Rate versus synchrony codes for cerebellar control of motor behavior

Abstract

Information transmission between neural populations could occur through either coordinated changes in firing rates or the precise transmission of spike timing. We investigate the code for information transmission from a part of the cerebellar cortex that is crucial for the accurate execution of a quantifiable motor behavior. Simultaneous recordings from Purkinje cell pairs in the cerebellum of rhesus macaques reveal how these cells coordinate their activity to drive smooth pursuit eye movements. Purkinje cells show millisecond-scale coordination of spikes (synchrony), but the level of synchrony is small and insufficient to impact the firing of downstream vestibular nucleus neurons. Analysis of previous metrics that purported to reveal Purkinje cell synchrony demonstrates that these metrics conflate changes in firing rate and neuron-neuron covariance. We conclude that the output of the cerebellar cortex uses primarily a rate rather than a synchrony code to drive the activity of downstream neurons and thus control motor behavior.

Keywords: Purkinje cells; cerebellum; neural codes; rate code; smooth pursuit; synchrony; ventral paraflocculus.

Figure 1.. Assaying synchrony in an exemplar pair of simultaneous recorded Purkinje cells.

A. Superimposed raw voltage traces from two PCs, aligned to the onset of 100 randomly chosen complex spikes in each PC. B. Same transparent traces as in (A) except spikes from each Purkinje cell are removed from the primary contact of the other Purkinje cell. C. Cross-correlograms showing each PC’s simple spikes triggered on the occurrence of a complex spike at t=0. D. Auto-correlograms triggered on the time of a simple spike for each neuron shown in (A). E. Superimposed raw voltage traces from the same pair of PCs as in (A), aligned to 100 randomly selected PC simple spikes from PC1. Black arrows denote the time of alignment in PC2. F. Same aligned responses with the voltage contributions from each PC removed from the other PC’s primary contact. G. Firing of PC2 aligned to the time of PC1’s simple spikes at t=0. H. Rate-corrected probability of PC2 firing in 1-ms bins in units of change in probability. Shaded region denotes 95% confidence intervals. Black arrowhead highlights the peak in PC2’s simple spike firing around the time of PC1’s spike.

Figure 2.. Simultaneously recorded Purkinje cells show small but non-zero synchrony.

A-C. Rate-corrected probability of firing averaged across a population of simultaneously recorded PCs (A), putative PCs that lack a recorded complex spike (B), and across all PC and putative PC pairs (C). Note that we determined which neuron of a PC-PC pair was the “trigger” neuron based on the shape of the rate-corrected cross-correlogram (see Methods), and thus the cross-correlogram is not expected to be symmetric. D. Distributions of rate-corrected synchrony across populations of Purkinje cells. Each dot represents a single simultaneously recorded PC pair. E. Rate-corrected probability of synchrony versus distance between the primary contacts for pairs of simultaneously recorded PCs. Black line denotes the best linear fit. F. Rate-corrected CCGs separated according to where the maximum value occurred between the t=0 to t=3 millisecond bins. G-I. Primary contact waveform (top) and example auto-correlograms (bottom) for populations of known PCs (D), expert-identified putative PCs (E), and randomly selected non-PCs (F). Shaded regions in all panels denote SEM across PC pairs.

Figure 3.. Purkinje cell synchrony is not enhanced by shared climbing fiber inputs and is rare across broader Purkinje cell populations.

A. Example ACGs (black) and CS-SS CCGs (orange) for two Purkinje cells that pause their simple spike responses following the same complex spike. B. Rate-corrected CCGs for the example pair shown in (left) as well as across a population of five PC pairs that show SS pauses to the same complex spike (right). Shaded regions denote SEM across the five PC pairs. C. Three-dimensional cross correlogram of simultaneously-recorded triplets of PCs showing the probability of a spike in PC3 at different times relative to spikes in PC1 and PC2. D. Same as (C) but showing the average across 47 PC triplets. E. Distribution of rate-corrected probability of firing in PC3 when spikes occurred simultaneously in PC1 and PC2, taken from the value of the pixel at t=(0,0) for the 47 triplets shown in (D). Vertical red line shows the mean. F. Distribution of the probability of observing simultaneous spikes in PC1 and PC2 across n=47 triplets. Vertical red line shows the mean.

Figure 4.. Purkinje cells do not synchronize preferentially at any time during pursuit eye movements.

A. Firing rates and rasters for an exemplar Purkinje cell during smooth pursuit in the preferred (top raster) and anti-preferred (bottom raster) pursuit directions. Blue and red traces show average firing rate across time. Black and purple dots denote simple and complex spikes, respectively. Bottom panels show example eye (black) and target (dotted) velocity and position traces for a pursuit trial with a pursuit speed of 20 deg/s. Gray shaded regions denote 95% confidence intervals across pursuit trials. B. Probability distributions of preferred directions for simple spike (top, blue) and complex spikes (bottom, purple) populations of Purkinje cells. C. Pair-wise angular difference between preferred simple spike (top, blue) and complex spike (bottom, purple) directions for simultaneously recorded Purkinje cells. Red vertical lines denote the angular mean across all pairs. The mean difference between the SS-on directions was 14.7° (not significantly different than zero, t(116)=0.69, p=0.17). The circular dispersion was $\overline{R}=0.65$. The mean angular difference of CS-on directions was 6.3° (t(31)=−1.1, p=0.2); circular dispersion was $\overline{R}=0.84$. D. Top graph shows probability of observing millisecond-scale synchrony between pairs of simultaneously recorded Purkinje cells in the preferred (blue) and anti-preferred (red) simple spike directions for 20 deg/s pursuit. Black traces show the rate-corrected null probabilities of intersection at millisecond time scales. Bottom plots show the within-cell measured probability of synchrony minus the rate-corrected null probabilities. E. Same as (D) except null hypothesis probabilities are computed using the jitter-corrected method with windows of 5 milliseconds. F. Same as in (D), except null hypothesis probabilities are computed by shuffle correction across trials. G. Same as for (D), but relative to the preferred CS direction (CS-on). Shaded regions in D-G denote SEM across PC pairs. Data in D-G were smoothed using a boxcar filter with a 50 ms width.

Figure 5.. The “Synchrony Index” incorrectly discovers temporally-specific Purkinje cell coordination.

A. Responses during pursuit of an example pair of PCs. Blue and red traces show SS-on and SS-off directions, continuous and dashed traces show PC1 and PC2. B: Rasters for each neuron across smooth pursuit trials. Spikes that occurred in the same millisecond bin in the two neurons are plotted as blue or red symbols. C. Top graph shows the probability of synchronous spikes in the two example PCs as a function of time during pursuit. Blue and red traces show data for SS-on and SS-off directions, superimposed black traces show the synchrony expected given the firing rates of the two PCs. Bottom graph uses the same color scheme to plot the rate-corrected probability of synchronous spikes. D. Blue and red traces show the synchrony index averaged across trials for SS-on and SS-off directions of the example pair of PCs from (A-C). E: Same as (D) but averaged across the recorded population of 116 pairs. F. Same as (D) but averaged across a simulated population of PCs with the degree of covariance measured in our data. G. Same as (C) except for the simulated population of PCs.

Figure 6.. Purkinje cell synchrony is not required to account for the responses of identified downstream neurons.

A. Schematic diagram showing the convergence of a subpopulation of PCs that share the same climbing fiber input onto a single floccular target neuron (FTN) in the vestibular nucleus. B. Simulated pair-wise covariance values for a population of 40 PCs that provide input to a single model FTN. Each off-diagonal covariance value was pulled from the distribution measured across PC-PC pairs in our dataset. C. Plot showing how synchrony in the input spike train affects the number of synchronous input spikes to the model target neuron whenever any spike occurs. Red arrow is plotted where the derived curve crosses 2.50 input spikes/ms, the value predicted given the pair-wise covariances shown in (B). D. Exemplar recording from a floccular target neuron that receives monosynaptic inputs from ventral parafloccular Purkinje cells. Plot shows n=200 superimposed voltage traces aligned to the onset of single shock stimulation (red vertical line) in the floccular complex. Data from a prior publication. E. Average firing rate responses across a population of n=44 FTNs, aligned to the onset of stimulation. F. Probability distribution of preferred directions of smooth pursuit for all FTNs. G. The transparent error bands show the mean±SEM of average firing rate responses across a population of n=44 FTNs, aligned to the onset of stimulation, from a prior publication. Dark green and red traces show the predictions from a weighted linear sum of PCs from the sample in the present paper. Error bands denote mean±SEM measured from the FTN responses.