Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, United Kingdom
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ABSTRACT |
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Burton, Brian G., Ben W. Tatler, and Simon B. Laughlin. Variations in Photoreceptor Response Dynamics Across the Fly Retina. J. Neurophysiol. 86: 950-960, 2001. Gradients in the spatial properties of retinal cells and their relation to image statistics are well documented. However, less is known of gradients in temporal properties, especially at the level of the photoreceptor for which no account exists. Using light flashes and white-noise-modulated light and current stimuli, we examined the spatial and temporal properties of a single class of photoreceptor (R1-6) within the compound eyes of male blowfly, Calliphora vicina. We find that there is a trend toward higher performance at the front of the eye, both in terms of spatiotemporal resolution and signal-to-noise ratio. The receptive fields of frontal photoreceptors are narrower than those of photoreceptors at the side and back of the eye and response speeds are 20% faster. The signal-to-noise ratio at high frequencies is also greatest at the front of the eye, allowing a 30-40% higher information rate. The power spectra of signals and noise indicate that this elevation of performance results both from shorter responses to individual photons and from a more reliable registration of photon arrival times. These distinctions are characteristic of adaptational changes that normally occur on increasing illumination. However, all photoreceptors were absorbing light at approximately the same mean photon rate during our recordings. We therefore suggest that frontal photoreceptors attain a higher state of light adaptation for a given photon rate. This difference may be achieved by a higher density of (Ca2+ permeable) light-gated channels. Consistent with this hypothesis, membrane-impedance measurements show that frontal photoreceptors have a higher specific conductance than other photoreceptors. This higher conductance provides a better temporal performance but is metabolically expensive. Across the eye, temporal resolution is not proportional to spatial (optical) resolution. Neither is it matched obviously to optic flow. Instead we examine the consequences of an improved temporal resolution in the frontal region for the tracking of small moving targets, a behavior exhibited by male flies. We conclude that the temporal properties of a given class of retinal neuron can vary within a single retina and that this variation may be functionally related to the behavioral requirements of the animal.
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INTRODUCTION |
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To understand the design of the
visual system, it is important to consider the properties of its input.
It is widely thought that the purpose of the early stages of vision is
to encode as much visual information as possible by making efficient
use of neurons that are of limited dynamic range and reliability
(Atick and Redlich 1992; van Hateren
1992a
). For this purpose, the general statistical structure of
the world such as the distribution of contrasts (Laughlin
1981
) or the correlation structure (Burton and Moorhead
1987
; Dong and Atick 1995
; van Hateren
and van der Schaaf 1996
) have been examined. Such low-order,
global properties have been useful in explaining the form of the
spatiotemporal filtering that occurs in the retina (Atick and
Redlich 1992
; Srinivasan et al. 1982
; van
Hateren 1992a
) and the lateral geniculate nucleus (Dong
and Atick 1995
). However, rather than treating the retinal image as statistically homogeneous (stationary), there is now growing
acknowledgment of the inhomogeneities that occur due to the influence
of habitat or behavior on vision (Szél et al.
1996
; Virsu and Hari 1996
) and to the fact that
vision is an active process (Eckert and Buchsbaum 1993
;
Reinagel and Zador 1999
). For example, retrogressive
optic flow associated with forward movement imposes a gradient in image
velocity with retinal eccentricity (Gibson 1950
). Smooth
tracking of objects by the fovea also contributes to image velocity in
the periphery (Eckert and Buchsbaum 1993
). Finally,
human observers selectively foveate parts of the image with high
contrast, low correlation and therefore high-information content
(Mannan et al. 1997
; Reinagel and Zador
1999
). Here, using the blowfly as a model, we examine whether
differences in local image content or local image velocities have
influenced the temporal tuning of photoreceptors.
Different photoreceptor types often possess different spatial and
temporal properties. In primate retina, for example, the diameters (and
consequently receptive field sizes) of rods and cones increase with
retinal eccentricity (Curcio et al. 1990). Similar
spatial gradients exist in invertebrate retinas (e.g., Hardie
1979
). However, differences in the temporal properties of
photoreceptors have only been documented between distinct receptor classes (Anderson and Laughlin 2000
; Yau
1994
) or between homologous receptors from different species or
sexes (Hornstein et al. 2000
; Laughlin and
Weckström 1993
). There is as yet no account of a systematic trend in the temporal properties of any single class of
photoreceptor across any one retina. The achromatic R1-6
photoreceptors of the blowfly, with their ability to offer excellent in
vivo intracellular recordings, are a good model for investigating this possibility.
Many dipteran species display gradients in the geometry of the
ommatidia (sampling units) across the eye (Land 1981,
1997
). Often, the lens diameters and the densities with which
ommatidia sample visual space are greatest in the anterior of the eye
(Land 1981
; Land and Eckert 1985
;
Stavenga 1975
). Where this is the case, the anterior
forms a higher-resolution image than elsewhere, and this region may be
identified as an "acute zone" (Horridge 1978
). Are
the temporal properties of the photoreceptors in the acute zone
distinct from those in other areas? An antero-posterior gradient in
spatial resolution has been explained as a response to optic-flow
patterns and to the demands of pursuit behavior (Land
1997
). How do the temporal properties of blowfly photoreceptors fit into these schemes?
There is good reason to believe that photoreceptor responses might vary
across the eye. Under conditions of progressive light adaptation,
photoreceptors reduce both the magnitude and duration of their bump
responses to individual photons (Howard et al. 1987; Juusola et al. 1994
; Wong and Knight
1980
). Comparative studies also show that the durations of
photoreceptor impulse responses in species with different flight speeds
vary over a fivefold range, even when fully light-adapted
(Laughlin and Weckström 1993
). Finally,
differences in temporal properties of photoreceptors have been observed
between the two sexes of both Bibio markii (Laughlin
and Weckström 1993
) and Musca domestica
(Hornstein et al. 2000
). Males of both species have
measurably faster photoreceptors than females, and this is associated
with better spatial resolution (Laughlin and Weckström
1993
).
In the following, we measure the spatial and temporal properties of photoreceptors in male blowfly at three different eye positions: at the front of the eye, at the side, and at the back (Fig. 1). We find that these properties display systematic trends with retinal position such that the acute zone can encode a higher bandwidth of images and achieves higher signal-to-noise ratios. We discuss the purpose of the trends in temporal resolution in terms of optical gradients, optic flow, and the pursuit of small targets and conclude that pursuit seems to account for them best.
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METHODS |
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Animals and preparation
Intracellular microelectrode recordings were taken from R1-6
photoreceptors of male wild-type blowflies, Calliphora
vicina. Photoreceptor membrane potentials were recorded from the
left compound eye in response to either light or current stimuli. The recording electrode was located in one of three positions relative to
the longitudinal axis of the body (Fig. 1) at the front of the eye,
slightly dorsally, in the middle of the acute zone (Horridge 1978), on the equator at 90° from the mid-sagittal plane, and on the equator at >140° from the mid-sagittal plane. These three positions are referred to as being at the front, side and back of the
eye, respectively.
Acceptable cells were those with a resting potential of up to 60 mV,
a resistance of
30 M
, and a maximum response to a 1-ms flash of
light of
50 mV. The optical axis of the cell was determined using a
point source mounted on a cardan arm. Owing to the low packing
densities of photoreceptors and the high curvature of the eye at its
margin, those nominally at 90° are within a range of ±5°. Those at
the back include anything with an optical axis between 140° and
170°. Throughout recording, air temperature was maintained at circa
21°C.
Stimuli and recording
All stimulus generation and recordings were carried out by a PC
interfaced with an LED driver and an Axoclamp 2A amplifier (Axon
Instruments). For light stimuli, voltage measurements were made with
the amplifier in "bridge mode." For current stimuli, both the
current delivered to the photoreceptor and its voltage response to that
current were recorded simultaneously by the discontinuous switched
current-clamp (DCC) technique. Light stimuli were generated with a
blue-green LED (max = 505 nm, LEDtronics) and
were delivered to the eye via a light guide. Diaphragms at the exit
aperture of the light guide were used to adjust stimulus size.
Current and voltage recordings were made from photoreceptors in both
dark- and light-adapted states. Dark-adapted recordings were made after
30 min dark adaptation. Light-adapted recordings were made at the
highest mean intensity sustainable by the LED. The photon flux
corresponding to this intensity was extrapolated from rates of photon
absorptions measured at very low light intensities where the bump
responses to individual photons may be distinguished. This method
returned an average extrapolated figure of 3.1 × 106
s1 photons per receptor,
equivalent to moderate daylight. [Note, the photon fluxes calculated
from contrast-normalized signal-to-noise ratios (Table
1, Analysis) in the
light-adapted condition are less than this figure due to the influence
of the intracellular pupil (Howard et al. 1987
).]
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The spatial filtering properties of a dark-adapted photoreceptor and its overlying lens were determined from the receptor's voltage responses to flashes of light presented at different positions in the receptive field. The average response at every position was corrected for the nonlinear relationship between flash intensity and voltage response amplitude to obtain the angular sensitivity function (Fig. 2). The light source subtended an angle of 17' at the eye.
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The temporal filtering properties of a photoreceptor were obtained
using white-noise-modulated light or current stimuli (de Ruyter
van Steveninck 1986; Kouvalainen et al. 1994
;
Weckström et al. 1992
). Stimuli were presented as
5 Gaussian pseudorandom time traces, each repeated 50 times. All traces
were 0.512 s in duration. Light stimuli were delivered from a
wide-field source, subtending an angle of 30° at the eye. They had
the same time-averaged intensity as the adapting light and a contrast
standard deviation of 0.25, where contrast is defined as instantaneous
light intensity divided by time-averaged intensity. Current stimuli had
a mean of 0 nA and a standard deviation of 0.2 nA. Sampling of the
photoreceptor voltage response was at the same rate as stimulus
production (2 kHz). For current stimuli, the DCC switch rate was well
above this (between 3.5 and 5.0 kHz). To avoid aliasing noise from
frequencies >1 kHz, all responses were low-pass filtered by a 4-pole
Butterworth filter with a cutoff frequency of 500 Hz prior to A/D conversion.
After measuring the light and current responses of a photoreceptor, the extracellular voltage was recorded to determine the characteristics of instrumental noise. Again, low-pass filtering was at 500 Hz and sampling was at 2 kHz.
The preceding procedures were repeated on different photoreceptors in different eye positions in different flies. The data presented are collected from 109 recordings in 47 animals.
Analysis
For each photoreceptor, the contrast gain function,
G(f), was estimated from
the voltage responses,
VC,m,n(f), to the pseudorandom light stimuli (expressed as contrast),
Cn(f)
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(1) |
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(2) |
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(3) |
The conventional signal-to-noise ratio,
SNRV(f), was calculated
with the signal defined as the power spectrum of the average photoreceptor voltage responses to the light contrast stimuli. That is
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(4) |
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(5) |
The information rate, I, associated with
SNRV(f) was obtained
from the formula (van der Lubbe 1997)
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(6) |
Statistics
All of the quantities measured in different eye regions (spectra corner frequencies, photon fluxes) have been compared by ANOVA. Where significant differences were detected between eye regions, these differences were examined pair-wise by two-tail Student's t-test. In all tests, significance was considered at the 5% level. No transformation of the data was required before analysis except in the case of photon fluxes. Histograms for photon flux, obtained by dividing transfer power by noise power (see RESULTS, Signal-to-noise ratio), were highly positively skewed, and so the photon flux data were compared on a log scale. For clarity, test results are not presented in the main body of the text. The reader is referred instead to Table 2.
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RESULTS |
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Spatial filtering
The resolution of the image formed in the retina is affected
by two factors, blurring and sampling. Blurring is caused by diffraction at the lens aperture and the finite diameter and wave-guide properties of the photoreceptor rhabdomere (Smakman et al.
1984; Snyder 1979
). Sampling is represented by
the density of ommatidia per unit visual angle. We have not measured
sampling. However, it is known that sampling density is matched to
blurring across the eye in blowfly (Hardie 1985
).
Blurring is therefore a useful indicator of the resolution of the
retinal image. The degree of blurring is represented by the angular
sensitivity function of the photoreceptor. The wider the angular
sensitivity function, the wider the angle over which the photoreceptor
integrates incident light and the more blurred the image. We take the
acceptance angle, the full width of the angular sensitivity function at
half-maximum height, as a measure of the resolution of the image.
Our data show a clear trend in acceptance angle, , with
eccentricity (Fig. 2, Table 1). Although the only significant
differences (Table 2) are between the frontal position (1.57 ± 0.11°, n = 22) and the other two positions, mean
is greater at the back of the eye (2.36 ± 0.12°,
n = 33) than at the side (2.18 ± 0.17°, n = 14). These observations indicate that there is more
blurring of static images at the side of the eye and particularly at
the back than at the front. Frontal images therefore contain higher spatial frequencies than nonfrontal images. This is demonstrated by the
frequency representation of the angular sensitivity function, the
modulation transfer function (MTF). Calculations of MTF
corner-frequency (Fig. 4, Tables 1 and 2), the frequency at which
transfer power has fallen to half-maximum, show anterior receptors to
have a significantly higher corner frequency (0.218 ± 0.014 cycles/°, n = 22) than receptors at both the side
(0.154 ± 0.011 cycles/°, n = 14) and back
(0.143 ± 0.008 cycles/°, n = 33) of the eye.
Temporal filtering
The contrast gain function,
G(f), of the
photoreceptor is the temporal equivalent of the (spatial) MTF. It
specifies the relative sensitivity of the photoreceptor to different
temporal frequencies and thus indicates temporal resolution. For a
moving image, integration of light signals over time will attenuate the
higher spatial frequencies [motion blur (Srinivasan and Bernard
1975)]. Therefore for moving images, the contrast gain
function can be as important a determinant of image quality as the MTF.
Figure 3A shows the amplitudes of the average contrast gain functions in the three different parts of the eye considered in this study. These functions show consistency in both the maximum gain (10 mV/contrast) and general shape. However, there is a clear effect of retinal position on corner frequency. Corner frequencies are significantly higher (Table 2) at the front (61.8 ± 1.5 Hz, n = 35) of the eye and than at both the side (49.6 ± 1.5 Hz, n = 34) and back (53.0 ± 0.9 Hz, n = 40). That is, frontal photoreceptors are 20% faster than photoreceptors elsewhere. This difference in temporal resolution is illustrated clearly by a comparison of the corresponding impulse responses, obtained as the inverse Fourier transform of the contrast gain functions (Fig. 3B). Although the onset latency of the impulse response is constant across the eye, frontal photoreceptors achieve a higher peak response and at a shorter time than other receptors. Impulse width is also shorter.
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The temporal properties of a photoreceptor are functionally related to
its spatial properties through image velocity. When an image moves, the
higher spatial frequencies generate the higher temporal frequencies.
For a given image velocity, high spatial frequencies will be lost if
the temporal frequencies they generate are too fast for the receptor to
code. An indication of the range of velocities over which the receptor
can code all the spatial frequencies presented by the optics is
therefore given by the characteristic velocity (van
Hateren 1993), defined as the ratio of temporal to spatial
corner frequencies (see also Glantz 1991
; Howard
1981
; Srinivasan and Bernard 1975
). Because
anterior photoreceptors have both higher spatial and temporal
bandwidths than other photoreceptors, they will always be able to code
higher spatial frequencies at any given image speed. However, using the
average spatial and temporal corner frequencies already presented (Fig.
4), the characteristic velocities for the
front, side, and back of the eye are found to be 283, 322, and 370 °/s, respectively. These figures suggest that although anterior
photoreceptors perform best, the balance of spatial and temporal
bandwidths they exhibit is more appropriate for lower image speeds.
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Impedance
Membrane impedance,
Z(f), characterizes the
filtering performed by the photoreceptor membrane on injected current.
It is largely affected by the morphology of the photoreceptor and the
numbers and types of membrane channels the photoreceptor possesses
(Laughlin 1994; Weckström and Laughlin
1995
). By measuring impedance, therefore we can reveal the
effect that the membrane has on the temporal tuning of the
phototransduction current and suggest reasons for any regional
differences in terms of differences in cell shape and channel composition.
Figure 5A presents the average dark-adapted impedance amplitudes of photoreceptors in the three eye positions. At all frequencies, impedance amplitude is less in frontal photoreceptors than in receptors at the side and back of the eye, suggesting that anterior photoreceptors are larger than receptors elsewhere. In an RC filter (an approximation of the dark-adapted membrane), the amplitude at high frequencies is inversely related to capacitance, while that at low frequencies is directly related to resistance. Low gain at all frequencies therefore indicates the low-resistance and high-capacitance characteristic of a large membrane area.
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Figure 5C presents the same impedances as in Fig.
5A, normalized to unit amplitude. In the dark-adapted state,
the membrane corner frequencies at the front (95.7 ± 4.9 Hz,
n = 17) and back (92.0 ± 4.9 Hz,
n = 27) of the eye are significantly greater than those
at the side (75.8 ± 4.6 Hz, n = 20; Table 2).
These differences indicate that anterior and posterior photoreceptors
have a proportionately lower resistance for their membrane area than
lateral receptors. In an RC filter, corner frequency is inversely
related to the product of resistance and capacitance. Therefore given
that capacitance per unit area is invariant for biological membranes
(Hille 1992), the corner frequency may only be increased
by increasing conductance per unit area (specific conductance),
regardless of the total area of the cell.
Light-adapted rhabdomeric photoreceptors generally have lower
resistances and larger bandwidths than dark-adapted receptors (compare
Fig. 5, C with D). These changes reflect the
activation of light-gated channels and an increased activation of
voltage-sensitive K+ channels (Laughlin
1989, 1994
). As in the dark-adapted condition, overall
resistance is least in photoreceptors at the front of the eye (Fig.
5B). Now, however, the corner frequencies of photoreceptor membranes at the front (287 ± 18 Hz, n = 33) are
significantly greater than those at both the side (195 ± 10 Hz, n = 34) and the back (210 ± 10 Hz,
n = 37; Table 2). Again, this difference suggests that
frontal photoreceptors have a higher specific conductance than other
receptors. Frontal photoreceptors also exhibit greater low-frequency
attenuation (Fig. 5D). Their lower relative membrane resistance may therefore derive partly from a relatively stronger K+ conductance. K+ channels
are known to attenuate low frequencies by counteracting changes in
light-gated current occurring at time scales comparable with the
K+ channels' kinetics (Weckström et
al. 1991
).
Noise
A further indication of phototransduction performance is the power
spectrum of the noise,
N(f). A major component
of this will be Poisson shot noise associated with the random arrival of photons. The shape of this component reflects the shape of a
quantum bump, the response of the receptor to a single photon absorption (Wong and Knight 1980; Yeandle
1958
). Noise power therefore provides information about bump
duration. The shorter the bump, the greater the noise bandwidth (Fig.
6).
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A comparison of noise bandwidths in the different eye regions demonstrates trends similar to those observed for photoreceptor contrast gain functions, G(f) (Fig. 6A). In frontal photoreceptors, noise corner frequencies (129 ± 2 Hz, n = 31) are significantly greater than those in receptors at either the side (98 ± 3 Hz, n = 34) or back (101 ± 2 Hz, n = 38) of the eye (Table 2). Again, posterior corner frequencies are greater than lateral corner frequencies, although not significantly so. These results indicate that bump durations vary with retinal position and are fastest at the front of the eye (Table 1).
Signal-to-noise ratio
The quality of the signal passed by a photoreceptor may be quantified in terms of signal-to-noise ratio (SNR). We consider two types of SNR: SNRV(f), involving voltage response (output) power and SNRG(f), involving the contrast gain function of the cell (see METHODS). Both SNR measures provide details about functional aspects of the photoreceptor response.
SNRV(f) is the ratio of signal and noise powers in the photoreceptor's output (Eq. 4). It is employed directly in the calculation of the photoreceptor's information rate (Eq. 6), a measure of the statistical dependence between a photoreceptor's input and its output. We find that frontal photoreceptors achieve higher SNRV(f) at the high frequencies than other receptors (Fig. 6B). They therefore pass high frequencies more reliably and have a higher total information rate. For the white-noise stimuli used in these experiments, information rates obtained for photoreceptors at the front, side and back of the eye were 822 ± 65 bits/s (n = 31), 638 ± 34 bits/s (n = 34), and 573 ± 27 bits/s (n = 38), respectively. Information rates at the front of the eye are significantly higher than at the other two positions (Table 2). In fact, the anterior receptors signal 29% more information than the lateral and 43% more than the posterior receptors. These figures indicate how differences in the temporal properties of photoreceptors across the eye have a substantial effect on coding performance.
Besides the shapes of individual bumps, the photoreceptor response is
affected both by internal noise (Juusola et al. 1994; Lillywhite and Laughlin 1979
) and variation in the
latency time between the absorption of a photon and the production of a
bump (de Ruyter van Steveninck and Laughlin 1996
;
Wong et al. 1980
). These two factors are represented by
the contrast-normalized signal-to-noise ratio,
SNRG(f) (de
Ruyter van Steveninck and Laughlin 1996
). In the absence of
internal noise and latency dispersion,
SNRG(f) would be a
constant across all frequencies and would be equal to the photon flux
received by the photoreceptor. Otherwise,
SNRG(f), is reduced at
low frequencies by internal noise and at high frequencies by latency
dispersion. Notably,
SNRG(f) is independent
of bump duration. Thus by examining
SNRG(f), we are able to
dissect out the contribution made by bump duration to the speed of the
impulse response. We find that the
SNRG(f) of
photoreceptors in the different eye positions diverge at the higher
frequencies (Fig. 6C). Corner frequencies of
SNRG(f) in frontal
photoreceptors (73.8 ± 2.4 Hz, n = 30) are
significantly higher than those at both lateral (60.2 ± 2.9 Hz,
n = 34) and posterior (58.4 ± 2.3 Hz,
n = 38) positions (Table 2). It appears that frontal
photoreceptors exhibit less dispersion in bump latency than other
receptors. They signal photon arrival times more reliably.
Finally, we also find that the maximum
SNRG(f) are very similar
at all eye positions (Fig. 6C). The figures obtained for
photoreceptors at the front, side and back of the eye are 6.42 × 105 ± 1.24 × 105,
5.50 × 105 ± 6.5 × 104, and 4.15 × 105 ± 3.2 × 104
s1, respectively. If
these maxima occur in the region of the spectrum where the effects of
internal noise and latency dispersion are negligible, then they
indicate that the rates of photon absorption in the receptors were the
same (see Table 2).
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DISCUSSION |
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We have measured the spatial and temporal properties of
photoreceptors in different parts of the eye of male blowfly, C. vicina. Our results demonstrate retinal gradients in both. The
acceptance angles, , of photoreceptors were found to increase
from 1.59° at the front of the eye to 2.36° at the back. These
figures are consistent with those found in C. stygia, where
a progressive increase in acceptance angle has been demonstrated from
circa 1.6° at the front of the eye to 2.5° at the side
(Hardie 1979
). Temporal properties of photoreceptors
have not previously been measured in different parts of the same eye in
any species, however. It is on these that we shall focus.
Like the spatial measurements, all aspects of temporal coding examined in this study demonstrate the special status of the front of the eye. Photoreceptor contrast gain functions and impulse responses show that frontal photoreceptors are 20% faster than receptors elsewhere (Figs. 3 and 4). They also attain higher signal-to-noise ratios than other receptors at high frequencies (Fig. 6B) and consequently attain a substantially higher information rate (30-40%). Noise-power spectra (Fig. 6A) and contrast-normalized signal-to-noise ratio (Fig. 6C) indicate that the superior bandwidth of frontal photoreceptors is achieved through both a shorter bump duration and a smaller bump latency dispersion (see Signal-to-noise ratio). Finally, despite their high temporal resolution, frontal photoreceptors appear to be adjusted to lower image velocities than anywhere else in the eye because photoreceptor characteristic velocity is lowest at the front of the eye (see Temporal filtering). Compared with the differences between coding parameters measured in frontal and nonfrontal receptors, the differences between the same parameters measured in lateral and posterior eye positions are generally modest. In fact, of all the corner frequencies measured, only the dark-adapted impedance corner frequencies differ significantly between photoreceptors at the side and back of the eye. The implications of these and other observations both for the mechanisms of phototransduction and for retinal coding will now be discussed.
Mechanisms for regional tuning
Measurements of contrast normalized signal-to-noise ratio,
SNRG(f), (Fig.
6C) indicate that photoreceptors in all eye positions were
absorbing photons at a rate of circa 5 × 105
s1. Yet many of the
differences observed between photoreceptors are reminiscent of changes
that occur under conditions of normal light adaptation. For example,
the higher corner frequencies of the contrast gain function (Fig.
3A), the shorter bump durations (Fig. 6A) and the
smaller bump latency dispersions (Fig. 6C) of frontal
receptors are consistent with a higher state of light adaptation in
these cells (de Ruyter van Steveninck and Laughlin 1996
;
Juusola et al. 1994
). It is tempting therefore to
explain regional differences in the temporal properties of
photoreceptors in terms of the molecular mechanisms that underlie light
adaptation, such as rhabdomeral Ca2+
concentration (Dorlöchter and Stieve 1997
;
Zuker 1996
).
Any mechanism that regulates intracellular Ca2+
concentration could be responsible for tuning photoreceptor responses
around the eye. A likely candidate is the number or density of
light-gated channels. Because fly photoreceptor light-gated channels
are known to permit Ca2+ (Hardie and Minke
1992), a higher density of these channels could increase the
degree of light adaptation at a given photon flux, especially if
light-adaptation acts locally at the site of Ca2+
influx (Minke and Payne 1991
). In support of this
proposition for channel densities, we note that light-gated channels
influence the impedance of the membrane by increasing its conductance.
The higher impedance corner frequency of frontal photoreceptors in the
light-adapted condition (Fig. 5, B and D) is
therefore consistent with a higher density of such channels.
Frontal impedance functions exhibit greater low-frequency attenuation (Fig. 5D), suggesting that a greater density of K+ channels also contributes to the elevated conductance of anterior receptors. The relative contributions of light-gated and K+ channels to membrane conductance is unknown. Nevertheless, the fact that the maximum gain of the contrast gain function is constant across the eye (Fig. 3A) would indicate that K+ shunt conductance always balances the current generated by the light-gated channels. That is, light-gated and K+ channel densities may be matched across the retina.
Whether or not channel density is the ultimate explanation for our
results will require more investigation with the appropriate tools.
Nevertheless, the hypothesis is parsimonious in that it does not
require different photoreceptors to possess essentially different
physiologies. Instead, one anatomical variable (channel density) is
proposed to act on the same adaptational machinery in all
photoreceptors to bring about the observed differences in response
properties. Indeed differences in the densities of Ca2+-permissive transduction channels are known
to be responsible for the frequency tuning of hair cells in the turtle
cochlea, and this effect is mediated by the influence of
Ca2+ on mechano-acoustic adaptation
(Fettiplace and Fuchs 1999). It would be of great
interest if the mechanisms for regional tuning of photoreceptor
frequency responses mirrored those observed in a vertebrate for a
different sensory modality.
Retinal gradients and the coding of images
Frontal photoreceptors can code higher frequencies than receptors elsewhere. Our results also show that the frontal photoreceptors achieve higher signal-to-noise ratio bandwidths and information rates through a reduction in bump latency dispersion (Fig. 6, B-D). What factors make it beneficial to employ photoreceptors with different response speeds in different parts of the eye?
Variations in the temporal properties of photoreceptors are almost
certainly a reflection of local differences in the availability of
temporal power and the biological significance of that power. The
arguments for tuning photoreceptors to input bandwidth are both
computational and energetic. Computationally, it makes little sense to
introduce high-frequency noise by having fast bumps if there are no
high-frequency signals to encode. Conversely, only when there are
high-frequency signals present should photoreceptors encode them,
especially because photoreceptors are of limited dynamic range
(van Hateren 1992a,b
). Energetically, high frequencies are expensive to encode and should be ignored when uneconomical. The
energetic costs of having a faster phototransduction cascade with less
dispersion are not known. However, the costs of impedance are well
understood (Laughlin et al. 1998
). Impedance is governed by the ion channels of the membrane. The more channels there are and
the higher their density, the less the effects of channel noise on
signal reliability (White et al. 2000
) and the greater the bandwidth of the cell. However, the elevated ion fluxes associated with more channels require more energy to be maintained.
If differences in response dynamics reflect differences in the availability of temporal power, we should seek reasons for the nonuniform distribution of this power across the retina. We consider three hypotheses: gradients in optical performance increase high temporal frequency power in regions of high spatial resolution; gradients in retinal velocity are established by ego-motion (optic-flow) and these increase the temporal bandwidth of signals in regions of high velocity; and the nonuniform distribution of behaviorally relevant objects favors temporal resolution in particular retinal regions.
In the case of the male blowfly, our data allow us to distinguish
between these three possibilities. The first (temporal bandwidth matches spatial bandwidth) may be discarded because it is clear that
temporal resolution is not dictated simply by optical performance (cf.
Glantz 1991; Howard 1981
). If it were
then the characteristic velocity of photoreceptors would be constant.
Instead, temporal and spatial bandwidths diverge with increasing
retinal eccentricity (Fig. 4). The second possibility (temporal
bandwidth matches optic flow) is also difficult to reconcile with our
data. The likely form of optic flow that could impose a gradient on the
expected local velocities of different parts of the retinal image is
the retrogressive flow associated with forward translatory movement (Gibson 1950
). Yet this predicts the highest velocities
in lateral regions of the eye where we find temporal resolution is
poorest and characteristic velocity is intermediate between the
anterior and posterior conditions (Fig. 4). We are therefore left with the third hypothesis: there are advantageous high-frequency signal components at the front of the eye that make it worth investing in the
extra bandwidth of the frontal photoreceptors. A likely possibility is
that these high frequencies are associated with the tracking of small
targets (Hornstein et al. 2000
).
In many dipterans the male uses the frontal eye region to pursue
potential mates (Land 1997). This is an acute zone, with larger facet diameters and higher angular density of frontal ommatidia (Land and Eckert 1985
) (Fig. 2). Thus the acute zone
occupies a relatively large area of the eye and makes a
disproportionate demand on the animal's resources. This extra optical
investment in spatial bandwidth is accompanied by the expenditure of
energy on temporal bandwidth.
Why pursuit behavior in particular should make the extra investment in
the acute zone worthwhile may be understood by considering the pursuit
stimulus. A small target such as another fly essentially appears as a
point against the background. The spatial frequency bandwidth of an
ideal (infinitesimal width) point is infinite. In this case, therefore
the amount of stimulus power obtained by the retina is proportional to
the spatial bandwidth of its lenses. This explains the premium on high
spatial resolution in the acute zone (Land 1997).
Compare this to the situation when the stimulus of interest is simply
the general structure of the environment. The power of natural scenes
falls off in proportion to the square of spatial frequency
(Burton and Moorhead 1987
; Field 1987
).
In this case, there are diminishing returns in stimulus power obtained
by increasing retinal spatial resolution. For the acute zone of a
chasing fly, there is therefore a greater imperative for high spatial
resolution than for animals whose retinas are designed for coding
natural scenes only (Atick and Redlich 1992
; van
Hateren 1992b
). Furthermore, if a target is seen against a natural scene background, then it is the higher spatial frequencies that possess the greatest signal-to-noise ratio. These should be coded
to resolve the target.
This argument holds for moving stimuli. If the high spatial frequencies
of a stationary point have high returns in terms of stimulus power,
then so do the high temporal frequencies of a moving point. Just how
fast photoreceptors should be will depend on the image (target)
velocities normally experienced by the animal. The sorts of target
velocities experienced by a chasing fly are not known for
Calliphora. Nevertheless if the temporal bandwidths of
photoreceptors reflect the bandwidths of their input after spatial
filtering by the lenses, then the characteristic velocity of the
photoreceptors should reflect the range of image velocities normally
experienced. In this regard, we note that the characteristic velocities
of frontal photoreceptors were smaller than those of the other
receptors in our study. Thus we predict that, while the acute zone is
designed for high spatiotemporal resolution of a target, this target is
perhaps not moving as fast as the stimuli that appear in the periphery
of the fly's vision. This is what one would expect if the consequence
of pursuit is the maintenance of the target within a small region of
the visual field, despite the target's velocity (Eckert and
Buchsbaum 1993).
Conclusion
We have measured the spatial and temporal properties of a single class of photoreceptor at different positions in the retina of the male blowfly. We have established that both properties change across the retina and have argued that this represents an adaptation for pursuit behavior. Naturally, the tracking of moving targets is a general problem, and it is likely that similar specializations in the temporal properties of photoreceptors and interneurons may exist in other animals, especially when the target is small.
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ACKNOWLEDGMENTS |
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We thank J. Anderson and E. Hornstein for advice in data acquisition and analysis and E. Hornstein for comments on the manuscript. The LED driver used in these experiments was constructed by G. Harrison. The Calliphora colony was maintained by N. Hall and J. Lester.
This work was supported by the Biotechnology and Biological Sciences Research Council (UK), the Gatsby Foundation (UK), and the Rank Prize Fund.
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FOOTNOTES |
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Address for reprint requests: S. B. Laughlin, Dept.of Zoology, University of Cambridge, Downing St., Cambridge CB2 3EJ, UK (E-mail: s.laughlin{at}zoo.cam.ac.uk).
Received 21 December 2000; accepted in final form 11 May 2001.
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REFERENCES |
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