Visual acuity of fly photoreceptors in natural conditions - dependence on UV sensitizing pigment and light-controlling pupil
Department of Neurobiophysics, University of Groningen, Nijenborgh 4, NL 9747 AG Groningen, The Netherlands
e-mail: stavenga{at}phys.rug.nl
Accepted 19 February 2004
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Summary |
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Key words: rhabdomere, waveguide mode, acceptance angle, sky light, diffraction, light adaptation
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Introduction |
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Fly visual pigments utilize a special chromophore, 3-hydroxyretinal
(Vogt and Kirschfeld, 1983).
Connected to the opsin of the R1-R6 photoreceptors, it yields a main
absorption band in the blue-green and a minor absorption band in the
ultraviolet (UV). R1-R6 rhodopsin can bind the alcohol 3-hydroxyretinol, which
then functions as a sensitizing pigment. The sensitizing pigment absorbs UV
light and, when bound to the rhodopsin, efficiently transfers the absorbed
energy to the visual pigment chromophore
(Kirschfeld et al., 1977
). The
absorption spectrum of the sensitizing pigment-rhodopsin complex consequently
exhibits two main bands, with more or less equally high peaks in the UV and
blue-green wavelength region. This characteristic underlies the typical
broad-band, double-peaked sensitivity spectrum of fly R1-R6 photoreceptors
(Stark et al., 1977
;
Kirschfeld et al., 1983
).
The absorption boost in the UV is assumed to substantially improve visual
performance. However, the signal increase may be minor, because the photon
content of natural patterns in the UV is small compared with that of the
dominant longer wavelengths, especially the green region. The question of
whether the sensitizing pigment is really an advantage for fly photoreceptors
is especially relevant considering the presence of the pupil mechanism.
Activated by bright light, the set of pigment granules in a photoreceptor
substantially reduces the light flux in the rhabdomere
(Kirschfeld and Franceschini,
1969; Roebroek and Stavenga,
1990
).
Electrophysiological experiments on fly photoreceptors have shown that
light adaptation changes both the angular and the spectral sensitivity. It
narrows the angular sensitivity for short wavelength light and increases the
spectral sensitivity in the UV with respect to the sensitivity in the
blue-green. Both effects were attributed to the pupil mechanism, and this has
been underscored by quantitative modelling
(Hardie, 1979;
Vogt et al., 1982
;
Smakman et al., 1984
). The
experiments and calculations were performed with monochromatic light. Here, I
investigate the consequences of the pupil mechanism under natural illumination
conditions, where the light source is spectrally broadband.
In the present paper, I investigate the sensitivity gain afforded by the sensitizing pigment vs the sensitivity drop by the light-activated pupil. To assess the maximal advantage of the sensitizing pigment for vision under natural conditions, a light source with a high UV-visible photon ratio is used, i.e. a very blue sky. It thus emerges that the sensitizing pigment noticeably raises the absolute sensitivity of a dark-adapted photoreceptor, but light adaptation of the pupil rapidly overrules this sensitivity increase. Pupil closure narrows the angular sensitivity function, which improves spatial acuity. The effect of the sensitizing pigment on the angular sensitivity is negligible.
It is often assumed that insect eyes are constrained by diffraction, because of the small size of the facet lenses, and that UV rhodopsins, first discovered in insects, are used to push the diffraction limit. However, the spatial resolution of a photoreceptor is determined by the optics of both the dioptrical system and the visual waveguide that contains the visual pigment: the facet lens and rhabdomere in the case of flies. The present analysis shows that, generally, waveguide optics compromises acuity least at wavelengths most limited by diffraction, and diffraction gets the upper hand only in the light-adapted state.
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Materials and methods |
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Visual pigment spectra
The sensitivity spectrum of fly photoreceptors depends on the diet
(Stark et al., 1977). In
vitamin A-deprived flies, the main sensitivity band is in the blue-green, with
a peak at
490 nm, and a minor band exists in the UV. The sensitivity
spectrum resembles the absorption spectrum of a rhodopsin
(Fig. 2, R), as given by
template formulae (Stavenga et al.,
2000
). Feeding a vitamin A-poor fly with retinoids causes a rapid
increase in UV sensitivity. The sensitivity spectrum progressively features a
fine structure, characteristic of the binding of sensitizing pigment to
rhodopsin molecules. In wellfed flies, the UV peak can be distinctly higher
than that in the blue-green, possibly indicating binding of more than one
sensitizing pigment molecule per rhodopsin
(Hamdorf et al., 1992
).
Fig. 2 assumes that the peak
value of the molecular absorbance coefficient of the sensitizing pigment (S)
is identical to that of the rhodopsin (R) and that the spectra can be
algebraically added when one (R+S) or two (R+2S) sensitizing pigment molecules
are bound per rhodopsin.
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Integrated optics of the fly facet lens-rhabdomere system
Light absorption by the visual pigment molecules of a fly photoreceptor can
be calculated with the recently developed model for the fly's facet
lens-rhabdomere optics (Stavenga,
2003a,b
,
2004
). The model is briefly as
follows. Light emitted by a distant point source that enters the facet lens
causes a classical Airy-diffraction pattern in the focal plane, where the tip
of the rhabdomere is located (Fig.
3A). The diameter of the facet lens and the F-number were
taken to be Dl=25 µm and F=2.2, respectively
(the F-number is the ratio of focal distance and lens diameter; see
Stavenga et al., 1990
). Part
of the incident light enters the rhabdomere, where it propagates in specific
waveguide patterns, so-called modes (Fig.
3B). Whether a mode is allowed or not depends on the value of the
,
where Dr is the rhabdomere diameter,
n1 and n2 are the refractive indices
of the rhabdomere interior and surrounding medium, respectively, and
is the light wavelength. The mode with number p=1 is allowed for
V<2.405, mode p=2 is allowed for V<3.832,
mode p=3 for V<3.847, etc.
(Stavenga, 2003a
). The visual
pigment in the rhabdomere absorbs light from the individual modes
proportionally to the absorbance coefficient of the rhabdomere medium and the
fraction of the mode that exists within the rhabdomere boundary. This fraction
increases with V but decreases with increasing p. Fly
rhabdomeres taper and their distal tip diameter is somewhat variable
(Boschek, 1971
). Therefore,
four distal rhabdomere diameters were explored in the calculations:
Dr=1.4, 1.6, 1.8 and 2.0 µm. All rhabdomeres
V-number: V=
D were assumed to taper
parabolically to a proximal value of 1.0 µm, whilst their length was 250
µm. The refractive index values of rhabdomere interior and surrounding
medium were n1=1.363 and n2=1.340,
respectively. The absorbance coefficient of the rhodopsin at its peak
wavelength,
max=490 nm, was set at
490=0.006 µm-1 (Stavenga,
2003b
,
2004
). The total amount of
light absorbed by the visual pigment from the different modes determines the
light sensitivity of the photoreceptor. The light sensitivity to a point
source measured as a function of incident angle yields the angular
sensitivity. This function usually approximates a Gaussian, and its halfwidth
is called the acceptance angle,
(Fig. 3a). The light
sensitivity measured as a function of wavelength yields the spectral
sensitivity. The angular sensitivity slightly depends on wavelength, and the
spectral sensitivity slightly depends on the angle of light incidence
(Stavenga, 2004
).
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The pupil mechanism
Fly R1-R6 photoreceptors contain small pigment granules that together enact
a light-control or pupil function (Fig.
3B). The pigment granules are remotely located from the rhabdomere
in the dark but, upon illumination with bright light, they migrate towards the
rhabdomere. There they absorb light from the boundary wave of the modes
propagating in the rhabdomere, thus reducing the light available for the
visual pigment. Modes with increasing p-number have boundary waves
extending further outside the waveguide boundary, and the pupil therefore
progressively absorbs light from modes with increasing p. The effect
of the pupil mechanism on the light flux in the rhabdomere was modelled with
the same assumptions as used before
(Stavenga, 2004), i.e. the
pupil was fully concentrated in the most distal part of the photoreceptor, in
line with experimental evidence (Roebroek
and Stavenga, 1990
); the pupil granules were homogeneously
distributed outside a cylinder with radius
(Dr/2)+h, where pupil distance (h)=0,
0.2, 0.4, 0.6, 0.8, 1.0 µm and
(see
Fig. 4A, inset); and for the
absorption spectrum of the pigment in the pupil granules the spectrum measured
by Vogt et al. (1982
) was
used. The reduction in light flux resulting in various states of pupil closure
was calculated as before (for details, see
Stavenga, 2004
).
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A spectrally broadband and spatially extended light source, such as the blue sky of Fig. 1, usually illuminates a fly photoreceptor. The amount of light absorbed by the visual pigment in the rhabdomere then follows from the wavelength and space integral of the function that describes the light absorption from a monochromatic point source as a function of angle of incidence. The first step to determine the light sensitivity of a fly photoreceptor for sky light is therefore the derivation of the angular and spectral sensitivities.
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Results |
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When Dr=1.4 µm
(Fig. 4A), only one waveguide
mode is allowed for >456 nm, the cut-off wavelength of the second
mode. For wavelengths above 456 nm, pupil absorption diminishes the absolute
sensitivity, but this does not affect the acceptance angle because only one
mode exists. The situation changes for
<456 nm, because the two
modes that can then exist have different boundary waves. With increasing pupil
closure (i.e. with decreasing h; see
Fig. 4A, inset), the pupil
absorbs progressively more strongly from the second mode than from the first
mode. This means that the second mode vanishes and the first mode increasingly
determines the value of
. In the process of pupil closure,
therefore first decreases for blue light, near
450 nm.
Later on,
also diminishes in the UV
(Fig. 4A).
When Dr=2.0 µm
(Fig. 4B), the cut-off
wavelengths of the second, third, fourth and fifth modes are 651, 409, 407 and
305 nm, respectively. Upon pupil closure, decreases initially most
prominently at wavelengths between 400 and 650 nm, again because of the
dominant contribution of the second mode to the angular sensitivity. With
progressing pupil closure,
finally also falls in the UV
(Fig. 4B).
The following from geometric optics for a rhabdomere with
distal diameter Dr is given by
r=Dr/f=DrDl/F,
where f is the facet lens' focal distance. With
Dl=25 µm and F=2.2, the diameters
Dr=1.4 and 2.0 µm yield
r=1.46° and 2.08°, respectively
(Fig. 4). The
values calculated with the wave-optics model for dark-adapted photoreceptors
depend on wavelength but fluctuate around the geometric value.
0(
), the acceptance angle in the maximally
light-adapted state (h=0 µm), runs approximately parallel to
l(
)=
/Dl for both
diameter values (Fig. 4).
l is the halfwidth of an Airy-diffraction curve, which
would be the
of a point detector, i.e. a photoreceptor with a
rhabdomere of negligible diameter (Snyder,
1979
). A non-negligible rhabdomere diameter broadens the
acceptance angle by a factor,
0/
l,
that is similar for both Dr=1.4 and 2.0 µm: 1.19 and
1.20; average over the wavelength range 450-600 nm (see
van Hateren, 1984
;
Stavenga, 2004
).
The acceptance angles in the UV wavelength range slightly increase with an
increase in the amount of sensitizing pigment. The effect of the sensitizing
pigment on diminishes when the pupil closes
(Fig. 4).
Spectral sensitivity of fly photoreceptors R1-R6
The sensitivity spectrum of a photoreceptor is similar to the absorption
spectrum of the visual pigment when spectrally selective filtering pigments
are absent. Minor spectral modifications result from self-screening, the
effect of diminishing contribution to absorption by visual pigment located
increasingly proximally in the rhabdomere. More important modulations are
caused by waveguide effects, because the excitation of waveguide modes
strongly depends on both the angle of incidence and wavelength of the light
source (Fig. 4).
Integration of the light absorption over the angle of incidence at all
wavelengths yields the absorption spectrum with an extended light source.
Fig. 5 presents the absorption
spectra of a photoreceptor illuminated by a spatially uniform, monochromatic
light source, the wavelength of which varied from 300 to 610 nm, with a
radiance of 1 W sr-1 µm-2. The rhabdomere had a
distal diameter Dr=2.0 µm, tapering to 1.0 µm, and
length 250 µm and contained visual pigment with a peak absorbance
coefficient of the rhodopsin of 490=0.006
µm-1. One or two sensitizing pigment molecules per rhodopsin
were added (see Fig. 2 and
Materials and methods).
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Fig. 5 shows that the
absorption spectra resulting for fly rhodopsin without sensitizing pigment
(Fig. 5A), with one
(Fig. 5B) and with two
(Fig. 5C) sensitizing pigment
molecules per rhodopsin resemble the absorbance spectra of the visual pigment
complexes (Fig. 2) when the
pupil pigment granules are remote from the rhabdomere (h=).
The absorption band in the UV of Fig.
5C has a somewhat depressed relative height compared with the UV
band of the visual pigment's molecular absorbance spectrum
(Fig. 2), due to
self-screening. Pupil closure results in reduced light absorption by the
visual pigment at all wavelengths. This occurs due to reduction of the light
power propagating in the second mode, predominantly in the blue-green
wavelength range. When pupil activation is moderate, the absorbance band in
the blue-green shifts towards the blue. The pupil increasingly filters the
higher order modes in the UV, but the contribution of these modes to the light
power absorbed by the visual pigment is relatively minor. The outcome is thus
that the closing pupil predominantly suppresses the blue-green band of the
visual pigment's absorbance spectrum and much less affects the UV peak. The
same calculations performed for rhabdomeres with smaller diameters give very
similar results. Light-adapted photoreceptors with no sensitizing pigment
obtain a more or less flat absorption spectrum, but with sensitizing pigment,
pupil closure produces spectra with a clear UV peak.
Intracellular recordings of fly photoreceptors in different light-adapted
states showed a shifted blue-green peak and a change in relative height of the
blue-green vs UV band, resembling the spectra of
Fig. 5
(Hardie, 1979;
Vogt et al., 1982
). The
hypothesis that a short-wavelength-filtering pupil caused these effects is now
substantiated in reasonably quantitative detail (see also
Stavenga, 2004
).
Absolute light sensitivity of a fly photoreceptor for sky light
The pupil-induced prominent UV band
(Fig. 5), i.e. an increased UV
sensitivity relative to the sensitivity in the blue-green, might suggest that
the function of the sensitizing pigment is to enhance light absorption from
natural, UV-rich patterns. This hypothesis can be tested by calculating the
light absorption from the sky, because this natural light source has a
prominent band in the UV. The amount of absorbed light is obtained by
integration of the sky radiance (Fig.
1) multiplied by the (absolute) sensitivity for an extended light
source (Fig. 5) over the
wavelength range of the photoreceptor's spectral sensitivity.
Fig. 6 presents the total
photon absorption as a function of rhabdomere diameter (all with the facet
lens of diameter Dl=25 µm and F=2.2) for a
dark-adapted photoreceptor. One sensitizing pigment molecule per rhodopsin
increases the photoreceptor absorption by 14-18% with respect to pure
rhodopsin, whilst two sensitizing pigment molecules per rhodopsin increase the
absorption by 20-27%, depending on the distal rhabdomere diameter
(Fig. 6). The wavelength
integrals of the visual pigment spectra of
Fig. 2 reveal that one or two
sensitizing pigment molecules per rhodopsin increase the molecular absorbance
coefficient by 38% or 76%, respectively. These numbers are much larger than
those for the integral photon absorptions. This is due firstly to
self-screening and secondly to the modest number of UV vs blue-green
photons, even in the UV-rich sky. Of course, the light-capture increase by the
sensitizing pigment vanishes for light sources that emit few UV photons, such
as natural light reflected from green plants.
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Angular sensitivity changes due to a closing pupil
Fig. 6 shows that the
sensitizing pigment enhances light sensitivity under light conditions where
the pupil is not activated, but pupil closure rapidly erases the gain in light
absorption. Since the pupil also causes a decrease in , we can
speculate that the sensitizing pigment has a special beneficial effect on the
improved spatial acuity in natural conditions. This possibility can be
investigated by calculating the angular sensitivity for sky light.
Fig. 7 presents the light
absorption in photons per second by a 2.0 µm rhabdomere, containing a
visual pigment with one sensitizing pigment molecule per rhodopsin, from a
patch of sky (Fig. 1) measuring
1 square degree (3.05x10-4 sr) seen at various angles. Pupil
closure reduces the absolute absorption
(Fig. 7A), and normalization
shows that it narrows the angular sensitivity curve
(Fig. 7B). The shapes of the
angular sensitivity curves are well approximated by Gaussians.
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Pupil absorbance and photoreceptor acceptance angle
Fig. 8 presents the
values resulting from Gaussian fits to the angular sensitivity
curves for the four rhabdomere diameters
(Fig. 6), combined with the
three visual pigment complexes and the seven states of the pupil
(Fig. 5), plotted as a function
of pupil absorbance. The pupil absorbance was calculated as follows (see
Stavenga, 2004
). First, the
total photon absorption by the visual pigment,
Pabs(h), from an extended, uniform sky
(Fig. 1) was calculated for the
various states of the pupil, given by pupil distance h. Of course,
Pabs(
), the photon absorption in the dark-adapted
state, is maximal. The absorption reduces to
Pabs(h) when the pupil closes or, equivalently,
its transmittance decreases from its maximal value T(
)=1 to
T(h)=Pabs(h)/Pabs(
).
The pupil absorbance then follows from the definition:
A(h)=-log10T(h);
A(
)=0 corresponds to the dark-adapted state
(Fig. 8). The
(A) curves for the three different visual pigment cases
(R, R+S, R+2S) at a given Dr are very similar at pupil
absorbances below 0.7, which suggests that the sensitizing pigment then has
virtually no effect on the spatial acuity. Extreme pupil closure and
sensitizing pigment content lowers the acceptance angle by a few percent.
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Fig. 8 shows that an
increase in pupil absorbance is accompanied by a decrease in for
all rhabdomere values. The decrease stabilizes for pupil absorbances above
1.5. The question can now be asked: are these high absorbance values
actually attained in fly photoreceptors under natural conditions? An answer
can be obtained from electrophysiological and optical experiments.
Illumination of a photoreceptor with a step of light depolarizes the cell
membrane, which rapidly reaches a peak and then levels off to a plateau
(Hardie, 1985).
Fig. 9A reproduces peak and
plateau potential values derived from intracellular recordings of a
Musca photoreceptor (Vogt et al.,
1982
). The data are plotted together with the ratio of the
sensitivity for test flashes of 500 and 359 nm light,
S500/S359, as a function of the log
intensity of the applied orange adapting light. The measured sensitivity ratio
was
1 in the dark-adapted state, approximating the case of
Fig. 5B, where the visual
pigment has one sensitizing pigment molecule per rhodopsin.
Fig. 9A shows that the
sensitivity ratio gradually dropped when the intensity of the adapting light
increased by several log units. The adapting light apparently activated the
pupil, which caused a decrease in the ratio
S500/S359, settling at
0.35 in
the fully light-adapted state (Fig.
9A).
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Discussion |
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The absorption spectrum of the visual pigment of fly photoreceptors is
modelled with a vitamin A1-based rhodopsin template. The rhodopsin of flies is
based on vitamin A3 (Kirschfeld,
1986), but its absorption spectrum probably follows the same rules
as that of vitamin A1 rhodopsins (Stavenga
et al., 1993
). The simple algebraic addition of a sensitizing
pigment is most likely an oversimplification, but exact absorption spectra of
visual pigment plus sensitizing pigment are not known, and the modelling
results are probably insensitive to it.
Concerning the pupil, it is assumed to exert its light-controlling action
at the extreme distal end of the photoreceptor, as if it in fact functions as
a light filter in front of the visual pigment. The pupil pigment granules are
distributed in the photoreceptor soma
(Boschek, 1971), but
experimental data strongly argue in favour of a distal pupil
(Roebroek and Stavenga, 1990
).
What counts for a photoreceptor is not the number of absorbed photons
converting rhodopsin molecules but the change in membrane potential created
and the signal transmitted by the photoreceptor synapse. Under bright light
conditions, the distal end of the photoreceptor is strongly light adapted and
consequently more desensitized than the proximal elements of the
photoreceptor's phototransduction machinery. The part of the photoreceptor
proximal to the pupil will then determine the photoreceptor's performance. The
rhabdomeres of R1-R6 photoreceptors taper, so that an extreme gradient in
longitudinal adaptation causes a relatively stronger contribution of the
proximal part of the photoreceptor's phototransduction machinery. As we do not
know whether or not the molecular composition of the microvilli varies along
the photoreceptor length, adaptation effects are difficult to assess.
The absorption spectrum of the pupil granules used in the modelling was
measured in squash preparations (Vogt et
al., 1982), making the precise shape of the spectrum slightly
uncertain, but this will have no major effects on the calculated results. The
density of the granules is another uncertainty, but the concentration was
chosen so that measured absorbances could be accommodated by the model (see
Stavenga, 2004
). Furthermore,
the distribution of the pupillary granules was assumed to be homogeneous
outside a cylinder with radius (Dr/2)+h that
surrounds the rhabdomere. The soma of a fly photoreceptor in fact occupies
only a small sector, and thus the pupil can only affect a restricted part of
the boundary wave. Presumably, however, the absorbances of pupils fully and
partially surrounding the rhabdomere are proportional.
Only waveguide modes propagating bound to the rhabdomere have been taken
into account. Unbound modes travel along the rhabdomere for a limited distance
and lose their light power by radiation. The light absorption from unbound
modes broadens the angular sensitivity curves, thus reducing the wavelength
dependence of , i.e. the spectra of
Fig. 4 become flatter,
especially those below or near pupil threshold. Also, the unbound modes will
have a smoothing effect on the spectral sensitivity near the cut-off
wavelengths.
Notwithstanding all assumptions and approximations, the modelling provides
considerable insight into the consequences of the sensitizing pigment and the
actions of the pupil. The model calculations show that the UV-absorbing
sensitizing pigment of fly R1-R6 photoreceptors boosts the sensitivity for
UV-rich skylight by 14-27%, depending on the size of the rhabdomere and the
presence of one or two sensitizing pigment molecules per rhodopsin
(Fig. 6). The sensitivity
increase will be less for light sources with a less prominent UV content than
the sky. The conclusion thus is that the sensitizing pigment has a sizeable
benefit only when the light source contains a substantial amount of UV and
that its value will become rather unimpressive when UV content is minor. The
employment of sensitizing pigment nevertheless is probably well worth the
costs. As pointed out by Kirschfeld
(1992), the mass of a
sensitizing pigment molecule is less than 2% of that of a rhodopsin molecule,
meaning that a sensitivity improvement of more than a few percent will already
pay off.
Installing the sensitizing pigment purely for improving light sensitivity
can only be of limited value, i.e. at light intensities below or near pupil
threshold. This presumably holds for strongly shaded areas, but direct
measurements will be necessary to substantiate this point. The few percent
gain in sensitivity is rapidly lost when the pupil is activated, which occurs
at intensities depolarizing the receptor by 10
mV(Fig. 9). These intensities
are easily reached in daylight (Anderson
and Laughlin, 2000
), in the sunlit areas where flies are often
active, and most probably when males are chasing high-contrast females against
the blue sky. Such bright lights substantially reduce R1-R6
.
Pupil closure causes narrowing of the angular sensitivity function, by an
extreme factor of 0.6, somewhat depending on rhabdomere diameter and
visual pigment composition (Fig.
8). The sampling of spatial frequencies thus changes appreciably,
although the sampling basis, the interommatidial angle, remains constant. The
narrowing of the angular sensitivity by bright light possibly counters the
motion blurring that smears visual objects during high-speed aerial acrobatics
in both pursuing and pursued flies (Burton
and Laughlin, 2003
), activities typically enjoyed in warm,
bright-light conditions.
The interplay of increased sensitivity by the sensitizing pigment, being
14-27%, and the reduced sensitivity by the pupil, necessary for improving
spatial acuity, has special relevance for the so-called lovespot in the
dorso-frontal area of the eyes of male flies. The central R7 and R8
photoreceptors, redesigned to supplement the sensitivity of the achromatic
contrast system mediated by the R1-R6 photoreceptors
(Hardie, 1985), yield a
sensitivity increase of perhaps 10%. This, of course, is to the detriment of
the chromatic channel normally mediated by the pair of central photoreceptors.
We should note here that the pupil of R7 is probably less effective than that
in R1-R6, due to the smaller soma, but the rhabdomere diameter is also
smaller, yielding a smaller acceptance angle. In this way, loss in absolute
sensitivity, unavoidable for achieving a small acceptance angle, is recovered
by recruiting R7 to join the R1-R6 system. Large facet lenses and adjustments
in the phototransduction machinery are additional factors for realizing
enhanced contrast detection by photoreceptors in the male lovespot
(Burton and Laughlin,
2003
).
It is important to note here that the facet lens and rhabdomere waveguide
together determine the total light absorption of a photoreceptor. The facet
lens diameter is enlarged in areas of fly eyes with high acuity, but the
F-number of the facet lenses remains virtually constant across the
eye (Stavenga et al., 1990).
The F-number is the only parameter of the facet lens that determines
the photoreceptor absorption from an extended light source, given a certain
size of the rhabdomere (Stavenga,
2003a
). If the tip of the rhabdomere coincides with the focal
plane of the facet lens, the size of the visual field is inversely
proportional to the focal distance and, with F constant, also to the
facet lens diameter. The larger facets of the lovespot hence cause a smaller
photoreceptor receptive field. A dark object, perhaps a distant female, more
readily creates a visible contrast in a small spatial field than in a wider
field, and in this way males have a visual discrimination advantage over
females (Burton and Laughlin,
2003
). Of course, larger facets take up more space, which is lost
for eye parts elsewhere. Consequently, the high acuity in the lovespot comes
at the cost of lower acuity in other eye areas. But, for hunters, it is
important to have exquisite eye sight in forward-looking directions, whereas
chased animals must distribute their visual attention more uniformly.
Pupil closure reduces the light flux in the rhabdomere and thus expands the
intensity working range of the photoreceptor
(Howard et al., 1987). Using
data from the housefly Musca, an extreme pupil absorbance of 0.8 was
deduced (Fig. 9B). Much higher
absorbance values, up to
2 in saturation, were determined in
electrophysiological and optical measurements on the blowfly
Calliphora (Howard et al.,
1987
; Roebroek and Stavenga,
1990
). A high pupil absorbance removes, or at least reduces, the
difference in sensitivity between the dark-adapted R1-R6 and R7, R8
photoreceptors, estimated to be
1.3 log units
(Anderson and Laughlin, 2000
).
The different pupil absorbances of housefly and blowfly may indicate that the
effectiveness of the pupil mechanism depends on species, which also follows
from direct optical measurements on hoverflies, where the pupil transmittance
dropped locally by no more than a factor of 2, i.e. a maximal absorbance of no
more than 0.3 could be measured (Stavenga,
1979
). The connected change in angular sensitivity will be minor,
suggesting a lifestyle with less variable light conditions, but this point
needs further study.
The pupil is well able to achieve a high acuity by cutting out the higher
order waveguide modes, but the case of the fly R1-R6 photoreceptors shows that
acuity is not pushed to the lowest values achievable. Because diffraction
increases with wavelength and broadband natural patterns always have an
excessive number of long-wavelength photons, a UV rhodopsin is necessary to
realize the smallest acceptance angle. The of fully light-adapted
R1-R6 fly photoreceptors is slightly larger than would be possible with a pure
UV rhodopsin, even when the blue-green peak of the rhodopsin is suppressed in
favour of the sensitizing pigment (Figs
4,
8). We have to realize,
however, that acuity is the result of both facet lens and waveguide optics.
Acuity increases with an increasing facet lens diameter, a decreasing
rhabdomere diameter and a more active pupil that removes higher order modes.
Where the optimum is depends on many factors that are determined by the
habitat and the animal's behavior, e.g. the intensity range where it is
active, its flight velocities and sex.
In the dark-adapted state, is only slightly wavelength
dependent and approximates the constant value following from geometrical
optics,
r (Fig.
4). The closing pupil initially reduces
in the middle
wavelength range, where the pupil absorbs light propagated in the second mode
(Fig. 4). The pupil reduces
in the UV only when the light adaptation process approaches
saturation.
then approximates values dictated by diffraction,
r=
/Dl.
Diffraction is often assumed to be the crucial factor that limits imaging
by the small facet lenses of insect eyes, and it is hence thought that insects
have extended their sensitivity into the UV by developing UV-transparent
lenses and UV-absorbing rhodopsins, so that optimal acuity is achieved. This
notion, going back to Mallock
(1894), neglects the important
contribution to visual acuity by the visual waveguides, the rhabdomeres of
flies and the fused rhabdoms of bees and butterflies.
Fig. 4 shows that diffraction
is dominant when the rhabdomere is so slender that only one mode is allowed
or, in a wider rhabdomere, when the pupil has extinguished all higher order
modes. Several waveguide modes are excited in a fat rhabdomere and/or at short
wavelengths. The second and third mode are excited by off-axis illumination,
which results in broadening of the angular sensitivity curve
(Fig. 7; Stavenga, 2004
). This
broadening increases with visual pigment absorption
(Fig. 4) and can almost fully
compensate the limitations set by diffraction. This conclusion holds in
principle for all eyes that employ lens-waveguide systems. The widespread
opinion that insect eyes, with their small facet lenses, are more constrained
by diffraction than other eyes therefore needs revision. Vision research of
recent decades has sufficiently demonstrated that UV vision is by no means the
prerogative of insects or invertebrates. Furthermore, the larger eyes of
vertebrates also suffer from diffraction, but are perhaps more constrained by
optical errors, such as spherical and chromatic aberration.
The present model calculations indicate that the sensitizing pigment of fly
eyes primarily functions for enhancing light sensitivity at low light levels
and that the pupil functions to improve visual performance at high light
levels by expanding the photoreceptor working range and improving spatial
acuity. Its third function, namely to shift the photochemical cycle of the
visual pigment, thus favouring rhodopsin photoreconversion
(Stavenga, 2002), requires a
separate study.
List of symbols
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References |
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