Restrictions on Rotational and Translational Diffusion o f Pigment in the Membranes o f a Rhabdomeric Photoreceptor TIMOTHY

H. GOLDSMITH

and R U D I G E R

WEHNER

From the Department of Biology, Yale University, New Haven, Connecticut 06520, the Department of Zoology, University of Zurich, Switzerland, and the Marine Biological Laboratory, Woods Hole, Massachusetts 02543

A a ST RA C T Individual, isolated r h a b d o m s from d a r k - a d a p t e d crayfish (Orconectes, Procambarus) were studied with a laterally incident microbeam that could be placed in single stacks o f microvilli. Concentration gradients o f metarhodopsin along the lengths o f microvilli were p r o d u c e d by local bleaches, accomplished by irradiation with small spots o f orange light at p H 9 in the presence o f glutaraldehyde or formaldehyde. No subsequent redistribution o f pigment was observed in the dark, indicating an absence o f translational diffusion. On the basis o f comparison with other systems, glutaraldehyde, but not formaldehyde (0.75%), would be expected to prevent diffusion o f protein in the membrane. U n d e r the same conditions photodichroism is observed, indicating an absence o f free Brownian rotation. Photodichroism is larger in glutaraldehyde than in formaldehyde, suggesting that the bifunctional reagent quiets some molecular motion that is present after treatment with formaldehyde. Quantitative comparison of photodichroism with mathematical models indicates that the pigment absorption vectors are aligned within -+50° o f the microvillar axes and are tilted into the surface o f the m e m b r a n e at an average value o f about 20°. T h e photoconversion o f rhodopsin to metarhodopsin is accompanied by an increase in molar extinction of about 20% at the hmax and a reorientation o f the absorption vector by several degrees. T h e transition moment either tilts f u r t h e r into the m e m b r a n e or loses some o f its axial orientation, or both. T h e change in orientation is 3.5 times larger in formaldehyde than in glutaraldehyde. INTRODUCTION

The disk membranes of amphibian rod outer segments have recently been s h o w n to b e f l u i d m o s a i c s , c o n s i s t e n t w i t h a g e n e r a l m o d e l o f b i o l o g i c a l m e m b r a n e s as s u m m a r i z e d by S i n g e r a n d N i c o l s o n (1972). W i t h i n t h e p l a n e s o f t h e photoreceptor membranes, the rhodopsin molecules undergo rotational diffus i o n , w i t h a r e l a x a t i o n t i m e o f 20 /,~s ( C o n e , 1972). T r a n s l a t i o n a l d i f f u s i o n o f visual p i g m e n t in t h e p l a n e s o f t h e disks c a n also b e m e a s u r e d a c r o s s t h e w i d t h o f t h e o u t e r s e g m e n t s ( L i e b m a n a n d E n t i n e , 1974; P o o a n d C o n e , 1974). T h e m e a s u r e d h a l f - t i m e s f o r d i f f u s i o n a l e q u i l i b r i u m a r e 23-35 s, c o r r e s p o n d i n g to d i f f u s i o n c o e f f i c i e n t s 2 - 6 × 10 -9 c m 2 s -1. T H E J O U R N A L OF G E N E R A L P H Y S I O L O G Y ' V O L U M E

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T h e bifunctional r e a g e n t glutaraldehyde has p r o v e d useful in altering the mobility o f r h o d o p s i n in amphibian p h o t o r e c e p t o r membranes: both translation (Liebman and Entine, 1974; Poo and Cone, 1974) and rotation (Brown, 1972; Cone, 1972) are blocked by the presence o f a few percent glutaraldehyde. T r e a t m e n t with f o r m a l d e h y d e , on the o t h e r h a n d , neither prevents rotation n o r slows the rate o f translational diffusion (loc. cir.). Moreover, in the retinas o f an invertebrate (squid) that have been treated with glutaraldehyde, the presence o f r h o d o p s i n and its p h o t o p r o d u c t s , alkaline and acid m e t a r h o d o p s i n , can be d e m o n s t r a t e d by means o f their fast photovoltages (early r e c e p t o r potentials) (Hagins and McGaughy, 1967). Glutaraldehyde t h e r e f o r e appears to block diffusional movements o f r h o d o p s i n by cross-linking and (at least to a first approximation), neither diffusional m o v e m e n t s n o r certain o t h e r properties o f the r h o d o p s i n molecule (spectrum, changes attendant on isomerization) are grossly altered by the presence per se o f reactive aldehyde groups. Although the p h o t o r e c e p t o r m e m b r a n e s o f a r t h r o p o d s have not been examined as carefully, there are reasons to suspect that they may differ in fluidity. T h e evidence is based on m e a s u r e m e n t s o f dichroic absorption and o f the sensitivity o f the animals to polarized light. As m e a s u r e m e n t s o f dichroism are also a central part o f the present work, it is desirable to build on an u n d e r s t a n d ing that begins with the absorption properties o f vertebrate o u t e r segments. T h e absorption vectors o f vertebrate r h o d o p s i n molecules lie roughly coplanar with the disk m e m b r a n e s . As shown in Fig. 1 A, (which follows the terminology o f Laughlin et al., 1975, and o f Snyder and Laughlin, 1975), absorbance can be resolved into three mutually p e r p e n d i c u l a r vectors: otx and Otw in the plane o f the m e m b r a n e and ota at right angles to the m e m b r a n e . Because the molecules are free to rotate a r o u n d axes parallel to ota, all values o f 4~ occur, and or1 = Otw. I f the molecules were strictly coplanar with the m e m b r a n e , ota would be 0. Because the absorption vectors are tilted into the m e m b r a n e at an angle 0, however, there is some absorption when the e-vector is at right angles to the m e m b r a n e . Consequently, a stack o f such disks viewed f r o m the side (Fig. 1 B) exhibits intrinsic linear dichroism. T h e absorbance m e a s u r e d with e-vector parallel to the m e m b r a n e s and p e r p e n d i c u l a r to the axis o f the stack D± is several times greater than the absorbance m e a s u r e d with e-vector parallel to the stack. T h e ratio R = Dj_/Du = aw/Ota has generally been m e a s u r e d to be 3-5 (Liebman, 1962; Wald et al., 1963; Hfirosi and MacNichol, 1974a, b; Hfirosi, 1975). Laughlin et al. (1975) and Israelachvili et al. (1976) have pointed out that m e a s u r e d dichroism in both vertebrate and invertebrate m e m b r a n e systems will be influenced by the fact that the refractive index is greater for light polarized in the plane o f the m e m b r a n e than at right angles. This f o r m dichroism is given by n,,4/nc 4, where nm and nc are the refractive indices o f the m e m b r a n e and cytoplasm, respectively. T h e effect o f f o r m dichroism is to u n d e r e s t i m a t e intrinsic dichroism. One aim o f measuring dichroic ratios in p h o t o r e c e p t o r cells is to infer the molecular orientations o f the pigment molecules. Liebman (1962) has a t t e m p t e d to calculate the tilt angle that the c h r o m o p h o r e s assume in disk m e m b r a n e s and has derived expressions based on two models: I, all molecules are tilted at some fixed angle which we shall call Of; and II, the molecules are r a n d o m l y distributed

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a~

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R__D_,, D± FIGURE 1. Comparison of the photoreceptor membranes of vertebrate outer segments (A, B) and arthropod microvilli (C, D), modified from Laughlin et al. (1975), and Snyder a n d Laughlin (1975). A, Vertebrate disk membrane. T h e absorption of a pigment molecule or the population of pigment molecules can be resolved into three orthogonal coefficients, oq and aw in the plane of the m e m b r a n e , and an in the "height" or thickness of the membrane. If the transition moment is linear, ah is produced by its tilt (0) into the membrane. As the molecules are free to rotate a r o u n d axes normal to the m e m b r a n e , all angles ~b occur. B, T h e rod or cone outer segment consists of a stack of membranes which exhibit dichroism when viewed from the side. Absorbance with e_L is greater than with e,f (axes referred to the stack), and the dichroic ratio, R = D±/Dfl. C, The photoreceptor membranes of crayfish are microvilli, but the local absorption coefficients can be defined in an analogous way. 0 represents tilt into the membrane; ~bis measured in the tangent plane of the cylinder, from the microvillar axis. D, T h e microvilli of crayfish are assembled in bands or layers about 25 /xm diam (in the middle of the rhabdom) and 5 /zm thick. All the microvilli in one layer are parallel to each other and at right angles to the microvilli of adjacent layers. This diagram shows one complete b a n d and parts of the two contiguous layers. Isolated organelles can be viewed from the side and a small measuring beam placed in a single layer. When the rhabdom's margin appears symmetrically scalloped, "waists" correspond to layers in which the microvilli are viewed from the side, and "hips" to layers in which the microvilli are viewed end-on. T h e plane of polarization of the measuring beam is referred to the microvillar axes in waists, as shown. In vivo the rhabdom is s u r r o u n d e d by seven retinular cells, but these detach when the tissue is disrupted. In each band there is a central plane, normal to the microvillar axes, which is defined by the closed ends of the microvilli originating from cells on opposite sides of the ommatidium.

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t h r o u g h a r a n g e o f 0, whose limit we shall r e f e r to as Oa. T h e calculated values o f Ot a n d 0d clearly d e p e n d on the m e a s u r e d values o f dichroic ratio that one accepts a n d on w h e t h e r o n e adjusts for f o r m dichroism. T h e m e m b r a n e s o f r h a b d o m e r i c p h o t o r e c e p t o r s are not plane sheets but are rolled into cylindrical microvilli (Fig. 1 C). By analogy, a b s o r b a n c e at any point on the m e m b r a n e can be resolved into t h r e e mutually p e r p e n d i c u l a r vectors: al, parallel to the long axis o f the microvillus; Otw, at right angles to Oil but also in a t a n g e n t plane; a n d oth, in the "height" or thickness o f the m e m b r a n e . T h e microvilli are a r r a n g e d in parallel arrays, a n d in crustacea these f o r m two o r t h o g o n a l sets (Fig. I D). In the eye, light irradiates the microvilli f r o m the side, a n d it is possible to study individual stacks o f parallel microvilli by irradiating small regions o f isolated crustacean r h a b d o m s f r o m the side. It is t h e r e f o r e m o r e c o n v e n i e n t to r e f e r the planes o f polarization o f the m e a s u r i n g b e a m s to the microvillar axes, as d e f i n e d in Fig. 1C, D, r a t h e r t h a n to the axis of the rhabdom. Moody a n d Parriss (1961) were the first to e x p l o r e theoretically the a b s o r p t i o n in such a system, showing that for a r a n d o m a r r a y o f c h r o m o p h o r e s in the t a n g e n t planes o f the microvilli (~h = 0, 0 = 0, all values o f 4) equally p r o b a b l e , ctl = aw), the dichroic ratio should be 2.0. Any higher dichroic ratio would imply that there is some net orientation o f the c h r o m o p h o r e s with the microvillar axes or, to express the restriction in t e r m s o f Fig. 1 C, not all values o f ~b are occupied with equal probability, a n d the m e a n value is less t h a n 45 ° . In the general case (0~ 0), the intrinsic dichroism is 2 al/(ah + aw) a n d the net dichroism is 2 Rfotl/ (ah + Rtaw), w h e r e Rf is the f o r m dichroism (Laughlin et al., 1975; Snyder a n d Laughlin, 1975). T h e first m e a s u r e m e n t s o f dichroism in crustacean r h a b d o m s gave values of a b o u t 2 which were i n t e r p r e t e d as being consistent with the Moody-Parriss (1961) m o d e l ( W a t e r m a n et al., 1969). More recent m e a s u r e m e n t s , however, have yielded higher values with a significant n u m b e r of e x a m p l e s g r e a t e r t h a n 3 (Goldsmith, 1975). T h e s e results indicate that the c h r o m o p h o r e s are not randomly o r i e n t e d in the m e m b r a n e surface, having some t e n d e n c y to orientation along the microvillar axes. T h i s conclusion can also be r e a c h e d by a n o t h e r route. Electrophysiological m e a s u r e m e n t s o f the polarization sensitivity o f single phot o r e c e p t o r cells o f crustacea (Shaw, 1969; W a t e r m a n a n d F e r n a n d e z , 1970; Muller, 1973; Mote, 1974) have yielded values as high as 10-14, and the most likely e x p l a n a t i o n is that polarization sensitivity is a reflection o f dichroic ratio (see discussion o f alternatives in Goldsmith, 1975). Net orientation o f c h r o m o p h o r e s with respect to the microvillar axes implies that Brownian rotation is restricted. I f rotational diffusion is not free, this raises the additional possibility that translational m o v e m e n t s o f the p i g m e n t might also be constrained. T h e p u r p o s e of the p r e s e n t work was to test these two hypotheses e x p e r i m e n t a l l y , a n d the results indicate that in crayfish r h a b d o m s b o t h kinds o f m o v e m e n t are i n d e e d restricted. Because the e x p e r i m e n t s on translational diffusion are conceptually simpler, they are described first. T h e evidence on rotational diffusion comes f r o m m e a s u r e m e n t s of p h o t o i n d u c e d dichroism. In o r d e r to analyze these e x p e r i m e n t s quantitatively, however, it was necessary to develop f u r t h e r the theoretical m o d e l in which a b s o r b a n c e in microvilli is

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related to molecular orientation. T h e details are described in the A p p e n d i x , with the b r o a d outlines presented in Results. Finally, we have f o u n d that the process o f isomerization o f r h o d o p s i n to m e t a r h o d o p s i n is a c c o m p a n i e d by a c h a n g e in orientation o f the transition m o m e n t that is equivalent to an increase o f several degrees in 0 a n d / o r 4). A preliminary account o f some o f this work has a p p e a r e d in abstract (Goldsmith a n d W e h n e r , 1975; W e h n e r a n d Goldsmith, 1975). MATERIALS

AND

METHODS

Crayfish, usually Orconectes (Connecticut Valley Biological Supply, Northampton, Mass.), occasionally Procambarus (Carolina Biological Supply, Burlington, North Carolina) were used in this study, generally within 10 days of receipt from the suppliers. Animals were dark-adapted for at least several hours and usually overnight before use. A suspension of tissue fragments including intact rhabdoms from which the surrounding retinular cells had separated was prepared by macerating the eye and eyestalk in 1 ml of van Harreveld's (1936) saline at 0°C in a heavy-walled centrifuge tube, with a stout glass rod. Formaldehyde (prepared from paraformaldehyde to avoid the presence of alcohol) was added to a final concentration of 0.75% (0.25 M), or glutaraldehyde to 2.5%, and the preparation was kept at 0°C for at least 15 min before portions were sampled for study at room temperature. The aldehyde solutions were buffered at about pH 7.2 with N-2-hydroxyethylpiperazine-N'-2-ethane sulfonic acid (HEPES). To examine individual rhabdoms, a drop or two of tissue suspension was placed between microscope cover Slips and sealed within a ring of silicone vacuum grease. When rapid bleaching of metarhodopsin was desired the sample was made alkaline with a few microliters of a saturated solution of sodium borate. Spectra were recorded with a dual beam recording microspectrophotometer based on the design of Liebman and Entine (1964). Further details of the instrument and data handling can be found in Goldman et al. (1975). Individual rhabdoms were located with the deep red light of the microscope illuminator filtered with a 712-nm interference filter. As described previously (Waterman et al., 1969; Goldsmith, 1975), it is possible to select rhabdoms and place a microbeam within an individual stack of microvilli, with the direction of propagation of the light either parallel or perpendicular to the microvillar axes (see also Fig. 1). RESULTS

A. Bleaching of the Pigment R h a b d o m s from d a r k - a d a p t e d eyes show a b r o a d absorption band with )~maxnear 530 n m at neutral or alkaline p H (Goldsmith, 1977). O n brief e x p o s u r e to light, the absorbance increases and shifts to shorter wavelengths, indicating the formation o f a m e t a r h o d o p s i n with ~'max near 515 nm. This m e t a r h o d o p s i n is typical o f m a n y invertebrates in that it is quite stable in the dark, and the r h a b d o m u n d e r g o e s only slow f u r t h e r bleaching (Goldsmith, 1972, 1977). T h e metarhodopsin can be caused to photobleach, however, in the presence o f either glutaraldehyde or f o r m a l d e h y d e and at alkaline p H (Fig. 2). (A possible explanation [Goldsmith, 1977] is that light absorbed by m e t a r h o d o p s i n has a finite probability o f c o n v e r t i n g the c h r o m o p h o r e f r o m the all-trans not only to ll-c/s, but to one or m o r e o t h e r cis isomers as well, and that this creates new c o n f o r m e r s o f the protein with additional a m i n o g r o u p s exposed. At high p H these exist in the

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unprotonated form and consequently they react readily with aldehydes. Therefore, the combination of light, free aldehyde, and alkaline pH causes crayfish m e t a r h o d o p s i n to b l e a c h , as i l l u s t r a t e d in Fig. 2.) T h i s is a p h o t o l y s i s w h i c h

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Wavelength (nrn) F[CURE 2. Photobleaching o f a rhabdorn at p H 9 in the presence of 2.5% glutaraldehyde: half-strength van Harreveld's solution. T h e initial spectrum (dark) is shown by the large filled circles. Successive exposures of 0.1,0.2, 0.4, and 0.8 min to bright yellow light from the field illuminator (Wratten filter no. 9; log transmittance shown in inset, whose abscissa runs from 475 to 525 nm) caused the spectrum to shift to shorter wavelengths and fall as shown by the small filled circles. T h e 0.8 min exposure completed the bleaching, for a second 0.8 min of irradiation caused no additional change. T h e slope of the final bleached base line is caused principally by light scattering. T h e 0.1-min irradiation not only caused isornerization of the c h r o m o p h o r e and the formation o f metarhodopsin, but bleached about one-third of the metarhodopsin as well. T h e broken curve shows the a p p r o x i m a t e spectrum immediately after conversion o f all the rhodopsin to metarhodopsin, but before any significant photolysis of the latter. This curve cannot be measured u n d e r the conditions o f this e x p e r i m e n t and has been calculated from the difference spectrum of Fig. 12 (elq, little free aldehyde, p H ~7) and a relative molar extinction coefficient of about 1.1, taken from Table I. It shows what existed transiently u n d e r these conditions. Spectra were recorded at 22°C and a scanning rate of 20 nm s -1. T h e measuring beam was polarized parallel to the microvillar axes. Vertical scale is given by the calibration bar in units of absorbance (optical density). d e p e n d s o n t h e a l d e h y d e , a n d is t h u s d i f f e r e n t f r o m t h e f o r m a t i o n o f a l k a l i n e m e t a r h o d o p s i n in c e p h a l o p o d m o l l u s k s ( H u b b a r d a n d St. G e o r g e , 1958). C o m p a r e d to t h e i s o m e r i z a t i o n o f r h o d o p s i n to m e t a r h o d o p s i n , it is slow. A s i m i l a r

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behavior o f metarhodopsin in the crustaceans Libinia (Hays and Goldsmith, 1969) and Homarus (Bruno et al., 1977) has been reported in more detail. This manner of photobleaching metarhodopsin permits us to examine rhabdoms for the presence o f translational diffusion of metarhodopsin by creating local concentration gradients o f pigment and looking for a subsequent redistribution of the remaining absorption, as described in section B. Because the rhodopsin and metarhodopsin molecules presumably differ to a small degree in shape but not in weight, one would expect that their diffusion coefficients would be similar. T h e aldehydes play two roles. T hey prevent gross structural alterations of the microvilli that are potentiated by light (Waterman e t al., 1969; see also Loew, 1976) and that preclude a quantitative analysis of absorbance changes. Second, by hastening the bleaching of metarhodopsin the sensitivity of the system is greatly improved, for the absorbance changes are much larger than those that accompany isomerization at neutral or acid pH. Finally, as described in section D, the same system can also be used to investigate photoinduced dichroism and Brownian rotation. B. Restrictions on Translational Diffusion

T o test for translational diffusion of metarhodopsin, the geometrical arrangement of microvilli was exploited in the following manner. In layers o f microvilli in which the long axes of the microvilli were oriented at right angles to the optical axis of the microscope, the plane of abutment of the closed ends of the microvilli arising from opposite sides of the rhabdom marks a plane of membrane discontinuity across which no pigment should be able to diffuse. If a bleaching beam is placed in such a layer and confined to one side of this plane (Fig. 3, I), any bleaching that occurs on the opposite side of the rhabdom must have been caused by scattered light. Moreover, any pigment bleached by the actinic spot cannot be replaced by diffusion from the opposite side of the rhabdom. When the bleaching light is centered over the central plane, it should deplete pigment from the distal ends of both sets of opposed microvilli. If diffusion of pigment occurs on a time scale similar to that observed in vertebrate photoreceptor membranes, measuring beams subsequently placed anywhere in the same layer of microvilli should record equal concentrations of pigment. This configuration of bleaching and test spots is shown by the diagrams in Fig. 3, II). Spectra were recorded at sites A and B. By use of deep red light, a small rectangular aperture was then placed in the beam of the field illuminator in the plane o f the field stop, and a local, fractional bleach of metarhodopsin was effected. T h e spectra were rerecorded at the measuring sites; the aperture was removed; a full-field, total bleach was performed; and the final base lines were recorded. T h e results of these experiments are also tabulated in Fig. 3. With the bleaching beam confined to one-half of a layer of microvilli, an exposure that bleaches 60-75% of the metarhodopsin u n d e r the bleaching beam destroys less than half the pigment on the opposite side of the rhabdom. T h e same result is obtained when the bleaching beam is centered so as to irradiate the closed ends of both sets of microvilli. It is not surprising that there is no apparent diffusion

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o f m e t a r h o d o p s i n in the p r e s e n c e o f the cross-linking r e a g e n t , g l u t a r a l d e h y d e ; the i m p o r t a n t f i n d i n g is that the s a m e result o c c u r s in 0.75% f o r m a l d e h y d e as well. B e c a u s e o f the d i f f e r e n t kinetics o f p h o t o d e c a y o f m e t a r h o d o p s i n in g l u t a r a l d e h y d e a n d f o r m a l d e h y d e , quantitative c o m p a r i s o n s o f " f r a c t i o n I

II

IO/J,rn BLEACHING BEAM

MEASURING BEAMS FRACTION BLEACHED A(or A') GLUTARALDEHYDE 0.46~0.03 0.76±0.03 B 0.46±0,04 (n=lO) (n=lO) (n=9) FORMALDEHYDE 0.32±0.03 0.64±0.04 n=9) (n=9)

B 0.71±0.01

(n=5)

0.37±0,03 0.61±0.02 (n=22) (n=14)

FIGURE 3. Absence of translational diffusion of metarhodopsin in crayfish rhabdoms. The diagrams at the top, drawn approximately to scale (except for the sizes of the microvilli), show three adjacent layers of microvilli viewed from the side, as well as the placement of bleaching and measuring beams in the central layer. I is a control for light scatter in which the bleaching beam is confined to microvilli on one side of the rhabdom, and pigment is measured at the same site (B) and in the microvilli on the opposite side (A), both before and after the bleaching exposure. II shows the experimental arrangement, in which a centrally placed measuring beam (B) irradiates the terminal 2-3 /zm of all microvilli in the layer, and pigment is measured at this site as well as at the opposite ends of the microvilli (A, A'). The bleaching beam was approximately 5 × 10 tzm in the object plane, and the measuring beam about 5 x 6 t~m. Bleaching exposure was 1 min in 2.5% glutaraldehyde and 1.6 min in 0.75% formaldehyde. Both suspending solutions were approximately 0.5 osM, pH 9 (see Materials and Methods). The bleaching light contained wavelengths longer than 470 nm (Wratten filter no. 9, spectrum in inset of Fig. 2) so as to minimize photoregeneration of rhodopsin. A t-test of the significance of the difference between the means was performed for the following pairs: glutaraldehyde, I B and II B; formaldehyde, I A and II A; and formaldehyde, I B and I I B . None of the differences approaches significance (P = 0.27, 0.34 and 0.42). b l e a c h e d " b e t w e e n these two m e d i a are n o t m e a n i n g f u l . T h e i m p o r t a n t c o m p a r isons are b e t w e e n e a c h e x p e r i m e n t (II) a n d its c o r r e s p o n d i n g c o n t r o l (I). I n the p r e s e n c e o f e i t h e r a l d e h y d e , b l e a c h i n g at sites lateral to the central b l e a c h i n g b e a m can be quantitatively a c c o u n t e d f o r by laterally scattered light. T h u s o v e r a time scale o f a b o u t 2 min, translational d i f f u s i o n o f m e t a r h o d o p s i n a l o n g the l e n g t h s o f the microvilli is n o t d e t e c t e d . I f the d i f f u s i o n w e r e very m u c h slower t h a n the rate o f photolysis, the a s y m m e t r i c distribution o f m e t a r h o d o p s i n p r o d u c e d d u r i n g a 1.6-min irradia-

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tion should slowly dissipate in the dark, at least in the f o r m a l d e h y d e - t r e a t e d r h a b d o m s . T h e concentration o f p i g m e n t u n d e r the central bleaching site should rise and the concentrations at the edges o f the r h a b d o m should fall. This is not observed. T h e m e a s u r e m e n t is complicated, however, by the fact that u n d e r o u r experimenal conditions (free f o r m a l d e h y d e present, p H 9), the m e t a r h o d o p s i n slowly d e n a t u r e s in the dark. Experiments were t h e r e f o r e und e r t a k e n to see if the rate o f absorbance loss in the dark after a local 1.6omin irradiation was slower u n d e r the bleaching slit than at the sides o f the r h a b d o m , as would be the case if slow, lateral diffusion were o c c u r r i n g simultaneously with thermal bleaching. In a given r h a b d o m , decay at peripheral and central m e a s u r i n g spots a p p e a r e d to follow first-order kinetics, with identical rate constants at the two m e a s u r i n g sites. Half-times varied in different r h a b d o m s , however, f r o m 9 to 25 min. T h e results o f five experiments are shown in Fig. 4, where the decay time has been normalized to permit pooling o f the data. In a sixth e x p e r i m e n t the decay at the two m e a s u r i n g sites could not be described by a single rate constant, but absorbance loss was faster, not slower, at the site o f previous irradiation, a result opposite to that expected from a diffusional redistribution o f the r e m a i n i n g m e t a r h o d o p s i n . Put together, the results o f Figs. 3 and 4 indicate that there is no detectable diffusion o f m e t a r h o d o p s i n over distances o f about 10 ~ m d u r i n g a time span o f about 20 min. 0',%$ o

IOH-m oN

-0.2

• -o.,

......

°"eQ.

~FRACTIONAL ~..i..~________~ PHOTO-

"~.oe o.

\

"

B'EAC.

~,,,o -0.6

o •

~ • %

.

o • o\ o X•

-0.8

lnC/CC -I.0

..

.~,

:

MEASURING

~

SITES FOR DARK DECAY

E~

I,,,~,, o

-1.2

-I.4 -I.6

o

,

o:2 0.4 o16 o18 ,.5

~

J

I

°L"',,

J

,.2 ,/4 ,.'6 ,.8 2.o 2.2 2.4 TI/2 FIGURE 4. First-order dark decay of metarhodopsin that remains after fractional photobleaches. Closed circles: site under the bleaching beam. Open circles: opposite ends of the microvilli. Results are shown for five experiments. In any individual rhabdom, decay at both sites was described by the same rate constant; in order to pool the data from several experiments, however, the time axis has been normalized. Tl/2 varied in different rhabdoms from 9 to 25 min. Decay of absorbance is described by the same kinetics at sites A and B (terminology of Fig. 3); thus, after a bleaching exposure that destroys part of the pigment, there is no evidence for a slow redistribution of the remaining metarhodopsin along the lengths of the microvilli. Bleaching exposure, 1.6 min, wavelengths longer than 470 nm. Suspending medium included 0.75% formaldehyde, pH 9.

462

T H E J O U R N A L OF G E N E R A L P H Y S I O L O G Y " V O L U M E 7 0 ' 1 9 7 7

C. Dichroism of Rhabdoms and the Implications for Molecular Orientation T h e expression for the dichroic ratio o f an a r r a y o f parallel microvilli, R0 =

2Rfal Rraw + ah '

(Snyder a n d Laughlin, 1975), can be m o d i f i e d by replacing the coefficients al, aw, ah with n o r m a l i z e d a b s o r b a n c e coefficients calculated f r o m the a n g u l a r distributions o f c h r o m o p h o r e s in ~b a n d 0 (see Figs. 1 and 15, a n d A p p e n d i x ) . As described in the A p p e n d i x , the distribution o f axial orientations is a s s u m e d to be u n i f o r m for all angles smaller t h a n the limiting value, ~ba. T h a t is, all angles smaller than the limits o f the distribution are allowed and are equally p o p u l a t e d . As for molecular tilt into the m e m b r a n e , we have followed L i e b m a n (1962) a n d c o n s i d e r e d two possibilities: m o d e l I, all o f the a b s o r p t i o n vectors are canted into the m e m b r a n e at a fixed angle Or; a n d m o d e l I I , the a b s o r p t i o n vectors occupy a u n i f o r m distribution between 0 = 0 a n d 0 = 0a. Eq. (Sa) and (8b) ( A p p e n d i x ) describe the dichroic ratio (Ro = D,/D±) as a function o f ¢ka a n d 0a (or Of). T h e f o u r curves labeled R0 in Fig. 5 A a n d B, calculated f r o m Eq. (8b), show dichroic ratio as a function o f ~ba for various a s s u m e d values o f 0a a n d f o r m dichroism. ( T h e curves labeled R, and R± have to do with p h o t o i n d u c e d dichroism and will be described later.) T h e curves in Fig. 5 A are for e x t r e m e cases a n d assume no f o r m dichroism. T h e solid c u r v e shows dichroic ratio when the c h r o m o p h o r e s are virtually confined to the t a n g e n t planes o f the microvilli (0a = 0.01°). T h e filled circle on the r i g h t h a n d end o f the curve c o r r e s p o n d s to a r a n d o m distribution o f the c h r o m o p h o r e s within this plane (~ba = +-90 °, all angles t h e r e f o r e occupied), the case originally d e v e l o p e d by Moody a n d Parriss (1961). I f the c h r o m o p h o r e s are m o r e nearly aligned with the microvillar axes (smaller values o f ¢ba), the dichroic ratio rises. T h e most recent m e a s u r e m e n t s o f microvillar dichroism indicate ratios g r e a t e r than 2.0 (Goldsmith, 1975), implying that not all axial orientations (~b) occur with equal probability. T h e b r o k e n curve (R0) in Fig. 5 A, on the o t h e r h a n d , shows dichroism when all angles o f tilt occur (0a = 90°). With this a s s u m p t i o n , the m a x i m u m dichroic ratio o b s e r v e d is 4.0, even with c o m p l e t e a l i g n m e n t o f the c h r o m o p h o r e s with the microvillar axes (~ba = 0°). Because m e a s u r e d dichroic ratios o f r h a b d o m s occasionally, a n d polarization sensitivities o f retinular cells frequently, exceed this value (reference above), we also conclude that not all angles o f tilt into the m e m b r a n e are equally p r o b a b l e . In Fig. 5 B are theoretical plots o f dichroic ratio (R0) calculated on the p r e m i s e that f o r m dichroism is 1.56 (see below), a n d for two i n t e r m e d i a t e values o f 0a, 20 ° (broken curve) a n d 40 ° (solid curve). (As described in the A p p e n d i x , 40 ° is the a p p r o x i m a t e limit o f the distribution o f 0a if the c h r o m o p h o r e s are tilted into microvillar and r o d disk m e m b r a n e to the same extent [model II].) T h e o p e n circle on the r i g h t h a n d e n d o f the solid curve R0 is t h e r e f o r e the e x p e c t e d dichroic ratio in microvilli constructed o f m e m b r a n e with a b o u t the same p r o p erties as r o d disk m e m b r a n e , merely rolled into cylinders. With r a n d o m orientation o f c h r o m o p h o r e s (~ba = 90°), the dichroic ratio is 1.67 r a t h e r than 2.0

GOLDSMITH AND WEHNER Restricted Diffusion of Pigment in Photoreceptors

463

( S n y d e r a n d L a u g h l i n , 1975). H i g h e r d i c h r o i c r a t i o s c a n b e a c h i e v e d b y d e c r e a s i n g e i t h e r 0a o r ~bd, o r b o t h . C o m p a r e d to t h e o r i e n t a t i o n p a r a m e t e r s , t h e v a l u e o f f o r m d i c h r o i s m h a s a r e l a t i v e l y s m a l l i n f l u e n c e o n t h e d i c h r o i c r a t i o . Fig. 6 s h o w s d i c h r o i c r a t i o (R0) as A e d = 0.01"

B

1.0

Rf =

---8

d = 20*

Rf = 1.56

I0O 5o

k:a,

f 0

}. io o

§ c3

5

2,,- .

"'x-.

. . . . .

I

0.5

0

,

,

*

300

i

=

=

60*

=

i

O*

i

J

i

300

~

t

J

600

i

i

90*

FIGURE 5. Theoretical plots o f microvillar dichroism as a function of the limit of the distribution o f axial orientation, qba, for various assumed values o f 0d (limit o f the distribution o f c h r o m o p h o r e tilt) and Rt (form dichroism). Dichroic ratio (R = DJDj_) is defined as [absorbance measured with e-vector parallel to the microvilli]/ [absorbance with e-vector p e r p e n d i c u l a r to the microvilli]. R0, the dichroic ratio o f d a r k - a d a p t e d microvilli, is calculated from Eq. (8 b). R,, dichroism after a fractional bleach with the e-vector o f the actinic beam polarized parallel (e,) to the microvilli, as calculated from Eq. (11 b, with k~l ]~lmax,as defined in the A p p e n d i x . Similarly, R_L, the dichroic ratio after a fractional bleach with e.L, is calculated from Eq. 14 b, with k j_ at its m a x i m u m value. Fig. 5 A shows results for two extreme cases: the c h r o m o p h o r e s confined to the tangent planes o f the microviili (Oa =0°), and all angles o f tilt allowed (Oa = 90°). Form dichroism is assumed to be absent. T h e lower terminus of the solid curve labeled R0 (filled circle) is the condition described in the model of Moody and Parriss (1961), (random orientation of c h r o m o p h o r e s in the tangent planes o f the microvilli) and corresponds to a dichroic ratio o f 2.0. Fig. 5B shows results o f calculations for two intermediate values of Oa and with form dichroism o f 1.56. See text for further details. =

a f u n c t i o n o f f o r m d i c h r o i s m (R0 f o r o n e s p e c i f i c s o l u t i o n o f Eq. ( 8 a ) ( m o d e l I) a n d two specific s o l u t i o n s o f Eq. ( 8 b ) ( m o d e l I I ) . T h e v a l u e s o f (#d, Od, a n d Of u s e d in t h e s e c a l c u l a t i o n s w e r e s e l e c t e d o n t h e basis o f e x p e r i m e n t a l r e s u l t s d e s c r i b e d in a s e c t i o n t h a t follows; h o w e v e r , t h e i m p o r t a n t p o i n t to n o t e at this j u n c t u r e is t h a t a m a x i m u m u n c e r t a i n t y in Rf l e a d s to a n e r r o r in R0 o f o n l y ---10%. I n w h a t f o l l o w s , t h e r e f o r e , we n e e d to s u s t a i n o n l y a m o d e s t i n t e r e s t in

464

THE

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70 • 1977

the value o f f o r m dichroism selected for calculation, a convenient circumstance as Rf has not yet been reliably measured. A study o f the birefringence o f isolated crayfish r h a b d o m s has yielded estimates o f f o r m dichroism o f 1.26 and 1.56 u n d e r different e x p e r i m e n t a l conditions (Goldsmith and Paulson, Unpublished observations). D. Photoinduced Dichroism

If individual m e t a r h o d o p s i n molecules are not able to rotate t h r o u g h all angles limited by ---4~d in the tangent planes o f the microvilli, it should be possible to

-

Model "13"

/

-

Model T

(% =50 o ; Of =20 °) =°5 o

"6 n." 4

~

o

t

Model vr

(¢'d = 50° ; ed =40°)

.-~ 3 r-,

I.O

I.I

1.2

1.5

1.4

1.5

1.6

Form D i c h r o i s m ( R f )

FIGURE 6. Shallow dependence o f dichroic ratio (B0) on form dichroism (R0, calculated from Eq. (8a), mode] I, and from Eq. (8b), model I I . (The specific values o f ~d, 0d, and 0~ that have been used in the calculation are drawn f r o m analyses o f photodichroism, as described later). See text.

increase the dichroic ratio by bleaching part o f the population with light polarized p e r p e n d i c u l a r to the microvilli (e±) and to decrease the dichroic ratio with a bleaching light having parallel e-vector (etl). After such a fractional bleach, the remaining pigment should t h e r e f o r e exhibit p h o t o i n d u c e d dichroism. As with vertebrate p h o t o r e c e p t o r m e m b r a n e s , p h o t o i n d u c e d dichroism in the presence o f the cross-linking reagent glutaraldehyde would not be surprising, but photoinduced dichroism in the presence o f f o r m a l d e h y d e would be evidence that Brownian rotation does not occur freely. Figs. 7 and 8 show two examples o f r h a b d o m s treated with f o r m a l d e h y d e in which photodichroism has been induced. In the e x p e r i m e n t o f Fig. 7 the dichroic ratio was increased f r o m 2.46 to 3.39 by a fractional bleach with e-. In Fig. 8 the dichroic ratio was decreased from 2.37 to 1.83 by a partial bleach with ell. T h e initial spectra in Figs. 7 and 8 reflect the presence o f rhodopsin. After a partial bleach with o r a n g e light, however, only m e t a r h o d o p s i n remains. In o r d e r to minimize changes in absorbance due to the conversion of r h o d o p s i n to

GOLDSMITH AND WEHNER Restricted Diffusion of Pigment in Photoreceptors

465

metarhodopsin, measurements were made at the isosbestic wavelengths. T h e

essential point o f Figs. 7 and 8 is not the precise value of dichroic ratio, but that dichroic ratio o f the metarhodopsin can be either increased or decreased, d e p e n d i n g on the plane o f polarization of the bleaching light. Experiments such as those in Figs. 7 and 8 indicate that the metarhodopsin molecules cannot turn through all values o f ~b. In order quantitatively to analyze

~1~1~

1.3s

*

i-

~. o \

,/

I,:

I

400

I

450

I

I

:

5

I

500

I

I

...

I%o

I

550 Wovelength(nrn)

\

I

o

I

600

jill

650

FIGURE 7. Photodichroism: example of an experiment in which the dichroic ratio of a layer of microvilli was increased from 2.46 to 3.39 by a fractional bleach with light polarized perpendicular (e±) to the microvillar axes. (See Fig. 1 for axes of reference.) Spectra were recorded initially, after several seconds' exposure to the polarized actinic beam, and again after a 2-min irradiation with unpolarized light that bleached all remaining pigment. Difference spectra (in units of absorbance) were calculated by subtracting the final bleached base line from each of the earlier spectra: D~t, optical density measured with ell for the full complement of pigment; D0±, the same, but measuring beam with e±; Dtt, optical density of pigment (now metarhodopsin), measured with etl, remaining after a partial bleach with e±; D±, the same, but measured with e±. R0, initial dichroic ratio; R±, dichroic ratio after partial bleach with e.; R±/Ro, photodichroism. Fraction bleached is calculated at a wavelength near the isosbestic point for the rhodopsin-metarhodopsin conversion; therefore, changes in absorbance at this wavelength measure the a m o u n t of metarhodopsin bleached and are not affected by absorbance changes associated with the conversion of rhodopsin to metarhodopsin. The pH was ~9 and the suspending medium contained 0.75% formaldehyde. T h e bleaching light was yellow (see inset, Fig. 2).

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this kind o f result, however, it is necessary to d e v e l o p f u r t h e r the m o d e l o f microvillar dichroism. This has b e e n d o n e in A p p e n d i x B. Rll, the dichroic ratio after fractional bleaches with e,, is given by Eq. (11 a) (model I) and (11 b ) (model II); R±, the dichroic ratio after a fractional bleach with e±, is given by Eq. (14a) (model I) a n d (14b) (model II). T h e only additional a s s u m p t i o n m a d e in deriving Eq. ( l l a , b) and (14a, b) is that the probability that a molecule will be bleached is directly p r o p o r t i o n a l to its probability o f absorption.

z'x,

/

Ro:=2.37

O.OIAD

D,

hv

e, •

/

•

•

R"=b-l'l=l'83

/ "°

~ - : 1.29

/

/

/ D, o/.~

\

o..*

"o.%% ;',,%~\

Do/

/.c 400

I

I

450

I

L

I

L

500 550 Wavelength (nm)

I

~

600

•

k

~

6 0

FIGURE 8. Photodichroism: example of an experiment in which the dichroic ratio of a layer of microvilli was decreased from 2.37 to 1.83 by a fractional bleach with light polarized parallel (e,) to the microvillar axes. Labeling and other experimental details otherwise as described in the caption to Fig. 7. Fig. 5 A , B shows the dichroic ratios R, and R± for each o f the cases o f R0 discussed in section C. In each instance the hypothetical bleach was "saturating," in that kll a n d h . were assigned their m a x i m a l values (see A p p e n d i x ) . E x a m i n a tion o f the curves in Fig. 5 shows that p h o t o i n d u c e d dichroism can be e x p e c t e d to alter the dichroic ratio by a factor o f a p p r o x i m a t e l y 1.5-3.0 (R±/Ro or Ro/Rtl) o v e r a wide r a n g e o f values o f ~bd, 0d, a n d Rf. ( T h e cusps on the curves f o r R ± in Fig. 5 B are o f little practical significance; they occur when Eq. (13 c ) a n d (1:3d) give the same value for k±max). Model I generates curves similar to those in Fig. 5, except (a) the values o f Of are a b o u t half as large as 0d for equivalent values o f R0, and (b) with 0 fixed,

Restricted Diffusion of Pigment in Photorece#tors

GOLDSMITH AND W~'HNER

467

c o r r e s p o n d i n g curves o f R0, R~, a n d R± c o n v e r g e for low values o f (A,~,T h i s is because w h e n the population o f c h r o m o p h o r e s occupies a limited distribution o f angles, t h e r e is less p h o t o d i c h r o i s m . In the limiting case (+ a n d 0 both fixed), there is no possibility o f p h o t o i n d u c i n g dichroism with e~l, and R~ = R0. In o r d e r to a p p l y the m a t h e m a t i c a l m o d e l to e x p e r i m e n t a l data, two transformations are m a d e ; the first is c o n v e n i e n t , the second is necessary. P h o t o i n d u c e d dichroism is d e f i n e d as R + / R o a n d Ro/RI~, thereby restricting attention to the c h a n g e in dichroic ratio i n d u c e d by the bleaching b e a m , a n d facilitating c o m p a r ison between results with ett a n d e~ bleaching lights. P h o t o i n d u c e d dichroism, thus d e f i n e d , is a positive n u m b e r larger t h a n 1.0. Second, p h o t o i n d u c e d dichroism must be related to s o m e m e a s u r a b l e p a r a m e t e r . D e g r e e o f bleach in the o p t i m a l angle (i.e. e x p r e s s e d in terms o f fractions of/~max a n d k±max) c a n n o t be m e a s u r e d directly; however, fractional a b s o r b a n c e loss, m e a s u r e d with light polarized parallel to the e-vector o f the bleaching b e a m , can. Fig. 9 shows theoretical curves for p h o t o i n d u c e d dichroism as a function o f the fraction o f the p i g m e n t - m e a s u r e d with e-vector coincident with the plane o f polarization o f the bleaching b e a m - t h a t has b e e n bleached. T h e curves in Fig. 9 were calculated for 0~ = 40 ° a n d Rf - 1.26; but as the value o f Rt has a small effect, they t h e r e f o r e c o r r e s p o n d to a case very similar to that shown with the solid curves in Fig. 5 B. As Fig. 9 indicates, the model makes two interesting predictions. First, the m a g n i t u d e o f the p h o t o i n d u c e d dichroism d e p e n d s on the gO°90 ~

o . R~

*d=/ /o.

2.0

Ro

E

///t

// //,,,'j:

//70 ~

5

/

~5

R,f = t. 2 6

0=,

o-

/ 6~/s60"

/ ,; ¢~, /

2

~o.

/

a

4o@,~"

/

n l.O

0.2 0.4 0.6 0.8 Fraction Bleached in Polarization Axis of Actinic Beam

FIGURE 9. Theoretical plots of photoinduced dichroism in microvilli, Ro/R, or R J Ro, vs. fraction of the absorbance (measured with e-vector parallel to the plane of polarization of the actinic beam) that has been bleached, and based on model II. Fraction bleached = (D~I - D,I)/D~I or (Do~ - Dl)/Doi, where Do is the initial density (absorbance) of pigment, D is the absorbance after a fractional bleach, and the subscripts II and ± refer to the plane of polarization of the measuring beam with respect to the microvillar axes. Absorbances are based on partial and total bleaches, thereby eliminating the effect of light scatter. R0 = initial dichroic ratio (from Eq. [8]); R~ = dichroic ratio after a fractional bleach with e-vector parallel (e~) to the microvilli (from Eq. [ 11 b]); R~ = dichroic ratio after fractional bleach with e± (from Eq. 14 b). Each family of curves shows expected results for various values of 4)a on the assumption that 0d = 40°, and the form dichroism (Re) is 1.26. Solid curves are for bleaching light with e,; broken curves for a bleaching light with e±. For most values of 4)a, the curves for e, lie above their counterparts for e,.

468

T H E J O U R N A L OF GENERAL P H Y S I O L O G Y ' V O L U M E

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d e g r e e o f orientation o f the c h r o m o p h o r e s with the microvillar axes, being smaller (for any given fraction bleached), the smaller is ~a. T h u s a family o f curves is r e q u i r e d to show all possible degrees o f p h o t o d i c h r o i s m as a function o f fraction o f p i g m e n t bleached. Second, for any fraction bleached, and for all but the largest values o f 4~a, the m a g n i t u d e o f the p h o t o i n d u c e d dichroism d e p e n d s on the plane o f polarization o f the bleaching b e a m , b e i n g g r e a t e r for e± t h a n for ell. This is shown by the fact that for 4~d < +--80°, curves in the family d r a w n with dashed lines (e~) lie above their c o u n t e r p a r t s in the family d r a w n with solid lines T h e theoretical curves in Fig. 9 are based on the a s s u m p t i o n that individual molecules have b e e n frozen in place, as m i g h t be achieved in g l u t a r a l d e h y d e . In f o r m a l d e h y d e , however, the molecules m i g h t c o n t i n u e to wobble within the allowed distribution. It this h a p p e n e d , the p h o t o i n d u c e d dichroism would be less t h a n e x p e c t e d for a rigid array. (This can be u n d e r s t o o d by recalling the limiting case, t u r n i n g t h r o u g h +90 °, for which w h e r e should be no photoinduced dichroism, a n d all points should plot on the abscissa in g r a p h s o f the f o r m o f Fig. 9.) Fig. 10 c o m p a r e s e x p e r i m e n t a l results o b t a i n e d in g l u t a r a l d e h y d e a n d 2.5

~J-- glutaraldehyde / / /

~,

E

2.0

....n.... formaldehyde

//I

~5

//

0

/

0.2 0.4 0.6 0.8 FractionBleachedin PolarizationAxisof Actinic Beam

FIGURE 10. Photoinduced dichroism of crayfish rhabdoms fixed in glutaraldehyde (filled circles) and formaldehyde (open circles). The two uppermost curves are theoretical functions indicating the expected photodichroism if all possible axial orientations of chromophore occurred with equal frequency (&d = 90°) and the population was "frozen" in place by the treatment with glutaraldehyde. (Solid curve is for Ro/R,; broken curve for R.dRo; 0a = 40°; Rf = 1.26.) The curves through the data points have no theoretical significance. That the experimental points fall well under the two theoretical curves indicates that the absorption vectors have a significant net orientation with respect to the microvillar axes (compare Fig. 9). The numeral by each data point is the number of rhabdoms entering the average. Vertical error bars indicate ~ 1 SE, and the data have been grouped so that the horizontal error bars are all smaller than the symbols marking the data points. An analysis of variance indicates that the photodichroism in glutaraldehyde is significantly greater than in formaldehyde (P < 0.01).

GOLDSMITH

AND

469

RestrictedDiffusion of Pigment in Photoreceptors

WEHNER

f o r m a l d e h y d e . As a n t i c i p a t e d , b o t h curves lie well u n d e r the theoretical functions f o r Oa = -+90 °. T h e points f o r r h a b d o m s in g l u t a r a l d e h y d e , h o w e v e r , fall above those in f o r m a l d e h y d e , s u g g e s t i n g t h a t t h e b i f u n c t i o n a l a l d e h y d e has q u i e t e d s o m e m o l e c u l a r m o t i o n t h a t is p r e s e n t in f o r m a l d e h y d e . Fig. 11 is a f u r t h e r analysis o f results o b t a i n e d in the p r e s e n c e o f g l u t a r a l d e 2.0

90 °

Rj.

--°--

•

-.,~/ ,

50" /

I•5

Model I (fixedlilt)

/Z5// ~//'/ // /,

2.0'--

/T /

40.

" " //

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,,

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~_°

//

Model ~

1.5 ~~I~.~l/Od:40°

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//

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//~

40 °

I A "[ I i I , I ,, 0.2 0.4 0.6 0.8 Froction Bleoched in Polarization Axis of Actinic 8earn i

0

FIGURE 11. Comparison of measurements of photodichroism with theroretical curves. Model I, the chromophores are assumed to be tilted into the membrane at a fixed angle (Or) of 20°. Filled circles give photodichroism (R0/l~0 after fractional bleaching with eli; open circles show photodichroism (R±/R0) after bleaching with e±. In each case, the photodichroism increases with fraction of pigment bleached and, as predicted by theory, the points for e. lie above those for eii. As shown by the theoretical functions, the data fit reasonably well the curves for ~bd = 50°. Fit deteriorates as Of departs as much as 10° from the value shown. Model II, the filled circles follow ~bd = 50°; the open circles appear to fit slightly better the curve for ~bd = 40°. Other values o f 0d (not shown) give less satisfactory fits. Both model I and model II therefore agree in indicating that the chromophores lie within a fan of about +50 ° with the microvillar axis. h y d e in w h i c h the d a t a f o r e, a n d e l b l e a c h i n g lights a r e t r e a t e d separately. H e r e , too, t h e r e is a d i f f e r e n c e • G r e a t e r values o f p h o t o d i c h r o i s m a r e o b s e r v e d w h e n the b l e a c h i n g light is p o l a r i z e d p e r p e n d i c u l a r to the microvilli, as predicted by t h e o r y . T h e u p p e r h a l f o f the f i g u r e c o m p a r e s the d a t a with the p r e d i c t i o n s o f m o d e l I. Rf is a s s u m e d to be 1.26 a n d Of = 20 °. T h e r e is a g o o d fit to ~bd = 50 °, w h i c h c a n n o t be i m p r o v e d by o t h e r choices o f Of. T h e l o w e r h a l f o f the f i g u r e shows the c o m p a r i s o n with m o d e l I I . Rr is 1.26, a n d Oa = 40 ° •

470

T H E J O U R N A L OF G E N E R A L P H Y S I O L O G Y " V O L U M E 7 0 " 1 9 7 7

Theoretical curves for ~bd = 40 ° and 50° are shown and, as before, the fit is not readily i m p r o v e d by o t h e r choices of tilt p a r a m e t e r . If0o is m a d e grossly smaller, it becomes m o r e difficult to fit the data for ett and e.L with curves that have a c o m m o n value o f $0. T h e results may t h e r e f o r e be taken as a reasonable estimate o f the orientation p a r a m e t e r So, indicating that the absorption vectors lie within +-50 ° o f the microvillar axes. T h e implications for polarization sensitivity will be e x a m i n e d in the Discussion. E. Change in Orientation on Isomerization

Fig. 12 shows the d i f f e r e n c e spectrum for the conversion o f visual pigment to m e t a r h o d o p s i n when the r h a b d o m s are suspended in a m e d i u m containing 2.5% glutaraldehyde. In o r d e r to slow the subsequent destruction o f m e t a r h o d o p s i n , the p H was 7.4 r a t h e r than 9. Results are shown for m e a s u r e m e n t s with the evector o f the measuring beam parallel (closed circles) and p e r p e n d i c u l a r (open circles) to the axes o f the microvilli, and the difference spectra have been normalized at the long wave-length peak of the d i f f e r e n c e spectrum (wavelength o f m a x i m u m absorbance decrease). T h e curves for ~l and e . are not identical, as there is a relatively greater increase in absorbance for e±. I f the dichroic ratio for the initial (dark) pigment were the same as for m e t a r h o d o p s i n , the difference spectra should be superimposible. T h e relatively greater increase in absorbance with ej. means that the dichroic ratio o f m e t a r h o d o p s i n must be smaller than the dichroism o f the pigment originally present. Fig. 13 shows the same d i f f e r e n c e spectra when the r h a b d o m s are in 0.75% f o r m a l d e h y d e . T h e results are qualitatively similar, but the d i f f e r e n c e between the curves for ell and e± is even greater than in glutaraldehyde. T h e change in molecular orientation that accompanies isomerization must t h e r e f o r e be larger in f o r m a l d e h y d e than in glutaraldehyde. In glutaraldehyde, the positive peak in the normalized d i f f e r e n c e spectrum reaches values o f 0.8 for elq and 1.0 for e , . If there were no changes in orientation o f the c h r o m o p h o r i c region, the difference spectra should both peak at some intermediate value. Both 0.8 and 1.0 fall below the c o r r e s p o n d i n g values o f 1.1 and 2.1 obtained in f o r m a l d e h y d e . In other words, any possible intermediate value for the peak o f the d i f f e r e n c e spectrum in f o r m a l d e h y d e lies outside the range observed in glutaraldehyde. This means that in f o r m a l d e h y d e c o m p a r e d to glutaraldehyde, not only is there a greater orientation change accompanying isomerization, but a p p a r e n t l y a relatively greater increase in molar extinction coefficient is involved as well. T h a t is, if,=hmax~metais the molar extinction coefficient o f m e t a r h o d o p s i n at the hmax, and ~rlaoo the same for r h o d o p s i n , the ratio ~hma x Emeta/Erhod amax/ Xmaxseems to be greater in f o r m a l d e h y d e than in glutaraldehyde. T h e m e t h o d used to disentangle the orientation p a r a m e t e r s f r o m the ratios o f molar absorbance is described in detail in the A p p e n d i x . Its application d e p e n d s on knowledge o f the shapes o f the difference spectra for total bleaches and for m e t a r h o d o p s i n in the presence o f both glutaraldehyde and f o r m a l d e h y d e . T h e s e are available f r o m e x p e r i m e n t s (Goldsmith, 1977). T h e analysis also rests on the assumptions that (a) a b r i e f irradiation with o r a n g e light converts virtually all the r h o d o p s i n to m e t a r h o d o p s i n , and (b) m e t a r h o d o p s i n is the only photoproduct. Brief successive exposures to the actinic source indicate that the first

GOLDSMITH AND WEHNER RestrictedDi[fusion of Pigment in Photoreceptors

471

condition is met. E x p e r i m e n t s on the p h o t o b l e a c h i n g o f m e t a r h o d o p s i n indicate that it is spectrally h o m o g e n e o u s (Goldsmith, 1977) a n d , as with o t h e r a r t h r o pods, t h e r e is as yet no evidence for the f o r m a t i o n o f isorhodopsin. As m e t a r h o dopsin is bleached, p h o t o p r o d u c t s are f o r m e d with a b s o r p t i o n m a x i m a at

T~

+1.0

/!~\~J"

*h0

Difference Spectrum for Crayfish

/~

~[

Difference Spectrum

I~-'~,Tt \ ~\

~/

o 25 M

form'oldehyde

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~

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,

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0.25 M cjlutaraldehyde ',~ ,

,

I

;

,

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o,

II

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(.)

.5

\/

"6

nf -I.0

I

I

400

-h0

I

500 Wovelength(nm)

600

I

400

500

600

Wavelength(nm)

FIGURE 12. (Left) Difference spectrum for the photoconversion of the original pigment to metarhodopsin, after fixation in 2.5% glutaraldehyde. In order to minimize bleaching of metarhodopsin, the isomerizing exposure was 0.05 min, the (unpolarized) light contained only wavelengths longer than 585 nm, and the pH was 7.4. These conditions permit complete conversion to metarhodopsin with no measured bleaching of metarhodopsin. Average of 10 experiments (+SEM), normalized at the wavelength of maximum absorbance decrease. Note that the shape of the difference spectrum depends on the plane of polarization of the measuring light. FIGURE 13. (Right) Difference spectra for the photoconversion to metarhodopsin in the presence of 0.75% formaldehyde. Experimental conditions otherwise as described in the caption to Fig. 12. Average of nine experiments normalized at 575 nm, the wavelength of maximum absorbance loss. Note that in formaldehyde the shape of the difference spectrum is more sharply dependent on the plane of polarization of the measuring light than it is in glutaraldehyde (Fig. 12). shorter wavelengths, but the d i f f e r e n c e spectra o f Figs. 12 a n d 13 were measured u n d e r conditions d e s i g n e d to minimize the destruction o f m e t a r h o d o p s i n . M o r e o v e r , the analysis is based on a b s o r b a n c e changes at 475 n m a n d 575 n m , wavelengths w h e r e a b s o r p t i o n by such final p h o t o p r o d u c t s is not great. We t h e r e f o r e believe the second a s s u m p t i o n is also valid.

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Results o f calculations are shown in Table I. With model I, in the presence o f glutaraldehyde the relative molar extinction ¢~rneta/~rhofl~ is 1.09, and in the I, c k m a x / q : k m a x / presence o f f o r m a l d e h y d e it is 1.20. In neither case is the result strongly d e p e n d e n t on the values o f f o r m dichroism or the r a n g e o f orientation parameters assumed. I f one assumes that all of the orientation change that accompanies isomerization takes place as an increase in either d)d or 0d, the change in either case is about 0.9 ° in glutaraldehyde and 3.1 ° in f o r m a l d e h y d e . I f model II is applied, the results are similar except that the increase in the fan o f tilt angles is about 6° . For both models and each assumed set o f conditions, however, the orientation change in f o r m a l d e h y d e is ~3.5 times larger than in glutaraldehyde. TABLE

I

CHANGE IN ORIENTATION AND RELATIVE MOLAR EXTINCTION WITH ISOMERIZATION Of' -

0re

or meta

rhod

~d' - +d*

0d' - 0d§

~,ax/~maxll

Model I Formaldehyde Glutaraldehyde

3.05°+-0.t4°¶ 0.88°+-0.06 °

2.980-+0.80 ° 0.84°-+0.17 °

1.20+-0.01 1.09

Model II Formaldehyde Glutaraldehyde

3.26°+0.17 ° 0.920+-0.05 °

5.94 °+- 1.16 ° 1,66°+- 0.31 °

1.20---0.01 1.09

* C a l c u l a t e d f o r d)d' = 40° a n d 50°; Rf = 1.26 a n d 1.56. 1: Of' = 20 °. § 0d' = 40 °. II ~nax/¢~max meta rhod = Nxmax/M~ax; see D i s c u s s i o n for a n a l t e r n a t i v e i n t e r p r e t a t i o n o f t h e r e s u l t s in this column. ¶ Median and range of calculated values.

F. Absence of Anisotropic Scatter T h e e x p e r i m e n t s on local bleaching d e m o n s t r a t e d the presence o f significant lateral scatter o f a small bleaching beam. Presumably, the measuring beams, too, are subject to an equivalent scattering by the r h a b d o m . In i n t e r p r e t i n g microspectrophotometric m e a s u r e m e n t s made with plane-polarized light, it becomes i m p o r t a n t to know the e x t e n t to which the m e a s u r i n g beam is depolarized by scatter. Fig. 14 shows the f o r m o f an e x p e r i m e n t designed to answer this question. Bleached r h a b d o m s were placed on the stage o f a polarizing microscope with the optic axes o f the birefringent layer either parallel or p e r p e n d i c u lar to the transmission axis o f the polarizer. A mask was placed in the plane o f the field stop so that its image snugly f r a m e d the r h a b d o m , as shown by the diagram in Fig. 14. A photomultiplier tube was coupled to the trinocular head o f the microscope, and the intensity o f light transmitted by the r h a b d o m was measured as a function o f the angle, d), between polarizer and analyzer. F u r t h e r details are given in the caption to Fig. 14.

Restricted Diffusion of Pigment in Photoreceptors

GOLDSMITH AND WEHNER

473

As Fig. 14 shows, the intensity fell to less than 1% o f its full value without d e p a r t i n g f r o m the cosZ6 function, indicating that the scattered light collected by the microscope objective is not significantly depolarized. This in t u r n d e m o n strates that depolarization by scatter is not d e g r a d i n g o u r m i c r o s p e c t r o p h o t o metric m e a s u r e m e n t s o f dichroism. 100

i el I !

•

•Q

i/" 50

/ /"

30

/

o,

/

%o

\

/

\

\

?os.

I0

\

/

= E

5 3

Y I e

R

0.5 0.05

0.03

_ ; 0 ol

i 610o~

~

I

~

]

I

f

t

I

t

10

-30 ° 0° 30 ° 6 o Angle between Polorizer and Analyzer:

t

J 90 °

FIGURE 14. Linearly polarized light is not significantly depolarized as a consequence of scatter on passing laterally through a rhabdom. P, polarizer; A, analyzer; and R, rhabdom surrounded by a mask (placed in the plane of the field stop) and oriented with the optic axes of individual layers of microvilli either parallel or perpendicular to the transmission axes of the polarizer to eliminate rotation due to birefringence. Transmitted intensity was measured with a photomultiplier as a function of ~b, the angle between the polarizer and analyzer. With crossed polarizers, less than 0.7% of the light is transmitted, indicating that virtually all the light passing through the organelle into the collecting optics has maintained its plane of polarization. The wavelength band was broad (440-580 nm), and the numerical aperture of the collecting lens was 0.85, compared with 0.4 on the microspectrophotometer. DISCUSSION

Use of Aldehyde Fixatives As the a p p a r e n t absence o f diffusion o f m e t a r h o d o p s i n in crayfish p h o t o r e c e p tor m e m b r a n e s is observed after t r e a t m e n t with f o r m a l d e h y d e , it is a p p r o p r i a t e to explore the significance o f this condition.

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Brown (1972) r e p o r t e d that vertebrate p h o t o r e c e p t o r s fixed for 5-6 h in 5% f o r m a l d e h y d e at 25°C failed to exhibit photodichroism (and thus were still fluid), an observation c o n f i r m e d by Cone (1972). Edidin et al. (1976) f o u n d that 0.5% f o r m a l d e h y d e had no effect on the diffusion o f fluorescein-labeled m e m b r a n e proteins o f mouse fibroblasts, but they did observe that in this system 5% f o r m a d e h y d e blocked m o v e m e n t . In o u r e x p e r i m e n t s , 0.75% f o r m a l d e h y d e was used, and the r h a b d o m s were kept at 0°C for varying periods o f time (several minutes to several hours) before m e a s u r e m e n t at 20-22°C. On the basis o f this o t h e r work with m e m b r a n e protein it t h e r e f o r e does not seem likely that in o u r experiments the absence o f diffusion o f m e t a r h o d o p s i n was caused by the presence o f f o r m a l d e h y d e . Although this conclusion needs a m o r e rigorous p r o o f , it is s u p p o r t e d by two additional a r g u m e n t s . First, there clearly are differences between glutaraldehyde- and formaldehyde-fixed r h a b d o m s in the extent to which the m e t a r b o d o p s i n molecules can move or change shape: (a) the greater photodichroism in glutaraldehyde-fixed material (Fig. 10) indicates that this reagent d a m p s out some Brownian chatter that persists in f o r m a l d e h y d e ; (b) the smaller change in orientation on isomerization in glutaraldehyde (Figs. 12, 13; Table I) bespeaks either a more rigid m i c r o e n v i r o n m e n t or constraints on the possible conformational changes the molecule can u n d e r g o , or both. A second a r g u m e n t is perhaps more compelling. T h e presence o f photoinduced dichroism requires the absence o f molecular rotation. If Brownian rotation were normally present but were artifactually eliminated by aldehyde fixation, both glutaraldehyde and f o r m a l d e h y d e might "freeze" the population o f molecules so that all normally allowed angles o f axial orientation would be occupied. But the m e a s u r e m e n t s o f photodichroism fall well u n d e r the theoretical curves for $d = --+90°, indicating that not all axial orientations occur with equal probability (Figs. 10, 11). In o t h e r words, the m e a s u r e m e n t s o f photodichroism made in the presence o f glutaraldehyde, where we expect cross-linking (Richards and Knowles, 1968) to have blocked molecular diffusion, provide a n o t h e r line of evidence that free Brownian rotation does not occur. It should be recognized, however, that this a r g u m e n t carries the b u r d e n o f its own assumption, namely, that fixation does not arrest molecular rotations with the transition moments in certain p r e f e r r e d orientations.

Basis for the Absence of Diffusion T h e concept o f m e m b r a n e s as fluid mosaics is s u p p o r t e d by much evidence (Singer and Nicolson, 1972) including diffusional studies on cells o t h e r than p h o t o r e c e p t o r s (Edidin, 1974). T h e few quantitative estimates o f diffusion constant that have been r e p o r t e d , however, suggest that there may be variation in m e m b r a n e fluidity a m o n g d i f f e r e n t kinds o f cells. In lower organisms there is a wide range (several tens o f degrees centigrade) o f lipid phase transition t e m p e r a t u r e s , d e p e n d i n g on conditions o f growth (e.g., Steim et al., 1969; Overath et al., 1970; Eletr and Keith, 1972; Murata et al., 1975). Although the presence o f cholesterol in the plasma m e m b r a n e s o f higher animals obscures such transitions (Edidin, 1974), differences in fluidity may well occur between species o f animal as distantly related as frog and crayfish. Israelachvili and

GOLDSMITHAND WEHNER RestrictedDiffusion of Pigment in Photoreceptors

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Wilson (1976) have suggested that the fact that microvilli are neither planar nor s p h e r i c a l - a n d thus lack constancy of curvature over their s u r f a c e s - i s in itself evidence that the membranes are rigid. T h e rhabdoms of squid are reported to exhibit dichroic ratios as high as 6 (Hagins and Liebman, 1963). T h e photoreceptor membranes of crayfish may therefore be intermediate in fluidity between rod outer segment disks and the purple membrane of Halobacterium, with its highly ordered bacteriorhodopsin molecules (Henderson and Unwin, 1975). Vertebrate photoreceptor membranes are characterized by a very low content of cholesterol and a high content of long-chain polyunsaturated fatty acids (see Daemen, 1973, for review), conditions that may be responsible for the relatively rapid diffusion of rhodopsin in these organelles. Corresponding lipid analysis of rhabdomeric membranes are not as numerous, but data now available indicate that squid (Mason et al., 1973), Limulas (Benolken et al., 1975), and insects (Zinkler, 1975) have several times as much cholesterol as, and probably a somewhat lower content of polyunsaturated fatty acids than vertebrate rods. This implies that their membranes may be stiffer and diffusion of rhodopsin correspondingly slower. As no analyses of the lipid content of crayfish rhabdoms have been done, the argument cannot be carried further at this point. Basis for Molecular Orientation

Although a relatively stiff lipid environment could explain the absence of measurable translational diffusion and perhaps even rotational diffusion, it would not seem to account for a net alignment of chromophores with the microvillar axes. Laughlin et al. (1975) and Snyder and Laughlin (1975) have proposed that orientation of rhodopsin in microvillar membranes might arise from thermodynamic constraints in turning an elongate rhodopsin molecule within the curved surface of a microvillus. T h e y postulate that an elongate protein with polar and nonpolar regions on its exterior might float in the membrane with its long axis roughly parallel to the microvillus, but that rotating it 90° about an axis normal to the surface of the membrane would cause its ends to lift out of the lipid phase and might therefore be accompanied by a significant energy barrier. Vertebrate rhodopsin in digitonin micelles is asymmetric, as it orients to shear (Wright et al., 1972, 1973). T h e radius of crayfish microvilli is about 350 ~ (Eguchi, 1965), and minimum estimates of the length of vertebrate rhodopsin of 75 A (Wu and Stryer, 1972) and 90/~ (Yeager, 1976) have been reported. In the latter study, evidence was also obtained that the long axis lies at right angles to the membrane, which does not support Snyder and Laughlin's model. Moreover, a 75-A molecule rotated 90 ° on the surface of a cylinder 350 A in radius has its ends lifted out of the membrane by only 2 ~. Finally, although this model speaks to the presence of axial orientation of pigment molecules, it does not predict an absence of translational diffusion. Still another kind of mechanism that might be invoked to account both for molecular orientation and absence of measurable diffusion is attachment of the rhodopsin molecules to a relatively fixed matrix. One thinks in this context of spectrin, the membrane-associated protein of red blood cells (Marchesi and

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Steers, 1968; Marchesi et al., 1976). Clearly, much m o r e work will have to be done before the molecular architecture o f these m e m b r a n e s is u n d e r s t o o d .

Choice of Angular Distribution Functions Model I supposes that tilt o f the absorption vector into the m e m b r a n e is the same for every molecule. Model II assumes that tilt angles are uniformly distributed t h r o u g h all allowed angles. T h e s e two assumptions bracket a range o f additional possibilities including, for example, a Boltzmann distribution over a limited range o f 0. T h a t the e x p e r i m e n t a l results on photodichroism are reasonably compatible with either model shows that the specific choice o f angular distribution function is not critical. T h e fit o f results to model I is perhaps slightly superior. I f tilt angle is constant (fixed 0), the presence o f photodichroism demonstrates that the transition moments must be distributed t h r o u g h a range o f values o f ~b. Considerations o f symmetry suggest that these values occur to both sides o f the microvillar axis, and a Boltzmann distribution is a physically plausible supposition. F u r t h e r work will be required to see w h e t h e r there is any basis in e x p e r i m e n t for favoring one o f several possible mathematical models.

Change in Orientation on Isomerization T h e transition m o m e n t reorients several degrees as r h o d o p s i n is c o n v e r t e d to metarhodopsin. T h e result is that the absorption vector associated with metar h o d o p s i n is either tilted m o r e out o f the plane o f the m e m b r a n e , or has a r e d u c e d alignment with the microvillar axes, or both. A change o f the same m a g n i t u d e has also been seen in lobster (Homarus) ( B r u n o et al., 1977). Acid m e t a r h o d o p s i n o f c e p h a l o p o d mollusks reorients in the same sense, but the change ( - 1 5 °) is several times larger (Tafiber, 1975; Schlecht and Ta/iber, 1975). In frog (Rana) o u t e r segments m e t a r h o d o p s i n I is r e p o r t e d to have approximately the same orientation as r h o d o p s i n ( T o k u n a g a et al., 1976), but m o r e recent m e a s u r e m e n t s f r o m the same laboratory indicate that m e t a r h o d o p s i n I is tilted about 3° f u r t h e r out o f the plane o f the disk m e m b r a n e than r h o d o p s i n (F. T o k u n a g a , personal communication). Results f r o m three phyla are thus qualitatively similar. T h e hypsochromic shift in kmax o f crayfish rhodopsin to m e t a r h o d o p s i n is about 20 n m in both f o r m a l d e h y d e and glutaraldehyde. Moreover, the halfbandwidth o f both r h o d o p s i n and m e t a r h o d o p s i n is 4,550 -+ 80 cm -1 in either f o r m a l d e h y d e or glutaraldehyde (Goldsmith, 1977). T o a first a p p r o x i m a t i o n , t h e r e f o r e , the isomerized c h r o m o p h o r e finds its a p p r o p r i a t e , " m e t a r h o d o p s i n " relationship with the surface o f the opsin in the presence o f either aldehyde. A closer look, however, indicates that there are detectable differences. T h e reorientation o f the transition m o m e n t , although small, is 3.5 times larger in f o r m a l d e h y d e than glutaraldehyde, regardless o f which model or which parameters are used in the calculation (Table I). T h e reorientation of the transition m o m e n t t h e r e f o r e seems to involve not just isomerization o f the c h r o m o p h o r e but some concomitant shifting o f the surface o f the opsin as well. This shifting is constrained by a reagent that readily cross-links via bridges o f variable length (Richards and Knowles, 1968).

GOLDSMITHAND WEHNER RestrictedDiffusion of Pigmentin Photoreceptors

477

T h e a p p a r e n t l y greater molar extinction o f m e t a r h o d o p s i n in f o r m a l d e h y d e as o p p o s e d to g l u t a r a l d e h y d e - t r e a t e d r h a b d o m s can be i n t e r p r e t e d as indicating (with equal bandwidths) that the oscillator strength o f m e t a r h o d o p s i n is r e d u c e d - 1 0 % by glutaraldehyde. On the o t h e r h a n d , the same e x p e r i m e n t a l result could have been caused by a small loss o f m e t a r h o d o p s i n t h r o u g h photobleaching. Although the e x p e r i m e n t was designed to minimize this possibility, a loss o f m e t a r h o d o p s i n would be indistinguishable (in Eq. [23] and [24]) f r o m a real decrease in the relative extinction coefficient (N/M), but would not affect conclusions about the orientation parameters. T h e possibility o f a few percent loss o f pigment cannot t h e r e f o r e be excluded as an alternative explanation for the lower value of N / M , but it does not account for the smaller reorientation o f transition m o m e n t that is seen in glutaraldehyde.

Implications for Polarization Sensitivity T h e orientation p a r a m e t e r s estimated f r o m the m e a s u r e m e n t s o f p h o t o d i c h r o ism can be used to predict the linear dichroism that should be observed in r h a b d o m s f r o m d a r k - a d a p t e d eyes. For example, 4~d = 40°-50°, 0d = 40 ° (model II) c o r r e s p o n d s to a dichroic ratio R0 = 5-7 (Fig. 5 B). This is about twice the value m e a s u r e d on the isolated r h a b d o m by m i c r o s p e c t r o p h o t o m e t r y (Goldsmith, 1975). It is in good a g r e e m e n t with an average ratio o f polarization sensitivity o f 6.2 m e a s u r e d in crayfish retinular cells by Shaw (1969), although it is lower by a factor o f two than the largest such values (Shaw, 1969; W a t e r m a n and F e r n a n d e z , 1970). In view o f the technical differences in making these two kinds o f m e a s u r e m e n t , the results o f studies o f photodichroism and electrophysiological studies o f polarization sensitivity are in reasonable h a r m o n y . T h e situation would be m o r e satisfactory, however, if we could account for the consistently lower values o f dichroic ratio m e a s u r e d directly by microspectrop h o t o m e t r y . A f u r t h e r analysis o f this p r o b l e m , too lengthy for inclusion in this Discussion, will be p r e s e n t e d elsewhere. Several factors conceivably affecting dichroic ratio can be briefly m e n t i o n e d here. (a) Depolarization by scatter is not a significant source o f trouble (Fig. 14). (b) Depolarization caused by d e p a r t u r e f r o m collimation (the effect o f numerical a p e r t u r e o f the c o n d e n s o r [H~irosi and Malerba, 1975]) degrades o u r dichroic ratios by only a few percent. (c) D e p a r t u r e o f the microvilli f r o m cylindrical cross-sections, to the extent it occurs, appears to be r a n d o m (Eguchi, 1965). (d) Some relaxation o f the molecules f r o m their orientation in vivo when the r h a b d o m s are separated f r o m their retinular cells is a possibility (Goldsmith, 1975), but there is no clear evidence pro or con. (e) Some rotational misalignment o f the r h a b d o m s a r o u n d their long axes is inevitable, but by measuring dichroic ratio in two contiguous bands o f microvilli it is possible to recognize and correct for this problem (Goldsmith, 1975). (f) Rotational misalignment o f the r h a b d o m about the axis o f propagation o f the measuring beam will p r o d u c e a more serious degradation o f dichroic ratio. Although such misalignment should be readily seen, its c o u n t e r p a r t at the level o f microvillar orientation is not observable in the light microscope. For example, u n d u l a t i n g microvilli will have significantly less dichroism than straight cylinders. T h e relative effects o f such disorganization on dichroism and photodichroism are currently being explored.

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T H E J O U R N A L OF G E N E R A L P H Y S I O L O G Y " V O L U M E

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• 1977

Packing Density of Photopigment W h e n cut in cross-section, the microvilli are seen to o c c u p y a h e x a g o n a l lattice, a n d the a v e r a g e d i a m e t e r o f the microvilli is 7 × 10 -2 ftm ( E g u c h i , 1965). I n m a k i n g a b s o r b a n c e m e a s u r e m e n t s o n isolated r h a b d o m s the a v e r a g e p a t h l e n g t h is f o u n d to be ~ 2 5 /xm. T h e n u m b e r o f microvilli t r a v e r s e d by the m e a s u r i n g b e a m , rj, is t h e r e f o r e 25/(7 × 10 -~) (cos30 °) = 412. T h e n u m b e r o f molecules p e r unit a r e a o f m e m b r a n e , no, can be c o m p u t e d f r o m Eq. (6) (see also Eq. [18], [19], a n d [20]). 2.3D011

no

"oRfML(~b, 0)'

o r f r o m Eq. 7, 2.3D0 ±" 2

no = ~M[RfW(6, O) + H(dp, 0)]" I n p e r f o r m i n g the calculations, values o f ~DoH a n d ~D0 ± are o b t a i n e d f r o m m e a s u r e m e n t s o f a b s o r b a n c e , a n d values o f t h e n o r m a l i z e d a b s o r p t i o n coefficients L(~b, 0), W(~b, 0), a n d H(~b, 0 ) - w h i c h describe h o w a b s o r b a n c e is partit i o n e d a m o n g al, aw, a n d a n - are o b t a i n e d f r o m Eq [18], [19], a n d [20], by using estimates ofqba, Of, a n d 0a f r o m e x p e r i m e n t s o n p h o t o d i c h r o i s m . M = 3a0 w h e r e a0, the Beers law m o l e c u l a r a b s o r p t i o n coefficient, is a s s u m e d to be 1.56 × 10 -16 c m 2, c o r r e s p o n d i n g to a m o l a r a b s o r p t i o n coefficient (~) o f 40,600 liter c m -1 mo1-1. T h i s f i g u r e , m e a s u r e d f o r v e r t e b r a t e r h o d o p s i n (Wald a n d B r o w n , 1955), is a r e a s o n a b l e estimate f o r crayfish r h o d o p s i n , if o n e j u d g e s f r o m t h e h y d r o x y l a m i n e d i f f e r e n c e s p e c t r u m p u b l i s h e d by W a l d (1967). I n principle, u s i n g e i t h e r Eq. 6 o r Eq. 7 to calculate ~90 s h o u l d give the s a m e result. I n practice, Eq. (7) yields values a l m o s t two times h i g h e r . T h i s is b e c a u s e the d i c h r o i c ratio that is m e a s u r e d in d a r k - a d a p t e d r h a b d o m s is smaller t h a n that calculated f r o m Eq. (8) (by u s i n g values o f qbd, 0r, a n d 0d r e f e r r e d to above). T h i s d i s c r e p a n c y was m e n t i o n e d in the p r e c e d i n g section. O n the o t h e r h a n d , choices o f Rf a n d o f m o d e l I o r m o d e l I I are relatively less i m p o r t a n t . C a l c u l a t e d values o f 77o are s u m m a r i z e d in T a b l e I I a n d are in the r a n g e 1-2 × 10 TM molecules c m -2. At a density o f 1-2 × 10 TM molecules c m -2 a n d o n t h e a s s u m p t i o n o f a h e x a g o n a l lattice, the m e a n distance b e t w e e n c e n t e r s o f molecules is 76-107 ~ . TABLE

II

C A L C U L A T E D DENSITIES OF RHODOPSIN MOLECULES PER U N I T AREA OF M I C R O V I L L A R MEMBRANE

Rt

no (model I) molecules cm-2

molecules cm-2

no (model II)

Eq. (6) (el,)

1.56 1.26

1.01-0.34× 1012 1.25+-0.42× 1012

1.03+0.35× 10TM 1.28±0.43× 1012

Eq. (7) (e±)

1.56 1.26

1.85±0.87× 10lz 2.15± 1.01 × 10TM

1.79-+0.84× 10TM 2.06-+0.97 × 1012

Calculations based on Eq. (6) and (7), as described in the text. rtDm~= 0.091 ± 0.0300 SD; average R0 (measured; corrected for self-screening; uncorrected for possible rotational misalignment) = 2.81 -+ 0.942 SD ('oD0± = T?Do/Ro);d~d = 500; Of = 20° (model I); 0d = 40° (model II).

GOLDSMITHAND WEHNER RestrictedDiffusion of Pigment in Photoreceptors

479

T h e r e are two recent f r e e z e - f r a c t u r e studies o f crayfish microvilli in which 8090-,~ d i a m e t e r particles have b e e n o b s e r v e d at a similar density on the protoplasmic leaflet o f the cleaved m e m b r a n e s . F e r n a n d e z a n d Nickel (1976) r e p o r t that in e x a m p l e s showing densest packing, the c e n t e r - t o - c e n t e r distance is 85 ~ , a n d Eguchi a n d W a t e r m a n (1976) find a v e r a g e interparticle distances o f 110 _+ 10 A. ( T h e latter a u t h o r s ' evidence for t u r n o v e r o f particles with light a d a p t a t i o n f u r t h e r suggests that the f r e e z e - f r a c t u r e images reflect the p r e s e n c e o f r h o d o p sin as well as indicating a possible reason why their a v e r a g e values o f particle density are a b o u t 20% h i g h e r t h a n those o f F e r n a n d e z a n d Nickel.) As X-ray diffraction o f the disk m e m b r a n e s o f r o d o u t e r s e g m e n t s indicates a b o u t 70/~ between nearest r h o d o p s i n n e i g h b o r s (Blasie et al., 1969), the density o f packing o f visual p i g m e n t in a r t h r o p o d a n d v e r t e b r a t e p h o t o r e c e p t o r m e m b r a n e s appears similar. Values o f "O0 can be c o n v e r t e d into concentrations o f p i g m e n t in the total v o l u m e o f the r h a b d o m by the following a r g u m e n t . Let d be the d i a m e t e r o f a microvillus (d = 7 x 10 -6 cm). T h e surface a r e a o f a 1-cm length o f microvillus is t h e r e f o r e ~'d cm z, a n d the n u m b e r o f microvilli in 1 cm 3 o f r h a b d o m is 1/d × 1/d cos30 °. T h e total m e m b r a n e surface in 1 cm 3 o f r h a b d o m is t h e r e f o r e 7r/d cos30 ° = 5.18 x 105 cm 2. 1 cm a o f r h a b d o m thus contains 5.18 x 105 cm 2 x 70 molecules. For 7/0 = 1-2 x l0 TM, the c o n c e n t r a t i o n is a b o u t 0.9-1.7 m M . T h e s e estimates can be c o m p a r e d with values o f 3.1-3.8 m M (Hfirosi, 1975; L i e b m a n , 1975) calculated for various a m p h i b i a n o u t e r segments.

Other Photoreceptors Have Oriented Pigment Molecules T h e a r t h r o p o d r h a b d o m is not the only place w h e r e p h o t o r e c e p t o r molecules are o r i e n t e d a n d w h e r e the system seems designed for differential r e s p o n s e to linearly polarized light. H a u p t (1972, 1973) has described the p h o t o c o n t r o l o f chloroplast orientation i n the filamentous g r e e n alga Mougeotia. A l t h o u g h the p i g m e n t that mediates this r e s p o n s e is p h y t o c h r o m e , the system shares several features with the crayfish r h a b d o m . (a) T h e p i g m e n t molecules are lo~:ated in the cortical cytoplasm, either in the plasma m e m b r a n e or attached to its i n n e r surface. (b) T h e transition m o m e n t s are not r a n d o m l y disposed in the m e m b r a n e , but have a fixed, in this case helical, p a t t e r n a r o u n d the surface o f the cylindrical cell. (c) P h o t o c o n v e r s i o n o f the r e d - a b s o r b i n g f o r m (P6~0) to the far r e d - a b s o r b i n g f o r m (P730) is a c c o m p a n i e d by a significant reorientation o f the absorption vector. In the P660 f o r m the a b s o r p t i o n vector lies in the t a n g e n t plane o f the cylindrical cell, whereas in the P730 f o r m it is t i p p e d m o r e nearly n o r m a l to the plasma m e m b r a n e , b e c o m i n g radially o r i e n t e d with respect to the cylindrical cell. T h e s e conclusions, based on elegant e x p e r i m e n t s in which the cells were stimulated with m i c r o b e a m s o f plane-polarized light, indicate a relatively rigid a n c h o r i n g o f the p i g m e n t molecules in a matrix either associated with or identical to the p l a s m a l e m m a . APPENDIX

Dichroism of Microvilli Consider a cylindrical microvillus irradiated normal to its axis with collimated light, polarized either parallel, ell, or perpendicular, e~, to the microvillar axis (Fig. 1). Each

480

THE JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 70 •

1977

molecule of pigment lies near the surface of the cylinder with its transition moment making an angle $, measured in the tangent plane, with a generator of the cylinder; and an angle 0, also measured from the generator, but in the plane defined by the long axis of the cylinder and a radius of the cylinder. ~ is thus the angle, measured in the tangent plane, between the chromophore's axis and the microvillar axis; and 0 is the tilt of the chromophore's axis into the membrane. At an arbitrary point on the circumference of the cylinder, located at an azimuthal angle $ from a reference radius (see Fig. 1 C), the transition moments of all molecules can be resolved into three mutually perpendicular absorption vectors: ~l, parallel to the longitudinal axis of the cylinder; aw, perpendicular to oq and lying in the tangent plane; and (xh, lying along a radius of the cylinder. T h e absorbance measured with polarized light is found by s u m m i n g absorbance through all angles of" $ from 0 to 2zr and averaging over 2~r. For ell, absorbance is i n d e p e n d e n t of ~ and is simply proportional to al. For ez, however, absorbance is proportional to aw

i0

cos2~/dqJ+ ah

f0

sin2t~ dqJ = 1_ (~v, + '~h).

2

f02~ dqJ

T h e intrinsic dichroic ratio of the cylinder, R~, is thus given by p

O/1

R 0 = ½(aw + ah ).

(1)

T h e total dichroism, R0, is obtained after taking form dichroism into account (Snyder and Laughlin, 1975). Ro = Dol~l Do±

2Rfal

(2)

(Xh + Rfoz w'

n 4

where Rf = 24, and nm and nc are refractive indices of the m e m b r a n e and cytoplasm, rt c

respectively. We shall now consider how the absorbance coefficients, a, depend upon the angular orientation of the chromophores. For each molecule (Fig. 15) a ° = M cos26 cosZ0,

(3)

s ° = M sinZ~bcos20,

(4)

a ° = M sin20,

(5)

where M is the molecular absorbance coefficient for a molecule aligned with its transition moment parallel to the e-vector of the irradiating source. For a completely r a n d o m distribution of molecules, all values of 0 and 4) would be equally populated. Measured values of microvillar dichroism, however, are too high to be consistent with random orientation (Goldsmith, 1975) and imply some degree of orientation with the microvillar axes. T h e simplest assumption for oriented chromophores is that they are rigidly locked in the membrane at fixed angles Of and ~bf. This hypothesis, however, is not consistent with the experimental observation of photoinduced dichroism. Building on Liebman's (1962) analysis of dichroism in rods, we have explored two models. Model I assumes that the chromophores are tilted into the m e m b r a n e at some fixed angle Of, but that they are free to occupy all angles (b between limiting values +~bd.

WEI-INER Restricted Diffusion of Pigment in Photoreceptors

GOLDSMITH AND

481

Small values o f 4~a and Ot t h e r e f o r e m e a n relatively s t r o n g orientation with the microvillar axis. tho = ---90° c o r r e s p o n d s to r a n d o m o r i e n t a t i o n o f absorption vectors in the t a n g e n t plane. M o d e l II is similar, e x c e p t that r a t h e r than the tilt angles b e i n g fixed, they are distributed b e t w e e n 0 = 0 a n d s o m e limiting value 0 = 0d ( Rt sin2~bd k±max =

1/sinZOd,

(13C)

and for sin20a < Rt sinZqbd, k±max = 1/(Rf sin2~a).

(13d)

As with e,i, we treat only partial bleaches that do not totally d e p o p u l a t e any but the optimal angle. T h e absorbance DII after a fractional bleach with e_ is found by substituting np (Eq. [12]) for n in Eq. (6). Similarly, D± is obtained by substituting np (Eq. [12]) for n in Eq. (7). T h e new dichroic ratio, R± = is then given by Eq. 14a (model I) or 14b (model II).

D,/D±

Mo&lI Rf cos2Otf~ cos2dpddp- Rtk±cos2Otsin2Off~_~dcos2dpd~PI

l

Rj. =

R~k. cos40t f*d

-

(14a)

sinZcb d~b + ~bd sinZ0r - k_ ~bd sin40r

~ - COS20f

-

c°s2~b sin2~b d~

a --~d

Rtk±sin2Of cos20f

f?

sin2~b dtb -

R 2 cos40f

*d

f?

sin4~b d~b

~a

Model H

l

[

~d

Rf f~,~dcos2~b d(b

OdcosaOdO-k.f' ~d,c°sZ&d~h ~ foOdC°S3Osin2OdOI

fo

fo

- Rfki j " sin2~ c0s24) d4~

cosS0 dO

*a

2

,. Od

-

k± ~d

sin40 cos0 dO -

Rtk±

*d

Od

sin2~ dd)

cos30 sin20 dO

Oa

~f k±

d~b

cosS0 dO

As before, in evaluating Eq. (14a) or (14b) we observe the condition 0 < k < k±max. T h e curves in Fig. 5, denoted Rll and R±, show c o m p u t e d results for Eq. l l b and 14b for k = klnax •

For comparison with experimental data, we define photoinduced dichroism after bleaching with el~as the dichroic ratio before the actinic exposure divided by the dichroic ratio after exposure, In the case of bleaches with e . , it is the reciprocal, Photoinduced dichroism, a ratio of ratios, is therefore a positive n u m b e r greater than unity and is calculated from Eq. (8), (11), and (14) for various values of and Although the coefficients kll and k_ are not directly measurable, the fraction of pigment bleached in the polarization axis of the actinic beam is and can be c o m p u t e d from the numerators of Eq. (8), (11), and (14) for e,, and the denominators for e±. For el~,

Ro/R,.

k±/k.max.

R./Ro. kb~/kl~nax,

GOLDSMITH AND WEHNER RestrictedDiffusion of Pigment in Photoreceptors

485

the fraction bleached is (Dolj - Dl~/Do,; and for e . , the fraction bleached is (Do. - D±)/Do±. Photoinduced dichroism and fraction bleached are the functions plotted in Figs. 9-11. As pointed out above, Eq. (11) and (14) do not describe dichroic ratio over the complete range of bleaching. They are valid only when the irradiating exposure is small enough that none other than the most vulnerable angle is completely bleached. This is why the theoretical curves in Fig. 9 do not cover all values of "fraction bleached"; the curves terminate near points set by the definitions ofkl~ax and k-max. This limitation, however, is of no practical consequence in comparing theory with experimental data. T h e reason is that as fraction bleached approaches 1.0 and the photodichroism increases steeply, the accuracy of measurement deteriorates precipitously, because one of the absorbance values sinks into the noise level.

Changes in Molecular Orientation on Isomerization; Relative Molar Absorbance of Pigment and Photoproduct In solution, the difference spectrum associated with the isomerization of rhodopsin to metarhodopsin reflects the fact that the absorbance spectra of these two forms are not identical. In the rhabdom, the difference spectrum also depends on the plane of polarization of the measuring light, indicating that isomerization is accompanied by a change in molecular orientation (see Figs. 12, 13). Heretofore we have written absorbance coefficients for the pigment, al, aw, and ah (Eq. [3-5]; Fig. 15). Now it becomes necessary to distinguish more carefully between rhodopsin and its photoproduct by defining three corresponding coefficients, /3], /3w, and Oh for the metarhodopsin. Reiterating the a r g u m e n t that underlies Eq. (6) and (7), the normalized absorbance coefficients for rhodopsin can be written

L(c~, O) = al/M =

f f

cos~4~ cos20 ds ,

(15a)

,

(16a)

W(4~, O) = aw/M =

H(c~, O) = a J M

=

,

(17a)

where M is the molecular absorbance coefficient for rhodopsin perfectly oriented parallel to the plane of polarization of the measuring light. Similar functions can also be written for metarhodopsin,

L'(flp, O) = OLIN,

(15 6)

W'(c~, O) = Ow/N,

(166)

H'(c~, O) = Oh~N, where N is the molecular absorbance coefficient for perfectly oriented metarhodopsin. Specifically, integrating Eq. (6) and (7) in the case of model I,

486

THE JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 70 " 1977

L(4,,,, 0,) = ~cos'O,ffd*. cos2¢ d,~ = cos ,0, [1~ + 4 - - ~ - .4J' W(¢d, O0 = ~

j_,~. sin'¢ de = cos'O~

~

(18a)

-j,

(19)

H(41d, Of) = sin'0f.

(20 a)

The corresponding normalized absorbance coefficients for metarhodopsin differ by the substitution of 0t' for Of (if tilt angle changes on isomerization), and ~bd' for ¢ba (if the fan of axial orientations changes). For model II, cos'41 d4i L ( ¢ d , Of) = a - * .

W(4,a, Of) =

cos30 dO

24~d sinOd

= [1 + 4sin24~"] ~ - d J [COS203d+ 2] ,

(18b)

]

(19 b)

/ °*~sin2~b d4) fo°"cosa0 dO

i

~a

,

0, sin'0 c o s 0 dO

H(~bd, 0d) = "

sin0d

sin'0a

3

( 2 0 b)

L'(~b, 0), W'(4~, 0), and H'(~b, 0) are obtained by substituting ~bd' for (ha and 0d' for Oa. Note that L(dO, O) + W(6, O) + H(~b, 0) = 1 and L'(4,, O) + W'(eo, O) + H'(4,, o) = 1. The change in absorbance on isomerization-the difference s p e c t r u m - i s 2.3AD,i(M = Rt[b(k) #, - a(k) oq],

(21a)

R~ 1 2.3AD±(k) = ~ [b(k) ~w - a(k) aw] + ~ [b(k)/3h - a(k) ah],

(22 a)

where AD is the absorbance change per unit path length and concentration, ~rhod M(k) a00 = =E(rhod a)-= xmax M x~,, '

and

= Eo.)meta= N(k)_ b(,k) emeta N~m,,. x,,~,

The functions a(M and b(~) are therefore the relative absorbance spectra of rhodopsin and metarhodopsin, and can be determined from experimentally measured difference spectra for total bleaches, as presented in Goldsmith (1977). We can write for the absorbance changes at two selected wavelengths near the positive and negative peaks of the difference spectra --ADIm75 --= ~ 3 [0"67s C~I -- b575 i(tl]'

(21b)

ADII475 = ~ 3 [b475 ~1 -- a475 O/l]"

(21 £)

Let Qll = ADli475/-AD,.~75. QJi is measured directly from the normalized difference spectrum (Figs. 12, 13). Combining Eq. (21b), (21c), (15a), and (15b), and rearranging, N = [1.0 - W(4~, 0) - H(+, 0)][Q1#575 + a475] m L'(cb, 0)[Qiib575 + b475]

(23)

GOLVSMXTH AND WEHN~R Restricted Diffusion of Pigment in Photoreceptors

487

T h e data m e a s u r e d with e± can be treated in a similar fashion: Rf 1 -- AD±575 = (2.3)(2) [a5,5 aw - 65,5 flw] + ( 2 . ~ ) AD±475 = (2.3)(2)R~[6475/~w - a475 Otw] + ~

1

[as,50th

-

-

6575 ~[~h],

[b475 Bh - a,,i,s ah].

(22 b) (22 C)

Let Q± = ADi4,s/-AD±5,5. C o m b i n i n g Eq. (16a), (16 b), (17 a), (17 b), (22 b), a n d (22c) a n d r e a r r a n g i n g , N = [W(~b, O)R~ + H(4a, O)][Q±a57s + a4,5] M [W'(~b, O)Rf + H'(~a, O)][Q.bs,5 + 64,5]"

(24)

T o restate the p r o b l e m , we would like to know N / M , the relative extinction coefficient, as well as how ~ba' a n d Oa' (or Of') differ from the original angles ~bd a n d 0a (or 00. T h e answers lie in Eq. (23) a n d (24). As described, the coefficients O~l,Q±, a575, a4,5, bsrs, a n d b4rs can be m e a s u r e d in e x p e r i m e n t s , as in principle can Rf. T h e p a r a m e t e r s ~ba' = 40 ° - 50 °, 0a' = 40 °, a n d Of' = 20 ° provide a reasonable fit to the data on p h o t o d i c h r o i s m (Fig. 11), a n d can be used in Eq. (18), (19), a n d (20) to calculate L'(~b, 0), W'(~b, 0), a n d H'(~b, 0). By replacing W(~b, 0) a n d H(dp, O) with their integrated forms (Eq. [19] a n d [20]), we see that the two equations, (23) a n d (24), involve three u n k n o w n s , ( N / M ) , dpa, a n d 0d (or 0r). This is not the impasse it might a p p e a r to be, for it is possible to obtain a reasonable estimate of the m a g n i t u d e of the orientation changes that a c c o m p a n y isomerization by a s s u m i n g , first, that all changes occur in ~d a n d the tilt angle r e m a i n s constant (0d = 0d' or Of = 0f'). Eq. (23) a n d (24) are t h e n solved for N / M a n d qbd. Next, similar calculations are repeated on the a s s u m p t i o n that only tilt angle 0d (or Of) changes, while axial o r i e n t a t i o n r e m a i n s constant (~ba = ~bd'). Solution o f Eq. (23) a n d (24) now yields 0d (or Of) a n d a n o t h e r value for N / M . Representative n u m e r i c a l results are given in Table I a n d are f u r t h e r described in Results.

Note added in proof: The calculated areal density of rhodopsin of I-2 × 10TM molecules cm -2 is in fair agreement with a figure of 0.8 × 1012cm -2 that Lisman and Bering (1977. J. Gen. Physiol. 70. In press) report for Limulus photoreceptors, on the basis of electrophysiological measurements. We are grateful to Dr. Gary D. Bernard for many helpful discussions. The research of Timothy H. Goldsmith is supported by United States Public Health Service grant EY00222. Rfidiger Wehner received support from grant 3.814.72 of the Swiss National Science Foundation and from the University of Zurich, and was a Rand Fellow of the Marine Biological Laboratory, Woods Hole, Mass., during the tenure of this work.

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