Propagation of Oscillations in the Indirect Pathway of the Basal Ganglia.

Oscillatory signals propagate in the basal ganglia from prototypic neurons in the external globus pallidus (GPe) to their target neurons in the substantia nigra pars reticulata (SNr), internal pallidal segment, and subthalamic nucleus. Neurons in the GPe fire spontaneously, so oscillatory input signals can be encoded as changes in timing of action potentials within an ongoing spike train. When GPe neurons were driven by an oscillatory current in male and female mice, these spike-timing changes produced spike-oscillation coherence over a range of frequencies extending at least to 100 Hz. Using the known kinetics of the GPe→SNr synapse, we calculated the postsynaptic currents that would be generated in SNr neurons from the recorded GPe spike trains. The ongoing synaptic barrage from spontaneous firing, frequency-dependent short-term depression, and stochastic fluctuations at the synapse embed the input oscillation into a noisy sequence of synaptic currents in the SNr. The oscillatory component of the resulting synaptic current must compete with the noisy spontaneous synaptic barrage for control of postsynaptic SNr neurons, which have their own frequency-dependent sensitivities. Despite this, SNr neurons subjected to synaptic conductance changes generated from recorded GPe neuron firing patterns also became coherent with oscillations over a broad range of frequencies. The presynaptic, synaptic, and postsynaptic frequency sensitivities were all dependent on the firing rates of presynaptic and postsynaptic neurons. Firing rate changes, often assumed to be the propagating signal in these circuits, do not encode most oscillation frequencies, but instead determine which signal frequencies propagate effectively and which are suppressed.SIGNIFICANCE STATEMENT Oscillations are present in all the basal ganglia nuclei, include a range of frequencies, and change over the course of learning and behavior. Exaggerated oscillations are a hallmark of basal ganglia pathologies, and each has a specific frequency range. Because of its position as a hub in the basal ganglia circuitry, the globus pallidus is a candidate origin for oscillations propagating between nuclei. We imposed low-amplitude oscillations on individual globus pallidus neurons at specific frequencies and measured the coherence between the oscillation and firing as a function of frequency. We then used these responses to measure the effectiveness of oscillatory propagation to other basal ganglia nuclei. Propagation was effective for oscillation frequencies as high as 100 Hz.

Spontaneous Activity of the Local GABAergic Synaptic Network Causes Irregular Neuronal Firing in the External Globus Pallidus.

Autonomously firing GABAergic neurons in the external globus pallidus (GPe) form a local synaptic network. In slices, most GPe neurons receive a continuous inhibitory synaptic barrage from 1 or 2 presynaptic GPe neurons. We measured the barrage's effect on the firing rate and regularity of GPe neurons in male and female mice using perforated patch recordings. Silencing the firing of parvalbumin-positive (PV+) GPe neurons by activating genetically expressed Archaerhodopsin current increased the firing rate and regularity of PV- neurons. In contrast, silencing Npas1+ GPe neurons with Archaerhodopsin had insignificant effects on Npas1- neuron firing. Blocking spontaneous GABAergic synaptic input with gabazine reproduced the effects of silencing PV+ neuron firing on the firing rate and regularity of Npas1+ neurons and had similar effects on PV+ neuron firing. To simulate the barrage, we constructed conductance waveforms for dynamic clamp based on experimentally measured inhibitory postsynaptic conductance trains from 1 or 2 unitary local connections. The resulting inhibition replicated the effect on firing seen in the intact active network in the slice. We then increased the number of unitary inputs to match estimates of local network connectivity in vivo As few as 5 unitary inputs produced large increases in firing irregularity. The firing rate was also reduced initially, but PV+ neurons exhibited a slow spike-frequency adaptation that partially restored the rate despite sustained inhibition. We conclude that the irregular firing pattern of GPe neurons in vivo is largely due to the ongoing local inhibitory synaptic barrage produced by the spontaneous firing of other GPe neurons.SIGNIFICANCE STATEMENT Functional roles of local axon collaterals in the external globus pallidus (GPe) have remained elusive because of difficulty in isolating local inhibition from other GABAergic inputs in vivo, and in preserving the autonomous firing of GPe neurons and detecting their spontaneous local inputs in slices. We used perforated patch recordings to detect spontaneous local inputs during rhythmic firing. We found that the autonomous firing of single presynaptic GPe neurons produces inhibitory synaptic barrages that significantly alter the firing regularity of other GPe neurons. Our findings suggest that, although GPe neurons receive input from only a few other GPe neurons, each local connection has a large impact on their firing.

Comparison of unitary synaptic currents generated by indirect and direct pathway neurons of the mouse striatum.

Two subtypes of striatal spiny projection neurons, iSPNs and dSPNs, whose axons form the "indirect" and "direct" pathways of the basal ganglia, respectively, both make synaptic connections in the external globus pallidus (GPe) but are usually found to have different effects on behavior. Activation of the terminal fields of iSPNs or dSPNs generated compound currents in almost all GPe neurons. To determine whether iSPNs and dSPNs have the same or different effects on pallidal neurons, we studied the unitary synaptic currents generated in GPe neurons by action potentials in single striatal neurons. We used optogenetic excitation to elicit repetitive firing in a small number of nearby SPNs, producing sparse barrages of inhibitory postsynaptic currents (IPSCs) in GPe neurons. From these barrages, we isolated sequences of IPSCs with similar time courses and amplitudes, which presumably arose from the same SPN. There was no difference between the amplitudes of unitary IPSCs generated by the indirect and direct pathways. Most unitary IPSCs were small, but a subset from each pathway were much larger. To determine the effects of these unitary synaptic currents on the action potential firing of GPe neurons, we drove SPNs to fire as before and recorded the membrane potential of GPe neurons. Large unitary potentials from iSPNs and dSPNs perturbed the spike timing of GPe neurons in a similar way. Most SPN-GPe neuron pairs are weakly connected, but a subset of pairs in both pathways are strongly connected.NEW & NOTEWORTHY This is the first study to record the synaptic currents generated by single identified direct or indirect pathway striatal neurons on single pallidal neurons. Each GPe neuron receives synaptic inputs from both pathways. Most striatal neurons generate small synaptic currents that become influential when occurring together, but a few are powerful enough to be individually influential.

Dissociable Roles of Pallidal Neuron Subtypes in Regulating Motor Patterns.

We have previously established that PV+ neurons and Npas1+ neurons are distinct neuron classes in the external globus pallidus (GPe): they have different topographical, electrophysiological, circuit, and functional properties. Aside from Foxp2+ neurons, which are a unique subclass within the Npas1+ class, we lack driver lines that effectively capture other GPe neuron subclasses. In this study, we examined the utility of Kcng4-Cre, Npr3-Cre, and Npy2r-Cre mouse lines (both males and females) for the delineation of GPe neuron subtypes. By using these novel driver lines, we have provided the most exhaustive investigation of electrophysiological studies of GPe neuron subtypes to date. Corroborating our prior studies, GPe neurons can be divided into two statistically distinct clusters that map onto PV+ and Npas1+ classes. By combining optogenetics and machine learning-based tracking, we showed that optogenetic perturbation of GPe neuron subtypes generated unique behavioral structures. Our findings further highlighted the dissociable roles of GPe neurons in regulating movement and anxiety-like behavior. We concluded that Npr3+ neurons and Kcng4+ neurons are distinct subclasses of Npas1+ neurons and PV+ neurons, respectively. Finally, by examining local collateral connectivity, we inferred the circuit mechanisms involved in the motor patterns observed with optogenetic perturbations. In summary, by identifying mouse lines that allow for manipulations of GPe neuron subtypes, we created new opportunities for interrogations of cellular and circuit substrates that can be important for motor function and dysfunction.SIGNIFICANCE STATEMENT Within the basal ganglia, the external globus pallidus (GPe) has long been recognized for its involvement in motor control. However, we lacked an understanding of precisely how movement is controlled at the GPe level as a result of its cellular complexity. In this study, by using transgenic and cell-specific approaches, we showed that genetically-defined GPe neuron subtypes have distinct roles in regulating motor patterns. In addition, the in vivo contributions of these neuron subtypes are in part shaped by the local, inhibitory connections within the GPe. In sum, we have established the foundation for future investigations of motor function and disease pathophysiology.

Local inhibition in a model of the indirect pathway globus pallidus network slows and deregularizes background firing, but sharpens and synchronizes responses to striatal input.

The external segment of globus pallidus (GPe) is a network of oscillatory neurons connected by inhibitory synapses. We studied the intrinsic dynamic and the response to a shared brief inhibitory stimulus in a model GPe network. Individual neurons were simulated using a phase resetting model based on measurements from mouse GPe neurons studied in slices. The neurons showed a broad heterogeneity in their firing rates and in the shapes and sizes of their phase resetting curves. Connectivity in the network was set to match experimental measurements. We generated statistically equivalent neuron heterogeneity in a small-world model, in which 99% of connections were made with near neighbors and 1% at random, and in a model with entirely random connectivity. In both networks, the resting activity was slowed and made more irregular by the local inhibition, but it did not show any periodic pattern. Cross-correlations among neuron pairs were limited to directly connected neurons. When stimulated by a shared inhibitory input, the individual neuron responses separated into two groups: one with a short and stereotyped period of inhibition followed by a transient increase in firing probability, and the other responding with a sustained inhibition. Despite differences in firing rate, the responses of the first group of neurons were of fixed duration and were synchronized across cells.

Periodic unitary synaptic currents in the mouse globus pallidus during spontaneous firing in slices.

Neurons in the external globus pallidus (GPe) are autonomous pacemakers, but their spontaneous firing is continually perturbed by synaptic input. Because GPe neurons fire rhythmically in slices, spontaneous inhibitory synaptic currents (IPSCs) should be evident there. We identified periodic series of IPSCs in slices, each corresponding to unitary synaptic currents from one presynaptic cell. Optogenetic stimulation of the striatal indirect pathway axons caused a pause and temporal resetting of the periodic input, confirming that it arose from local neurons subject to striatal inhibition. We determined the firing statistics of the presynaptic neurons from the unitary IPSC statistics and estimated their frequencies, peak amplitudes, and reliabilities. To determine what types of GPe neurons received the spontaneous inhibition, we recorded from genetically labeled parvalbumin (PV) and Npas1-expressing neurons. Both cell types received periodic spontaneous IPSCs with similar frequencies. Optogenetic inhibition of PV neurons reduced the spontaneous IPSC rate in almost all neurons with active unitary inputs, whereas inhibition of Npas1 neurons rarely affected the spontaneous IPSC rate in any neurons. These results suggest that PV neurons provided most of the active unitary inputs to both cell types. Optogenetic pulse stimulation of PV neurons at light levels that can activate cut axons yielded an estimate of connectivity in the fully connected network. The local network is a powerful source of inhibition to both PV and Npas1 neurons, which contributes to irregular firing and may influence the responses to external synaptic inputs.NEW & NOTEWORTHY Brain circuits are often quiet in slices. In the globus pallidus, network activity continues because of the neurons' rhythmic autonomous firing. In this study, synaptic currents generated by the network barrage were measured in single neurons. Unitary synaptic currents arising from single presynaptic neurons were identified by their unique periodicity. Periodic synaptic currents were large and reliable, even at the cell's natural firing rates, but arose from a small number of other globus pallidus neurons.

Indirect pathway control of firing rate and pattern in the substantia nigra pars reticulata.

Unitary pallido-nigral synaptic currents were measured using optogenetic stimulation, which activated up to three unitary synaptic inputs to each substantia nigra pars reticulata (SNr) cell. Episodic barrages of synaptic conductances were generated based on in vivo firing patterns of globus pallidus pars externa (GPe) cells and applied to SNr cells using conductance clamp. Barrage inputs were compared to continuous step conductances with the same mean. Barrage inputs and steps both slowed SNr neuron firing and produced disinhibition responses seen in peristimulus histograms. Barrages were less effective than steps at producing inhibition and disinhibition responses. Barrages, but not steps, produced irregular firing during the inhibitory response. Phase models of SNr neurons were constructed from their phase-resetting curves. The phase models reproduced the inhibition and disinhibition responses to the same inputs applied to the neurons. The disinhibition response did not require rebound currents but arose from reset of the cells' oscillation. The differences in firing rate and irregularity in response to barrage and step inhibition resulted from the high sensitivity of SNr neurons to inhibition at late phases in their intrinsic oscillation. During step inhibition, cells continued rhythmic firing at a reduced rate. During barrages, brief bouts of intense inhibition stalled the cells' phase evolution late in their cycle, close to firing, and even very brief respites from inhibition rapidly released single action potentials. The SNr cell firing pattern reflected the fine structure of the synaptic barrage from GPe, as well as its onset and offset.NEW & NOTEWORTHY The pallido-nigral pathway connects the striatum to spontaneously active basal ganglia output neurons in the substantia nigra. Each substantia nigra neuron receives powerful inhibitory synaptic connections from a small group of globus pallidus cells and may fire during pauses in pallidal activity. Despite lacking any hyperpolarization-activated rebound currents, they fire quickly to even brief pauses in the pallido-nigral inhibition. The mechanism of their rapid disinhibitory response is explained by features of their phase-resetting curves.

Frequency-dependent entrainment of striatal fast-spiking interneurons.

Striatal fast-spiking interneurons (FSIs) fire in variable-length runs of action potentials at 20-200 spikes/s separated by pauses. In vivo, or with fluctuating applied current, both runs and pauses become briefer and more variable. During runs, spikes are entrained specifically to gamma-frequency components of the input fluctuations. We stimulated parvalbumin-expressing striatal FSIs in mouse brain slices with broadband noise currents added to direct current steps and measured spike entrainment across all frequencies. As the constant current level was increased, FSIs produced longer runs and showed sharper frequency tuning, with best entrainment at the stimulus frequency matching their intrarun firing rate. We separated the contributions of previous spikes from that of the fluctuating stimulus, revealing a strong contribution of previous action potentials to gamma-frequency entrainment. In contrast, after subtraction of the effect inherited from the previous spike, the remaining stimulus contribution to spike generation was less sharply tuned, showing a larger contribution of lower frequencies. The frequency specificity of entrainment within a run was reproduced with a phase resetting model based on experimentally measured phase resetting curves of the same FSIs. In the model, broadly tuned phase entrainment for the first spike in a run evolved into sharply tuned gamma entrainment over the next few spikes. The data and modeling results indicate that for FSIs firing in brief runs and pauses firing within runs is entrained by gamma-frequency components of the input, whereas the onset timing of runs may be sensitive to a wider range of stimulus frequency components.NEW & NOTEWORTHY Specific types of neurons entrain their spikes to particular oscillation frequencies in their synaptic input. This entrainment is commonly understood in terms of the subthreshold voltage response, but how this translates to spiking is not clear. We show that in striatal fast-spiking interneurons, entrainment to gamma-frequency input depends on rhythmic spike runs and is explained by the phase resetting curve, whereas run initiation can be triggered by a broad range of input frequencies.

Cortical Circuits of Callosal GABAergic Neurons.

Anatomical studies have shown that the majority of callosal axons are glutamatergic. However, a small proportion of callosal axons are also immunoreactive for glutamic acid decarboxylase, an enzyme required for gamma-aminobutyric acid (GABA) synthesis and a specific marker for GABAergic neurons. Here, we test the hypothesis that corticocortical parvalbumin-expressing (CC-Parv) neurons connect the two hemispheres of multiple cortical areas, project through the corpus callosum, and are a functional part of the local cortical circuit. Our investigation of this hypothesis takes advantage of viral tracing and optogenetics to determine the anatomical and electrophysiological properties of CC-Parv neurons of the mouse auditory, visual, and motor cortices. We found a direct inhibitory pathway made up of parvalbumin-expressing (Parv) neurons which connects corresponding cortical areas (CC-Parv neurons → contralateral cortex). Like other Parv cortical neurons, these neurons provide local inhibition onto nearby pyramidal neurons and receive thalamocortical input. These results demonstrate a previously unknown long-range inhibitory circuit arising from a genetically defined type of GABAergic neuron that is engaged in interhemispheric communication.

Predicting the response of striatal spiny neurons to sinusoidal input.

Spike-timing effects of small-amplitude sinusoidal currents were measured in mouse striatal spiny neurons firing repetitively. Spike-timing reliability varied with the stimulus frequency. For frequencies near the cell's firing rate, the cells altered firing rate to match the stimulus and became phase locked to it. The stimulus phase of firing during lock depended on the stimulus frequency relative to the cell's unperturbed firing rate. Interspike intervals during sinusoidal stimulation were predicted using an iterative map constructed from the cells' phase-resetting curve. Variability of interspike intervals was reduced by stimulation at all frequencies higher than about half the cell's unperturbed rate, and interspike intervals were accurately predicted by the map. Long sequences of spike times were predicted by iterating on the map. The accuracy of that prediction varied with frequency. Spike time predictability was highest near and during phase lock. The map predicted the phase of firing on the input and its dependence on stimulus frequency. Prediction errors, when they occurred, were of two kinds: unpredicted variation in interspike interval from intrinsic cell noise and accumulation of prediction errors from previous interspike intervals. Each type of prediction error arose from a different mechanism, and their impact was also predicted from the phase model. When two oscillatory input currents were presented simultaneously, striatal neurons responded selectively to only one of them, the one closest in frequency to the cell's unperturbed firing rate. Their spike times encoded the frequency and phase of that single oscillatory input.NEW & NOTEWORTHY During repetitive firing, the timing of action potentials is determined by the interaction between the input and voltage-sensitive currents throughout the interspike interval. This interaction is encapsulated in the neuron's phase-resetting curve. The phase-resetting curve predicted spike timing to small sinusoidal currents over a wide range of stimulus frequencies. Firing patterns were most sensitive to oscillatory components near the cell's own firing rate, even in the presence of noise and other inputs.

Effect of Phase Response Curve Shape and Synaptic Driving Force on Synchronization of Coupled Neuronal Oscillators.

The role of the phase response curve (PRC) shape on the synchrony of synaptically coupled oscillating neurons is examined. If the PRC is independent of the phase, because of the synaptic form of the coupling, synchrony is found to be stable for both excitatory and inhibitory coupling at all rates, whereas the antisynchrony becomes stable at low rates. A faster synaptic rise helps extend the stability of antisynchrony to higher rates. If the PRC is not constant but has a profile like that of a leaky integrate-and-fire model, then, in contrast to the earlier reports that did not include the voltage effects, mutual excitation could lead to stable synchrony provided the synaptic reversal potential is below the voltage level the neuron would have reached in the absence of the interaction and threshold reset. This level is controlled by the applied current and the leakage parameters. Such synchrony is contingent on significant phase response (that would result, for example, by a sharp PRC jump) occurring during the synaptic rising phase. The rising phase, however, does not contribute significantly if it occurs before the voltage spike reaches its peak. Then a stable near-synchronous state can still exist between type 1 PRC neurons if the PRC shows a left skewness in its shape. These results are examined comprehensively using perfect integrate-and-fire, leaky integrate-and-fire, and skewed PRC shapes under the assumption of the weakly coupled oscillator theory applied to synaptically coupled neuron models.

Unitary synaptic connections among substantia nigra pars reticulata neurons.

Neurons in substantia nigra pars reticulata (SNr) are synaptically coupled by local axon collaterals, providing a potential mechanism for local signal processing. Because SNr neurons fire spontaneously, these synapses are constantly active. To investigate their properties, we recorded spontaneous inhibitory postsynaptic currents (sIPSCs) from SNr neurons in brain slices, in which afferents from upstream nuclei are severed, and the cells fire rhythmically. The sIPSC trains contained a mixture of periodic and aperiodic events. Autocorrelation analysis of sIPSC trains showed that a majority of cells had one to four active unitary inputs. The properties of the unitary IPSCs (uIPSCs) were analyzed for cells with one unitary input, using a model of periodic presynaptic firing and stochastic synaptic transmission. The inferred presynaptic firing rates and coefficient of variation of interspike intervals (ISIs) corresponded well with direct measurements of spiking in SNr neurons. Methods were developed to estimate the success probability, amplitude distributions, and kinetics of the uIPSCs, while removing the contribution from aperiodic sIPSCs. The sIPSC amplitudes were not increased upon release from halorhodopsin silencing, suggesting that most synapses were not depressed at the spontaneous firing rate. Gramicidin perforated-patch recordings indicated that the average reversal potential of spontaneous inhibitory postsynaptic potentials was -64 mV. Because of the change in driving force across the ISI, the unitary inputs are predicted to have a larger postsynaptic impact when they arrive late in the ISI. Simulations of network activity suggest that this very sparse inhibitory coupling may act to desynchronize the activity of SNr neurons while having only a small effect on firing rate.

Cell-type-specific resonances shape the responses of striatal neurons to synaptic input.

Neurons respond to synaptic inputs in cell-type-specific ways. Each neuron type may thus respond uniquely to shared patterns of synaptic input. We applied statistically identical barrages of artificial synaptic inputs to four striatal cell types to assess differences in their responses to a realistic input pattern. Each interneuron type fired in phase with a specific input-frequency component. The fast-spiking interneuron fired in relation to the gamma-band (and higher) frequencies, the low-threshold spike interneuron to the beta-band frequencies, and the cholinergic neurons to the delta-band frequencies. Low-threshold spiking and cholinergic interneurons showed input impedance resonances at frequencies matching their spiking resonances. Fast-spiking interneurons showed resonance of input impedance but at lower than gamma frequencies. The spiny projection neuron's frequency preference did not have a fixed frequency but instead tracked its own firing rate. Spiny cells showed no input impedance resonance. Striatal interneurons are each tuned to a specific frequency band corresponding to the major frequency components of local field potentials. Their influence in the circuit may fluctuate along with the contribution of that frequency band to the input. In contrast, spiny neurons may tune to any of the frequency bands by a change in firing rate.

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.

Phase Delays between Mouse Globus Pallidus Neurons Entrained by Common Oscillatory Drive Arise from Their Intrinsic Properties, Not Their Coupling.

A hallmark of Parkinson's disease is the appearance of correlated oscillatory discharge throughout the cortico-basal ganglia (BG) circuits. In the primate globus pallidus (GP), where the discharge of GP neurons is normally uncorrelated, pairs of GP neurons exhibit oscillatory spike correlations with a broad distribution of pairwise phase delays in experimental parkinsonism. The transition to oscillatory correlations is thought to indicate the collapse of the normally segregated information channels traversing the BG. The large phase delays are thought to reflect pathological changes in synaptic connectivity in the BG. Here we study the structure and phase delays of spike correlations measured from neurons in the mouse external GP (GPe) subjected to identical 1-100 Hz sinusoidal drive but recorded in separate experiments. First, we found that spectral modes of a GPe neuron's empirical instantaneous phase response curve (iPRC) elucidate at what phases of the oscillatory drive the GPe neuron locks when it is entrained and the distribution of phases at which it spikes when it is not. Then, we show that in this case the pairwise spike cross-correlation equals the cross-correlation function of these spike phase distributions. Finally, we show that the distribution of GPe phase delays arises from the diversity of iPRCs and is broadened when the neurons become entrained. Modeling GPe networks with realistic intranuclear connectivity demonstrates that the connectivity decorrelates GPe neurons without affecting phase delays. Thus, common oscillatory input gives rise to GPe correlations whose structure and pairwise phase delays reflect their intrinsic properties captured by their iPRCs.

Firing rate and pattern heterogeneity in the globus pallidus arise from a single neuronal population.

Intrinsic heterogeneity in networks of interconnected cells has profound effects on synchrony and spike-time reliability of network responses. Projection neurons of the globus pallidus (GPe) are interconnected by GABAergic inhibitory synapses and in vivo fire continuously but display significant rate and firing pattern heterogeneity. Despite being deprived of most of their synaptic inputs, GPe neurons in slices also fire continuously and vary greatly in their firing rate (1-70 spikes/s) and in regularity of their firing. We asked if this rate and pattern heterogeneity arises from separate cell types differing in rate, local synaptic interconnections, or variability of intrinsic properties. We recorded the resting discharge of GPe neurons using extracellular methods both in vivo and in vitro. Spike-to-spike variability (jitter) was measured as the standard deviation of interspike intervals. Firing rate and jitter covaried continuously, with slow firing being associated with higher variability than faster firing, as would be expected from heterogeneity arising from a single physiologically distinct cell type. The relationship between rate and jitter was unaffected by blockade of GABA and glutamate receptors. When the firing rate of individual neurons was altered with constant current, jitter changed to maintain the rate-jitter relationship seen across neurons. Long duration (30-60 min) recordings showed slow and spontaneous bidirectional drift in rate similar to the across-cell heterogeneity. Paired recordings in vivo and in vitro showed that individual cells wandered in rate independently of each other. Input conductance and rate wandered together, in a manner suggestive that both were due to fluctuations of an inward current.

Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators.

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

Spike width and frequency alter stability of phase-locking in electrically coupled neurons.

The stability of phase-locked states of electrically coupled type-1 phase response curve neurons is studied using piecewise linear formulations for their voltage profile and phase response curves. We find that at low frequency and/or small spike width, synchrony is stable, and antisynchrony unstable. At high frequency and/or large spike width, these phase-locked states switch their stability. Increasing the ratio of spike width to spike height causes the antisynchronous state to transition into a stable synchronous state. We compute the interaction function and the boundaries of stability of both these phase-locked states, and present analytical expressions for them. We also study the effect of phase response curve skewness on the boundaries of synchrony and antisynchrony.

SK and Kv4 Channels Limit Spike Timing Perturbations in Pacemaking Dopamine Neurons.

Midbrain dopamine (DA) neurons are among the best characterized pacemaker neurons, having intrinsic, rhythmic firing activity even in the absence of synaptic input. However, the mechanisms of DA neuron pacemaking have not been systematically related to how these cells respond to synaptic input. The input-output properties of pacemaking neurons can be characterized by the phase-resetting curve (PRC), which describes the sensitivity of interspike interval (ISI) length to inputs arriving at different phases of the firing cycle. Here we determined PRCs of putative DA neurons in the substantia nigra pars compacta in brain slices from male and female mice using gramicidin-perforated current-clamp recordings with electrical noise stimuli applied through the patch pipette. On average, and compared with nearby putative GABA neurons, DA neurons showed a low, nearly constant level of sensitivity across most of the ISI, but individual cells had PRCs showing relatively greater sensitivity at early or late phases. Pharmacological experiments showed that DA neuron PRCs are shaped by small-conductance calcium-activated potassium and Kv4 channels, which limit input sensitivity across early and late phases of the ISI. Our results establish the PRC as a tractable experimental measurement of individual DA neuron input-output relationships and identify two of the major ionic conductances that limit perturbations to rhythmic firing. These findings have applications in modeling and for identifying biophysical changes in response to disease or environmental manipulations.

Phase response curves of subthalamic neurons measured with synaptic input and current injection.

Infinitesimal phase response curves (iPRCs) provide a simple description of the response of repetitively firing neurons and may be used to predict responses to any pattern of synaptic input. Their simplicity makes them useful for understanding the dynamics of neurons when certain conditions are met. For example, the sizes of evoked phase shifts should scale linearly with stimulus strength, and the form of the iPRC should remain relatively constant as firing rate varies. We measured the PRCs of rat subthalamic neurons in brain slices using corticosubthalamic excitatory postsynaptic potentials (EPSPs; mediated by both AMPA- and NMDA-type receptors) and injected current pulses and used them to calculate the iPRC. These were relatively insensitive to both the size of the stimulus and the cell's firing rate, suggesting that the iPRC can predict the response of subthalamic nucleus cells to extrinsic inputs. However, the iPRC calculated using EPSPs differed from that obtained using current pulses. EPSPs (normalized for charge) were much more effective at altering the phase of subthalamic neurons than current pulses. The difference was not attributable to the extended time course of NMDA receptor-mediated currents, being unaffected by blockade of NMDA receptors. The iPRC provides a good description of subthalamic neurons' response to input, but iPRCs are best estimated using synaptic inputs rather than somatic current injection.