Simmons DV, Higgs MH, Lebby S, Wilson CJ. (2020) Indirect pathway control of firing rate and pattern in the substantia nigra pars reticulata. J Neurophysiol. 2020 Feb 1;123(2):800-814.

Unitary pallidonigral synaptic currents were measured using optogenetic stimulation, which activated up to three unitary synaptic inputs to each SNr cell. Episodic barrages of synaptic conductances were generated based on in vivo firing patterns of GPe cells and applied to SNr cells using conductance clamp.  Barrage inputs were compared to continuous step conductances with the same mean. Barrage inputs and steps both slowed SNr neuron firing and produced disinhibition responses seen in peristimulus histograms.  Barrages were less effective than steps at producing inhibition and disinhibition responses. Barrages, but not steps, produced irregular firing during the inhibitory response. Phase models of SNr neurons were constructed from their phase resetting curves.  The phase models reproduced the inhibition and disinhibition responses to the same inputs applied to the neurons.  The disinhibition response did not require rebound currents but arose from reset of the cells' oscillation. The differences in firing rate and irregularity in response to barrage and step inhibition resulted from the high sensitivity of SNr neurons to inhibition at late phases in their intrinsic oscillation.  During step inhibition, cells continued rhythmic firing at a reduced rate. During barrages, brief bouts of intense inhibition stalled the cells' phase-evolution late in their cycle, close to firing, and even very brief respites from inhibition rapidly released single action potentials.  The SNr cell firing pattern reflected the fine structure of the synaptic barrage from GPe, as well as its onset and offset.

Figure 1.  IPSPs and IPSCs evoked by optogenetic stimulation of the GPe®SNr axons. A.  Distribution of axons after viral transfection of GPe parvalbumin+ neurons with ChR2 and tdTomato.  The injection in GPe labeled many cell bodies and local axonal arborizations, as well as a light projection to the striatum, a very dense terminal field in the subthalamic nucleus (STN), and a moderate projection to the substantia nigra pars reticulata (SNr).  Within the SNr, axonal arborizations often formed pericellular nests (arrows in inset at higher magnification).  B. IPSP and spiking delay produced in a spontaneously firing SNr neuron by stimulating GPe axons in SNr with a brief (1 ms) pulse of blue light (arrow).  C.  IPSC evoked by a similar light flash in another neuron. A small step response at the onset of the trace was used for monitoring access resistance. D.  Higher-resolution trace of the same light-evoked GPe®SNr IPSC shown in C.  Note the appearance of multiple components with apparently different latencies. E.  Derivative of the IPSC trace shown in D, revealing three clear components.

Figure 2. Composition of GPE→SNr IPSCs.  A. Light pulses of increasing intensity and the associated total charge delivered by evoked IPSCs.  Light intensities associated with the three steps in the IPSC integral are colored grey (below threshold), green (low-threshold unitary) and red (low- plus higher-threshold unitary).  B.  Superimposed IPSCs from the three light intensity levels.  The light onset is at the blue arrow (0 ms).  C.  The number of unitary IPSCs composing maximal responses evoked in 17 neurons. 

Figure 3.  An example cell comparing the effects of IPSG barrages and steps on firing.  A.  Barrages of simulated IPSGs delivered by conductance clamp (left) and steps adjusted to the average of the barrages (right), applied in variable-length episodes separated by pauses.  Both stimuli reduced firing rate, but firing regularity was only disrupted by barrages.  B. Comparisons of single episodes from each condition.  During pauses and conductance steps, spiking regularities were comparable, despite the difference in rates.  During the barrage, regularity was decreased, as indicated by the increase of coefficient of variation of intervals (CV). 

Figure 4.  Peristimulus time histograms for inhibition and disinhibition. A.  Example histograms for onset of step inhibition (gray), and for disinhibition at the offset of the step (brown) or barrage (green), showing the measurements used.  The firing rate during the pause (in the absence of inhibition) is indicated by the gray histogram for negative times, and its average (baseline firing rate) is the gray dotted line. The steady-state firing rates during the barrage and step are the averages of their respective histograms for the 100 ms preceding the offset of inhibition (green and brown dotted lines).  Average rate changes are labeled Barrage Delta and Step Delta.  The changes in rate following the offset of inhibition include a transient overshoot.  The overshoots are measured as the integral of the initial region above the baseline firing rate (shaded areas).  B. Comparison of the rate changes produced by barrage and step inhibition in 18 neurons.  On average, the step inhibition was more effective at changing mean rate (signed rank test, N = 18, p = 0.00028), and produced a larger overshoot (signed rank test, N = 18, p = 0.00046). C. Onset and offset histograms for an example cell.  The histograms for the first and second spikes after the offset are shown in red and blue, respectively.  These correspond to the first two peaks in the PSTH after removal of inhibition.  D. The overshoot is not a change in rate.  Interspike intervals for the baseline firing (black), for the interval between the first and second spike after removal of inhibition (purple), and for the steady-state inhibitory period (gray).  The interspike interval histogram for the first post-inhibitory ISI did not differ from that of the baseline rate.  Thus, the overshoot does not occur because of any change in interspike intervals, but is caused by resetting the oscillation so that the cell is more likely to fire at the same time on each trial. There was no significant difference between the intervals between the first and second post-inhibitory spike and the mean baseline interspike interval for the sample of 18 neurons (signed rank test, p = 0.62).

Figure 5.  The PRC for SNr cells.  A.  Examples of 9 (out of 18) SNr neurons showing the range of variation in PRC size and shape among these cells. The error bars are standard errors of the estimates for the PRC values, calculated for 50 different phases in the cell’s firing cycle.  B.  The noise waveform (top) and the changes in spiking (bottom) used to calculate the PRC.  The firing rate in the absence of noise was used to estimate the unperturbed firing rate. The PRC was calculated by regressing the variations in ISI against the amplitudes of the brief noise pulses that occurred throughout the ISI.  C. Comparison between PRC for a single cell measured using noise (black) and with 1000 single pulses (red). Responses to single trials are gray points. D.  Mean PRC for all 18 cells.

Figure 6.  The phase model.  A.  Example IPSG waveform, synaptic current, and phase trajectories for an IPSG applied at three different times in the interspike interval.  At early phases (left), the driving force is small and the PRC amplitude is small, so the effect of the IPSG on spike timing is small.  The phase trajectory in the absence of the IPSG is shown as a dotted line.  At later phases, the synaptic driving force is larger, so the current increases.  The effect of synaptic current is also enhanced by the increased value of the PRC late in the cycle.  B. Phase trajectories for a phase model of an example SNr neuron for barrage (left) or step (right) conductance changes.  When the inhibitory conductance is present, the cell tends to linger at late phases, where the inhibition is most effective at slowing phase advance.  For the barrage stimulus, there are brief times when there are few IPSGs, and during these times the cell escapes inhibition, producing irregular firing.  This causes firing to be faster and more irregular during barrage inhibition compared to steps.

Figure 7.  The PSTH of the phase model neuron.  A.  An example showing the PSTH for step onset, step offset, and barrage offset, showing the measurements used.  B. The steady-state change in frequency and overshoot amplitudes for step versus barrage stimuli in phase models constructed for each cell (compare with data from the corresponding neurons, shown in Fig. 4). As in real cells, the conductance steps consistently produced stronger inhibition (signed rank test, n = 18, p = 0.00033). The models also showed greater effectiveness of step conductances in producing disinhibition overshoots (signed rank test, n = 18, p = 0.0005). C. Example PSTHs as in Fig. 4. The histograms for the first and second spikes after the offset are shown in red and blue, respectively.  These correspond to the first two peaks following inhibition offset.   D.  Interspike interval histograms showing that the disinhibition overshoot is not associated with any increased excitability, as expected based on the model construction.  Interspike intervals for the baseline firing (black), for the interval between the first and second spike after inhibition offset (purple), and for the steady-state inhibitory period (gray). 

Figure 8.  Time-evolution of the probability distribution of phase.  A.  Phase trajectories for a phase model SNr neuron during barrage (left) or step (right) inhibitory conductance input.  The conductance input is the top trace, and the evolution of phase is shown below.  During the pause in synaptic conductance (t > 200 ms) the cell’s phase advances at the intrinsic firing rate (ω), with only slight perturbations caused by intrinsic noise. In the presence of synaptic inhibition (between 0 and 200 ms), phase advance is slowed.  The slowing is intermittent during the barrage input, but is relatively constant during the step.  Inhibition is most effective at late phases, so the cell spends more time at late phases while inhibited. For the barrage input, action potentials occur during brief pauses in the inhibitory conductance.  B.  Heat map created by superimposing many traces like the ones in A and converting to probability, and the corresponding PSTH, aligned to the onset of inhibition as in A. Dotted line is the unperturbed firing rate.  C.  The distribution of phase at the end of the 200 ms inhibitory period. For both barrage and step inputs, the cell on average is more likely to be at a late phase.  The conductance step produces a more dramatic distortion of the phase distribution.  When the stimulus is over, the phase distribution will move to the right at constant speed.  The peak created in the phase probability distribution produces the disinhibition overshoot.

Figure 9.  Distortion of the phase distribution and the resulting disinhibition overshoot depend on the shape of the PRC. A.  A comparison of two PRCs (left), the probability distribution of phase at the end of the inhibitory period (center), and the disinhibition PSTH (right), for two cell models. One model used the mean PRC for the sample of SNr neurons, which has a large peak at late phases (black), and one was based on the single neuron in the sample with the flattest PRC (red).  The late peak in the PRC produced lingering of the cell at late phases, and buildup of phase probability at late phases, which was much less for the flat PRC. The reduced peak in the phase distribution led to a smaller disinhibition overshoot in the PSTH.  B.  A similar comparison of the effect of PRC skew.  A phase model based on the mean SNr PRC (black) is compared with its left-right reversed mirror image (green).  During inhibition, the reversed-PRC model produced a slowing of the phase trajectory and a peak in the phase probability at early phases.  Upon the termination of inhibition, the peak in phase probability propagated to the right at the cell’s unperturbed firing rate, and produced a disinhibition overshoot almost an entire cycle later.  The late disinhibition overshoot was also smaller and less defined, because intrinsic cell noise erodes the peak in the phase distribution as it propagates to the right (Simmons et al. 2018).