Rate versus synchrony codes for cerebellar control of motor behavior

Abstract

Control of movement requires the coordination of multiple brain areas, each containing populations of neurons that receive inputs, process these inputs via recurrent dynamics, and then relay the processed information to downstream populations. Information transmission between neural populations could occur through either coordinated changes in firing rates or the precise transmission of spike timing. We investigate the nature of the code for transmission of signals to downstream areas 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 cerebellar flocculus of rhesus macaques revealed 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 likely insufficient to impact the firing of downstream neurons in the vestibular nucleus. Further, analysis of previous metrics for assaying 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 code rather than synchrony code to drive activity of downstream neurons and thus control motor behavior.

Impact statement: Information transmission in the brain can occur via changes in firing rate or via the precise timing of spikes. Simultaneous recordings from pairs of Purkinje cells in the floccular complex reveals that information transmission out of the cerebellar cortex relies almost exclusively on changes in firing rates rather than millisecond-scale coordination of spike timing across the Purkinje cell population.

Figure 1.. Simultaneously recorded Purkinje cells show small but non-zero spike timing synchrony.

A. Superimposed raw voltage traces from two PCs, aligned to the onset of a complex spike in each cell. 100 voltage traces are shown for each PC. B. Cross-correlograms showing each PC’s simple spikes triggered on the occurrence of a complex spike at t=0 (i.e., CS-SS cross-correlogram). C. Superimposed raw voltage traces from the same pair of PCs as in (A), aligned to 100 randomly selected PC simple spikes from PC1. D. Auto-correlograms triggered on the time of a simple spike for each neuron shown in (A). E. Firing of PC2 aligned to the time of PC1’s simple spikes at t=0 (black). Red curve shows the rate-corrected probability of PC2 firing in 1-ms bins in units of change in probability (right axis). Shaded region denotes 95% confidence intervals. F-H. Rate-corrected probability of firing averaged across a population of simultaneously recorded PCs (F), putative PCs that lack a recorded complex spike (G), and across all PC and putative PC pairs (H). Shaded regions denote SEM across PC pairs. I. Rate-corrected probability of synchrony versus distance between the primary contact for pairs of simultaneously recorded PCs. Black line denotes the best linear fit. J. Rate-corrected CCGs separated according to where the maximum value occurred between the t=0 to t=3 millisecond bins. K-M. Primary channel waveform (top) and example auto-correlograms (bottom) for populations of known PCs (K), expert-identified putative PCs (L), and randomly selected non-PCs (M).

Figure 2.. Synchrony among Purkinje cells that share the same complex spike response mirror the complete population.

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 (B) (left) as well as across a population of five PC pairs that show pauses to the same complex spike (right). Shaded regions in (B) denote SEM across the five PC pairs.

Figure 3.. 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. Example eye (black) and target (dotted) velocity and position traces for a pursuit trial with a pursuit speed of 20 deg/s appear in the bottom panels. 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. Pairwise 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. D. Probability of observing millisecond-scale synchrony between pairs of simultaneously recorded Purkinje cells in the preferred simple spike (blue) and anti-preferred (red) directions for 20 deg/s pursuit. Black lines 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 for (D), but relative to the preferred CS direction (CS-on). F. Same as (D) except null hypothesis probabilities are computed using the jitter-corrected method with windows of 5 milliseconds. G. Same as in (D), except null hypothesis probabilities are computed by shuffle correction across trials. Shaded regions in D-G denote SEM across PC pairs.

Figure 4.. Alternative metrics to assay synchrony incorrectly discover temporally-specific Purkinje cell coordination.

A. Exemplar paired PC recordings measured during smooth pursuit eye movements in the CS-on direction. The two traces show mean firing rates during pursuit for the two neurons in a pair. B: Rasters for each neuron across smooth pursuit trials. Spikes that occurred in the same millisecond bin in the two neurons are plotted as red symbols. The green trace shows the synchrony index averaged across trials. C. Synchrony index (± SEM) across n=32 pairs of PCs in the CS-on (purple) and CS-off directions (orange). Data provide a direct comparison to the bottom graph in Figure 3E.

Figure 5.. No evidence for a temporal code for transmission of information from Purkinje cells to 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. Distribution of rate-corrected covariance values for all PC-PC pairs in our dataset. Red vertical line represents the mean across n=117 pairs. C. Simulated pair-wise covariance matrix for a population of n=40 model PCs that provide inputs to a single model FTN. D. Black curve shows the number of synchronous input spikes to the model target neuron in a given ms as a function of the fraction of input PCs with synchronous spikes. Red arrow denotes estimated fraction of fully synchronous spike trains from the simulated population of neurons with pair-wise covariances shown in (C). Panels E-I show reanalysis of data from a previous publication. E. Exemplar recording from a floccular target neuron that receives monosynaptic inputs from floccular Purkinje cells. Plot shows n=200 superimposed voltage traces aligned to the onset of single shock stimulation (red vertical line) in the floccular complex. F. Average firing rate responses across a population of n=44 FTNs, aligned to the onset of stimulation. G. Probability distribution of preferred directions of smooth pursuit for all FTNs. H. Firing rate responses of FTNs for contraversive (green) and ipsiversive (red) pursuit. The pale shading shows the mean ± 1 SEM of the measured firing rate. Lines show the best fit predictions from the population of Purkinje cells recorded for this paper.