Sensorimotor Transformation for Visually Guided Saccades

132

Ann. N.Y. Acad. Sci. 1039: 132–148 (2005). © 2005 New York Academy of Sciences.doi: 10.1196/annals.1325.013

Sensorimotor Transformation for Visually Guided Saccades

LANCE M. OPTICAN

Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health, DHHS, Bethesda, Maryland 20892-4435, USA

ABSTRACT: Visually guided movements require the brain to perform a sen-sorimotor transformation. The key to understanding this transformation is tounderstand the different roles of the superior colliculus (SC) and cerebellum(CB). The SC has a three-layered structure. Cells in the top layer have visual,but not motor, responses. However, cells in the deeper layers have both visualand motor responses. Thus, for a long time it was thought that the SC encodedboth the retinal location of a sensory stimulus and the desired change in eyemovement needed to acquire it. However, copious evidence has accumulatedthat shows that the SC encodes only the retinal location of a visual target, andnot the movement needed to foveate it. Thus, the information needed to makeaccurate movements must come from another part of the brain, which is pro-posed to be the cerebellum. Here it is shown how the cerebellum could performthe sensorimotor transformation.

KEYWORDS: saccade; control system; modeling; eye movement; brain; superi-or colliculus; cerebellum; vermis; fastigial nucleus; spatial-temporal trans-form; sensorimotor transform

INTRODUCTION

The sensory-to-motor conversion problem is simple to state for rapid eye move-ments (saccades) made to visual targets. When a target light is illuminated, it is im-aged on the fovea at a site that is a function of both target and eye positions. To rotatethe eye so that the image of the target falls on the fovea, the brain must convert theretinal eccentricity into an appropriate ocular displacement. In the brain, the locationof the target’s image is represented by an active spot on a retinotopic map, whereastension in the extraocular muscles is determined by the firing rate of motor neurons.Thus, the brain must convert spatial information in the visual system to temporallymodulated activity in motor neurons, taking into account the many factors that de-termine the mapping from a retinal site to the required eye displacement. How thebrain performs this sensorimotor transformation (SMT) is one of the central ques-tions in neuroscience, and it must be answered before we can say that we understandhow the brain controls movement.

Address for correspondence: Dr. Lance M. Optican, Bldg. 49, Room 2A50, Laboratory ofSensorimotor Research, National Eye Institute, NIH, Bethesda, MD 20892-4435. Voice: 301-496-9375; fax: 301-402-0511.

[email protected]

133OPTICAN: SENSORIMOTOR TRANSFORMATION

The need for an SMT is self-evident, but the mechanism for accomplishing it haseluded description. A strong form of the SMT was stated by Robinson,1 who as-sumed that a desired eye position signal was spatially coded and was then explicitlyconverted to a temporal code. Robinson called this explicit converter the spatial-to-temporal transform (STT). The requirement that the same signal exist in two codescomes from a control systems approach to making movements. The principal ele-ment in a control model is a comparator that computes motor error by subtractingcurrent position (or displacement) from desired position (or displacement) (FIG. 1).For this comparator to work, the same signal (desired eye position) has to be presentin two domains, spatial, because the retina is the input, and temporal, because thefeedback signal (current eye position) is encoded by the firing rate of the cells in theneural integrator (NI). Thus, the STT operator was needed to convert the spatial rep-resentation of desired position (e.g., in the SC) into a temporal representation (firingrate) of desired position. Despite 30 years of research on the sensorimotor transform,there is no evidence that the brain uses an STT operator. In the absence of such evi-dence, an alternative mechanism has been proposed that uses only physiologicallyidentified neurons.2,3 In that model (see FIG. 3) no comparator is needed becausenone of its signals are encoded both spatially and temporally. Thus, Robinson’s ex-

FIGURE 1. Schematic of key elements of classic models of saccadic control. Desiredeye position (Ed), is obtained by an explicit STT operator from a spatial map of target dis-placements in the SC. The context of the movement is relayed to the cerebellum (CBLM),which adapts to learn a compensatory signal (Eadap) which is added to the Ed signal. (NB:Eadap is an open-loop signal, and thus cannot be used to compensate for errors in an individ-ual saccade.) An efference copy of current eye position (Ê) is subtracted from this sum tocompute the remaining motor error for the movement. If the omnipause neurons are silent,the gate is closed and motor error drives the medium lead burst neurons (MLBNs), whoseoutput is the desired eye velocity ( ). The displacement integrator (NI) computes Ê from

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134 ANNALS NEW YORK ACADEMY OF SCIENCES

plicit STT operator is not needed. Instead, I have proposed that the cerebellum per-forms the necessary SMT implicitly. Here I explain how the SMT might beimplemented in the brain.

MODEL

The globe, extraocular muscles, orbital pulleys, and other orbital tissues form theoculomotor plant. This plant is dominated by its viscosity, so it can be approximatelydescribed as a first-order linear system. The innervation needed to generate a sac-cade is then made up of two components, a pulse and a step. The pulse is a transientinnervation that generates a large torque that moves the eye quickly against the vis-cosity in the orbit. The step is a tonic level of innervation that generates a smalltorque to hold the eye in its final position against the elasticity in the orbit. The tonicinnervation can be produced easily if the transient component, called the pulse, isknown.4 Thus, all models of the saccadic system have at their heart a circuit for gen-erating a pulse of innervation with the appropriate height and width, such that thearea under the pulse (i.e., its integral) is equal to the desired change in ocular orien-tation. Robinson proposed a simple feedback circuit that used an integrator to pro-duce an efference copy of eye position that could be fed back and compared with thedesired eye position to generate the burst (FIG. 1).5 This model was modified by Jür-gens et al. to use a resettable integrator that produced an efference copy of thechange in eye orientation (displacement) that could be compared to the desired dis-placement.6 Some form of this local feedback circuit is at the heart of every contem-porary model of the saccadic system.

Although control system models have had great success in reproducing eyemovement behavior, they have been less successful at explaining the responses ofneurons in the brain that fire around the time of the saccade. Indeed, it takes the co-operation of many areas in the brain to execute a saccade. However, classic controlsystem models compute analogs of physical signals, for example, desired eye dis-placement and motor error, rather than neuronal activities. Control models generatethe innervation needed to make a saccade by using a motor error signal to drive aninverse model of the dynamics of the eye plant (usually simplified as a resettable, ordisplacement integrator). Unfortunately, control signals such as desired displace-ment and motor error have not been found in the brain.7,8

In contrast, network models can reproduce both the behavioral and neuronal char-acteristics of the saccadic system. Thus, it should be possible to understand how thebrain performs the SMT by studying network models. Although many parts of thebrain are involved in vision and movement, there are two main candidates for a rolein the SMT. The first is a well-known structure, the superior colliculus (SC), whichhas been studied intensively for more than 40 years.9–12 The other structure is themidline cerebellum (CB), the cortex (vermis), and the deep cerebellar nuclei (fasti-gial nuclei, FN), which has been intensively studied for about 15 years.13–22

In my recent network model,2,3,7,8 the SC and CB play novel roles, using infor-mation about the desired target and the movement context to generate saccades. Byunderstanding the roles of each area in this model, it is possible to give new inter-pretations to the signals found in the brain. These new interpretations explain howthe brain performs the SMT for visually guided saccades, and thus solve this classic


mystery. The one-dimensional model simulated here describes one detail of the pro-cess, the effects of the convergence of distributed activity across the vast populationof vermis neurons onto the much smaller population of FN neurons.

Superior Colliculus

In the network model, the intermediate and deep layers of the SC contain a loga-rithmically warped map of the contralateral visual hemifield.10,23 When a light isflashed in one hemifield a corresponding region in the contralateral SC becomes ac-tive. If electrical stimulation is delivered to that site, a saccadic eye movement willbe made to that point in the hemifield. The overlap between the visual and motor re-ceptive fields of neurons in the SC was the basis for assuming that the output of theSC was a motor command directing the brain stem to make a saccade with a fixeddisplacement vector. Recent experiments, however, suggest a different role for theSC.

Understanding the role of the SC requires us to consider experiments where thevisual target and the evoked saccade are not the same. Several types of experimentscan dissociate the visual target and the motor goal. For example, if a target is flashedwhen the eye is not in primary position, the eye movement that must be made is afunction of both the retinal location of the target and the position of the eyes.24

Hence, the evoked saccades are different for different initial positions, even if theretinal error is the same. However, if the SC is stimulated electrically rather than vi-sually the ensuing saccadic displacement is the same whether or not the eye is in pri-mary position.25 Thus, unnatural (e.g., electrical) stimulation evokes saccades thatdo not take the initial position of the eye into account.

Another example comes from double-step adaptation experiments, in which thetarget jumps to one eccentric position to elicit a saccade, but then makes anotherjump (onward or backward) when the saccade starts. At first, two saccades are elic-ited, one to the first position of the target, and another to the second position. Overseveral hundred saccades, the brain adapts the size of the first saccade until it is ap-propriate for the second target location. After the brain has adapted, the SC is activeat the sites appropriate for the two targets, but there is no activity at the locus corre-sponding to the adapted saccade.26,27

A more behaviorally realistic example corresponds to saccades made to movingtargets. Suppose that a target appears in the periphery, and moves toward (or away)from the fovea. This elicits both a saccade and a pursuit movement. However, theamplitude of the saccade is not matched to the site of the target’s original appear-ance; rather, it is adjusted to take into account the velocity of the target.28–30 Thus,saccades are smaller for targets moving toward the fovea, and larger for targets mov-ing away from the fovea. However, single-unit recordings have shown that the siteof activity in the SC corresponds to the initial appearance of the target, not the am-plitude of the adjusted saccade.9

A final example comes from the study of strongly curved saccades. Normally,saccades are only slightly curved. However, if two targets flash close together in timeon some occasions a single saccade will be made that starts toward the first target butturns in midflight and goes to the second target. This saccade has a strongly curvedtrajectory. When saccades are strongly curved, the question arises as to the source ofthe drive signal for the curved component. For example, a saccade may start toward


a rightward target, and then curve around to a target below its current position. Thecurved portion of that saccade requires a downward drive. Single-unit studies haveshown that the active loci in the SC correspond only to the visual target locations,and not to the final (downward) direction of the curved saccade.31–33

Experiments that dissociate retinal error and desired ocular displacement showthat although the locus of SC activity usually correlates with the desired movement,that correlation is not obligatory. Whenever the target location and the desired move-ment are different, neurons in the SC always encode the target location in retinotopiccoordinates2,3,8,34 and never encode the desired movement. The desired movementmust be computed somewhere else, based on the retinotopic target error, the currenteye position, the velocity of the target, and so forth. All of these factors contributeto what may be called the context of the movement.

Because the direction of the target usually approximates the direction of the de-sired saccade, SC neurons could send a reasonably accurate directional drive signalto the brain stem, which would start the eyes moving toward the target. If the SC neu-rons burst when a target is selected and send an initial drive signal to the brain stem,it makes sense for the SC to also start the saccade by blocking the brain-stem inhib-itory circuit (e.g., omnipause neurons) that is preventing saccades. Thus, I hypothe-size that the SC plays three roles in generating a saccade: it indicates which target(in retinotopic coordinates) has been selected, initiates a movement by suppressingbrain-stem inhibition, and sends a drive signal to start the eye moving in approxi-mately the right direction. The drive output is the weighted sum of the SC popula-tion’s activity. The locus of activity on the SC determines the ratio of horizontal tovertical drive, that is, the angle of the drive, and the level of activation affects thespeed of the movement. The direction of this drive is fixed throughout the move-ment, because the SC does not receive feedback about the eye movement, and thuscan neither steer nor stop the saccade.3,35–37 Indeed, SC lesions spare saccadicaccuracy.38

Cerebellum: Vermis and Fastigial Nuclei

It should not be surprising that the SC does not indicate the endpoint for the motorsystem, because endpoints depend on context, which is not represented in the SC.Thus, another circuit must provide the endpoint control. Where should we look for apart of the brain that can steer and stop the saccade? The CB receives informationabout both the goal and context (e.g., eye position, target velocity) of the movement,and lesions of the CB induce enduring dysmetrias.39 This suggests that the CB playsa role in controlling the endpoint of a movement. When the fastigial nuclei alone arelesioned there is an increased variability of saccade endpoints.20 Furthermore, end-point accuracy is lost: after unilateral lesions, ipsiversive saccades are hypermetric andcontraversive saccades are hypometric; after bilateral lesions, saccades are hypermet-ric in both directions. When the vermis alone is lesioned, all aspects of saccadic controlare affected, including initiation, accuracy, and dynamics. Symmetric vermis lesionslead to hypometric saccades and an increased variability in saccade amplitude.40

From these results, it can be inferred that the feedforward pathway in the brainstem is noisy and can neither steer nor stop the saccade. An intact CB is necessaryto compensate for these brain-stem limitations. That implies that the CB must playthree roles: determine its contribution to the drive signal, steer the saccade to com-


pensate for variability in the feed forward pathway, and stop the saccade. Thesefunctions imply that the CB is in the feedback pathway and takes over the role of theneural integrator of the classic control system model (FIG. 1).

In my model, the cerebellar vermis contains a topographic motor (motorotopic)map (FIG. 2A), that is, a distributed representation of eye movements.41 It is extremelyimportant to note that the vermis is continuous across the midline. In fact, the vermisis the only cortical structure with this property. In the cerebral cortex, the two hemi-spheres of the brain are not continuous, and to get a signal from one side to the otherrequires sending it through a commissure. Such fiber tracts can introduce a delay ofmany milliseconds. A continuous structure, such as the vermis, could send a signalfrom one side to the other without any added delay. I do not think that this structuralfeature is incidental. Below, I argue that it is the key to solving the SMT problem.

The only cells that project out of the vermis are the Purkinje cells, which inhibitneurons in the fastigial nucleus on the same side. The FN neurons cross over as theyleave the cerebellum, and project to many structures on the other side. In particular,the fastigial neurons project to the contralateral inhibitory and excitatory burst neu-rons (IBNs and EBNs) in the brain stem and midbrain, which convey the pulse signalfor saccades, and to the SC. The FN is quite small, and only the caudal portion isinvolved in saccades.14 Thus, there must be a considerable amount of convergencefrom the vermis to the caudal FN (cFN). Furthermore, the output of the Purkinjecells is inhibitory, so the behavior of cFN neurons must be the opposite of the vermisneurons. One way to conceptualize this configuration is to think of the cFN as beinglaid out in a virtual motor map with movement vectors opposite to the vermis map(FIG. 2B). Of course, unlike the much larger SC and vermis, a small nucleus like the

FIGURE 2. Motorotopic maps in the cerebellum. (A) The vermis and paravermis areassumed to have a topographic map of movement vectors. Gray arrows indicate amplitudeand direction of movements elicited by stimulating at those sites. (B) It is assumed that eachcell in the fastigial nuclei receives convergent input from many vermis cells in a small neigh-borhood. This can be represented by a virtual movement map. Note that the direction of themovement vectors in the map is opposite to those in the vermis map.


cFN probably does not contain a real topographic map. Nonetheless, a virtual map(FIG. 2B) is useful to visualize the effects of an organized projection from the mo-torotopic map in the vermis (i.e., if nearby cells in the vermis tend to converge onthe same FN cell).

The key question is how does the CB integrate the feedback, and steer and stopthe movement? We had clues from the electrical stimulation of the vermis and thelesion studies of the vermis and the cFN. Another clue comes from the timing of neu-ronal activity in the CB relative to the saccade. The burst of activity in the cFN leadsthe start of contraversive saccades, and lags the start of ipsiversive saccades.16,19

Furthermore, the size of the lag for ipsiversive saccades increases for increasing sac-cade amplitude.16 For contralateral saccades, FNs have a more or less constant lag,but the burst duration increases with amplitude.17,42 I infer from these clues that theactivity in the cerebellar vermis is suppressed at a contraversive locus correspondingto the contribution needed for a saccade, and that a wave of inhibition spreads acrossthe vermis toward the midline, crosses the midline, and finally inhibits cells in theipsilateral vermis. This gives rise to activity in the FNs, which appears to be a waveof excitation that spreads through the fastigial nuclei, from contralateral to ipsilater-al. The speed and direction of this spread are a function of eye velocity.2,3

The CB can accomplish this coordinated spread if the vermis acts as a spatial in-tegrator of the feedback signal (an efference copy of the eye velocity).43,44 If the CBacts as a spatial integrator, it needs two separate mechanisms to initialize activity ata specific locus on the CB, and update the locus of activity on the CB according tothe velocity feedback. This initial locus corresponds to the CB’s contribution to themovement and is dependent upon the movement context. It is important to realizethat this locus is not the motor error, because the SC drive is also contributing to themovement.8 The CB must learn its required contribution as a function of its inputs.This paper looks at some of the consequences of such a spread that might be observ-able experimentally.

METHODS

The highly simplified model described here explains one detail of the model of sac-cadic control (FIG. 3) described in more detail elsewhere.2,3,8 Only the cerebellar func-tions for a one-dimensional eye movement are represented here. These simulations areused to show the spreading wave and the effects of convergence from the vermis to thefastigial nuclei. Thus, this model does not present any hypotheses about the cellularmechanisms or circuits that may be involved in the brain. Instead, I show here simu-lated neural responses in the vermis and FNs, assuming that there is a motorotopic mapin the cerebellar vermis that converges onto the deep cerebellar nuclei.

The cerebellum was modeled as two cell populations, one representing the vermisand the other the fastigial nuclei. Discrete-time simulations were run with a programwritten in Matlab (The MathWorks, Natick, MA). The time step was 1 ms. The oc-ulomotor final common path (including the ocular plant) was simplified to an inte-grator. The equation describing eye position (E) was:

where deye is the eye velocity and opn is the omnipause neuron that prevents saccades.

E(t) = E(t − 1) + deye(t − 1) · (1 − opn(t − 1)) (1)


The vermis was represented by 200 cells in a one-dimensional, bilateral, motor-otopic map (FIG. 4). Cell activity ranged from 0 to 1, and was initialized to a back-ground activity of 0.5. When a target appeared, the activity of the vermis cellsincreased to 0.85. When the saccade began, the activities of the cells in the contralat-eral vermis corresponding to the target location ± 25° were set to 0 and smoothed bya Gaussian filter (σ = 20°). The inhibition in the vermis propagated toward the op-posite side as a function of the integral of the eye velocity. However, the gain of thisfeedback signal was greater than one, so that the wave of inhibition crossed over intothe ipsilateral vermis about halfway through the movement. The equation governingthe spread of the edge of inhibition was:

where edge is the leading edge of the wave of inhibition spreading through the ver-mis, A is the saccade amplitude, and E is the current eye displacement (all in degrees

edge = A − 2 · E(t) (2)

FIGURE 3. Block diagram of parallel-pathway model of the saccadic system. Cere-brum, frontal eye fields (FEF) and lateral intraparietal cortex (LIP), and SC determine thedesired target. This information is sent to the cerebellum. The output of the SC helps gatethe movement (Veto), and sends an initial directional drive. The cerebellum integrates feed-back from the brain stem, allowing it to steer (pilot drive) and stop (choke) the movement.


of visual angle). Equation 2 is a simplification of the mechanism controlling thespread of inhibition, and was chosen arbitrarily to force the activity across the mid-line before the end of the saccade. The crossover generates the choke command thatgoes from the ipsilateral fastigial nucleus to the brain stem.2

The fastigial nuclei were represented by just 10 cells on each side (FIG. 4), initial-ized to a background activity of 0.5. The cells corresponding to the target locationreceived an input of one from mossy fibers, and an inhibition that was a Gaussianweighted average (σ = 20°) of the vermis cells converging on that fastigial cell. Theratio of convergence was 10:1, because both the vermis and fastigial nuclei coveredthe same oculomotor range. The equation governing the fastigial cells, fni, was a lowpass filter:

(3)fni t( ) τ fni t 1–( ) 1 τ–( ) 1 1N---- vermisk t( )k∑–

⎝ ⎠⎜ ⎟⎛ ⎞

+⋅=

FIGURE 4. One-dimensional model of the cerebellum almost at the end of a saccade.White circles are active neurons, and gray circles are inhibited neurons. Dashed arrows in-dicate (inhibitory) convergence from vermis to FN. The model has two inputs: desired targetin retinotopic coordinates, Td, and CONTEXT, representing other inputs (e.g., eye positionand target velocity). These inputs are used to determine the locus of initial suppression ofactivity in the vermis. Feedback of eye velocity ( ) causes the suppression to spread acrossthe vermis from the side contralateral to the movement, through the midline, to the ipsilat-eral side. When the contralateral vermis is inhibited, the FNs on that side are disinhibitedand send out a contraversive drive signal. When the suppression crosses over to the ipsilat-eral vermis, the FNs on that side are disinhibited, which results in the contraversive drivesignal being choked off in the brain stem.

E·


where i ranges from 1 to 10 and the range of k covers the N = 10 vermis cells thatconverge onto the ith fastigial cell. The decay constant was set to 0.5, correspondingto a time constant for the FNs of about 1.44 ms. FNs could only receive input fromthe ipsilateral vermis. The difference between the sum of the contralateral and ipsi-lateral FN cells corresponded to how much of the movement was left.

The simulation loop was closed by obtaining eye velocity from the combined FNand SC drives:

where ∆F is the sum of contralateral minus ipsilateral activity in the FN, F is the sumover all N of the FN cells, sc is the total output of the SC, A is saccade amplitude,and deye is the total velocity drive. This model is too simplistic to account for sac-cade velocity profiles, but a square root (Eq. 7) was introduced to represent the softsaturation of eye velocity with increasing saccade amplitude.

Neuronal activity in the model was simulated as a continuous membrane potentialcorresponding to firing rate. Trains of action potentials (spikes) were used only fordisplaying the output of the neurons. Spikes were generated by a Poisson processwith a mean and variance equal to twice the membrane potential.

RESULTS

Making a Saccade

Let us consider what happens in the brain once a visual target has been selected.First, there is a burst of activity at the appropriate locus on the SC map. Through amechanism that remains unknown, the SC burst must block the inhibition holdingoff the premotor neurons, that is, it should somehow shut off the omnipause neurons(OPNs). The SC output also goes to the premotor neurons, providing a drive signalthat starts the eyes moving in the retinotopic direction.25 Note that this drive signalhas a fixed direction throughout the movement, because in this model the SC doesnot receive any motor error feedback signals that could allow it to redirect itsdrive.2,3

During a saccade, mossy fiber inputs reach the vermis and the FNs. However, thevermis inhibits the ipsilateral FN so strongly that the net effect is to block the outputof the FN (FIG. 4). Before the CB can generate an output, it must determine what itscontribution to the movement should be based on the location of the desired target

(4)

(5)

(6)

(7)

∆F fni t( ) fni t( )Ipsi∑–

Contra∑=

F fni t( )N∑=

sc sign A( ) N F–( )⋅=

deye sign A( ) sc ∆F+⋅=


in retinotopic coordinates and other information, such as the position of the eyes inthe orbit,24 the velocity of the target,9 or the response required by the behavioral sit-uation.45 All of this information is brought into the CB on mossy fibers. Thus, beforeeach saccade, the CB has all the information that it needs to determine what its con-tribution to the movement must be.8 Thus, the Purkinje cells receive a vast constel-lation of inputs that, through pattern recognition trained by previous experience,causes some of them to turn off. The underlying FNs are thus disinhibited and beginfiring. The population output of the FNs decussates to provide a drive to the premo-tor neurons on the opposite side. The FN signal also inhibits the SC on the oppositeside (cf. Eq. 6).

A saccade starts when the SC releases the inhibition on the premotor neurons andthe drive from the SC begins to move the eyes. In the meantime, the vermis has rec-ognized from movement context that the contribution of the CB to this movementshould have a specific (learned) vector. The Purkinje cells at the location on the ver-mis map corresponding to that motor vector are inhibited. This disinhibits the under-lying FN neurons, which begin to fire. The FNs provide a drive signal to thepremotor neurons that adds to the collicular output. The brain has now achieved thefirst part of the movement: it has selected the target and initiated the movement. Tocomplete the next half, the brain must monitor the movement, compensate for anynoise or perturbations, and stop the eye when it is looking at the target. The CB ac-complishes this by using an efference copy of eye velocity, fed back from the pre-motor neurons, to update its motor map. What that means in this context is that thevermis acts as a spatial integrator: it converts the eye velocity vector to a new distri-bution of activity on the vermis map that corresponds to how much of the CB’s com-ponent has already been provided. Because of this feedback updating, the output ofthe FNs can change direction, steering the eye toward the target.2,3

The CB is able to stop the saccade when the endpoint is reached because depres-sion in the vermis spreads across the midline to the ipsilateral vermis, which gener-ates a presynaptic inhibition in the premotor circuitry that chokes off the burst to themotor neurons. This stops the saccade without an antagonist brake signal (whichmight create an overshoot).2,3

Cerebellar Activity

This model does not specify the mechanism by which the vermis learns to sup-press its activity at the correct site. It also has no spatial integrator mechanism toconvert the feedback eye velocity into a spread of activity across the vermis. Thechoice of any specific mechanism would be completely arbitrary, because there is in-sufficient data at this time to guide the modeling. The point of the simplified simu-lations shown here is simply to demonstrate the effects of the spread across thevermis and convergence from the vermis to the FNs. Raster diagrams of the activityin the vermis and FNs during saccades were plotted as a function of saccadeamplitude.

Experimental evidence from single-unit experiments has shown that there is a re-lationship between the activity in FN neurons and the size of the saccades. Earlystudies showed that changing saccades over a small range, about 5° to 25°, in head-fixed monkeys led to systematic changes in the amplitude and/or latency of the FNactivity.16,20 A more recent study has increased the range of movements using head-


free monkeys.42 When saccades were smaller than about 25°, the results in head-freeand head-fixed monkeys agreed. However, when the saccades became much larger,up to 100°, a new phenomenon became apparent: the FN neurons paused before theyburst, and the duration of that pause increased with saccade amplitude. This increasewas seen for both contra- and ipsiversive saccades. The saccade model describedhere can explain this relationship between pause duration and saccade amplitude.

Suppose the recording electrode is placed at a location in the cFN correspondingto a rightward, upward saccade, but the target is at the site for a leftward, downwardsaccade (FIG. 5A). Thus, the initial activity in the vermis is on the side contralateralto the electrode. The cells under the electrode will be inhibited by the overlying ver-

FIGURE 5. Schematic of electrode recording from the virtual motorotopic map in thefastigial nuclei. (A) Initial conditions when the saccade is ipsiversive to the electrode. Ini-tially, the FNs are inhibited (gray), except at the initial locus on the contralateral side(white). (B) When the movement is over, the activity has spread across the midline andreached the electrode. This gives a pause–burst pattern of activity, where the pause durationis a function of the amplitude of the saccade, because the locus on the FN map for biggersaccades starts more eccentrically. (C, D) As above, but activity for a very large contraver-sive saccade. The electrode records a brief pause before the burst, because the initial FN ac-itivity is more eccentric than the electrode.


mis at the start of the saccade. The electrode will only record a burst of activity afterthe wave of inhibition in the vermis has spread across to the opposite side (FIG. 5B).The pattern of activity seen by the electrode would be a pause with a duration depen-dent upon the ipsilateral saccade’s amplitude, followed by a burst. The interpretationof the model is similar for contralateral saccades. When the target is more eccentricthan the recording site (FIG. 5C), the cells under the electrode will be inhibited untilthe sweep of activity reaches the electrode (FIG. 5D). If the initial locus of activity isunder the electrode, then there will be only a brief, or even no, pause. However, ifthe target is much less eccentric than the electrode, the sweep of activity will startmedial to the electrode, which would not record a burst of activity.

Simulation

An example of the population activity in the model during a 60° rightward sac-cade is shown in FIGURE 6. The top panel shows the eye movement and two spiketrains. The upper spike train is from a neuron at the 15° locus on the vermis map; the

FIGURE 6. Simulation of a 60° rightward saccade by a one-dimensional model. Top:Eye movement and spike activity in vermis (circles) and fastigial nuclei (crosses) at 15° lo-cus (arrowhead). Middle: Activity on the vermis map (200 cells). Before and after the sac-cade activity is at the background rate (medium gray). At the beginning of the saccade,ipsilateral neurons burst (light gray to white), and contralateral neurons pause (dark gray).As the saccade progresses, a wave of inhibition (black) spreads across the vermis, cancelingthe burst. Bottom: Activity on the virtual fastigial map (20 cells) is the inverse of the activityin the vermis: as the saccade progresses, a wave of excitation (white) spreads through theFN. Note that the massive convergence from the vermis causes FN neurons near the edge ofthe wave to have intermediate activity levels. Gray scale indicates firing rate, normalized toa peak rate of one. Saccade starts at time zero.


lower train is from a neuron at the 15° locus on the virtual fastigial nucleus map (ar-rowheads). The two maps themselves are shown in the middle and bottom panels.The row of cells in the one-dimensional model extends along the ordinate in eachgraph. (The abscissa in all three rows gives the time relative to saccade onset.) In thissimulation, just before the movement the activity of all the cells in the vermis is in-creased. That inhibits the FNs and prevents any movements. (This increase may notbe needed in all the cells, or for every saccade, because not all FNs show an earlypause; thus, the early burst should probably be stochastic.) Then the activity of thevermis cells at the locus of activity on the map corresponding to the movement con-tribution needed is inhibited (middle map, black areas). This allows their corre-sponding FNs to burst (bottom map, white areas), starting the movement. As thesaccade proceeds, feedback causes the inhibition to spread across the vermis, whichallows the corresponding FNs to burst. As the saccade nears the target, the ipsilateral

FIGURE 7. Simulations of one-dimensional model for different saccade amplitudesand directions. Top: Family of rightward (ipsiversive) and leftward (contraversive) sac-cades. Saccades start at time zero. Middle: Raster diagram of activity of one vermis neuronat the 15° locus. Each dot represents a spike in the model neuron, and each row of dots isplotted at the amplitude of the saccade. Behavior is essentially burst–pause for all directionsand amplitudes, with only the duration of the burst and pause varying. Bottom: Raster dia-gram for an FN neuron at 15°. The behavior is pause–burst, or pause–burst–pause, depend-ing upon amplitude and direction. This behavior is more varied than that of the vermisneurons, because of the massive convergence from the vermis to the FNs. The FN simula-tions appear very similar to the data in FIGURE 3 of Brettler et al.42


FNs need to fire, so that the motor drive in the brain stem will be choked off.2,3 Anexact description of how inhibition spreads from the contralateral to the ipsilateralvermis is not available. The simulation uses Equation 2 to accomplish this spread,which gives rise to the linear spread of inhibition across the vermis and the corre-sponding spread of the burst from the contralateral to the ipsilateral FN neurons.

FIGURE 6 shows the activity of all the neurons in the model for one saccade.FIGURE 7 shows the activity of one pair of vermis and fastigial neurons at 15° (dashedline in top left graph) for saccades ranging in size from −90° (leftward) to +90°(rightward). The top panel shows the simulated family of ipsiversive and contraver-sive eye movements. The other panels show raster plots of the activity of these twocells. Each dot in a row shows one spike, and each row shows the response to onesaccade. The row is plotted at the amplitude of the corresponding saccade. The mod-el shows a clear trend. The duration of the early pause for this fastigial neuron in-creases with ipsiversive saccade amplitude above about 20°. The duration of thepause also increases for contraversive saccades larger than about 20°, but the pauseis less complete because of all the convergence from the vermis to the fastigial nu-clei. The results of these simulations are similar to the data from Brettler et al.42

Thus, a spreading wave in the cerebellum acting as a spatial integrator could accountfor much of their data.

DISCUSSION

These results support several new hypotheses for the control of visually guidedsaccades. The basic structure of the motor controller is parallel, with one pathwayresponsible for initiating movements, and the other for piloting them to the correctendpoint. The superior colliculus dominates one of the two branches, and performsthree functions: (1) It embeds a retinotopic, target acquisition map. (2) It blocks theinhibitory circuit when a target has been chosen. (3) It sends a fixed direction (retin-otopic) drive to start the movement. In the absence of the other pathway, the SC path-way is sufficient to make a saccade that starts in approximately the right direction,but it will be dysmetric because it will only stop when some other mechanism (in-sensitive to the endpoint) restarts the omnipause neurons.

The cerebellum dominates the other branch, and performs five functions: (1) Ituses learned pattern recognition of mossy fiber inputs (the movement context) to de-fine its contribution to the movement. (2) It suppresses activity at a locus in the ver-mis corresponding to that contribution. (3) It updates a spatial map in the vermis,thus integrating the velocity feedback signal. (4) It steers the movement toward thecorrect endpoint by altering its pilot drive signal. (5) It chokes off the drive to themotor neurons when that endpoint is reached.

This network model allows us to understand how the brain performs one of itsmost fundamental processes: converting sensory information into movement com-mands. The solution to the sensorimotor transformation problem has not emerged allat once due to a single discovery, but gradually, as many different researchers con-tributed data and ideas over the decades. This is an example of a stealth discovery: amajor breakthrough in the understanding of brain function that has occurred almostwithout notice.


ACKNOWLEDGMENT

I am grateful to Dr. C. Quaia for many discussions on this topic, and for com-ments on the paper.

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Sensorimotor Transformation for Visually Guided Saccades

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