Regular patterns in cerebellar Purkinje cell simple spike trains

Abstract

Background: Cerebellar Purkinje cells (PC) in vivo are commonly reported to generate irregular spike trains, documented by high coefficients of variation of interspike-intervals (ISI). In strong contrast, they fire very regularly in the in vitro slice preparation. We studied the nature of this difference in firing properties by focusing on short-term variability and its dependence on behavioral state.

Methodology/principal findings: Using an analysis based on CV(2) values, we could isolate precise regular spiking patterns, lasting up to hundreds of milliseconds, in PC simple spike trains recorded in both anesthetized and awake rodents. Regular spike patterns, defined by low variability of successive ISIs, comprised over half of the spikes, showed a wide range of mean ISIs, and were affected by behavioral state and tactile stimulation. Interestingly, regular patterns often coincided in nearby Purkinje cells without precise synchronization of individual spikes. Regular patterns exclusively appeared during the up state of the PC membrane potential, while single ISIs occurred both during up and down states. Possible functional consequences of regular spike patterns were investigated by modeling the synaptic conductance in neurons of the deep cerebellar nuclei (DCN). Simulations showed that these regular patterns caused epochs of relatively constant synaptic conductance in DCN neurons.

Conclusions/significance: Our findings indicate that the apparent irregularity in cerebellar PC simple spike trains in vivo is most likely caused by mixing of different regular spike patterns, separated by single long intervals, over time. We propose that PCs may signal information, at least in part, in regular spike patterns to downstream DCN neurons.

Figure 1. Simulation of PC to DCN synaptic conductance.

(A) Saturating level of release probability (Rss) taken from Pedroarena and Schwarz (2003) could be modeled with a double exponential function (red line, see Materials and Methods for details). (B) Simulated synaptic conductance profiles in response to 10, 30 and 100 Hz PC firing, respectively. These results should be compared to Figure 7A of Pedroarena and Schwarz (2003).

Figure 2. Regular patterns in cerebellar Purkinje cell simple spike trains.

(A) Raster plot of PC SS in an anesthetized rat (AnR). (B) CV₂ distributions of SS trains recorded from anesthetized mice (AnM, left), awake mice (AwM, middle, blue: neurons in cerebral motor cortex), and mean of 92 CV₂ distributions (Pooled, right) which were significantly different from those of inhomogeneous Poisson processes with similarly modulated firing rates (p<0.05, χ² test; *: p<0.001, χ² goodness of fit residual test; red line: CV₂ = 0.2). Insets and right panel: mean±s.e.m. (black: PC, green: inhomogeneous Poisson process) (C) Extracting regular spiking patterns by setting CV₂ threshold at 0.2 (white dotted lines). White dashes: CV₂ values calculated from the two surrounding ISIs, red: first ISI of regular patterns, pink: successive ISIs in regular patterns, dark blue: ISIs not belonging to a regular pattern).

Figure 3. Effect of CV₂ threshold on patterns.

(A) Mean (± s.e.m.) of normalized number of patterns in spike trains classified with different values of the CV₂ threshold, ranging from 0 to 0.5, in 92 PCs (filled circles) and in simulated spike trains from Poisson processes with similar firing rate profiles as in the PCs (open circles). Arrow: maximum number of patterns, *: range where there was no statistical difference (p>0.05). Inset: same distribution but for all possible thresholds. (B) Raster plots with indication of the spike timings belonging to patterns (red dotted lines: start of patterns, red solid lines: following spikes in each pattern) and singles (blue). Black dots: difference in classified patterns when threshold was 0.2 (upper trace) and 0.24 (lower trace).

Figure 4. Characteristics of regular spike patterns.

(A) ISI distribution of overall ISIs (black), patterns (red) and singles (blue) from a representative sample PC spike train of AnR (left), AnM (middle) and AwM (right). Insets: magnified plot of indicated area (lower) and 90 P (90 percentile, upper) of each population, *: p<0.01, Student t test. (B) The relation between pattern mean ISI and pattern size in AnR (left, cyan), AnM (middle, magenta) and AwM (right, yellow). Insets: maximum pattern mean ISI (90 percentile) of different pattern sizes. *: p<0.001, Wilcoxon signed rank test. (C) Percentage ISIs belonging to patterns (upper, *: p<0.001, Student t test), Average maximum pattern size (middle, *: p<0.001, Student t test), and Pattern size distribution (lower, p<0.05, χ² test). Cyan: AnR, magenta: AnM, yellow: AwM.

Figure 5. Simulated synaptic conductance in PC to DCN synapse caused by spontaneous PC spiking.

(A) A representative example of the simulated synaptic conductance (G_syn) induced by PC (black) of AnR (upper panel), AnM (middle panel) and AwM (lower panel), and by corresponding realizations of an inhomogeneous Poisson process (green). Rasters: spikes belonging to patterns (black and green dotted lines: start of patterns, black and green solid lines: following spikes in patterns, blue lines: singles), numbers: number of all spikes in the 500 ms window. (B) Distribution of G_syn values for PCs (black) compared to Poisson processes (green). Bin = 0.2 nS. Red bar: bins where PCs contained significantly more G_syn values. p<0.05.

Figure 6. Coincident patterns in nearby PC pairs in AnR.

(A) Eight cross-correlograms of timings of spikes belonging to regular patterns extracted from recordings of nearby PC pairs, with each pair colored differently. Insets: cross-correlograms of the shuffled spike trains of two pairs (black) superimposed on original cross-correlogram of patterns (blue and gray: pairs showing strongest and weakest synchronization respectively). (B) The relation of pattern mean ISIs in 4 pairs in which pattern starts coincided significantly (inset: cross-correlograms of the first spikes of regular patterns in the 4 pairs). Red dotted line: diagonal.

Figure 7. A representative example of regular patterns in tactile stimulus evoked PC SS responses.

(A) Peri-event raster plot of patterns (red) and singles (blue) during tactile stimulation in AnR. (B) Mean rate (± s.e.m.) of overall spikes (black), realization of Poisson process (green), pattern spikes (red) and singles (blue). Bin = 20 ms. (C) Simulated G_syn for the trial indicated by arrow in (A) (bin = 1 ms). (D) CV (SD/Mean) of simulated G_syn (*: p<0.001, Student t test, bin 20 ms). Black dotted line: stimulation time. (E) Mean firing rate (upper panel) and percent ISIs belonging to regular patterns (lower panel) in 200 ms before and after stimulation (upper panel) of simulated spike trains from inhomogeneous Poisson process (green) and from recorded PCs (black). *: p<0.005, Wilcoxon signed ranks test. (F) Pattern mean ISI distribution before (dotted line) and after (solid line) tactile stimulation. Inset: Pattern size distribution before (open) and after (filled) stimulation.

Figure 8. Regular patterns and singles related to the membrane potential (MP).

Dendritic patch-clamp recording of PC in anesthetized rat (data from Loewenstein et al. 2005). Voltage trace: large spikes are complex spikes, small ones are simple spikes. Dotted black line: threshold to define up and down-states (MP = −55 mV). Raster plot at top: simple spikes were sorted as either pattern spikes (dotted red lines: start of patterns, solid red lines: following spikes in each pattern) or single spikes (blue lines). All patterns were during up-state, but singles occurred both during up (filled circles) and down (open circles) states.