Time-invariant feed-forward inhibition of Purkinje cells in the cerebellar cortex in vivo

Abstract

Key points: We performed extracellular recording of pairs of interneuron-Purkinje cells in vivo. A single interneuron produces a substantial, short-lasting, inhibition of Purkinje cells. Feed-forward inhibition is associated with characteristic asymmetric cross-correlograms. In vivo, Purkinje cell spikes only depend on the most recent synaptic activity.

Abstract: Cerebellar molecular layer interneurons are considered to control the firing rate and spike timing of Purkinje cells. However, interactions between these cell types are largely unexplored in vivo. Using tetrodes, we performed simultaneous extracellular recordings of neighbouring Purkinje cells and molecular layer interneurons, presumably basket cells, in adult rats in vivo. The high levels of afferent synaptic activity encountered in vivo yield irregular spiking and reveal discharge patterns characteristic of feed-forward inhibition, thus suggesting an overlap of the afferent excitatory inputs between Purkinje cells and basket cells. Under conditions of intense background synaptic inputs, interneuron spikes exert a short-lasting inhibitory effect, delaying the following Purkinje cell spike by an amount remarkably independent of the Purkinje cell firing cycle. This effect can be explained by the short memory time of the Purkinje cell potential as a result of the intense incoming synaptic activity. Finally, we found little evidence for any involvement of the interneurons that we recorded with the cerebellar high-frequency oscillations promoting Purkinje cell synchrony. The rapid interactions between interneurons and Purkinje cells might be of particular importance in fine motor control because the inhibitory action of interneurons on Purkinje cells leads to deep cerebellar nuclear disinhibition and hence increased cerebellar output.

Figure 1. Isolation of Purkinje cells and molecular layer interneurons by tetrode recordings

A, example of raw traces. The four channels of the tetrode allow the isolation of one interneuron (red arrowheads; same cell as in C) and two Purkinje cells (light and dark blue arrowheads; dark blue same cell as in B). B and C, average (unfiltered) waveforms on the four channels and autocorrelograms of a Purkinje cell (B) and a molecular layer interneuron (C). D, complex spikes isolated for the Purkinje cell in B and cross‐correlogram between complex spikes (CS) and simple spikes (SS), showing the characteristic pause after the occurrence of complex spikes. E, average unfiltered spike waveform of Purkinje cells (blue) and of interneurons (red). Interneuron spikes are slightly narrower and have a smaller rebound positivity, as seen when normalized by amplitude (red dashed line). F and G, distributions of ISIs for Purkinje cells and interneurons are distinct. F, cumulative distribution of ISIs for Purkinje cells (blue) and interneurons (red) and (G) fit of these distributions with a log‐normal function: $f\left(x\right)=\frac{e^{-\left({\left(log\left(x\right)-\mu \right)}^2/\left(2{\sigma }^2\right)\right)}}{\sqrt{2\pi }\sigma x}$(Pouzat and Chaffiol (2009). Bins in histograms B–D: 0.5 ms.

Figure 2. Short‐term correlations between recorded cells

A, D and G, specimen cross‐correlograms of two neighbouring neurons recorded simultaneously from a single tetrode, average normalized cross‐correlograms (B, E and H) and number of pairs with significant correlations for each bin (C, F and I, positive in red, negative in blue) for Purkinje cell pairs (A–C), interneuron pairs (D–F) and interneuron–Purkinje cell pairs (G–I). Bin = 1 ms. For the missing value at 0, see Methods.

Figure 3. Molecular layer interneurons mediate feed‐forward inhibition

A, normalized cross‐correlogram for all interneuron–Purkinje cell pairs. Each recording session is separated by a horizontal line. The cross‐correlogram of each pair was normalized (as in Fig. 2 H), and is represented by a single line on the image with the colour corresponding to the value of the cross‐correlogram at each time point. B, correlogram with all interneuron spikes (black) or with only interneuron spikes preceded and followed by ISIs longer than 50 ms (red). Note that the red line is located slightly above the black line, indicating a slightly higher firing probability of Purkinje cell spikes before and after the interneuron if no interneuron spike takes place during that period of time. C, average of Purkinje cell current, triggered on spontaneous interneuron spikes, recorded by whole cell patch‐clamping in vitro reveals incoming excitation before the inhibitory current. D, the increase in Purkinje cell normalized spike count before and the decrease after the interneuron spike (in vivo data, averaged over the ±2–8 ms window) are correlated (normalization as in A). E–F, correlations for various connectivity patterns in a simple model of interneuron + Purkinje cell (see Methods) y‐axis: Purkinje cell spike count per interneuron spike (bin = 0.5 ms). E, in a model with an inhibitory connection between the Purkinje cell and the interneuron, a monophasic reduction of firing (green) is observed. Injecting shared common noise inputs in a interneuron – Purkinje cell pair that is not synaptically connected produces a broad synchronization of the Purkinje cell and interneuron (orange). F, a pattern of cross‐correlogram similar to that observed in vivo (B) is found when the interneuron and Purkinje cell receive both common and independent noise and the interneuron inhibits the Purkinje cell (blue). G, cross‐correlograms of simulated spike trains computed for varying amounts of shared inputs; the numbers correspond to the square root of the product of the fraction of shared inputs in each cell (e.g. 0.28 corresponds to 40% and 20% of shared inputs in the cells $\sqrt{0{.4}^{*}0.2}$). H, amplitude of the peak and trough of the simulated cross‐correlograms as a function of the square root of the product of the fraction of shared inputs in each cell ($\sqrt{{{\sigma }_{\mathrm{Purk}}}^{*}{\sigma }_{\mathrm{IN}}}$). Grey shadings in B and C are the SEM.

Figure 4. Interneurons modulate Purkinje cell firing probability

A–C, principle of analysis. A, schematic Purkinje cell and interneuron spike train. For every interneuron spike, we call t _back the time between the last Purkinje cell and the interneuron spike and t _forward the time between the interneuron spike and the next Purkinje cell spike. The Purkinje cell ISI distribution (A and B, black) is used to predict the expected latency after the interneuron spike (B and C, prediction of t _forward, orange), knowing the time subsequent to the last Purkinje cell spike (A and B, t _back, blue). This prediction is compared with the observed distribution of latencies to the first Purkinje cell spike after the interneuron spike (A and C, t _forward, green). C, example of observed (green) and expected ± SEM (orange respectively full and dashed lines) t _forward distributions for one interneuron–Purkinje cell pair. The observed distribution is significantly lower than that expected for delay values in the range t. The strength of inhibition can be defined as the difference of probability for these delays (orange area a between the two curves), divided by the integral of the expected distribution of intervals for the same delays (a + b). D, difference between the two distributions shown in C, revealing the delays after the interneuron spikes at which the Purkinje cell fires significantly less (blue) or more (red) than expected. E, histogram of percentage of pairs showing significant modulations at each time bin. F, strength of modulation expressed as the percentage change in Purkinje cell spike occurrence from expected value (black line; SEM in grey). G, average probability residuals (as in D) after all (black, continuous line), non‐synchronous (black, dashed line) or only synchronous (red) interneuron spikes for recordings where two interneurons could be recorded simultaneously. The increase in inhibition strength by synchrony is calculated by comparing the negative residuals obtained with the two conditions. Data are from 36 pairs from seven recording sites in seven rats.

Figure 5. The inhibition‐induced delay is independent of the Purkinje cell firing cycle in irregular neurons

A, principle of the DSC computation (detailed in the Method section): the DSC detects how the average delay t _forward from an interneuron (IN) spike to the next Purkinje cell (PC) spike deviates from the expected average value, as a function of the delay t _back between the interneuron spike and the previous PC spike; the expected value is derived either from the ISI distribution (grey), or from the distribution of the t _forward obtained with a randomized interneuron spike train (obtained by shuffling of the interneuron ISI, green; this distribution is shifted to the right compared to the ISI distribution because randomly shuffled interneuron spikes have more chances to fall in long ISIs than in short ISIs). B–D, example of DSC (i.e. the deviation from expected latency, t _forward, as a function of the delay subsequent to the last Purkinje cell spike (t _back). Black dots are individual spikes; red curve is the average using 1 ms bins; and green shows the best linear fit. B, in vivo, the latency does not depend on the delay subsequent to the last Purkinje cell spike. C, in vitro, under the low noise condition, ISIs occurring after interneuron spikes late in the Purkinje cell firing cycle (longer t _back and shorter expected t _forward) deviate more from the expected value than those occurring early. D, increasing noise level in vitro lowers the DSC slopes, which become closer to that observed in vivo. E, population boxplot of the slope of linear fit (green curves in B–D) for all tested cells. F, values of the DSC slope (with confidence interval) for pairs recorded in vivo, as a function of the PC firing rate. Red lines: linear fit and confidence interval on the slope value (not significantly different from 0; P = 0.65). G, slope of linear fit across all recording conditions. Triangles, in vivo; squares: in vitro high noise; circles: in vitro low noise. H, a simple model (see Methods) qualitatively reproduces the dependence of the DSC slope on the coefficient of variation of the ISIs.

Figure 6. The forgetful neuron: long‐tailed ISI distributions are associated with flat DSC

Illustration of the relationship between firing irregularity and flat DSC (i.e. independence of the impact of a synaptic input to the recent firing history of the postsynaptic cell) in a single‐compartment model of Purkinje cell. A and B, example of ISI distribution of PC recorded in vitro (A) and in vivo (B). The mean ISI is indicated by a black dashed line and the memory time (B) is indicated by an orange dashed line. An exponential fit (see Methods) of the tail of the ISI distribution (green, fit; red, confidence interval) has been overlaid on the histogram. The greyed area indicates the part of the histogram with less than 10 counts per bin, which was not taken into account for the fit. B, inset: ISI distribution and fit in logarithmic scale. C, memory time constant for Purkinje cell recordings in vivo is generally lower than the average ISI (1/rate), P = 0.03. D–F, distribution of interspike intervals as their CV is increased (CV = 0, 0.22 and 0.75, respectively in D, E and F), at the same time as the mean discharge rate is kept constant (30 Hz, dashed black line). This is achieved by increasing the variance of the fluctuating input at the same time as lowering its mean. The memory time T ₀ (orange line) is defined as the time at which the tail of the distribution becomes exponential (Ostojic, 2011). G–I, DSCs corresponding to (D) to (F).

Figure 7. Interneurons are not involved in fast oscillations of Purkinje cells

A, superimposed spike‐triggered average (STA) of one interneuron and two Purkinje cells from the same 30 min recording. A ∼200 Hz wave is visible in the STA of Purkinje cells (blue) but not in that of the interneuron (red). B, same as A for the cell population (26 Purkinje cells and 11 interneurons). C, superimposed power spectra of values (same cells as in A) and of the local field potential (LFP, green). The high‐frequency component is present in the LFP and in the STA of the Purkinje cells (blue) but not in that of the interneuron (red). Inset: power spectrum of the STA of all the interneurons; there is no peak at high frequency (except maybe a small peak for the cell plotted in green). D, peak frequency in the spectra of STA values is correlated with the peak frequency in the spectra of the LFP for Purkinje cells (red) but not interneurons (blue).