The origins of motor noise Javier Medina, Leslie Osborne, William Bialek, and Stephen Lisberger Sloan-Swartz Center at UCSF

Remarkable precision and accuracy

A tractable motor system, also precise and accurate

Smooth pursuit in the time domain

Initiation of pursuit involves using a representation of visual motion to estimate (and track) target direction and speed How precise are sensation and action?

Anatomy of pursuit Area “MT” of the extrastriate visual cortex contains the sensory representation of visual motion that drives pursuit.

MT responses are noisy

MT responses are noisy If I told you the number of spikes emitted by this MT neuron, then you could tell me target direction within about 30 degrees. I will show you that pursuit does much better than this.

Pursuit is somewhat imprecise

Pursuit is somewhat imprecise

A hypothesis for analyzing the variation. Here, the variation in the vector of eye velocities is decomposed into components related to the direction of target motion, the speed of target motion, and the time since the onset of target motion.

Pursuit is somewhat imprecise

Lots of data in a situation where accuracy counts

Determine the dimensions and magnitude of variation in pursuit Compute the residual for each trial as the response in that trial minus the average response for the given target motion. Pool all the residuals, giving us a large number of repetitions, increasing certainty in the analysis. Compute the “covariance matrix” for the first 125 ms of pursuit and find its eigenvectors: three account for >95% of the variation.

Determine the dimensions and magnitude of variation in pursuit Compute the residual for each trial as the response in that trial minus the average response for the given target motion. Pool all the residuals, giving us a large number of repetitions, increasing certainty in the analysis. Compute the “covariance matrix” for the first 125 ms of pursuit and find its eigenvectors: three account for >95% of the variation. Project onto the natural sensory coordinate system: almost all of the variation can be accounted for in terms of errors in estimating the speed, direction, and timing of target motion.

How precise is pursuit?

What have we learned? The direction of pursuit is 10x more precise than can be deduced from the responses of single MT neurons. Variation in pursuit maps onto a sensory coordinate frame - - direction, speed, and time. The precision of pursuit is very similar to that of perception. These observations would be expected if the sensory representation of target motion were variable, and most of the variation in pursuit (and perception) arose in that sensory representation.

Anatomy of pursuit How much noise reduction occurs at different levels of the pursuit circuit? Before and after the floccular complex of the cerebellum, for example?

Mean cerebellar responses during pursuit

Variation in cerebellar responses

How strongly do neural responses and firing rate co-vary? We cannot simply correlate firing rate with eye velocity -- it would be comparing apples and oranges. Instead, we apply the inverse model technique, deriving the linear model that can account for average firing rate in terms of the average eye acceleration, velocity, and position. Next we use the average model to predict the firing rate for each individual trial. Finally, we correlate actual firing rate with predicted firing rate. Now we’re comparing apples with apples.

The inverse model predicts average simple spike firing rate well

Co-variation of actual and predicted PC firing

Co-variation of actual and predicted PC firing

Co-variation of actual and predicted PC firing

Co-variation of actual and predicted PC firing

Conventional glimpse of the correlation

Conventional glimpse of the correlation

Firing rate/eye movement correlation across population of Purkinje cells

Conclusions Variation in pursuit behavior can be accounted for in a sensory framework, and has approximately the same variation as perceptual judgments. There is strong trial-by-trial co-variation between firing rate in the cerebellum and eye velocity at the initiation of pursuit. It seems unlikely that we will record the same strong correlations between, say, firing rate in MT and eye velocity (we’re working on this). Therefore, there has been substantial noise reduction between MT and the floccular complex (3 to 4 fold out of 10 fold?) Substantial noise reduction between MT and the cerebellum is consistent with the hypothesis that the variation in pursuit behavior originates heavily from variation in estimating the sensory parameters of target motion.

Collaborators Leslie Osborne Bill Bialek Sonja Hohl Javier Medina Thanks for inspiration and perspiration to: all present and former members of the laboratory and collaborators Thanks for videos to: Don Slaught and David Schoppik Research supported by the Howard Hughes Medical Institute, the Sloan-Swartz Center for Theoretical Neurobiology at UCSF, the National Eye Institute, and the National Institute for Neurological Disease and Stroke