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First published online October 18, 2006
Journal of Experimental Biology 209, 4339-4354 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02517
A `bright zone' in male hoverfly (Eristalis tenax) eyes and associated faster motion detection and increased contrast sensitivity
1 Discipline of Physiology, School of Molecular and Biomedical Science, The
University of Adelaide, SA 5005, Australia
2 Vision Group, Department of Cell and Organism Biology, Lund University,
Lund, Sweden
* Author for correspondence at present address: California Institute of Technology, Bioengineering, Pasadena, CA 91125, USA (e-mail: astraw{at}caltech.edu)
Accepted 29 August 2006
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Summary |
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Key words: insect vision, motion detection, sexual dimorphism
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Introduction |
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), it has been
clear that facet lenses are often not uniform in size across the compound eye.
Insects, like other animals including humans, sample the visual world with
sensitivity and resolution that vary across space. In general, it may be
difficult to ascribe specific functionality to these regionalized properties
because the same compound eyes and ocelli must serve a variety of visual
behaviors. One success at ascribing specific functionality arose from the
discovery of sexual dimorphism in the retina of muscoid flies Calliphora
vicina and Musca domestica. Males have an `acute zone' in the
fronto-dorsal portion of the visual world where the angle between adjacent
ommatidial axes (
) is nearly half that in the lateral eye
(Land and Eckert, 1985). Males
keep the image of females they are pursuing in this region
(Boeddeker et al., 2003;
Wagner, 1986;
Wehrhahn, 1979), and the male
acute zone is thought to be an optical specialization for detection and
tracking of females. This region of increased angular resolution comes at a
significant cost. To overcome limits on spatial resolution due to optical
diffraction, increased angular resolution demands not only more facets with
smaller interommatidial angles but also larger facet diameter, leading to a
significant increase in eye size
(Kirschfeld, 1976;
Land, 1997;
van Hateren, 1989).
Large lenses are not the only investment made by male muscoid flies in the
region of the acute zone. Additional, sex-specific `7r' photoreceptors appear
to have been modified from the typical R7 receptors to have properties similar
to those of R1-6, creating a 7% increase in signal-to-noise by contributing to
the same postsynaptic cells (Franceschini
et al., 1981; Hardie,
1983; Hardie et al.,
1981). The R1-6 photoreceptors in this region have finer angular
sensitivity, are faster by 
20%, and have a higher metabolic cost than
lateral photoreceptors (Burton et al.,
2001; Hornstein et al.,
2000). Furthermore, there are several male-specific interneurons
with receptive fields in this region
(Hausen and Strausfeld, 1980).
Functionally, these properties all appear to be adaptations for detecting and
chasing small targets, namely conspecific females.
Historically, several design principles have been used to explain
properties of eyes and neurons, including maximizing information transmission,
minimizing redundancy, exploiting statistical correlation, and reducing
unnecessary energy expenditure (Burton et
al., 2001; de Ruyter van
Steveninck and Laughlin, 1996;
Laughlin, 1981;
Laughlin et al., 1998;
Srinivasan et al., 1982).
Thus, acute zones indicate that demand for information is not uniform across
visual space, and their presence suggests that some regions of the visual
world are particularly important for specific behaviors. More generally,
different behaviors may require different information from the visual system.
While at the optical and photoreceptor level it seems that specializations
such as increased contrast sensitivity and spatial resolution would be
beneficial for any behavior, these specializations come with at least one
additional cost - that of increased eye size and mass. Thus, a functional
adaptation to serve one behavior may compromise performance of other tasks.
For later stages of visual processing, such as motion detection, it is unclear
whether a single set of elementary motion detectors (EMDs) might serve as the
basis for both visual course correction and target chasing behaviors with
potentially conflicting demands or whether estimates of visual motion may be
computed independently.
Local properties of fly motion detection and the `matched filter hypothesis'
How does non-uniform visual sampling affect the properties of visual
interneurons and behavior? Fly lobula plate tangential cells (LPTCs) are
neurons sensitive to visual motion over a large portion of the visual world.
In the muscoid flies Calliphora, Musca and Phaenecia, the
large receptive fields of LPTCs have non-uniform directional selectivity
(Hausen, 1982;
McCann, 1974), and the local
preferred directions (LPDs) of these neurons appear matched to particular
components of optic flow induced by particular types of self-motion such as
rotation about particular axes (Krapp et
al., 1998; Krapp and
Hengstenberg, 1996; Krapp et
al., 2001). This has increased interest in the concept of
motion-matching, whereby optic flow may be estimated by the correlation of
local motion direction and velocity with the local response properties within
large receptive fields (Bülthoff et
al., 1989). As shown by Krapp and colleagues, the distribution of
directions of local motion experienced across the visual world during, for
example, roll rotation, are similar to the LPDs of fly VS (vertical system)
cells. Combined with extensive work on other cell classes, this work provides
a compelling explanation for the receptive field structure of fly LPTCs. These
cells may be `matched filters' for specific components of self-motion induced
optic flow, such as yaw rotation, roll rotation and forward translation.
Furthermore, modeling efforts have shown that biologically inspired models
based on such matched filters can accurately estimate the components of
optical flow due to self translation and rotation in a rapid, feed-forward
manner (Dahmen et al., 2001;
Franz et al., 2004;
Franz and Krapp, 2000). In
other flies, the LPD organization is largely unknown, although the subject is
of inherent interest because anatomical
(Buschbeck and Strausfeld,
1997) and physiological
(O'Carroll et al., 1996;
O'Carroll et al., 1997)
characteristics of LPTCs vary in a correlated manner with visual behavior. Yet
small-field motion-sensitive neurons of the medulla and pre-synaptic to LPTCs
are highly conserved at the anatomical level
(Buschbeck and Strausfeld,
1996), suggesting that the anatomy and physiology of LPTCs may
have high `evolutionary plasticity' that underlies behavioral differences
between groups within the flies.
The remarkable similarity in the local preferred directions of LPTCs with
the predicted patterns of local velocities during different types of
self-motion raises the question of how other local properties of LPTCs might
be correlated with visual input. In particular, local velocity tuning is a
critical factor when assessing whether LPTCs may act as matched filters.
Previous experiments used a spot moving in a small circular orbit at constant
angular velocity repeated in each of many locations over the receptive field
to measure both the local preferred direction and the `local motion
sensitivity', the magnitude of response modulation to this particular stimulus
(Krapp and Hengstenberg,
1997). Yet the velocity tuning of these neurons remains unclear
because these cells behave locally much like EMDs of the correlator type, in
which output is not proportional to velocity per se, but instead to a
combination of spatial and temporal frequencies and contrast
(Egelhaaf and Borst, 1993;
Egelhaaf et al., 1989).
Furthermore, differences in local contrast sensitivity and local gain also
affect the physiological properties of these cells. Without information on
these properties and their variation across the receptive fields of these
neurons, the local responses of fly LPTCs will be difficult to predict for
arbitrary moving patterns. With such data, however, increasingly accurate
predictions of the responses to velocity can be made
(Boeddeker et al., 2005;
Dror et al., 2001;
Lindemann et al., 2005;
Shoemaker et al., 2005).
In this study, we found that male Eristalis tenax hoverflies have
a `bright zone' similar to that of the blowfly Chrysomia megacephala
(van Hateren et al., 1989),
which results in increased light capture but is not accompanied by large
changes in interommatidial angle. Additionally, we sought investigate
Eristalis LPTCs in the context of the matched filter hypothesis and
to explore the effect of the male-specific bright zone on the performance of
these motion detecting neurons. To do so, we developed a stimulus that allows
exploration of the local spatial-, temporal- and contrast-sensitivity of
wide-field motion detecting neurons and used it to investigate
Eristalis HS cells. Furthermore, as part of the characterization of
the local properties of Eristalis LPTCs, we performed an analysis
that allowed us to determine the relative contribution of Type 1 and Type 2
EMDs, those with inputs from neighboring ommatidia and next-but-one neighbors,
respectively (Buchner, 1976;
Buchner, 1984).
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; Rutowski and Warrant,
2002) and was performed on two male and two female flies. Briefly,
the small end was cut from a plastic pipette tip leaving an opening large
enough for a fly's head to protrude through. The fly was fixed in position by
gluing the proboscis to the tube with dental wax, and this preparation was
then mounted at the centre of curvature of a Leitz goniometer (Wetzlar,
Germany). The goniometer was placed onto the foot-plate of an Askania
macroscope (Rathenow, Germany). It was then manipulated so that the flat
posterior eye edge was parallel to the plane of the stage. The head was
further manipulated so that (1) the origin of the three goniometer axes was in
the centre of the head, and (2) the three goniometer axes were lined up with
the dorsal-ventral (yaw), anterior-posterior (roll) and left-right (pitch)
axes, respectively, of the fly's head. With the stage horizontal, both eyes
then looked vertically upwards into the objective of the macroscope, and when
observed in this position, the eyes were oriented exactly anteriorly (from the
animal's point of view). The goniometer allowed us to tilt the stage (and thus
the head) in defined angular steps of elevation and azimuth, with
elevation=0° and azimuth=0° defined as the anterior orientation
described above (f in Fig.
1). Dorsal (d) corresponds to an elevation of +90°
and lateral (l) to an elevation of 0° and azimuth of +90°.
The exact anterior coordinates (azimuth=elevation=0°) were confirmed when
observing the deep pseudopupil whose appearance in both eyes is
mirrorsymmetrical along the eye equator
(Franceschini, 1975).
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To illuminate the eyes we introduced a half-silvered mirror, angled at 45°, just beneath the objective of the macroscope. Collimated white light (from a halogen source) was directed laterally to the mirror so that the eyes were illuminated and viewed along the same axis (`orthodromic illumination'). This type of illumination reveals a luminous pseudopupil. Using chalk dust sprinkled lightly on the eye to provide landmarks, we took a series of photographs of the luminous pseudopupil in the left eye at 10° intervals of elevation and azimuth. Due to the structure of the apparatus we could not go beyond elevations of +70° or -70° or an azimuth of 80°. Hence, our observations of the appearance and location of the pseudopupil were restricted to the frontal region of the eye, which is, in the context of our study, the region of greatest interest.
From each photograph we were able to determine the facet coordinates of the
facet found at the centre of the pseudopupil, using the landmarks as a guide.
Using established formulae that correct for elevation distortions in the
projection (Land and Eckert,
1985), we calculated the average local interommatidial angle
() and facet diameter (D) for each combination of
elevation and azimuth. These data were plotted on a sphere representing 3D
space around the animal, and contours were interpolated to connect regions of
space viewed by parts of the eye with the same average local
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Electrophysiology
Lobula plate tangential cells (LPTCs) of wild-caught hoverflies
Eristalis tenax L. were recorded intracellularly. All recordings were
done from the left lobula plate, and the responses described are from
ipsilateral receptive fields. Electrodes were pulled on a Sutter P-97 puller
(Novato, CA, USA) and filled with 2 mol l-1 KCl, and had tip
resistances of 20-40 M 
. The calibration of 3D position and orientation
was done with reference to morphological features of the fly head, using the
planar back surface of the head and the animal's midline to define the
vertical and longitudinal axes of the animal's head, respectively.
Stimulus
Stimuli were displayed on a CRT (LG Flatron 915 FT+; Seoul, S. Korea)
updated at 200 Hz with a mean luminance of 41 cd m-2 under the
control of a x86 PC running Windows 2000 with an nVidia graphics card
and drivers. The flat screen of our CRT was placed close enough to the fly to
subtend an approximately 100° horizontal field of view. The Vision Egg
stimulus generation software library (made freely available by A.D.S. at
www.visionegg.org),
was used to generate and display Gaussian windowed (s.d.=7.1°) sinusoidal
gratings (Gabor wavelets) corrected with perspective distortion calibrated
according to each fly's position. Thus, from the fly's location, a specified
spatial wavelength subtended exactly the same angle regardless of screen
position. Similar stimuli can be produced by the `mouse_gabor_perspective'
demonstration program distributed with the Vision Egg.
Calculating local preferred directions and local motion sensitivity
To characterize neurons encountered in the present study, we measured local
preferred direction using a sinusoidal grating method adapted from O'Carroll
et al. (O'Carroll et al.,
1997) (Fig. 2C)]. A
localized grating near the spatial and temporal frequency optimum of the cells
under study (0.1 cycles deg.-1, 5 Hz) was used (other grating
parameters as described above). Following presentation of a mid-luminance gray
screen, an initial 3 s period of motion at 180° (leftward) was shown in an
attempt to ensure that any effects due to motion adaptation would be similar
in different trials and that the cell was in a consistent state prior to
further stimulation. The stimulus consisted of a series of 16 motion
directions presented in sequence, each for 200 ms and at a 22.5° increment
from the previous direction. In this way, 16 sequentially tested directions
mapped out local directional tuning. To further minimize the possibility that
motion adaptation corrupted the local preferred direction (LPD) estimate, the
direction of motion was changed in a clockwise manner initially and then in
the counter-clockwise direction in a second, otherwise equivalent trial. The
LPD was calculated separately for the clockwise and counter-clockwise trials
by fitting with a cosine function (using a simplex error minimization
routine), which accurately describes the direction tuning of LPTCs
(Hausen, 1982;
van Hateren, 1990) as
described by the function:
 | (1) |
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LPD is the phase offset, or local
preferred direction (LPD).
Estimating contrast-response and contrast sensitivity
The primary means of determining the contrast-response relationship in this
study was with a `contrast ramp'
(O'Carroll, 2001;
O'Carroll et al., 1997). In
control experiments (e.g. Figs
3,
4), the validity of this
approach was confirmed by a contrast step technique, which has been used in
earlier studies of contrast sensitivity in the fly
(Dvorak et al., 1980;
Srinivasan and Dvorak,
1980).
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);
however, later portions of the response are reduced by motion adaptation
(Maddess and Laughlin, 1985).
By taking the mean membrane potential from 50 to 150 ms after the onset of
stimulation, we attempted to minimize effects of motion adaptation while
measuring steady-state responses. Because the response of Eristalis
HS cells are well fit by a correlator model with a time constant of
approximately 35 ms (Harris et al.,
1999), onset transients should be minimal during this period.
Despite the attempt to overcome these issues when dealing with the contrast
step method, it seems that adaptation will always make analysis of step
responses problematic (O'Carroll,
2001), at least when attempting to characterize the response of
unadapted motion detectors, as in this study.
A contrast ramp stimulus is faster than the step technique in determining
the contrast-response relationship because it sweeps through a range of
monotonically increasing contrasts in a short period of time. In this study,
we used 1 s ramps given by the equation:
 | (2) |
where t is time (s), A=0.3, B=0.7,
n=10. With these values, contrast rises approximately linearly for
about 0.6 s to a value of near 0.2 and then rapidly increases to a final value
of 1.0. We argue that this method reduces errors in the contrast-response
measurement because contrast is always increasing and motion adaptation is
thought to be contrast sensitive (Harris
et al., 2000). Thus, response at any moment will only be affected
by any potential motion adaptation resulting from stimulation at prior lower
contrasts. Furthermore, the total stimulus duration is relatively brief,
further limiting the effect of adaptation. The effect of onset transients
should also be minimized because there is no sudden onset luminance step.
In an effort to overcome the effects of `noise' (response variability due to pattern sensitivity, neural response variability, and measurement errors), each ramp was presented at least three times at a randomized starting phase. The average of these responses was computed, transformed from the time domain to a logarithmic contrast domain, and fit with a Weibull cumulative distribution function. The transformation to the logarithmic contrast domain subtracted an estimated neural latency. For the results presented here, a value of 15 ms was found to provide the best fit between contrast ramp data and contrast step data. Before fitting the data, it was `padded' with zero response values in the very low contrast range (<0.01) to force the fit to have a near zero value at low contrast. The Weibull function was chosen for its ability to fit a wide range of monotonically increasing functions with only a gain term and two other parameters, which were computed with a simplex error minimization routine.
The resulting fits were used to compute contrast sensitivity, a unitless
value equal to the reciprocal of the threshold contrast required to evoke a
criterion response. For this study, a fixed criterion response value of 2 mV
above the resting potential was used as a threshold, analogous to the fixed
criterion used by Srinivasan and Dvorak
(Srinivasan and Dvorak, 1980).
Other authors have used a `detectability criterion', e.g. a response criterion
of a just noticeable (to the experimenter) difference
(Dvorak et al., 1980) or the
standard deviation of the resting membrane potential of the cell
(O'Carroll et al., 1997). In
preliminary experiments, we verified that no qualitative shifts were observed
when the criterion was half of the usual value (although lower criteria yield
higher sensitivity values). Changing the criterion within a low-response range
seemed primarily to be a trade-off between noise and high sensitivity, and
thus the present approach seems equally valid to detectability-based
analyses.
Estimating contributions from Type 1 and Type 2 EMDs
In the spatial domain, correlator models are highly constrained by the
hexagonal spacing of the input. This property has been previously exploited to
provide confirmation of the validity of the correlator model in application to
fly optomotor responses (Buchner,
1976; Buchner,
1984; van Hateren,
1990) and to directly compare the sampling distance of fly LPTCs
with the spacing of ommatidia (Schuling et
al., 1989; Srinivasan and
Dvorak, 1980). We used this property combined with the known
angular spacing of Eristalis ommatidia
(Fig. 1A,C) to estimate the
relative contributions of the EMD types 1 and 2 (with inputs from neighboring
ommatidia and next-but-one neighboring ommatidia, respectively). Responses in
the spatial-frequency domain were fit with a two-EMD correlator model with
three free parameters using a simplex error minimization routine. Only a
single free parameter, the relative contribution from the EMD types, controls
the most critical feature of the model, the location of the zero crossing and
the nearby sharp rolloff.
The response of the model is given by:
 | (3) |
where the response R is given as a function of spatial frequency
Fs. The overall gain is set by the parameter k,
while the tanh function and the parameters s were necessary to model
saturation at high contrasts. The relative contributions of Type 1 and Type 2
correlators are given by g1 and g2,
which were under the control of a single free parameter. The response of each
EMD is found with a simplified analytic correlator model in the spatial domain
using the formulation given elsewhere
(Dror et al., 2001). In this
context, because contrast and temporal frequency are constant for any fit,
these factors are implicitly included in the parameters fit above and are
removed from the model used:
 | (4) |
where n is 1 or 2, corresponding to the EMD type.
h is the angular separation in the direction of
correlation calculated from , the interommatidial angle shown in
Fig. 1, by the relation
h=cos(30°) . The modulation transfer
function MTF(Fs) approximates the low-pass filtering
properties of the optics, and we used a Gaussian angular sensitivity function
of the form given by (Götz,
1964):
 | (5) |
where 
is the acceptance angle. This was calculated using the
approximation 
, which is the relation determined
from electrophysiological measurements of in Chrysomyia
(van Hateren et al., 1989) and
is similar to the relationship between electrophysiologically measured
Eristalis angular sensitivity functions
(James, 1990) and the data of
Fig. 1.
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), which shares additional specializations
found in Musca, such as a central rhabdomere (R7/R8) that contributes
to lamina monopolar cells (LMCs) with the same absolute and spectral
sensitivity as R1-6 (Franceschini et al.,
1981; Hardie,
1983; Hardie et al.,
1981). Although little is known about the behavior of
Chrysomyia, the bright zone is suggested to serve a detect-and-track
role. This also seems the most likely explanation for Eristalis. In
the case of Eristalis, however, a detailed behavioral analysis
(Collett and Land, 1978) shows
that males track females in a manner similar to Calliphora and are
also capable of a feat not observed in other flies - computation of an
open-loop intercept course upon first seeing a target.
Local preferred directions in Eristalis
Fig. 2 shows the local
preferred direction (LPD) and local motion sensitivity (LMS) for HS cells in
Eristalis. Within the area of the receptive field we investigated,
the distribution of LPDs and LMSs are similar to those of Calliphora
HS cells, with a horizontally extended streak of large LMS to front-to-back
ipsilateral motion. In this study, we encountered two classes of HS cells with
dorsal receptive fields, one with maximal LMS at elevations between +30°
and +60° (above the equator), and the other with maximal LMS near
+30°. The neuroanatomy and receptive field properties of HS neurons in
Eristalis are less well described than those of the blowfly, but our
earlier work on these cells in female E. tenax highlights several
likely similarities and differences
(O'Carroll et al., 1997).
Although nothing has yet been published for the equivalent organization of HS
neurons in male flies of either species, the physiological location of these
receptive fields corresponds to the anatomical locations of the dendritic
arborizations of the female cells
(O'Carroll et al., 1997).
While further work is clearly required to describe and classify receptive
field properties and neuroanatomy of these dorsal HS cells, we adopt here a
classification for these two classes consistent with the blowfly and female
E. tenax data. Hence we classify the more dorsal neurons as HSN (N:
north) and the less northern neurons as HSNE (NE: north-equatorial). The
frontal portion of the large receptive field of HSNE and, particularly, HSN
cells in male Eristalis corresponds in location to the bright zone
described above. The most sensitive region of the receptive field of
Eristalis HSN is more dorsal than the Calliphora HSN, which
more closely resembles the Eristalis HSNE in receptive field location
(Hausen, 1982;
Krapp et al., 2001).
The stimulus employed to measure the LPD and LMS values is theoretically
subject to the effects of motion adaptation as described in the methods.
However, curves measured with the stimulus motion direction rotating in a
clockwise manner were similar to those obtained from a counter-clockwise
rotation. The median difference in clockwise and counter-clockwise measured
LPDs across all locations, animals, sexes and cell types was 22°. The
differences in LMS values were also quite small. The direction of LPD change
was consistently opposite to the direction of the stimulus stepwise rotation,
indicating that motion adaptation is responsible for the small shift in LPDs.
Because the gain control component of motion adaptation is insensitive to the
direction of the adapting stimulus (Harris
et al., 2000), this effect is presumably due to a motion induced
after hyperpolarization-like effect.
In summary, the local preferred directions and local motion sensitivities
resemble those of Calliphora measured at equivalent positions. This
similarity suggests data from Eristalis HS cells may be suitable for
exploring the matched filter hypothesis. Because LMS measured here and in
earlier studies is not a predictor of the local velocity response
characteristics (Krapp et al.,
2001), an accurate prediction of local correlator output can only
be made with accurate estimates of other local properties. In particular, the
contrast-response relationship and its dependence on spatial and temporal
frequency is required.
Response as a function of contrast
After determining the LPD and LMS of HS cells, small patches were selected
from the large receptive field for further detailed analysis. Because the
distribution of LPDs and LMSs is so regular from fly to fly, we chose a
stereotyped frontal and lateral location used in all experiments to test local
properties. Sinusoidal gratings were localized to this region by
multiplication with a Gaussian contrast window (i.e. a Gabor patch) with
s.d.=7.1° and motion was always presented in the LPD as measured above.
For HSN cells, the frontal location was centered at an azimuth and elevation
of 0°, 60° with motion to 150° (up and left). The lateral location
was at an azimuth and elevation of 90°, 60° with motion to 207°
(down and left). For HSNE cells, the frontal location was centered at an
azimuth and elevation of 0°, 30° with motion to 180° (leftward).
The lateral location was at an azimuth and elevation of 90°, 30° with
motion also to 180°.
The contrast-response relationship of these neurons in small patches was investigated using two alternative techniques (see Materials and methods). The first is a traditional contrast step technique in which contrast is stepped to a fixed value while membrane potential is recorded, as shown in Fig. 3A. This method suffers from two experimental difficulties. First, as described in the methods, selecting a time period for analysis is problematic because of the competing effects of onset transients and motion adaptation. For example, the response shown to contrast 0.215 appears to adapt rapidly. Second, the time required to perform a series of such experiments is prohibitive for intracellular recordings when trying to measure the contrast-response at a wide range of spatial and temporal frequencies. To overcome the problems of the contrast step, we used a contrast ramp method. Fig. 3B illustrates the time course of stimulus and response. Fig. 3C compares the results from the contrast step experiment of Fig. 3A with the contrast ramp experiment of Fig. 3B along with an analytic curve (Weibull function) used to fit the contrast ramp data. As can be seen, these two methods produce similar results, and the analytic curve fit to the contrast ramp data accurately captures the contrast-response relation measured with either method.
To determine if the contrast ramp method consistently replicates the contrast step method and to determine the goodness-of-fit of the analytic function, experiments of the type shown in Fig. 3C were repeated with varying parameters in several cells. Fig. 4 shows that, for several Eristalis HS cells under varying stimulus conditions, the contrast-response relation measured using the contrast ramp method (and an associated fit using an analytic function) is similar to the relation found when measured with the contrast step method. Because it is much faster at measuring the contrast-response relationship, we used the contrast ramp as the primary stimulus with which to measure spatio-temporal contrast sensitivity.
Spatio-temporal surfaces
Fig. 5 shows the mean
responses of a male HSN cell to multiple presentations of a contrast ramp
stimulus of varying spatial and temporal frequency plotted on a logarithmic
contrast axis. The stimulus was presented in the frontal location. The
analytic fits (shown in red) differ only slightly from the data where there is
little noise. Where there is substantial noise, the automatic fits appear
similar to the best possible `by eye', suggesting that the analytic fits can
be used to accurately estimate the response of these cells.
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To visualize this spatio-temporal data, it is convenient to construct a contour plot showing the response estimated using the analytic fits. Fig. 6A,B shows the estimated response surface in the high-contrast regime for the frontal and lateral portions of the receptive field of the male HSN neuron in Fig. 5. The results from this cell are similar to those of other cells; responses to lateral stimuli were consistently weaker than responses to frontal stimuli
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Evident in the contour plot of Fig.
6B, and to a lesser degree in
Fig. 6A, is a diagonally
orientated `ridgeline', which appears to run from northeast to southwest. This
diagonal orientation appears in the response and contrast sensitivity data
indicates that the responses of these cells are not completely separable in
space and time. In fact, the dominant orientation appears to be in the
iso-velocity direction, and these cells therefore exhibit a degree of tuning
directly for grating velocity rather than purely temporal and spatial
frequency. Such `speed tuning' can be obtained from a correlator model with
imperfectly balanced subunit subtraction
(Egelhaaf et al., 1989;
Zanker et al., 1999). The `VT'
descending neurons of the honeybee exhibit a much larger degree of velocity
tuning when tested with sinusoids and may be involved in flight speed control
(Ibbotson, 2001).
Regional and sex-specific variation in spatio-temporal properties
We compared response amplitude, contrast sensitivity, and tuning to
temporal and spatial frequencies across receptive field locations and sexes.
To facilitate these comparisons, slices were taken across spatio-temporal
surfaces resulting in spatial and temporal frequency tuning curves. The
response amplitudes and contrast sensitivity of HSN cells to a variety of
temporal (Fig. 7) and spatial
frequencies (Fig. 8) indicate
that the most pronounced difference between frontal and lateral parts of the
receptive field is a substantially increased gain and sensitivity to frontal
stimuli, particularly in males, in which this region of the receptive field is
associated with the optical bright zone. Maximal contrast sensitivity in males
in this region is 12.9 (Fig.
7E), and in females it is 8.6
(Fig. 8E). Laterally, these
values fall to 8.1 and 3.5 in males and females, respectively
(Fig. 8F). HSNE (Figs
9,
10) cells show a similar
trend, although the magnitude of the differences is less.
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In HSN cells, there is also a large sexual dimorphism in the temporal
frequency domain. The frontal portion of the male HSN receptive field is tuned
to faster stimuli than that of females, with the optimum near 13 Hz in males
and 3.5 Hz in females in both the high-and low-contrast regimes
(Fig. 7A,C). In the lateral
portions of the receptive field, the situation is similar, although the optima
are slower at 3.5 Hz in males and 1.4 Hz in females
(Fig. 7B,D). HSNE cells
(Fig. 9) have much less
pronounced temporal frequency tuning differences between the sexes. The
frontal to lateral variation is similar to the HSN data. Male
Eristalis HS cells were known to have faster temporal frequency
tuning than females (O'Carroll et al.,
1997), and this study shows that this sex difference is largely
confined to HSN cells.
Fig. 8 shows the spatial frequency tuning of male (filled squares) and female (open circles) Eristalis HSN cells measured frontally and laterally. Also shown are model motion detector responses that estimate the contribution of Type 1 and Type 2 EMDs based on the interommatidial angle taken from Fig. 1 and some limited assumptions about spatial processing (see Materials and methods). The model parameters that provide a best fit to the data are shown in Table 1 and are illustrated in graphical form as insets in Fig. 8. Other than contrast sensitivity and gain changes, the curves show only subtle differences in spatial frequency tuning between frontal and lateral portions of the receptive field and between males and females. Similar observations for HSNE cells apply (Fig. 10).
|
Because temporal frequency tuning curves measured frontally show stronger responses to fast stimuli than those measured laterally and because the spatial frequency tuning curves have significantly less regional variation, the `preferred velocities' of the frontal regions of HSN and HSNE neurons are predicted to be faster than laterally. This is true for both sexes but is most evident in the male HSN neuron.
The model motion detector responses provide a good fit to the
experimentally measured data. Type 1 EMDs appear to dominate the response of
both HSN and HSNE cells (Table
1). This agrees with previous experimental work on other flies in
light-adapted conditions (Buchner,
1984; Srinivasan and Dvorak,
1980). The amount of saturation in the model can be inferred from
the flatness of the curve, and the overall gain can be inferred by the height
of the curve. The effects of saturation can be seen as a broad, flat peak,
particularly in the high contrast male data
(Fig. 8A,
Fig. 10A). This saturation
necessitated a saturating component in the model motion detector used to fit
the responses. Model responses descend below zero at some high spatial
frequencies, a prediction of `spatial aliasing', which is sometimes observed
in Eristalis cells when stimulating with local grating patches (e.g.
Fig. 6A,B). The amount of
spatial aliasing predicted is greater than observed. Because the model used
does not explicitly sum the outputs of two correlators to produce the Type 1
EMD output but only uses a single correlator with short baseline, the amount
of aliasing is overestimated (van Hateren,
1990). With a larger optical acceptance angle ,
spatial aliasing would be attenuated because of greater low-pass filtering,
and adjusting the ratio of to from the value of 1.0
used here varied the magnitude of predicted spatial aliasing but had little
effect on the estimated contributions of Type 1 and Type 2 EMDs (not shown).
Therefore, this difference is not expected to have any significant effect on
the conclusion that motion detection is dominated by Type 1 (nearest neighbor)
EMDs in light-adapted Eristalis HSN cells.
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Discussion |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Contrast sensitivity
The relationship between contrast and response is important to the function
of these cells because it is strongly non-linear and plays an important role
determining response characteristics (Dror
et al., 2001; Egelhaaf et al.,
1989; Shoemaker et al.,
2001). By measuring the contrast-response relationship rather than
responses to a particular contrast, this study was able to characterize
responses in both low- and high-response regimes. The low-response regime is
important because in this regime of small signal amplitudes, the system is
most linear, and can be used, for example, to investigate essential properties
of motion detection without additional non-linearities such as saturation
(Reichardt et al., 1983) or
adaptation (de Ruyter van Steveninck et
al., 1986; Harris et al.,
2000; Maddess and Laughlin,
1985). The high-response regime is presumably behaviorally
relevant but is difficult to interpret, at least in restrained animals where
electrophysiology has typically been performed. This may be due to additional
non-linearities such as saturation. One example from the fly
Bombylius suggests that saturation due to high contrast into to fly
LPTCs leads to broad tuning curves, masking the underlying contribution from
multiple input channels (O'Carroll,
2001).
Matched filter hypothesis
As discussed in the introduction, the local preferred directions (LPDs) of
lobula plate tangential cells (LPTCs) appear to match the pattern of optic
flow induced by self motion. Over the regions our stimulus device allowed us
to test, we found that in Eristalis HS cells, local preferred
directions (LPDs) are similar to those of Calliphora HS cells. (See
Results for a more detailed comparison of LPDs between Eristalis and
Calliphora.) Our results in Eristalis appear inconsistent
with the suggestion that HS cells may function as matched filters for yaw
rotation in Calliphora (Krapp et
al., 2001). The Eristalis HS cells studied have faster
preferred velocities frontally rather than laterally at the same elevation
angle; yaw rotation produces motion of constant velocity both frontally and
laterally. We note, however, that a more detailed interpretation of HS
receptive fields in Calliphora, including the effects of
contralateral input, suggests a possible role in translation detection
(Krapp, 2000). In the present
study, we found no evidence of contralateral input to the Eristalis
HS cells. As discussed below, this is particularly evident in males and could
be the result of conflicting demands that target detection circuitry imposes
on upstream processing elements of the visual system and results in
compromised performance of Eristalis HS cells in estimating yaw
rotation. The general trend, however, was also found in females and it may be
some Eristalis-specific phenomenon. Alternatively, the faster
temporal frequency tuning in frontally directed EMDs could be a more general
phenomenon not yet observed in other fly species.
Prediction of responses to naturalistic, global optic flow is not simply a
linear summation of LPD and LMS values. One needs to take into account local
variation of spatial, temporal and contrast sensitivity and how these local
response properties are integrated spatially and temporally into membrane
potential at the output regions of the neuron. The large regional differences
in contrast sensitivity and temporal frequency tuning we found, in HSN for
example, are not particularly evident in the map of LPD/LMS, and thus
highlight the difficulty of predicting responses based solely on this
characterization. Indeed, one study
(Karmeier et al., 2003) shows
that the responses of the V1 cell, a spiking LPTC predicted to be sensitive to
pitch-like optic flow, responds strongly to any global motion with a strong
frontal downward component (although the preferred rotation axis stays
unchanged even if lift translation is combined with rotation). An alternative,
but not mutually exclusive, view of LPTC encoding of self motion has recently
been proposed, which suggests that HS may encode both rotational and
translational information in different frequency bands, although the means
flies might use to decode this information is unclear
(Kern et al., 2005).
Nevertheless, some wide-field properties are well predicted from LPDs and
LMSs, such as the preferred rotation axes of VS neurons
(Karmeier et al., 2005).
The bright zone: sex-specific specialization for target detection?
The high contrast sensitivity and fast temporal frequency tuning directed
fronto-dorsally in male Eristalis HSN cells coincides with a
sex-specific region of large diameter facet lenses. In most other insects,
including flies, large lenses are associated with fine angular resolution, but
in this case, male interommatidial angles across the eye are similar to those
of the female, being most closely spaced near the equator. Thus male
photoreceptors in the `bright zone' capture more light than photoreceptors
elsewhere, such as in the male blowfly Chrysomyia megacephala
(van Hateren et al., 1989).
The enhanced contrast sensitivity of the portion of the receptive field
directed toward this region indicates that higher retinal illuminance made
available by the optics is utilized by the motion detection system.
The suggestion that light capture is at a premium in the fronto-dorsal
region of male Eristalis eyes leads to the question of sex-specific
behavior. Within 100 ms of seeing a moving object, male Eristalis
compute and initiate an intercept course based on the position and velocity of
the moving target in addition to some `hardwired' biological constants such as
the size and speed of conspecific females
(Collett and Land, 1978). This
interception behavior of Eristalis (and Volucella) is
fundamentally different from the tracking behavior of other flies in that it
requires that the initial flight is directed away from the retinal image of
the target. If the target was indeed a conspecific female and the initial
open-loop interception behavior was successful, it would be followed by
closed-loop tracking similar to that found in other flies
(Land and Collett, 1974).
Although different in computation (computing an intercept course requires
turning away from a target while the reverse is true for tracking), both of
these visually guided behaviors distinguish males from females and presumably
push the visual system to its limit. This sex-specific behavior is
hypothesized to have driven the evolution of sex-specific specializations at
the optical and neural levels.
Although evidence regarding regionally specific properties of motion
detection comes from HSNE and particularly HSN cells in the present study, it
is unknown whether these cells are directly involved with target detection or
tracking behaviors. Large stimuli are required to produce maximal responses in
these HS cells, and the retinal image of another fly at distances greater than
a few millimeters would be substantially smaller than even the small stimuli
used in this study. In male Eristalis, a class of small-target motion
detecting (STMD) neurons in the lobula selectively responds to small objects
(Nordstrom et al., 2006).
Despite being tuned to respond preferentially to very small objects, these
STMDs share a similar fronto-dorsal receptive field (within the `bright zone')
with HSN. One possibility is that a single common set of elementary motion
detectors (EMDs) may serve as upstream input to the dual tasks of target and
wide field motion detection. In this fronto-dorsal region of the visual world,
these computational tasks may place conflicting demands on the temporal tuning
of the elementary motion detectors; Eristalis HS cells are suggested
to stabilize hovering, a task requiring sensitivity to low velocities and
observed in both sexes when feeding and maneuvering, but the fast temporal
tuning in males indicates alternate demands
(O'Carroll et al., 1997). An
increase of contrast sensitivity would be beneficial to both low-velocity
detection and small target detection and may increase performance of the
compromise solution to acceptable levels for both tasks. In other words,
although we believe HS cells are involved in course control and hovering
stabilization in both sexes, our results suggest that in males, EMDs upstream
from the HSN neuron, in particular, may be subjected to conflicting demands
imposed by target tracking behaviors. Fast motion detectors require fast input
signals, which must come from fast photoreceptors. Fast fly photoreceptors are
energetically expensive (Laughlin et al.,
1998) and have lower signal-to-noise ratios
(Laughlin, 1994). The above
arguments suggest that fast, highly contrast-sensitive motion detection in
male Eristalis is an expensive adaptation in terms of optics (large
facets), photoreceptor energy expenditure, and possibly the ability to detect
low speeds useful for stabilizing hovering.
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Acknowledgments |
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