102:110-118, 2009. First published Apr 15, 2009;  doi:10.1152/jn.91320.2008 J NeurophysiolAbtine Tavassoli and Dario L. Ringach

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Dynamics of Smooth Pursuit Maintenance

Abtine Tavassoli and Dario L. RingachDepartments of Neurobiology and Psychology, Jules Stein Eye Institute, David Geffen School of Medicine, University of California,Los Angeles, California

Submitted 15 December 2008; accepted in final form 10 April 2009

Tavassoli A, Ringach DL. Dynamics of smooth pursuit maintenance.J Neurophysiol 102: 110–118, 2009. First published April 15, 2009;doi:10.1152/jn.91320.2008. Smooth pursuit eye movements allow theapproximate stabilization of a moving visual target on the retina. Tostudy the dynamics of smooth pursuit, we measured eye velocityduring the visual tracking of a Gabor target moving at a constantvelocity plus a noisy perturbation term. The optimal linear filterlinking fluctuations in target velocity to evoked fluctuations in eyevelocity was computed. These filters predicted eye velocity to novelstimuli in the 0- to 15-Hz band with good accuracy, showing thatpursuit maintenance is approximately linear under these conditions.The shape of the filters were indicative of fast dynamics, with puredelays of merely �67 ms, times-to-peak of �115 ms, and effectiveintegration times of �45 ms. The gain of the system, reflected inthe amplitude of the filters, was inversely proportional to the sizeof the velocity fluctuations and independent of the target meanspeed. A modest slow-down of the dynamics was observed as thecontrast of the target decreased. Finally, the temporal filters recov-ered during fixation and pursuit were similar in shape, supportingthe notion that they might share a common underlying circuitry.These findings show that the visual tracking of moving objects bythe human eye includes a reflexive-like pathway with high contrastsensitivity and fast dynamics.

I N T R O D U C T I O N

Smooth pursuit eye movements allow a moving visual targetto be stabilized on the retina. The system is configured as anegative feedback loop: retinal slip velocity (the error signal) isthe difference between the desired target velocity and actualeye velocity (Keller and Heinen 1991; Lisberger et al. 1987;Robinson et al. 1986; Thier and Ilg 2005). A useful strategy instudying smooth pursuit consists in measuring how motionsignals are integrated in space and time to drive eye move-ments and comparing the results to the integration properties ofneurons selective to visual motion in the brain (Born and Pack2002; Born et al. 2006; Heinen and Watamaniuk 1998; Masson2004; Masson et al. 2000; Osborne and Lisberger 2007; Os-borne et al. 2005, 2007; Schoppik et al. 2008; Spering andGegenfurtner 2007). In particular, an important feature of thissystem is the pure delay between the onset of retinal imagemotion and the onset of smooth pursuit eye movements, whichplays a key role in establishing limits on stability and gain ofpursuit (Goldreich et al. 1992; Krauzlis and Lisberger 1994;Lisberger et al. 1987; Ringach 1995; Robinson et al. 1986).

One way in which the delay between the onset of imagemotion and the onset of eye motion has been estimated inprevious studies is by means of the step-ramp paradigm, where

a fixated visual target jumps in one direction and immediatelystarts moving in the opposite direction at a constant velocity(Rashbass 1961; Robinson 1965). For an appropriate size ofthe initial step, this stimulus evokes smooth pursuit initiationwithout the occurrence of early saccades, facilitating the esti-mation of latency (Carl and Gellman 1987; Rashbass 1961;Robinson 1965). Using a variety of visual targets, pure delaysduring the initiation of smooth pursuit in human subjects arefound to be broadly distributed between 100 and 300 ms(Braun et al. 2008; Knox 1998; Lindner and Ilg 2000; Rashbass1961; Robinson 1965; Spering et al. 2005). The shortestlatencies of pursuit initiation have been obtained in a “gap-paradigm,” where the fixation is extinguished 100–200 msbefore the onset of the target, yielding delays of �90 ms(Krauzlis and Miles 1996b).

Mathematical analysis and numerical simulations haveshown that, if such long and variable latencies were to applyduring the maintenance phase of pursuit, they could create agrave problem, because achieving gains near one would alsomake the system unstable and prone to oscillations (Goldreichet al. 1992; Krauzlis and Lisberger 1994; Ringach 1995;Robinson et al. 1986). Notably, measurements of pursuit la-tency during its maintenance phase tend to be on the low endof the distribution of values obtained for pursuit initiation.Indeed, delays of �93 ms were reported in response to stepincreases in target velocity during pursuit (Behrens et al.1985); around �110 ms in response to brief, biphasic pertur-bations of target velocity (a single cycle of a sinusoidalfunction) (Churchland and Lisberger 2002); and �85 ms inresponse to a positional error induced by a briefly flashedvisual stimulus near the target (Blohm et al. 2005). Thus itseems plausible that the delays during pursuit maintenancemight actually be considerably smaller than those inferred fromthe initiation of the movement. One aim of this study was tore-examine the measurement of latencies during pursuit initi-ation and maintenance in the same subjects and the same visualconditions.

Another important goal of our experiments was to measurethe detailed dynamics of pursuit maintenance and assess itslinearity. We approached this problem by having subjects tracka small Gabor target moving at a constant velocity plus awhite-noise perturbation signal (Fig. 1). From these data, wecomputed the optimal linear filter that linked fluctuations in thevelocity of the target to the evoked fluctuations in eye velocity(Mulligan 2002; Osborne and Lisberger 2007). By analyzingthe shape of the resulting temporal filters, we were able toestimate not only pure delays but also the time-to-peak of theresponses and the integration time of the system. Importantly,once the optimal linear filter was recovered, we were able totest the linearity of pursuit maintenance by predicting the mean

Address for reprint requests and other correspondence: D. L. Ringach, Dept.of Neurobiology and Psychology, Jules Stein Eye Inst., David Geffen Schoolof Medicine, Univ. of California, Los Angeles, CA 90095 (E-mail:dario@ucla.edu).

J Neurophysiol 102: 110–118, 2009.First published April 15, 2009; doi:10.1152/jn.91320.2008.

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eye velocity in response to novel stimuli and assessing itsgoodness-of-fit to the measured responses.

To anticipate the results, we found that pursuit maintenanceis surprisingly fast and well-described as a linear system. Puredelays estimated by white-noise analysis were noticeablysmaller than those obtained for pursuit initiation in a step-rampparadigm or in response to brief biphasic perturbations of thetarget velocity during pursuit. The gain of the system waslargely determined by the SD of the target velocity fluctua-tions, decreasing as the size of the fluctuations increased.Interestingly, the linear filters obtained during pursuit andfixation were similar in shape to each other, supporting thehypothesis they might share a common mechanism of gazestabilization (Krauzlis 2004). These findings indicate that thevisual tracking of moving objects by the human eye includes areflexive-like pathway with high contrast sensitivity and fastdynamics.

M E T H O D S

Stimulus generation and presentation

Observers were seated in a dimly illuminated room facing aViewsonic G225f monitor with a refresh rate of 120 Hz at a viewingdistance of 100 cm. The active screen area subtended 22° of visualangle in the horizontal direction and 15° of visual angle in the verticaldirection, and the screen resolution was 1,024 � 768 pixels. Thescreen was viewed binocularly, but only the movements of the righteye were monitored. The subject’s head was stabilized by a chin restand a support for the forehead. Visual stimuli were generated using aCambridge Research Visage system under the control of Matlab. Thevisual target consisted of a Gabor patch constructed with a verticallyoriented sinusoidal grating with a spatial frequency of 1 cycle/° as thecarrier, multiplied by a Gaussian window with an SD of 0.2° (Gegen-furtner et al. 2003). The Gabor was antisymmetric, and the phase was

randomly changed between 0 and 180° from trial to trial. Each trialstarted with the subject fixating a Gabor patch located at the center ofthe screen. After a 0.5-s delay, the target would jump to �5° along thehorizontal meridian and start moving in the opposite direction. Thedirection of drift was randomized from trial to trial. As our analysisdepends on the collection of sufficiently large steady-state pursuit seg-ments, we maximized the duration of each trial by using a large initialjump. The Gabor patch moved rigidly with a position given byx�t� � x�n�t� � �5°�V0�n � 1��t � �k�0

n N�k�t��t. Here, n � 0,1, . . . represents the nth frame in the stimulus sequence, �t is theframe duration (in our case, 1/120 Hz or 8.33 ms), t � n�t representstime from the onset of the motion, V0 represents the mean velocity ofthe stimulus, and N(k�t) represents a Gaussian perturbation drawnindependently for each frame with an SD of �s.

We collected data at baseline velocities of V0 � 2, 4, 8, and 16°/sand perturbation SD of �s � �V0, where the SD factor � � 0.125,0.25, 0.5, and 1. We also collected data for a “fixation” conditionwhere V0 � 0 and �s � 0.5, 1, 2, 4, 8, and 16°/s.

To compare the smooth pursuit latencies estimated during pursuitmaintenance with those obtained in pursuit initiation, we ran sessionsof step-ramp trials. For these trials, the initial jump was of �0.5°, andthe stimulus was moving at a constant velocity of 4°/s without anyvelocity noise. We estimated the latency in each individual trial as theintersection of two regression lines of the eye position trace (sampledat 1 kHz): one to the baseline before the onset of movement andanother to the trace during the tracking (Carl and Gellman 1987). Wealso tried a method based on the velocity signal, computed bydifferentiation of the position signal and filtering by a Hammingwindow of length 81 samples. The intersection of the regression of therising phase of the velocity signal with zero provided an estimate ofthe latency in each trial (Krauzlis and Miles 1996a). This secondmethod resulted in a distribution of latencies that was not statisticallydifferent from the one based on position (data not shown).

We also measured eye velocity responses to brief temporal pertur-bations of the target velocity consisting of a single cycle of a sinewave during tracking (Churchland and Lisberger 2002; Schwartz andLisberger 1994). The perturbation cycle had a frequency of 5 Hz,amplitude of 2.83°/s, and a mean velocity of 4°/s. The amplitude valuewas chosen to match an SD of 2°/s for the perturbation signal. In 25%of the trials, the velocity initially increased during the perturbation(peak-first condition), in another 25% of the trials, the velocityinitially decreased (peak-last), and in the remaining 50% of the trials,there was no perturbation (no perturbation condition). For eachsubject, a total of 400 trials were measured with these conditionsrandomly interleaved.

Observers

The two authors [males, age 30 (A.T.) and 43 yr (D.R.)], bothtrained psychophysical observers with normal (A.T.) and corrected tonormal vision (D.R.), participated in all the experiments. Four naïvesubjects [males, age 46 (Z.L.), 20 (P.L.), 30 (J.F.), and 70 yr (D.T.)],with normal vision but no prior psychophysical experience, weretested on a subset of experiments to verify the consistency of the mainfindings across experienced and naïve subjects. All the experimentswere conducted with the approval of the Chancellor’s Office for theProtection of Research Subjects at UCLA, with subjects providingtheir informed consent.

Eye movement recording and processing

Eye movements were recorded by an SR-Research Eyelink-IIsystem at a sampling frequency of 1 kHz. Each session consisted of100 pursuit trials, with nine-point calibration stimuli interspersedevery 25 trials. Each trial began with the Gabor patch centered on thescreen and the subject indicating his readiness by pressing a button.Eye position data were sampled at 1 kHz and saved on disk for later

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FIG. 1. Experimental design. A small Gabor target (top), jumps horizon-tally to the left or right and moves in the opposite direction with a meanvelocity V0. Riding on top of this mean velocity, there is a discrete-time,Gaussian white-noise signal, with an SD �s (middle). The resulting position ofthe target over time, obtained by integration of the velocity signal, is shown atthe bottom. Eye velocity during smooth pursuit segments in response to suchstochastic motion trials were isolated and analyzed. The best linear filterlinking the stimulus and eye velocity fluctuations about their means estimatedby cross-correlating the 2 signals.

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processing. These traces were subsequently differentiated and sub-sampled at 120 Hz using Matlab’s resample function. This broughtboth eye and target velocity signals to a common sampling frequencyof 120 Hz. Saccades were automatically detected by thresholding thevelocity trace at 4 SD of the average eye velocity fluctuations. Datasegments from within 100 ms of detected saccades (either before orafter) were excluded from analysis, as was the initiation of pursuit.Different saccade detection algorithms were tried, leading to similarresults. Thus our findings were not sensitive to this preprocessing step.

The optimal linear filter was computed by the cross-correlation ofthe velocity perturbation signal, N(n�t), and the eye velocity signal,Veye(n�t), at time lags corresponding to integer number of stimulusframes. The result, normalized by the variance of the target velocityfluctuations, results in the estimated impulse response of the system,h(n�t) (Mulligan 2002). The data points in Fig. 2A show the estimatedcorrelation values at these intervals.

An important technical point must be included here regarding thestimulus and data timing. Note that as defined above, N(k�t) repre-sents the instantaneous velocity between the k 1-th and kth frame inthe stimulus sequence. However, our eye data collection was triggeredwith the vertical sync pulse of the monitor before the presentation of

the first frame in the stimulus sequence. Because the stimulus isshown approximately half a frame later (because it appears in themiddle of the screen), these two offsets cancel each other out, so thereis no need for a correction of the timing.

Because of the surprisingly short delays observed in our data, wetook extreme caution to ensure that the timing of the signals wasaccurate. Both the eye movement data and the TTL signal from theVisage system were sampled and time-stamped by the Eyelink-IIboard, thus preventing any issues arising from clock synchronizationacross machines. The appearance of the TTL signal at the VSYNCpreceding the first stimulus frame was verified by monitoring the TTLsignal and the output of a photocell pointing at the center of the screenwith an oscilloscope during the flashed presentation of a brightstimulus on the first frame of a stimulus sequence.

Analysis of the shape of the linear filters

From each measured impulse response, we estimated its latency,time-to-peak, and half-width at half-height (or effective width) asfollows. First, we calculated the mean baseline response at times t 0. This provides one line in the graph we define as L1. Second, we

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FIG. 2. A linear model provides a reasonable description of pursuit maintenance. A: optimal temporal filters estimated in 1 stimulus condition (a baselinevelocity of 4°/s and a Gaussian perturbation noise with an SD of 2°/s) for 5 subjects. The pure delay, time-to-peak, and full-width at half-height were estimatedfrom the linear regression to the slopes of the dominant peak and the baseline (blue lines in bottom graph). B: predicted vs. measured velocity traces. Gray linesshow the mean eye velocity in response to pursuit of the same perturbation noise (average of 20 trials). Red curves show the predicted response obtained byconvolving the impulse response with the stimulus noise. The impulse response was measured from a different set of noise trials. C: scatterplot of measured vs.predicted eye velocity fluctuations show no obvious nonlinearity (such as saturation of response). Red points show the average eye velocity for different windowsof predicted eye velocity. Correlation coefficients between predicted and measured responses are in the inset.

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found the sample points that were closest to the half-maximum valueof the kernel on both sides of the peak. These samples, along with fourof their immediate neighbors (2 on each side), were used to computetwo additional regression lines: L2, fitting the rising phase of theresponse; L3, fitting the falling phase of the response. The intersectionbetween L1 and L2 defined our estimate of latency. The intersectionbetween L1 and L3 defined our estimate of decay (Fig. 2A, bluedashed lines in the bottom panel for observer D.T.). The differencebetween decay and latency times divided by two provides an estimateof full-width at half-height.

Linear predictions

We selected a set of five noise patterns to be used repeatedly indifferent trials. These five perturbation patterns were presented 20times each, in different directions, in a 100-block trial. The mean eyevelocity in response to each perturbation was computed. The impulseresponse estimated from a different set of noise trials was used topredict this response by convolving it with the actual perturbations.The data shown in Fig. 2 were obtained at V0 � 4°/s and �s � 2°/s.The coherence between predicted and measured signals was computedusing Matlab’s cohere function. For the prediction of responses to thesine-wave perturbation (Fig. 5), we simply convolved the waveformwith the impulse response estimated for V0 � 4°/s and �s � 2°/s,because these have matching values of mean velocity and SD.

R E S U L T S

Examples of the optimal linear filters recovered duringpursuit of a target with mean velocity V0 � 4°/s and perturba-tion size of �s � 2°/s are shown in Fig. 2A. The filters had anearly dominant peak followed, in two experienced subjects(subjects A.T. and D.R.), by weaker ringing at later times.Naïve subjects (Z.L., P.L., and D.T.) showed somewhatbroader peaks and no obvious ringing. We concentrate here onthe dominant peak, which can be characterized by its latency,time-to-peak, and full-width at half-height (or effective width).The delays and time-to-peaks were reasonably consistentacross subjects, with delays of �67 ms and times-to-peak of�115 ms (Fig. 2A). Assuming linearity, the temporal filterrepresents the expected response to a brief velocity pulse ofunit area and therefore is sometimes referred to as the impulseresponse of the system.

To assess the ability of these filters to account for eyevelocity responses during pursuit, we measured the meanresponse to the repeated presentation of the same noise pertur-bation (total of 5 noise patterns repeated 20 times each inrandom order and drift direction) and compared it with theprediction generated by convolving the stimulus with theimpulse response. We found that predicted and measuredvelocity traces matched very well (Fig. 2B, gray lines representmeasured responses and red lines represent the predictions).We observed no obvious nonlinear relationships (such ascompressive nonlinearities) between the predicted and mea-sured responses (Fig. 2C), and the average correlation coeffi-cient between the signals was 0.62 � 0.06 (SD). Note that thepredictions seem to account better for the slower temporalcomponents in the response (Fig. 2B). This is made evident inthe shape of the empirical coherence between the predicted andmeasured responses (Fig. 3), which peaks at �5 Hz, reachingvalues as high as 0.85, and it is significant up to frequencies of15 Hz, confirming the ability of the pursuit system to followhigh temporal frequencies (Goldreich et al. 1992).

We estimated linear filters for various combinations of meanvelocity and perturbation size in two subjects. Across all theseconditions, pursuit dynamics were consistently fast, with adelay of �65 ms (68.5 � 3.0 ms for A.T. and 61.5 � 4.0 msfor D.R.), a peak response of �110 ms (110.4 � 4.4 ms forA.T. and 99.2 � 4.5 ms for D.R.), and a full-width at halfheight of �40 ms (42.1 � 2.8 ms for A.T. and 37.1 � 3.5 msfor D.R.). Notably, when latencies were measured during theinitiation phase of pursuit using a step-ramp paradigm underthe same experimental conditions and in the same subjects, theoutcome was a distribution of significantly longer latencies,averaging 155 ms (Fig. 4; 1-sided t-test, P 1010). Thisshows that estimating pure delays during the initiation andmaintenance of pursuit yields different values, even whenperformed on the same subjects and with identical visualtargets.

A previous study estimated the latency pursuit to briefvelocity perturbations during tracking at �110 ms (Churchlandand Lisberger 2002). Because this value is higher than the onesestimated by our technique, we replicated their paradigm togain insight into the reasons behind the discrepancy. The meanresponses to one sinusoidal cycle perturbing the velocity of atarget moving at a baseline speed of 4°/s is shown in Fig. 5. Foreach of the five subjects, we measured the average eyefluctuations evoked by a perturbation of a single sinusoidalcycle with its peak coming first or last (Fig. 5, top) and to acontrol condition where the perturbation was absent. Theamplitude of the sinusoid was 2.83°/s, so that its effectiveSD was �s � 2.83/�2 � 2 °/sec. The red lines show the predictedeye fluctuations obtained by convolving the stimulus waveformwith the optimal filter estimated independently from our white-noise experiments with V0 � 4°/s and �s � 2°/s. The predic-tions provide a good fit to the responses, accounting for anaverage 60% of the variance in the traces. Two curious trendscan be observed in these data that seem to indicate systematicdepartures from linearity. First, there is a tendency for thepredictions to peak-first stimuli to be better than peak-last.Second, the initial phase of the responses appear to be better fitthan the later phase. Despite these differences, the fact that onecan predict �60% of the total response variance to such stimuliby linear filters obtained from completely different measure-ments is remarkable.

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FIG. 3. Coherence between linear predictions and measured responses. Thegraph shows that linear predictions account for a substantial amount of theresponse variance within the 0- to 15-Hz band in 5 subjects.

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The estimated delays in these experiments (indicated byshort vertical line segments in each trace) ranged between 89and 115 ms. These values are in fact closer to those obtained byChurchland and Lisberger (2002) but are still higher than theones obtained by the analysis of the optimal linear filters.

How could the linear prediction (which is based on theoptimal linear filters) be reasonably accurate while the result-ing delay estimates be clearly higher? The reason is that thesinusoidal shape of the perturbation makes the stimulusramp-up slowly at what is considered to be the onset of theperturbation. This causes any initial response to be small andsusceptible to masking by noise, leading to a consequentoverestimation of the latency. The fact that our linear predic-tions accurately predict the responses to the sinusoidal pertur-bations shows a self-consistency between these two datasetsand provides yet another measure of the linearity of the system.

Next, we analyzed the family of filters obtained by runningthe experiment with different combinations of the baselinevelocity, V0, and perturbation size,�s. We ran all combinationsof baseline velocities of V0 � 2, 4, 8 and 16°/s and noise SDof �s � �V0, where � � 0.125, 0.25, 0.5, and 1. The resultingfilters for all these conditions in two subjects are shown in Fig.6A. To analyze the variability in filter shapes across all condi-tions, we calculated the singular-value decomposition andfound the spectrum to be dominated by the first eigenvalue(Fig. 6B, inset). This means that the entire set of filters can bereasonably approximated by the scaling of a single profile (asshown in Fig. 6B). When the gain of the filter was plottedagainst the SD of the noise, all points fell onto a single curve(Fig. 6C), meaning that gain was largely determined by the sizeof the velocity fluctuations. The curve shows an inverse rela-tionship between the size of the fluctuations and the gain of thefilter.

To obtain some information about the likely visual pathwaysinvolved in driving these fast responses, we asked how theoptimal filter depended on the contrast of the visual target(Spering et al. 2005). Consistent with prior reports, we foundan increase in the latency, time-to-peak, and effective widthincrease with decreasing target contrast, implying a slowingdown of the dynamics as the stimulus weakened (Fig. 7A)

(Mulligan 2002; Spering et al. 2005). Nevertheless, even forthe smallest contrast tested, the latencies never went above 80ms, and effective widths never exceeded 65 ms (Fig. 7B).

Finally, to test the hypothesis that fixation and pursuit mayshare similar underlying mechanisms of gaze stabilization, wecompared the shape of the optimal filters obtained duringsteady-state pursuit and in a “fixation” condition, where thebaseline velocity of the target was zero. The amplitude of theoptimal temporal filters in the fixation condition were smaller

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FIG. 5. Responses and linear predictions to brief sinusoidal perturbations.A single-cycle sinusoidal perturbation was introduced during the tracking of aGabor target (top), as previously done by Chruchland and Lisberger (2002).The traces show the mean response to each of the stimuli in 5 subjects. The redline represents the linear prediction of the response obtained by convolving theoptimal filter for each subject (obtained independently from white-noise trials)with the sinusoidal perturbation. The correlation coefficient between thepredicted and measured responses is shown in the inset.

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than those in the pursuit condition, (Fig. 8, solid curves). Tocompare the shape of the filters, we normalized the fixationfilter to have the same maximal amplitude as that of the pursuitfilter (Fig. 8, dashed curves). It can be seen that the pure delayand time-to-peak of the filters are nearly identical. In the laterphase of the response, however, the optimal filters for thepursuit condition tended to show a more biphasic response.This is particularly evident in the naïve subjects (Fig. 8,subjects P.L. and J.F.). One possible reason for the observeddifferences may be the effect of practice in the task, which weare now exploring. Nevertheless, the nearly perfect agreementof the filters in the initial phase of the response seems consis-tent with the notion that gaze stabilization during pursuit andfixation share a common underlying circuitry.

D I S C U S S I O N

A psychophysical reverse correlation method was used torecover the temporal filter that best linked fluctuations in targetvelocity to fluctuations in eye velocity during steady-statepursuit movements (Mulligan 2002; Osborne and Lisberger2007). The use of discrete-time Gaussian white noise as theperturbation term offers three main advantages. First, the targetvelocity fluctuations are unpredictable, thereby ruling out acontribution of top-down predictive mechanisms of targettrajectories to our measurements (Barnes and Asselman 1991;Bennett and Barnes 2004; Churchland et al. 2003; Deno et al.1995; Fukushima 2003; Jarrett and Barnes 2001; Kowler 1989;van den Berg 1988). Second, the method is very efficient and

filters with good signal-to-noise were obtained with few(�100) pursuit trials. This is because every segment of steady-state pursuit contributes data that goes into the computation ofthe filter. Third, the estimation of the linear filter can beperformed by simple cross-correlation of the target and eyevelocity signals.

In an earlier study, Mulligan (2002) had a subject track thetwo-dimensional random walk of a Gaussian luminance spotand estimated optimal filters. The resulting temporal filterswere strongly biphasic and clearly different from that the oneswe obtained in our pursuit condition. It is likely that the pursuitof a target performing a two-dimensional random walk iscloser to our fixation condition, for which we observed bipha-sic filters in some of the subjects (Fig. 8). It is also possible thatthe shape of the filters obtained by Mulligan (2002) includedthe temporal filtering used to compute the eye velocity signal(which, unfortunately, is not described in detail in his study).

We assessed the linearity of the system by generating pre-dictions to new noise patterns (Fig. 2) and to single-cycle,sinusoidal perturbations (Fig. 4). The predictions were reason-able, accounting for an average 60% of the variance in the eyevelocity traces, indicating that smooth pursuit is approximatelylinear under the conditions tested. Departures from linearityhave previously been reported for perturbations with largeamplitudes (�10–20°/s), but these differences diminished asthe size of the perturbations decreased (Churchland and Lis-berger 2002). Our tests of linearity were restricted to pertur-bations of small size, with noise SD of 2°/s, so our data are not

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FIG. 6. Estimates of the impulse responseunder different experimental conditions. A: esti-mates of temporal filters obtained for a numberof baseline velocities and noise SD factors. B: asingular value decomposition of the family offilters shows that they can be reasonably de-scribed as the scaling of a single shape. Inset:the spectrum of a singular value decompositionof the family of impulse responses. A singledominant eigenvalue is evident. The graphshows the 1st principal component for the 2subjects. C: the gain of the impulse response,represented here by the integral of the impulseresponse in each case, is largely determined bythe SD of the target fluctuations. The dashed linecorresponds to a fit of the empirical curveA/[1 (�stim/�0)�] to the data of both subjects.Estimated parameters have values �0 � 1.92°/s,� � 1.16, and A � 1.05°/s. The value �0 �1.92°/s can be interpreted as an estimate ofintrinsic noise at the input to visual motiondetectors. Points are color coded according tothe mean target velocity.

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in contradiction with those in this previous study. Despite thisapproximate linearity, we observed some signs of systematicdeviations in our predictions to brief perturbations that deservefurther study (Fig. 5): the linear predictions were consistentlybetter for the peak-first condition and there was a tendency fora discrepancy between the predicted and measured responses todiverge toward the late phase of the perturbation. In addition,one should consider that our experiments were performed overa limited range of velocities and that linearity may be furthercompromised at higher pursuit speeds.

A central observation was that the dynamics of pursuitmaintenance were fast, with latencies of �67 ms and effective

widths of �45 ms. In contrast, latencies measured duringpursuit initiation using a step-ramp paradigm averaged �155ms under the same conditions in the same subjects. Even underoptimal conditions in a gap-paradigm, which yields the small-est latencies for pursuit initiation, delays are on the order of�90 ms (Krauzlis and Miles 1996b).

The dynamics of pursuit maintenance were only moderatelyslowed down by luminance contrast, with latencies remainingbelow 80 ms for the lowest contrasts tested (Fig. 7). Thesefindings are in general agreement with the effect of contrastreported by Mulligan (2002). In comparison, latencies in thestep-ramp task measured under varying contrast levels range

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FIG. 7. Dependence of the optimal linear filter on the con-trast of the visual target. A: temporal filters estimated at differ-ent contrast levels for 2 subjects. The dynamics of pursuit areslowed down as the contrast of stimulus decreases. The panelsshow the impulse response measured at different contrast levelsfor a baseline velocity of 4°/s and a Gaussian perturbation noisewith an SD of 2°/s. B: dependence of latency, time-to-peak, andeffective width as a function of target contrast.

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FIG. 8. Gaze stabilization during pursuit and fixation havesimilar dynamics. The raw filters (solid curves) show that thegain of gaze stabilization during a fixation condition (a baselinevelocity of 0) is smaller than that obtained during pursuit.However, the shapes of the filters in the 2 conditions are similarin the early phase of the response, as shown by the normalizedresponses (dashed lines). In the late phase, the optimal filters ofsome subjects show a more biphasic responses.

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widely between 100 and 300 ms (Braun et al. 2008; Ilg 1997;Spering et al. 2005), pointing to further differences between thedynamics of pursuit measured during its maintenance andinitiation phases.

These findings show that the dynamics of pursuit mainte-nance and initiation are different from one another. Indepen-dently of the possible origins of the discrepancy, a lesson fromthese results is that the use of measurements obtained duringpursuit initiation to model and explain properties of pursuitmaintenance (including its gain and stability), may not beentirely justified.

There might be several reasons for the differences seen inthe latencies of pursuit initiation and maintenance. One reasonis simply that pursuit initiation and maintenance might becontrolled by different mechanisms. This possibility seemsconsistent with a recent study of individual differences inhuman observers, showing that pursuit initiation is dominatedby first-order motion mechanisms while pursuit maintenance isdriven by position tracking mechanisms (Wilmer and Na-kayama 2007). However, it is unclear if position trackingmechanisms alone can be fast enough to support the rapiddynamics shown in our measurements (Blohm et al. 2005;Masson and Stone 2002; Pola and Wyatt 1980). It is alsopossible that delays measured in the step-ramp paradigm con-found pursuit initiation with other processes, such as disen-gagement from fixation or the initiation of pursuit in thedirection of the step. The former idea is supported by thefinding that latencies measured in a step-ramp paradigm de-pend on whether or not a temporal gap is introduced betweenthe disappearance of fixation and appearance of a movingtarget (Krauzlis and Miles 1996a,b). The latter notion is con-sistent with the finding of �20% longer latencies in thestep-ramp paradigm than in a simple ramp (Carl and Gellman1987; Robinson 1965). A further hurdle with the estimation oflatency measurements during pursuit initiation is that they aresusceptible to contamination by anticipatory movements (Frey-berg and Ilg 2008; Krauzlis and Miles 1996a; Merrison andCarpenter 1995; van den Berg and Collewijn 1987). The use ofunpredictable perturbations during steady-state pursuit in ourexperimental design circumvents these problems.

Our estimates of pure delays during pursuit are closer to, butstill considerably smaller than, those resulting from the averageresponses to brief velocity perturbations during tracking (Behrenset al. 1985; Churchland and Lisberger 2001, 2002; Schwartzand Lisberger 1994). For example, delays of �93 ms werereported in response to step increases in target velocity duringpursuit (Behrens et al. 1985) and delays of �110 ms inresponse to biphasic perturbations of target velocity (Church-land and Lisberger 2002). The exact method used to estimatelatencies may differ from study to study, so we replicated theexperimental design of Churchland and Lisberger (2002) andfound that, the responses to brief velocity perturbations wereconsistent with the predictions of the optimal linear filter. Thelonger delays in this experimental paradigm are a simplyconsequence of the gradual ramping-up of the perturbationsignal.

Measurements of the optimal linear filter under varyingmean target velocities and perturbations sizes were well ac-counted for by a single change in gain. The gain decreased asthe SD of the target fluctuations increased. An interestingconsequence of this behavior is that, given a fixed target

velocity, the SD of the eye velocity signal is independent of thesize of the fluctuations in the target velocity. This behavior isexpected if visual motion detectors decrease their gain as thevariance of the input signal increases (Borst et al. 2005;Brenner et al. 2000).

We conjecture that the short latencies and narrow effectivewidths of the estimated impulse response indicates that ourtechnique is isolating a reflexive-like pathway that contributesto gaze stabilization during pursuit and fixation. Note that thetemporal filter is estimated over 200 s of steady-state pursuitdata. Any variability in the dynamics of the system over timewould effectively smooth the resulting temporal profile. Thesharp features of the impulse response, such as the cornerdefining pure delay (Fig. 2A), indicate that pursuit maintenanceoperates without substantial temporal variability, as one wouldexpect in a reflexive-like movement. In addition, the similarityin the shape of the optimal filters during fixation and pursuit, inparticular in the early phase of the response, suggests these twosystems share a common component for the stabilization ofgaze, as suggested previously (Krauzlis 2004). Note that ourmeasurements of gaze stabilization dynamics during pursuitand fixation are not in contradiction with the differencesobserved in the dynamics of stimulus onset and offset (Luebkeand Robinson 1988). Our study concerns the responses totarget velocity fluctuations about a fixed mean velocity,whereas Luebke and Robinson (1988) studied the dynamics ofpursuit during jumps in mean velocity, including a conditionthat brought the velocity to zero (that is, a transition tofixation).

To appreciate the fast dynamics of the linear filters, one shouldnote that their effective width, in the order of �45 ms, iscomparable to that of individual direction selective cells in mon-key V1 and middle temporal area (MT) (Bair and Movshon2004). This leaves no opportunity for further temporal integrationof motion signals in downstream areas. In addition, responselatencies in MT are �45 ms (Bair and Movshon 2004), leavingbarely �20 ms of transmission delay for the eyes to move. Apossible circuit for fast pursuit dynamics is one mediated by thedirect projection from MT/MST to the pretectal nucleus of theoptic tract, which has previously been shown to exhibit shortlatencies of �55 ms during pursuit (Mustari et al. 1988).

Caution should be exercised when comparing timing frommonkey electrophysiological data with human behavioral data.Future electrophysiological and behavioral research is neededto show the exact pathways involved in generating the fastpursuit dynamics observed here. An approach that might befruitful in dissecting the underlying circuitry consists in usinga similar reverse-correlation method during electrophysiologi-cal recordings. This would allow the comparison of behavioraland electrophysiological data in the same subject and allow thestudy of fluctuations in neuronal firing with fluctuations intarget and eye velocities at different points along the smoothpursuit pathway (Schoppik et al. 2008).

G R A N T S

This work was supported by National Eye Institute Grants EY-12816 andEY-18322.

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