-activated potassium channels, through their selective coupling to voltage-gated calcium channels, are critical determinants of the precision, pace, and pattern of action potential generation in rat subthalamic nucleus neurons in vitro

Evoked resonant neural activity long-term dynamics can be reproduced by a computational model with vesicle depletion

Subthalamic deep brain stimulation (DBS) robustly generates high-frequency oscillations known as evoked resonant neural activity (ERNA). Recently the importance of ERNA has been demonstrated through its ability to predict the optimal DBS contact in the subthalamic nucleus in patients with Parkinson's disease. However, the underlying mechanisms of ERNA are not well understood, and previous modelling efforts have not managed to reproduce the wealth of published data describing the dynamics of ERNA. Here, we aim to present a minimal model capable of reproducing the characteristics of the slow ERNA dynamics published to date. We make biophysically-motivated modifications to the Kuramoto model and fit its parameters to the slow dynamics of ERNA obtained from data. Our results demonstrate that it is possible to reproduce the slow dynamics of ERNA (over hundreds of seconds) with a single neuronal population, and, crucially, with vesicle depletion as one of the key mechanisms behind the ERNA frequency decay in our model. We further validate the proposed model against experimental data from Parkinson's disease patients, where it captures the variations in ERNA frequency and amplitude in response to variable stimulation frequency, amplitude, and to stimulation pulse bursting. We provide a series of predictions from the model that could be the subject of future studies for further validation.

Mathematical derivation and mechanism analysis of beta oscillations in a cortex-pallidum model

In this paper, we develop a new cortex-pallidum model to study the origin mechanism of Parkinson's oscillations in the cortex. In contrast to many previous models, the globus pallidus internal (GPi) and externa (GPe) both exert direct inhibitory feedback to the cortex. Using Hopf bifurcation analysis, two new critical conditions for oscillations, which can include the self-feedback projection of GPe, are obtained. In this paper, we find that the average discharge rate (ADR) is an important marker of oscillations, which can divide Hopf bifurcations into two types that can uniformly be used to explain the oscillation mechanism. Interestingly, the ADR of the cortex first increases and then decreases with increasing coupling weights that are projected to the GPe. Regarding the Hopf bifurcation critical conditions, the quantitative relationship between the inhibitory projection and excitatory projection to the GPe is monotonically increasing; in contrast, the relationship between different coupling weights in the cortex is monotonically decreasing. In general, the oscillation amplitude is the lowest near the bifurcation points and reaches the maximum value with the evolution of oscillations. The GPe is an effective target for deep brain stimulation to alleviate oscillations in the cortex.

Molecular and functional profiling of cell diversity and identity in the lateral superior olive, an auditory brainstem center with ascending and descending projections

The lateral superior olive (LSO), a prominent integration center in the auditory brainstem, contains a remarkably heterogeneous population of neurons. Ascending neurons, predominantly principal neurons (pLSOs), process interaural level differences for sound localization. Descending neurons (lateral olivocochlear neurons, LOCs) provide feedback into the cochlea and are thought to protect against acoustic overload. The molecular determinants of the neuronal diversity in the LSO are largely unknown. Here, we used patch-seq analysis in mice at postnatal days P10-12 to classify developing LSO neurons according to their functional and molecular profiles. Across the entire sample (n = 86 neurons), genes involved in ATP synthesis were particularly highly expressed, confirming the energy expenditure of auditory neurons. Two clusters were identified, pLSOs and LOCs. They were distinguished by 353 differentially expressed genes (DEGs), most of which were novel for the LSO. Electrophysiological analysis confirmed the transcriptomic clustering. We focused on genes affecting neuronal input-output properties and validated some of them by immunohistochemistry, electrophysiology, and pharmacology. These genes encode proteins such as osteopontin, Kv11.3, and Kvβ3 (pLSO-specific), calcitonin-gene-related peptide (LOC-specific), or Kv7.2 and Kv7.3 (no DEGs). We identified 12 "Super DEGs" and 12 genes showing "Cluster similarity." Collectively, we provide fundamental and comprehensive insights into the molecular composition of individual ascending and descending neurons in the juvenile auditory brainstem and how this may relate to their specific functions, including developmental aspects.

Modulation of SK Channels via Calcium Buffering Tunes Intrinsic Excitability of Parvalbumin Interneurons in Neuropathic Pain: A Computational and Experimental Investigation

Parvalbumin-expressing interneurons (PVINs) play a crucial role within the dorsal horn of the spinal cord by preventing touch inputs from activating pain circuits. In both male and female mice, nerve injury decreases PVINs' output via mechanisms that are not fully understood. In this study, we show that PVINs from nerve-injured male mice change their firing pattern from tonic to adaptive. To examine the ionic mechanisms responsible for this decreased output, we used a reparametrized Hodgkin-Huxley type model of PVINs, which predicted (1) the firing pattern transition is because of an increased contribution of small conductance calcium-activated potassium (SK) channels, enabled by (2) impairment in intracellular calcium buffering systems. Analyzing the dynamics of the Hodgkin-Huxley type model further demonstrated that a generalized Hopf bifurcation differentiates the two types of state transitions observed in the transient firing of PVINs. Importantly, this predicted mechanism holds true when we embed the PVIN model within the neuronal circuit model of the spinal dorsal horn. To experimentally validate this hypothesized mechanism, we used pharmacological modulators of SK channels and demonstrated that (1) tonic firing PVINs from naive male mice become adaptive when exposed to an SK channel activator, and (2) adapting PVINs from nerve-injured male mice return to tonic firing on SK channel blockade. Our work provides important insights into the cellular mechanism underlying the decreased output of PVINs in the spinal dorsal horn after nerve injury and highlights potential pharmacological targets for new and effective treatment approaches to neuropathic pain.SIGNIFICANCE STATEMENT Parvalbumin-expressing interneurons (PVINs) exert crucial inhibitory control over Aβ fiber-mediated nociceptive pathways at the spinal dorsal horn. The loss of their inhibitory tone leads to neuropathic symptoms, such as mechanical allodynia, via mechanisms that are not fully understood. This study identifies the reduced intrinsic excitability of PVINs as a potential cause for their decreased inhibitory output in nerve-injured condition. Combining computational and experimental approaches, we predict a calcium-dependent mechanism that modulates PVINs' electrical activity following nerve injury: a depletion of cytosolic calcium buffer allows for the rapid accumulation of intracellular calcium through the active membranes, which in turn potentiates SK channels and impedes spike generation. Our results therefore pinpoint SK channels as potential therapeutic targets for treating neuropathic symptoms.

Distinct excitability of thalamocortical neurons correlates with the presence of cerebellar afferents

Thalamocortical (TC) neurons within the ventrolateral thalamus (VL) receive projections from the cerebellum and the basal ganglia (BG) to facilitate motor and non-motor functions. Tonic and rebound firing patterns in response to excitatory cerebellar and inhibitory BG inputs, respectively, are a canonical feature of TC neurons and plays a key role in signal processing. The intrinsic excitability of TC neurons has a strong influence on how they respond to synaptic inputs, however, it is unknown whether their afferents influence their firing properties. Understanding the input-specific firing patterns could shed light into movement disorders with cerebellar or BG involvement. Here, we used whole-cell electrophysiology in brain slices from C57BL/6 mice to investigate the firing of TC neurons with optogenetic confirmation of cerebellar or BG afferents. TC neurons with cerebellar afferents exhibited higher tonic and rebound firing rates than those with BG afferents. This increased firing was associated with faster action potential depolarization kinetics and a smaller afterhyperpolarization potential. We also found differences in the passive membrane properties and sag currents during hyperpolarization. Despite higher rebound firing in TC neurons with cerebellar afferents, there were no differences in T-type calcium channel function compared to those with BG inputs. These data suggest input-specific differences in sodium and SK, but not T-type calcium channels, impact firing properties in TC populations. Altogether, we showed that the pronounced divergence observed in TC neuron firing properties correlate with its heterogeneous anatomical connectivity, which could signify a distinct signal integration and processing by these neurons.

Keypoints

Thalamocortical neurons in the VL with cerebellar afferents have higher intrinsic tonic and rebound firing properties than those with basal ganglia afferents.Membrane resistance and action potential depolarization slope were different based on the presence of cerebellar afferents.Despite elevated rebound burst firing, T-type mediated currents did not correlate with increased firing in neurons with cerebellar afferents.

The mechanism of Parkinson oscillation in the cortex: Possible evidence in a feedback model projecting from the globus pallidus to the cortex

The origin, location and cause of Parkinson's oscillation are not clear at present. In this paper, we establish a new cortex-basal ganglia model to study the origin mechanism of Parkinson beta oscillation. Unlike many previous models, this model includes two direct inhibitory projections from the globus pallidus external (GPe) segment to the cortex. We first obtain the critical calculation formula of Parkinson's oscillation by using the method of Quasilinear analysis. Different from previous studies, the formula obtained in this paper can include the self-feedback connection of GPe. Then, we use the bifurcation analysis method to systematically explain the influence of some key parameters on the oscillation. We find that the bifurcation principle of different cortical nuclei is different. In general, the increase of the discharge capacity of the nuclei will cause oscillation. In some special cases, the sharp reduction of the discharge rate of the nuclei will also cause oscillation. The direction of bifurcation simulation is consistent with the critical condition curve. Finally, we discuss the characteristics of oscillation amplitude. At the beginning of the oscillation, the amplitude is relatively small; with the evolution of oscillation, the amplitude will gradually strengthen. This is consistent with the experimental phenomenon. In most cases, the amplitude of cortical inhibitory nuclei (CIN) is greater than that of cortical excitatory nuclei (CEX), and the two direct inhibitory projections feedback from GPe can significantly reduce the amplitude gap between them. We calculate the main frequency of the oscillation generated in this model, which basically falls between 13 and 30 Hz, belonging to the typical beta frequency band oscillation. Some new results obtained in this paper can help to better understand the origin mechanism of Parkinson's disease and have guiding significance for the development of experiments.

Targeting Circuit Abnormalities in Neurodegenerative Disease

Despite significant improvement in our ability to diagnose both common and rare neurodegenerative diseases and understand their underlying biologic mechanisms, there remains a disproportionate lack of effective treatments, reflecting the complexity of these disorders. Successfully advancing novel treatments for neurodegenerative disorders will require reconsideration of traditional approaches, which to date have focused largely on specific disease proteins or cells of origin. This article proposes reframing these diseases as conditions of dysfunctional circuitry as a complement to ongoing efforts. Specifically reviewed is how aberrant spiking is a common downstream mechanism in numerous neurodegenerative diseases, often driven by dysfunction in specific ion channels. Surgical modification of this electrical activity via deep brain stimulation is already an approved modality for many of these disorders. Therefore, restoring proper electrical activity by targeting these channels pharmacologically represents a viable strategy for intervention, not only for symptomatic management but also as a potential disease-modifying therapy. Such an approach is likely to be a promising route to treating these devastating disorders, either as monotherapy or in conjunction with current drugs. SIGNIFICANCE STATEMENT: Despite extensive research and improved understanding of the biology driving neurodegenerative disease, there has not been a concomitant increase in approved therapies. Accordingly, it is time to shift our perspective and recognize these diseases also as disorders of circuitry to further yield novel drug targets and new interventions. An approach focused on treating dysfunctional circuitry has the potential to reduce or reverse patient symptoms and potentially modify disease course.

Altered neural cell junctions and ion-channels leading to disrupted neuron communication in Parkinson's disease

Parkinson’s disease (PD) is a neurological disorder that affects the movement of the human body. It is primarily characterized by reduced dopamine levels in the brain. The causative agent of PD is still unclear but it is generally accepted that α-synuclein has a central role to play. It is also known that gap-junctions and associated connexins are complicated structures that play critical roles in nervous system signaling and associated misfunctioning. Thus, our current article emphasizes how, alongside α-synuclein, ion-channels, gap-junctions, and related connexins, all play vital roles in influencing multiple metabolic activities of the brain during PD. It also highlights that ion-channel and gap-junction disruptions, which are primarily mediated by their structural-functional changes and alterations, have a role in PD. Furthermore, we discussed available drugs and advanced therapeutic interventions that target Parkinson’s pathogenesis. In conclusion, it warrants creating better treatments for PD patients. Although, dopaminergic replenishment therapy is useful in treating neurological problems, such therapies are, however, unable to control the degeneration that underpins the disease, thereby declining their overall efficacy. This creates an additional challenge and an untapped scope for neurologists to adopt treatments for PD by targeting the ion-channels and gap-junctions, which is well-reviewed in the present article.

A bidirectional Hopf bifurcation analysis of Parkinson's oscillation in a simplified basal ganglia model

In this paper, we study the parkinson oscillation mechanism in a computational model by bifurcation analysis and numerical simulation. Oscillatory activities can be induced by abnormal coupling weights and delays. The bidirectional Hopf bifurcation phenomena are found in simulations, which can uniformly explain the oscillation mechanism in this model. The Hopf1 represents the transition between the low firing rate stable state (SS) and oscillation state (OS), the Hopf2 represents the transition between the high firing rate stable state (HSS) and the OS, the mechanisms of them are different. The Hopf1 and Hopf2 bifurcations both show that when the state transfers from the stable region to the oscillation region, oscillatory activities always originate from the beta frequency band, and then gradually evolve into the alpha frequency band, the theta frequency band and delta frequency band in this model. We find that the changing trends of the DF and oscillation amplitude (OSAM) are contrary, oscillation activities in lower frequency band are more stable than that in higher frequency band. The effect of the delay in inhibitory pathways is greater than that of in excitatory pathways, and appropriate delays improve the discharge activation level (DAL) of the system. In all, we infer that oscillations can be induced by the follow factors: 1. Improvement of the DAL of the globus pallidus externa (GPe); 2. Reduce the DAL of the GPe from the HSS or the discharge saturation state; 3. The GPe can also resonate with the subthalamic nucleus (STN).

Mathematical model of subthalamic nucleus neuron: Characteristic activity patterns and bifurcation analysis

The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, the bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease.

Chronic unpredictable stress induces depression-related behaviors by suppressing AgRP neuron activity

Previous studies have shown that AgRP neurons in the arcuate nucleus (ARC) respond to energy deficits and play a key role in the control of feeding behavior and metabolism. Here, we demonstrate that chronic unpredictable stress, an animal model of depression, decreases spontaneous firing rates, increases firing irregularity and alters the firing properties of AgRP neurons in both male and female mice. These changes are associated with enhanced inhibitory synaptic transmission and reduced intrinsic neuronal excitability. Chemogenetic inhibition of AgRP neurons increases susceptibility to subthreshold unpredictable stress. Conversely, chemogenetic activation of AgRP neurons completely reverses anhedonic and despair behaviors induced by chronic unpredictable stress. These results indicate that chronic stress induces maladaptive synaptic and intrinsic plasticity, leading to hypoactivity of AgRP neurons and subsequently causing behavioral changes. Our findings suggest that AgRP neurons in the ARC are a key component of neural circuitry involved in mediating depression-related behaviors and that increasing AgRP neuronal activity coule be a novel and effective treatment for depression.

Sex-dependent alterations in the physiology of entorhinal cortex neurons in old heterozygous 3xTg-AD mice

While the higher prevalence of Alzheimer’s disease (AD) in women is clear, studies suggest that biological sex may also influence AD pathogenesis. However, mechanisms behind these differences are not clear. To investigate physiological differences between sexes at the cellular level in the brain, we investigated the intrinsic and synaptic properties of entorhinal cortex neurons in heterozygous 3xTg-AD mice of both sexes at the age of 20 months. This brain region was selected because of its early association with AD symptoms. First, we found physiological differences between male and female non-transgenic mice, providing indirect evidence of axonal alterations in old females. Second, we observed a transgene-dependent elevation of the firing activity, post-burst afterhyperpolarization (AHP), and spontaneous excitatory postsynaptic current (EPSC) activity, without any effect of sex. Third, the passive properties and the hyperpolarization-activated current (Ih) were altered by transgene expression only in female mice, whereas the paired-pulse ratio (PPR) of evoked EPSC was changed only in males. Fourth, both sex and transgene expression were associated with changes in action potential properties. Consistent with previous work, higher levels of Aβ neuropathology were detected in 3xTg-AD females, whereas tau deposition was similar. In summary, our results support the idea that aging and AD neuropathology differentially alter the physiology of entorhinal cortex neurons in males and females.

The theoretical mechanism of Parkinson's oscillation frequency bands: a computational model study

Excessive synchronous oscillation activities appear in the brain is a key pathological feature of Parkinson's disease, the mechanism of which is still unclear. Although some previous studies indicated that β oscillation (13-30 Hz) may directly originate in the network composed of the subthalamic nucleus (STN) and external globus pallidus (GPe) neurons, specific onset mechanisms of which are unclear, especially theoretical evidences in numerical simulation are still little. In this paper, we employ a STN-GPe mean-field model to explore the onset mechanism of Parkinson's oscillation. In addition to β oscillation, we find that some other common oscillation frequency bands can appear in this network, such as the α oscillation band (8-12 Hz), the θ oscillation band (4-7 Hz) and δ oscillation band (1-3 Hz). In addition to the coupling weight between the STN and GPe, the delay is also a critical factor to affect oscillatory activities, which can not be neglected compared to other parameters. Through simulation and analysis, we propose two possible theories may induce the system to transfer from the stable state to the oscillatory state in this model: (1). The oscillation activity can be induced when the firing activation level of the population increases to large enough; (2). In some special cases, the population may stay in the high firing rate stable state and the mean discharge rate of which is too large to induce oscillations, then oscillation activities may be induced as the MD decreases to moderate value. In most situations, the change trends of the MD and oscillation dominant frequency are contrary, which may be an important physiological phenomenon shown in this model. The delays and firing rates were obtained by simulating, which may be verified in the experiment in the future.

A Basal Ganglia Computational Model to Explain the Paradoxical Sensorial Improvement in the Presence of Huntington's Disease

The basal ganglia (BG) represent a critical center of the nervous system for sensorial discrimination. Although it is known that Huntington's disease (HD) affects this brain area, it still remains unclear how HD patients achieve paradoxical improvement in sensorial discrimination tasks. This paper presents a computational model of the BG including the main nuclei and the typical firing properties of their neurons. The BG model has been embedded within an auditory signal detection task. We have emulated the effect that the altered levels of dopamine and the degree of HD affectation have in information processing at different layers of the BG, and how these aspects shape transient and steady states differently throughout the selection task. By extracting the independent components of the BG activity at different populations, it is evidenced that early and medium stages of HD affectation may enhance transient activity in the striatum and the substantia nigra pars reticulata. These results represent a possible explanation for the paradoxical improvement that HD patients present in discrimination task performance. Thus, this paper provides a novel understanding on how the fast dynamics of the BG network at different layers interact and enable transient states to emerge throughout the successive neuron populations.

Maladaptive Downregulation of Autonomous Subthalamic Nucleus Activity following the Loss of Midbrain Dopamine Neurons

Abnormal subthalamic nucleus (STN) activity is linked to impaired movement in Parkinson’s disease (PD). The autonomous firing of STN neurons, which contributes to their tonic excitation of the extrastriatal basal ganglia and shapes their integration of synaptic input, is downregulated in PD models. Using electrophysiological, chemogenetic, genetic, and optical approaches, we find that chemogenetic activation of indirect pathway striatopallidal neurons downregulates intrinsic STN activity in normal mice but this effect is occluded in Parkinsonian mice. Loss of autonomous spiking in PD mice is prevented by STN N-methyl-D-aspartate receptor (NMDAR) knockdown and reversed by reactive oxygen species breakdown or K_ATP channel inhibition. Chemogenetic activation of hM3D(Gq) in STN neurons in Parkinsonian mice rescues their intrinsic activity, modifies their synaptic integration, and ameliorates motor dysfunction. Together these data argue that in PD mice increased indirect pathway activity leads to disinhibition of the STN, which triggers maladaptive NMDAR-dependent downregulation of autonomous firing.

McIver et al. describe the cellular and circuit mechanisms responsible for the loss of autonomous subthalamic nucleus (STN) spiking in dopamine-depleted mice and demonstrate that chemogenetic rescue of intrinsic STN activity reduces Parkinsonian motor dysfunction.

Multistable properties of human subthalamic nucleus neurons in Parkinson's disease

Behaviors are realized through concerted activity in neural circuits. This activity results from a combination of neural connectivity and the properties of the involved neurons. By studying the activity of neurons in the human subthalamic nucleus during surgery for Parkinson’s disease, we report that these neurons have multiple stable states, and that brief electrical stimuli can lead to transitions between states. We thus suggest that these neurons function as finite state machines. The different states could influence the function of key motor circuits of the basal ganglia, and thus knowledge of these states in disease or in response to treatment could help to define new treatment strategies for people with movement disorders.

To understand the function and dysfunction of neural circuits, it is necessary to understand the properties of the neurons participating in the behavior, the connectivity between these neurons, and the neuromodulatory status of the circuits at the time they are producing the behavior. Such knowledge of human neural circuits is difficult, at best, to obtain. Here, we study firing properties of human subthalamic neurons, using microelectrode recordings and microstimulation during awake surgery for Parkinson’s disease. We demonstrate that low-amplitude, brief trains of microstimulation can lead to persistent changes in neuronal firing behavior including switching between firing rates, entering silent periods, or firing several bursts then entering a silent period. We suggest that these multistable states reflect properties of finite state machines and could have implications for the function of circuits involving the subthalamic nucleus. Furthermore, understanding these states could lead to therapeutic strategies aimed at regulating the transitions between states.

Nucleus accumbens shell small conductance potassium channels underlie adolescent ethanol exposure-induced anxiety

Alcohol use typically begins in adolescence, increasing the likelihood of adult mental disorders such as anxiety. However, the cellular mechanisms underlying the consequences of adolescent alcohol exposure as well as the behavioral consequences remain poorly understood. We examined the effects of adolescent or adult chronic intermittent ethanol (CIE) exposure on intrinsic excitability of striatal medium-sized spiny neurons (MSNs) and anxiety levels. Rats underwent one of the following procedures: (1) light-dark transition (LDT) and open-field (OF) tests to evaluate anxiety levels and general locomotion; (2) whole-cell patch clamp recordings and biocytin labeling to assess excitability of striatal MSNs, as well as morphological properties; and (3) western blot immunostaining to determine small conductance (SK) calcium-activated potassium channel protein levels. Three weeks, but not 2 days, after CIE treatment, adolescent CIE-treated rats showed shorter crossover latency from the light to dark side in the LDT test and higher MSN excitability in the nucleus accumbens shell (NAcS). Furthermore, the amplitude of the medium afterhyperpolarization (mAHP), mediated by SK channels, and SK3 protein levels in the NAcS decreased concomitantly. Finally, increased anxiety levels, increased excitability, and decreased amplitude of mAHP of NAcS MSNs were reversed by SK channel activator 1-EBIO and mimicked by the SK channel blocker apamin. Thus, adolescent ethanol exposure increases adult anxiety-like behavior by downregulating SK channel function and protein expression, which leads to an increase of intrinsic excitability in NAcS MSNs. SK channels in the NAcS may serve as a target to treat adolescent alcohol binge exposure-induced mental disorders, such as anxiety in adulthood.

The onset mechanism of Parkinson's beta oscillations: A theoretical analysis

In this paper, we build a basal ganglia-cortex-thalamus model to study the oscillatory mechanisms and boundary conditions of the beta frequency band (13-30 Hz) that appears in the subthalamic nucleus. First, a theoretical oscillatory boundary formula is obtained in a simplified model by using the Laplace transform and linearization process of the system at fixed points. Second, we simulate the oscillatory boundary conditions through numerical calculations, which fit with our theoretical results very well, at least in the changing trend. We find that several critical coupling strengths in the model exert great effects on the oscillations, the mechanisms of which differ but can be explained in detail by our model and the oscillatory boundary formula. Specifically, we note that the relatively small or large sizes of the coupling strength from the fast-spiking interneurons to the medium spiny neurons and from the cortex to the fast-spiking interneurons both have obvious maintenance roles on the states. Similar phenomena have been reported in other neurological diseases, such as absence epilepsy. However, some of those interesting mutual regulation mechanisms in the model have rarely been considered in previous studies. In addition to the coupling weight in the pathway, in this work, we show that the delay is a key parameter that affects oscillations. On the one hand, the system needs a minimum delay to generate oscillations; on the other hand, in the appropriate range, a longer delay leads to a higher activation level of the subthalamic nucleus. In this paper, we study the oscillation activities that appear on the subthalamic nucleus. Moreover, all populations in the model show the dynamic behaviour of a synchronous resonance. Therefore, we infer that the mechanisms obtained can be expanded to explore the state of other populations, and that the model provides a unified framework for studying similar problems in the future. Moreover, the oscillatory boundary curves obtained are all critical conditions between the stable state and beta frequency oscillation. The method is also suitable for depicting other common frequency bands during brain oscillations, such as the alpha band (8-12 Hz), theta band (4-7 Hz) and delta band (1-3 Hz). Thus, the results of this work are expected to help us better understand the onset mechanism of parkinson's oscillations and can inspire related experimental research in this field.

The Potential of L-Type Calcium Channels as a Drug Target for Neuroprotective Therapy in Parkinson's Disease

The motor symptoms of Parkinson's disease (PD) mainly arise from degeneration of dopamine neurons within the substantia nigra. As no disease-modifying PD therapies are available, and side effects limit long-term benefits of current symptomatic therapies, novel treatment approaches are needed. The ongoing phase III clinical study STEADY-PD is investigating the potential of the dihydropyridine isradipine, an L-type Ca²⁺ channel (LTCC) blocker, for neuroprotective PD therapy. Here we review the clinical and preclinical rationale for this trial and discuss potential reasons for the ambiguous outcomes of in vivo animal model studies that address PD-protective dihydropyridine effects. We summarize current views about the roles of Cav1.2 and Cav1.3 LTCC isoforms for substantia nigra neuron function, and their high vulnerability to degenerative stressors, and for PD pathophysiology. We discuss different dihydropyridine sensitivities of LTCC isoforms in view of their potential as drug targets for PD neuroprotection, and we conclude by considering how these aspects could guide further drug development.

The beta oscillation conditions in a simplified basal ganglia network

Parkinson's disease is a type of motor dysfunction disease that is induced mainly by abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons. Periodic oscillatory activities with frequencies of 13-30 Hz are the main physiological characteristics of Parkinson's disease. In this paper, we built a class of STN-GP networks to explore beta oscillation conditions. A theoretical formula was obtained for generating oscillations without internal GP connections. Based on this formula, we studied the effects of cortex inputs, striatum inputs, coupling weights and delays on oscillation conditions, and the theoretical results are in good agreement with the numerical results. The onset mechanism can be explained by the model, and the internal GP connection has little effect on oscillations. Finally, we compared oscillation conditions with those in previous studies and found that the delays and coupling weights required for generating oscillations may decrease as the number of nuclei increases. We hope that the results obtained will inspire future theoretical and experimental studies.

Robust desynchronization of Parkinson's disease pathological oscillations by frequency modulation of delayed feedback deep brain stimulation

The hyperkinetic symptoms of Parkinson's Disease (PD) are associated with the ensembles of interacting oscillators that cause excess or abnormal synchronous behavior within the Basal Ganglia (BG) circuitry. Delayed feedback stimulation is a closed loop technique shown to suppress this synchronous oscillatory activity. Deep Brain Stimulation (DBS) via delayed feedback is known to destabilize the complex intermittent synchronous states. Computational models of the BG network are often introduced to investigate the effect of delayed feedback high frequency stimulation on partially synchronized dynamics. In this study, we develop a reduced order model of four interacting nuclei of the BG as well as considering the Thalamo-Cortical local effects on the oscillatory dynamics. This model is able to capture the emergence of 34 Hz beta band oscillations seen in the Local Field Potential (LFP) recordings of the PD state. Train of high frequency pulses in a delayed feedback stimulation has shown deficiencies such as strengthening the synchronization in case of highly fluctuating neuronal activities, increasing the energy consumed as well as the incapability of activating all neurons in a large-scale network. To overcome these drawbacks, we propose a new feedback control variable based on the filtered and linearly delayed LFP recordings. The proposed control variable is then used to modulate the frequency of the stimulation signal rather than its amplitude. In strongly coupled networks, oscillations reoccur as soon as the amplitude of the stimulus signal declines. Therefore, we show that maintaining a fixed amplitude and modulating the frequency might ameliorate the desynchronization process, increase the battery lifespan and activate substantial regions of the administered DBS electrode. The charge balanced stimulus pulse itself is embedded with a delay period between its charges to grant robust desynchronization with lower amplitudes needed. The efficiency of the proposed Frequency Adjustment Stimulation (FAS) protocol in a delayed feedback method might contribute to further investigation of DBS modulations aspired to address a wide range of abnormal oscillatory behavior observed in neurological disorders.

Bioelectrical control of positional information in development and regeneration: A review of conceptual and computational advances

Positional information describes pre-patterns of morphogenetic substances that alter spatio-temporal gene expression to instruct development of growth and form. A wealth of recent data indicate bioelectrical properties, such as the transmembrane potential (Vmem), are involved as instructive signals in the spatiotemporal regulation of morphogenesis. However, the mechanistic relationships between Vmem and molecular positional information are only beginning to be understood. Recent advances in computational modeling are assisting in the development of comprehensive frameworks for mechanistically understanding how endogenous bioelectricity can guide anatomy in a broad range of systems. Vmem represents an extraordinarily strong electric field (∼1.0 × 106 V/m) active over the thin expanse of the plasma membrane, with the capacity to influence a variety of downstream molecular signaling cascades. Moreover, in multicellular networks, intercellular coupling facilitated by gap junction channels may induce directed, electrodiffusive transport of charged molecules between cells of the network to generate new positional information patterning possibilities and characteristics. Given the demonstrated role of Vmem in morphogenesis, here we review current understanding of how Vmem can integrate with molecular regulatory networks to control single cell state, and the unique properties bioelectricity adds to transport phenomena in gap junction-coupled cell networks to facilitate self-assembly of morphogen gradients and other patterns. Understanding how Vmem integrates with biochemical regulatory networks at the level of a single cell, and mechanisms through which Vmem shapes molecular positional information in multicellular networks, are essential for a deep understanding of body plan control in development, regeneration and disease.

Specificity in the interaction of high-voltage-activated Ca2+ channel types with Ca2+-dependent afterhyperpolarizations in magnocellular supraoptic neurons

Magnocellular oxytocin (OT) and vasopressin (VP) neurons express an afterhyperpolarization (AHP) following spike trains that attenuates firing rate and contributes to burst patterning. This AHP includes contributions from an apamin-sensitive, medium-duration AHP (mAHP) and from an apamin-insensitive, slow-duration AHP (sAHP). These AHPs are Ca²⁺ dependent and activated by Ca²⁺ influx through voltage-gated Ca²⁺ channels. Across central nervous system neurons that generate Ca²⁺-dependent AHPs, the Ca²⁺ channels that couple to the mAHP and sAHP differ greatly, but for magnocellular neurosecretory cells this relationship is unknown. Using simultaneous whole cell recording and Ca²⁺ imaging, we evaluated the effect of specific high-voltage-activated (HVA) Ca²⁺ channel blockers on the mAHP and sAHP. Block of all HVA channels via 400 μM Cd²⁺ inhibited almost the entire AHP. We tested nifedipine, conotoxin GVIA, agatoxin IVA, and SNX-482, specific blockers of L-, N-, P/Q-, and R-type channels, respectively. The N-type channel blocker conotoxin GVIA (1 μM) was the only toxin that inhibited the mAHP in either OT or VP neurons although the effect on VP neurons was weaker by comparison. The sAHP was significantly inhibited by N-type block in OT neurons and by R-type block in VP neurons although neither accounted for the entirety of the sAHP. Thus the mAHP appears to be elicited by Ca²⁺ from mostly N-type channels in both OT and VP neurons, but the contributions of specific Ca²⁺ channel types to the sAHP in each cell type are different. Alternative sources to HVA channels may contribute Ca²⁺ for the sAHP. NEW & NOTEWORTHY Despite the importance of afterhyperpolarization (AHP) mechanisms for regulating firing behavior of oxytocin (OT) and vasopressin (VP) neurons of supraoptic nucleus, which types of high-voltage-activated Ca²⁺ channels elicit AHPs in these cells was unknown. We found that N-type channels couple to the medium AHP in both cell types. For the slow AHP, N-type channels contribute in OT neurons, whereas R-type contribute in VP neurons. No single Ca²⁺ channel blocker abolished the entire AHP, suggesting that additional Ca²⁺ sources are involved.

Model and Analysis for the Onset of Parkinsonian Firing Patterns in a Simplified Basal Ganglia

Parkinson's disease (PD) is a degenerative neurological disease that disrupts the movement cycle in the basal ganglia. As the disease progresses, dopamine depletion leads to changes to how the basal ganglia functions as well as the appearance of abnormal beta oscillations. There is much debate on just exactly how these connection strengths change and just how the oscillations emerge. One leading hypothesis claims that the oscillations develop in the globus pallidus external, subthalamic nucleus, and globus pallidus internal loop. We introduce a mathematical model that calculates the average firing rates of this loop while still accounting for the larger closed loop of the entire basal ganglia system. This model is constructed such that physiologically realistic results can be obtained while not sacrificing the use of analytic methods. Because of this, it is possible to determine how the change in the connection strengths can drive the necessary changes in firing rates seen in recordings and account for the generation of trademark beta oscillations of PD without relying on highly specific time delays, stochastic approaches, or numerical approximations. Additionally, we find that the entire cortico-basal ganglia-thalamo-cortical loop is essential for abnormal oscillations to originate.

The oscillatory boundary conditions of different frequency bands in Parkinson's disease

Parkinson's disease (PD) is a neurodegenerative disease that is common in the elderly population. The most important pathological change in PD is the degeneration and death of dopaminergic neurons in the substantia nigra of the midbrain, which results in a decrease in the dopamine (DA) content of the striatum. The exact cause of this pathological change is still unknown. Numerous studies have shown that the evolution of PD is associated with abnormal oscillatory activities in the basal ganglia, with different oscillation frequency ranges, such as the typical beta band (13-30 Hz), the alpha band (8-12 Hz), the theta band (4-7 Hz) and the delta band (1-3 Hz). Although some studies have implied that abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons may be a key factor required to induce these oscillations, the relative mechanism is still unclear. The effects of other nerve nuclei in the basal ganglia, such as the striatum, on these oscillations are still unknown. The thalamus and cortex both have close input and output relationships with the basal ganglia, and many previous studies have indicated that they may also exert effects on Parkinson's disease oscillation, but the mechanisms involved are unclear. In this paper, we built a corticothalamic-basal ganglia (CTBG) mean firing-rate model to explore the onset mechanisms of these different oscillation phenomena. We found that, in addition to the STN-GP network, Parkinson's disease oscillations may also be induced by changing the coupling strength and delays in other pathways. Different frequency bands appear in the oscillating region, and various boundary conditions are depicted in parameter diagrams. The onset mechanism is well explained both by the model and by the numerical simulation results. Therefore, this model provides a unifying framework for studying the mechanism of Parkinson's disease oscillations, and we hope that the results obtained in this work can inspire future experimental studies.

Similar nicotinic excitability responses across the developing hippocampal formation are regulated by small-conductance calcium-activated potassium channels

The hippocampal formation forms a cognitive circuit that is critical for learning and memory. Cholinergic input to nicotinic acetylcholine receptors plays an important role in the normal development of principal neurons within the hippocampal formation. However, the ability of nicotinic receptors to stimulate principal neurons across all regions of the developing hippocampal formation has not been determined. We show in this study that heteromeric nicotinic receptors mediate direct inward current and depolarization responses in principal neurons across the hippocampal formation of the young postnatal mouse. These responses were found in principal neurons of the CA1, CA3, dentate gyrus, subiculum, and entorhinal cortex layer VI, and they varied in magnitude across regions with the greatest responses occurring in the subiculum and entorhinal cortex. Despite this regional variation in the magnitude of passive responses, heteromeric nicotinic receptor stimulation increased the excitability of active principal neurons by a similar amount in all regions. Pharmacological experiments found this similar excitability response to be regulated by small-conductance calcium-activated potassium (SK) channels, which exhibited regional differences in their influence on neuron activity that offset the observed regional differences in passive nicotinic responses. These findings demonstrate that SK channels play a role to coordinate the magnitude of heteromeric nicotinic excitability responses across the hippocampal formation at a time when nicotinic signaling drives the development of this cognitive brain region. This coordinated input may contribute to the normal development, synchrony, and maturation of the hippocampal formation learning and memory network. NEW & NOTEWORTHY This study demonstrates that small-conductance calcium-activated potassium channels regulate similar-magnitude excitability responses to heteromeric nicotinic acetylcholine receptor stimulation in active principal neurons across multiple regions of the developing mouse hippocampal formation. Given the importance of nicotinic neurotransmission for the development of principal neurons within the hippocampal formation, this coordinated excitability response is positioned to influence the normal development, synchrony, and maturation of the hippocampal formation learning and memory network.

Switchable slow cellular conductances determine robustness and tunability of network states

Neuronal information processing is regulated by fast and localized fluctuations of brain states. Brain states reliably switch between distinct spatiotemporal signatures at a network scale even though they are composed of heterogeneous and variable rhythms at a cellular scale. We investigated the mechanisms of this network control in a conductance-based population model that reliably switches between active and oscillatory mean-fields. Robust control of the mean-field properties relies critically on a switchable negative intrinsic conductance at the cellular level. This conductance endows circuits with a shared cellular positive feedback that can switch population rhythms on and off at a cellular resolution. The switch is largely independent from other intrinsic neuronal properties, network size and synaptic connectivity. It is therefore compatible with the temporal variability and spatial heterogeneity induced by slower regulatory functions such as neuromodulation, synaptic plasticity and homeostasis. Strikingly, the required cellular mechanism is available in all cell types that possess T-type calcium channels but unavailable in computational models that neglect the slow kinetics of their activation.

Brain information processing involves electrophysiological signals at multiple temporal and spatial timescales, from the single neuron level to whole brain areas. A fast and local control of these signals by neurochemicals called neuromodulators is essential in complex tasks such as movement initiation and attentional focus. The neuromodulators act at the cellular scale to control signals that propagate at potentially much larger scales. The present paper highlights the critical role of a cellular switch of excitability for the fast and localized control of cellular and network states. By turning ON and OFF the cellular switch, neuromodulators can robustly switch large populations between distinct network states. We stress the importance of controlling the switch at a cellular level and independently of the connectivity to allow for tunable spatiotemporal signatures of the network states.

Integrating Brain and Biomechanical Models-A New Paradigm for Understanding Neuro-muscular Control

To date, realistic models of how the central nervous system governs behavior have been restricted in scope to the brain, brainstem or spinal column, as if these existed as disembodied organs. Further, the model is often exercised in relation to an in vivo physiological experiment with input comprising an impulse, a periodic signal or constant activation, and output as a pattern of neural activity in one or more neural populations. Any link to behavior is inferred only indirectly via these activity patterns. We argue that to discover the principles of operation of neural systems, it is necessary to express their behavior in terms of physical movements of a realistic motor system, and to supply inputs that mimic sensory experience. To do this with confidence, we must connect our brain models to neuro-muscular models and provide relevant visual and proprioceptive feedback signals, thereby closing the loop of the simulation. This paper describes an effort to develop just such an integrated brain and biomechanical system using a number of pre-existing models. It describes a model of the saccadic oculomotor system incorporating a neuromuscular model of the eye and its six extraocular muscles. The position of the eye determines how illumination of a retinotopic input population projects information about the location of a saccade target into the system. A pre-existing saccadic burst generator model was incorporated into the system, which generated motoneuron activity patterns suitable for driving the biomechanical eye. The model was demonstrated to make accurate saccades to a target luminance under a set of environmental constraints. Challenges encountered in the development of this model showed the importance of this integrated modeling approach. Thus, we exposed shortcomings in individual model components which were only apparent when these were supplied with the more plausible inputs available in a closed loop design. Consequently we were able to suggest missing functionality which the system would require to reproduce more realistic behavior. The construction of such closed-loop animal models constitutes a new paradigm of computational neurobehavior and promises a more thoroughgoing approach to our understanding of the brain's function as a controller for movement and behavior.

The role of cortical oscillations in a spiking neural network model of the basal ganglia

Although brain oscillations involving the basal ganglia (BG) have been the target of extensive research, the main focus lies disproportionally on oscillations generated within the BG circuit rather than other sources, such as cortical areas. We remedy this here by investigating the influence of various cortical frequency bands on the intrinsic effective connectivity of the BG, as well as the role of the latter in regulating cortical behaviour. To do this, we construct a detailed neural model of the complete BG circuit based on fine-tuned spiking neurons, with both electrical and chemical synapses as well as short-term plasticity between structures. As a measure of effective connectivity, we estimate information transfer between nuclei by means of transfer entropy. Our model successfully reproduces firing and oscillatory behaviour found in both the healthy and Parkinsonian BG. We found that, indeed, effective connectivity changes dramatically for different cortical frequency bands and phase offsets, which are able to modulate (or even block) information flow in the three major BG pathways. In particular, alpha (8–12Hz) and beta (13–30Hz) oscillations activate the direct BG pathway, and favour the modulation of the indirect and hyper-direct pathways via the subthalamic nucleus—globus pallidus loop. In contrast, gamma (30–90Hz) frequencies block the information flow from the cortex completely through activation of the indirect pathway. Finally, below alpha, all pathways decay gradually and the system gives rise to spontaneous activity generated in the globus pallidus. Our results indicate the existence of a multimodal gating mechanism at the level of the BG that can be entirely controlled by cortical oscillations, and provide evidence for the hypothesis of cortically-entrained but locally-generated subthalamic beta activity. These two findings suggest new insights into the pathophysiology of specific BG disorders.

Potassium Channels: A Potential Therapeutic Target for Parkinson's Disease

The pathogenesis of the second major neurodegenerative disorder, Parkinson's disease (PD), is closely associated with the dysfunction of potassium (K⁺) channels. Therefore, PD is also considered to be an ion channel disease or neuronal channelopathy. Mounting evidence has shown that K⁺ channels play crucial roles in the regulations of neurotransmitter release, neuronal excitability, and cell volume. Inhibition of K⁺ channels enhances the spontaneous firing frequency of nigral dopamine (DA) neurons, induces a transition from tonic firing to burst discharge, and promotes the release of DA in the striatum. Recently, three K⁺ channels have been identified to protect DA neurons and to improve the motor and non-motor symptoms in PD animal models: small conductance (SK) channels, A-type K⁺ channels, and K_V7/KCNQ channels. In this review, we summarize the physiological and pharmacological effects of the three K⁺ channels. We also describe in detail the laboratory investigations regarding K⁺ channels as a potential therapeutic target for PD.

Neural mass models describing possible origin of the excessive beta oscillations correlated with Parkinsonian state

In Parkinson's disease, the enhanced beta rhythm is closely associated with akinesia/bradykinesia and rigidity. An increase in beta oscillations (12-35 Hz) within the basal ganglia (BG) nuclei does not proliferate throughout the cortico-basal ganglia loop in uniform fashion; rather it can be subdivided into two distinct frequency bands, i.e. the lower beta (12-20 Hz) and upper beta (21-35 Hz). A computational model of the excitatory and inhibitory neural network that focuses on the population properties is proposed to explore the mechanism underlying the pathological beta oscillations. Simulation results show several findings. The upper beta frequency in the BG originates from a high frequency cortical beta, while the emergence of exaggerated lower beta frequency in the BG depends greatly on the enhanced excitation of a reciprocal network consisting of the globus pallidus externus (GPe) and the subthalamic nucleus (STN). There is also a transition mechanism between the upper and lower beta oscillatory activities, and we explore the impact of self-inhibition within the GPe on the relationship between the upper beta and lower beta oscillations. It is shown that increased self-inhibition within the GPe contributes to increased upper beta oscillations driven by the cortical rhythm, while decrease in the self-inhibition within the GPe facilitates an enhancement of the lower beta oscillations induced by the increased excitability of the BG. This work provides an analysis for understanding the mechanism underlying pathological synchronization in neurological diseases.

A neural mass model of basal ganglia nuclei simulates pathological beta rhythm in Parkinson's disease

An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network. Moreover, it is shown that the generation and frequency of these pathological beta oscillations are varied by the coupling strength and the intrinsic characteristics of the basal ganglia. Simulation results reveal that increase of the coupling strength induces the generation of the beta oscillation, as well as enhances the oscillation frequency. However, for the intrinsic properties of each nucleus in the excitatory-inhibitory network, the STN primarily influences the generation of the beta oscillation while the GPe mainly determines its frequency. Interestingly, describing function analysis applied on this model theoretically explains the mechanism of pathological beta oscillations.

Changes in SK channel expression in the basal ganglia after partial nigrostriatal dopamine lesions in rats: Functional consequences

Parkinson's disease (PD) is a progressive neurodegenerative disease originating from the loss of dopamine (DA) neurons in the substantia nigra pars compacta (SNC). The small-conductance calcium-activated potassium (SK) channels play an essential role in the regulation of midbrain DA neuron activity patterns, as well as excitability of other types of neurons of the basal ganglia. We therefore questioned whether the SK channel expression in the basal ganglia is modified in parkinsonian rats and how this could impact behavioral performance in a reaction time task. We used a rat model of early PD in which the progressive nigrostriatal DA degeneration was produced by bilateral infusions of 6-hydroxydopamine (6-OHDA) into the striatum. In situ hybridization of SK2 and SK3 mRNA and binding of iodinated apamin (SK2/SK3 blocker) were performed at 1, 8 or 21 days postsurgery in sham and 6-OHDA lesion groups. A significant decrease of SK3 channel expression was found in the SNC of lesioned animals at the three time points, with no change of SK2 channel expression. Interestingly, an upregulation of SK2 mRNA and apamin binding was found in the subthalamic nucleus (STN) at 21 days postlesion. These results were confirmed using quantitative real time polymerase chain reaction (qRT-PCR) approach. Functionally, the local infusion of apamin into the STN of parkinsonian rats enhanced the akinetic deficits produced by nigrostriatal DA lesions in a reaction time task while apamin infusion into the SNC had an opposite effect. These effects disappear when the positive modulator of SK channels (CyPPA) is co-administered with apamin. These findings suggest that an upregulation of SK2 channels in the STN may underlie the physiological adjustment to increased subthalamic excitability following partial DA denervation.

Properties of Neurons in External Globus Pallidus Can Support Optimal Action Selection

The external globus pallidus (GPe) is a key nucleus within basal ganglia circuits that are thought to be involved in action selection. A class of computational models assumes that, during action selection, the basal ganglia compute for all actions available in a given context the probabilities that they should be selected. These models suggest that a network of GPe and subthalamic nucleus (STN) neurons computes the normalization term in Bayes’ equation. In order to perform such computation, the GPe needs to send feedback to the STN equal to a particular function of the activity of STN neurons. However, the complex form of this function makes it unlikely that individual GPe neurons, or even a single GPe cell type, could compute it. Here, we demonstrate how this function could be computed within a network containing two types of GABAergic GPe projection neuron, so-called ‘prototypic’ and ‘arkypallidal’ neurons, that have different response properties in vivo and distinct connections. We compare our model predictions with the experimentally-reported connectivity and input-output functions (f-I curves) of the two populations of GPe neurons. We show that, together, these dichotomous cell types fulfil the requirements necessary to compute the function needed for optimal action selection. We conclude that, by virtue of their distinct response properties and connectivities, a network of arkypallidal and prototypic GPe neurons comprises a neural substrate capable of supporting the computation of the posterior probabilities of actions.

Choosing an appropriate action as quickly and accurately as possible in a given situation is critical for the survival of animals and humans. One of the brain regions involved in action selection is a set of subcortical nuclei known as the basal ganglia. The importance of understanding information processing in the basal ganglia is further emphasised by the fact that their disturbed interactions in Parkinson’s disease results in profound difficulties in movement. Computational models have suggested how the basal ganglia could select actions in the fastest possible way for the required accuracy level. These models further predict that a part of basal ganglia, called the external globus pallidus (GPe), needs to calculate a particular function of its inputs. This paper proposes how this function could be computed in a mathematical model of a network within GPe. Furthermore, it shows that the experimentally observed connectivity and response properties of GPe neurons fulfil the requirements necessary to support optimal action selection. This suggests the GPe neurons have properties that allow them to contribute to optimal action selection in the whole basal ganglia.

Asynchronous presynaptic glutamate release enhances neuronal excitability during the post-spike refractory period

KEY POINTS

Many excitatory synapses in the brain release glutamate with both synchronous and asynchronous components. Immediately following an action potential, neurons display a reduced excitability due to the post-spike afterhyperpolarization (AHP). This gives rise to a relative refractory period. When an action potential is evoked by glutamate synaptic input possessing asynchronous release, the delayed glutamate release events act to depolarize the neuron during the AHP and overcome the relative refractory period. These results demonstrate a new role for asynchronous release in regulating post-spike excitability and the relative refractory period in central neurons.

ABSTRACT

Post-spike afterhyperpolarizations (AHPs) functionally inhibit neuronal excitability for tens to hundreds of milliseconds following each action potential. This imposes a relative refractory period during which synaptic excitation is less effective at evoking spikes. Here we asked whether some synapses have mechanisms in place that allow them to overcome the AHP and drive spiking in target cells during this period of reduced excitability. We examined glutamate synapses onto oxytocin and vasopressin neurons in the paraventricular nucleus of the hypothalamus. These synapses can display pronounced asynchronous glutamate release following a single presynaptic spike, with the time course of release being similar to that of the post-spike AHP. To test whether asynchronous release is more effective at overcoming the relative refractory period, we evoked a single action potential with either a brief synchronous depolarization or an asynchronous potential and then assessed excitability at multiple time points following the spike. Neurons receiving asynchronous depolarizing synaptic inputs had a shorter relative refractory period than those receiving synchronous depolarizations. Our data demonstrate that synapses releasing glutamate in an asynchronous and delayed manner are ideally adapted to counter the AHP. By effectively overcoming the relative refractory period, the kinetics of excitatory synaptic input can play an important role in controlling post-spike excitability.

Computational Models Describing Possible Mechanisms for Generation of Excessive Beta Oscillations in Parkinson's Disease

In Parkinson's disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe). Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson's disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters.

Serotonin regulation of subthalamic neurons

The subthalamic nucleus (STN) is a key component of the basal ganglia. As the only basal ganglia nucleus comprised of mostly glutamatergic neurons, STN neurons provide a key driving force to their target neurons. Thus, regulation of STN neuron activity is important. One STN regulator is the serotonin (5-HT) system. The STN receives a dense 5-HT innervation. 5-HT1A, 5-HT1B, 5-HT2C, and 5-HT4 receptors are expressed in the STN. 5-HT may regulate the STN via several mechanisms. First, 5-HT may affect STN neuron excitability directly by either inhibiting a subpopulation of STN neurons via activation of 5-HT1A receptors or exciting STN neurons through activation of 5-HT2C and 5-HT4 receptors. Second, 5-HT may affect synaptic inputs to the STN. Via activation of 5-HT1B receptors on the afferent terminals, 5-HT inhibits glutamatergic input to the STN, but the inhibitory effect on GABAergic input is smaller. Third, 5-HT may regulate the STN glutamatergic output by activating presynaptic 5-HT1B receptors, thus reducing burst firing in target neurons. Last, 5-HT may affect glutamate release at the intra-STN axon collaterals and regulate the recurrent excitation. These mechanisms may work in concert to fine-tune the intensity and pattern of STN activity and reduce STN output bursts.

Heterosynaptic regulation of external globus pallidus inputs to the subthalamic nucleus by the motor cortex

The two principal movement-suppressing pathways of the basal ganglia, the so-called hyperdirect and indirect pathways, interact within the subthalamic nucleus (STN). An appropriate level and pattern of hyperdirect pathway cortical excitation and indirect pathway external globus pallidus (GPe) inhibition of the STN are critical for normal movement and are greatly perturbed in Parkinson's disease. Here we demonstrate that motor cortical inputs to the STN heterosynaptically regulate, through activation of postsynaptic NMDA receptors, the number of functional GABAA receptor-mediated GPe-STN inputs. Therefore, a homeostatic mechanism, intrinsic to the STN, balances cortical excitation by adjusting the strength of GPe inhibition. However, following the loss of dopamine, excessive cortical activation of STN NMDA receptors triggers GPe-STN inputs to strengthen abnormally, contributing to the emergence of pathological, correlated activity.

SK channel blockade reverses cognitive and motor deficits induced by nigrostriatal dopamine lesions in rats

Parkinson's disease has traditionally been viewed as a motor disorder caused by the loss of dopamine (DA) neurons. However, emotional and cognitive syndromes can precede the onset of the motor deficits and provide an opportunity for therapeutic intervention. Potassium channels have recently emerged as potential new targets in the treatment of Parkinson's disease. The selective blockade of small conductance calcium-activated K+ channels (SK channels) by apamin is known to increase burst firing in midbrain DA neurons and therefore DA release. We thus investigated the effects of systemic administration of apamin on the motor, cognitive deficits and anxiety present after bilateral nigrostriatal 6-hydroxydopamine (6-OHDA) lesions in rats. Apamin administration (0.1 or 0.3 mg/kg i.p.) counteracted the depression, anxiety-like behaviors evaluated on sucrose consumption and in the elevated plus maze, social recognition and spatial memory deficits produced by partial 6-OHDA lesions. Apamin also reduced asymmetric motor deficits on circling behavior and postural adjustments in the unilateral extensive 6-OHDA model. The partial 6-OHDA lesions (56% striatal DA depletion) produced 20% decrease of iodinated apamin binding sites in the substantia nigra pars compacta in correlation with the loss of tyrosine hydroxylase positive cells, without modifying apamin binding in brain regions receiving DAergic innervation. Striatal extracellular levels of DA, not detectable after 6-OHDA lesions, were enhanced by apamin treatment as measured by in vivo microdialysis. These results indicate that blocking SK channels may reinstate minimal DA activity in the striatum to alleviate the non-motor symptoms induced by partial striatal DA lesions.

Predicting the responses of repetitively firing neurons to current noise

We used phase resetting methods to predict firing patterns of rat subthalamic nucleus (STN) neurons when their rhythmic firing was densely perturbed by noise. We applied sequences of contiguous brief (0.5–2 ms) current pulses with amplitudes drawn from a Gaussian distribution (10–100 pA standard deviation) to autonomously firing STN neurons in slices. Current noise sequences increased the variability of spike times with little or no effect on the average firing rate. We measured the infinitesimal phase resetting curve (PRC) for each neuron using a noise-based method. A phase model consisting of only a firing rate and PRC was very accurate at predicting spike timing, accounting for more than 80% of spike time variance and reliably reproducing the spike-to-spike pattern of irregular firing. An approximation for the evolution of phase was used to predict the effect of firing rate and noise parameters on spike timing variability. It quantitatively predicted changes in variability of interspike intervals with variation in noise amplitude, pulse duration and firing rate over the normal range of STN spontaneous rates. When constant current was used to drive the cells to higher rates, the PRC was altered in size and shape and accurate predictions of the effects of noise relied on incorporating these changes into the prediction. Application of rate-neutral changes in conductance showed that changes in PRC shape arise from conductance changes known to accompany rate increases in STN neurons, rather than the rate increases themselves. Our results show that firing patterns of densely perturbed oscillators cannot readily be distinguished from those of neurons randomly excited to fire from the rest state. The spike timing of repetitively firing neurons may be quantitatively predicted from the input and their PRCs, even when they are so densely perturbed that they no longer fire rhythmically.

Most neurons receive thousands of synaptic inputs per second. Each of these may be individually weak but collectively they shape the temporal pattern of firing by the postsynaptic neuron. If the postsynaptic neuron fires repetitively, its synaptic inputs need not directly trigger action potentials, but may instead control the timing of action potentials that would occur anyway. The phase resetting curve encapsulates the influence of an input on the timing of the next action potential, depending on its time of arrival. We measured the phase resetting curves of neurons in the subthalamic nucleus and used them to accurately predict the timing of action potentials in a phase model subjected to complex input patterns. A simple approximation to the phase model accurately predicted the changes in firing pattern evoked by dense patterns of noise pulses varying in amplitude and pulse duration, and by changes in firing rate. We also showed that the phase resetting curve changes systematically with changes in total neuron conductance, and doing so predicts corresponding changes in firing pattern. Our results indicate that the phase model may accurately represent the temporal integration of complex patterns of input to repetitively firing neurons.

Effective connectivity of the subthalamic nucleus-globus pallidus network during Parkinsonian oscillations

In Parkinsonism, subthalamic nucleus (STN) neurons and two types of external globus pallidus (GP) neuron inappropriately synchronise their firing in time with slow (∼1 Hz) or beta (13-30 Hz) oscillations in cortex. We recorded the activities of STN, Type-I GP (GP-TI) and Type-A GP (GP-TA) neurons in anaesthetised Parkinsonian rats during such oscillations to constrain a series of computational models that systematically explored the effective connections and physiological parameters underlying neuronal rhythmic firing and phase preferences in vivo. The best candidate model, identified with a genetic algorithm optimising accuracy/complexity measures, faithfully reproduced experimental data and predicted that the effective connections of GP-TI and GP-TA neurons are quantitatively different. Estimated inhibitory connections from striatum were much stronger to GP-TI neurons than to GP-TA neurons, whereas excitatory connections from thalamus were much stronger to GP-TA and STN neurons than to GP-TI neurons. Reciprocal connections between GP-TI and STN neurons were matched in weight, but those between GP-TA and STN neurons were not; only GP-TI neurons sent substantial connections back to STN. Different connection weights between and within the two types of GP neuron were also evident. Adding to connection differences, GP-TA and GP-TI neurons were predicted to have disparate intrinsic physiological properties, reflected in distinct autonomous firing rates. Our results elucidate potential substrates of GP functional dichotomy, and emphasise that rhythmic inputs from striatum, thalamus and cortex are important for setting activity in the STN-GP network during Parkinsonian beta oscillations, suggesting they arise from interactions between most nodes of basal ganglia-thalamocortical circuits.

K(+) channels: function-structural overview

Potassium channels are particularly important in determining the shape and duration of the action potential, controlling the membrane potential, modulating hormone secretion, epithelial function and, in the case of those K(+) channels activated by Ca(2+), damping excitatory signals. The multiplicity of roles played by K(+) channels is only possible to their mammoth diversity that includes at present 70 K(+) channels encoding genes in mammals. Today, thanks to the use of cloning, mutagenesis, and the more recent structural studies using x-ray crystallography, we are in a unique position to understand the origins of the enormous diversity of this superfamily of ion channels, the roles they play in different cell types, and the relations that exist between structure and function. With the exception of two-pore K(+) channels that are dimers, voltage-dependent K(+) channels are tetrameric assemblies and share an extremely well conserved pore region, in which the ion-selectivity filter resides. In the present overview, we discuss in the function, localization, and the relations between function and structure of the five different subfamilies of K(+) channels: (a) inward rectifiers, Kir; (b) four transmembrane segments-2 pores, K2P; (c) voltage-gated, Kv; (d) the Slo family; and (e) Ca(2+)-activated SK family, SKCa.

Mechanism of the medium-duration afterhyperpolarization in rat serotonergic neurons

Most serotonergic neurons display a prominent medium-duration afterhyperpolarization (mAHP), which is mediated by small-conductance Ca(2+) -activated K(+) (SK) channels. Recent ex vivo and in vivo experiments have suggested that SK channel blockade increases the firing rate and/or bursting in these neurons. The purpose of this study was therefore to characterize the source of Ca(2+) which activates the mAHP channels in serotonergic neurons. In voltage-clamp experiments, an outward current was recorded at -60 mV after a depolarizing pulse to +100 mV. A supramaximal concentration of the SK channel blockers apamin or (-)-bicuculline methiodide blocked this outward current. This current was also sensitive to the broad Ca(2+) channel blocker Co(2+) and was partially blocked by both ω-conotoxin and mibefradil, which are blockers of N-type and T-type Ca(2+) channels, respectively. Neither blockers of other voltage-gated Ca(2+) channels nor DBHQ, an inhibitor of Ca(2+)-induced Ca(2+) release, had any effect on the SK current. In current-clamp experiments, mAHPs following action potentials were only blocked by ω-conotoxin and were unaffected by mibefradil. This was observed in slices from both juvenile and adult rats. Finally, when these neurons were induced to fire in an in vivo-like pacemaker rate, only ω-conotoxin was able to increase their firing rate (by ~30%), an effect identical to the one previously reported for apamin. Our results demonstrate that N-type Ca(2+) channels are the only source of Ca(2+) which activates the SK channels underlying the mAHP. T-type Ca(2+) channels may also activate SK channels under different circumstances.

Endothelial small-conductance and intermediate-conductance KCa channels: an update on their pharmacology and usefulness as cardiovascular targets

Most cardiovascular researchers are familiar with intermediate-conductance KCa3.1 and small-conductance KCa2.3 channels because of their contribution to endothelium-derived hyperpolarization. However, to immunologists and neuroscientists, these channels are primarily known for their role in lymphocyte activation and neuronal excitability. KCa3.1 is involved in the proliferation and migration of T cells, B cells, mast cells, macrophages, fibroblasts, and dedifferentiated vascular smooth muscle cells and is, therefore, being pursued as a potential target for use in asthma, immunosuppression, and fibroproliferative disorders. In contrast, the 3 KCa2 channels (KCa2.1, KCa2.2, and KCa2.3) contribute to the neuronal medium afterhyperpolarization and, depending on the type of neuron, are involved in determining firing rates and frequencies or in regulating bursting. KCa2 activators are accordingly being studied as potential therapeutics for ataxia and epilepsy, whereas KCa2 channel inhibitors like apamin have long been known to improve learning and memory in rodents. Given this background, we review the recent discoveries of novel KCa3.1 and KCa2.3 modulators and critically assess the potential of KCa activators for the treatment of diabetes and cardiovascular diseases by improving endothelium-derived hyperpolarizations.

Signal enhancement in the output stage of the basal ganglia by synaptic short-term plasticity in the direct, indirect, and hyperdirect pathways

Many of the synapses in the basal ganglia display short-term plasticity. Still, computational models have not yet been used to investigate how this affects signaling. Here we use a model of the basal ganglia network, constrained by available data, to quantitatively investigate how synaptic short-term plasticity affects the substantia nigra reticulata (SNr), the basal ganglia output nucleus. We find that SNr becomes particularly responsive to the characteristic burst-like activity seen in both direct and indirect pathway striatal medium spiny neurons (MSN). As expected by the standard model, direct pathway MSNs are responsible for decreasing the activity in SNr. In particular, our simulations indicate that bursting in only a few percent of the direct pathway MSNs is sufficient for completely inhibiting SNr neuron activity. The standard model also suggests that SNr activity in the indirect pathway is controlled by MSNs disinhibiting the subthalamic nucleus (STN) via the globus pallidus externa (GPe). Our model rather indicates that SNr activity is controlled by the direct GPe-SNr projections. This is partly because GPe strongly inhibits SNr but also due to depressing STN-SNr synapses. Furthermore, depressing GPe-SNr synapses allow the system to become sensitive to irregularly firing GPe subpopulations, as seen in dopamine depleted conditions, even when the GPe mean firing rate does not change. Similar to the direct pathway, simulations indicate that only a few percent of bursting indirect pathway MSNs can significantly increase the activity in SNr. Finally, the model predicts depressing STN-SNr synapses, since such an assumption explains experiments showing that a brief transient activation of the hyperdirect pathway generates a tri-phasic response in SNr, while a sustained STN activation has minor effects. This can be explained if STN-SNr synapses are depressing such that their effects are counteracted by the (known) depressing GPe-SNr inputs.

Improved conditions for the generation of beta oscillations in the subthalamic nucleus--globus pallidus network

A key pathology in the development of Parkinson's disease is the occurrence of persistent beta oscillations, which are correlated with difficulty in movement initiation. We investigated the network model composed of the subthalamic nucleus (STN) and globus pallidus (GP) developed by A. Nevado Holgado et al. [(2010) Journal of Neuroscience, 30, 12340-12352], who identified the conditions under which this circuit could generate beta oscillations. Our work extended their analysis by deriving improved analytic stability conditions for realistic values of the synaptic transmission delay between STN and GP neurons. The improved conditions were significantly closer to the results of simulations for the range of synaptic transmission delays measured experimentally. Furthermore, our analysis explained how changes in cortical and striatal input to the STN-GP network influenced oscillations generated by the circuit. As we have identified when a system of mutually connected populations of excitatory and inhibitory neurons can generate oscillations, our results may also find applications in the study of neural oscillations produced by assemblies of excitatory and inhibitory neurons in other brain regions.

Biophysical basis of the phase response curve of subthalamic neurons with generalization to other cell types

Experimental evidence indicates that the response of subthalamic neurons to excitatory postsynaptic potentials (EPSPs) is well described by their infinitesimal phase response curves (iPRC). However, the factors controlling the shape of that iPRC, and hence controlling the way subthalamic neurons respond to synaptic input, are unclear. We developed a biophysical model of subthalamic neurons to aid in the understanding of their iPRCs; this model exhibited an iPRC type common to many subthalamic cells. We devised a method for deriving its iPRC from its biophysical properties that clarifies how these different properties interact to shape the iPRC. This method revealed why the response of subthalamic neurons is well approximated by their iPRCs and how that approximation becomes less accurate under strong fluctuating input currents. It also connected iPRC structure to aspects of cellular physiology that could be estimated in simple current-clamp experiments. This allowed us to directly compare the iPRC predicted by our theory with the iPRC estimated from the response to EPSPs or current pulses in individual cells. We found that theoretically predicted iPRCs agreed well with estimates derived from synaptic stimuli, but not with those estimated from the response to somatic current injection. The difference between synaptic currents and those applied experimentally at the soma may arise from differences in the dynamics of charge redistribution on the dendrites and axon. Ultimately, our approach allowed us to identify novel ways in which voltage-dependent conductances interact with AHP conductances to influence synaptic integration that will apply to a wide range of cell types.

Sub- and suprathreshold adaptation currents have opposite effects on frequency tuning

Natural stimuli are often characterized by statistics that can vary over orders of magnitude. Experiments have shown that sensory neurons continuously adapt their responses to changes in these statistics, thereby optimizing information transmission. However, such adaptation can also alter the neuronal transfer function by attenuating if not eliminating responses to the low frequency components of time varying stimuli,which can create ambiguity in the neural code. We recorded from electrosensory pyramidal neurons before and after pharmacological inactivation of either calcium-activated (I(AHP)) or KCNQ voltage-gated potassium currents (I(M)). We found that blocking each current decreased adaptation in a similar fashion but led to opposite changes in the neuronal transfer function. Indeed, blocking I(AHP) increased while blocking I(M) instead decreased the response to low temporal frequencies. To understand this surprising result, we built a mathematical model incorporating each channel type. This model predicted that these differential effects could be accounted for by differential activation properties. Our results show that the mechanisms that mediate adaptation can either increase or decrease the response to low frequency stimuli. As such, they suggest that the nervous system resolves ambiguity resulting from adaptation through independent control of adaptation and the neuronal transfer function.

Hyperpolarisation-activated cyclic nucleotide channel 4 (HCN4) involvement in Tourette's syndrome autoimmunity

OBJECTIVES

We previously found that antibodies in Tourette's syndrome (TS) patients' sera reacted with a 120 kDa protein from rat brain tissue. Here, we sought to identify this protein and determine if it was involved in TS pathogenesis.

METHODS

The 120 kDa protein was identified using immunoprecipitation, Western blotting, and mass spectrometry. ELISAs were used to quantify anti-120 kDa protein antibodies in serum of interest using samples from 32 TS patients, 47 patients with attention deficit hyperactivity disorder (ADHD) and 14 healthy controls. Involvement of the 120 kDa protein in TS was confirmed using co-localisation assays with GH3 cells. TS sera were micro-infused into SD rats' brain striatum and their stereotypical behaviours were monitored.

RESULTS

The brain protein was identified as hyperpolarisation-activated cyclic nucleotide channel 4 (HCN4). TS patients' sera contained significantly more anti-HCN4 antibodies than ADHD patient and control sera. After microinfusing TS serum, SD rats exhibited increased stereotyped tic behaviours, which were correlated with the amount of infused anti-HCN4 antibody.

CONCLUSIONS

Anti-HCN4 antibodies in the brain might contribute to the pathogenesis of tic symptoms in TS patients. However, further studies are needed to investigate the validity of this animal model of TS induced by microinfusing anti-HCN4 antibody.