Variations in Photoreceptor Response Dynamics Across the Fly Retina

Brian G. Burton, Ben W. Tatler, and Simon B. Laughlin

Department of Zoology, University of Cambridge, Cambridge CB2 3EJ, United Kingdom


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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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Fig. 1. Positions of recording sites. A plan view of a male blowfly shows the three recording sites. Arrows indicate the retinal positions and optical axes of photoreceptors designated as being at the front, side, and back of the eye. The locations on the corneal surface where the lenses of study photoreceptors are found are marked by the foot of each right-arrow. Note, the optical axis of a photoreceptor is not necessarily normal to the corneal surface, particularly at the side of the eye (Stavenga 1979).


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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 MOmega , 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 (lambda 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 s-1 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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Table 1. Spatial and temporal parameters of photoreceptors at different eye positions

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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Fig. 2. Angular sensitivity functions at different retinal positions. Recordings taken from photoreceptors at the 3 eye positions in 12 different animals. For each photoreceptor, mean (±SE, n = 10) sensitivities are plotted at 0.25° intervals over an 8° range covering the photoreceptor's receptive field (see METHODS). The data are fitted with a Gaussian model (---) from which acceptance angle, Delta rho , is extracted. Frontal receptors have the narrowest angular sensitivity functions and consequently represent a higher resolution image than other receptors.

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)
<IT>G</IT>(<IT>f</IT>)<IT>=</IT><FENCE><FR><NU>⟨<IT>V</IT><SUB><IT>C</IT><IT>,</IT><IT>m</IT><IT>,</IT><IT>n</IT></SUB>(<IT>f</IT>)⟩<SUB><IT>m</IT></SUB></NU><DE><IT>C<SUB>n</SUB></IT>(<IT>f</IT>)</DE></FR></FENCE><SUB><IT>n</IT></SUB> (1)
where m indexes the individual presentations of a given pseudorandom stimulus, n indexes the different stimuli presented (see Stimuli and recording), and f denotes temporal frequency. < .> x indicates an ensemble average across examples, x. The impedance, Z(f), of the membrane was estimated in a similar way, where VC,m,n(f) is now replaced by VI,m,n(f), the responses of the cell to the pseudorandom current stimuli, In(f)
<IT>Z</IT>(<IT>f</IT>)<IT>=</IT><FENCE><FR><NU>⟨<IT>V</IT><SUB><IT>I</IT><IT>,</IT><IT>m</IT><IT>,</IT><IT>n</IT></SUB>(<IT>f</IT>)⟩<SUB><IT>m</IT></SUB></NU><DE><IT>I<SUB>n</SUB></IT>(<IT>f</IT>)</DE></FR></FENCE><SUB><IT>n</IT></SUB> (2)
The noise associated with a single presentation of a given stimulus was found as the deviation of the photoreceptor response, VC,m,n(f), from its average across all presentations of the same stimulus (see de Ruyter van Steveninck 1986; Kouvalainen et al. 1994). The power spectrum of this noise was averaged across all presentations of all pseudorandom stimuli to give an estimate of photoreceptor noise, N(f)
<IT>N</IT>(<IT>f</IT>)<IT>=</IT>⟨<IT>‖</IT><IT>V</IT><SUB><IT>C</IT><IT>,</IT><IT>m</IT><IT>,</IT><IT>n</IT></SUB>(<IT>f</IT>)<IT>−</IT>⟨<IT>V</IT><SUB><IT>C</IT><IT>,</IT><IT>m</IT><IT>,</IT><IT>n</IT></SUB>(<IT>f</IT>)⟩<SUB><IT>m</IT></SUB><IT>‖<SUP>2</SUP></IT>⟩<SUB><IT>m</IT><IT>,</IT><IT>n</IT></SUB> (3)
This estimate was adjusted for both statistical bias (Kouvalainen et al. 1994) and electrode noise (de Ruyter van Steveninck 1986). N(f) was modeled as a Gamma function (Juusola et al. 1994; Wong and Knight 1980) above 20 Hz. Estimated bump duration and corner frequency were obtained directly from the model (Wong et al. 1980).

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
SNR<SUB>V</SUB>(<IT>f</IT>)<IT>=</IT><FR><NU>⟨<IT>‖</IT>⟨<IT>V</IT><SUB><IT>C</IT><IT>,</IT><IT>m</IT><IT>,</IT><IT>n</IT></SUB>)(<IT>f</IT>)⟩<SUB><IT>m</IT></SUB><IT>‖<SUP>2</SUP></IT>⟩<SUB><IT>n</IT></SUB></NU><DE><IT>N</IT>(<IT>f</IT>)</DE></FR> (4)
where N(f) is defined as in Eq. 3. The contrast-normalized signal-to-noise ratio (de Ruyter van Steveninck and Laughlin 1996), SNRG(f), was calculated with the "signal" defined instead as the contrast gain power, |G(f)|2. That is
SNR<SUB>G</SUB>(<IT>f</IT>)<IT>=</IT><FR><NU><IT>‖</IT><IT>G</IT>(<IT>f</IT>)<IT>‖<SUP>2</SUP></IT></NU><DE><IT>N</IT>(<IT>f</IT>)</DE></FR> (5)
where G(f) is defined as in Eq. 1. For both signal-to-noise ratios, powers were adjusted for bias and electrode noise (Kouvalainen et al. 1994).

The information rate, I, associated with SNRV(f) was obtained from the formula (van der Lubbe 1997)
<IT>I</IT><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>2</IT></DE></FR> <LIM><OP>∫</OP><LL><IT>−∞</IT></LL><UL><IT>∞</IT></UL></LIM><IT> log<SUB>2</SUB> </IT>(<IT>1+SNR<SUB>V</SUB></IT>(<IT>f</IT>))<IT>d</IT><IT>f</IT> (6)
valid for a linear channel transmitting a Gaussian signal subject to Gaussian noise.

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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Table 2. Differences between parameters measured in photoreceptors at different eye positions


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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, Delta rho , 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 Delta rho 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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Fig. 3. Temporal filtering at different retinal positions. A: contrast gain function amplitude, |G(f)|, obtained as an average across all animals. Photoreceptors in all parts of the eye achieve the same maximum contrast gain amplitude at circa 20 Hz. Above this frequency, frontal photoreceptors maintain greater sensitivity than receptors at the side and back of the eye. B: impulse response. The impulse response, obtained as the inverse Fourier transform of G(f), has a higher amplitude and a shorter duration in frontal photoreceptors.

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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Fig. 4. Temporal and spatial bandwidths at different retinal positions. Histogram showing the spatial () and temporal () corner frequencies of the photoreceptor at different eye positions. Anterior photoreceptors have significantly higher temporal and spatial corner frequencies than lateral and posterior receptors. The ratio of temporal to spatial corner frequency that defines the characteristic velocity is greatest at the back of the eye. Error bars, SE.

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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Fig. 5. Membrane impedance amplitude, |Z(f)|. A and C: dark-adapted impedance. Photoreceptors at the front of the eye have smaller impedance amplitudes than receptors elsewhere (A), indicating a lower resistance and a higher capacitance (larger surface area). Normalized impedances (C) show that bandwidths are also highest at the front of the eye. B and D: light-adapted impedance. When the cell is depolarized by light-gated currents, the cell develops a notable attenuation of low frequencies because voltage-sensitive K+ channels are activated. Resistance is lowered (B). Frontal photoreceptors retain their higher bandwidths and show the greatest low-frequency attenuation (D). A-D: all spectra are averages across all animals used.

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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Fig. 6. Shot-noise and signal-to-noise ratio. A: noise power spectra, N(f). Noise power consists of low-frequency internal noise and broadband shot noise. Shot-noise corner frequencies are greatest at the front of the eye, suggesting frontal photoreceptors have the shortest bumps. B: output signal-to-noise ratio, SNRV(f). SNRV(f) bandwidths are greatest at the front of the eye. This provides frontal photoreceptors with the highest information rate. C: contrast-normalized signal-to-noise ratio, SNRG(f). Photoreceptors in all eye regions achieve similar maximum SNRG(f), indicating similar photon catches. Frontal photoreceptors have the highest SNRG(f) bandwidths, indicating they exhibit the smallest dispersion in bump latencies. D: histogram showing the corner frequencies of the photoreceptor noise () and contrast-normalized signal-to-noise ratio () at different eye positions. Error bars, SE. A-C: all spectra are averages across all animals used.

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 s-1, 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).


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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, Delta rho , 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 s-1. 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.


    ACKNOWLEDGMENTS

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.


    FOOTNOTES

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.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

0022-3077/01 $5.00 Copyright © 2001 The American Physiological Society