Membrane Channel Interactions Underlying Rat Subthalamic Projection Neuron Rhythmic and Bursting Activity

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.

Role of the volume conductor on simulations of local field potential recordings from deep brain stimulation electrodes

OBJECTIVE

Local field potential (LFP) recordings from deep brain stimulation (DBS) electrodes are commonly used in research analyses, and are beginning to be used in clinical practice. Computational models of DBS LFPs provide tools for investigating the biophysics and neural synchronization that underlie LFP signals. However, technical standards for DBS LFP model parameterization remain to be established. Therefore, the goal of this study was to evaluate the role of the volume conductor (VC) model complexity on simulated LFP signals in the subthalamic nucleus (STN).

APPROACH

We created a detailed human head VC model that explicitly represented the inhomogeneity and anisotropy associated with 12 different tissue structures. This VC model represented our "gold standard" for technical detail and electrical realism. We then incrementally decreased the complexity of the VC model and quantified the impact on the simulated LFP recordings. Identical STN neural source activity was used when comparing the different VC model variants. Results Ignoring tissue anisotropy reduced the simulated LFP amplitude by ~12%, while eliminating soft tissue heterogeneity had a negligible effect on the recordings. Simplification of the VC model to consist of a single homogenous isotropic tissue medium with a conductivity of 0.215 S/m contributed an additional ~3% to the error.

SIGNIFICANCE

Highly detailed VC models do generate different results than simplified VC models. However, with errors in the range of ~15%, the use of a well-parameterized simple VC model is likely to be acceptable in most contexts for DBS LFP modeling.

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.

Molecular Determinants of Mechanical Itch Sensitization in Chronic Itch

Chronic itch is associated with sensitization of the somatosensory nervous system. Recent studies have identified the neural circuits transmitting acute itch; however, the mechanisms by which itch transforms into a pathological state remain largely unknown. We have previously shown that Aβ low-threshold mechanoreceptors, together with spinal urocortin 3-positive (Ucn3+) excitatory interneurons and neuropeptide Y-positive (NPY+) inhibitory interneurons, form a microcircuit that transmits and gates acute mechanical itch. Here, using whole-cell patch-clamp recordings, we observed increased excitability in spinal Ucn3+ neurons under chronic itch conditions. In contrast to Ucn3+ neurons, the excitability of spinal NPY+ neurons was largely reduced under chronic itch conditions. To explore the molecular mechanisms underlying sensitization of this microcircuit, we examined the mRNA expression levels of voltage-gated ion channels in recorded spinal Ucn3+ and NPY+ neurons by single-cell quantitative real-time PCR (qRT-PCR). We found that the expression levels of Nav1.6 and Cav2.3 channels were increased in spinal Ucn3+ neurons in chronic itch mice, while the expression level of SK3 channels was decreased. By contrast, the expression levels of Nav1.6 and BK channels were decreased in spinal NPY+ neurons in chronic itch mice. To determine the contribution of different ion channels in chronic itch sensitization, we then used a Markov Chain Monte Carlo method to parameterize a large number of biophysically distinct multicompartment models of Ucn3+ and NPY+ neurons. These models included explicit representations of the ion channels that we found to be up- or down-regulated under chronic itch conditions. Our models demonstrated that changes in Nav1.6 conductance are predominantly responsible for the changes in excitability of both Ucn3+ and NPY+ neurons during chronic itch pathogenesis. Furthermore, when simulating microcircuits of our Ucn3+ and NPY+ models, we found that reduced Nav1.6 conductance in NPY+ models played a major role in opening the itch gate under chronic itch conditions. However, changing SK, BK, or R-type calcium channel conductance had negligible effects on the sensitization of this circuit. Therefore, our results suggest that Nav1.6 channels may play an essential role in mechanical itch sensitization. The findings presented here may open a new avenue for developing pharmaceutical strategies to treat chronic itch.

An electrophysiological perspective on Parkinson's disease: symptomatic pathogenesis and therapeutic approaches

Parkinson's disease (PD), or paralysis agitans, is a common neurodegenerative disease characterized by dopaminergic deprivation in the basal ganglia because of neuronal loss in the substantia nigra pars compacta. Clinically, PD apparently involves both hypokinetic (e.g. akinetic rigidity) and hyperkinetic (e.g. tremor/propulsion) symptoms. The symptomatic pathogenesis, however, has remained elusive. The recent success of deep brain stimulation (DBS) therapy applied to the subthalamic nucleus (STN) or the globus pallidus pars internus indicates that there are essential electrophysiological abnormalities in PD. Consistently, dopamine-deprived STN shows excessive burst discharges. This proves to be a central pathophysiological element causally linked to the locomotor deficits in PD, as maneuvers (such as DBS of different polarities) decreasing and increasing STN burst discharges would decrease and increase the locomotor deficits, respectively. STN bursts are not so autonomous but show a "relay" feature, requiring glutamatergic synaptic inputs from the motor cortex (MC) to develop. In PD, there is an increase in overall MC activities and the corticosubthalamic input is enhanced and contributory to excessive burst discharges in STN. The increase in MC activities may be relevant to the enhanced beta power in local field potentials (LFP) as well as the deranged motor programming at the cortical level in PD. Moreover, MC could not only drive erroneous STN bursts, but also be driven by STN discharges at specific LFP frequencies (~ 4 to 6 Hz) to produce coherent tremulous muscle contractions. In essence, PD may be viewed as a disorder with deranged rhythms in the cortico-subcortical re-entrant loops, manifestly including STN, the major component of the oscillating core, and MC, the origin of the final common descending motor pathways. The configurations of the deranged rhythms may play a determinant role in the symptomatic pathogenesis of PD, and provide insight into the mechanism underlying normal motor control. Therapeutic brain stimulation for PD and relevant disorders should be adaptively exercised with in-depth pathophysiological considerations for each individual patient, and aim at a final normalization of cortical discharge patterns for the best ameliorating effect on the locomotor and even non-motor symptoms.

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.

Biophysical characterization of local field potential recordings from directional deep brain stimulation electrodes

OBJECTIVE

Two major advances in clinical deep brain stimulation (DBS) technology have been the introduction of local field potential (LFP) recording capabilities, and the deployment of directional DBS electrodes. However, these two technologies are not operationally integrated within current clinical DBS devices. Therefore, we evaluated the theoretical advantages of using directional DBS electrodes for LFP recordings, with a focus on measuring beta-band activity in the subthalamic nucleus (STN).

METHODS

We used a computational model of human STN neural activity to simulate LFP recordings. The model consisted of 235,280 anatomically and electrically detailed STN neurons surrounding the DBS electrode, which was previously optimized to mimic beta-band synchrony in the dorsolateral STN. We then used that model system to compare LFP recordings from cylindrical and directional DBS contacts, and evaluate how the selection of different contacts for bipolar recording affected the LFP measurements.

RESULTS

The model predicted two advantages of directional DBS electrodes over cylindrical DBS electrodes for STN LFP recording. First, recording from directional contacts could provide additional insight on the location of a synchronous volume of neurons within the STN. Second, directional contacts could detect a smaller volume of synchronous neurons than cylindrical contacts, which our simulations predicted to be a ~0.5 mm minimum radius.

CONCLUSIONS

STN LFP recordings from 8-contact directional DBS electrodes (28 possible bipolar pairs) can provide more information than 4-contact cylindrical DBS electrodes (6 possible bipolar pairs), but they also introduce additional complexity in analyzing the signals.

SIGNIFICANCE

Integration of directional electrodes with DBS systems that are capable of LFP recordings could improve localization of targeted volumes of synchronous neurons in PD patients.

Dendritic distributions of L-type Ca2+ and SKL channels in spinal motoneurons: a simulation study

Persistent inward currents are important to motoneuron excitability and firing behaviors and also have been implicated in excitotoxicity. In particular, L-type Ca2+ channels, usually located on motoneuron dendrites, play a primary role in amplification of synaptic inputs. However, recent experimental findings on L-type Ca2+ channel behaviors challenge some fundamental assumptions that have been used in interpreting experimental and computational modeling data. Thus, the objectives of this study were to incorporate recent experimental data into an updated, high-fidelity computational model in order to explain apparent inconsistencies and to better elucidate the spatial distributions, expression patterns, and functional roles of L-type Ca2+ and SKL channels. Specifically, the updated model incorporated asymmetric channel activation/deactivation kinetics, depolarization-dependent facilitation, randomness in channel gating, and coactivation of SKL channels. Our simulation results suggest that L-type Ca2+ and SKL channels colocalize primarily on distal dendrites of motoneurons in a punctate expression. Also, punctate expression, as opposed to a homogeneous expression, provides high synaptic current amplification, limits bistability and firing rates, and robustly regulates the Ca2+ persistent inward current, thereby reducing risk of excitotoxicity. The hysteresis and bistability observed experimentally in current-voltage and frequency-current relationships result from the L-type Ca2+ channels' distal location and intrinsic warm-up. Accordingly, our results indicate that punctate expression of L-type Ca2+ and SKL channels is a potent mechanism for regulating excitability, which would provide a strong neuroprotective effect. Our results could provide broader insights into the functional significance of warm-up and punctate expression of ion channels to regulation of cell excitability.NEW & NOTEWORTHY Recent experimental findings on L-type Ca2+ channels challenge fundamental assumptions used in interpreting experimental and computational modeling data. Here, we incorporated recent experimental data into an updated, high-fidelity computational model to explain apparent inconsistencies and better elucidate the distributions, expression patterns, and functional roles of L-type Ca2+ and SKL channels. Our results indicate that punctate expression of L-type Ca2+ and SKL channels is a potent mechanism for regulating motoneuron excitability, providing a strong neuroprotective effect.

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.

Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network

Increased beta-band oscillatory activity in the basal ganglia network is associated with Parkinsonian motor symptoms and is suppressed with medication and deep brain stimulation (DBS). The origins of the beta-band oscillations, however, remains unclear with both intrinsic oscillations arising within the subthalamic nucleus (STN)-external globus pallidus (GPe) network and exogenous beta-activity, originating outside the network, proposed as potential sources of the pathological activity. The aim of this study was to explore the relative contribution of autonomous oscillations and exogenous oscillatory inputs in the generation of pathological oscillatory activity in a biophysically detailed model of the parkinsonian STN-GPe network. The network model accounts for the integration of synaptic currents and their interaction with intrinsic membrane currents in dendritic structures within the STN and GPe. The model was used to investigate the development of beta-band synchrony and bursting within the STN-GPe network by changing the balance of excitation and inhibition in both nuclei, and by adding exogenous oscillatory inputs with varying phase relationships through the hyperdirect cortico-subthalamic and indirect striato-pallidal pathways. The model showed an intrinsic susceptibility to beta-band oscillations that was manifest in weak autonomously generated oscillations within the STN-GPe network and in selective amplification of exogenous beta-band synaptic inputs near the network's endogenous oscillation frequency. The frequency at which this resonance peak occurred was determined by the net level of excitatory drive to the network. Intrinsic or endogenously generated oscillations were too weak to support a pacemaker role for the STN-GPe network, however, they were considerably amplified by sparse cortical beta inputs and were further amplified by striatal beta inputs that promoted anti-phase firing of the cortex and GPe, resulting in maximum transient inhibition of STN neurons. The model elucidates a mechanism of cortical patterning of the STN-GPe network through feedback inhibition whereby intrinsic susceptibility to beta-band oscillations can lead to phase locked spiking under parkinsonian conditions. These results point to resonance of endogenous oscillations with exogenous patterning of the STN-GPe network as a mechanism of pathological synchronization, and a role for the pallido-striatal feedback loop in amplifying beta oscillations.

Computational Modeling of Ultrasonic Subthalamic Nucleus Stimulation

OBJECTIVE

To explore the potential of ultrasonic modulation of plateau-potential generating subthalamic nucleus neurons (STN), by modeling their interaction with continuous and pulsed ultrasonic waves.

METHODS

A computational model for ultrasonic stimulation of the STN is created by combining the Otsuka-model with the bilayer sonophore model. The neuronal response to continuous and pulsed ultrasonic waves is computed in parallel for a range of frequencies, duty cycles, pulse repetition frequencies, and intensities.

RESULTS

Ultrasonic intensity in continuous-wave stimulation determines the firing pattern of the STN. Three observed spiking modes in order of increasing intensity are low frequency spiking, high frequency spiking with significant spike-frequency and spike-amplitude adaptation, and a silenced mode. Continuous-wave stimulation has little capability to manipulate the saturated spiking rate in the high frequency spiking mode. In contrast, STN firing rates induced by pulsed ultrasound insonication will saturate to the pulse repetition frequency with short latencies, for sufficiently large intensity and repetition frequency.

CONCLUSION

Computational results show that the activity of plateau-potential generating STN can be modulated by selection of the stimulus parameters. Low intensities result in repetitive firing, while higher intensities silence the STN. Pulsed ultrasonic stimulation results in a shorter saturation latency and is able to modulate spiking rates.

SIGNIFICANCE

Stimulation or suppresion of the STN is important in the treatment of Parkinson's disease, e.g., in deep brain stimulation. This explorative study on ultrasonic modulation of the STN, could be a step in the direction of minimally invasive alternatives to conventional deep brain stimulation.

Biophysical basis of subthalamic local field potentials recorded from deep brain stimulation electrodes

Clinical deep brain stimulation (DBS) technology is evolving to enable chronic recording of local field potentials (LFPs) that represent electrophysiological biomarkers of the underlying disease state. However, little is known about the biophysical basis of LFPs, or how the patient's unique brain anatomy and electrode placement impact the recordings. Therefore, we developed a patient-specific computational framework to analyze LFP recordings within a clinical DBS context. We selected a subject with Parkinson's disease implanted with a Medtronic Activa PC+S DBS system and reconstructed their subthalamic nucleus (STN) and DBS electrode location using medical imaging data. The patient-specific STN volume was populated with 235,280 multicompartment STN neuron models, providing a neuron density consistent with histological measurements. Each neuron received time-varying synaptic inputs and generated transmembrane currents that gave rise to the LFP signal recorded at DBS electrode contacts residing in a finite element volume conductor model. We then used the model to study the role of synchronous beta-band inputs to the STN neurons on the recorded power spectrum. Three bipolar pairs of simultaneous clinical LFP recordings were used in combination with an optimization algorithm to customize the neural activity parameters in the model to the patient. The optimized model predicted a 2.4-mm radius of beta-synchronous neurons located in the dorsolateral STN. These theoretical results enable biophysical dissection of the LFP signal at the cellular level with direct comparison to the clinical recordings, and the model system provides a scientific platform to help guide the design of DBS technology focused on the use of subthalamic beta activity in closed-loop algorithms. NEW & NOTEWORTHY The analysis of deep brain stimulation of local field potential (LFP) data is rapidly expanding from scientific curiosity to the basis for clinical biomarkers capable of improving the therapeutic efficacy of stimulation. With this growing clinical importance comes a growing need to understand the underlying electrophysiological fundamentals of the signals and the factors contributing to their modulation. Our model reconstructs the clinical LFP from first principles and highlights the importance of patient-specific factors in dictating the signals recorded.

Differential potassium channel gene regulation in BXD mice reveals novel targets for pharmacogenetic therapies to reduce heavy alcohol drinking

Alcohol (ethanol) dependence is a chronic relapsing brain disorder partially influenced by genetics and characterized by an inability to regulate harmful levels of drinking. Emerging evidence has linked genes that encode K_V7, K_IR, and K_Ca2 K⁺ channels with variation in alcohol-related behaviors in rodents and humans. This led us to experimentally test relations between K⁺ channel genes and escalation of drinking in a chronic-intermittent ethanol (CIE) exposure model of dependence in BXD recombinant inbred strains of mice. Transcript levels for K⁺ channel genes in the prefrontal cortex (PFC) and nucleus accumbens (NAc) covary with voluntary ethanol drinking in a non-dependent cohort. Transcripts that encode K_V7 channels covary negatively with drinking in non-dependent BXD strains. Using a pharmacological approach to validate the genetic findings, C57BL/6J mice were allowed intermittent access to ethanol to establish baseline consumption before they were treated with retigabine, an FDA-approved K_V7 channel positive modulator. Systemic administration significantly reduced drinking, and consistent with previous evidence, retigabine was more effective at reducing voluntary consumption in high-drinking than low-drinking subjects. We evaluated the specific K⁺ channel genes that were most sensitive to CIE exposure and identified a gene subset in the NAc and PFC that were dysregulated in the alcohol-dependent BXD cohort. CIE-induced modulation of nine genes in the NAc and six genes in the PFC covaried well with the changes in drinking induced by ethanol dependence. Here we identified novel candidate genes in the NAc and PFC that are regulated by ethanol dependence and correlate with voluntary drinking in non-dependent and dependent BXD mice. The findings that Kcnq expression correlates with drinking and that retigabine reduces consumption suggest that K_V7 channels could be pharmacogenetic targets to treat individuals with alcohol addiction.

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.

Theoretical analysis of the local field potential in deep brain stimulation applications

Deep brain stimulation (DBS) is a common therapy for treating movement disorders, such as Parkinson's disease (PD), and provides a unique opportunity to study the neural activity of various subcortical structures in human patients. Local field potential (LFP) recordings are often performed with either intraoperative microelectrodes or DBS leads and reflect oscillatory activity within nuclei of the basal ganglia. These LFP recordings have numerous clinical implications and might someday be used to optimize DBS outcomes in closed-loop systems. However, the origin of the recorded LFP is poorly understood. Therefore, the goal of this study was to theoretically analyze LFP recordings within the context of clinical DBS applications. This goal was achieved with a detailed recording model of beta oscillations (∼20 Hz) in the subthalamic nucleus. The recording model consisted of finite element models of intraoperative microelectrodes and DBS macroelectrodes implanted in the brain along with multi-compartment cable models of STN projection neurons. Model analysis permitted systematic investigation into a number of variables that can affect the composition of the recorded LFP (e.g. electrode size, electrode impedance, recording configuration, and filtering effects of the brain, electrode-electrolyte interface, and recording electronics). The results of the study suggest that the spatial reach of the LFP can extend several millimeters. Model analysis also showed that variables such as electrode geometry and recording configuration can have a significant effect on LFP amplitude and spatial reach, while the effects of other variables, such as electrode impedance, are often negligible. The results of this study provide insight into the origin of the LFP and identify variables that need to be considered when analyzing LFP recordings in clinical DBS applications.

Spatiotemporal visualization of deep brain stimulation-induced effects in the subthalamic nucleus

Deep brain stimulation (DBS) is a successful surgical therapy used to treat the disabling symptoms of movement disorders such as Parkinson's disease. It involves the chronic stimulation of disorder-specific nuclei. However, the mechanisms that lead to clinical improvements remain unclear. Consequently, this slows the optimization of present-day DBS therapy and hinders its future development and application. We used a computational model to calculate the distribution of electric potential induced by DBS and study the effect of stimulation on the spiking activity of a subthalamic nucleus (STN) projection neuron. We previously showed that such a model can reveal detailed spatial effects of stimulation in the vicinity of the electrode. However, this multi-compartmental STN neuron model can fire in either a burst or tonic mode and, in this study, we hypothesized that the firing mode of the cell will have a major impact on the DBS-induced effects. Our simulations showed that the bursting model exhibits behaviour observed in studies of high-frequency stimulation of STN neurons, such as the presence of a silent period at stimulation offset and frequency-dependent stimulation effects. We validated the model by simulating the clinical parameter settings used for a Parkinsonian patient and showed, in a patient-specific anatomical model, that the region of affected tissue is consistent with clinical observations of the optimal DBS site. Our results demonstrated a method of quantitatively assessing neuronal changes induced by DBS, to maximize therapeutic benefit and minimize unwanted side effects.

Roles of the subthalamic nucleus and subthalamic HCN channels in absence seizures

Absence seizures consist of a brief and sudden impairment of consciousness. They are characterized by bilaterally synchronized spike and wave discharges (SWDs), which reflect abnormal oscillations in the thalamocortical loops. Recent studies have suggested that the basal ganglia are involved in generation of the SWDs, but their roles are poorly understood at the molecular and cellular levels. Here we studied the pathophysiological roles of the basal ganglia, using in vivo and in vitro measurements of tottering mice, a well-established model of absence epilepsy. We found that the membrane excitability in subthalamic nucleus (STN) neurons was enhanced in tottering mice, which resulted from reduced hyperpolarization-activated cyclic nucleotide-gated (HCN) channel activity. Pharmacological blockade and activation of HCN channel activity in vitro bidirectionally altered the membrane excitability of the STN neurons. Furthermore, these pharmacological modulations of HCN channel activity in the STN in vivo bidirectionally altered the mean SWD duration. In addition, STN deep brain stimulation modulated SWDs in a frequency-dependent manner. These results indicate that STN is involved in the rhythm maintenance system of absence seizures.

NMDA-induced burst firing in a model subthalamic nucleus neuron

Experiments in rat brain slice show that hyperpolarized subthalamic nucleus (STN) neurons engage in slow, regular burst firing when treated with an N-methyl-d-aspartate (NMDA) bath. A depolarization-activated inward current (DIC) has been hypothesized to contribute to this bursting activity. To explore the mechanism for STN burst firing in this setting, we augmented a previously published conductance-based computational model for single rat STN neurons to include both DIC and NMDA currents, fit to data from published electrophysiological recordings. Simulations show that with these additions, the model engages in bursting activity at <1 Hz in response to hyperpolarizing current injection and that this bursting exhibits several features observed experimentally in STN. Furthermore, a reduced model is used to show that the combination of NMDA and DIC currents, but not either alone, suffices to generate oscillations under hyperpolarizing current injection. STN neurons show enhanced burstiness in Parkinson's disease patients and experimental models of parkinsonism, and the burst mechanism studied presently could contribute to this effect.

Selective participation of somatodendritic HCN channels in inhibitory but not excitatory synaptic integration in neurons of the subthalamic nucleus

The activity patterns of subthalamic nucleus (STN) neurons are intimately linked to motor function and dysfunction and arise through the complex interaction of intrinsic properties and inhibitory and excitatory synaptic inputs. In many neurons, hyperpolarization-activated cyclic nucleotide-gated (HCN) channels play key roles in intrinsic excitability and synaptic integration both under normal conditions and in disease states. However, in STN neurons, which strongly express HCN channels, their roles remain relatively obscure. To address this deficit, complementary molecular and cellular electrophysiological, imaging, and computational approaches were applied to the rat STN. Molecular profiling demonstrated that individual STN neurons express mRNA encoding several HCN subunits, with HCN2 and 3 being the most abundant. Light and electron microscopic analysis showed that HCN2 subunits are strongly expressed and distributed throughout the somatodendritic plasma membrane. Voltage-, current-, and dynamic-clamp analysis, two-photon Ca(2+) imaging, and computational modeling revealed that HCN channels are activated by GABA(A) receptor-mediated inputs and thus limit synaptic hyperpolarization and deinactivation of low-voltage-activated Ca(2+) channels. Although HCN channels also limited the temporal summation of EPSPs, generated through two-photon uncaging of glutamate, this action was largely shunted by GABAergic inhibition that was necessary for HCN channel activation. Together the data demonstrate that HCN channels in STN neurons selectively counteract GABA(A) receptor-mediated inhibition arising from the globus pallidus and thus promote single-spike activity rather than rebound burst firing.

A model of pathological oscillations in the basal ganglia and deep brain stimulation in Parkinson's disease

A model of pathological oscillatory activity within the basal ganglia in Parkinson's disease is presented. Synchronous oscillatory activity of the subthalamic nucleus (STN) and globus pallidus external (GPe) is simulated at both the parkinsonian tremor (3-9) Hz and beta (15-30) Hz frequencies. The model extends previous models to incorporate cortical inputs to the subthalamic nucleus through the 'hyperdirect' pathway, changes in coupling between STN neurons due to dopamine depletion and the plateau potential generating capacity of STN neurons. The effect of deep brain stimulation (DBS) across a range of frequencies on the oscillatory activity is examined. High frequency DBS attenuates synchronous oscillatory activity within the STN-GPe network at both the tremor and beta frequencies. The efficacy of the DBS input in quenching the pathological oscillations is shown to vary systematically with the frequency, pulse width and amplitude of the applied stimulus.

Quantifying the neural elements activated and inhibited by globus pallidus deep brain stimulation

Deep brain stimulation (DBS) of the globus pallidus pars interna (GPi) is an effective therapy option for controlling the motor symptoms of medication-refractory Parkinson's disease and dystonia. Despite the clinical successes of GPi DBS, the precise therapeutic mechanisms are unclear and questions remain on the optimal electrode placement and stimulation parameter selection strategies. In this study, we developed a three-dimensional computational model of GPi-DBS in nonhuman primates to investigate how membrane channel dynamics, synaptic inputs, and axonal collateralization contribute to the neural responses generated during stimulation. We focused our analysis on three general neural elements that surround GPi-DBS electrodes: GPi somatodendritic segments, GPi efferent axons, and globus pallidus pars externa (GPe) fibers of passage. During high-frequency electrical stimulation (136 Hz), somatic activity in the GPi showed interpulse excitatory phases at 1-3 and 4-5.5 ms. When including stimulation-induced GABA(A) and AMPA receptor dynamics into the model, the somatic firing patterns continued to be entrained to the stimulation, but the overall firing rate was reduced (78.7 to 25.0 Hz, P < 0.001). In contrast, axonal output from GPi neurons remained largely time-locked to each pulse of the stimulation train. Similar entrainment was also observed in GPe efferents, a majority of which have been shown to project through GPi en route to the subthalamic nucleus. The models suggest that pallidal DBS may have broader network effects than previously realized and the modes of therapy may depend on the relative proportion of GPi and/or GPe efferents that are directly affected by the stimulation.

D2-like dopamine receptors modulate SKCa channel function in subthalamic nucleus neurons through inhibition of Cav2.2 channels

The activity patterns of subthalamic nucleus (STN) neurons are intimately related to motor function/dysfunction and modulated directly by dopaminergic neurons that degenerate in Parkinson's disease (PD). To understand how dopamine and dopamine depletion influence the activity of the STN, the functions/signaling pathways/substrates of D2-like dopamine receptors were studied using patch-clamp recording. In rat brain slices, D2-like dopamine receptor activation depolarized STN neurons, increased the frequency/irregularity of their autonomous activity, and linearized/enhanced their firing in response to current injection. Activation of D2-like receptors in acutely isolated neurons reduced transient outward currents evoked by suprathreshold voltage steps. Modulation was inhibited by a D2-like receptor antagonist and occluded by voltage-dependent Ca2+ (Cav) channel or small-conductance Ca2+-dependent K+ (SKCa) channel blockers or Ca2+-free media. Because Cav channels are targets of G(i/o)-linked receptors, actions on step- and action potential waveform-evoked Cav channel currents were studied. D2-like receptor activation reduced the conductance of Cav2.2 but not Cav1 channels. Modulation was mediated, in part, by direct binding of Gbetagamma subunits because it was attenuated by brief depolarization. D2 and/or D3 dopamine receptors may mediate modulation because a D4-selective agonist was ineffective and mRNA encoding D2 and D3 but not D4 dopamine receptors was detectable. Brain slice recordings confirmed that SKCa channel-mediated action potential afterhyperpolarization was attenuated by D2-like dopamine receptor activation. Together, these data suggest that D2-like dopamine receptors potently modulate the negative feedback control of firing that is mediated by the functional coupling of Cav2.2 and SKCa channels in STN neurons.

Neuroinformatics and modeling of the basal ganglia: bridging pharmacology and physiology

The subthalamic nucleus (STN) is the primary target for the chronic deep brain stimulation treatment of Parkinson's disease. STN neurons exhibit a variety of characteristic properties that may play a key role in the overall population response to deep brain stimulation. Neuroinformatics techniques, in particular computational modeling, provide a method of bringing together pharmacological phenomena, such as the loss of dopamine, with electrophysiological characteristics. Developing accurate models of STN neurons plays an important part in the process of uncovering the link between the changes in STN pharmacology, physiology and synaptic input that occurs with Parkinson's disease and the effectiveness of treatments targeting the STN. We review a general procedure for developing computational models and present a model of STN neurons that reveals important membrane channel interactions. In particular, changes in these channel interactions under parkinsonian conditions may underlie changes in characteristic physiology, critical in determining the mechanisms of deep brain stimulation.

Computational models simulating electrophysiological activity in the basal ganglia

Modeling of the basal ganglia has played a substantial role in gaining insight into the mechanisms involved in the computational processes performed by this elusive group of nuclei. Models of the basal ganglia have undergone revolutionary changes over the last twenty years due to the rapid accumulation of neuroscientific data. In this chapter, we present distinct modeling approaches that can be used to enhance our understanding of the functional dynamics of information processing within the basal ganglia, and their interactions with the rest of the brain. Specific examples of recently developed models dealing with the analysis of computational processing issues at different structural levels of the basal ganglia are discussed.

Computational analysis of subthalamic nucleus and lenticular fasciculus activation during therapeutic deep brain stimulation

The subthalamic nucleus (STN) is the most common target for the treatment of Parkinson's disease (PD) with deep brain stimulation (DBS). DBS of the globus pallidus internus (GPi) is also effective in the treatment of PD. The output fibers of the GPi that form the lenticular fasciculus pass in close proximity to STN DBS electrodes. In turn, both STN projection neurons and GPi fibers of passage represent possible therapeutic targets of DBS in the STN region. We built a comprehensive computational model of STN DBS in parkinsonian macaques to study the effects of stimulation in a controlled environment. The model consisted of three fundamental components: 1) a three-dimensional (3D) anatomical model of the macaque basal ganglia, 2) a finite element model of the DBS electrode and electric field transmitted to the tissue medium, and 3) multicompartment biophysical models of STN projection neurons, GPi fibers of passage, and internal capsule fibers of passage. Populations of neurons were positioned within the 3D anatomical model. Neurons were stimulated with electrode positions and stimulation parameters defined as clinically effective in two parkinsonian monkeys. The model predicted axonal activation of STN neurons and GPi fibers during STN DBS. Model predictions regarding the degree of GPi fiber activation matched well with experimental recordings in both monkeys. Only axonal activation of the STN neurons showed a statistically significant increase in both monkeys when comparing clinically effective and ineffective stimulation. Nonetheless, both neural targets may play important roles in the therapeutic mechanisms of STN DBS.