Abstract
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.
Introduction
The striatum can inhibit movement by interrupting the tonic synaptic inhibition exerted by the external pallidal segment (GPe) on basal ganglia output neurons in the substantia nigra pars reticulata (SNr) and pallidal inner segment (GPi). The resulting disynaptic disinhibition by this indirect pathway is thought to act in opposition to the direct pathway, by which the striatum monosynaptically inhibits the same output neurons (e.g., Hikosaka et al., 2000) to facilitate movement.
The GPe neurons of the indirect pathway are intrinsic oscillators that fire tonically in slices (e.g., Chan et al., 2004) and in vivo, even in the absence of synaptic input (Kita et al., 2004). Changes in their firing bidirectionally adjust an ongoing inhibition of the (also tonically firing) basal ganglia output neurons. Their firing patterns may include pauses and resumptions of firing (e.g., Kaplan et al., 2022), the effects of which we have previously described (Simmons et al., 2020). However, they are also entrained by, and may participate in, propagating basal ganglia oscillations over a wide range of frequencies and in a variety of behavioral states, including δ (1-4 Hz) frequency oscillations (Magill et al., 2000, 2001; Goldberg et al., 2003; Mallet et al., 2012; Mizrahi-Kliger et al., 2018), the β (12.5-30 Hz) frequency oscillations associated with Parkinson’s disease, and much higher frequency oscillations associated with dyskinesia (e.g., Petersson et al., 2019; Rauschenberger et al., 2022). Presumably, oscillations conveyed by the direct and indirect pathways also work in opposition.
A GPe cell may fire many times in one cycle of the slowest oscillations, and produce rate modulation measurable by counting action potentials in small windows of time. Oscillations at frequencies nearer to the firing rate of the GPe cell cannot modulate its rate because the cell can only fire once on each cycle. For oscillations at frequencies higher than the cell’s firing rate to be propagated by the GPe neuron, they must change spike timing rather than rate. In any case, postsynaptic neurons do not have access to the rate of an input spike train or rate changes representing an oscillation. They receive only the continuous waveform of synaptic current generated by the train of presynaptic action potentials. A neuron can propagate an oscillatory signal only if it generates an effective periodic synaptic current in a postsynaptic neuron at the frequency of the oscillation. This propagated oscillation is superimposed on a barrage of synaptic currents generated by the ongoing tonic firing and composed of a wide range of frequencies. These incidental components of the synaptic current are an unavoidable byproduct of the use of action potentials to encode the oscillation, and they may be collectively large. The ionic mechanisms that drive repetitive firing in SNr and GPi neurons do not integrate those currents to produce a smoothly changing current but respond to each synaptic current by shifting the phase of their intrinsic oscillations (Higgs and Wilson, 2016; Simmons et al., 2020). For the input oscillation to propagate to the postsynaptic neuron, the oscillatory component of the synaptic current must be sufficient to control firing despite the noisy disturbance created by the background barrage.
We measured the effectiveness of oscillatory currents applied specifically to the SNr-projecting GPe neuron type in controlling the timing of their spontaneous firing and that of their synaptic targets, the basal ganglia output neurons in the SNr.
Materials and Methods
Institutional approval
All experiments were conducted in accordance with the National Institutes of Health guidelines and were approved by the Institutional Animal Care and Use Committee of the University of Texas at San Antonio.
Mice used, and viral constructs and injections for optogenetics
Experiments were performed on 23 mice 74-193 d of age, of which 7 were PV-Cre/Arch-GFP cross, 3 were PV-Cre with viral injection of Arch-GFP, 1 was a PV-Cre with injection of a ChR2-tdtomato virus, 2 were Npas1-Cre-tdTomato, and 10 were C57B/6 with no genetic label.
Transgenic mice used
In 4 PV-Cre mice, parvalbumin-positive (PV+) neurons were identified by viral transduction of either Channelrhodopsin-tdTomato (AAV9.CAGGS.Flex.ChR2.tdTomato-WPRE.SV40, University of Pennsylvania Vector Core) or Archaerhodopsin (Arch; AAV9.Flex.CBA.Arch-GFP.WPRE.SV.40, University of Pennsylvania Vector Core). Viruses were injected stereotaxically at a volume of 150 nl. The injection sites were (relative to bregma) 0 mm anterior, 2.5 mm lateral, and 3.0 mm ventral. To evaluate the generality of findings across mouse strains, nonfluorescent neurons were recorded in two Npas1-cre-tdTomato mice, and identified as prototypic cells using electrophysiological criteria. Neurons were also recorded in WT animals and identified electrophysiologically. Recording experiments were performed at least 4 weeks after injection.
Slices
Mice were deeply anesthetized with isoflurane, decapitated, and 300 µm parasagittal slices were cut on a vibrating microtome (Leica) either at the level of the globus pallidus or the substantia nigra. Slices were cut in ice-cold solution containing the following (in mm): 110 choline chloride, 2.5 KCl, 1.25 NaH2PO4, 0.5 CaCl2, 7 MgSO4, 25 glucose, 11.6 Na ascorbate, 3.1 Na pyruvate, and 26 NaHCO3, bubbled with 95% O2, 5% CO2. They were then maintained in ACSF containing the following (in mm): 126 NaCl, 2.5 KCl, 1.25 NaH2PO4, 2 CaCl2, 1 MgSO4, and 10 glucose, bubbled with 95% O2, 5% CO2, and 0.005 L-glutathione, 1 Na pyruvate, and 1 Na ascorbate. The slices were heated to 34°C for 30 min and then allowed to cool to room temperature until use.
Perforated patch recording
Recording was performed on the stage of an Olympus BX50WI microscope. The brain slice was superfused at 34°C with ACSF containing the following (in mm): 126 NaCl, 2.5 KCl, 1.25 NaH2PO4, 2 CaCl2, 1 MgSO4, and 10 glucose, bubbled with 95% O2, 5% CO2. Neurons were visualized using an Olympus 40× water immersion objective and Dodt gradient contrast optics. Perforated patch recordings were obtained using micropipettes filled with a solution containing the following (in mm): 140 KmeSO4, 10 HEPES, 7.5 NaCl, and 0.5 μg/ml gramicidin. Gramicidin was mixed in DMSO (0.5 mg/ml) and diluted (1:1000) in filtered electrode solution without additional filtration. Micropipettes were pulled to have resistances between 3 and 7 mΩ using a Flaming-Brown puller (P-97, Sutter Instruments), first tip-filled with the same solution lacking gramicidin, and then back-filled with gramicidin-containing solution. After obtaining a GΩ seal, cells were allowed 10-30 min for stabilization of access resistances between 20 and 70 mΩ. Recordings were performed in current-clamp configuration using a Multiclamp 700B amplifier (Molecular Devices) filtering at 10 kHz, and digitized at 40 kHz using an ITC-18 A/D converter (HEKA Instruments) controlled by a Macintosh computer and custom software written In IgorPro (WaveMetrics). Conductance waveforms were delivered using a second computer with RTXI (Real Time eXperimental Interface software; http://rtxi.org) and a National Instruments PCIe-6251 A/D board. Data sampling and current generation in conductance clamp were done at 20 kHz. Trains of inhibitory postsynaptic conductance (IPSG) waveforms to be used for substantia nigra neuron conductance clamp were calculated offline using spike trains recorded from GPe neurons and the properties of unitary pallido-nigral synaptic currents. The driving force of currents injected by RTXI was dynamic and calculated at every time step as the difference between the membrane potential of substantia nigra neurons and −75 mV, the GABAergic reversal potential of pallido-nigral currents (Simmons et al., 2020). Currents generated by the conductance clamp software and from Igor were combined using a homemade analog summing amplifier and delivered to the Multiclamp current command input.
Perforated patch recordings were required to maintain stable repetitive firing over the period required for completion of the experiment (20-40 min). Access resistance was monitored continuously, and the experiment was terminated on any sudden change indicating that the patch had ruptured. Rupture of the patch was always followed by a decrease in firing rate and regularity and ultimately termination of spontaneous activity. Because the recorded membrane potential is used by the conductance clamp circuit to generate synaptic currents, correct capacitance and access resistance compensation are critical, and these were monitored and corrected as needed during recordings of that type.
Data analysis was performed using routines written for Mathematica (Wolfram Research).
Cell identification
Cells expressing fluorescent markers and/or opsins were identified visually and/or by their responses to opsin activation. Light was applied to the slices by epi-illumination using a white LED (MLS-5500 Mightex Systems) driven by a Thorlabs LEDD1B driver, controlled by an analog voltage from one of the D/A channels of the ITC-18. ChR2 was activated, and GFP was visualized using a blue (475 nm) filter cube and Arch was activated and tdTomato visualized using green light (560 nm). Because fluorescence imaging was not always clear, and the fluorescent reporter was largely in dendrites and axons of the GPe neurons, steady currents generated in neurons by a 500 ms light pulse were a more reliable indication of cell identity than microscopic identification. To ensure that spike-oscillation resonance was not a unique feature of one mouse strain (Table 1), we sampled neurons from PV-cre mice, Npas1-cre mice, and from C57B/6 mice with no genetic marker. No differences were found between strains, so all prototypic neurons used were pooled in the results. PV+ neurons were considered identified prototypic neurons of the indirect pathway. In Npas1-cre and WT mice, prototypic cells were identified based on their responses to 20 s, −60 pA current pulses using the method described by Jones et al. (2023).
Mouse strains
Neurons recorded in substantia nigra pars reticulata were selected on the basis of their narrow action potentials (<0.5 ms) and brief afterhyperpolarizations. This distinguished them from presumably dopaminergic neurons present in the same slices, which had much longer action potentials (>0.6 ms), slow rhythmic firing (<10 spikes/s), and long multicomponent afterhyperpolarizations (e.g., Higgs et al., 2023).
Vector strength and vector angle
Sinusoidal stimuli had frequencies ranging from 1 to 100 Hz (by 1 Hz), and each was presented for 10 s. Firing coherence with injected sinusoidal current was calculated from the sequence of spike angles (or phases), expressed as a fraction of the enclosing stimulus period as follows:
Spike angles were converted to unit vectors. Vector strength was calculated as the length of the vector sum of those vectors, normalized by the number of spikes in the sequence as follows:
The vector angle was the angle formed by the resultant vector as follows:
The vector angle gives an estimate of the average phase on the input oscillation at which the neuron fired, and the vector strength is an estimate of the reliability of firing at that angle. A vector strength of zero is interpreted as firing at random with respect to the oscillation, and a vector strength of one would mean that the cell fired at the same phase on the oscillation every time.
Constructing synaptic conductance and current waveforms
Spike trains were translated to conductance waveforms by convolution of the spike times (as a point process) with a biexponential function for the synaptic conductance with amplitude a and using measured rise and decay exponentials τr (1.0 ms) and τd (2.6 ms) from Connelly et al. (2010), for time since an action potential occurring at time t0 as follows:
To include the effects of synaptic depression, the amplitude a was allowed to change following each action potential according to the model used by Connelly et al. (2010) and Lavian and Korngreen (2019). At the time of each action potential, the value of a at that time was used to calculate the resulting IPSG, but the value of a to be applied to the subsequent IPSG was reduced to 67% of its previous value. Between action potentials, a was allowed to recover toward its baseline value of 71 nS, with a time constant of 1.7 s.
To include the effect of synaptic amplitude fluctuations, the synaptic conductance amplitude used was drawn from a normal distribution truncated so that the negative values were set to zero (so that negative values were considered failures). The mean of the distribution was the current (possibly depressed) value of a and the standard deviation was the square root of a, to produce the linear relationship between amplitude and 1/CV2 as described by Connelly et al. (2010). Synaptic conductance waveforms applied to substantia nigra neurons by conductance clamp were calculated in this way.
Synaptic conductance waveforms were converted to approximate current waveforms to find the spectrum of current and the amplitudes at the stimulus frequency. To do so, currents were calculated using an average driving force of −15 mV, based on a GABA reversal potential of −75 mV and an average interspike membrane potential of −60 mV (Simmons et al., 2018).
The spectrum of synaptic current
Discrete Fourier transforms of 10 s current waveforms were calculated using Mathematica’s built-in Fourier function. Amplitude spectra, rather than power spectra, were used so that the value of the spectrum at each frequency is equal to the amplitude of the corresponding sinusoidal current component in the original waveform. Spectra were calculated at a frequency step of 0.1 Hz and were truncated at 100 Hz.
Experimental design and statistical analysis
Spike-oscillation coherence spectra were tested for statistical significance using the Raleigh Test (Fisher, 1993), with Bonferroni correction for multiple comparison (over the 100 frequencies of oscillation).
Results
In situ, oscillatory synaptic input to the GPe may arise from the confluence of excitatory and inhibitory synaptic pathways. To represent an oscillatory input independently of source, we used sine wave current injections with amplitudes ranging from 8 to 80 pA and frequencies from 1 to 100 Hz, injected into single mouse GPe neurons in slices (Fig. 1A). Recordings were done using the perforated patch method to preserve spontaneous firing patterns of the neurons.
Oscillatory coherence of prototypic GPe neurons. A, Experimental arrangement. GPe cells recorded in perforated patch were injected with sinusoidal currents with frequencies from 1 to 100 Hz. The phase of every action potential with respect to the current waveform was measured. B, Examples of firing driven by 20 pA sinusoidal currents at three different stimulus frequencies in the same identified prototypic GPe neuron. C, Interval-by-interval firing rates (1/interspike interval) during the first 1 s of a 10 s sinusoidal stimulation at each frequency for the neuron in B. D, Histograms represent the probability of firing as a function of stimulus phase in the same neuron at the same three frequencies. Dashed-line histograms superimposed represent control histograms for spontaneous firing (zero amplitude oscillations). The control vector strengths were 0.001, 0.097, and 0.065 for 3, 34, and 100 Hz, respectively. E, Spike-oscillation coherence measured by vector strength (above) and vector angle (below) for the same cell over the range of stimulus frequencies. Dashed line indicates the neuron’s spontaneous firing rate. The coherence spectra for each cell in the sample are shown in Extended Data Figure 1-1. F, The average number of action potentials per stimulus cycle for the neuron in B–E, at each stimulus frequency. Inset, Distribution of the number of stimulus cycles per action potential at stimulus frequency of 100 Hz. G, The frequency at the peak of coherence (maximum vector strength) versus unperturbed firing rate in the sample of 20 GPe neurons.
Figure 1-1
The vector strength spectra (at left) and corresponding current peak spectra (at right) for each of the 20 neuron used in Figure 1. Dotted line rectangles surround the graph-pair for each neuron. Download Figure 1-1, TIF file.
Frequency dependence of effects on firing
We applied 20 pA sinusoidal currents (40 pA peak-to-peak) at 100 frequencies ranging from 1 to 100 Hz. Each waveform was applied for 10 s, with flanking 0.5 s periods of unperturbed firing to monitor changes in spontaneous activity. Twenty GPe neurons were tested in this way, all of which were identified as prototypic cells. Of them, 11 were identified as PV+ by fluorescence and/or by the presence of a direct light-evoked Arch hyperpolarization, and the remainder were cells recorded in slices not containing any PV+ reporter but identified by their spontaneous depolarization and resumption of firing during prolonged hyperpolarizing current steps of ≥−60 pA. This test has been shown to identify prototypic PV+ versus nonprototypic Npas1+ neurons in slices (Jones et al., 2023). Intrinsic firing rates varied from 7.3 to 74.1 spikes/s and did not vary between mouse strains. Both the fastest and the slowest firing neurons in the sample were genetically identified PV+ cells.
Examples showing the response to three frequencies spanning the range are shown in Figure 1B, C. The average firing rate of the neurons over the entire 10 s stimulus period was unaltered from the baseline unstimulated rate. At very-low-oscillation frequencies, the spontaneous firing of the GPe neuron was continuously modulated, reproducing the profile of the input oscillation (Fig. 1B,C, left). Increases in rate during the depolarizing phase of the oscillation were matched by decreases during the hyperpolarizing phase. Firing rate modulation disappeared as the oscillation frequency exceeded approximately half the neuron’s firing rate. At frequencies beyond half the neuron’s rate, no oscillation could be detected in the firing rate, but the oscillatory input produced changes in the timing of action potentials so that they aligned on the depolarizing phase of the oscillation. At frequencies near the neuron’s own rate, a spike occurred on nearly every cycle (Fig. 1B, middle); but at frequencies higher than that the neurons skipped cycles, firing only on the peaks of cycles occurring nearest to the time that the neuron would have fired spontaneously (Fig. 1B, right). This resulted in small irregular spike-to-spike fluctuations in rate (Fig. 1C, right). We considered the possibility that the alignment of firing to the phase of the oscillation, even when spikes did not occur on every cycle, might be sufficient to propagate the oscillation to postsynaptic neurons.
To measure the spike-oscillation coherence, the phase of each action potential was measured relative to the oscillation (as in Fig. 1A), and we constructed histograms of phase (Fig. 1D). We measured the stimulus phase as ranging from 0 to 1, so the peak of the depolarizing phase was 0.25 and the hyperpolarizing phase peak was 0.75. A phase histogram for a neuron unresponsive to the stimulus would be flat. To quantify coherence with the stimulus waveform, we used the vector strength, measured as the normalized vector sum of the spike phases. The corresponding angle (the circular average phase) is the vector angle. We calculated these as a function of stimulus frequency for each of 20 neurons. There were statistically significant phase preferences at all frequencies (Bonferroni-corrected Raleigh Test, p < 0.001). There was a continuous increase in vector strength as the stimulus frequency increased from 1 Hz to a frequency near the cell’s intrinsic firing rate (Fig. 1E, dashed line). Vector strength decreased with oscillation frequency after this peak, but increased again with increases in the frequency of oscillation. It was not instructive to construct an average profile for the sample because the locations of the peaks varied widely among cells. For most of the cells, the peak vector strength occurred when the stimulus frequency matched their firing rates, but in some neurons the increase in vector strength at frequencies higher than the firing rate exceeded the peak near the firing rate (Fig. 1G). At all frequencies, the GPe neurons preferentially fired on the depolarizing first half of the oscillatory cycle, as indicated by a vector angle <0.5 at all oscillation frequencies (Fig. 1E, bottom). A vector strength versus frequency curve like the one shown in Figure 1E is shown for each of the 20 neurons in the sample in Extended Data Figure 1-1.
The spike-oscillation coherence seen at the highest frequencies required an impressive precision of spike timing control by the oscillation. At 100 Hz, the depolarizing phase of the stimulus is only 5 ms long, so the precision of spike timing change was <2.5 ms. Firing rate was not altered by the high-frequency oscillation, so the cell fired on only a fraction of stimulus cycles (Fig. 1F). The proportion of cycles on which the neuron fired at any one frequency varied stochastically, but on average it matched the ratio of cell rate to stimulus frequency (Fig. 1F, inset).
The rate modulations that occurred with low-frequency stimuli were the most visible effects of the oscillation to the experimenter examining the spike train by eye, but vector strength at such frequencies was always relatively low compared with frequencies that produced no rate modulation, as in the example in Figure 1E. Vector strength captures the extent to which the oscillation controls spiking, but perhaps not how well spiking can propagate the oscillation. How can we measure the feature of the firing pattern that best represents the propagation of the oscillation?
The currency of communication
It is common to assume that an increase in firing rate in the GPe neuron will produce a corresponding decrease in firing rate for its targets in the SNr, subthalamic nucleus (STN) and GPi, but postsynaptic neurons have no direct way of measuring the firing rate of the GPe neuron. They receive only a sequence of synaptic currents, one for each presynaptic action potential. The tonic firing of a GPe neuron creates a barrage of synaptic currents in target neurons, and this barrage is present regardless of the presence of an input oscillation. How can the component of synaptic current caused by the oscillation’s effect on firing be differentiated from the ongoing barrage produced by tonic firing? Synaptic current is the only thing communicated to the postsynaptic cell, and it is the currency into which changes in spike rate or pattern must be translated.
To assess the signal propagated by the GPe neuron, we constructed the synaptic current waveform that would be generated in an SNr neuron by the spike train of each GPe neuron in our sample from Figure 1. The recorded spike trains with and without an oscillatory input were convolved with a synaptic conductance waveform matching that of the pallido-nigral synapse (Fig. 2A,B) (Connelly et al., 2010; Simmons et al., 2020).
Calculating the synaptic conductance generated by a GPe neuron on its SNr target cell. A, Firing of a prototypic GPe neuron in the absence of any stimulus. B, Convolution of the spike times of the cell in A, using the average conductance waveform for the pallido-nigral synapse (from Simmons et al., 2020). C, Synaptic depression at the pallido-nigral synapse using the measurements by Connelly et al. (2010). D, Synaptic conductance produced by the spike train in A, depressing to a steady state. E, The amplitude of the steady-state IPSG peaks as a function of firing rate. F, The time-average synaptic conductance at steady state for a single GPe neuron’s synapse on a postsynaptic SNr neuron as a function of firing rate. At rates >20 spikes/s, changes in firing rate produce little change in average inhibitory conductance. G, Synaptic conductance waveform calculated from the response of an example GPe neuron during stimulation with a 2 Hz 20 pA sine wave current, calculated without synaptic depression or stochastic fluctuations in synaptic current. Red represents the sine wave current. H, Synaptic conductance waveform calculated for the same neuron and same stimulus, but including synaptic depression. I, Synaptic conductance waveform calculated for the same neuron and stimulus, including the effect of synaptic depression and stochastic fluctuations in IPSG amplitude.
GPe→SNr synapses undergo rapid synaptic depression at typical spontaneous GPe neuron firing rates (Connelly et al., 2010). A similarly severe tonic depression at background firing rates is seen in the synaptic responses in the GPi/EP (Lavian and Korngreen, 2019) and the STN (Atherton et al., 2013). Following the phenomenological model used by Connelly et al. (2010) and Lavian and Korngreen (2019), we used a paired pulse ratio of 0.67, whereby each synaptic event produces an amplitude reduction of 0.33, which recovers with a time constant of 1.76 s (Fig. 2C). As a baseline peak conductance in the absence of depression, we used 71 nS (Connelly et al., 2010; Simmons et al., 2020). The effect of synaptic depression on average synaptic conductances at a steady rate is shown in Figure 2D–F. Figure 2D shows the time course of depression after onset of firing at 28 spikes/s from a silent baseline. In the 20-100 spikes/s firing rate range for GPe neurons, synaptic transmission depresses to ∼5% of the baseline amplitude (Fig. 2E). This result is close to that of experimental measurements in the SNr by Connelly et al. (2010), and similar measurements from the GPi (Lavian and Korngreen, 2019) and STN (Atherton et al., 2013). The synaptic conductance exerted by the GPe neuron averaged over time while firing at constant rate becomes saturated by depression (Fig. 2F). Without synaptic depression, when firing rate is modulated by a 2 Hz oscillation, IPSGs of constant amplitude are triggered by each spike (Fig. 2G). With synaptic depression, IPSG amplitudes wax and wane with the change in rate (Fig. 2H). When the neuron slows its firing in the hyperpolarizing phase of the oscillation, the depression is relieved and IPSGs increase in amplitude, whereas increases in firing rate produce nearly proportionate decreases in amplitude. In this way, synaptic depression severely mitigates the influence of rate modulation. This model of depression also implies that rate modulation will be much more effective for slowly firing GPe neurons, which have suffered less depression in response to the background firing rate.
In addition to synaptic depression, GPe→SNr synaptic transmission is subject to stochastic fluctuations in amplitude, caused by the probabilistic nature of synaptic transmission. To reproduce the stochastic fluctuation, we used the measurement of 1/CV2 in Connelly et al. (2010) to construct the probability distribution of synaptic conductance amplitude (Connelly et al., 2010; Simmons et al., 2020). Figure 2I shows the effect of stochastic fluctuations with the same spike train used in Figure 2G, H.
The propagated signal
The 3 Hz oscillation propagated to the postsynaptic SNr neuron is not apparent in the synaptic conductance waveform shown in Figure 2I. This is not because it lacks a 3 Hz component, but because it also contains many other frequencies. Most prominent among these are the average firing rate of the GPe neuron and frequency components responsible for the exponential rise and fall of the IPSG waveform. Embedded in these oscillation-independent components, we should find the 3 Hz oscillation propagated to the next cell.
To compare the size of the propagated oscillation to the original 20 pA oscillatory stimulus, we first converted the conductance waveforms to synaptic currents (in pA, the same units as the stimulus). The synaptic current produced by the conductance waveform depends on the membrane potential of the SNr neuron, which is constantly changing as a part of that neuron’s intrinsic firing. To make a synaptic current averaged over the interspike interval (excluding the action potentials), we used the average value of the SNr neuron’s membrane potential during intrinsic firing (−60 mV) and a GABA equilibrium potential (−75 mV) as reported by Simmons et al. (2018) to calculate an average driving force of −15 mV. We then decomposed synaptic current waveforms like those in Figure 3A into their constituent sinusoidal components and constructed spectra of the amplitudes of those components in pA. The spacing between frequency components was 0.1 Hz, and we used the first 1001 components to make spectra ranging from 0 to 100 Hz. In these spectra, two components have special importance: the first one at 0 Hz, which represents the average current produced by the synaptic train. The second, the component at the stimulus frequency, represents the stimulus-driven oscillation propagated in the synaptic current waveform.
The frequency spectrum of propagated synaptic current. A, Creation of the frequency spectrum. Current calculated for a conductance waveform as in Figure 2 for a GPe cell with a 10 Hz stimulus. Current is decomposed into sinusoidal components. The amplitudes are plotted to form a spectrum of synaptic current. B–D, Top traces, Example synaptic current waveforms calculated from the spike times of a prototypic GPe neuron firing spontaneously (B) or with oscillations at 34 Hz (C) and 85 Hz (D). Bottom traces, Corresponding current spectra. E, The amplitude of spectral peaks at the oscillation frequency for a range of oscillation frequencies, calculated either without depression or synaptic amplitude fluctuations, with depression but no synaptic fluctuations, and with depression and synaptic fluctuations. The values without depression were scaled by the average steady-state depression at the cell’s spontaneous firing rate. F, Average inhibitory current generated by the synaptic conductance for each of the 20 GPe neurons, each firing at its spontaneous rate. G, Background noise, measured as SD of the synaptic current waveform, for each of the GPe neurons in the sample.
Oscillatory stimuli did not alter the average current or overall spectra of the barrage produced by spontaneous firing but produced peaks at the stimulus frequencies (Fig. 3B–D). In the absence of any oscillatory input, the tonic activity of the GPe neuron produced small, broad peaks in the spectrum of synaptic current at the cell’s intrinsic rate, and often at its first harmonic (Fig. 3B). The time average of the inhibitory current is also evident in the spectrum at frequency 0 Hz. In the presence of the oscillation, an additional spectral peak occurred at the oscillation frequency, and its amplitude varied with oscillation frequency (Fig. 3B,C). This peak was present at all frequencies but was largest when the stimulus oscillation frequency matched the cell’s intrinsic firing rate (Fig. 3E). Synaptic depression reduced these oscillation-dependent peaks at low oscillation frequencies (0-10 Hz), but stochastic fluctuation had no effect on their magnitude.
If there were no synaptic depression, the average inhibitory current generated by one GPe neuron would increase linearly with firing rate. Our sample of GPe neurons included cells firing at rates varying from 7 to >70 spikes/s; but because of synaptic depression, their firing rates had a very weak effect on the time-average of the inhibitory current (Fig. 3F). We measured the noisy oscillation-independent current of the background barrage using the SD of the inhibitory current (Fig. 3G). In the absence of depression, the SD of synaptic current would increase with the square root of firing rate. With synaptic depression, the SD of the current waveform decreased substantially with increases in firing rate (Fig. 3G). Stochastic fluctuations in synaptic current had only a small effect on the average current but had a larger effect on the SD. The presence of background firing in GPe neurons produces a barrage of fast IPSCs that should slow and de-regularize firing in the target neurons (Simmons et al., 2018). This occurs whether there is an oscillatory input to the GPe neurons or not. The de-regularizing effect of the barrage IPSCs from background firing decreases when the GPe neurons increase firing rate because of synaptic depression. With increases in firing rates, IPSCs become smaller and the SD of the resulting current waveform is reduced. Oscillatory inputs propagate in the presence of this irregular synaptic barrage and its intrinsic dynamics, and must compete with it for control of the postsynaptic cell.
Oscillation amplitude
Propagated oscillations are expected to gain advantage over the irregular background barrage with increased oscillatory drive to the GPe neuron. To measure the dynamic range of propagation, we varied the amplitude of the sinusoidal current applied to the GPe neuron over a 10-fold range, from 8 to 80 pA, using a subset of stimulus frequencies. Amplitudes >80 pA could directly drive firing, altering the average firing rate, so were avoided (not shown). This experiment was performed in 8 GPe neurons, all identified PV+ prototypic cells. With a 2 Hz, 16 pA stimulus, rate modulation of GPe cells was weak but clearly present (Fig. 4A). Increasing amplitude over the entire range produced a corresponding increase in firing modulation. Cells driven with low-frequency low-amplitude oscillations had continuous rate modulations as shown in Figure 1; but with very-high-amplitude oscillations, they fired in high-frequency bursts separated by periods of silence (Fig. 4B). At stimulus frequencies at or above the cell’s firing rate, the same range of stimulus intensities did not continuously modulate rate but produced an increase in spike-oscillation coherence from almost undetectable (Fig. 4C) to very strong and obvious by inspection (Fig. 4D).
Dependence of propagation on oscillation amplitude. A, Membrane potential and spiking responses of a prototypic GPe neuron stimulated at 2 Hz and 16 pA. B, The same, but with an 80 pA oscillation. C, The same neuron, stimulated at 80 Hz and 16 pA. D, Stimulation at 80 Hz and 80 pA. Red represents stimulus currents. E, F, Spectra of synaptic current for 80 Hz oscillation at the two stimulus amplitudes. The cell’s intrinsic frequency (42 spikes/s) is reflected in a broad peak in the spectrum of the barrage. G, Magnitude of the stimulus-frequency spectral peak for an example GPe neuron at each of 8 frequencies, for stimulus intensities from 8 to 80 pA. H, Average spectral peak current for the sample of 8 GPe neurons at 5 stimulus frequencies and 10 amplitudes.
Increases in stimulus intensity did not affect the average current or the background components of synaptic current spectra but increased the amplitude of the spectral peak at the stimulus frequency (compare Fig. 4E,F). Although the propagation of oscillation increased at all oscillation frequencies with increases in stimulus amplitude, the slope of the relationship with stimulus amplitude differed according to stimulus frequency (Fig. 4G,H). Frequencies lower than half the cell’s firing rate, which produced rate modulation, propagated more poorly than other frequencies at low stimulus amplitudes, as already described. However, these lower frequencies benefited more from increased oscillation amplitude, and their propagation continued to increase at the highest amplitude used. This occurred because these large amplitude oscillations produced periodic pauses in the GPe cell firing, and thus pauses in the IPSC trains. Increases in IPSC amplitude by relief of synaptic depression that occurred at lower amplitudes did not occur during the absence of IPSCs in these pauses, so could not counteract the effect of rate modulation. The absence of stimulus-independent frequency components during these pauses in IPSCs increased the propagation of the low stimulus frequencies.
At all stimulus amplitudes, GPe neurons most effectively propagated oscillations at frequencies near their background firing rate and that produced no rate modulation. For the sample used in Figure 4, firing rates ranged from 17.6 to 52.3 spikes/s, with an average of 34.2 ± 10.5 (SD) spikes/s. Thus, the 20 and 40 Hz oscillations used for the experiments in Figure 4 produced the largest peaks in the synaptic current spectra in most cells. Propagation of the oscillatory stimulus was most sensitive to amplitude changes at these frequencies and reached an asymptotic value earlier. This is evident in the case of the example GPe neuron illustrated in Figure 4G. At frequencies near the peak of sensitivity, the response increased rapidly with stimulus amplitude, enhancing the preferential response sensitivity near the cell’s own firing rate. The response at this preferred frequency did not increase much further after 34 pA, but the responses at other frequencies continued to increase. At 2 Hz, which was well below the peak sensitivity, and at 80 Hz, which was well above it, the oscillation amplitude rose more gradually with stimulus intensity (Fig. 4H).
Increasing the amplitude of the oscillatory input to a GPe neuron increased the propagated oscillatory synaptic current at all oscillation frequencies without increasing the stimulus-independent barrage. The maximum oscillatory current generated by one GPe neuron was always less than the amplitude of stimulus current driving the GPe neuron, and this maximum current occurred at oscillation frequencies near the firing rate of the GPe neuron.
Convergent input to the SNr neuron
SNr cells receive convergent synaptic input from a small number (∼4) of pallido-nigral neurons (Simmons et al., 2020). GPe neurons sharing a common oscillatory input might therefore deliver a fourfold larger oscillatory current to the SNr cell, but the background synaptic barrages will also sum. We calculated signal propagation by a group of GPe neurons sharing a common oscillatory input by delivering their summed synaptic conductance waveforms to an SNr neuron, and measuring their influence on that cell’s firing pattern.
To estimate the current expected for convergent input from the GPe, we combined the synaptic conductance waveforms generated from the spike trains of 4 GPe neurons from our sample. Two different sets of GPe neurons were used in this experiment: one in which the presynaptic GPe neurons had similar firing rates (near the average for GPe neurons) and one with rates spread over a larger range. The spectra of the 4 neurons with similar rates are shown in Figure 5A. The magnitude of oscillation current propagated by the combination of neurons at each frequency is approximately the sum of that for the individual cells (Fig. 5B). This is because the spectral peak at the oscillation frequency was dominated by the coherent propagated oscillation, not by the (incoherent) background barrage. The average (0 Hz) current also summed, and was 31.4 ± 34.5 (SD) pA. The current spectra for the other set of neurons with diverse firing rates (Fig. 5C) combined to form a more broadband spectrum of propagation (Fig. 5D). In both cases, propagation of oscillatory current remained comparable to the original GPe oscillatory input, even those higher than the rate of the fastest GPe cell.
Convergence of GPe neuron conductance barrage on SNr neurons. A, Synaptic current oscillatory peak spectra of 4 GPe neurons from the recorded sample with similar firing rates, calculated using a 15 mV synaptic driving force. Dashed lines indicate the cells’ spontaneous firing rates. B, Synaptic current oscillatory peak spectrum for the convergence of the 4 neurons. C, Peak spectra for a second group of 4 GPe neurons representing a broader range of firing rates. D, Peak spectrum for the combined synaptic currents of the subset shown in B.
To test the responses of SNr neurons to this convergent synaptic input, we used conductance clamp to deliver the combined conductance waveforms to SNr neurons. The spike trains of each of the 4 neurons in a set were converted to a conductance waveform as described in Figure 2, and these waveforms were added at each oscillation frequency (1-100 Hz) to obtain a set of 100 net conductance waveforms applied by the convergent GPe neuron at the postsynaptic SNr neuron. These were used as conductance clamp stimuli, using the driving force calculated in real time from the SNr neuron’s membrane potential (Fig. 6B). An example net conductance waveform for one oscillation frequency and the resulting SNr cell membrane potential are shown in Figure 6A, C. This experiment was performed in two samples of SNr neurons: once using GPe→SNr synaptic conductances calculated from GPe neurons with the oscillation current applied (as in Fig. 5), and once for the same conductance waveforms (obtained with the oscillating current present) but with any coherence of the IPSC barrage with the propagated oscillation removed by shuffling the interspike intervals. This shuffled experiment served as a control for the contribution of the oscillatory stimulus as it contained a statistically identical synaptic barrage, but without the periodicity of IPSCs imposed by the oscillatory stimulus current. The effects on firing rate of SNr neurons were the same for the two sets of synaptic conductance waveforms, indicating that the effect of the input on rate was a result of the background barrage, and not the oscillation. The average firing rate of the combined sample of 21 SNr neurons tested decreased by 14.2 ± 7.5 (SD) spikes/s (Fig. 6D). Likewise, the increase in spike time variability, as indicated by the CV, increased on average from 0.12 ± 0.7 (SD) to 0.37 ± 0.15 (SD) (Fig. 6E). Baseline CV was more variable among the neurons receiving the oscillatory stimulus (range 0.04-0.28) compared with neurons receiving the stimulus with shuffled interspike intervals (range 0.1- 0.2). The reason for this is unknown but was not because of any difference in the stimulus, as baseline CV was measured in its absence. The effect of the background synaptic barrage on firing regularity was profound in both groups of neurons. In the presence of the barrage from 4 GPe neurons, the autonomous firing of the SNr cells was densely perturbed, making it difficult to identify their intrinsic rhythmicity (Fig. 6C).
Dynamic clamp application of spontaneous GPe→SNr synaptic inhibition barrage. A, Sample of the combined synaptic conductance waveform from the 4 neuron set in Figure 5B. B, Scheme for applying the synaptic conductance waveform to a spontaneously active SNr neuron. C, The membrane potential and spike train from an SNr neuron during application of the synaptic conductance waveform in A. D, Comparison of the firing rates of SNr neurons with and without conductance clamp application of synaptic conductances generated by combinations of 4 GPe neurons. The conductance waveforms were generated from GPe neurons propagating an oscillatory current applied to their somata, as in Figures 1-4 (red) or GPe neurons whose propagated oscillation was removed by shuffling interspike intervals (blue). E, The irregularity of SNr neuron firing, as measured by the coefficient of variation, in the presence or absence of the synaptic barrage from the GPe.
Intrinsic frequency sensitivity of SNr neurons
Propagation of oscillations from the GPe neuron to the SNr neuron depends on the frequency sensitivity of the GPe neuron and the GPe→SNr synapse, but it also depends on the frequency sensitivity of the SNr neuron. To determine the intrinsic frequency sensitivity of SNr neurons in the presence of a realistic background IPSC barrage from the GPe, we applied a 20 pA sinusoidal current at frequencies from 1 to 100 Hz, in the presence of the synaptic conductance barrage from four presynaptic GPe neurons with intervals shuffled to remove the effect of the propagated GPe oscillation (as used for the experiment in Fig. 6). The spike-oscillation coherence of 10 SNr cells was measured using vector strength at each frequency.
Like GPe neurons, the SNr neurons exhibited spiking resonance for frequencies near their own firing rate. An example is shown in Figure 7A, and the average for the sample of 10 SNr neurons is shown in Figure 7B. Because of rate variability among neurons, the curve for the sample is a composite of curves with different sensitivity peaks, and so shows a broader frequency spectrum. SNr neurons’ spiking resonance occurred in the presence of a powerful noisy stimulus that obscured the cells’ rhythmic firing. The individual responses of the 10 neurons tested are shown in Extended Data Figure 7-1, along with the relationship between firing rate and spectral peak sensitivity. Like GPe neurons driven by sinusoids, SNr neurons’ spike timing shifted so that they preferentially fired on the peaks of the depolarizing phase of the oscillatory current, as indicated by vector angles in the first half of the cycle at all frequencies. Despite the preference for oscillations near their own firing rates, SNr cells in our sample maintained a substantial and statistically significant coherence over the entire frequency range tested (1-100 Hz) indicating their ability to respond to frequencies well above their own firing rate (Fig. 7A,B).
Frequency-dependent oscillation propagation from GPe to SNr neurons. A, Top, Intrinsic frequency selectivity of an SNr neuron, measured as the spike-oscillation coherence to a sinusoidal current injection in the presence of a background synaptic barrage from the 4 GPe neurons shown in Figure 5A. Dashed line indicates the firing rate of the SNr neuron during the synaptic barrage. Bottom, Preferred phase of firing of the SNr neuron at all stimulus frequencies. Coherence spectra for each cell in the sample are presented in Extended Data Figure 7-1. B, Average frequency selectivity and phase preference for the sample of 10 SNr neurons during the background barrage and direct application of sinusoidal currents. C, Top, Spike-oscillation coherence for an SNr neuron during application of the convergent conductance waveforms from Figure 5A. Bottom, The preferred firing phase of the SNr neuron for each oscillation frequency. D, Spike-oscillation coherence (top) and the vector angle (bottom) for propagated GPe→SNr oscillations for the sample of 7 SNr neurons during application of the convergent conductance waveforms from Figure 5A. Firing rates ranged from 11.3 to 43.0 (mean = 22.8 ± 11.7) spikes/s. E, Spike-oscillation coherence for an SNr neuron during application of the convergent conductance waveforms from Figure 5B. Bottom, The preferred firing phase of the SNr neuron for each oscillation frequency. F, Spike-oscillation coherence (top) and the vector angle (bottom) for propagated GPe→SNr oscillations for the sample of 4 SNr neurons during application of the conductance waveforms from Figure 5B. Firing rates ranged from 16.1 to 20.4 (mean = 17.7 ± 2.3) spikes/s. G–I, Spike-phase histograms for oscillation frequencies of 21 Hz (G), 40 Hz (H), and 75 Hz (I). J, The phase shift of the GPe→SNr synaptic conductance across all oscillation frequencies. Dashed line indicates the phase shift predicted by the IPSG centroid. Inset, The IPSG waveform. Dashed line indicates the centroid. Error bars indicate SEM.
Figure 7-1
Intrinsic frequency sensitivity of the sample of SNr neurons used to make the average in Figure 7B. The vector strength spectra for each of the 10 SNr neurons tested using a conductance clamped background synaptic barrage constructed by shuffling the interspike intervals of the 4 GPe neurons in Figure 5A, and superimposing 20 pA sinusoidal currents. Dotted lines represent the SNr neurons’ average firing rates during the application of the barrage. The graph at right compares the cells’ firing rates to the stimulus frequency of highest vector strength. Download Figure 7-1, TIF file.
Propagation of GPe oscillations to the SNr
To measure the composite frequency sensitivity of the entire pathway, SNr neuron activity was driven with the combined conductance waveforms of the four presynaptic GPe neurons sharing a common oscillation. In this case, the input oscillation was applied only to the GPe neurons and was not directly applied to the SNr neuron. The vector strength and vector angle spectra for an example SNr neuron receiving the propagated oscillations from the GPe cell ensemble from Figure 5A are shown in Figure 7C. Spike-oscillation coherence, measured by vector strength, varied with oscillation frequency but was substantial, and statistically significant at all oscillation frequencies from 1 to 100 Hz (e.g., see the degree of coherence shown in Fig. 7G–I). The vector strength spectrum resembles that of the summed GPe→SNr oscillation current (Fig. 5B), except that the SNr neuron vector strength is higher in the range 10-30 Hz, where oscillation amplitude is smaller in the current spectrum. The vector angle, the preferred phase for spiking during one cycle of the stimulus, is shown below the vector strength. At very low stimulus frequencies, the SNr neuron fires preferentially during the trough of the oscillation (∼0.75), as expected because of the inhibitory nature of the GPe→SNr synapse. This should be compared with the vector angle in Figure 7A, which shows the preferred phase of firing for an SNr neuron driven directly with a sine wave current. Unlike the response to directly applied oscillatory current, the SNr response to synaptically propagated oscillation increasingly lagged the trough of the oscillatory stimulus with increases in oscillation frequency. At ∼40 Hz, the cell preferentially fired at the end of the oscillatory cycle (phase of 1) and wrapped around, leading the stimulus waveform with further increases in oscillation frequency. The average spectral response for 7 neurons given this combined stimulus is shown in Figure 7D. Similar results were obtained with SNr neurons subjected to the other combined stimulus generated from GPe neurons (from Fig. 5B) having a broader range of firing rates. The spectra of the response of an example neuron to this conductance waveform are shown in Figure 7E, and the average spectra for the group of four SNr neurons tested using that waveform are in Figure 7F. Despite the differences in the frequency selectivity of the GPe neurons making up the input waveform, these two example GPe ensembles produced very similar coherence profiles in the SNr neurons (compare Fig. 7C and Fig. 7E).
The frequency-dependent shift in phase of propagated oscillations
Because the indirect pathway is inhibitory, it might be expected that SNr neurons would preferentially fire when the GPe neuron does not, meaning at phases of 0.5-0.75. At the lowest oscillation frequencies, this expectation was confirmed, but the phase lag of SNr firing relative to the oscillation increased with increasing frequency over the entire range. This progression is illustrated by phase histograms for the example SNr neuron at oscillation frequencies of 21 Hz (Fig. 7G), 40 Hz (Fig. 7H), and 75 Hz (Fig. 7I). This phase lag occurred when the oscillation was propagated synaptically but not when it was directly applied to the SNr neuron (e.g., compare bottom parts of Fig. 7A and Fig. 7C). The cause of this phase shift in the SNr neuron when driven synaptically is apparent from the phase of the GPe→SNr synaptic conductance component at each frequency (Fig. 7J). The centroid of the IPSG occurs at a latency of ∼3.7 ms from IPSG onset (Fig. 7J, inset). This produces a small phase shift at 1 Hz (0.038), a substantial one at 27 Hz (0.1), and a large phase shift at 100 Hz (0.37). As a result, the phase of the sinusoidal synaptic current grows from ∼0.5 at 1 Hz to ∼1 at 80 Hz, and wraps around to a phase lead of ∼0.2 at 100 Hz. The phase shift of the IPSG accounts for the phase shift of SNr neurons’ spike responses to the propagated oscillation from GPe compared with injected current (compare Fig. 7A and Fig. 7C). We did not add a spike conduction delay from the GPe to the SNr, and in situ the total delay and phase shift would be larger by that amount.
Discussion
Spiking resonance
All synaptic currents arriving within the interspike interval of a repetitively firing neuron alter the timing of its next action potential. The influence of input current arriving at any moment is determined by its size, sign, and timing relative to the prior action potential (e.g., Stiefel and Ermentrout, 2016). For a low-frequency sinusoidal input current, each interspike interval samples only a portion of the sinusoid, for example, only the depolarizing or hyperpolarizing portion. Depolarization applied across an entire interspike interval hastens the next action potential and hyperpolarization delays it, so firing rate is modulated continuously by the oscillation.
For oscillation frequencies near the cell’s firing rate, neurons adjust their firing times to place each spike at about the same phase on the input oscillation for every interspike interval (e.g., Wilson, 2017). Preferential coherence with input frequencies near the neuron’s average firing rate, called spiking resonance, is a common feature of many repetitively firing neurons in the basal ganglia and elsewhere (e.g., Beatty et al., 2015; Puelma Touzel and Wolf, 2015; Tikidji-Hamburyan et al., 2015; Wilson et al., 2018; Marín et al., 2020; Stark et al., 2022).
When the oscillation is faster, more than one cycle of the oscillation falls within the interspike interval; the speedup of the cell’s evolution toward firing produced during the depolarizing part of each cycle is counteracted by the opposite effect during the hyperpolarizing part. The unmatched partial cycle of the oscillation at the end of the interspike interval becomes the determining portion. In GPe and SNr neurons, interspike intervals vary sufficiently so that the unmatched part of the oscillatory cycle is sometimes depolarizing, and sometimes hyperpolarizing. If it is depolarizing, it hastens spiking and the cell fires on the depolarization of that cycle. If hyperpolarizing, it delays the next action potential, causing it to occur on the depolarizing part of a subsequent cycle. The shifts in action potential timing required to fire coherently with the oscillation are small and have little effect on either the rate or the regularity of firing. At frequencies above their own firing rate, the neurons in our sample skipped cycles stochastically while maintaining their intrinsic firing rates, so that the average number of skipped cycles reflected the ratio of the cell’s average period and that of the oscillation. The strong coherence that results may go unnoticed without quantification.
The frequency sensitivity of oscillation propagation
The oscillatory current propagated during low-frequency rate modulation is limited by synaptic depression. Pallido-nigral (and also GPe→STN and GPe→GPi) synapses undergo synaptic depression at the normal tonic firing rates of prototypic GPe neurons (Connelly et al., 2010; Atherton et al., 2013; Lavian and Korngreen, 2019). During rate modulation, the increase in firing rate during the depolarizing phase of the oscillation is counteracted by a decrease in the amplitude of synaptic currents, and synaptic currents increase in amplitude during decreased firing in the hyperpolarizing phase. Rate modulation produced at low-oscillation frequencies can be propagated effectively when the cells are driven into a burst and pause pattern, but at moderate amplitudes frequencies closer to the cell’s background rate are propagated more effectively by coherence. Propagation by spike coherence extends to very high oscillation frequencies, and these signals may be missed entirely in experiments that measure continuously varying firing rate changes in vivo.
The strength of propagation by coherence depends on the frequency sensitivity of the GPe neurons, the pallido-nigral synapses, and the nigral neurons themselves. The peak frequency sensitivities of GPe and SNr neurons are determined by their firing rates. Changes in firing rate may not always be the signal in interneuronal communication, but they might instead (or also) be a mechanism for tuning coherence to a specific frequency range.
Synaptic convergence enhances propagation
Unlike the direct striato-nigral synaptic pathway, which provides each SNr cell with thousands of weak unitary inputs (Connelly et al., 2010; Wilson, 2013), only about four indirect pathway pallido-nigral cells innervate each SNr neuron (Simmons et al., 2020). Their summation can produce oscillatory synaptic currents at the SNr neuron larger than the original signal received by the GPe neurons. It is meaningful that there is little convergence in the indirect pathway. If each SNr neuron received synaptic input from 100 tonically active GPe cells, they would all be silenced. The decrease in rate produced by the tonic inhibitory barrage from GPe may be compensated by tonic excitatory inputs, for example, from the STN (Ibañez-Sandoval et al., 2006; Bosch et al., 2012). The increase in firing irregularity cannot be compensated by other inputs. The GPe barrage makes the cells’ firing less rhythmic, approximating the firing patterns seen in these cells in vivo (e.g., Seeger-Armbruster and von Ameln-Mayerhofer, 2013; Lobb and Jaeger, 2015; Lin et al., 2022). Firing irregularity may have functional benefits, for example, increasing the speed and strength of the response to disinhibitory or excitatory inputs from elsewhere (Simmons et al., 2020)
The frequency-dependent phase shift between GPe and SNr
The indirect pathway is inhibitory, so SNr neurons driven by GPe oscillations are expected to fire in antiphase with the oscillator. Instead, SNr neurons show an increasing phase lag with respect to the GPe oscillation as the frequency of the oscillation increases. The phase shift occurs because synaptic current kinetics produce a small effective delay between their onset time and their peak effect. This phase shift is caused by the nature of the synaptic current and not the SNr cell response, and it should also occur in the local field potential in the SNr. In situ, there should be an additional conduction time delay (Kita and Kitai, 1991), which will increase the phase shift by an additional amount. It may be misleading to infer the origin of either a field potential or a spike timing oscillation in the SNr from its phase relationship with the GPe.
The indirect pathway and other GPe projections
We experimentally isolated the pallido-nigral limb of the indirect pathway, but in situ it operates in tandem with the pallido-subthalamo-nigral limb. The neurons of STN, like those of the SNr, are pacemakers and their responses to synaptic currents are similar to GPe neurons (Wilson et al., 2014). GPe→STN connections have sparse convergence (Baufreton et al., 2009) and strong synaptic depression (Atherton et al., 2013). Neurons in the GPe→STN limb of the indirect pathway should respond to both the background synaptic barrage and oscillatory signals from GPe neurons in a way similar to SNr cells. Understanding the joint operation of the two limbs of the indirect pathway will require quantitative characterization of unitary synaptic conductances generated by STN neurons.
We studied the prototypic cells of the GPe because these cells form the majority of the projections to basal ganglia output neurons in the GPi and SNr. Neurons of other types found in the GPe, having projections elsewhere, are also pacemakers (e.g., Jones et al., 2023), and may also propagate oscillatory inputs to their targets.
Rate, oscillations, and models of Parkinson’s disease
The effect of synaptic depression especially diminished the influence of steady-state changes of firing rate (as shown in Fig. 2F), like those occurring in Parkinson’s disease or after experimental dopamine depletion. This may explain why there could be reliable steady-state changes in GPe firing rate in models of Parkinson’s disease, without a consistent change in GPi (Wichmann et al., 1999; Bergman et al., 1994; Raz et al., 2000; Wichmann and Soares, 2006; Tachibana et al., 2011; but see also Filion and Tremblay, 1991). These models often exhibit changes in firing pattern, including oscillations (e.g., Deffains and Bergman, 2019; Crompe et al., 2020).
Decreases in GPe neuron firing rates and the resulting reduction of synaptic depression would enhance the influence of GPe neurons and increase the variance of the noisy currents generated by the background barrage in the target structures. This may explain why increases in SNr spike time variance are observed in animal models of Parkinson’s disease (e.g., Dorval and Grill, 2014). Not all changes in the GPi or SNr are communicated from the GPe, however. In the SNr, dopamine depletion can produce changes in firing rate and pattern independent of GPe (or any other) afferent input (Cáceres-Chávez et al., 2018).
Implications for nonperiodic signals in the indirect pathway
All time-varying signals can be understood as the sum of oscillations with various frequencies and phases. The principles that govern propagation of oscillations determine the propagation of all signals generated in the basal ganglia, periodic or not. Responses to aperiodic inputs to GPe neurons producing rapid changes in rate, including pulses, pauses, bursts, can be decomposed into a mixture of fast- and slow-frequency components (governing transient and sustained components). Our finding that the GPe faithfully propagates oscillations over a wide frequency range implies a capability for encoding input signals covering a range of temporal scales, including those changing even more rapidly than the firing rates of the GPe neuron.
Footnotes
This work was supported by National Institute of Neurological Disorders and Stroke Grant R35NS097185 to C.J.W. and F31 NS127499 to J.A.J. We thank Matthew Higgs, Erick Olivares, and Hitoshi Kita for helpful advice and comments on the manuscript.
The authors declare no competing financial interests.
- Correspondence should be addressed to Charles J. Wilson at Charles.Wilson{at}utsa.edu