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

GPe neurons driven periodically exhibit phase locking

GPe neurons (n = 16) were recorded in acute brain slices (from N = 14 mice) in the perforated patch configuration to preserve their autonomous firing over the long recording duration. Each neuron was subjected to a sequence of 100 10-second-long sinusoidal current waveforms at frequencies 1, 2, 3, …, 100 Hz, each with an amplitude of 20 pA. This amplitude, although small in comparison with in vivo synaptic currents, proved to be sufficient for inducing rate modulation and spike entrainment in our experimental setup. In 3 of the 16 neurons, the cell did not survive all 100 trials, but all neurons were recorded up to 50 Hz. As we reported previously (Wilson and Jones, 2023), the sinusoidal drive influences the timing of the spikes (Fig. 1A) causing the spike times to distribute nonuniformly across the phases of the sinusoidal waveform in a frequency-dependent manner. We call this distribution the spike phase distribution and denote it Pj(ϕ;f) of the j^th neuron for driving frequency f. In the example depicted in Figure 1B, for low and high driving frequencies (top and bottom panels), the GPe spikes distributed broadly across phases—the spike phase distribution itself was sinusoidal—and peaked at phase 0.25, which corresponds to the peak of the sinusoidal waveform. However, when the driving frequency was close to the intrinsic firing rate of the neuron, the spike phase distribution became narrower and peaked at a later phase that varied among neurons (∼0.4 in Fig. 1B, middle). The degree of phase locking is captured by the vector strength (Fig. 1D, VS; see Materials and Methods), which increases as the distribution in Figure 1B is more sharply peaked (and unimodal). The VS increased as the driving frequency approached the intrinsic firing rate of the neuron, indicating that the neuron was more strongly entrained when driven by a frequency similar to its own intrinsic rate. As the driving frequency approached the intrinsic rate of the GPe neurons, the cyclic averaged phase angle of firing (Fig. 1E, VA) shifted away from stimulus phase 0.25 (the peak of the sinusoidal driving current) toward larger phase shifts. What determines the stimulus phase at which the GPe neurons became maximally entrained, and why does this phase vary among neurons?

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Figure 1.

GPe neurons driven periodically exhibit phase locking. A, Voltage trace of one example cell driven by a periodic current input at three different frequencies. Spike times were mapped to stimulus phase, and the distributions of spike phases are shown in B. C, Mean firing rate of the neuron during the 100 periods of stimulation. Red arrows indicate the stimulation frequencies shown in A and B. Dashed lines indicate a 1:1 ratio of firing rate to driving frequency (left) and a 1:2 ratio (right). D, Vector strength and E, vector angle as a function of stimulus frequency for the example cell.

Fourier modes of the iPRC dictate the phase at which phase locking occurs

We hypothesized that the diversity of stimulus phases at which different GPe neurons entrain is related to the heterogeneity of their iPRCs. To see why, we first digress with a simplified iPRC. Consider a triangular iPRC (of unity height) that is driven by a sinusoidal input whose frequency matches the neuron's intrinsic firing rate. The iPRC is parameterized by a single parameter θ, which is the location (between 0 and 1) at which the triangle peaks (Fig. 2A). As described in the Materials and Methods section, the iPRC can be decomposed into (a constant term plus) an infinite series of cosine functions each with the following: (1) a frequency that is an integer (n = 1, 2, 3…) multiple (or harmonic) of the fundamental frequency; (2) an amplitude; and (3) and angle, between 0 and 1 (Eq. 1 in Materials and Methods). Figure 2B depicts the first four cosine functions, or modes, of the triangular iPRC. Their amplitude is indicated with a black vertical line, and their angle is the distance of that line from 1 (indicated by a red line) divided by the period of that mode (indicated by a magenta line). The amplitudes of the modes decrease like 1/n² (see Materials and Methods) and their angles increase linearly (Fig. 2C). Figure 2A includes a sequence of curves, each representing a partial sum of the first N terms (with N = 0, 1, 2, 3, 4). As the number of modes used in the partial sum is increased, the approximation of the iPRC improves.

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Figure 2.

Fourier modes of the iPRC dictate the phase of spikes on the sine wave input at locking. A, Triangular iPRCs with θ value of (i.e., location of peak at) 0.9 (solid black) and sequences of curves representing a partial sum of the first N terms or modes of the Fourier decomposition (with N = 0, 1, 2, 3, 4, gray lines). B, First four modes of the iPRC shown in A, black vertical lines show the mode amplitude and their angle is then represented by the fraction of the horizontal red line in proportion to the period of that mode, indicated by a magenta line. C, Amplitudes (black exes) and angles (red diamonds) of the first 10 modes of the iPRC shown in A. D, Triangular iPRCs with θ values of 0.5 (blue) and 0.9 (red); dashed lines show the first (or fundamental) Fourier mode component of each iPRCs. E, Predicted return map indicating the phases of sequential spikes when each of the iPRCs shown in A is driven by a sinusoidal stimulus at the neuron's natural frequency; diamonds and dashed lines show the stable locking phase (ψ) for each iPRC. F, Phase at locking (ψ) closely matches the Fourier first mode of the iPRC (Δ₁) as predicted by the theoretical approximation. G, Relationship between the sinusoidal input (black solid line), the iPRC (solid colored line), its first Fourier mode (dashed colored line), and the orthogonal function to the stimulus (cosine, dashed black line). The iPRC and its first Fourier mode are aligned with the stimulus phase at two sequential spike times (ψ & 1 + ψ, vertical lines). It is apparent that the Fourier mode of the iPRC nearly merges with the cosine function orthogonal to the sine wave stimulus. All curves are normalized for easy comparison. H, Two examples of iPRCs estimated from GPe neurons; filled symbols and error bars show the iPRC estimated by the multilinear regression method, solid lines show the parameterized fit to each iPRC, and dashed lines show the first Fourier mode component of the iPRCs. I, Solid lines show return maps predicted by the phase model. Colored dots show ϕ_next versus ϕ_prev in the experimental data. Locking phases indicated by horizontal dashed lines are calculated as the vector angle. J, Correspondence between the phase of the first mode of the iPRC and the phase of locking, calculated as the vector angle for the spikes at the locking frequency for all 16 cells in the sample (r = 0.887; p < 10⁻⁵).

In order to calculate the phase of the sinusoidal input at which the neuron will lock to its sinusoidal input, we will consider two different triangular iPRCs, a skewed one (θ=0.9) and a symmetrical one (θ=0.5) (Fig. 2D). We need to first calculate the return map that represents the phase of the next spike on the input, ϕnext, as a function of the previous spike's phase, ϕprev (Fig. 2E). This is achieved by integrating the phase equation of the neuron driven by sinusoidal input (Eq. 2 in Materials and Methods) for all values of ϕprev between 0 and 1 and plotting the resultant ϕnext (Wilson, 2017). The phase locking occurs at the phase at which the return map crosses the identity line (Fig. 2E, diagonal) with a slope that is smaller than 1 (that guarantees that this fixed point on the return map is stable). Note that the stimulus phase of locking depends on the shape of the iPRC. For the rightward skewed iPRC (red), the phase locking occurs slightly above 0.25 and for the symmetrical iPRC (blue) it occurs at ∼0.5 (Fig. 2E).

To gain an intuitive understanding of what determines the phase locking, we sought an approximate solution of the phase equation (Eq. 2 in Materials and Methods) under the assumption that the phase φ that appears as the argument of the iPRC [Z(φ)] can be replaced with the solution of the unperturbed phase equation (namely that φ(t)=tT). Although this is never strictly true because it assumes the stimulus does not alter the neuron’s phase, it is a useful approximation when the stimulus amplitude is small and the driving is at precisely the intrinsic frequency of the neuron (so the period is not expected to change). In this approximation, the phase locking occurs at the phase ψ that equals the phase Δ1 of the fundamental mode of the iPRC when it is written as cos(2π[φ+Δ1]). For the triangular iPRC, we found (see Materials and Methods) that Δ1=34−θ2. Indeed, if we plot the phase ψ at which phase locking occurs based on the numerical solution of the full phase equation, against Δ1, we find that the points lie very close to the identity line (Fig. 2F). Figure 2G clarifies why this is. When driving the neuron with a sinusoid described by sin(2π[tT+ϕ]), integration of its product with the term cos(2π[φ(t)+Δ1])=cos(2π[tT+Δ1]) (in the approximated solution of Eq. 2) equals zero if ϕ=Δ1 (because sine and cosine functions of the same frequency are orthogonal if their phase shifts equal each other). Geometrically, this means that if we plot the iPRC so that it spans from one phase-locked spike to the next (Fig. 2G, vertical dashed lines) along the sine wave input (Fig. 2G, solid black sinusoid), then the fundamental Fourier mode of the iPRC (Fig. 2G, dashed sinusoids) will very nearly merge with the cosine wave (Fig. 2G, dotted black sinusoid) that corresponds (i.e., that is shifted to the left by 0.25 relative) to that sine wave. In the approximate solution, where ψ=Δ1, the fundamental mode of the iPRC merges precisely with the cosine wave. The discrepancy between the approximate and full solutions of the phase equation depends on the shape of the PRC (Fig. 2F, compare red and blue dots; see below) and on the amplitude of the oscillatory driving (which determines to what extent the dotted solutions bulge away from the unity line in Fig. 2F).

Note that in this simplified model, the more skewed red empirical iPRC leads to phase locking at a smaller phase shift than the more symmetrical blue empirical iPRC. Thus, the fundamental Fourier mode of the iPRC generates an “equivalence class” among neurons, in the sense that neurons whose iPRCs’ fundamental modes shares the same angle will all lock at the same phase when driven at a frequency equal to their intrinsic firing rate. Conversely, any difference between neurons in the fine structure of their iPRCs that does not affect the fundamental mode will not impact this entrainment and phase locking. Another corollary of this finding is that if the neuron is driven at the n^th harmonic of its intrinsic rate, then the phase locking will occur at the phase of the n^th Fourier mode of the iPRC (see Materials and Methods). In line with a previous study of ours (Goldberg et al., 2013), these findings underscore the importance of the iPRCs’ Fourier modes in understanding how pacemaker neurons respond to periodic inputs (see Discussion).

These results were based on a highly idealized iPRC, and on the Z(φ)=Z(tT) approximation, which is valid only for vanishingly small stimuli (see Materials and Methods). To determine whether the results apply more broadly, we tested the results using the empirical iPRCs of all 16 of our recorded neurons (Fig. 2H) and numerically integrated the phase model of each neuron to generate return maps (Fig. 2I). These reproduced the correspondence between the phase Δ1 of the first mode of the iPRC and the stimulus phase ψ of locking, calculated as the vector angle for the neurons’ spikes at the locking frequency (Fig. 2J; Pearson’s correlation r = 0.887; p < 10⁻⁵). Note the similarity between the phase of the fundamental modes of the empirical iPRCs (Fig. 2H, dotted lines) and that of the triangular iPRCs (Fig. 2D, dotted lines), which demonstrates the notion of the “equivalence class” of the skewed iPRCs and of the symmetrical ones and clarifies that it is the fundamental mode that mostly influences the shape of the return maps and their stable fixed points.

Return maps determine the shape of the spike phase distributions across frequencies

The formalism of using the return maps (which are calculated from the phase equation and using the GPe neurons’ empirical iPRC) to predict the spike phase distributions Pj(ϕ;f) is not restricted to the case of phase locking. In Figure 3A, we depict (in red) the scatterplot of all the empirical pairs (ϕprev,ϕnext) representing consecutive phases of the sinusoidal input at which the GPe neuron spiked. In Figure 3B, we depict the spike phase histograms (red), which correspond to the density of points on the scatterplot for each frequency. The deterministic return maps predicted from the empirical iPRC for the same three frequencies (Fig. 3A, blue) correspond closely to the red scatterplots. Moreover, if we assume a certain degree of additive noise to the deterministic return maps (see Materials and Methods for how the noise level was determined), then we find that the resulting spike phase distributions (Fig. 3B, black lines) match the empirical histograms (Fig. 3B, red bars). To estimate the goodness-of-fit, we calculated the average across all GPe neurons of the Pearson’s correlations between the predicted and empirical phase distribution (Fig. 3B, blue steps vs red bars, respectively) as a function of the driving frequency (Fig. 3C) and found a high degree of correlation of ∼0.75 across all frequencies.

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Figure 3.

Return maps determine the shape of the spike phase distributions across frequencies. A, Examples illustrating the alignment between a neuron's return maps and its spike phases at three different frequencies of sinusoidal driving input (8, 52, and 80 Hz). The blue line shows the return map generated by the phase model using the neuron's iPRC, while red dots depict recorded pairs of consecutive spike phases on the sinusoidal input. B, The spike phase histograms (red) correspond to the density of red points in A. The black line in B shows the predicted density from the return maps for the same three frequencies. C, Pearson’s correlations between the predicted (black steps) and empirical phase distributions (red bars) were calculated across all GPe neurons and plotted as a function of the driving frequency.

Pairwise CIFs during sinusoidal driving are predicted from the phase distributions across all frequencies

We have seen that the iPRCs and phase maps can give rise to diverse spike phase distributions, and the modes of these distributions can occur at various phase delays in a frequency-dependent fashion. Can the heterogeneity of iPRC shape among neurons give rise to the diversity of their pairwise CIFs? Intuitively this seems correct. Consider two GPe neurons whose spike phase distributions (at a specific frequency) possess modes (i.e., where they peak) at different phases. The maximal value of their pairwise CIF should be located at the phase difference between these respective modes. In the Materials and Methods, we present the general derivation that shows that the structure of the pairwise CIF of two neurons is equal to the cross-correlation function of their respective spike phase distributions. In Figure 4A–C, we depict several examples of empirical pairwise CIFs (green curve) with the CIF that is predicted from the two empirical spike phase distributions (purple curve) that are shown to the left (blue and orange distributions). The correspondence is impressive, with even some of the fine structure of the CIF being explained by cross-correlating the phase distributions. To estimate the goodness-of-fit between the predicted and empirical CIFs, we calculated the average across all (16 × 15/2=) 120 GPe neuron pairs of Pearson’s correlations between the predicted and empirical CIFs (purple vs green, respectively) as a function of the driving frequency (Fig. 4D) and found a high degree of correlation of ∼0.6 across all frequencies. Moreover, because Pearson’s correlations are independent of amplitude, we also determined that the amplitudes of the empirical CIFs were highly correlated the amplitude of predicted CIFs (Fig. 4E).

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Figure 4.

Pairwise cross-intensity functions (CIFs) during sinusoidal driving are predicted from the spike phase distributions across all frequencies. A–C, Left, Examples of spike phase distribution functions (PDFs) for two neurons (blue and orange), with cell pairs and stimulus frequencies shown in the plots. Right, Corresponding empirical CIFs (green curves) and CIFs predicted from the same neurons’ spike phase distributions (purple curves). A, Stimulation at low frequencies (8–11 Hz). B, Stimulation at frequencies near neurons’ firing rates (38–55 Hz). C, Stimulation at high frequencies (79–86 Hz). The four rows are various examples for each of the three frequency ranges in no particular order. D, Goodness-of-fit evaluated by Pearson’s correlations between predicted and empirical CIFs across all GPe neuronal pairs in the sample as a function of driving frequency. E, Scatterplot of amplitudes of CIFs that were predicted from the PDFs versus the amplitude of the empirical CIFs (dashed line is the identity line).

What is striking about the various pairwise CIFs (Fig. 4A–C) is that they exhibit diverse delays between the neurons that depend on their iPRCs, firing rates, and stimulus frequencies. This occurs even though each neuron was recorded separately on different brain slices in different mice, and neurons are therefore entirely independent of each other.

In summary, our analysis demonstrates that the iPRCs beget the return maps, which beget the phase distributions, which beget the pairwise CIFs. In other words, the heterogeneity in iPRCs is sufficient to explain the diversity of pairwise CIFs. Of particular relevance to previous interpretations of GPe neuron cross-correlations, our analysis shows that neurons driven by common input are not generally expected to produce CIFs with zero phase delay.

The two main features of CIFs of pairs of neurons subjected to common drive are their amplitude and their phase delay (or just “phase”). The amplitude indicates the strength of association between the neurons. In order to characterize how the amplitude of the CIFs calculated for the pairs of independent, sinusoidally driven GPe neurons depends on the driving frequency, we plotted the maximal amplitude of the pairwise CIFs as a function of two parameters: the driving frequency and the geometric mean of the intrinsic firing rates of the two neurons (Fig. 5A). The first salient feature of this rendition is the large amplitudes at high driving frequencies particularly for the pairs with the lower intrinsic firing rates. The reason for this is that when the driving frequency is high, all spiking for all neurons tends to occur at the peaks of the stimulus that is closest to the end of the intrinsic period of the neurons (Fig. 1A, bottom). On the one hand, this input does not entrain the much slower neuron. Nevertheless, the rapid upswing closest to the end of the intrinsic period will recruit the next spike, and so the spiking for both cells occurs tightly around the phase of the peak (i.e., 0.25) of the stimulus cycle (Fig. 4C). The peak of the CIF will be high because it is the cross-correlation function of two unimodal, narrow distributions located around phase 0.25 of the input. The second salient property of the surface plot in Figure 5A is the ridge of large amplitudes that runs diagonally along the curve where the driving frequency equals the geometric mean firing rate. The presence of this ridge is intuitively clear, because it represents the case where one or both of the GPe neurons are being driven near their intrinsic firing rate. This too will give rise to narrow, unimodal phase distributions, which in turn will contribute to a prominent peak in the CIF.

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Figure 5.

Experimental CIFs show frequency-dependent amplitude and broad distributions of phase delays. A, Amplitude of CIF as a function of two parameters: the driving frequency and the geometric mean of the intrinsic firing rates of the two neurons. B, Probability distribution function (PDF) of the CIFs’ phase delays across all pairs of GPe neurons as a function of the driving frequency; asterisk denotes occurrence of antiphase CIFs in the beta range. These data show that pairs of GPe neurons had a broad distribution of phase delays, particularly in response to driving frequencies in the beta range.

To characterize how the diversity of phase delays between neurons depends on the driving frequency, we plotted the probability distribution functions (PDFs) of the CIFs’ phase delays across all pairs of GPe neurons as a function of the driving frequency (Fig. 5B). This plot reveals that the broadest distribution of phase differences occurs for frequencies near the intrinsic firing rates of the GPe neurons (∼30 spikes/s) and at roughly double that frequency, which are the frequencies at which the strongest phase locking occurs. Note that in Figure 5B, there is a truncated large and narrow peak located at very low driving frequencies and at zero phase delay. At these very low driving frequencies, the spiking of both neurons is rate modulated (Fig. 1A, top), which means that the CIF is a cross-correlations of the rates of two GPe neurons driven by an identical sinusoidal input, so naturally both rates will peak at the same phase and the cross-correlation function will always peak at zero.

This analysis also demonstrates that beta-frequency periodic driving of completely independent GPe neurons is expected to generate CIFs with a broad distribution of nonzero phase delays.

Intranuclear connectivity decorrelates entrained GPe neurons without changing phase delays

We found that unconnected GPe neurons, driven by the same stimulus frequency, exhibit broad distributions of phase delays in their CIFs, and the amplitudes of these CIFs depend on the cells’ firing rates and the stimulus frequency. To investigate the impact of local connectivity within the GPe on the CIFs of neurons receiving common sinusoidal inputs, we employed a network of simulated phase model GPe neurons.

As a preliminary step, we examined whether unconnected phase model neurons could replicate the behavior observed in uncoupled neurons in our experiments. Similar to the experimental data, unconnected phase model neurons were subjected to sinusoidal inputs ranging from 1 to 100 Hz. The stimuli were presented to a set of 1,000 GPe model neurons with iPRCs and firing rates comparable with those in the experimental sample. We applied the same CIF analysis used for the experimental data to the resulting spike trains (Fig. 6).

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Figure 6.

Unconnected in silico phase model neurons produce CIF amplitude and phase delay distributions that closely resemble the experimental data. A, Amplitude of CIF as a function of two parameters: the driving frequency and the geometric mean of the intrinsic firing rates of the two neurons. B, Probability distribution function (PDF) of the CIFs’ phase delays across all pairs of GPe neurons in the unconnected network as a function of the driving frequency. Mean ± SD of CIF amplitude (C) and angle (D) as a function of stimulation frequency for experimental data (red) and unconnected model neurons (blue).

The amplitude of the pairwise CIFs in unconnected phase model neurons was reminiscent of the profile observed in the experimental data (compare Figs. 5A, 6A), including the ridge of large amplitudes running diagonally on the stimulation frequency versus pairwise geometric mean plane. The mean and standard deviation of CIF amplitudes for every stimulation frequency in the set of unconnected phase model neurons were similar to those observed in the experimental data (Fig. 6C). Furthermore, the CIF phase delay angles across the stimulus frequencies for unconnected phase model neurons closely matched the distributions observed in the experimental data (compare Figs. 5B, 6B).

Next, we utilized the network model to study the impact of neuronal connectivity on CIFs. When connected, GPe neurons constantly receive a barrage of synaptic inputs from other GPe neurons. This barrage of inhibitory synaptic inputs decreases the regularity of interspike intervals and thereby alters the response to external inputs (Simmons et al., 2020). To quantify the specific contribution of local connectivity, we compared the CIFs from the connected network with those from an equivalent ensemble of unconnected phase model neurons and a separate ensemble of unconnected neurons receiving a steady inhibitory barrage that approximated the average inhibition of the connected network but without its correlated temporal structure. To facilitate a direct comparison of CIFs, we applied a constant depolarizing current in both scenarios to offset the inhibition-induced reduction in firing rate. The same set of phase model neurons was used in all three configurations.

The principal effect of local connectivity on neurons’ CIFs is a dramatic decrease in CIF amplitude across all frequencies of stimulation studied, as shown in Figure 7A. This reduction can be partly attributed to the irregularity induced by the synaptic barrage (Fig. 7B). To clarify this, we plotted the distribution of CIF amplitudes for all pairs in the sample [N × (N − 1) / 2 pairs, N = 1,000] at three stimulation frequencies (Fig. 7C, 8, 35, and 80 Hz). Here, connected neurons (green) display a distribution skewed toward lower CIF amplitudes at all frequencies compared with unconnected neurons (black), while the unconnected neurons with barrage (red) show a similar skew, but only at the high frequency of 80 Hz. The influence of synaptic coupling on CIF phase delays is subtler (Fig. 7D); connected neurons and those receiving the barrage (green and red, respectively) exhibit distributions that are slightly skewed toward in-phase angles compared with unconnected neurons (black). It is worth mentioning the bimodal distribution of CIF phase delays at 35 Hz in neurons receiving the inhibitory barrage (red line 7D, middle panel). The origin of this distribution is explained by the neurons’ firing rates. The peak near zero delay is populated by neuron pairs whose rates are both above or below the stimulation frequency. The peak near 0.3 is populated by neuron pairs whose rates are one above and one below the stimulation frequency. The bimodal distribution is also present in connected and unconnected neurons (green and black lines) but with a greater overlap. The effect of CIF amplitude and subtler effect on CIF phase are also evident in the examples shown in Figure 7, E1 and E2, where we present CIFs of two neuron pairs at different stimulation frequencies. It is evident that the connected neurons (green) exhibit a reduced CIF amplitude at all frequencies, compared with the unconnected neurons (black), and this is true for the unconnected barrage configuration (red) only at the high stimulation frequency of 80 Hz. The CIF phase delay angle remained relatively stable across configurations but tended to gravitate toward antiphase angles as the stimulation frequency was increased.

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Figure 7.

Impact of local neuronal connectivity on CIFs in GPe neurons. CIF amplitude as a function of stimulation frequency and the geometric mean rate of the neuron pair in the connected network (A) and for the unconnected network with the inhibitory barrage (B). C, Probability density functions of CIF amplitudes at selected stimulation frequencies (8, 35, and 80 Hz). Black, red, and green lines represent unconnected neurons, unconnected neurons with barrage, and connected neurons, respectively. D, Probability density functions of CIF angles at same stimulation frequencies as in C. E1, E2, Example CIFs from two pairs of neurons at different stimulation frequencies for each model configuration.

These results were not dependent on the specific structure of the iPRCs in the GPe network, because repeating the same simulations with an identical iPRC for each neuron resulted in CIFs with similar amplitudes and phases (data not shown). Moreover, altering the network architecture from the small-world to random or rich-club organization (with a long tail in the distribution of postsynaptic connections per neuron) while maintaining the mean number of connections did not significantly alter the distribution of CIF amplitudes and phases. Changing the total number of connections did impact CIF amplitudes, but not phases. As connectivity decreased, CIF amplitudes smoothly approached the disconnected distribution of amplitudes, while increasing the number of connections decreased the CIFs amplitudes (data not shown). Thus, the attenuation of CIF amplitudes by local GPe connectivity is robust to changes in the intrinsic properties of the GPe neurons that alter their iPRCs and to changes in network configuration. These findings suggest that local synaptic connections in the GPe decorrelates GPe neurons when they are driven by common input, by reducing CIF amplitudes without notably altering their phase delays.