Matthew H. Higgs and Charles J. Wilson. J Neurophysiol. 115(6):2814-29.

Neurons in substantia nigra pars reticulata (SNr) are synaptically coupled by local axon collaterals, providing a potential mechanism for local signal processing. Because SNr neurons fire spontaneously, these synapses are constantly active. To investigate their properties, we recorded spontaneous IPSCs (sIPSCs) from SNr neurons in brain slices, in which afferents from upstream nuclei are severed and the cells fire rhythmically. The sIPSC trains contained a mixture of periodic and aperiodic events. Autocorrelation analysis of sIPSC trains showed that a majority of cells had 1-4 active unitary inputs. The properties of the unitary IPSCs (uIPSCs) were analyzed for cells with one unitary input, using a model of periodic presynaptic firing and stochastic synaptic transmission. The inferred presynaptic firing rates and CVISI corresponded well with direct measurements of spiking in SNr neurons. Methods were developed to estimate the success probability, amplitude distributions, and kinetics of the uIPSCs, removing the contribution from aperiodic sIPSCs. The sIPSC amplitudes were not increased upon release from halorhodopsin silencing, suggesting that most synapses were not depressed at the spontaneous firing rate. Gramicidin-perforated patch recordings indicated that the average reversal potential of spontaneous IPSPs was -64 mV. Because of the change in driving force across the inter-spike interval (ISI), the unitary inputs are predicted to have a larger postsynaptic impact when they arrive late in the ISI. Simulations of network activity suggest that this very sparse inhibitory coupling may act to desynchronize the activity of SNr neurons while having only a small effect on firing rate.

Figure 1: Spontaneous IPSCs in SNr neurons. A. Recordings in control extracellular solution and in the presence of TTX (1 M), obtained with CsCl intracellular solution at -70 mV. B. Recordings in control solution and in the presence of picrotoxin (100 M), obtained with KCl intracellular solution at -70 mV.

Figure 2: Analysis of periodicity in sIPSC trains. In A-C, left panels show the autocorrelation of the digitized sIPSC train and right panels show the corresponding power spectrum. A. A cell with one active unitary input shows a single series of evenly spaced harmonic peaks in the autocorrelation and the spectrum. B. A cell with no recognizable unitary input shows no clear peaks in the autocorrelation or the spectrum. C. A cell with two unitary inputs shows a complex pattern of peaks in the autocorrelation and the spectrum. The vertical marks above the spectrum indicate the two harmonic components, each with equally spaced peaks. D. Histogram of number of identified unitary inputs to each SNr neuron.

Figure 3: Model fit to autocorrelation of spike train and sIPSC trains. A. Autocorrelation of spike train recorded from an SNr neuron using the perforated-patch method, fitted with a sum of Gaussian components representing the first-order and higher-order inter-spike intervals. The fit parameters indicate a mean firing rate of 21.13 Hz and a CVISI of 0.69. B. Autocorrelation of sIPSC train from a cell with one unitary input, fitted with a similar model including a periodic input and an aperiodic input (see Materials and Methods). The fit parameters show an aperiodic event rate (r0) of 2.51 s-1, a presynaptic firing frequency (f1) of 16.15 s-1, CVISI of 0.41, and a periodic event rate (r1) of 10.89 s-1. Based on r1/f1, the unitary synaptic success probability was 0.674. C. Autocorrelation of sIPSC train from a cell with two unitary inputs, fitted with a model including two periodic inputs and an aperiodic input.

Figure 4: Stochastic transmission at unitary synaptic connections. A. Recording from an SNr neuron showing a train of sIPSCs with clear synaptic successes and failures and a relatively low rate of aperiodic events. Note the series of regularly spaced sIPSCs interrupted by gaps of 2-3 times the shorter intervals. B. Sequence of inter-event intervals in the same cell, showing multiples of the most common interval length. C. Unitary synaptic success probability, P(success), of each cell with exactly one unitary input, plotted as a function of the inferred presynaptic firing frequency, f1. Both parameters were determined by model fitting as described in Materials and Methods. The correlation between f1 and P(success) was not significant.

Figure 5: Estimating the unitary IPSC amplitude distribution and kinetics. A. Method for clocking sIPSCs with respect to the surrounding periodic events. Top plot is the digitized sIPSC train surrounding a reference event, which has been removed (vertical dotted line). Middle plot is a bandpass filter represented by a Gaussian-windowed cosine function. The filter frequency and bandwidth were determined based on the power spectrum of the entire digitized sIPSC train (see Materials and Methods). Bottom plot is the local clock signal produced by convolving the digitized sIPSC train with the filter. The asterisk (*) represents the operation of convolution. B. The local clock signals surrounding 50 reference sIPSCs. Most but not all of the reference events align with the peak of the clock signal. C. Phase distribution of sIPSCs with respect to the local clock signal. D. sIPSC amplitude versus clock phase. In the example cell, most of the larger sIPSCs appeared at central phases, indicating that they came from the unitary input. E. Top: amplitude distributions for "center-phase" sIPSCs at phases of 0.25-0.75 (gray bars) and "side-phase" sIPSCs at phases of 0-0.25 and 0.75-1 (black bars). Bottom: uIPSC amplitude distribution obtained by subtracting the side-phase distribution from the center-phase distribution. F. Unitary synaptic success probability versus mean uIPSC amplitude for each cell with exactly one unitary input (r = 0.45, p < 0.01). G. Estimated average uIPSC waveform for the example cell (see Materials and Methods). The 20-80% rise time was 0.35 ms, and the decay time constant was 2.66 ms.

Figure 6: Investigation of possible synaptic depression using halorhodopsin. 

A. Ventrolateral portion of coronal brain slice from a rat injected with AAV1 CamKII eNpHR 3.0 EYFP. The green fluorescence indicates expression of virus-encoded EYFP throughout most of substantia nigra (D, dorsal; V, ventral; M, medial; L, lateral).
B. Loose-patch extracellular recording from a halorhodopsin-expressing SNr neuron. Orange bar indicates the timing of 590 nm illumination. Activation of halorhodopsin completely suppressed the cell's autonomous firing for 10 s. At light offset, the cell resumed firing with increased frequency. C. Effect of halorhodopsin activation on sIPSCs in two SNr neurons. Left trace shows a cell with a large halorhodopsin current (upward shift in baseline during illumination). Right trace shows a cell with little or no halorhodopsin current. In both cells, halorhodopsin activation strongly suppressed sIPSC activity, with only a relatively low rate of large sIPSCs returning by the end of the 10 s period of illumination. D. All sIPSC amplitudes in the example cell from panel C, right, combining the data from 10 trials. The sIPSCs occurring immediately after light offset were not larger than the baseline events. E. Mean sIPSC rates of each cell before illumination (baseline), during the light, and during the first 1 s after illumination (post). F. Mean sIPSC amplitude of each cell during the baseline period and the post-illumination period. The lack of increase of sIPSC amplitudes upon offset of illumination suggests that the unitary synaptic inputs were not depressed by the baseline autonomous firing.

Figure 7: Spontaneous IPSPs in SNr neurons. A. Top trace: example of sIPSPs recorded by the gramicidin-perforated patch method during autonomous firing. The sIPSPs appear as sudden downward deflections in the inter-spike voltage trajectories. The pattern of sIPSPs suggests that this cell received at least two unitary inputs. Bottom trace, second derivative of voltage trace, smoothed by convolution with a Gaussian filter (0.5 ms SD). Note the large negative excursions corresponding to the onset of the sIPSPs. The sIPSPs were detected from the second derivative trace; the dashed gray line indicates the detection threshold for this cell. B. Histogram showing the number of sIPSPs detected as a function of phase within the ISI. A phase of 0 represents the previous spike time, and a phase of 1 represents the next spike time. To avoid detection artifacts associated with spikes, analysis was restricted to sIPSPs occurring at phases of 0.1 to 0.9. As expected for a conductance input with varying driving force (Vm - Erev), a larger number of sIPSPs were detected at phases of 0.5-0.9 (black bars) compared to phases of 0.1-0.5 (gray bars). C. Membrane potential at the onset of each sIPSP, plotted as a function of phase. The curvature of the plot represents the inter-spike membrane potential trajectory. D. Amplitude of each sIPSP, plotted as a function of phase. The amplitude was measured from the second derivative trace used for event detection. Because of the increased driving force, larger-amplitude sIPSPs were found at late phases. E. Estimation of the sIPSP reversal potential (Erev) (see Materials and Methods). The graph shows the predicted number of late-phase sIPSPs (0.5-0.9) that would have been detected at randomly chosen early phases (0.1-0.5), plotted as a function of the assumed value of Erev. The dashed line indicates the total number of late-phase sIPSPs, and the dotted line indicates the actual number of sIPSPs detected at early phases. In this cell, a correct prediction was obtained with an assumed Erev of -60.4 mV. F. Spike time response curves (STRCs) for sIPSPs in three cells (dotted gray lines), and average STRC (black line; error bars are SD). The data indicate that sIPSPs at later phases caused greater lengthening of the ISI.

Figure 8: Measurement of synaptic latency of inhibitory coupling. A. IPSPs in a connected pair of SNr cells.  The synaptic connection was one-way, with the cell shown in gray being presynaptic to the one shown in black.  The amplitude, time course, and phase-dependence of the IPSP were similar to those seen for periodic spontaneous IPSPs. B. Membrane potential of the presynaptic and postsynaptic neurons averaged on the peak of the presynaptic cell’s action potential.  The onset of the IPSP in the postsynaptic neuron occurred 1.6 ms after the peak of the action potential.

Figure 9: Effects of sparse inhibitory coupling in a model network. A. Model configuration. Left panel indicates the uncoupled control network. The network had 100 cells, which received a common sine wave input and independent white noise (). Each cell was represented by a phase model with an autonomous firing frequency of 20 Hz and a linear STRC. Right panel indicates the sparsely coupled network. Each of the 100 cells made and received an average of four inhibitory connections distributed randomly among the cell population. Each unitary connection produced a phase shift in its postsynaptic neurons calculated from the STRC. B. Spike rasters and PSTH (last 0.5 s of 2 s simulation) for shared 6 Hz inputs (top) and 20 Hz inputs (bottom) with amplitudes of 2.5 times the peak conductance of the uIPSC. The left panels are for the uncoupled control network, and the right panels are for the coupled network. With the 6 Hz input the cells usually fired three spikes on each input cycle. With the 20 Hz input the cells usually fired once per cycle. In each case, the addition of sparse coupling reduced the degree of synchrony produced by the shared input. C. Steady-state entropy of cell phases for simulations with shared sine wave inputs of varying frequency (1 to 50 Hz) and amplitude (0-6 nS) delivered to the control network (left) and the coupled network (right). Warm colors indicate low entropy, showing synchronization of the cells by the shared input. Sparse coupling reduced the ability of shared input to synchronize the network at all effectively synchronizing input amplitudes and frequencies.  Dots indicate the input frequencies and amplitude used for the examples in B. D. Effect of sparse coupling on average network firing rate in the absence of the sinusoidal input.  Synaptic strength was varied from 0 to 5 times the amplitude used in the simulations above.  Note the relatively weak effect of coupling on mean firing rate. E.  Effect of the synaptic density of inhibitory coupling on desynchronization. The shared sinusoidal input frequency was 6 Hz, and its amplitude was 3 nS. The maximal desynchronizing effect (highest entropy) was obtained with the sparsest connectivity.