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Spatio-temporal frequency characteristics of the optomotor response in zebrafish
Vision Research 43 (2003) 21–30 www.elsevier.com/locate/visres
Spatio-temporal frequency characteristics of the optomotor response in zebrafish Hans Maaswinkel, Lei Li
*
Department of Physiology, University of Kentucky College of Medicine, 800 Rose Street, Lexington, KY 40536, USA Received 1 July 2002; received in revised form 29 August 2002
Abstract The optomotor response (OMR) is a simple experimental paradigm that is widely used in the study of visual system functions. In the current paper we investigated how spatial and temporal properties of repetitive stimuli determine the OMR in zebrafish. The experiments showed that the OMR has the temporal characteristic of a low-pass filter when the spatial frequencies are low and of a band-pass filter when the spatial frequencies are high. These findings are discussed on the basis of inherent sampling constraints of any motion detector. We found some indications that the strength and direction of the OMR vary with the spatio-temporal frequency of the stimulus pattern as has previously been described for other species. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Optomotor response; Motion detection; Spatio-temporal frequencies; Zebrafish
1. Introduction The optomotor response (OMR) is the locomotor behavior of an animal induced by a moving repetitive stimulus pattern. In most studies this pattern consists of vertical stripes, which might be in black and white (Clark, 1981), different gray contrasts (Lindsey, Chawla, & Townes-Anderson, 2002), or different colors (Schaerer & Neumeyer, 1996). The OMR has been described in different animal species as far apart as drosophila (David, 1979), the four-eyed fish anablebs (Saidl & Fabiane, 1998), tiger salamander (Lindsey et al., 2002), crayfish (Glantz, 2001), zebrafish (Clark, 1981), and humans (Klein, Fisher, Hartnegg, Heiss, & Roth, 2000). The OMR has been hypothesized to play a role in the control of speed and direction of body movement (Srinivasan, Poteser, & Kral, 1999), or, more generally, that it stimulates the neuronal mechanism involved in the processing of the optic flow, necessary for visual guided self-motion (Kern, Lutterklas, Petereit, Lindemann, & Engelhaaf, 2001). That vertical bars are especially effective stimuli that elicit OMR, might be due to the fact that orthogonal cues are prevalent in the environment (Coppola, *
Corresponding author. Tel.: +1-859-323-4757; fax: +1-859-3231070. E-mail address: [email protected] (L. Li).
Purves, McCoy, & Purves, 1998) and that the visual system is more tuned to these stimuli, than to slanted ones (Coppola, White, Fitzpratick, & Purves, 1998; Proverbio, Exposito, & Zani, 2002). Topics that have been studied using the OMR are among others: first- and second-order components of movement detection (Orger, Smear, Anstis, & Baier, 2000), functions of different regions of the retina (Saidl & Fabiane, 1998) and of the brain (Spinger, Easter, & Agranoff, 1977), the contribution of color vision to motion detection (Anstis, Hutahajan, & Cavanagh, 1998; Schaerer & Neumeyer, 1996), development of visual perception (Clark, 1981), motion perception during aging (Klein et al., 2000), the effect of rearing conditions (Bilotta, 2000), and the role of neurotransmitters in motion detection (Mora-Ferrer, 2002). It is also useful for the screening of visual mutants (Neuhauss et al., 1999) and toxicological research (Dutta, Marcelino, & Richmonds, 1992). The OMR procedure has been used to study phenomena, which do not involve motion detection per se as well, such as contrast sensitivity. Usually a flickering light source or a stationary or flickering grating pattern serves the purpose. However, these tests, when performed with lower vertebrates, require complex settings and conditioning procedures, e.g. to suppress respiration in the goldfish (Bilotta, Demarco, & Powers, 1995; Bilotta & Powers, 1992). To overcome this problem, the OMR
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test can be used as an alternative (Lindsey et al., 2002). This, however, raises the question how spatial and temporal aspects are connected in the OMR. In general, the movement of a stimulus can be described in terms of direction and velocity. However, the motion of a repetitive stimulus pattern can also be described in terms of temporal frequency, which is the product of spatial frequency and velocity. The temporal frequency description can be important, because every detector has a spatial and temporal frequency characteristic of its own (Derrington, 2000). Thus, the operation frequencies of the detector can constrain the object frequencies that can be detected (Shannon & Weaver, 1949). Aliasing (i.e. deviation of direction and/or velocity of perceived motion from actual motion) occurs when the frequency of the detector is lower than twice the frequency to be detected. For non-repetitive stimuli, aliasing impairs resolution by filtering out high-spatial frequencies, however, effects on motion detection seem to be minimal (Anderson & Burr, 1985). Repetitive stimulus pattern, on the other hand, are very vulnerable to aliasing. Even slowly drifting high-spatial frequency gratings can be perceived as reversing movement direction and changing velocity when presented to a peripheral zone of the retina called the Ôaliasing zoneÕ (Anderson & Hess, 1990; Coletta, Williams, & Tiana, 1990). The OMR has originally been one of the classic fields in which aliasing has been studied (Gotz, 1964; Hassenstein & Reichardt, 1956; Reichardt & Varju, 1959). In Drosophila, for example, it has been found that the strength and direction of the OMR depend on the spatio-temporal frequencies of the stimulus pattern (Gotz, 1964). In the current study, the relationship between spatial and temporal frequency in motion detection were investigated in zebrafish. By using a wide range of spatial frequencies and velocities (and hence temporal frequencies), we examined the OMR characteristics, bearing the above mentioned fundamental principles of any motion detector in mind concerning possible misperception of velocity and direction of movement, and the possibility to measure velocity either by temporal frequency or angular velocity.
2. Material and methods 2.1. Subjects Zebrafish (Danio rerio) were maintained as described (Westerfield, 1995). They were between 6 and 12 months old and were kept in a 14–10 h light/dark cycle (light, 6 a.m.–8 p.m., room fluorescent light).
Fig. 1. Schematic view of the OMR apparatus. The drum (D) rotates clockwise (shown by arrow) or counterclockwise around the transparent fish container (C). In the center of the container a column (P) is placed. The inset shows an example of a stimulus pattern, printed on paper and attached on the inside of the drum. The fish is depicted as following the direction of the rotation of the drum, i.e. it shows a positive OMR (arrow).
consists of a drum, 15 cm in diameter, which can rotate clockwise and counter-clockwise with a speed up to 100 rotations per min (rpm). At the inside of the drum a strip of paper can be attached. In the current study the paper bore either a grating pattern, consisting of black and white vertical stripes, or it was uniformly gray (the gray-level was adjusted halfway between the gray levels of the black and white stripes). In the center of the drum, a circular transparent fish tank (11 cm in diameter) was suspended. A column (3 cm in diameter) was placed in the center of the fish tank to prevent the fish from swimming through the center. A light source was suspended above the apparatus. The light intensity measured at the water surface was 4.75 lW/cm2 . To calculate the subjective angular velocities of the stripes, the zebrafish was assumed to swim halfway between the column and the wall of the fish tank. 2.3. Procedures
2.2. OMR apparatus The apparatus is modified from the one previously described by Li and Dowling (1997) (see also Fig. 1). It
All experiments described here were carried out between 10 a.m. and 1 p.m. The fish were placed in the dark testing room to habituate for approximately 20
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min. Each fish was then tested for the OMR in two consecutive one-minute trials. The direction of rotation of the stimulus pattern was in one trial clockwise, in the other anticlockwise, in a random sequence. This was done in order to exclude any directional bias. The number of full turns of the zebrafish around the column in the center in either direction was scored. A Ôpositive responseÕ was defined as a full turn in the same direction as the stimulus patterns, a Ônegative responseÕ as a full turn in the opposite direction. The Ôproportion of positive responsesÕ (PPR) was calculated by dividing the number of the positive responses (from both trials) by the number of all responses. In case the fish did not show any positive or negative responses during both trials, the PPR was set at 0.5, which is the baseline level for random swimming. 2.3.1. Experiment 1. Responses for different spatial frequencies The drum was rotated at a constant speed of 10 rpm, corresponding to a subjective angular velocity of 103 deg/s (degrees per second). The OMR was tested for seven spatial frequencies: 0.01, 0.02, 0.04, 0.08, 0.16, 0.31, 0.62 c/deg (cycles per degree). The PPR was plotted for every spatial frequency (PPR/spatial-frequency curve). As control, fish were tested with the same spatial frequencies at a velocity of 0 rpm. The data from both groups were compared for every spatial frequency using a t-test. 2.3.2. Experiment 2. Responses for different temporal frequencies The fish were tested with all seven spatial frequencies mentioned in experiment 1 at different rotation speeds of the drum: 0, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 rpm, corresponding to the following subjective angular velocities: 0, 52, 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030 deg/s. For every stimulus pattern, a PPR/velocity function was drawn. The temporal frequencies for these rotation speeds were calculated for every spatial frequency and expressed in cycles per second (cps). The response characteristics were presented in a velocity/ spatial-frequency diagram and a temporal-frequency/ spatial-frequency diagram.
3. Results 3.1. Experiment 1. Responses for different spatial frequencies Fig. 2 shows the PPR for all studied spatial frequencies for velocities of 0 and 103 deg/s. For spatial frequencies up to 0.08 c/deg, the zebrafish swam most often in the direction of the moving stimulus when tested with a velocity of 103 deg/s. Their PPR was signifi-
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Fig. 2. PPR/spatial-frequency function for all tested frequencies for a velocity of zero () and 103 deg/s (). Note that the PPR is significantly greater than 0.5 only for the low-spatial frequencies. Error bars represent SEM. < 0:05, < 0:01, < 0:005.
cantly greater than for velocity zero, where they did not have such a preferential swimming direction. For higher spatial frequencies (0.16–0.62 c/deg), however, no OMR could be found. The PPR was for both rotating and stationary drum statistically not different and close to 0.5. Thus, 0.08 c/deg is the highest frequency under which OMR occurs at the given velocity of 103 deg/s (10 rpm). This is very close to the results found by others (Bilotta, 2000; Clark, 1981; see also Section 4). In experiment 2 we will investigate how the response limit depends on velocity and temporal frequency, using a range of drum rotation speeds between 5 and 100 rpm. 3.2. Experiment 2. Responses for different temporal frequencies Fig. 3 shows the PPR/velocity functions for the null stimulus and all seven spatial frequencies. It is apparent, that the velocities to which the fish react positively are different for different spatial frequencies, and that there is often a lower and an upper limit beyond which no PPR is significantly higher than 0.5. The null stimulus (a uniform gray paper without stripes) did not elicit any significant OMR. Thus the PPR fluctuated slightly around 0.5. For the lowest spatial frequency (0.01 c/deg), zebrafish responded over the entire range of tested velocities. With increasing spatial frequency, i.e. from 0.02 to 0.08 c/deg, the OMR disappeared for the higher velocities. With further elevation of the spatial frequency, i.e. from 0.16 to 0.62 c/deg, the OMR disappeared at lower velocities as well, so that the PPR is greater than 0.5 in only a small window of velocities. To give a graphic overview over all the data, the 3D mesh plots (Fig. 4A and B) were drawn to show PPR in the spatial-frequency/velocity or the spatial-frequency/
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Fig. 3. PPR/velocity functions for the seven spatial frequencies (A–G) and for the null stimulus (H) for all velocities (0–1030 deg/s). Note that the PPR for the null stimulus is for none of the velocities statistically different from its value at velocity 0 deg/s. Error bars are SEM, < 0:05.
temporal-frequency domain, respectively. The light gray areas coincide approximately with the PPR values that are significantly different from the PPR found for zebrafish tested with a stationary drum. For low-spatial frequencies, the PPR is high only for low-velocities and temporal frequencies. An exception is the PPR for 0.01 c/deg, were for the highest speed of the test apparatus (100 rpm) the PPR was greater than 0.5. For high-spatial frequencies the PPR was greater than 0.5 for higher velocities or temporal frequencies, and dropped down
again when velocities or temporal frequencies further increased. Notice that Fig. 4B is partially based on inferred data. For example, for 0.01-c/deg the highest temporal frequencies, for which the PPR is set at 0.5, have not been measured. Other values have been averaged from surrounding values. Fig. 5A represents the upper and lower response limits of OMR in a velocity/spatial frequency diagram. The upper response limit for a given spatial frequency is the velocity at and above which the PPR is not
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Fig. 4. Mesh plots (3D) of PPR. (A) PPR represented in the spatial-frequency/velocity domain. (B) PPR represented in the spatial-frequency/ temporal-frequency domain.
statistically different from 0.5. The lower response limit is the velocity at and below which the PPR is not significantly different from 0.5. For the lower spatial frequencies (up to 0.08 c/deg) the PPR has the characteristic of a low-pass filter (i.e. the PPR is greater than 0.5 for all velocities between 0 and the upper limit). For higher spatial frequencies (0.16 c/deg and up), on the other hand, the PPR has the characteristic of a band-pass filter (i.e. the PPR is greater than 0.5 in a velocity window, with a lower limit higher than 0 deg/s). Fig. 5B shows the temporal-frequency/spatial-frequency diagram. As expected, the low-pass character for low-spatial frequencies and the band-pass character for high-spatial frequencies were also found here. However, what strikes in this representation are the high-temporal frequencies (up to 256 cps) that elicit an OMR at higher spatial frequencies. The number of positive and negative responses for the lowest (0.01 c/deg) and highest spatial frequency (0.62 c/deg) are shown in Fig. 6. The striking fact for the spatial frequency of 0.01 c/deg (Fig. 6A) is that the number of positive responses first increased, then decreased with increasing velocity. It peaked between 400 and 600 deg/s, with a small dip at 500 deg/s. Then, starting from 700 deg/s, it decreased with further increase of velocity. For the spatial frequency of 0.62 c/deg (Fig. 6B), on the other hand, the numbers of positive and negative were about equal for most velocities. However, for nearly all velocities higher than zero, the total number of (positive and negative) responses was significantly different from the number of responses at velocity zero.
4. Discussion In this study, we examined how spatial and temporal frequency determines the OMR in zebrafish. The interesting finding is that the PPR/velocity and PPR/temporal-frequency functions act as low-pass filters when tested with low-spatial frequencies and as band-pass filters when tested with high-spatial frequencies. In the following we will expose these findings and search for interpretations. 4.1. Spatial and temporal frequency in the OMR We demonstrated in experiment 1 that for a lowvelocity (103 deg/s), zebrafish follow the rotation direction of the stripes only for low spatial frequencies. For higher spatial frequencies, such a preferential swimming direction was not observed. However, the swimming activity was randomized rather than reduced, i.e. they showed as many negative as positive responses. The occurrence of negative responses can either be a result of spontaneous behavior, or be an indication for intermittently occurring apparent motions in the opposite direction (see Section 4.4). In experiment 2 we found that the highest velocity for which the PPR was significantly greater than for velocity zero, was 1030 and 412 deg/s for the highest and lowest spatial frequency, respectively (Fig. 5A). In terms of temporal frequencies, we found very high-response limits for the higher spatial frequencies. For the 0.31c/deg stripes, for example, zebrafish reacted to frequencies as high as 256 cps. The PPR/temporal-frequency function had for lower spatial frequencies the character
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Fig. 5. OMR limits in the spatio-temporal domain. (A) Velocity/spatial-frequency diagram indicating the OMR limits. The upper and lower response limits, the velocity boundary between which the zebrafish show a positive OMR, are presented for seven spatial frequencies. (B) Temporal-frequency/spatial-frequency function for the same data. For comparison the critical flicker frequency as described for goldfish (Bilotta, Lynd, & Powers, 1998) is presented as dashed line.
of a low-pass filter, for higher spatial frequencies the character of a band-pass filter, e.g. for the 0.62-c/deg stripes the PPR was greater than 0.5 only between 128 and 256 cps (Fig. 5B). 4.2. Comparing the current results with other studies In fish, several aspects of OMR have been studied. It has for example been used to study wavelength sensitivity (Anstis et al., 1998), the contribution of color vision to motion detection (Schaerer & Neumeyer, 1996), the effect of neurotransmitters on motion detection (Mora-Ferrer, 2002) and as indicator for toxicological pollution (Dutta et al., 1992). In all those ÔappliedÕ studies, the range of spatial frequencies tested is similar to that used in the current paper, and the range of velocities to that used in our experiment 1. Clark (1981), who has carried out the most extensive study concerning the influence of different width of stripes and velocities
Fig. 6. Number of positive and negative responses for zebrafish tested in 2 min trials with the 0.01 c/deg-stripes (A) and with the 0.62 c/degstripes (B) over all velocities (0–1030 cps). Error bars are SEM.
on the OMR in zebrafish, varied the speed only between 5 and 15 rpm. We used a maximum of 100 rpm. To our knowledge, OMR has not been studied before in fish by varying the velocity/temporal-frequency over a wide range. The same is true for other non-mammalian vertebrates (e.g. Lindsey et al., 2002). The PPR/spatialfrequency function described here for low-temporal frequencies is similar as described by others for the OMR (Bilotta, 2000) and the optokinetic nystagmus (DeMarco, Nussdorf, Brockman, & Powers, 1989) in goldfish. The maximal spatial frequency, to which zebrafish react with a PPR significant higher than found for stationary stimuli (PPR around 0.5), seems to be slightly lower than found in other studies (Bilotta, 2000). Several factors might determine the PPR/spatial-frequency function, such as velocity, illumination, time of the day when the experiment was performed, testing procedure, or age of the fish. Psychophysical studies of the OMR with regard to motion detector functions and velocity/temporalfrequency limits have made extensively use of insects (Reichardt, 1969; Srinivasan et al., 1999). One of the most consistently found characteristics of the OMR in insects is that the direction and the strength of the OMR depend on the spatio-temporal frequencies of the grating pattern (Gotz, 1964; Reichardt & Varju, 1959). A fur-
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ther interesting finding is that insects can determine the velocity of a repetitive stimulus pattern either by its temporal frequency or its angular velocity, depending on the behavioral task (Srinivasan et al., 1999). In the brain of the honeybee, for example, both temporal-frequencytuned cells and velocity-tuned cells have been found (Ibbotson, 2001). The temporal-frequency-tuned cells (supposed to mediate OMR) peak at about 10 Hz and cut off at about 100 Hz. The velocity-tuned cells respond to angular velocities up to 1000 deg/s. For low-spatial frequencies, the OMR temporal frequency curve is a low-pass filter, and peaks for all spatial frequency at the same temporal frequencies (Reichardt, 1969). Similarly, we found in zebrafish, that for spatial frequencies up to 0.08 c/deg the lower and upper response limits vary only slightly and that the OMR has the character of a low-pass filter. For higher spatial frequencies, Gotz (1964) found that insects show a retrograde OMR, at least for lower angular velocities. With increasing velocities and increasing spatial frequencies, the OMR becomes again orthograde (Gotz, 1964). Our results are not exactly the same, but comparable. We found in the high-spatial/low-temporal-frequency domain that PPR was close to 0.5, and with increasing velocities (temporal frequencies) the PPR increased.
4.3. Brain areas involved in OMR Since motion detection depends on the spatio-temporal filtering characteristics of the detector, we will have a look at the brain systems that might be involved in OMR. In fish, ganglion cells of the retina project to at least three different groups of nuclei that interact with motor areas: the accessory optic area (AOS), the pretectal complex (PTC), and the tectum opticum (TO). Simpson (1984) suggested that the AOS, because its neurons react to wide-field stimuli and because of its anatomical connection with the vestibular system, plays a role in signaling selfmotion as extracted from the optic flow. The main behavioral deficit seen after lesion of the AOS is abolition of the optokinetic nystagmus. Indeed, prominent efferents from the AOS connect to the oculomotor nucleus and the inferior olive. The retinal inputs of the AOS are direction-selective ganglion cells. The stabilization of head and eye positions in space seem to be a major task of the AOS. Engelhaaf and Borst (1993) compare the AOS in vertebrate functionally with the Ôhorizontal systemÕ cells in the fly, because both respond to wide field stimuli. However, whereas the Ôhorizontal systemÕ cells seem to play a role in the OMR, there is so far no indication that the AOS has such a function. In zebrafish the ventral and dorsal accessory optic nuclei seem to be part of the AOS (Wullimann, Rupp, & Reichert, 1996). We are not aware of any functional studies of these nuclei.
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At least some of the nuclei of the PTC are functionally related and anatomically connected to the AOS (Simpson, Giolli, & Blanks, 1988). According to Ilg, Bremmer, and Hoffmann (1993), the PTC has also a role in visual pursuit of visual stimuli (at least in the Rhesus monkey). At this point, it is not clear if this system contributes OMR. The TO is the most likely brain region to have a major role in the OMR. Tectumless fish are impaired in the visual perception of objects (Spinger et al., 1977; Yager, Sharma, & Grover, 1977). There are ample indications that the TO is involved in visual guided orienting movements in space, including escape and approach responses (Herrero, Rodriguez, Salas, & Torres, 1998; Meyer, Schott, & Schaefer, 1970). Moreover, in several fish species movement sensitive neurons have been found in the TO (Sajovij & Levinthal, 1982b; Wartzok & Marks, 1973; Zenkin & Pigarev, 1969). Spinger et al. (1977) have demonstrated that goldfish did not show a clear OMR after ablation of both TO. Interestingly, the optokinetic nystagmus of these fish was not impaired. Sajovic and Levinthal (1982a, 1982b) have studied the response of tectal cells in zebrafish to light stimuli. They classified the cells into different categories according to their ON–OFF properties. Some of those cell types respond to moving stimuli, others not. However, the authors have not studied the velocity characteristics of the stimuli to which those neurons respond, neither in terms of angular velocity nor in terms of temporal frequencies. In goldfish, some tectal cells responded to target velocities of maximal 40 deg/s (Wartzok & Marks, 1973). Even zebrafish larvae can follow stimuli that move with an angular speed of about 1100 deg/s (Orger et al., 2000). Tectal cells that respond to so high velocities have so far not been described for any fish species. One possibility is that highvelocity-tuned cells are located in other brain areas of the fish. Another possibility is that zebrafish larvae could follow such fast-moving stimuli because of aliasing, since those velocities were measured with a grating pattern. Thus, the perceived (apparent) velocity might have been much lower. However, in insects cells respond to velocities of 1000 deg/s (Ibbotson, 2001), in humans to velocities of at least 500 deg/s (Kawakami et al., 2002). This makes it at least questionable that high-velocity detectors would not exist in the fish brain. The current state of knowledge in this field does not allow us to draw any conclusions about the spatio-temporal filter characteristics of motion detectors in fish. Spacing of photoreceptor, size of receptive fields etc of the retina could give some indications, however, those psychophysical considerations are beyond the scope of the current study. 4.4. Possible explanations for the OMR characteristics The low-pass characteristic of the PPR/temporal frequency curve we described here has an equivalent in
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insects (Section 4.2). The major new finding here is the band-pass filter character for higher spatial frequencies. We propose here some possible explanations for our findings, based on the generally accepted constraints of motion detectors and on experimental results from OMR studies with insects (Gotz, 1964; Reichardt & Varju, 1959). Aliasing in insects is based on the geometrical structure of the compound eye (Reichardt, 1969). Similarly, the distribution of photoreceptors and/or ganglion cells in the vertebrate retina has been proposed to be responsible for aliasing (Anderson & Hess, 1990; Coletta et al., 1990). These are examples of spatial aliasing. Temporal aliasing has also been described: apparent motion fluctuate over time and depend on the stimulus duration (Derrington & Henning, 1987; Schouten, 1967). Moreover, sample rates seem to play a role in the Ôwagon wheel effectÕ (Andrews, White, Binder, & Purves, 1996; Manning & Finlay, 1989; Purves, Paydarfar, & Andrews, 1996) and the Ôspinning wheel illusionÕ (Sterzer, Russ, Preibish, & Kleinschmidt, 2002; Wertheimer, 1912). One of the characteristics of temporal aliasing is that not only perceived velocity and direction are apparent (different from the real values, similar as has been described for the OMR in insects), but also that these values are unstable, that is vary over time (Derrington & Henning, 1987; Schouten, 1967). Thus, when testing a group of zebrafish in the temporal frequency window, where these reversals might occur, the average numbers of orthograde and retrograde OMRs might be about equal for any given condition. Thus, in assuming that aliasing occurs for spatial frequencies above 0.08 c/deg, we would expect to see an average PPR of 0.5 rather than lower or higher values. At the same time, the total number of responses should be higher than when rpm equals zero, because at any given time some fish respond with retrograde, others with orthograde OMR. We found indeed that the total number of responses was for most velocities higher than for the stationary drum. Interesting is that in about 30% of our pilot studies we found that the PPR was significantly lower than 0.5 for higher spatial frequencies. More problematic is why for those spatial frequencies the PPR becomes higher than 0.5 for higher temporal frequencies. In the literature similar phenomena have been described in two different contexts. Firstly, according to Purves et al. (1996) the Ôwagon wheel effectÕ was only seen under continuous illumination for low temporal frequencies (in that study the range was 2–20 Hz). Why it would disappear at higher frequencies is not clear. A theoretical possibility is that angular velocity detection takes over. Secondly, in insects the OMR is retrograde for high-spatial/lowtemporal frequencies (whereas in zebrafish it is zero under those circumstances). However, in insects (like in zebrafish), the OMR becomes again orthograde with further increase of the temporal frequency (Gotz, 1964).
We have here to discuss if the band-filter character for higher spatial frequencies could have been an artifact. The stimulus pattern might have been contaminated by lower spatial frequencies, which would reduce the temporal frequencies. For example, the paper strip on which the pattern was printed could have been ÔtaintedÕ or the rotating drum might have wobbled slightly, giving rise to unwanted cues. We have excluded these possibilities by testing the zebrafish with a uniform stimulus paper (null stimulus). Especially in the absence of a stripe pattern, the behavioral effect of the hypothesized lower spatial stimuli should have shown up. However, we did not find any preferential swimming direction for this stimulus paper. Even if such lower spatial frequencies existed, they would only explain why zebrafish could follow so high-velocities, but not provide an explanation for the band-pass filter characteristic, i.e., why they did not follow low-velocities. 4.5. Conclusion In sum, we found that zebrafish show the OMR over a wide range of velocities (up to 1030 deg/s) and of temporal frequencies (up to 256 cps). Furthermore, we found that for low-spatial frequencies the OMR has the characteristic of a low-pass filter in regard to temporal frequency, for high-spatial frequencies the characteristics of a band-pass filter. The low-pass filter characteristic is similar as has been described for insects. We suggest that the band-pass filter characteristic might result from constraints of the motion detector, resulting in aliasing. A similar phenomenon has previously been described for the OMR of insects, where in the highspatial/low-temporal frequency domain the net OMR is retrograde, rather than zero, as was found in zebrafish.
Acknowledgements The authors thank L. Liu for technical assistance and for maintaining zebrafish colonies. This work was supported in part by NIH grants R01 EY13147 and EY13680 (L.L.). References Anderson, S. J., & Burr, D. C. (1985). Spatial and temporal selectivity of the human motion detection system. Vision Research, 25, 1147– 1154. Anderson, S. J., & Hess, R. F. (1990). Post-receptoral undersampling in normal peripheral vision. Vision Research, 30, 1507–1515. Andrews, T. J., White, L. E., Binder, D., & Purves, D. (1996). Temporal events in cyclopean vision. Proceedings of the National Academy of Sciences USA, 93, 3689–3692. Anstis, S., Hutahajan, P., & Cavanagh, P. (1998). Optomotor test for wavelength sensitivity in guppyfish (Poecilia reticulata). Vision Research, 38, 45–53.
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Spatio-temporal frequency characteristics of the optomotor response in zebrafish Hans Maaswinkel, Lei Li
*
Department of Physiology, University of Kentucky College of Medicine, 800 Rose Street, Lexington, KY 40536, USA Received 1 July 2002; received in revised form 29 August 2002
Abstract The optomotor response (OMR) is a simple experimental paradigm that is widely used in the study of visual system functions. In the current paper we investigated how spatial and temporal properties of repetitive stimuli determine the OMR in zebrafish. The experiments showed that the OMR has the temporal characteristic of a low-pass filter when the spatial frequencies are low and of a band-pass filter when the spatial frequencies are high. These findings are discussed on the basis of inherent sampling constraints of any motion detector. We found some indications that the strength and direction of the OMR vary with the spatio-temporal frequency of the stimulus pattern as has previously been described for other species. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Optomotor response; Motion detection; Spatio-temporal frequencies; Zebrafish
1. Introduction The optomotor response (OMR) is the locomotor behavior of an animal induced by a moving repetitive stimulus pattern. In most studies this pattern consists of vertical stripes, which might be in black and white (Clark, 1981), different gray contrasts (Lindsey, Chawla, & Townes-Anderson, 2002), or different colors (Schaerer & Neumeyer, 1996). The OMR has been described in different animal species as far apart as drosophila (David, 1979), the four-eyed fish anablebs (Saidl & Fabiane, 1998), tiger salamander (Lindsey et al., 2002), crayfish (Glantz, 2001), zebrafish (Clark, 1981), and humans (Klein, Fisher, Hartnegg, Heiss, & Roth, 2000). The OMR has been hypothesized to play a role in the control of speed and direction of body movement (Srinivasan, Poteser, & Kral, 1999), or, more generally, that it stimulates the neuronal mechanism involved in the processing of the optic flow, necessary for visual guided self-motion (Kern, Lutterklas, Petereit, Lindemann, & Engelhaaf, 2001). That vertical bars are especially effective stimuli that elicit OMR, might be due to the fact that orthogonal cues are prevalent in the environment (Coppola, *
Corresponding author. Tel.: +1-859-323-4757; fax: +1-859-3231070. E-mail address: [email protected] (L. Li).
Purves, McCoy, & Purves, 1998) and that the visual system is more tuned to these stimuli, than to slanted ones (Coppola, White, Fitzpratick, & Purves, 1998; Proverbio, Exposito, & Zani, 2002). Topics that have been studied using the OMR are among others: first- and second-order components of movement detection (Orger, Smear, Anstis, & Baier, 2000), functions of different regions of the retina (Saidl & Fabiane, 1998) and of the brain (Spinger, Easter, & Agranoff, 1977), the contribution of color vision to motion detection (Anstis, Hutahajan, & Cavanagh, 1998; Schaerer & Neumeyer, 1996), development of visual perception (Clark, 1981), motion perception during aging (Klein et al., 2000), the effect of rearing conditions (Bilotta, 2000), and the role of neurotransmitters in motion detection (Mora-Ferrer, 2002). It is also useful for the screening of visual mutants (Neuhauss et al., 1999) and toxicological research (Dutta, Marcelino, & Richmonds, 1992). The OMR procedure has been used to study phenomena, which do not involve motion detection per se as well, such as contrast sensitivity. Usually a flickering light source or a stationary or flickering grating pattern serves the purpose. However, these tests, when performed with lower vertebrates, require complex settings and conditioning procedures, e.g. to suppress respiration in the goldfish (Bilotta, Demarco, & Powers, 1995; Bilotta & Powers, 1992). To overcome this problem, the OMR
0042-6989/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 6 9 8 9 ( 0 2 ) 0 0 3 9 5 - 4
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test can be used as an alternative (Lindsey et al., 2002). This, however, raises the question how spatial and temporal aspects are connected in the OMR. In general, the movement of a stimulus can be described in terms of direction and velocity. However, the motion of a repetitive stimulus pattern can also be described in terms of temporal frequency, which is the product of spatial frequency and velocity. The temporal frequency description can be important, because every detector has a spatial and temporal frequency characteristic of its own (Derrington, 2000). Thus, the operation frequencies of the detector can constrain the object frequencies that can be detected (Shannon & Weaver, 1949). Aliasing (i.e. deviation of direction and/or velocity of perceived motion from actual motion) occurs when the frequency of the detector is lower than twice the frequency to be detected. For non-repetitive stimuli, aliasing impairs resolution by filtering out high-spatial frequencies, however, effects on motion detection seem to be minimal (Anderson & Burr, 1985). Repetitive stimulus pattern, on the other hand, are very vulnerable to aliasing. Even slowly drifting high-spatial frequency gratings can be perceived as reversing movement direction and changing velocity when presented to a peripheral zone of the retina called the Ôaliasing zoneÕ (Anderson & Hess, 1990; Coletta, Williams, & Tiana, 1990). The OMR has originally been one of the classic fields in which aliasing has been studied (Gotz, 1964; Hassenstein & Reichardt, 1956; Reichardt & Varju, 1959). In Drosophila, for example, it has been found that the strength and direction of the OMR depend on the spatio-temporal frequencies of the stimulus pattern (Gotz, 1964). In the current study, the relationship between spatial and temporal frequency in motion detection were investigated in zebrafish. By using a wide range of spatial frequencies and velocities (and hence temporal frequencies), we examined the OMR characteristics, bearing the above mentioned fundamental principles of any motion detector in mind concerning possible misperception of velocity and direction of movement, and the possibility to measure velocity either by temporal frequency or angular velocity.
2. Material and methods 2.1. Subjects Zebrafish (Danio rerio) were maintained as described (Westerfield, 1995). They were between 6 and 12 months old and were kept in a 14–10 h light/dark cycle (light, 6 a.m.–8 p.m., room fluorescent light).
Fig. 1. Schematic view of the OMR apparatus. The drum (D) rotates clockwise (shown by arrow) or counterclockwise around the transparent fish container (C). In the center of the container a column (P) is placed. The inset shows an example of a stimulus pattern, printed on paper and attached on the inside of the drum. The fish is depicted as following the direction of the rotation of the drum, i.e. it shows a positive OMR (arrow).
consists of a drum, 15 cm in diameter, which can rotate clockwise and counter-clockwise with a speed up to 100 rotations per min (rpm). At the inside of the drum a strip of paper can be attached. In the current study the paper bore either a grating pattern, consisting of black and white vertical stripes, or it was uniformly gray (the gray-level was adjusted halfway between the gray levels of the black and white stripes). In the center of the drum, a circular transparent fish tank (11 cm in diameter) was suspended. A column (3 cm in diameter) was placed in the center of the fish tank to prevent the fish from swimming through the center. A light source was suspended above the apparatus. The light intensity measured at the water surface was 4.75 lW/cm2 . To calculate the subjective angular velocities of the stripes, the zebrafish was assumed to swim halfway between the column and the wall of the fish tank. 2.3. Procedures
2.2. OMR apparatus The apparatus is modified from the one previously described by Li and Dowling (1997) (see also Fig. 1). It
All experiments described here were carried out between 10 a.m. and 1 p.m. The fish were placed in the dark testing room to habituate for approximately 20
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min. Each fish was then tested for the OMR in two consecutive one-minute trials. The direction of rotation of the stimulus pattern was in one trial clockwise, in the other anticlockwise, in a random sequence. This was done in order to exclude any directional bias. The number of full turns of the zebrafish around the column in the center in either direction was scored. A Ôpositive responseÕ was defined as a full turn in the same direction as the stimulus patterns, a Ônegative responseÕ as a full turn in the opposite direction. The Ôproportion of positive responsesÕ (PPR) was calculated by dividing the number of the positive responses (from both trials) by the number of all responses. In case the fish did not show any positive or negative responses during both trials, the PPR was set at 0.5, which is the baseline level for random swimming. 2.3.1. Experiment 1. Responses for different spatial frequencies The drum was rotated at a constant speed of 10 rpm, corresponding to a subjective angular velocity of 103 deg/s (degrees per second). The OMR was tested for seven spatial frequencies: 0.01, 0.02, 0.04, 0.08, 0.16, 0.31, 0.62 c/deg (cycles per degree). The PPR was plotted for every spatial frequency (PPR/spatial-frequency curve). As control, fish were tested with the same spatial frequencies at a velocity of 0 rpm. The data from both groups were compared for every spatial frequency using a t-test. 2.3.2. Experiment 2. Responses for different temporal frequencies The fish were tested with all seven spatial frequencies mentioned in experiment 1 at different rotation speeds of the drum: 0, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 rpm, corresponding to the following subjective angular velocities: 0, 52, 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030 deg/s. For every stimulus pattern, a PPR/velocity function was drawn. The temporal frequencies for these rotation speeds were calculated for every spatial frequency and expressed in cycles per second (cps). The response characteristics were presented in a velocity/ spatial-frequency diagram and a temporal-frequency/ spatial-frequency diagram.
3. Results 3.1. Experiment 1. Responses for different spatial frequencies Fig. 2 shows the PPR for all studied spatial frequencies for velocities of 0 and 103 deg/s. For spatial frequencies up to 0.08 c/deg, the zebrafish swam most often in the direction of the moving stimulus when tested with a velocity of 103 deg/s. Their PPR was signifi-
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Fig. 2. PPR/spatial-frequency function for all tested frequencies for a velocity of zero () and 103 deg/s (). Note that the PPR is significantly greater than 0.5 only for the low-spatial frequencies. Error bars represent SEM. < 0:05, < 0:01, < 0:005.
cantly greater than for velocity zero, where they did not have such a preferential swimming direction. For higher spatial frequencies (0.16–0.62 c/deg), however, no OMR could be found. The PPR was for both rotating and stationary drum statistically not different and close to 0.5. Thus, 0.08 c/deg is the highest frequency under which OMR occurs at the given velocity of 103 deg/s (10 rpm). This is very close to the results found by others (Bilotta, 2000; Clark, 1981; see also Section 4). In experiment 2 we will investigate how the response limit depends on velocity and temporal frequency, using a range of drum rotation speeds between 5 and 100 rpm. 3.2. Experiment 2. Responses for different temporal frequencies Fig. 3 shows the PPR/velocity functions for the null stimulus and all seven spatial frequencies. It is apparent, that the velocities to which the fish react positively are different for different spatial frequencies, and that there is often a lower and an upper limit beyond which no PPR is significantly higher than 0.5. The null stimulus (a uniform gray paper without stripes) did not elicit any significant OMR. Thus the PPR fluctuated slightly around 0.5. For the lowest spatial frequency (0.01 c/deg), zebrafish responded over the entire range of tested velocities. With increasing spatial frequency, i.e. from 0.02 to 0.08 c/deg, the OMR disappeared for the higher velocities. With further elevation of the spatial frequency, i.e. from 0.16 to 0.62 c/deg, the OMR disappeared at lower velocities as well, so that the PPR is greater than 0.5 in only a small window of velocities. To give a graphic overview over all the data, the 3D mesh plots (Fig. 4A and B) were drawn to show PPR in the spatial-frequency/velocity or the spatial-frequency/
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Fig. 3. PPR/velocity functions for the seven spatial frequencies (A–G) and for the null stimulus (H) for all velocities (0–1030 deg/s). Note that the PPR for the null stimulus is for none of the velocities statistically different from its value at velocity 0 deg/s. Error bars are SEM, < 0:05.
temporal-frequency domain, respectively. The light gray areas coincide approximately with the PPR values that are significantly different from the PPR found for zebrafish tested with a stationary drum. For low-spatial frequencies, the PPR is high only for low-velocities and temporal frequencies. An exception is the PPR for 0.01 c/deg, were for the highest speed of the test apparatus (100 rpm) the PPR was greater than 0.5. For high-spatial frequencies the PPR was greater than 0.5 for higher velocities or temporal frequencies, and dropped down
again when velocities or temporal frequencies further increased. Notice that Fig. 4B is partially based on inferred data. For example, for 0.01-c/deg the highest temporal frequencies, for which the PPR is set at 0.5, have not been measured. Other values have been averaged from surrounding values. Fig. 5A represents the upper and lower response limits of OMR in a velocity/spatial frequency diagram. The upper response limit for a given spatial frequency is the velocity at and above which the PPR is not
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Fig. 4. Mesh plots (3D) of PPR. (A) PPR represented in the spatial-frequency/velocity domain. (B) PPR represented in the spatial-frequency/ temporal-frequency domain.
statistically different from 0.5. The lower response limit is the velocity at and below which the PPR is not significantly different from 0.5. For the lower spatial frequencies (up to 0.08 c/deg) the PPR has the characteristic of a low-pass filter (i.e. the PPR is greater than 0.5 for all velocities between 0 and the upper limit). For higher spatial frequencies (0.16 c/deg and up), on the other hand, the PPR has the characteristic of a band-pass filter (i.e. the PPR is greater than 0.5 in a velocity window, with a lower limit higher than 0 deg/s). Fig. 5B shows the temporal-frequency/spatial-frequency diagram. As expected, the low-pass character for low-spatial frequencies and the band-pass character for high-spatial frequencies were also found here. However, what strikes in this representation are the high-temporal frequencies (up to 256 cps) that elicit an OMR at higher spatial frequencies. The number of positive and negative responses for the lowest (0.01 c/deg) and highest spatial frequency (0.62 c/deg) are shown in Fig. 6. The striking fact for the spatial frequency of 0.01 c/deg (Fig. 6A) is that the number of positive responses first increased, then decreased with increasing velocity. It peaked between 400 and 600 deg/s, with a small dip at 500 deg/s. Then, starting from 700 deg/s, it decreased with further increase of velocity. For the spatial frequency of 0.62 c/deg (Fig. 6B), on the other hand, the numbers of positive and negative were about equal for most velocities. However, for nearly all velocities higher than zero, the total number of (positive and negative) responses was significantly different from the number of responses at velocity zero.
4. Discussion In this study, we examined how spatial and temporal frequency determines the OMR in zebrafish. The interesting finding is that the PPR/velocity and PPR/temporal-frequency functions act as low-pass filters when tested with low-spatial frequencies and as band-pass filters when tested with high-spatial frequencies. In the following we will expose these findings and search for interpretations. 4.1. Spatial and temporal frequency in the OMR We demonstrated in experiment 1 that for a lowvelocity (103 deg/s), zebrafish follow the rotation direction of the stripes only for low spatial frequencies. For higher spatial frequencies, such a preferential swimming direction was not observed. However, the swimming activity was randomized rather than reduced, i.e. they showed as many negative as positive responses. The occurrence of negative responses can either be a result of spontaneous behavior, or be an indication for intermittently occurring apparent motions in the opposite direction (see Section 4.4). In experiment 2 we found that the highest velocity for which the PPR was significantly greater than for velocity zero, was 1030 and 412 deg/s for the highest and lowest spatial frequency, respectively (Fig. 5A). In terms of temporal frequencies, we found very high-response limits for the higher spatial frequencies. For the 0.31c/deg stripes, for example, zebrafish reacted to frequencies as high as 256 cps. The PPR/temporal-frequency function had for lower spatial frequencies the character
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Fig. 5. OMR limits in the spatio-temporal domain. (A) Velocity/spatial-frequency diagram indicating the OMR limits. The upper and lower response limits, the velocity boundary between which the zebrafish show a positive OMR, are presented for seven spatial frequencies. (B) Temporal-frequency/spatial-frequency function for the same data. For comparison the critical flicker frequency as described for goldfish (Bilotta, Lynd, & Powers, 1998) is presented as dashed line.
of a low-pass filter, for higher spatial frequencies the character of a band-pass filter, e.g. for the 0.62-c/deg stripes the PPR was greater than 0.5 only between 128 and 256 cps (Fig. 5B). 4.2. Comparing the current results with other studies In fish, several aspects of OMR have been studied. It has for example been used to study wavelength sensitivity (Anstis et al., 1998), the contribution of color vision to motion detection (Schaerer & Neumeyer, 1996), the effect of neurotransmitters on motion detection (Mora-Ferrer, 2002) and as indicator for toxicological pollution (Dutta et al., 1992). In all those ÔappliedÕ studies, the range of spatial frequencies tested is similar to that used in the current paper, and the range of velocities to that used in our experiment 1. Clark (1981), who has carried out the most extensive study concerning the influence of different width of stripes and velocities
Fig. 6. Number of positive and negative responses for zebrafish tested in 2 min trials with the 0.01 c/deg-stripes (A) and with the 0.62 c/degstripes (B) over all velocities (0–1030 cps). Error bars are SEM.
on the OMR in zebrafish, varied the speed only between 5 and 15 rpm. We used a maximum of 100 rpm. To our knowledge, OMR has not been studied before in fish by varying the velocity/temporal-frequency over a wide range. The same is true for other non-mammalian vertebrates (e.g. Lindsey et al., 2002). The PPR/spatialfrequency function described here for low-temporal frequencies is similar as described by others for the OMR (Bilotta, 2000) and the optokinetic nystagmus (DeMarco, Nussdorf, Brockman, & Powers, 1989) in goldfish. The maximal spatial frequency, to which zebrafish react with a PPR significant higher than found for stationary stimuli (PPR around 0.5), seems to be slightly lower than found in other studies (Bilotta, 2000). Several factors might determine the PPR/spatial-frequency function, such as velocity, illumination, time of the day when the experiment was performed, testing procedure, or age of the fish. Psychophysical studies of the OMR with regard to motion detector functions and velocity/temporalfrequency limits have made extensively use of insects (Reichardt, 1969; Srinivasan et al., 1999). One of the most consistently found characteristics of the OMR in insects is that the direction and the strength of the OMR depend on the spatio-temporal frequencies of the grating pattern (Gotz, 1964; Reichardt & Varju, 1959). A fur-
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ther interesting finding is that insects can determine the velocity of a repetitive stimulus pattern either by its temporal frequency or its angular velocity, depending on the behavioral task (Srinivasan et al., 1999). In the brain of the honeybee, for example, both temporal-frequencytuned cells and velocity-tuned cells have been found (Ibbotson, 2001). The temporal-frequency-tuned cells (supposed to mediate OMR) peak at about 10 Hz and cut off at about 100 Hz. The velocity-tuned cells respond to angular velocities up to 1000 deg/s. For low-spatial frequencies, the OMR temporal frequency curve is a low-pass filter, and peaks for all spatial frequency at the same temporal frequencies (Reichardt, 1969). Similarly, we found in zebrafish, that for spatial frequencies up to 0.08 c/deg the lower and upper response limits vary only slightly and that the OMR has the character of a low-pass filter. For higher spatial frequencies, Gotz (1964) found that insects show a retrograde OMR, at least for lower angular velocities. With increasing velocities and increasing spatial frequencies, the OMR becomes again orthograde (Gotz, 1964). Our results are not exactly the same, but comparable. We found in the high-spatial/low-temporal-frequency domain that PPR was close to 0.5, and with increasing velocities (temporal frequencies) the PPR increased.
4.3. Brain areas involved in OMR Since motion detection depends on the spatio-temporal filtering characteristics of the detector, we will have a look at the brain systems that might be involved in OMR. In fish, ganglion cells of the retina project to at least three different groups of nuclei that interact with motor areas: the accessory optic area (AOS), the pretectal complex (PTC), and the tectum opticum (TO). Simpson (1984) suggested that the AOS, because its neurons react to wide-field stimuli and because of its anatomical connection with the vestibular system, plays a role in signaling selfmotion as extracted from the optic flow. The main behavioral deficit seen after lesion of the AOS is abolition of the optokinetic nystagmus. Indeed, prominent efferents from the AOS connect to the oculomotor nucleus and the inferior olive. The retinal inputs of the AOS are direction-selective ganglion cells. The stabilization of head and eye positions in space seem to be a major task of the AOS. Engelhaaf and Borst (1993) compare the AOS in vertebrate functionally with the Ôhorizontal systemÕ cells in the fly, because both respond to wide field stimuli. However, whereas the Ôhorizontal systemÕ cells seem to play a role in the OMR, there is so far no indication that the AOS has such a function. In zebrafish the ventral and dorsal accessory optic nuclei seem to be part of the AOS (Wullimann, Rupp, & Reichert, 1996). We are not aware of any functional studies of these nuclei.
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At least some of the nuclei of the PTC are functionally related and anatomically connected to the AOS (Simpson, Giolli, & Blanks, 1988). According to Ilg, Bremmer, and Hoffmann (1993), the PTC has also a role in visual pursuit of visual stimuli (at least in the Rhesus monkey). At this point, it is not clear if this system contributes OMR. The TO is the most likely brain region to have a major role in the OMR. Tectumless fish are impaired in the visual perception of objects (Spinger et al., 1977; Yager, Sharma, & Grover, 1977). There are ample indications that the TO is involved in visual guided orienting movements in space, including escape and approach responses (Herrero, Rodriguez, Salas, & Torres, 1998; Meyer, Schott, & Schaefer, 1970). Moreover, in several fish species movement sensitive neurons have been found in the TO (Sajovij & Levinthal, 1982b; Wartzok & Marks, 1973; Zenkin & Pigarev, 1969). Spinger et al. (1977) have demonstrated that goldfish did not show a clear OMR after ablation of both TO. Interestingly, the optokinetic nystagmus of these fish was not impaired. Sajovic and Levinthal (1982a, 1982b) have studied the response of tectal cells in zebrafish to light stimuli. They classified the cells into different categories according to their ON–OFF properties. Some of those cell types respond to moving stimuli, others not. However, the authors have not studied the velocity characteristics of the stimuli to which those neurons respond, neither in terms of angular velocity nor in terms of temporal frequencies. In goldfish, some tectal cells responded to target velocities of maximal 40 deg/s (Wartzok & Marks, 1973). Even zebrafish larvae can follow stimuli that move with an angular speed of about 1100 deg/s (Orger et al., 2000). Tectal cells that respond to so high velocities have so far not been described for any fish species. One possibility is that highvelocity-tuned cells are located in other brain areas of the fish. Another possibility is that zebrafish larvae could follow such fast-moving stimuli because of aliasing, since those velocities were measured with a grating pattern. Thus, the perceived (apparent) velocity might have been much lower. However, in insects cells respond to velocities of 1000 deg/s (Ibbotson, 2001), in humans to velocities of at least 500 deg/s (Kawakami et al., 2002). This makes it at least questionable that high-velocity detectors would not exist in the fish brain. The current state of knowledge in this field does not allow us to draw any conclusions about the spatio-temporal filter characteristics of motion detectors in fish. Spacing of photoreceptor, size of receptive fields etc of the retina could give some indications, however, those psychophysical considerations are beyond the scope of the current study. 4.4. Possible explanations for the OMR characteristics The low-pass characteristic of the PPR/temporal frequency curve we described here has an equivalent in
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insects (Section 4.2). The major new finding here is the band-pass filter character for higher spatial frequencies. We propose here some possible explanations for our findings, based on the generally accepted constraints of motion detectors and on experimental results from OMR studies with insects (Gotz, 1964; Reichardt & Varju, 1959). Aliasing in insects is based on the geometrical structure of the compound eye (Reichardt, 1969). Similarly, the distribution of photoreceptors and/or ganglion cells in the vertebrate retina has been proposed to be responsible for aliasing (Anderson & Hess, 1990; Coletta et al., 1990). These are examples of spatial aliasing. Temporal aliasing has also been described: apparent motion fluctuate over time and depend on the stimulus duration (Derrington & Henning, 1987; Schouten, 1967). Moreover, sample rates seem to play a role in the Ôwagon wheel effectÕ (Andrews, White, Binder, & Purves, 1996; Manning & Finlay, 1989; Purves, Paydarfar, & Andrews, 1996) and the Ôspinning wheel illusionÕ (Sterzer, Russ, Preibish, & Kleinschmidt, 2002; Wertheimer, 1912). One of the characteristics of temporal aliasing is that not only perceived velocity and direction are apparent (different from the real values, similar as has been described for the OMR in insects), but also that these values are unstable, that is vary over time (Derrington & Henning, 1987; Schouten, 1967). Thus, when testing a group of zebrafish in the temporal frequency window, where these reversals might occur, the average numbers of orthograde and retrograde OMRs might be about equal for any given condition. Thus, in assuming that aliasing occurs for spatial frequencies above 0.08 c/deg, we would expect to see an average PPR of 0.5 rather than lower or higher values. At the same time, the total number of responses should be higher than when rpm equals zero, because at any given time some fish respond with retrograde, others with orthograde OMR. We found indeed that the total number of responses was for most velocities higher than for the stationary drum. Interesting is that in about 30% of our pilot studies we found that the PPR was significantly lower than 0.5 for higher spatial frequencies. More problematic is why for those spatial frequencies the PPR becomes higher than 0.5 for higher temporal frequencies. In the literature similar phenomena have been described in two different contexts. Firstly, according to Purves et al. (1996) the Ôwagon wheel effectÕ was only seen under continuous illumination for low temporal frequencies (in that study the range was 2–20 Hz). Why it would disappear at higher frequencies is not clear. A theoretical possibility is that angular velocity detection takes over. Secondly, in insects the OMR is retrograde for high-spatial/lowtemporal frequencies (whereas in zebrafish it is zero under those circumstances). However, in insects (like in zebrafish), the OMR becomes again orthograde with further increase of the temporal frequency (Gotz, 1964).
We have here to discuss if the band-filter character for higher spatial frequencies could have been an artifact. The stimulus pattern might have been contaminated by lower spatial frequencies, which would reduce the temporal frequencies. For example, the paper strip on which the pattern was printed could have been ÔtaintedÕ or the rotating drum might have wobbled slightly, giving rise to unwanted cues. We have excluded these possibilities by testing the zebrafish with a uniform stimulus paper (null stimulus). Especially in the absence of a stripe pattern, the behavioral effect of the hypothesized lower spatial stimuli should have shown up. However, we did not find any preferential swimming direction for this stimulus paper. Even if such lower spatial frequencies existed, they would only explain why zebrafish could follow so high-velocities, but not provide an explanation for the band-pass filter characteristic, i.e., why they did not follow low-velocities. 4.5. Conclusion In sum, we found that zebrafish show the OMR over a wide range of velocities (up to 1030 deg/s) and of temporal frequencies (up to 256 cps). Furthermore, we found that for low-spatial frequencies the OMR has the characteristic of a low-pass filter in regard to temporal frequency, for high-spatial frequencies the characteristics of a band-pass filter. The low-pass filter characteristic is similar as has been described for insects. We suggest that the band-pass filter characteristic might result from constraints of the motion detector, resulting in aliasing. A similar phenomenon has previously been described for the OMR of insects, where in the highspatial/low-temporal frequency domain the net OMR is retrograde, rather than zero, as was found in zebrafish.
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