Neurophysiology of visually guided eye movements: critical review and alternative viewpoint

Abstract

In this article, we perform a critical examination of assumptions that led to the assimilation of measurements of the movement of a rigid body in the physical world to parameters encoded within brain activity. In many neurophysiological studies of goal-directed eye movements, equivalence has indeed been made between the kinematics of the eyes or of a targeted object and the associated neuronal processes. Such a way of proceeding brings up the reduction encountered in projective geometry when a multidimensional object is being projected onto a one-dimensional segment. The measurement of a movement indeed consists of generation of a series of numerical values from which magnitudes such as amplitude, duration, and their ratio (speed) are calculated. By contrast, movement generation consists of activation of multiple parallel channels in the brain. Yet, for many years, kinematic parameters were supposed to be encoded in brain activity, even though the neuronal image of most physical events is distributed both spatially and temporally. After explaining why the “neuronalization” of such parameters is questionable for elucidating the neural processes underlying the execution of saccadic and pursuit eye movements, we propose an alternative to the framework that has dominated the last five decades. A viewpoint is presented in which these processes follow principles that are defined by intrinsic properties of the brain (population coding, multiplicity of transmission delays, synchrony of firing, connectivity). We propose reconsideration of the time course of saccadic and pursuit eye movements as the restoration of equilibria between neural populations that exert opposing motor tendencies.

“Facts and theories are natural enemies. A theory may succeed for a time in domesticating some facts, but sooner or later inevitably the facts revert to their predatory ways. Theories deserve our sympathy, for they are indispensable in the development of science. They systematize, exposing relationship between facts that seemed unrelated; they establish a scale of values among facts, showing one to be more important than another; they enable us to extrapolate from the known to the unknown, to predict the results of experiments not yet performed; and they suggest which new experiments may be worth attempting. However, theories are dangerous too, for they often function as blinkers instead of spectacles. Misplaced confidence in a theory can effectively prevent us from seeing facts as they really are.” (Wilkie 1954)

VISUOMOTOR TRANSFORMATION AND ITS NUMERICAL PROCESSING

The procedures used to measure the movement of a rigid body (eyeball or object) influence the neurophysiological study of visuomotor transformation through notions that can either distort the underlying neuronal processes or even have no substrate. To start with the simplest example, we frequently read that gaze direction (or the line of sight) is shifted from one point to another. Attributing pointlike values (coordinates) to gaze and target inevitably leads to numerical differences, especially when the measurements are made with high resolution. However, numerical differences do not imply corresponding mismatches in brain activity. Objects in the physical world are obviously not mathematical points, and visual fixation does not involve a fovea composed of one single photoreceptor where all light beams would converge. Because of the divergence of anatomical projections, any object leads to the excitation of a large number of neurons. When we record their emission of action potentials, we discover that neurons (visual only, visuomotor, or motor) have a spatially extended response field. This extent indicates that any object in the visual field or any saccade is associated with the excitation of a large set of cells (see, e.g., McIlwain 1976; Sparks et al. 1976). Moreover, in many visual and visuomotor regions of the cerebral cortex, as in the superior colliculus (SC), neurons are laid out such that neighboring cells respond to the stimulation of neighboring regions of the visual field or fire a burst of action potentials during saccades to neighboring locations in the physical world. Despite the divergent connectivity, retinotopy is preserved.

The consequence is that neighboring objects, or saccades toward their location, excite populations of neurons that overlap. This functional overlap is overlooked when the focus is placed on the numerical difference between the gaze and target directions, an error considered to be the command specifying the goal of gaze orientation. Indeed, the overlap could participate in movement triggering insofar as gaze may not be shifted as long as the visuo-oculomotor system remains within a mode where opposite commands counterbalance each other (Fig. 1). In some experimentally induced pathological disorders (cerebellar: Guerrasio et al. 2010; Sato and Noda 1992; corticofrontal: Dias and Segraves 1999; collicular: Goffart et al. 2012) and even normal cases (Goffart et al. 2006), stable fixation is engaged even though gaze is not directed toward the target center but toward an offset location. No eye movement is triggered despite a numerical difference between gaze and target directions (nonzero error). Likewise, an altered balance between opposing commands can explain the offset of head direction with respect to a food target during a collicular or cerebellar lesion (Goffart and Pélisson 1998; Isa et al. 1992). The neural processes specifying the location where to look during fixation or where to direct the head may not specifically involve an “encoding” of spatial attributes (such as gaze, head, or target directions and their difference) but a balance of activity between sets of neurons exerting opposite directional tendencies (as documented in the cat brain stem by the group of Yoshikazu Shinoda; e.g., Takahashi et al. 2005, 2007, 2010). From this viewpoint, changes of gaze direction (during saccade and pursuit) do not result from reducing differences between signals encoding kinematic parameters. The movement is the behavioral outcome of a transition from an unbalanced state of activities to equilibrium of opposing tendencies distributed in several regions of the brain. Thus we can understand why alterations of saccade velocity happen during functional perturbation of regions (SC: Sparks et al. 1990; frontal eye field: Dias and Segraves 1999) that are classically considered as encoding the location where to look (Dassonville et al. 1992; Hanes and Wurtz 2001; Sparks 1989, Van Horn et al. 2013).

Fig. 1.

Visual fixation as equilibrium. A saccade may not be launched if the visuo-oculomotor system is within a mode where opposite commands (presumably issued by the left and right superior colliculi) counterbalance each other. The initiation of a slow eye movement could involve the same symmetry breaking, although with different groups of neurons (see text).

Contemporary techniques enable us to measure eye movements with such high temporal resolution that numerical estimates of instantaneous velocity and acceleration can be calculated. Thus we discovered that up to some amplitude a saccade exhibits a bell-shaped velocity profile and that maximum velocity and duration increase with saccade amplitude (Fuchs 1967a; Westheimer 1954). Attempts were then made to study how the instantaneous firing rate of neurons could account for the current velocity or acceleration of eye movements. However, we must keep in mind the fact that although a saccade is the behavioral outcome of flows of activity distributed within the brain (between the optic and extraocular motor nerves) and unfolding from target onset time to saccade landing time, the velocity profile is the outcome of a transformation (a set of arithmetic operations) performed over a shorter time interval within a numerical series. Between the brain activity and the behavioral measurements, a kind of geometrical projection is made between a multidimensional object and a one-dimensional segment. Moreover, if the sampling of eye position did not systematically start from the same threshold or its rate was not constant from one measurement to the other, matched-amplitude saccades would exhibit different velocity profiles. And yet, when the time course of neurons’ firing rate varies from one measurement to the other and differs from the time course of precisely measured saccades, we do not suspect a “neuronal sampling” problem. The notion of “noise” is put forward and considered as a biological phenomenon, as if the firing rate ought to precisely fit with the dimensionality of measurement. Variable discharges can result from the fact that eye movements are not the unique output that the activity of central neurons can influence: spikes can also be emitted as part of processes that do not lead to saccadic or pursuit eye movements. Neuroanatomical and electrophysiological studies indeed teach us that neurons do not form a homogeneous population: those that exhibit target- or eye movement-related activities are diverse and project to a multitude of regions in the brain (Moschovakis et al. 1996). Even though thermodynamic laws govern the cellular and molecular processes (Choquet and Triller 2013) and can account for the variability of neural discharges, the latter can also be caused by the measurement itself, i.e., by the fact that we map (as in projective geometry) a multidimensional physiological phenomenon (with time-overlapping processes) onto one single series of totally ordered numerical values (i.e., eye position values ranked according to their time stamp). Mapping the change of neuronal activity to the velocity of the movement of a rigid body (eyeball or object) supposes a one-to-one correspondence between a time series of numerical values on one hand and the time course of multiple and parallel flows of activity within the visuomotor brain on the other. Supposing such a correspondence is a reduction that overlooks the fact that the brain activity corresponding to any situation (measured here and now) is not reducible to a point of coordinates (x, y, z, t). Spatially and temporally distributed in the brain (see, e.g., Nowak and Bullier 1997; Schmolesky et al. 1998), the activity does not change like the measured coordinates of a moving body. For example, when we study the action potentials that saccade-related neurons in the SC emit during saccades toward a moving target, we discover that the population of active neurons does not change as fast as the target, that residual activity related to recently traveled locations persists (Goffart et al. 2017b; Keller et al. 1996b). Also, when we study saccades toward a transient moving target (Quinet and Goffart 2015a) or eye movements pursuing a target that suddenly disappears (Mitrani and Dimitrov 1978), we find many instances in which gaze is directed toward locations where the target never went, signaling the mass of neural activity that persists beyond the time when a physical event ends.

Diverse kinematic parameters (position, velocity, and acceleration errors) are considered as signals “encoded” in the firing rate of neurons, and the relationship between their linear combination and the firing rate has been statistically tested over more or less limited time intervals (e.g., Sun et al. 2017). The activity of single neurons in various brain regions is then proposed to convey kinematic functions. Depending upon the location of recorded neurons, such statistical procedures become questionable because they assume that the signals (action potentials) are transmitted across a medium identical to the physical medium (continuous, homogeneous, and with orthogonal spatial and temporal attributes). Techniques have indeed been developed to make the firing rate look continuous and to study linear correlations. However, the establishment of this continuity would be misleading if the parameter critical in neural transmission were not the time course of action potentials but the membrane potential and the timing (synchrony) of presynaptic action potentials “bombarding” the recorded neuron. These action potentials are emitted by presynaptic neurons distributed in several brain regions at times that are not necessarily synchronous.

When we consider, for example, the discharge of motor neurons that innervate the extraocular muscles, the correlation between the saccade kinematics and the sequence of action potentials can be interpreted relatively well because the latter cause the contraction of extraocular muscle fibers that, in turn, exert the torque responsible for the rotation of the eyeball (see, e.g., Sylvestre and Cullen 1999). However, if we now turn to the premotor neurons innervating the motor neurons, the interpretation is complicated by the fact that several inputs converge onto the motor neurons. The motor neurons indeed receive input from excitatory burst neurons located in the ipsilateral paramedian reticular formation (Strassman et al. 1986a), from inhibitory burst neurons in the contralateral medullary reticular formation (Strassman et al. 1986b), and from burst-tonic neurons located bilaterally in the left and right nuclei prepositus hypoglossi (NPH) and medial vestibular nuclei (MVN) (Moschovakis et al. 1996; Scudder et al. 2002; Sparks 2002). The discharges of these different groups of neurons do not exhibit identical time courses. Consequently, since the input to the motor neurons originates from neurons distributed across different origins, the correlation between the firing rate and the saccade kinematics becomes weakened. We realize then that the correlation inevitably becomes misleading when we study the firing rate of neurons that innervate those premotor neurons, like those located in the SC (Sparks and Gandhi 2003) or the caudal fastigial nuclei (Kleine et al. 2003).

One possible way to “save” the correlation between the spiking discharge and the kinematics would be to retrogradely track the origin of action potentials converging more or less synchronously onto the recorded neurons. However, this analysis is complicated by the fact that afferent signals are transmitted with diverse conduction speeds through axons of also diverse lengths. In other words, the firing of a premotor neuron can be driven by action potentials that are emitted at different times by presynaptic neurons located in different regions. Thus the time interval during which we estimate the instantaneous velocity of an eye movement is the outcome of action potentials emitted during a different but also longer time interval. The picture is further complicated by the fact that the neural transmission depends on the location of synaptic contacts (Lorente de No 1938) onto the cell (soma and/or dendrites) whose intrinsic properties also influence the time course and pattern of spiking discharge (see, e.g., Bras et al. 1987; Durand 1989). Finally, a more macroscopic viewpoint reveals that the activity does not remain bounded but spreads toward neighboring cells as shown in the SC (Anderson et al. 1998; Sparks et al. 1976) and primary visual cortex (Muller et al. 2014). In summary, the interpretation of the correlation between the firing rate of central neurons and the kinematics of eye movement should be made while remembering these limitations.

For assessing the changes taking place within the brain activity while a target is moving across the visual field or while gaze captures and pursues it, there is no logical necessity to pair the firing rate with kinematic notions; it was simplicity and convenience that led to making this choice (Poincaré 1921). Moreover, as Pellionisz and Llinás (1982) explained, the classical usage of separate space and time coordinates may not be applicable in the case of describing the inner workings of the central nervous system (see also Buzsáki and Llinás 2017). When we say that target velocity is the stimulus driving pursuit eye movements, such a relation should be restricted to the sets of numerical values that belong to the same medium (the physical domain) and for which the kinematics has proven its efficiency. This medium is different from the inner functioning of the brain. From the optic nerve to the oculomotor nerves, the neural activity does not go through a medium that is neutral, homogeneous, isotropic, and continuous. Imagining that a mathematical differentiation has been performed is questionable because neural activities are not reducible to points. The time series of measurements is a continuum that is not homeomorphic to the fundamentally parallel and distributed aspect of neurophysiological processes, at both the cellular and network levels.

All these fundamental pitfalls do not lead the neurophysiology of movements to a dead end but toward the necessity of establishing more solid ground. Below we discuss the models that consider error signals as stimuli driving the execution of saccadic and pursuit eye movements.

POSITION ERROR AND THE FEEDBACK CONTROL OF SACCADE AMPLITUDE

The simplest solution that has been proposed to model saccade execution is a process that reduces the difference (negative feedback loop) between a desired position of the eyes (an estimate of the selected target location) and an estimate of their current position. If we assume the neural encoding of such spatial attributes (instead of a neural encoding of desired and actual work, for example), they must be expressed in the same reference frame, for example, relative to the trunk (Laurutis and Robinson 1986; Robinson 1975). In this framework, the motor error signal that results from their comparison feeds the premotor neurons that themselves fire at a rate proportional to the size of the error. As gaze moves toward the target, the error diminishes and the firing of premotor neurons declines until they cease firing and stop exciting the motor neurons (Robinson 1975). This viewpoint was refined a few years later by replacing the encoding of position with an encoding of displacement (change in position; Jürgens et al. 1981). This displacement model was proposed as a possible alternative because electrophysiologists failed to find, in the visuomotor neuronal network, cells whose activity would signal the location of a target relative to the trunk. Instead, the large majority of encountered neurons (“visual” or “visuomotor”) exhibit a response field that moves with the eyes; they emit action potentials whenever a stimulus appears within a more or less bounded region of the visual field (retinotopically defined). The feedback signal has then been replaced by a signal encoding the eye displacement. Saccades would be driven by the same motor error signal; the only thing that has changed is the input (reference) and the signals updating the motor error.

The concept of the negative feedback loop was well accepted because it was a convenient and simple solution to a more fundamental question: the so-called “spatiotemporal transformation,” i.e., how a locus of activity (in the retina or in the SC) is transformed into a duration of motor neuron activity (Moschovakis et al. 1996, 1998; Scudder et al. 2002; Sparks 2002). The solution was simple since it removed the need to search within the brain activity for a process encoding the duration of saccades, as initially proposed in the chronometric hypothesis of Hans Kornhuber (Kornhuber 1971). With negative feedback control, there is no need for an internal chronometer; the saccade duration is a secondary by-product of the process reducing the mismatch between two spatial magnitudes (position or displacement) that some other processes would somehow estimate. The difference between the two proposed options (“position” vs. “displacement” options; Sparks 1989, 1999) is that the feedback signals must be “zeroed” after the end of each saccade in the displacement model. Otherwise, the combination of residual eye movement-related signals with signals elicited by the appearance of another target would lead to inaccurate saccades toward its location. A series of experiments were performed to confront these two hypotheses and refute the “position” option (Nichols and Sparks 1995). However, the question was reopened by subsequent experiments (Keller et al. 1996a) until the suggestion was made that the eye position feedback signals do not follow the same time course as the physical eye position (Schlag et al. 1998). For the first time, a mismatch was considered between on one hand the time course of neurally encoded eye position and on the other hand the time course of the physically measured eye position. Indeed, the neural signals would precede saccade onset, change as the eyes move, though not as fast, and lag the end of the saccade.

The feedback loop hypothesis is a conceptual framework that admittedly has been useful to generate experiments, make new observations, and interpret them. However, it also seems to be irrefutable insofar as it assumes signals and processes that cannot be negated if they do not exist. A first difficulty is brought up by the interpretation of saccade inaccuracy during cerebellar dysfunction. This dysmetria has been considered as resulting from an altered neural estimate of eye movement amplitude (Goffart et al. 1998, 2004; Keller 1989; Keller et al. 1983). Unfortunately, the origin of feedback signals carrying eye movement-related information remains unknown. Proprioceptive signals from extraocular muscles have been excluded because saccade accuracy is not altered after their deafferentation (Guthrie et al. 1983; Lewis et al. 2001). The exclusion of extraocular proprioception is also supported by the observation that saccades electrically evoked (by microstimulation in the fastigial nucleus or the pontine reticular formation) while a saccade is being prepared toward a visual target are not subsequently corrected (Noda et al. 1991; Sparks et al. 1987). Contrary to the cases in which microstimulation is applied in the frontal eye field or the SC (Schiller and Sandell 1983; Sparks and Mays 1983), the correction saccade misses the target by an error equal to the electrically evoked displacement. If proprioceptive signals were involved in the feedback control, gaze should aim at the target after the perturbation.

Corollary discharge (efference copy or sui generis sensation) was the proposed explanation. However, the problem is complicated by the fact that the eye movement-related signals from tonic neurons in the NPH and the MVN can also be excluded since their lesion does not alter saccade accuracy (Cannon and Robinson 1987; Kaneko 1997). If the estimate of gaze direction is not fed by proprioceptive signals or by tonic signals that directly drive the motor neurons, the question of how it is built remains unanswered. On the basis of neuromimetic modeling, the suggestion was made that the signals imagined in the models may not be explicitly conveyed by separate groups of neurons that neurophysiologists ought to identify. They would correspond to activities involving populations of neurons that are massively interconnected and distributed over several neuronal territories (Robinson 1992). In other words, the signals involved in the feedback control are not traceable by classical unit recording techniques. The major question then becomes to discover the spatiotemporal architecture of the network.

While the feedback control hypothesis encountered these complications for experimental testing, the chronometric hypothesis of Kornhuber (1971) was being revisited by the group of Peter Thier (Thier 2011). Putting the emphasis on the temporal measurements of saccades, this group suggested that the population response of Purkinje cells in the cerebellum gives a precise temporal signature of the onset and offset of saccades. Unfortunately, the population response was defined ad hoc: the onset and offset of the population response were defined as the activity that is four times the mean baseline activity. If different thresholds were used to quantify the timing of the population response, then the chronometric hypothesis would not be valid anymore. Moreover, the population was restricted to the subset of Purkinje cells that enhance their firing, ignoring those that have been shown to reduce their firing during saccades (Herzfeld et al. 2015; Soetedjo and Fuchs 2006; Suzuki and Keller 1988). Finally, the duration of the population burst does not increase when the size of saccades is experimentally enhanced with a paradigm called saccade amplitude adaptation (Catz et al. 2008). This result could have been considered as a refutation of the chronometric hypothesis, but another ad hoc argument (fatigue) was added to maintain a viewpoint that assimilates learning to an “optimization of a representation of time” (Thier et al. 2000) rather than to the modification of flows of activity within the brain networks.

Negative feedback control has also been proposed for the guidance of eye movements toward a moving visual target. Two main processes would operate in parallel (more or less independently): one process reduces the mismatch between gaze and target directions (see above), while the other reduces the velocity difference (velocity error) between the eye and target movements. Before discussing this hypothesis, we examine how the notion of target velocity (a notion that belongs to the language of kinematics) was introduced in the physiological sciences.

IS PURSUIT DRIVEN BY A TARGET VELOCITY NEURAL SIGNAL?

A little more than five decades ago, Rashbass (1961) designed a task in which the eyes, instead of making a saccade to a target moving toward the foveal field, drift away from it. They move away but in the same direction as the target motion, although with a lower speed. This observation was taken as evidence for considering target velocity as a stimulus driving the initiation of pursuit eye movements. In Rashbass’ task, the target appears at a location slightly eccentric in one visual hemifield (e.g., to the left) and moves slowly toward the foveal field (toward the right). Then, for a few tens of milliseconds, the eyes also move slowly in the same direction as the target (but away from its physical location). To observe this slow eye movement with no visible saccade, the target must start its motion from a location whose eccentricity is ~0.15–0.2 times its speed. In most experiments, the target moved with a constant speed < 10°/s, requiring a target motion onset from a 2° eccentric location. Thus the target center was located at the boundary of the foveal field. Obviously, a target, even a very small spot of light, does not excite one single cell but many cells. In the SC, for example, regardless of whether the target is located in the peripheral or central visual field, a large population of neurons is recruited and occupies a territory corresponding to several degrees of visual angle (Anderson et al. 1998; Goossens and Van Opstal 2006; Hafed et al. 2008; Hafed and Krauzlis 2008; Moschovakis et al. 2001; Sparks et al. 1976). A saccade is not launched toward the centripetal target because the equilibrium that specifies gaze direction is not broken; the visuo-saccadic oculomotor system is within a mode where opposite commands counterbalance each other (see visuomotor transformation and its numerical processing).

By contrast, the drift of the eyes (in the same direction as the target motion) tells us that initiating a slow eye movement involves another symmetry breaking. It results from an imbalance between commands that tonic neurons in the left and right NPH/MVN exert upon the motor neurons (McCrea and Horn 2006; McFarland and Fuchs 1992; Scudder and Fuchs 1992). Their equilibrium (akin to that shown in Fig. 1) can be broken by an imbalance of excitation, for instance, in their visual input from the pretectum, i.e., an imbalance between the left and right nuclei of the optic tract (NOT). Thus, in the Rashbass paradigm, an imbalance between opposite directional tendencies could drive the eyes in the same direction as the target. This explanation is consistent with observations made after unilateral inactivation of NOT: the monkey exhibits an irrepressible drift of the eyes toward the contralesional side (Inoue et al. 2000; L. Goffart, C. Bourrelly, J. C. Quinton, unpublished observations). The fact that the drift occurs even in the presence of a central visual target (Fig. 2) indicates that the bilateral activity which in the SC maintains gaze direction steady is not sufficient to counteract the drift caused by the imbalance of NOT activity. After some time, a correction saccade is made back toward the central target; the bilateral equilibrium supported by the fastigiocollicular activities (Goffart et al. 2012; Guerrasio et al. 2010; Krauzlis et al. 2017) has been broken by the recruitment of saccade-related cells.

Fig. 2.

Nystagmus observed after injection of a small amount of muscimol (0.6 µl) in the left nucleus of the optic tract (NOT). The eye drifts horizontally toward the contralesional side until a saccade is made toward the left. The unilateral suppression of NOT signals causes an imbalance of visual input to the nucleus prepositus hypoglossi, which itself affects the balance of tonic input onto the abducens motor neurons. Exp. 1 and Exp. 2 refer to two experimental sessions made on different days.

Such a slow drift does not happen during unilateral SC inactivation: the monkey is able to maintain gaze stable. Its direction is offset with respect to the target with an angle that is relatively constant even while the monkey is pursuing a moving target (Hafed et al. 2008). Despite the mismatch between gaze and target directions, the pursuit is preserved. Comparable observations have been reported during caudal fastigial inactivation (Robinson et al. 1997; see Figs. 1 in Bourrelly et al. 2018a, 2018b). Made in experimentally induced pathological conditions, these observations indicate that the target does not have to be centered within the foveal field to be smoothly pursued. As a matter of fact, several behavioral experiments in the normal subject have demonstrated this possibility (Fuchs 1967a; Pola and Wyatt 1980; Robinson 1965; Segraves and Goldberg 1994; Winterson and Steinman 1978). In summary, during the Rashbass paradigm, a velocity signal is not the unique explanation accounting for the observation that the eye moves away from the target. The motion of the target image across the foveae yields an imbalance of activity between the left and right NOT (Gamlin 2006; Hoffmann et al. 2009; Mustari and Fuchs 1990). Interestingly, the retinal motion declines while the eyes accelerate. What remains to be understood, then, is how the slow eye movement persists and increases to reach the same speed as the target, despite the reducing “velocity error.”

The idea that pursuit consists of matching the velocities of eye and target movements can be traced back to the studies of Rashbass (1961) and Robinson (1965). It pervades the contemporary sciences of eye movements so much that in most reviews pursuit eye movements are considered as involving a negative feedback loop for reducing the difference between estimates of eye and target velocities complemented by a positive feedback loop for sustaining the movement when the velocity error is zeroed (e.g., Barnes 2008; Carpenter 1988; Fukushima et al. 2013; Leigh and Zee 2015; Lisberger et al. 1987; Robinson et al. 1986).

However, Raymond Dodge, one of the earliest scientists who analyzed the time course of eye movements, reported that “since the pursuit movements invariably lag, they alone would give very erroneous data concerning the velocity of the object” and that “direct observation of an eye, following a uniformly moving object, discloses a relatively complex phenomenon, which apparently includes at least two distinct kinds of eye movements. A succession of rapid, jerk-like movements are separated by what appear to be longer regular movements of less velocity”(Dodge 1903). He also indicated that “even in slow movements of the object of regard, in which the twenty degrees was covered in about three seconds, the little jerks still persisted, though they were of extremely small amplitude. Since the velocity of the true pursuit movements constantly decreased with the velocity of the object of regard, it seems probable that we must regard the auxiliary jerks of the first type as constant accompaniments of the pursuit movements; and since they always appear in the direction of the pursuit, they indicate that the true pursuit movement tends to lag a little, and is supplemented from time to time by movements of the first type” (Dodge 1903).

The saltatory (not smooth) aspect of eye movements tracking a visual target has been noted in several other studies. de Weese Puckett and Steinman (1969) observed a mismatch between the velocity of pursuit eye movements and the constant velocity of a moving target, whereas Steinman et al. (1969) documented that highly experienced subjects were unable to match eye to target velocity, even when they voluntarily tried to do so. Interestingly, neither subject was able to make slow eye movements faster than the target. A few years later, Knowler et al. (1978) observed that pursuit eye movements could only match the target velocity after considerable practice. During almost daily practice for a month, the performance of one subject gradually and systematically rose to quasi-complete velocity matching. Whitteridge (1960) reported comparable observations made earlier by Stroud (see Whitteridge’s Fig. 11).

In the monkey, Fuchs (1967a) reported that “when first presented with a high velocity ramp, some monkeys also have difficulty attaining target speed. The response to the first presentation of a 30 deg/sec ramp is usually composed entirely of closely spaced […] saccades with no attempts to match target velocity. Only two target presentations later the monkey [Macaca speciosa] already tries a velocity correction although the movement is still primarily saccadic. Finally, after a total of about forty presentations, the monkey has mobilized his smooth response so as to be able to track the target for a sustained period of time.” Another study reports that one of their animals (M. mulatta) made mostly saccadic eye movements to the target motion and only occasional smooth pursuit (Neary et al. 1987). However, after they employed “a modified training procedure which required the monkey to accurately track a moving target and thus presumably pay close attention to its motion (the monkey had to keep its eye within an ‘electronic window’ which moved along with the target, to obtain the reward), the monkey began to show vigorous smooth pursuit movements to the square-wave target motion” (see also Neary 1986).

The evolution of oculomotor tracking with practice has recently been documented in a study testing a relatively large number of naive rhesus monkeys (M. mulatta). In this study, Bourrelly et al. (2016) show how inexperienced monkeys track a visual target that moves with a constant speed along a horizontal path and how the time course of their tracking eye movements gradually evolves across several days of practice with barely any spatiotemporal constraints. Indeed, the “electronic window” around the moving target within which the monkey had to direct its gaze was very large (10–12° horizontally and 6–10° vertically). If a smaller window had been used, the monkeys would have failed to track the target and the trial would have been aborted. It is therefore not surprising that studies that used small electronic windows reported faster pursuit eye movements. They were faster because the visual tracking was selected by experimental constraints to become so, smooth and devoid of saccades. In the study of Bourrelly et al. (2016), catch-up saccades were permitted, especially those that would aim at a future location of the target (because the electronic window extended beyond the current target location). However, these “predictive” saccades landing ahead of the moving target just did not happen; gaze direction lagged behind the target most of the time. With practice, more trials appeared during which gaze moved as if it were “attached” to the target. Initially, the monkeys did not exhibit such a smooth tracking; it was mostly saltatory, i.e., composed of catch-up saccades. From this initial state where the gaze tracked a past target location most of the time, the behavior evolved with successive trials and daily sessions into a mode where gaze appeared more often locked onto the current target location (Fig. 3).

Fig. 3.

Typical oculomotor behavior of a monkey tracking a visual target moving horizontally with a constant speed. The horizontal eye position is plotted as a function of time after target motion onset for 3 trials recorded during the first (Beginning, left) and last (End, right) training sessions. The time course of horizontal target position is illustrated by the dashed line. The selected trials were recorded in 5 monkeys (from top to bottom, monkeys A, B, C, M, and G) when the target moved in the upper right quadrant with a constant speed (20°/s). During the other randomly interleaved trials, the target moved similarly, horizontally and away from the vertical meridian, but in the lower right, the lower left, or the upper left quadrant. Additional methodological information can be found in Bourrelly et al. (2016).

Although most studies viewed this improvement as a gain increase in the positive feedback loop, to our knowledge, none of them explained what this gain change meant in neurophysiological words. Recently, the proposal was made that the enhancement of pursuit velocity could result from the recruitment of neurons in pursuit-related regions targeted by the oculomotor cerebellum and/or from the acquisition of a saccade-contingent burst by pursuit-related neurons (Bourrelly et al. 2018b; Goffart et al. 2017a). Finally, although the target moved along the same horizontal path and the reward was always given at the end of the trial, the monkeys did not make saccades directly toward the rewarded location. Given the large extent of the electronic window, such saccades would not have been punished, either.

This oculomotor performance was “mathematically” simulated and reproduced with dynamic neural field models (Quinton and Goffart 2018). In such models, a population of topologically organized units (themselves representing assemblies of neurons) drives the eye movements, with delays and projections expanding the population of active units. By altering the projections through a simple learning mechanism, the velocity of simulated pursuit eye movements was progressively increased, making it possible to synchronize the eye movement with the target motion; the number of catch-up saccades diminished as a consequence.

At this point, the idea that velocity error would be the signal that spontaneously drives pursuit eye movements becomes questionable, since the ability to move the eyes with the same velocity as the target appears to be the outcome of a learning (training) procedure (see also Botschko et al. 2018). Using a task that required the foveation of a small circular target in order to identify the orientation of striae contained inside (dynamic visual acuity), Barmack (1970) trained a monkey to execute horizontal pursuit eye movements at velocities of up to a maximum of 140°/s. However, no information was given about the time taken to reach this performance. Human subjects are capable of executing pursuit eye movements of 90°/s but after a few saccades are made. Neil Barmack suggested that the discrepancy did not result from different amounts of practice but from different testing conditions. Indeed, by requiring the identification of details within the target, the dynamic visual acuity task might provide a greater incentive to accurately pursue the target. However, the question then is whether the task consists of matching the eye velocity to the target velocity or maintaining the target foveation by matching the eye position to the target position or, for those who do not wish to plunge spatial notions within the brain, balancing opposing tendencies emitted in the left and right parts of the brain stem.

EYE AND TARGET POSITIONS DURING TRACKING

In the majority of cases, whenever a target moves in the peripheral visual field, the first eye movement is an interceptive saccade. Contrary to the claim that “in [their] programming […], target motion is used to predict the future target position so as to assure a spatial lead of the gaze at the saccade end, instead of attempting a precise capture of the target” (Klam et al. 2001; see also Berthoz 2012), most behavioral studies show that the saccades are such that they do not direct gaze toward a location where the target will be in the future. They direct gaze either toward its current location or toward a location lagging behind (Barmack 1970; Bourrelly et al. 2016, 2018a; Fleuriet et al., 2011; Fuchs 1967a, 1967b; Keller and Johnsen 1990; Robinson 1965). The saccades do not orient the foveae toward a location where gaze would wait for the target (like the traveler waits for a bus) to enter within the foveal field and initiate the pursuit.

The fact that saccades do not aim at the future but the current location of a moving object is strongly suggested by results of experiments during which the interceptive saccade is perturbed by the application of a brief electrical microstimulation in the deep SC (Fleuriet and Goffart 2012). Under such circumstances, the electrically induced change in eye position is corrected in flight or after a short delay, and gaze is brought back to the location where unperturbed saccades would have landed at about the same time. This observation is primarily made when the stimulation is applied at sites that are not involved in the generation of the interceptive saccade (i.e., at sites that evoke saccades with amplitude and direction close to those of the interceptive saccade). Otherwise, the interpretation is complicated by interactions between the electrically and visually evoked activities. When the microstimulation is applied in the SC opposite to the visually excited one, after the electrically induced change in gaze direction, most correction saccades do not overshoot along the motion path. They do not bring gaze toward a location where the target will be later; they either fall short or land accurately on the location where unperturbed saccades would have landed (see Figs. 2–4 in Fleuriet and Goffart 2012 and also Fig. 4 in Goffart et al. 2017a). In these experiments, the target was made invisible for a brief interval (150 or 300 ms) to avoid the possibility that visual signals guided the correction.

Two groups of signals can participate in the elaboration of the command that guides the interceptive saccade toward a transiently invisible target, regardless of whether its trajectory is perturbed or not: 1) the target motion-related signals that precede the interval of target invisibility but also 2) mnemonic signals that the target is expected to reappear and continue to move along the same path. Concerning the first group of signals, it is quite possible that after the moving target disappears activity persists within the visuomotor channels. The massive interconnectedness of neural populations in the brain likely contributes to the persistence of activity for durations that largely exceed the actual duration of the physical event (see, e.g., Edelman and Goldberg 2001; Mays and Sparks 1980; Sommer and Wurtz 2000). Behavioral studies suggest that the persistence is influenced by signals related to the target motion direction. As we said above, pursuit eye movement persists in the same direction beyond the time and location where a moving target disappeared (see, e.g., Mitrani and Dimitrov 1978). Likewise, a significant proportion of saccades made in response to a transient moving target land on positions situated beyond the location where the target disappeared (Quinet and Goffart 2015a). Thus the correction saccades reported in the perturbation experiments of Fleuriet and Goffart (2012) could be guided by residual visual signals. Concerning the second group of signals, the target reappeared 150 or 300 ms after its disappearance, continuing its motion along the same path with the same velocity. There was no uncertainty that the target would reappear and keep moving along the same path. The monkeys never experienced trials in which the target would start moving backward or change its direction during the interval of invisibility. Moreover, they were not trained to only make a saccade toward the transient moving target (as in Quinet and Goffart 2015a); they were rewarded after they continued to track the reappeared target until the end of the trial. Hence, additional central factors contributed to the guidance of correction saccades. If the residual signals that persist after target disappearance merge with prelude signals related to its upcoming reappearance, then the interval during which the target is absent is “filled in” by the brain activity. Such an interpolation would drive the activity of premotor neurons and guide the eye movement, regardless of whether it is a saccade or a pursuit eye movement. Therefore, the command that encodes at best the expected and current (here and now) location of the target and guides the gaze direction when a target becomes invisible could correspond to a merging of signals related to the recent past with signals carrying an expectancy of reappearing (built upon the past and repeated experience). If this explanation holds also for any moving target, constantly visible or briefly invisible, then its neural image does not need to be reduced to an internal model of its trajectory (a physical notion) (see also Quinton and Girau 2011 for similar observations in silico).

GENERAL CONCLUSIONS

For several decades, eye movements have been used as a probe to understand how neuronal networks in the brain process visual signals and how they endow foveated animals with the ability to locate a stimulus, even when it is moving. Notions of kinematics were used to “decode” the firing rate of neurons and to explain the neurophysiology underlying the generation of tracking eye movements. The appropriateness of these notions to a medium radically different from the physical world (the brain) was not questioned. Yet, an alternative explanation is possible: the maintenance of target foveation could consist of dynamically balancing opposing tendencies emitted in the left and right parts of the brain stem, as proposed for the control of saccade trajectory (Bourrelly et al. 2018a; Goffart et al. 2004; Van Gisbergen et al. 1981) and fixation (Goffart et al. 2012; Guerrasio et al. 2010). Regarding the question of how eye movements can reach the target speed, the acceleration could involve a process of neuronal recruitment: increasing the firing and the number of motion-related neurons moves the eyes faster, whereas decreasing them reduces the velocity. Thus the central problem for understanding the neural control of pursuit eye movement becomes characterizing the adjustment of the appropriate population size through recruiting neurons and synchronizing their firing rate.

Saccadic eye movements can also be used as a probe to study this question. Within the SC and downstream, a neuronal recruitment seems to be involved also in determining the total saccadic eye displacement, as suggested by recording and modeling studies (Badler and Keller 2002; Sparks et al. 1976) and by perturbation experiments using microstimulation (Quinet and Goffart 2015b; Sparks et al. 1987), local pharmacological inactivation (Goffart 2017; Goffart et al. 2017c), or the trigeminal blink reflex (Gandhi and Bonadonna 2005; Jagadisan and Gandhi 2017). The use of moving visual stimuli should enable investigation of whether this recruitment consists of including more neurons in the SC and/or more synchronized firing in the reticular formation. Indeed, in response to identical brief target motions (identical durations and displacements), not only do the saccades land on different locations depending upon whether the target accelerates or decelerates but their amplitude also increases linearly with time when the target accelerates (Quinet and Goffart 2015a). Finally, instead of grounding the encoding of eye velocity or acceleration in the sole firing rate of single neurons, we propose that the dynamics of eye movements reflects the transition from an unbalanced state to equilibrium between opposing motor tendencies. In any case, the neural processes underlying the generation of eye movements follow principles that are primarily defined by the intrinsic properties of the brain network and its diverse neurons rather than the physical laws of motion.

Such research should not be restricted to primates but extended to other species, even to invertebrates such as Mantis religiosa (Rossel 1980; Yamawaki et al. 2011) and perhaps Daphnia magna (Consi et al. 1990), in order to discover how biologically more rudimentary bilateral structures enable animals to dynamically adjust the orientation of their visual organ toward the location of an object, static or moving. The use of such animals guarantees that we do not fall under the anthropocentric “illusion that the relations an animal has with the objects in its environment take place in the same space and the same time as those which bind us to the objects of our human world. This illusion is fed by the belief in the existence of a unique world in which all living beings would be embedded. It follows the general and long-lasting conviction that there must be one single space and time for all living beings” (von Uexküll 1934).

Regarding the mathematical modeling, novel techniques combining spiking neuron networks (Kasap and van Opstal 2017; Paugam-Moisy and Bohte 2012) and dynamic neural fields (Amari 1977) should be developed or created to complement those that, during the last five decades, have overlooked the neuronal complexity and the parallel and distributed nature of visuomotor flows and considered behavioral parameters as encoded within their nodes rather than as their ultimate outcome. As Claude Bernard wrote, “our ideas are merely intellectual instruments which allow us penetrating inside the phenomenon; they must be changed after having fulfilled their role, like one changes a blunt scalpel blade which has served after enough time” (Bernard 1865).

GRANTS

Supported by the Centre National de la Recherche Scientifique, this work also received funding support from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013/ERC grant agreement no. AG324070 to Patrick Cavanagh).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

L.G., C.B., and J.-C.Q. performed experiments; L.G., C.B., and J.-C.Q. analyzed data; L.G. interpreted results of experiments; L.G. and C.B. prepared figures; L.G. drafted manuscript; L.G., C.B., and J.-C.Q. edited and revised manuscript; L.G., C.B., and J.-C.Q. approved final version of manuscript.