Fly colour vision

I’Mon Rcs. Vol. 12, pp. 13894396.

Pcrgamon Press 1972.

F’rinted in Gmat Britain.

FLY COLOUR VISION ALLAN W. SNYDER’and WILLIAMH. MILLARD ‘Department of Applied Mathematics, Institute of Advanced Studies, Australian Nationai University, Canberra, Australia and 2Department of Opthaimolo~ and Visual Science, Yale University School of Medicine, New Haven, Connecticut 06510, U.S.A. (Received 22 November 1971)

INTRODUCTION THE PRINCIPALorgans of sight in flies (Arthropods of the order Diptera) are the compound eyes. A compound eye covers almost half the head and is composed of several thousand closely packed cornea1 facets about 30 pm in dia. Each facet is a lens whose focal plane

lies near the distal ends of the photoreceptors (SEITZ, 1968 and KUIPER, 1966). A facet and its underlying optical and receptor structures is termed an ommati~um. Each ommati~um has eight receptor cells and hence eight rhabdomeres, which contain the visual pigment and are therefore the actual light receiving structures. As seen in cross-section, the rhabdomeres form six rods arranged in a trapezoidal pattern with a seventh near the center (Fig. 1). The more distal part of the central rhabdomere is part of receptor cell seven while the more proximal part belongs to receptor cell eight (TRUJILLO-CENOZ and MELAMED,1966). In flies the rhabdomeres are long cylinders (their length is more than 200 pm) separated by about O-3 pm within the ommatidium (LANGERand THORELL,1966). SEITZ (1968) has investigated the eye of the fly Calliphora using both physiological and physical methods. Of particular interest from his study are the values of the refractive index of the rhabdomere and its surround given as: I.349 for the rhabdomere and I.336 for the region between the rhabdomeres. We note from Fig. 1 that the rhabdomeres are not surrounded by a homogeneous medium, but have a part of the associated retinular cell on one side and a clear fluid-filled space on the other. Recent work by SEITZ(1970) on the Cdliphora eye provides some interesting information on the effects of light adaptation. In the light adapted eye the index of refraction of the retinular cell medium for rhabdomeres l-8 was determined to be I.341 ; however, for the dark-adapted eye a layer of vesicles 1 pm thick borders rhabdomeres l-6 decreasing the index of refraction of the retinular ceil medium to a value of 1.3385. The approximate radius of rhabdomeres l-6 is I pm. The centrally located rhabdomeres numbers 7 and 8 are one-half the radius of their neighbours, i.e. 0.5 pm. SEITZ(1968) states that he could not show any definite difference between the refractive index of rhabdomere number 7 and its surrounding neighbours. The photopigments of the rhabdomeres are localized in tightly packed tubules known as microvilli shown as the parallel dark lines within each rhabdomere of Fig. I. The dipoles of the absorbing pigment molecules are aligned along the microviliar membranes so that the total absorption of light is polarization sensitive. This polarization sensitivity is characterized by the dichroic ratio and has been measured for the Cdiphora eye. It is found that the intensity of light absorbed when the electromagnetic E vector is parallel to the microvilli 1389

ALLAN W. SNYDER AND WILLUM

1390

H. MILLER

of Fig. 1 is twice that when the E vector is perpendicular to the microvilli but still in the plane of Fig. 1 (KIRSCHFELD,1969). LANGERand THORELL(1968) measured the absorption spectra from individual rhabdomeres of the Cdliphora compound eye, using a dual beam microspectrophotometer. The centrally located rhabdomere (see Fig. 1) was found to have an absorption spectrum with a maximum at approximately 470 nm, while the surrounding rhabdomeres were found to have absorption maxima at 515 nm, as shown in Fig. 2.

0 300

400

500 Wavelength,

600

nm

FIG. 2. Two typical extinction spectra from individual rhabdomeres of the Cairiphora onunatidium. Msximal extinction at 515 nm is always found in rhabdorrpercsmmlbers i-6

and at 470 nm in rhabodmeres number 7 (the numbering convention of sense c&IscontaLning the rhabdomeres is indicated in Fig. 1). From LANDER (1%7j.

Based on this result, it has been suggested that the visual pigment within the central rhabdomere is different from that within the surrounding six rhabdomeres. Although this is certainly a possible interpretation, it is not necessarily correct. As we shall show, the absorption spectmm of a photoreceptor depends not only on the absorption property of the photopigment, but also on the electromagnetic properties of the receptors due to its dimensions and index of refraction. Light propagates along receptors in the form of modes as observed by ENOCH(1961) and VARELAand WIITANEN(1970). Qualitatively, if two photoreceptors, of dil%Mnt sixes, contained identical pigments, the smaller photoreceptor will absorb less for longer wavelengths. In this paper we determine theoretically the absorption spectrum of the larger receptor compared to the smaller using an electromagnetic analysis. We show that the difference in the measured absorption spectmm between the larger and smaller rhabdomeres of Culliphora may be due to the physical differences of the photoreceptors rather than to two different photopigments. ELECTROMAGNETIC PROPERTIES OF DIELECTRIC CYLINDERS Although the electromagnetic properties of a cylindrical dielectric cylinder or dielectric waveguide are known, e.g. SN~TZER(1971), we review here some solid concepts. Light propagation along a dielectric cylinder of higher index of refraction than its surround is a complicated phenomenon that can only crudely be thought of as total internal reflection. A complete solution can be obtained by solving Maxwell’s aquartions subject to the appropriate boundary conditions of the cylinder. It is found that the propagation

I.

1. Cross section of the 7 rhabdomeres and attached sense cells of one ommatidium of .\4u,wrr compound eye. The central rhabdomere is called number 7 while the surrounding rhabdomeres are labelled l-6.

.

_. ,.

FOG. 5. Cross section of the rhabdomeres and attached sense cells of one ommatidium of n long legged fly. Condylostylus.

Fly Colour Vision

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characteristics of a cylinder are entirely defined by the parameter dimensionless frequency (SNYDER,1969a) V = 2~ f d(n12 - n22) 0

(1)

where X is the wavelength of light in free space, p is the cylinder radius, n, and n2 are the indices of refraction of the cylinder and external medium. Specification of V defines the light guiding characteristics of the structure through the electromagnetic fields. The mathematical description of these fields is in general complicated, requiring numerical computation to extract specific data; however, SNYDER (1969a) has shown that, because the index of refraction between the photoreceptor and its surround is small, numerous approximations can be employed to derive a simplified field description useful for the analysis of photoreceptors. In general, light is not propagated in the cylinder as a beam of uniform cross section but in distinctly non-uniform patterns known as modes. As V defined by (1) increases from V = 0 to V $ 1, the number of mode possibilities increase from one to many. For V < 2.405 only one mode (which we call the HE,, mode) can exist. For fibers with a large V there are often so many modes or light patterns that they superimpose to form a uniform light intensity in cross section. Modes possess an interesting light-guiding characteristic. Depending on the wavelength, the total light intensity of a particular mode on a given receptor can be confined either inside or mostly outside the cylindrical boundary. This property concerns us because the light energy within the receptor is that which is available to the photopigment. We define 7 to be the ratio of the total modal light intensity within the receptor divided by the sum of modal light intensity both inside and outside the receptor. Mathematically 7 is expressed as (SNYDER,1969a) 7 =C

Ie(V)12dA s

(2)

A

where e(V) is the transverse electromagnetic modal field as presented by SNYDER(1969a), C is a constant independent of wavelength, A is the cross sectional receptor area and V is defined by (1). Specification of p, n, and n2 in (1) determines a particular $I) in (2). If we ignore the fact that the rhabdomeres have a nonhomogeneous surround and accept SEITZ’S (1968) data for Calliphora to be n, = 1.349, n, = 1.336, p = 1 pm for the 6 large and O-5pm for the smaller central receptor, then 9(h) is given by Fig. 3. We observe that the 6 larger receptors have a flatter frequency response than the central smaller one. Near 660 nm very little light energy is confined within the smaller receptor. Clearly the frequency response of the smaller receptor can be affected by its 7(h) characteristics whereas the larger receptor is comparatively unaffected. We have not discussed the receptor illumination; however, it is the characteristics of the illumination that determine the degree to which the mode is excited. Consider a receptor, like the fly’s central rhabdomere, in which only one mode can propagate. As shown by SNYDER(1966) and (1969b), a portion of the incident energy excites the mode while the remaining portion is radiated or scattered, i.e. not guided along the cylinder. An effective illumination for maximum mode excitation is that with a spatial distribution of light intensity matching that of the mode. As A changes, the illumination must change in order

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1392

to be maximally efkctive. For example, at h = 600 nm the mode has a small q(h) as seen from Fig. 3, so the illumination must extend far beyond the cylinder boundaries to excite significant modal energy. KUIPER(1966) has shown that the fly’s dioptric apparatus partly compensates for the necessary change of illumination, since the size of the Airy disc is proportional to h. Because of the fly photoreceptors’ physical parameters and the symmetrical illumination produced by its dioptric apparatus, only the HE,, mode is efficiently excited. Using KUIPER’S(1966) data on image formation, and SNYDER’S(1969b) analysis for mode excitation, we find that the total modal light intensity varies with wavelength approximately as 7)(X)given by Fig. 3.

60

450 Wavelength,

nm

FIG. 3. Fractionof modal light within the rhabdomcrcsof the fly CaNiplrora as given by equation(2) basedon the data of SEITZ(1968).

In summary, light propagates along a cylinder of the dimensions of a fly photoreceptor in the form of an electromagnetic mode. The amount of modal light energy within the fly’s nt is located, is highly sensitive to changes in central rhabdomere, where the wavelength in comparison to its six larger neighbours. LIGHT

ABSORBING

PROPERTIES

OF RHABDOMERES

The visual pigments may be characterized by their light absorbing properties, however, since the concentration of photopigment in the retinula cell of the fly eye is extremely small, it has been difkult to extract, isolate and directly measure an absorption spectrum. Without this information it may not be possible to interpret experiments such as microspectrophotometry and electrophysioiogy which measure the total rhabdomere frequency response, electromagnetic effects included. Before discussing experimental measurements, we consider the absorption properties of a receptor, based on a theoretical analysis. We model the photoreceptor by a cylinder @Ied with an absorbing material (the photopigment) and derive an expression for the light absorbed. This absorption is presumed to be proportional to visual sensation. Since the absorption of light in the photoreceptor over a distance comparable to a waveleng$h of light in the visual spectrum is small, the perturbation theory of SNYJXR (1969~) applies, leading to an expression for the HEi modal light

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intensity absorbed. We find that the fraction dI/I of light absorbed in a receptor Iength dl depends on the pigment concentration c, the extinction coefficient u(A) which is proportional to the pigment absorption spectrum and the fraction of light within the receptor 7(h). Thus dI - = c a(A) ?(A) dl I

By light intensity, I, we mean the total Iight intensity as measured by a photocell which in waveguide terminology is known as power. The difference between (3) and the equivalent expression given by DARTNALL(1962) for an extracted pigment in solution is due to the presence of 7(h). However, this modification is anticipated based on the fact that absorption is proportional to the amount of light within the receptor. From Fig. 3 we see that n(X) has much more effect on the smaller central fly receptor than on the 6 surrounding larger receptors, Therefore, the absorption spectrum of the smaller rhabdomere can be significantly different from its pigment’s extinction spectrum, a(X). To obtain the total intensity absorbed l&h) by a receptor of length 1, equation (3) is integrated. Recalling from our discussion of rhabdomere illumination that the modal light intensity excited is approximately that given by 77(h)it is shown that

LJS(8 = I* (4

7(q

(1

_

e-c’aahw]

21 Cla(A)7j2( A)

(W

where 1,(X)is the light incident on the ommatidium. Approximation (4b) holds when only a small portion of the modal light energy is absorbed by the pigment. Without a knowledge of the pigment absorption spectrum given by u(X) it is not possible to calculate J&; therefore, we next discuss rhabdome~ absorption me~urements. MEASUREMENT OF RHABDOMERE ABSORPTION Microspectrophotometry measures the light absorbed in a ceil as a function of frequency by passing a beam of light through the receptor and measu~ng the light transmitted. Due to the presence of non-bleaching pigment and various diffraction effects, the absorption spectrum is distorted. Because the receptor is bleached under bright light, a second measurement is taken and subtracted from this first to obtain a “difference spectrum”. The difference spectrum often used in experiments is AE(il) defined by KIRXHPEI.D (1969) to be

where I, is the light transmitted through the rhabdomere. I, has the approximate form I,(A) crl q(h) e-cla(A)~(A)+ S(X)

(6) S is the scattered light leaving the ommatidium which is not associated with the mode and has not passed through the photoreceptor. c, I, a and 7 are defined relative to equation (3). IsB is the light transmitted through the rhabdomere after it has been bleached with bright light rendering c = 0 so that I,(h) ‘v 70) + 82) VlSlON 12/8-F

(7)

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ALLANW. SNYDERAND WILLIAM H. MILLER

Since LANGER'S (1967) measurements show that AE is small, from (5), (6) and (7)

Measurements (LANGERand THORELL, 1966) of AE by microspectrophotometry show the effect of scattered light S(h) to be large so that AE(/\) is proportional to cla(X)q2(X)/S(h) and is related to the theoretical expression

given by equation (4b). LANGERand THORELL(1966) performed ~cros~tromet~ on single r~~omeres of the Calliphoru compound eye. The rhabdomeres were kept in situ so that they received light naturally from the flys’ dioptric apparatus. Two typical absorption spectra curves from LANGER’S(1967) experiments are shown in Fig. 2. The curve with the 515 nm peak is associated with rhabdomeres number I-6 while the 470 peak is associated with the central smaller rhabdomere number 7. Studies of excitation in individual visual cells by the use of intracellular electrodes appear to agree with the absorption curves at the 515 maximum (LANGER, $967); however, the action spectrum has a larger peak at 360 nm. B~RKHARKBT (1962) has shown by inserting electrodes into the lower (ventral) half of Calliphora that three types of receptor responses can be measured, with peak responses at 470,486 and 521 nm based on mean values. A partial explanation of the difference between mi~r~~trophotomet~ and electrophysioiogy measurements at low wav&ngths may be provided by an investigation of the light-scattering effects in microspectrophotometric experiments. SHvrzR (1969b) has shown that small particulate matter near the rhabdomeres scatters light in proportion to (I/h)2 so that at lower wave~en~~s AI?(;X)of apron (8) is depressed due to the larger S(A). COMPARISON OF EXPERIMENTAL RESULTS WITH THEORY We now consider the effect of the rhabdomere’s size on the interpretation of LANGER’S (1967) results. To do this we use expression (4b) to eakulate a theoretical absorption curve for the rhabdomeres. We have already stated that electromagnetic effects are smah for the larger rhabdomeres numbers l-6, i.e. q(h) z 1. Therefore, we can assume that LANG&S (1967) spectrophotometric results are a direct measurement of the pigment absorption, u(A), for rhabdomeres l-6. Since q(A) has a sign&ant influence for the smaller rhabdomere number 7 we cannot directly relate LANCER’S (1967) findings to a(h); however, for the purpose of comparison let us suppose that alI the rhabdomeres have a pigment absorption, a(X), like that measured by LANGER(1967)for the large receptors. Multiplying $(A} by LANGER’S (1967) 515 curve provides a theoretical absorption curve for the small central rhabdom resulting in a response peak at approximately 478 nm as illustrated in Fig. 4. ‘Due to the large absorption at 360 nm, the theoretical curve is in better agreement with the results of intracellular recording than that of ~~ros~trophoto~t~ (dashed curve). Our theoretical answer based on the assumption that ah receptors have the identical photopi~ent, is in close agreement with the measured response curves of LANG~R(1967). We have therefore shown that the size of the receptor can influence the absorption characteristics of the rhabdomeres and must be considered in interpreting micros~trophotu~t~~ and electrophysiologic measurements.

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Fly Colour Vision

47t nm 515 nm

I.OI e da” 0.5

-

0

I 300

500

400

Wavelength,

6

nm

FIG. 4. Solid lines represent the theoretical absorption for the large (515 nm curve) and small (478 nm curve) rhabdomeres of the fly Culliphoru as calculated from equation (4b) assuming a photopigment with a peak absorption at 515 nm. The dashed line is LANGER’S (1967)470 nm microspectrophotometry curve for the small rhabdomere.

The diameter of the central rhabdomere need not be smaller than its six neighbours to have a different absorption spectrum. As pointed out in the explanation of equation (l), the electromagnetic properties of a rhabdomere are determined by both its diameter and index of refraction. For example, rhabdomeres numbers l-6 could be identical to number 7 in diameter but if they had an appropriately increased refractive index determined by V of equation (l), they would behave electromagnetically as in Calliphora. The rhabdomeres of the long legged fly Condylostylus illustrated in Fig. 4, may be such an example (TRUJILLOCEN~Zand BERNARD,1972). Each rhabdomere has an approximate radius of 05 pm similar to the central rhabdomere of Calliphoru. However, Condulostylus’ rhabdomeres number l-6 have a higher density of microvilli (dark lines in Fig. 4) than number 7 and therefore a correspondingly larger index of refraction, since the refractive index is mainly due to the membrane lipid layers. We can determine from equation (1) the refractive index n, necessary for rhabdomeres l-6 to behave electromagnetically as Culliphora rhabdomeres 1-6, i.e. the n, that compensates for their diameters being reduced by half. It is found that n, N 1.388 which seems plausible but no data is available as a check. Therefore, we see that although Condylostylus’ receptors are the same size, rhabdomeres numbers l-6 act electromagnetically different from number 7 and may, depending on their refractive index, behave identically to Calliphora’s rhabdomeres numbers l-6. SUMMARY Light propagates along rhabdomeres of the fly Culliphoru in the form of an HEi, electromagnetic mode. The amount of modal light within the fly’s central (smaller) rhabdomere is highly sensitive to changes in wavelength. We have shown that a rhabdomere 1 pm in dia. can have an absorption peak at approximately 478 nm even though its photopigment absorbs maximally at 515 nm. Therefore, the shifted receptor response of the central rhabdomere found from microspectrophotometry, may be due either partly or entirely to its physical properties rather than to two different photosensitive materials. Acknowledgemenrs-The author appreciates the interest and suggestions of G. A. HORR~DOE and J. W. BLAMEY of The Australian National University, IAS. Special thanks go to G. D. BERNARD of Yale University for many valuable discussions.

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SNYDER AND WILLIAM H. MILLER

REFERENCES B~.~~CHARDT, D. (1962). Spectral sensitivity and other response characteristics of single visual cells in the arthropod eye. Symp. Sot. exp. &I. 16, 86-109. DAXTN~LL, H. J. A. (1962). nte Eye (edited by H. DAVSON)Vol. 2, chap. 17, p. 341. Academic Press, London. ENQCB,f. M . (1961). Nature of the transmission of energy in retina1 receptors. J. opt. Sot. Am. 51,1122-i 126. ~SCIiFELD, JC. (1969). Processing of Opricul Data 6y Organisms and Machines (edited by W. REICHARD’I’), Academic Press, London. KWER, J. W. (1966). The Functional Organization of tire Cornpowtd Eye (edited by C. G. BERNHARD), Pergamon Press, Oxford. LANGER,H. and THORELL,B. (1966). The Functioml Orgmimtion of the Compound Eye (edited by C. G. BERNHARD), Pergamon Press, Oxford. LANGER,H. (1967). Yerh. .&S&I. Zool., An. Suppi. 30, 195. SEITZ,G. (1968). Der strahltmgang im appositionsauge von Cutlipiroru erythrocephala. Z. uergl. physiol. 59, 205-231. SEITZ,G. (1970). Nachweis einer pupilienreaktion im auge der schmeibfhege. Z. aergl. physiol. 69,169~185. SNII‘ZER, E. (l%l). Cy~mdrical dielectric waveguide modes. J. opt. Sot. Am. S&491-498. SNYDER, A. W. (1966). Surface waveguide modes along a semi-infinite dielectric fibre excited by a plane wave. J; opi. Sot. Am. s6,601-610. SNYDER, A. W. (1969aj. Asymptotic expressions for eigenvafues and e~nfu~ti~s of a dielectric or optical waveguide. IEEE Tram h47T, M7%17, 1130-1138. SNYDER, A. W. (1%9b). Excitation and scattering of modes on a dielectric or optical fibre. IEEE Trans. M77’, MTT-17, 1138-1144. SW~R, A. W. (1969~). Wave propagation along dielectric structutes with application to retinal receptors. Ph.D. Thesis, University of London. J. (1966). The Fmctionat Orgattization of the Compomd Eye (edited by TRU~LL~-CEN&,0. and ~@LAMED, C. G. BERNH,UU&Pergamon Press, Oxford. TRUIILL&ZEN&, 0. and mm, G. D. (1972). Some aspects of retinal organization of SympycnustIneoEus Leow @iptera, Doliihopodidae). 1. Uirrusrrucr. Res. Cm press). VARELA, G. F. and Wrrr~m, W. (1970). The optics of the compound eye, J. gen. Phy5iol. !%, 336-358. Abetrae&-The minute dimensions of a Cullipharu fly rhabdomere produce electromagnetic effects that can modii the rhabdomere’s absorption spectrum from that of its photopigment. We show that the resuBs of ~cr~~phot~~ which display a diierent receptor response peak for the smaller central rhabdomere in comparison with its six larger neighbours, may be due either partly or entirely to its physical properties rather than to two different photopi;$ments. R&mm&-Les faibles dimensions du &abdomen: de Ia mouche Callip!toru produisent des effets ~~~tro~~iq~~ qui peuvent d&lacer k spectre d’absorption .du ~~~p~~ celui de son photopigment. On montre que ies r&&tats ~~~~~t~q~ qui indiquent un maximum different dans la r&onse du r@pteur pour le petit rhabdon&re central, compare a ses six voisins plus grands, peut provenir partieflement ou entierement de ses proprietbs physiques pIut&t que de deux photopigments differants. Zusarnme&nssrmg-Die winzige Grosse des Rhabdoms bei der CaIhphoraFliege ftihtt zu eiektromagnetis&en Effekten, die das Absorptionsspektrum des Rhabdoms gegemiber dem des Photopigments vet&r&m k&men. Es wird gea@t, dass die Ergebnisae der Mikroswktralphotometrie,dieeinen Untersehied ~~~~R~ort~ des Rezeptorsindem Weineren benaebbatien erg&en, eher-zumindest teilzentraten Rh&dom und den sechs gr we&e--auf die physikaliihen Verhiihnisse als auf zwei unterseRisdtlche Photopigmente zurtickgefiihrt werden kiinnen.