A sensory-motor decoder that transforms neural responses in extrastriate area MT into smooth pursuit eye movements

Visual motion drives smooth pursuit eye movements through a sensory-motor decoder that uses multiple parallel components and neural pathways to transform the population response in extrastriate area MT into movement. We evaluated the decoder by challenging pursuit in monkeys with reduced motion reliability created by reducing coherence of motion in patches of dots. Reduced dot coherence caused deficits in both the initiation of pursuit and steady-state tracking, revealing the paradox of steady-state eye speeds that fail to accelerate to target speed in spite of persistent image motion. We recorded neural responses to reduced dot coherence in MT and found a decoder that transforms MT population responses into eye movements. During pursuit initiation, decreased dot coherence reduces MT population response amplitude without changing the preferred speed at the peak of the population response. The successful decoder reproduces the measured eye movements by multiplication of (i) the estimate of target speed from the peak of the population response with (ii) visual-motor gain based on the amplitude of the population response. During steady-state tracking, the decoder that worked for pursuit initiation failed. It predicted eye acceleration to target speed even when monkeys’ eye speeds were steady at a level well below target speed. We can account for the effect of dot coherence on steady-state eye speed if sensory-motor gain also modulates the eye velocity positive feedback that normally sustains perfect steady-state tracking. Then, poor steady-state tracking persists because of balance between deceleration caused by low positive feedback gain and acceleration driven by MT.

Experiments delivered randomly-interleaved trials with different directions, speeds, and circuit that differentiated frequencies below 25 Hz and filtered out higher frequencies above with 164 gain that decreased at -20 dB/decade. Samples at 1 kHz were saved along with codes that would 165 allow synchronization with neural data. 166 We used FHC single electrodes to map the recording chambers. We found and identified foveal 167 MT based on well-documented responses to motion that were speed and direction tuned and 168 constrained to within several degrees of the fovea of the visual field while the monkey was fixating 169 (Desimone and Ungerleider 1986). TREC tetrodes and Plexon 16 channel S-probes then were used 170 for the majority of the data collection and Plexon Omniplex systems were used for data recording. behavioral trial data and synced for analysis using custom functions written in Julia. 177 We defined coherence as the frame-to-frame probability that a given dot continues at the defined 178 direction and speed of the moving patch versus being moved randomly to another location within 179 the patch ( Figure 1A). It is important to note that coherence operates the same way for local motion 195 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 where t represents time in ms and a, b, and c represent the amplitude, the center, and the width of 196 each Gaussian. The full "sum-of-Gaussians" model M was: 197 = ( , ' , 90, 40) + ( , ( , 170, 60) + ( , ) , 300, 75) + ( , * , 500, 150) + 198 ( , + , 900, 300) + , (2) 199 We used an iterative procedure to end up with sets of parameters that allowed us to fit well the 200 responses of each neuron as a function of stimulus speed and dot coherence. First, we chose initial 201 parameters for each neuron based on the average of its time varying firing rates during pursuit 202 across stimulus speeds but fitting separately for pursuit in the preferred and null directions and 203 separately for 100%, 30%, and 10% dot coherences. Next, we fitted Equation (2)  The decoding equations we used were based on opponent vector averaging: where MTri is the normalized opponent response of the i th MT neuron, real or simulated, and psi is 230 the preferred speed of the i th neuron. The anti-noise term e prevents the decoded values from 231 exploding when firing rate is low, and is treated as a constant based on (Priebe and Lisberger 2004).

232
Decoding by gain modulation of the vector average of MT was calculated as:

233
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made initial rise in eye speeds slows and the maintained eye speeds also fall short of target speed with a 261 slight tendency to decay towards zero (Figure 2A, B). Our question -why eye speeds decline as 262 we reduce dot coherence -might be answered by changes in the peak or amplitude of speed tuning 263 curves in MT or may implicate specific downstream decoding mechanisms. was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 the initiation of pursuit, we measured the mean firing rate for each stimulus speed and dot 271 coherence in the interval from 60 to 120 ms after the onset of motion. Plotting the responses for 272 each dot coherence as a function of stimulus speed revealed clear speed-tuning curves and allowed 273 us to identify a preferred speed for each neuron. , and 10% dot coherences. Time 0 is aligned to onset of local motion. C-E: Average firing rates in spikes per second from 3 example MT neurons for stimulus motion in each's preferred speed and direction for 100%, 30%, and 10% dot coherence. F-H: Speed tuning curves for stimulus motion in the preferred direction as a function of dot coherence for the 3 example neurons. In A-H, the colors of the traces shift from cyan to green to dark green for 100%, 30%, and 10% dot coherences. I: Amplitude of the tuning curves as a function of dot coherence. J: The preferred speed from the tuning curve as a function of dot coherence. In I and J, each black line shows data for a different single neuron and the bold red and royal blue lines with symbols show the averages across all MT neurons recorded in monkeys Ar and Di. Asterisks indicate conditions where the averages differed significantly from those at 100% dot coherence. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint the amplitude of the speed tuning curve decreased but the peak of the curve, representing the 280 preferred speed, did not shift for these individual neurons or for the majority of our sample.

281
Analysis of the full population of neurons from both monkeys (black lines in Figure 2I, J) reveals 282 a consistent effect of motion coherence on the amplitude of the tuning curve, estimated as the 283 difference between the largest and smallest responses across the speeds we presented. We used the 284 difference as a metric of tuning amplitude to avoid the challenges of fitting tuning curves to data 285 that were very weakly tuned at low dot coherences. Most neurons (black lines) and the averages 286 across neurons for each monkey separately (colored lines) showed increases in tuning amplitude 287 as a function of dot coherence. Welch's t-tests revealed significant (p<0.05) differences between 288 the preferred speed amplitudes at 100% coherence compared to both 30% and 10% dot coherence 289 for both monkeys and between 100% and 70% coherence for monkey Ar.

290
The effect of dot coherence on preferred speed, defined as the stimulus speed that elicited the 291 largest response, was more variable ( Figure 2J). Yet, there was no consistent trend of changing  Figure 2J, black lines) showed no effect of dot coherence on preferred speed, 295 but some individual neurons seemed to change preferred speed dramatically sometimes moving 296 from preferring 32 deg/s to 2 deg/s and back to 32 deg/s as coherence changed from 100% to 30% 297 to 10%. Since both those values are at the limit of target speeds we presented, we suspect that the 298 observed chaos results from the challenges of estimating preferred speed for low neural response 299 amplitudes. 300 We looked more closely at the data for individual neurons and verified that most of the apparent 301 effects of dot coherence on preferred speed were the result of low amplitude tuning curves that 302 made it difficult to obtain a valid estimate of preferred speed. We utilized a metric that tested 303 statistically for each tuning curve whether the responses were different between the target speeds 304 that had the lowest versus highest responses on the speed tuning curve. This metric, which we will 305 call the "modulation statistic" gives a sense of whether the responses actually are tuned or, instead, 306 should be considered to be a flat line essentially at noise level. When we pull out the neurons that 307 had significant modulation statistics (p<0.05) over the spread of stimulus speeds we tested and 308 across dot coherences, we see that the preferred speeds for these neurons change very little as a 309 function of dot coherence ( Figure 3A-C). There are a few exceptions with significant modulation 310 statistics across all 3 dot coherences that did show increased or decreased preferred speeds as dot 311 coherence decreased, for example the tuning curves illustrated in Figure 3G-J. Among the neurons 312 with a shift in preferred speed, some increased and some decreased preferred speed with no bias 313 in decreased preferred speed to match the behavior; the majority of preferred speeds did not shift 314 by more than a few deg/s.

315
Neurons whose speed tuning curves did not show significant values of modulation statistic ( Figure   316 3D-F) had more and larger shifts in preferred speed as dot coherence decreased but again showed 317 balanced increases and decreases in speed. We conclude that decreased dot coherence does not 318 alter the preferred speed of MT neurons, but that some speed tuning curves become too noisy to 319 assess preferred speed because response amplitude decreased to the point of the curve becoming a 320 flat line. Because our full sample of neurons represents how dot coherence affects the MT 321 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. population response during our pursuit task, we retained all recorded neurons in the population for 322 all further analyses. Histograms showing how much the preferred speed of each neuron changes when the tuning curve range of the lower dot coherence was statistically significant under a Welch's T-Test with a p-value less than 0.05. Comparisons are between speed tuning curves at 100% versus 30% dot coherences (A) between 30% and 10% (B) and between 100% and 10% (C). D, E, F: The same analysis as in A-C but for neurons where the tuning curve range was not found to be statistically significant. G, H: Example speed tuning curves for 2 neurons where the preferred speed increased by at least 10 deg/s from 100% to 10% dot coherence. I, J: Example speed tuning curves for 3 neurons where the preferred speed decreased by at least 10 deg/s. In G-J, cyan, light green, and dark green show curves for dot coherences of 100%, 30%, and 10%.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint its response for a give set of parameters is plotted as a function of the neuron's preferred speed for 332 100% coherence dots. To assess the population response during pursuit initiation, we measured 333 firing rate in the interval from 60 to 120 ms after the onset of target motion. Firing rates for each 334 neuron are normalized relative to the peak firing for target motion in the preferred direction and 335 the opponent response is computed by subtracting identically-normalized responses to target 336 motion in the null direction. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint identical across graphs because not every neuron from monkey Ar was recorded during every 350 combination of dot coherence and stimulus speed because of trial and experiment constraints at The diagram in the upper right shows our conceptual framework for the flow of sensory information where the command for pursuit initiation results from multiplication of visual drive from estimating target speed by the gain of visual-motor transmission through FEF. A: Initiation eye speed in monkeys' data as a function of the target speed for 3 dot coherences (100%, 30%, and 10%). B: The gain of visual motor transformation based on MT population response amplitude as a function of target speed. C, E: The target speed used to initiate pursuit as a function of decoding by a vector average of the MT population response (C) and as a function of decoding by gain-modulated vector average of MT (E). D, F: Similar to C and E except that the initiation eye speed in monkeys' data is plotted as a function of vector average of MT (D) and gain-modulated vector average of MT (F). In A-F, cyan, green, and dark green lines show data and decodings for 100%, 30%, and 10% dot coherences. G: The difference between image speed and predictions of the two decoders. H: The difference between eye speed and the predictions of the two decoders. In G and H, purple and orange symbols show results for decoding based on an opponent vector average of MT versus a gain-modulated vector average. Multiple symbols at each dot coherence report data from multiple target speeds.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint eye speed 200 ms after the onset of target motion and plotting it as a function of stimulus speed 360 ( Figure 5A). In general, eye speed is less than stimulus speed. We then asked how to decode the (Churchland and Lisberger 2001a). If the real decoder follows the traditional strategy, then we 365 would expect the opponent vector average to predict the observed non-linear relationship of eye 366 speed to stimulus speed and dot coherence. Instead, the opponent vector-averaging decoder 367 predicts an output that is very close to actual stimulus speed regardless of target speed or dot 368 coherence ( Figure 5C). As a consequence, the decoder consistently overestimates eye speed 369 ( Figure 5D). We conclude, in agreement with previous studies that degraded stimulus contrast 370 (Krekelberg et al. 2006;Pack et al. 2005), that deficits in eye speed due to low dot coherence 371 probably do not occur simply because area MT underestimates target speed.  Decoding the recorded MT population response supports our conclusion that gain-modulation of 396 a vector averaging decoder is necessary to account for the effects of stimulus speed and dot 397 coherence on eye speed in the initiation of pursuit. However, there are some caveats. First, our 398 recorded population is small compared to the actual number of neurons in area MT. Second, we 399 used target speeds from 2 to 32 deg/s and so our population is limited to preferred speeds between 400 2 and 32 deg/s whereas MT contains many neurons that respond, and have preferred speeds, 401 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint outside of the range we used. Below, we address these issues by generating a larger simulated 402 population that evenly tiles a larger range of preferred speeds. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10. 1101/2023 curve to align to the selected preferred speed while keeping the height and width of the tuning 421 curves constant, the latter in log2 coordinates. We then used image speed to predict the normalized 422 firing rate from each model neuron in the simulated MT population for the initiation of pursuit or 423 during steady-state tracking.

424
The data and the simulated population overlap reasonably well during pursuit initiation for patches 425 of dots with both high (Figure 6A, C) and low coherence ( Figure 6B, D). However, the same is 426 not true during steady-state tracking ( Figure 6E-H). The most egregious failure of the speed tuning 427 curve during steady-state tracking is for motion of 100% coherence dots at 16 deg/s ( Figure 6G was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint leaving 100 neurons. We performed the same procedure for responses to target motion in the null 463 direction so we could calculate opponent responses as we did with the data.

464
Once we had the 100 templates ( Figure 7C, D) we created a model population response with a 465 variation of the same procedure used before. We drew 2058 sets of templates at random from our 466 100 neuron fits and randomly assigned each set with a preferred speed from the range of 1 to 64 467 deg/s in intervals of 0.125 in log base 2. We then shifted the speed tuning of each set of templates 468 so that it matched the randomly assigned preferred speed. After shifting, we had to interpolate and 469 extrapolate to generate model responses to the specific target speeds in our stimulus set. For target 470 speeds that fell within the five speeds we tested, we interpolated between the parameters of the 471 model. For target speeds that fell outside the five speeds we presented, we computed the average 472 change in each amplitude parameter across the speeds we did have fits for and used that estimate 473 to extrapolate in log2 coordinates to create responses to the target speed.  Figure 6 for predicted activity based on the sum-of-Gaussians fits to the data.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint with measurements from the actual data ( Figure 7E-L). Here, we averaged each model neuron's 478 response in intervals from 60-120 ms after onset of target motion for pursuit initiation and from 479 660-720 ms after onset of target motion for steady-state tracking and plotted the measurements as Inspection of Figure 2A and B reminds us of the conundrum during steady-state tracking: eye 532 speed lags behind target speed, especially for lower dot coherences, so there is a non-zero image 533 speed that fails to cause the eye to accelerate up to target speed. Now, we attempt to understand 534 the basis for the conundrum by analyzing the activity of MT neurons during steady-state tracking.

535
A key difference exists between the visual conditions during pursuit initiation versus steady-state 536 tracking because the eye moves along with the target during steady-state tracking. The difference 537 between the target speed and eye speed produces an image speed on the fovea. For 100% coherence 538 patches of dots, the difference between target and eye is minimal and the target is almost stationary 539 relative to the fovea as the eye moves, but for lower dot coherences (or the highest target speeds 540 at 100% coherence), eye speed is persistently slower than target speed and requires occasional 541 saccades to keep the target foveated. Also, the background produces oppositely-directed motion 542 across much of the retina. By analyzing MT activity during steady-state tracking, we sought to 543 determine if the visual representation of motion emanating from MT during steady-state tracking 544 represents image speed positively, in which case we would need to invoke additional downstream 545 deficits that prevent the required eye acceleration to catch up to the target. 546 We characterized the relationship between image speed and change in eye speed during steady-547 state tracking by measuring firing rate in the interval from 600 to 660 ms after target motion onset 548 and the change in eye speed in the interval from 660 to 780 ms after target motion onset. We used 549 the change in eye speed as our metric for steady-state eye movement versus the absolute eye speed 550 for the initiation of pursuit, but they are actually homologous because the eye speed during pursuit

555
When the moving target was 100% coherence dots, targets speeds less than 16 deg/s caused almost 556 perfect tracking so that image speed was small and change in eye speed negligible when target 557 speed ( Figure 9A, 4 of the 5 light green symbols). The one outlier symbol at an image speed of 10 558 deg/s and eye acceleration of -4 deg/s was for target speeds of 32 deg/s, when our monkeys did 559 not sustain eye speed close to target speed even for 100% coherence dots. The data for low dot 560 coherences agree qualitatively with the data for 100% coherence. In each case, especially the 561 higher target speeds caused the eye to lag behind the target and we measured and modest negative 562 changes in eye speed in spite of significant positive image speeds ( Figure 9A). The relationship 563 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 between change in eye speed and image speed was reasonably linear for each dot coherence, with 564 decreasing slopes as dot coherence decreased, meaning higher image speeds at a given target speed 565 ( Figure 9A). We attribute the relatively poor tracking for target motion at 32 deg/s to the high 566 density of slower target speeds in our stimulus set and its effect on the priors used by pursuit to 567 control the gain of visual-motor transmission and therefore eye speed (Darlington et al. 2017).

568
The same decoders used to predict image speed or (change in) eye speed successfully during 569 pursuit initiation failed to capture either during steady-state tracking. The opponent vector average 570 of MT activity during steady-state tracking overestimates image speed for most conditions (purple 571 symbols, Figure 9C, D); it predicts large, positive eye speeds (purple symbols, Figure 9C, D) for 572 both the data and model population responses. Gain-modulated vector averaging underestimates 573 image speed severely (yellow symbols, Figure 9C, D) and predicts positive changes in eye speed 574 when the eye is actually stable or decelerating (yellow symbols, Figure 9E, F). In summary, image 575 speed during steady-state tracking is captured poorly by both decoders while even gain-modulated 576 vector averaging consistently misestimates the sign of the change in eye speed, calling for eye 577 acceleration when we observe eye deceleration. We conclude that the visual signal is much more muddied during steady-state tracking when sum-of-Gaussians MT population response. In A and B, cyan, green, and dark green show results for 100%, 30%, and 10% dot coherences. C-F: The difference between data and the predictions of decoders for based on the model population response (C, E) and the actual data (D, F). C and D show results for image speed; E and F show results for eye speed. In C-F, purple versus orange box and whiskers and symbols show results for decoding with opponent vector average of MT versus a gain-modulated vector average. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint dot coherence. At the same time, the good agreement between the results of decoding the data 586 versus the model MT population responses provides additional support for the accuracy of the 587 sum-of-Gaussians modeling strategy.

588
MT neurons respond appropriately to imposed image motion during steady-state tracking 589 One possible explanation for the pursuit system's tolerance of persistent image motion during 590 steady-state tracking is that MT is no longer responding to motion in a way that the pursuit system 591 can use. Therefore, we next ask how individual neurons and the population in MT respond to 592 perturbations that cause image speed during steady-state tracking and how those responses 593 compare to what is expected given our data for pursuit initiation. We imposed pulses of target 594 speed during steady-state tracking to afford explicit control of image speed. . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 Individual neurons in MT respond to pulses of target motion during steady-state tracking in a way in spite of active visual motion drive. The same phenomena play out when we deliver speed and coherence pulses, though transiently.

692
The speed pulse ( Figure 12B) drives eye acceleration comparable to that during pursuit. It is larger 693 and more transient for 100% dot coherence than for 10% dot coherence. During steady-state 694 pursuit, the visual drive perfectly balances the motor command for deceleration for 10% dot 695 coherence. A pulse of target coherence from 100% to 10% and then back to 100% ( Figure 12C, 696 black dashed trace) creates a transient motor command for deceleration that dynamically balances 697 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 with the subsequent visual drive for eye acceleration. Both return to normal when dot coherence 698 returns to 100%. The model explains why the eyes stabilize at speeds below target speed during pursuit of low 702 coherence dots even though visual motion drive for eye acceleration is still present. This is 703 reinforced by our recordings in MT that demonstrate speed representations appropriate to cause 704 positive eye acceleration during steady-state tracking. Thus, the slow eye speeds during steady-705 Figure 12: A control theory model of pursuit explains how steady-state eye speed can fail accelerate to target speed. The top diagram shows the control theory model used in Behling and Lisberger (2020) and derived from the model of Churchland and Lisberger (2001). A-C: The top row of graphs plots eye speed in degrees per second as a function of time from onset of target motion in milliseconds. Blue and red traces show eye speeds for targets with 100% and 10% coherence. The middle and bottom rows of graphs plot eye acceleration commands separately for visual and motor components of the model, as a function of time from onset of target motion. Black traces show target speed. Solid and dashed green traces show visual eye acceleration commands for 100% coherence and 10% coherence. Solid and dashed purple traces show the motor component of eye acceleration for 100% and 10% coherence. The dashed black trace shows the total acceleration command for 10% coherence. A: Initiation and steady-state pursuit without a pulse of speed or coherence. B: Response to a speed pulse of 5 deg/s during steady-state tracking. C: Response to a pulse of dot coherence (shown with the black dashed line in the upper panel).
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023 state tracking are not from a misrepresentation of speed within the pursuit system but rather reflect 706 the impact of poor motion reliability on both the sensory feedforward and motor feedback 707 components of the system, in different ways that ultimately balance each other out.

709
Discussion 710 We began this project with the goal of using changes in motion reliability to better understand how 711 the representation of visual motion in area MT is transformed in downstream circuits to generate 712 both the initiation and steady-state of smooth pursuit eye movements. In our previous paper 713 (Behling and Lisberger 2020), we changed the coherence inside a patch of moving dots to control 714 motion reliability and observed that reduced dot coherence causes persistent deficits in eye speed 715 at the initiation of pursuit initiation as well as stable eye speeds that were slower than target speed 716 during steady-state tracking. We were perplexed by the failure of the pursuit system to correct the 717 persistent image motion during steady-state tracking. Thus, one of our major goals here was to 718 determine why eye speeds slower than target speed were tolerated as well as why eye speed at the 719 initiation of pursuit was affected by dot coherence. Our analysis provides an explanation for both 720 effects, an explanation that is couched in terms of the functional organization of the sensory-motor 721 decoder and its possible implementation in neural circuits.

722
Our strategy was to record from a major source of visual motion signals to drive pursuit, 723 extrastriate area MT (Born et al. 2000;Groh et al. 1997;Newsome et al. 1985) and quantify how 724 changes in dot coherence change the output of MT throughout the initiation and steady-state of a 725 pursuit tracking movement. We then used our data to ask not how target motion is transformed 726 into eye motion, but rather how the downstream sensory-motor decoder might decode output from 727 MT into the observed initiation and steady-state of pursuit. Our approach changes the strategy for 728 creating models of the pursuit system and thinking about how sensory signals are decoded by using 729 the MT population response as the input to a sensory-motor decoder, instead of using the 730 kinematics of target motion as the input. 731 We find that decrease dot coherence alters the amplitude but not the preferred speed of MT neurons 732 during the initiation of pursuit. We also find that the responses of MT neurons during steady-state 733 tracking are predicted poorly by their speed tuning during pursuit initiation, not a surprising finding 734 given that MT neurons have complex responses to motion outside the classical receptive field (e.g.

735
Born and Tootell, 1992) and the existence of large field image motion in the direction opposite to 736 eye and target motion during steady-state tracking, because the eyes are moving across a stationary 737 background. Because of the inability of speed tuning curves to predict MT responses during 738 steady-state tracking, we developed a descriptive model of the full MT response during pursuit.

739
Our "sum-of-Gaussians" model is not intended to reproduce any mechanisms of MT responses, 740 but rather to provide an accurate description that can be used in future computational models of 741 the pursuit circuit. The fact that we obtained essentially the same answers from decoding the 742 population response from actual data and a larger, more homogeneous model population response 743 implies that our model provides a reasonable description of the actual MT population response.

744
Our laboratory has developed a concept of the sensory-motor decoder for pursuit that is based on 745 the anatomy of the pursuit system and evidence that parallel downstream pathways perform 746 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made   image speed during steady-state tracking. We also used changes in dot coherence pulses to verify 789 that MT had machine-like responses to dot coherence during steady-state tracking. We conclude Figure 13: Conceptual model of the sensory-motor decoder for pursuit. Green pathways show the control of sensory-motor gain, blue pathway shows visual drive by estimates of target speed, red pathway shows motor feedback that sustains steady-state eye speed. The circles with "X" inside represent sites of multiplication where gain modulates other signals.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ; https://doi.org/10.1101/2023.05.12.540526 doi: bioRxiv preprint that area MT continues to provide viable visual motion drive during steady-state tracking that 791 should be driving the eye speed up to target speed. Thus, a third pathway was needed.

792
In Figure 13, the third pathway uses extraretinal signals related to eye movement as positive 793 feedback to sustain eye speed. Corollary discharge through the floccular complex of the 794 cerebellum has long been thought to be the substrate of the positive feedback (Lisberger and Fuchs 795 1978a; Stone and Lisberger 1990). To account for the paradox that the output from MT during 796 steady-state tracking of low-coherence dots should, but does not, drive eye acceleration up to target 797 speed, we propose that the visual-motor gain signal from FEFSEM also controls the gain of the 798 positive feedback. Then, reduced dot coherence should cause a tendency for steady-state eye speed 799 to decelerate, meaning that the eye acceleration command from MT needs to counteract the 800 deceleration merely to keep eye speed steady at less than target speed. Our control theory model 801 shows the plausibility of this explanation, even though biological details will need to be the topic 802 for future research.

803
The most parsimonious explanation for the deficits in pursuit during steady-state tracking of low 804 dot coherence targets is that the visual drive signal still is present and used by the pursuit system 805 and the downstream motor system is modulated instead. We anticipate that the same explanation decreases visual drive paired with loss of commands that normally sustain eye speed automatically. 812 We propose that there is parallel modulation of the sensory and motor paths before they integrate 813 to drive eye movements. Our findings build on previous work and provide a novel perspective in 814 the nuances and subtleties of sensory-motor control in an accessible and well-known system.

815
Future investigation of the responses in FEFSEM and the floccular complex of the cerebellum will 816 help pin down the implementation of our observed parallel modulation. 817 818 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 13, 2023. ;https://doi.org/10.1101https://doi.org/10. /2023